http://www.ovsa.njit.edu/wiki/api.php?action=feedcontributions&user=Ztwang&feedformat=atomEOVSA Wiki - User contributions [en]2019-11-20T09:09:45ZUser contributionsMediaWiki 1.23.14http://www.ovsa.njit.edu/wiki/index.php/Reference_Gain_CalibrationReference Gain Calibration2017-07-30T21:24:58Z<p>Ztwang: /* List of Analyzed Reference Calibrations */</p>
<hr />
<div>Reference complex gain calibration refers to determining the "system" amplitude and phase with high precision as a function of IF band (i.e. integrated over each 500 MHz IF band). A typical reference calibration would cover 34 bands, 2 polarizations, and 13 antennas. The routines to retrieve and analyze the data are in the module refcal_anal.py. Start from a time range during which the reference calibration observation occurred (check the [http://ovsa.njit.edu/phasecal/ phasecal results] to see which 1-hr scan had stable phases)<br />
<br />
<pre><br />
import refcal_anal as ra<br />
from util import Time<br />
#example time range of the refcal scan that took place BEFORE the observation<br />
trange=Time(['2017-04-08T14:00','2017-04-08T15:00'])<br />
</pre><br />
<br />
<!--BIN'S PREVIOUS TEXTS<pre><br />
import refcal_anal as ra<br />
from util import Time<br />
trange=Time(['2017-04-08T05:00','2017-04-08T15:30'])<br />
</pre>--><br />
<br />
Now read the data from that timerange<br />
<pre><br />
out=ra.rd_refcal(trange)<br />
</pre><br />
Note that there are optional arguments that can be given, such as projid='PHASECAL' (the default) and srcid='1229+060', but these are generally not needed.<br />
<br />
To correct for differential feed rotation (for refcal data after 05:00 UT on 2017-Jul-01), you can use:<br />
<pre><br />
out_corr = ra.unrot_refcal(out)<br />
</pre><br />
<br />
Take a look at the phases (averaged over each band): <br />
<pre><br />
ra.graph(out_corr)<br />
</pre><br />
By default it displays only bands 5, 11, 17, 23 and polarization XX. To change the bands and polarization to display, use the "bandplt" and 'pol' parameters (better to check more bands).<br />
<pre><br />
ra.graph(out_corr, bandplt=[5,13,19,25], pol=1)<br />
</pre><br />
<br />
<!--BIN'S PREVIOUS TEXTS: From the plot, one can determine which scans are the good ones to use and record the indices of useful scans as "scanidx". In this example, we were alternating between the low- and high-frequency receivers. The low-frequency receiver observations did not have delays adjusted. So we use scans with indices 1, 3, 5, 7, 9, 11, 13 which are associated with the high-frequency receiver scans. <br />
<pre><br />
scanidx=[1, 3, 5, 7, 9, 11, 13]<br />
</pre>,<br />
<br />
Then, we can further determine a finer selection of time range which has clean and stable phases (better to check more bands using ra.graph()). Observations within this time range (after the scanidx selection, if provided) will be used for averaging to get the reference phases/amplitudes. Data will be flagged if the SNR is less than minsnr, which can be supplied. The default minsnr is set to 1.0.<br />
<br />
<pre><br />
timerange=Time(['2017-04-08T05:00','2017-04-08T07:00'])<br />
<br />
refcal=ra.refcal_anal(out_corr,timerange=timerange,scanidx=scanidx)<br />
</pre>--><br />
<br />
Observations within this time range will be used for averaging to get the reference phases/amplitudes. Data will be flagged if the SNR is less than minsnr, which can be supplied. The default minsnr is set to 1.0. We can further determine a finer selection of time range within this scan that has clean and stable phases if needed, by setting the new timerange in "trange" below.<br />
<br />
<pre><br />
refcal=ra.refcal_anal(out_corr,timerange=trange,scanidx=[0])<br />
</pre><br />
<br />
It will generate four plots. First and second are phases and amplitudes of the data similar as those produced by ra.graph(), but with the selected time range for averaging highlighted (one can use "bandplt" and "pol" to choose bands and polarization to display as well). The 3rd plot is the averaged phase vs. frequency and the 4th is the averaged amplitude vs. frequency. Those data will be our "analyzed" reference calibration data saved in the returned dictionary (named "refcal" here). The dictionary contains the actual complex values (refcal['refcal']), a flag array with the same shape (refcal['flag']), and some timestamps, e.g., refcal['t_mid'] is the middle of the time range used for averaging. Both refcal['refcal'] and refcal['flag'] have a shape of (15, 2, 34) -- which corresponds to # of antennas, # of polarizations, and # of bands.<br />
<br />
If you determine some antenna, band, polarization need to be flagged/unflagged, they have to be manually changed in the returned refcal['flag'] array. In this example, Antenna 12 was not tracking, and the algorithm did not pick up all of them, so we have to do this manually -- setting refcal['flag'][11, :, :]=1<br />
<br />
<pre><br />
refcal['flag'][11]=1<br />
</pre><br />
<br />
If satisfied with the results (by looking at the plots), we can go ahead and send them to the SQL database<br />
<pre><br />
import cal_header as ch<br />
ch.refcal2sql(refcal)<br />
</pre><br />
<br />
To retrieve the refcal data back from SQL database based on, e.g., a solar data one wish to calibrate. We can provide a time: <br />
<pre><br />
t=Time('2017-04-07T19:40')<br />
refcal=ra.sql2refcal(t)<br />
</pre><br />
The resulted refcal have three keys: 'amp' (15 x 2 x 34 array), 'pha' (15 x 2 x 34 array), and 'timestamp' (in jd). The refcal data found will be the closest one PRIOR to the supplied observation time.<br />
<br />
== Updating the Reference Calibrations Table ==<br />
The table below lists the known good reference calibrations. To facilitate adding entries to this table, do the following, where the time is after the desired refcal, but before any later refcal:<br />
<pre><br />
t=Time('2017-06-23T19:40') # retrieves the refcal at 13:07 UT on that day<br />
refcal=ra.sql2refcal(t)<br />
ra.graph_results(refcal, savefigs=True)<br />
</pre><br />
This will create summary plots of the amplitude and phase, will write the two corresponding *.png files into the /common/webplots/refcal folder, and will print as a text string the lines needed to add an entry. Just cut from the terminal and paste into the wiki editor at the appropriate place to preserve time order.<br />
<br />
== List of Analyzed Reference Calibrations ==<br />
<br />
{| class="wikitable" style="text-align: center; width: 800px; height: 200px;"<br />
|-<br />
| Date || Timestamp || Source || Obs Trange || Scan Idx || Avg Trange || Bands || Phase Plot || Amp Plot || Comments<br />
|-<br />
| 2017/04/02 || 06:36:50 || 3c273 || 04:20~11:00 || All || 05:47~07:26 || 5, 7, 9, 11, 13, 15, 17, 19, 21, 23 || [[:File:20170402_refcal_pha.png|Phase]] || [[:File:20170402_refcal_amp.png|Amp]] || Ant 12 was not tracking. Delay center change at 11:38:17.<br />
|-<br />
| 2017/04/04 || 09:32:50 || 3c273 || 04:43~10:57 || All || 08:46~10:19 || 5, 7, 9, 11, 13, 15, 17, 19, 21, 23 || [[:File:20170404_refcal_pha.png|Phase]] || [[:File:20170404_refcal_amp.png|Amp]] || Ant 12 was not tracking. Delay center change at 16:43:51.<br />
|-<br />
| 2017/04/05 ||06:44:10 || 3c273 || 04:17~10:30 || All || 04:27~09:34 || 5, 7, 9, 11, 13, 15, 17, 19, 21, 23 || [[:File:20170405_refcal_pha.png|Phase]] || [[:File:20170405_refcal_amp.png|Amp]] || Ant 12 was not tracking.<br />
|-<br />
| 2017/04/06 || 09:54:50|| 3c273 || 04:14~10:49 || All || 05:39~08:11 || 5, 7, 9, 11, 13, 15, 17, 19, 21, 23 || [[:File:20170406_refcal_pha.png|Phase]] || [[:File:20170406_refcal_amp.png|Amp]] || Ant 12 was not tracking.<br />
|-<br />
| 2017/04/07 || 08:30:51|| 3c273 || 04:00~10:30 || 1, 3, 5, 7, 9, 11, 13, 15, 17 || 07:53~09:10 || 5~34 || [[:File:20170407_refcal_pha.png|Phase]] || [[:File:20170407_refcal_amp.png|Amp]] || Ant 12 was not tracking.<br />
|-<br />
| 2017/04/08 || 06:14:51 || 3c273 || 05:00~10:30 || 1, 3, 5, 7, 9, 11, 13 || 05:00~07:00 || 5~34 || [[:File:20170408_refcal_pha.png|Phase]] || [[:File:20170408_refcal_amp.png|Amp]] || Ant 12 was not tracking. Ant 13 not working. Delay center change at 2017-04-08T03:12:26. Another refcal record is added at 2017-04-09T06:14:45.<br />
|-<br />
| 2017/04/10 || 06:57:10 || 3c273 || 04:30~10:30 || 2, 6, 8 || || 5~34 || [[:File:20170410_refcal_pha.png|Phase]] || [[:File:20170410_refcal_amp.png|Amp]] || Ant 12 was not tracking. Delay center change at 2017-04-08 13:20:39. <br />
|-<br />
| 2017/04/16 || 06:36:48 || 3c273 || 03:00~11:00 || || 05:55~07:20 || 5~34 || [[:File:20170416_refcal_pha.png|Phase]] || [[:File:20170416_refcal_amp.png|Amp]] || Ant 12 was not tracking. <br />
|-<br />
| 2017/04/17 || 06:41:51 || 3c273 || 03:29~10:07 || All || 05:55~07:29 || 5~34 || [[:File:20170417_refcal_pha.png|Phase]] || [[:File:20170417_refcal_amp.png|Amp]] || Ant 12 was not tracking. Delay center change at 19:12:58.<br />
|-<br />
| 2017/04/26 || 08:06:52 || 3c273 || 02:50~09:28 || All || 07:21~08:57 || 5~34 || [[:File:20170426_refcal_pha.png|Phase]] || [[:File:20170426_refcal_amp.png|Amp]] || Ant 12 was not tracking. Delay center change at 04:37:28 and 11:51:26.<br />
|-<br />
| 2017/06/11 || 12:56:22 || 2253+161 || || 0 || || 5~34 || [http://ovsa.njit.edu/refcal/20170611_refcal_pha.png Phase] || [http://ovsa.njit.edu/refcal/20170611_refcal_amp.png Amp] || No calibration for: Ant 12<br />
|-<br />
| 2017/06/14 || 02:33:19 || 1229+020 || || 0 || || 5~34 || [http://ovsa.njit.edu/refcal/20170614_refcal_pha.png Phase] || [http://ovsa.njit.edu/refcal/20170614_refcal_amp.png Amp] || No calibration for: Ant 8 Ant 12<br />
|-<br />
| 2017/06/14 || 13:01:19 || 2253+161 || || 0 || || 5~34 || [http://ovsa.njit.edu/refcal/20170614_refcal_pha.png Phase] || [http://ovsa.njit.edu/refcal/20170614_refcal_amp.png Amp] || No calibration for: Ant 12<br />
|-<br />
| 2017/06/15 || 13:05:48 || || || 0 || || 5~34 || [http://ovsa.njit.edu/refcal/20170615_refcal_pha.png Phase] || [http://ovsa.njit.edu/refcal/20170615_refcal_amp.png Amp] || No calibration for: Ant 12<br />
|-<br />
| 2017/06/16 || 13:05:48 || || || 0 || || 5~34 || [http://ovsa.njit.edu/refcal/20170616_refcal_pha.png Phase] || [http://ovsa.njit.edu/refcal/20170616_refcal_amp.png Amp] || No calibration for: Ant 12<br />
|-<br />
| 2017/06/20 || 13:06:26 || || || 0 || || 5~34 || [http://ovsa.njit.edu/refcal/20170620_refcal_pha.png Phase] || [http://ovsa.njit.edu/refcal/20170620_refcal_amp.png Amp] || No calibration for: Ant 1 Ant 12<br />
|-<br />
| 2017/06/21 || 13:06:38 || || || 0 || || 5~34 || [http://ovsa.njit.edu/refcal/20170621_refcal_pha.png Phase] || [http://ovsa.njit.edu/refcal/20170621_refcal_amp.png Amp] || No calibration for: Ant 12<br />
|-<br />
| 2017/06/22 || 13:06:53 || || || 0 || || 5~34 || [http://ovsa.njit.edu/refcal/20170622_refcal_pha.png Phase] || [http://ovsa.njit.edu/refcal/20170622_refcal_amp.png Amp] || No calibration for: Ant 12<br />
|-<br />
| 2017/06/23 || 13:07:09 || || || 0 || || 5~34 || [http://ovsa.njit.edu/refcal/20170623_refcal_pha.png Phase] || [http://ovsa.njit.edu/refcal/20170623_refcal_amp.png Amp] || No calibration for: Ant 12<br />
|-<br />
| 2017/06/24 || 02:25:49 || || || 0 || || 5~34 || [http://ovsa.njit.edu/refcal/20170624_refcal_pha.png Phase] || [http://ovsa.njit.edu/refcal/20170624_refcal_amp.png Amp] || No calibration for: Ant 12<br />
|-<br />
| 2017/06/24 || 13:07:25 || || || 0 || || 5~34 || [http://ovsa.njit.edu/refcal/20170624_refcal_pha.png Phase] || [http://ovsa.njit.edu/refcal/20170624_refcal_amp.png Amp] || No calibration for: Ant 12<br />
|-<br />
| 2017/06/25 || 13:07:43 || || || 0 || || 5~34 || [http://ovsa.njit.edu/refcal/20170625_refcal_pha.png Phase] || [http://ovsa.njit.edu/refcal/20170625_refcal_amp.png Amp] || No calibration for: Ant 10 Ant 12<br />
|-<br />
| 2017/06/26 || 13:15:47 || || || 0 || || 5~34 || [http://ovsa.njit.edu/refcal/20170626_refcal_pha.png Phase] || [http://ovsa.njit.edu/refcal/20170626_refcal_amp.png Amp] || No calibration for: Ant 10 Ant 12<br />
|-<br />
| 2017/06/27 || 13:02:49 || 2253+161 || || 0 || || 5~34 || [http://ovsa.njit.edu/refcal/20170627_refcal_pha.png Phase] || [http://ovsa.njit.edu/refcal/20170627_refcal_amp.png Amp] || No calibration for: Ant 12<br />
|-<br />
| 2017/06/30 || 02:47:50 || 1229+020 || || 0 || || 5~34 || [http://ovsa.njit.edu/refcal/20170630_refcal_pha.png Phase] || [http://ovsa.njit.edu/refcal/20170630_refcal_amp.png Amp] || No calibration for: Ant 12<br />
|-<br />
| 2017/07/01 || 02:44:49 || 1229+020 || || 0 || || 5~34 || [http://ovsa.njit.edu/refcal/20170701_refcal_pha.png Phase] || [http://ovsa.njit.edu/refcal/20170701_refcal_amp.png Amp] || No calibration for: Ant 12<br />
|-<br />
| 2017/07/02 || 03:01:20 || 1229+020 || || 0 || || 5~34 || [http://ovsa.njit.edu/refcal/20170702_refcal_pha.png Phase] || [http://ovsa.njit.edu/refcal/20170702_refcal_amp.png Amp] ||<br />
|-<br />
| 2017/07/03 || 02:47:49 || 1229+020 || || 0 || || 5~34 || [http://ovsa.njit.edu/refcal/20170703_refcal_pha.png Phase] || [http://ovsa.njit.edu/refcal/20170703_refcal_amp.png Amp] || No calibration for: Ant 10<br />
|-<br />
| 2017/07/04 || 02:47:49 || 1229+020 || || 0 || || 5~34 || [http://ovsa.njit.edu/refcal/20170704_refcal_pha.png Phase] || [http://ovsa.njit.edu/refcal/20170704_refcal_amp.png Amp] ||<br />
|-<br />
| 2017/07/05 || 02:55:19 || 1229+020 || || 0 || || 5~34 || [http://ovsa.njit.edu/refcal/20170705_refcal_pha.png Phase] || [http://ovsa.njit.edu/refcal/20170705_refcal_amp.png Amp] ||<br />
|-<br />
| 2017/07/06 || 02:47:49 || 1229+020 || || 0 || || 5~34 || [http://ovsa.njit.edu/refcal/20170706_refcal_pha.png Phase] || [http://ovsa.njit.edu/refcal/20170706_refcal_amp.png Amp] || <br />
|-<br />
| 2017/07/07 || 13:12:49 || 2253+161 || || 0 || || 5~34 || [http://ovsa.njit.edu/refcal/20170707_refcal_pha.png Phase] || [http://ovsa.njit.edu/refcal/20170707_refcal_amp.png Amp] ||<br />
|-<br />
| 2017/07/09 || 02:35:49 || 1229+020 || || 0 || || 5~34 || [http://ovsa.njit.edu/refcal/20170709_refcal_pha.png Phase] || [http://ovsa.njit.edu/refcal/20170709_refcal_amp.png Amp] ||<br />
|-<br />
| 2017/07/09 || 13:16:49 || 2253+161 || || 0 || || 5~34 || [http://ovsa.njit.edu/refcal/20170709_refcal_pha.png Phase] || [http://ovsa.njit.edu/refcal/20170709_refcal_amp.png Amp] ||<br />
|-<br />
| 2017/07/10 || 13:14:17 || 0319+415 || || 0 || || 5~34 || [http://ovsa.njit.edu/refcal/20170710_refcal_pha.png Phase] || [http://ovsa.njit.edu/refcal/20170710_refcal_amp.png Amp] ||<br />
|-<br />
| 2017/07/11 || 13:14:18 || 0319+415 || || 0 || || 5~34 || [http://ovsa.njit.edu/refcal/20170711_refcal_pha.png Phase] || [http://ovsa.njit.edu/refcal/20170711_refcal_amp.png Amp] ||<br />
|-<br />
| 2017/07/12 || 13:14:24 || 0319+415 || || 0 || || 5~34 || [http://ovsa.njit.edu/refcal/20170712_refcal_pha.png Phase] || [http://ovsa.njit.edu/refcal/20170712_refcal_amp.png Amp] ||<br />
|-<br />
| 2017/07/13 || 13:14:59 || 0319+415 || || 0 || || 5~34 || [http://ovsa.njit.edu/refcal/20170713_refcal_pha.png Phase] || [http://ovsa.njit.edu/refcal/20170713_refcal_amp.png Amp] ||<br />
|-<br />
| 2017/07/14 || 13:15:35 || 0319+415 || || 0 || || 5~34 || [http://ovsa.njit.edu/refcal/20170714_refcal_pha.png Phase] || [http://ovsa.njit.edu/refcal/20170714_refcal_amp.png Amp] ||<br />
|-<br />
| 2017/07/16 || 02:48:33 || 1229+020 || || 0 || || 5~34 || [http://ovsa.njit.edu/refcal/20170716_refcal_pha.png Phase] || [http://ovsa.njit.edu/refcal/20170716_refcal_amp.png Amp] ||<br />
|-<br />
| 2017/07/16 || 13:16:48 || 0319+415 || || 0 || || 5~34 || [http://ovsa.njit.edu/refcal/20170716_refcal_pha.png Phase] || [http://ovsa.njit.edu/refcal/20170716_refcal_amp.png Amp] ||<br />
|-<br />
| 2017/07/17 || 13:14:54 || 0319+415 || || 0 || || 5~34 || [http://ovsa.njit.edu/refcal/20170717_refcal_pha.png Phase] || [http://ovsa.njit.edu/refcal/20170717_refcal_amp.png Amp] ||<br />
|-<br />
| 2017/07/18 || 13:15:31 || 0319+415 || || 0 || || 5~34 || [http://ovsa.njit.edu/refcal/20170718_refcal_pha.png Phase] || [http://ovsa.njit.edu/refcal/20170718_refcal_amp.png Amp] ||<br />
|-<br />
| 2017/07/19 || 13:16:16 || 0319+415 || || 0 || || 5~34 || [http://ovsa.njit.edu/refcal/20170719_refcal_pha.png Phase] || [http://ovsa.njit.edu/refcal/20170719_refcal_amp.png Amp] ||<br />
|-<br />
| 2017/07/20 || 13:16:49 || 0319+415 || || 0 || || 5~34 || [http://ovsa.njit.edu/refcal/20170720_refcal_pha.png Phase] || [http://ovsa.njit.edu/refcal/20170720_refcal_amp.png Amp] || No calibration for: Ant 10<br />
|-<br />
| 2017/07/21 || 13:20:57 || 0319+415 || || 0 || || 5~34 || [http://ovsa.njit.edu/refcal/20170721_refcal_pha.png Phase] || [http://ovsa.njit.edu/refcal/20170721_refcal_amp.png Amp] ||<br />
|-<br />
| 2017/07/22 || 13:21:36 || 0319+415 || || 0 || || 5~34 || [http://ovsa.njit.edu/refcal/20170722_refcal_pha.png Phase] || [http://ovsa.njit.edu/refcal/20170722_refcal_amp.png Amp] ||<br />
|-<br />
| 2017/07/23 || 13:34:22 || 0319+415 || || 0 || || 5~34 || [http://ovsa.njit.edu/refcal/20170723_refcal_pha.png Phase] || [http://ovsa.njit.edu/refcal/20170723_refcal_amp.png Amp] ||<br />
|-<br />
| 2017/07/24 || 13:22:58 || 0319+415 || || 0 || || 5~34 || [http://ovsa.njit.edu/refcal/20170724_refcal_pha.png Phase] || [http://ovsa.njit.edu/refcal/20170724_refcal_amp.png Amp] ||<br />
|-<br />
| 2017/07/25 || 13:23:38 || 0319+415 || || 0 || || 5~34 || [http://ovsa.njit.edu/refcal/20170725_refcal_pha.png Phase] || [http://ovsa.njit.edu/refcal/20170725_refcal_amp.png Amp] ||<br />
|-<br />
| 2017/07/26 || 18:00:49 || 0319+415 || || 0 || || 5~34 || [http://ovsa.njit.edu/refcal/20170726_refcal_pha.png Phase] || [http://ovsa.njit.edu/refcal/20170726_refcal_amp.png Amp] ||<br />
|-<br />
| 2017/07/28 || 02:42:36 || 1229+020 || || 0 || || 5~34 || [http://ovsa.njit.edu/refcal/20170728_refcal_pha.png Phase] || [http://ovsa.njit.edu/refcal/20170728_refcal_amp.png Amp] ||<br />
|-<br />
| 2017/07/29 || 13:37:40 || 0319+415 || || 0 || || 5~34 || [http://ovsa.njit.edu/refcal/20170729_refcal_pha.png Phase] || [http://ovsa.njit.edu/refcal/20170729_refcal_amp.png Amp] ||<br />
|-</div>Ztwanghttp://www.ovsa.njit.edu/wiki/index.php/Reference_Gain_CalibrationReference Gain Calibration2017-07-30T21:10:54Z<p>Ztwang: /* List of Analyzed Reference Calibrations */</p>
<hr />
<div>Reference complex gain calibration refers to determining the "system" amplitude and phase with high precision as a function of IF band (i.e. integrated over each 500 MHz IF band). A typical reference calibration would cover 34 bands, 2 polarizations, and 13 antennas. The routines to retrieve and analyze the data are in the module refcal_anal.py. Start from a time range during which the reference calibration observation occurred (check the [http://ovsa.njit.edu/phasecal/ phasecal results] to see which 1-hr scan had stable phases)<br />
<br />
<pre><br />
import refcal_anal as ra<br />
from util import Time<br />
#example time range of the refcal scan that took place BEFORE the observation<br />
trange=Time(['2017-04-08T14:00','2017-04-08T15:00'])<br />
</pre><br />
<br />
<!--BIN'S PREVIOUS TEXTS<pre><br />
import refcal_anal as ra<br />
from util import Time<br />
trange=Time(['2017-04-08T05:00','2017-04-08T15:30'])<br />
</pre>--><br />
<br />
Now read the data from that timerange<br />
<pre><br />
out=ra.rd_refcal(trange)<br />
</pre><br />
Note that there are optional arguments that can be given, such as projid='PHASECAL' (the default) and srcid='1229+060', but these are generally not needed.<br />
<br />
To correct for differential feed rotation (for refcal data after 05:00 UT on 2017-Jul-01), you can use:<br />
<pre><br />
out_corr = ra.unrot_refcal(out)<br />
</pre><br />
<br />
Take a look at the phases (averaged over each band): <br />
<pre><br />
ra.graph(out_corr)<br />
</pre><br />
By default it displays only bands 5, 11, 17, 23 and polarization XX. To change the bands and polarization to display, use the "bandplt" and 'pol' parameters (better to check more bands).<br />
<pre><br />
ra.graph(out_corr, bandplt=[5,13,19,25], pol=1)<br />
</pre><br />
<br />
<!--BIN'S PREVIOUS TEXTS: From the plot, one can determine which scans are the good ones to use and record the indices of useful scans as "scanidx". In this example, we were alternating between the low- and high-frequency receivers. The low-frequency receiver observations did not have delays adjusted. So we use scans with indices 1, 3, 5, 7, 9, 11, 13 which are associated with the high-frequency receiver scans. <br />
<pre><br />
scanidx=[1, 3, 5, 7, 9, 11, 13]<br />
</pre>,<br />
<br />
Then, we can further determine a finer selection of time range which has clean and stable phases (better to check more bands using ra.graph()). Observations within this time range (after the scanidx selection, if provided) will be used for averaging to get the reference phases/amplitudes. Data will be flagged if the SNR is less than minsnr, which can be supplied. The default minsnr is set to 1.0.<br />
<br />
<pre><br />
timerange=Time(['2017-04-08T05:00','2017-04-08T07:00'])<br />
<br />
refcal=ra.refcal_anal(out_corr,timerange=timerange,scanidx=scanidx)<br />
</pre>--><br />
<br />
Observations within this time range will be used for averaging to get the reference phases/amplitudes. Data will be flagged if the SNR is less than minsnr, which can be supplied. The default minsnr is set to 1.0. We can further determine a finer selection of time range within this scan that has clean and stable phases if needed, by setting the new timerange in "trange" below.<br />
<br />
<pre><br />
refcal=ra.refcal_anal(out_corr,timerange=trange,scanidx=[0])<br />
</pre><br />
<br />
It will generate four plots. First and second are phases and amplitudes of the data similar as those produced by ra.graph(), but with the selected time range for averaging highlighted (one can use "bandplt" and "pol" to choose bands and polarization to display as well). The 3rd plot is the averaged phase vs. frequency and the 4th is the averaged amplitude vs. frequency. Those data will be our "analyzed" reference calibration data saved in the returned dictionary (named "refcal" here). The dictionary contains the actual complex values (refcal['refcal']), a flag array with the same shape (refcal['flag']), and some timestamps, e.g., refcal['t_mid'] is the middle of the time range used for averaging. Both refcal['refcal'] and refcal['flag'] have a shape of (15, 2, 34) -- which corresponds to # of antennas, # of polarizations, and # of bands.<br />
<br />
If you determine some antenna, band, polarization need to be flagged/unflagged, they have to be manually changed in the returned refcal['flag'] array. In this example, Antenna 12 was not tracking, and the algorithm did not pick up all of them, so we have to do this manually -- setting refcal['flag'][11, :, :]=1<br />
<br />
<pre><br />
refcal['flag'][11]=1<br />
</pre><br />
<br />
If satisfied with the results (by looking at the plots), we can go ahead and send them to the SQL database<br />
<pre><br />
import cal_header as ch<br />
ch.refcal2sql(refcal)<br />
</pre><br />
<br />
To retrieve the refcal data back from SQL database based on, e.g., a solar data one wish to calibrate. We can provide a time: <br />
<pre><br />
t=Time('2017-04-07T19:40')<br />
refcal=ra.sql2refcal(t)<br />
</pre><br />
The resulted refcal have three keys: 'amp' (15 x 2 x 34 array), 'pha' (15 x 2 x 34 array), and 'timestamp' (in jd). The refcal data found will be the closest one PRIOR to the supplied observation time.<br />
<br />
== Updating the Reference Calibrations Table ==<br />
The table below lists the known good reference calibrations. To facilitate adding entries to this table, do the following, where the time is after the desired refcal, but before any later refcal:<br />
<pre><br />
t=Time('2017-06-23T19:40') # retrieves the refcal at 13:07 UT on that day<br />
refcal=ra.sql2refcal(t)<br />
ra.graph_results(refcal, savefigs=True)<br />
</pre><br />
This will create summary plots of the amplitude and phase, will write the two corresponding *.png files into the /common/webplots/refcal folder, and will print as a text string the lines needed to add an entry. Just cut from the terminal and paste into the wiki editor at the appropriate place to preserve time order.<br />
<br />
== List of Analyzed Reference Calibrations ==<br />
<br />
{| class="wikitable" style="text-align: center; width: 800px; height: 200px;"<br />
|-<br />
| Date || Timestamp || Source || Obs Trange || Scan Idx || Avg Trange || Bands || Phase Plot || Amp Plot || Comments<br />
|-<br />
| 2017/04/02 || 06:36:50 || 3c273 || 04:20~11:00 || All || 05:47~07:26 || 5, 7, 9, 11, 13, 15, 17, 19, 21, 23 || [[:File:20170402_refcal_pha.png|Phase]] || [[:File:20170402_refcal_amp.png|Amp]] || Ant 12 was not tracking. Delay center change at 11:38:17.<br />
|-<br />
| 2017/04/04 || 09:32:50 || 3c273 || 04:43~10:57 || All || 08:46~10:19 || 5, 7, 9, 11, 13, 15, 17, 19, 21, 23 || [[:File:20170404_refcal_pha.png|Phase]] || [[:File:20170404_refcal_amp.png|Amp]] || Ant 12 was not tracking. Delay center change at 16:43:51.<br />
|-<br />
| 2017/04/05 ||06:44:10 || 3c273 || 04:17~10:30 || All || 04:27~09:34 || 5, 7, 9, 11, 13, 15, 17, 19, 21, 23 || [[:File:20170405_refcal_pha.png|Phase]] || [[:File:20170405_refcal_amp.png|Amp]] || Ant 12 was not tracking.<br />
|-<br />
| 2017/04/06 || 09:54:50|| 3c273 || 04:14~10:49 || All || 05:39~08:11 || 5, 7, 9, 11, 13, 15, 17, 19, 21, 23 || [[:File:20170406_refcal_pha.png|Phase]] || [[:File:20170406_refcal_amp.png|Amp]] || Ant 12 was not tracking.<br />
|-<br />
| 2017/04/07 || 08:30:51|| 3c273 || 04:00~10:30 || 1, 3, 5, 7, 9, 11, 13, 15, 17 || 07:53~09:10 || 5~34 || [[:File:20170407_refcal_pha.png|Phase]] || [[:File:20170407_refcal_amp.png|Amp]] || Ant 12 was not tracking.<br />
|-<br />
| 2017/04/08 || 06:14:51 || 3c273 || 05:00~10:30 || 1, 3, 5, 7, 9, 11, 13 || 05:00~07:00 || 5~34 || [[:File:20170408_refcal_pha.png|Phase]] || [[:File:20170408_refcal_amp.png|Amp]] || Ant 12 was not tracking. Ant 13 not working. Delay center change at 2017-04-08T03:12:26. Another refcal record is added at 2017-04-09T06:14:45.<br />
|-<br />
| 2017/04/10 || 06:57:10 || 3c273 || 04:30~10:30 || 2, 6, 8 || || 5~34 || [[:File:20170410_refcal_pha.png|Phase]] || [[:File:20170410_refcal_amp.png|Amp]] || Ant 12 was not tracking. Delay center change at 2017-04-08 13:20:39. <br />
|-<br />
| 2017/04/16 || 06:36:48 || 3c273 || 03:00~11:00 || || 05:55~07:20 || 5~34 || [[:File:20170416_refcal_pha.png|Phase]] || [[:File:20170416_refcal_amp.png|Amp]] || Ant 12 was not tracking. <br />
|-<br />
| 2017/04/17 || 06:41:51 || 3c273 || 03:29~10:07 || All || 05:55~07:29 || 5~34 || [[:File:20170417_refcal_pha.png|Phase]] || [[:File:20170417_refcal_amp.png|Amp]] || Ant 12 was not tracking. Delay center change at 19:12:58.<br />
|-<br />
| 2017/04/26 || 08:06:52 || 3c273 || 02:50~09:28 || All || 07:21~08:57 || 5~34 || [[:File:20170426_refcal_pha.png|Phase]] || [[:File:20170426_refcal_amp.png|Amp]] || Ant 12 was not tracking. Delay center change at 04:37:28 and 11:51:26.<br />
|-<br />
| 2017/06/11 || 12:56:22 || 2253+161 || || 0 || || 5~34 || [http://ovsa.njit.edu/refcal/20170611_refcal_pha.png Phase] || [http://ovsa.njit.edu/refcal/20170611_refcal_amp.png Amp] || No calibration for: Ant 12<br />
|-<br />
| 2017/06/14 || 02:33:19 || 1229+020 || || 0 || || 5~34 || [http://ovsa.njit.edu/refcal/20170614_refcal_pha.png Phase] || [http://ovsa.njit.edu/refcal/20170614_refcal_amp.png Amp] || No calibration for: Ant 8 Ant 12<br />
|-<br />
| 2017/06/14 || 13:01:19 || 2253+161 || || 0 || || 5~34 || [http://ovsa.njit.edu/refcal/20170614_refcal_pha.png Phase] || [http://ovsa.njit.edu/refcal/20170614_refcal_amp.png Amp] || No calibration for: Ant 12<br />
|-<br />
| 2017/06/15 || 13:05:48 || || || 0 || || 5~34 || [http://ovsa.njit.edu/refcal/20170615_refcal_pha.png Phase] || [http://ovsa.njit.edu/refcal/20170615_refcal_amp.png Amp] || No calibration for: Ant 12<br />
|-<br />
| 2017/06/16 || 13:05:48 || || || 0 || || 5~34 || [http://ovsa.njit.edu/refcal/20170616_refcal_pha.png Phase] || [http://ovsa.njit.edu/refcal/20170616_refcal_amp.png Amp] || No calibration for: Ant 12<br />
|-<br />
| 2017/06/20 || 13:06:26 || || || 0 || || 5~34 || [http://ovsa.njit.edu/refcal/20170620_refcal_pha.png Phase] || [http://ovsa.njit.edu/refcal/20170620_refcal_amp.png Amp] || No calibration for: Ant 1 Ant 12<br />
|-<br />
| 2017/06/21 || 13:06:38 || || || 0 || || 5~34 || [http://ovsa.njit.edu/refcal/20170621_refcal_pha.png Phase] || [http://ovsa.njit.edu/refcal/20170621_refcal_amp.png Amp] || No calibration for: Ant 12<br />
|-<br />
| 2017/06/22 || 13:06:53 || || || 0 || || 5~34 || [http://ovsa.njit.edu/refcal/20170622_refcal_pha.png Phase] || [http://ovsa.njit.edu/refcal/20170622_refcal_amp.png Amp] || No calibration for: Ant 12<br />
|-<br />
| 2017/06/23 || 13:07:09 || || || 0 || || 5~34 || [http://ovsa.njit.edu/refcal/20170623_refcal_pha.png Phase] || [http://ovsa.njit.edu/refcal/20170623_refcal_amp.png Amp] || No calibration for: Ant 12<br />
|-<br />
| 2017/06/24 || 02:25:49 || || || 0 || || 5~34 || [http://ovsa.njit.edu/refcal/20170624_refcal_pha.png Phase] || [http://ovsa.njit.edu/refcal/20170624_refcal_amp.png Amp] || No calibration for: Ant 12<br />
|-<br />
| 2017/06/24 || 13:07:25 || || || 0 || || 5~34 || [http://ovsa.njit.edu/refcal/20170624_refcal_pha.png Phase] || [http://ovsa.njit.edu/refcal/20170624_refcal_amp.png Amp] || No calibration for: Ant 12<br />
|-<br />
| 2017/06/25 || 13:07:43 || || || 0 || || 5~34 || [http://ovsa.njit.edu/refcal/20170625_refcal_pha.png Phase] || [http://ovsa.njit.edu/refcal/20170625_refcal_amp.png Amp] || No calibration for: Ant 10 Ant 12<br />
|-<br />
| 2017/06/26 || 13:15:47 || || || 0 || || 5~34 || [http://ovsa.njit.edu/refcal/20170626_refcal_pha.png Phase] || [http://ovsa.njit.edu/refcal/20170626_refcal_amp.png Amp] || No calibration for: Ant 10 Ant 12<br />
|-<br />
| 2017/06/27 || 13:02:49 || 2253+161 || || 0 || || 5~34 || [http://ovsa.njit.edu/refcal/20170627_refcal_pha.png Phase] || [http://ovsa.njit.edu/refcal/20170627_refcal_amp.png Amp] || No calibration for: Ant 12<br />
|-<br />
| 2017/06/30 || 02:47:50 || 1229+020 || || 0 || || 5~34 || [http://ovsa.njit.edu/refcal/20170630_refcal_pha.png Phase] || [http://ovsa.njit.edu/refcal/20170630_refcal_amp.png Amp] || No calibration for: Ant 12<br />
|-<br />
| 2017/07/01 || 02:44:49 || 1229+020 || || 0 || || 5~34 || [http://ovsa.njit.edu/refcal/20170701_refcal_pha.png Phase] || [http://ovsa.njit.edu/refcal/20170701_refcal_amp.png Amp] || No calibration for: Ant 12<br />
|-<br />
| 2017/07/02 || 03:01:20 || 1229+020 || || 0 || || 5~34 || [http://ovsa.njit.edu/refcal/20170702_refcal_pha.png Phase] || [http://ovsa.njit.edu/refcal/20170702_refcal_amp.png Amp] ||<br />
|-<br />
| 2017/07/03 || 02:47:49 || 1229+020 || || 0 || || 5~34 || [http://ovsa.njit.edu/refcal/20170703_refcal_pha.png Phase] || [http://ovsa.njit.edu/refcal/20170703_refcal_amp.png Amp] || No calibration for: Ant 10<br />
|-<br />
| 2017/07/04 || 02:47:49 || 1229+020 || || 0 || || 5~34 || [http://ovsa.njit.edu/refcal/20170704_refcal_pha.png Phase] || [http://ovsa.njit.edu/refcal/20170704_refcal_amp.png Amp] ||<br />
|-<br />
| 2017/07/05 || 02:55:19 || 1229+020 || || 0 || || 5~34 || [http://ovsa.njit.edu/refcal/20170705_refcal_pha.png Phase] || [http://ovsa.njit.edu/refcal/20170705_refcal_amp.png Amp] ||<br />
|-<br />
| 2017/07/06 || 02:47:49 || 1229+020 || || 0 || || 5~34 || [http://ovsa.njit.edu/refcal/20170706_refcal_pha.png Phase] || [http://ovsa.njit.edu/refcal/20170706_refcal_amp.png Amp] || <br />
|-<br />
| 2017/07/07 || 13:12:49 || 2253+161 || || 0 || || 5~34 || [http://ovsa.njit.edu/refcal/20170707_refcal_pha.png Phase] || [http://ovsa.njit.edu/refcal/20170707_refcal_amp.png Amp] ||<br />
|-<br />
| 2017/07/09 || 02:35:49 || 1229+020 || || 0 || || 5~34 || [http://ovsa.njit.edu/refcal/20170709_refcal_pha.png Phase] || [http://ovsa.njit.edu/refcal/20170709_refcal_amp.png Amp] ||<br />
|-<br />
| 2017/07/09 || 13:16:49 || 2253+161 || || 0 || || 5~34 || [http://ovsa.njit.edu/refcal/20170709_refcal_pha.png Phase] || [http://ovsa.njit.edu/refcal/20170709_refcal_amp.png Amp] ||<br />
|-<br />
| 2017/07/10 || 13:14:17 || 0319+415 || || 0 || || 5~34 || [http://ovsa.njit.edu/refcal/20170710_refcal_pha.png Phase] || [http://ovsa.njit.edu/refcal/20170710_refcal_amp.png Amp] ||<br />
|-<br />
| 2017/07/11 || 13:14:18 || 0319+415 || || 0 || || 5~34 || [http://ovsa.njit.edu/refcal/20170711_refcal_pha.png Phase] || [http://ovsa.njit.edu/refcal/20170711_refcal_amp.png Amp] ||<br />
|-<br />
| 2017/07/12 || 13:14:24 || 0319+415 || || 0 || || 5~34 || [http://ovsa.njit.edu/refcal/20170712_refcal_pha.png Phase] || [http://ovsa.njit.edu/refcal/20170712_refcal_amp.png Amp] ||<br />
|-<br />
| 2017/07/13 || 13:14:59 || 0319+415 || || 0 || || 5~34 || [http://ovsa.njit.edu/refcal/20170713_refcal_pha.png Phase] || [http://ovsa.njit.edu/refcal/20170713_refcal_amp.png Amp] ||<br />
|-<br />
| 2017/07/14 || 13:15:35 || 0319+415 || || 0 || || 5~34 || [http://ovsa.njit.edu/refcal/20170714_refcal_pha.png Phase] || [http://ovsa.njit.edu/refcal/20170714_refcal_amp.png Amp] ||<br />
|-<br />
| 2017/07/16 || 02:48:33 || 1229+020 || || 0 || || 5~34 || [http://ovsa.njit.edu/refcal/20170716_refcal_pha.png Phase] || [http://ovsa.njit.edu/refcal/20170716_refcal_amp.png Amp] ||<br />
|-<br />
| 2017/07/16 || 13:16:48 || 0319+415 || || 0 || || 5~34 || [http://ovsa.njit.edu/refcal/20170716_refcal_pha.png Phase] || [http://ovsa.njit.edu/refcal/20170716_refcal_amp.png Amp] ||<br />
|-<br />
| 2017/07/17 || 13:14:54 || 0319+415 || || 0 || || 5~34 || [http://ovsa.njit.edu/refcal/20170717_refcal_pha.png Phase] || [http://ovsa.njit.edu/refcal/20170717_refcal_amp.png Amp] ||<br />
|-<br />
| 2017/07/18 || 13:15:31 || 0319+415 || || 0 || || 5~34 || [http://ovsa.njit.edu/refcal/20170718_refcal_pha.png Phase] || [http://ovsa.njit.edu/refcal/20170718_refcal_amp.png Amp] ||<br />
|-<br />
| 2017/07/19 || 13:16:16 || 0319+415 || || 0 || || 5~34 || [http://ovsa.njit.edu/refcal/20170719_refcal_pha.png Phase] || [http://ovsa.njit.edu/refcal/20170719_refcal_amp.png Amp] ||<br />
|-<br />
| 2017/07/20 || 13:16:49 || 0319+415 || || 0 || || 5~34 || [http://ovsa.njit.edu/refcal/20170720_refcal_pha.png Phase] || [http://ovsa.njit.edu/refcal/20170720_refcal_amp.png Amp] || No calibration for: Ant 10<br />
|-<br />
| 2017/07/21 || 13:20:57 || 0319+415 || || 0 || || 5~34 || [http://ovsa.njit.edu/refcal/20170721_refcal_pha.png Phase] || [http://ovsa.njit.edu/refcal/20170721_refcal_amp.png Amp] ||<br />
|-<br />
| 2017/07/22 || 13:21:36 || 0319+415 || || 0 || || 5~34 || [http://ovsa.njit.edu/refcal/20170722_refcal_pha.png Phase] || [http://ovsa.njit.edu/refcal/20170722_refcal_amp.png Amp] ||<br />
|-<br />
| 2017/07/23 || 13:34:22 || 0319+415 || || 0 || || 5~34 || [http://ovsa.njit.edu/refcal/20170723_refcal_pha.png Phase] || [http://ovsa.njit.edu/refcal/20170723_refcal_amp.png Amp] ||<br />
|-<br />
| 2017/07/24 || 13:22:58 || 0319+415 || || 0 || || 5~34 || [http://ovsa.njit.edu/refcal/20170724_refcal_pha.png Phase] || [http://ovsa.njit.edu/refcal/20170724_refcal_amp.png Amp] ||<br />
|-<br />
| 2017/07/25 || 13:23:38 || 0319+415 || || 0 || || 5~34 || [http://ovsa.njit.edu/refcal/20170725_refcal_pha.png Phase] || [http://ovsa.njit.edu/refcal/20170725_refcal_amp.png Amp] ||<br />
|-<br />
| 2017/07/26 || 18:00:49 || 0319+415 || || 0 || || 5~34 || [http://ovsa.njit.edu/refcal/20170726_refcal_pha.png Phase] || [http://ovsa.njit.edu/refcal/20170726_refcal_amp.png Amp] ||<br />
|-<br />
| 2017/07/28 || 02:42:36 || 1229+020 || || 0 || || 5~34 || [http://ovsa.njit.edu/refcal/20170728_refcal_pha.png Phase] || [http://ovsa.njit.edu/refcal/20170728_refcal_amp.png Amp] ||<br />
|-</div>Ztwanghttp://www.ovsa.njit.edu/wiki/index.php/Reference_Gain_CalibrationReference Gain Calibration2017-07-27T19:56:58Z<p>Ztwang: /* List of Analyzed Reference Calibrations */</p>
<hr />
<div>Reference complex gain calibration refers to determining the "system" amplitude and phase with high precision as a function of IF band (i.e. integrated over each 500 MHz IF band). A typical reference calibration would cover 34 bands, 2 polarizations, and 13 antennas. The routines to retrieve and analyze the data are in the module refcal_anal.py. Start from a time range during which the reference calibration observation occurred (check the [http://ovsa.njit.edu/phasecal/ phasecal results] to see which 1-hr scan had stable phases)<br />
<br />
<pre><br />
import refcal_anal as ra<br />
from util import Time<br />
#example time range of the refcal scan that took place BEFORE the observation<br />
trange=Time(['2017-04-08T14:00','2017-04-08T15:00'])<br />
</pre><br />
<br />
<!--BIN'S PREVIOUS TEXTS<pre><br />
import refcal_anal as ra<br />
from util import Time<br />
trange=Time(['2017-04-08T05:00','2017-04-08T15:30'])<br />
</pre>--><br />
<br />
Now read the data from that timerange<br />
<pre><br />
out=ra.rd_refcal(trange)<br />
</pre><br />
Note that there are optional arguments that can be given, such as projid='PHASECAL' (the default) and srcid='1229+060', but these are generally not needed.<br />
<br />
To correct for differential feed rotation (for refcal data after 05:00 UT on 2017-Jul-01), you can use:<br />
<pre><br />
out_corr = ra.unrot_refcal(out)<br />
</pre><br />
<br />
Take a look at the phases (averaged over each band): <br />
<pre><br />
ra.graph(out_corr)<br />
</pre><br />
By default it displays only bands 5, 11, 17, 23 and polarization XX. To change the bands and polarization to display, use the "bandplt" and 'pol' parameters (better to check more bands).<br />
<pre><br />
ra.graph(out_corr, bandplt=[5,13,19,25], pol=1)<br />
</pre><br />
<br />
<!--BIN'S PREVIOUS TEXTS: From the plot, one can determine which scans are the good ones to use and record the indices of useful scans as "scanidx". In this example, we were alternating between the low- and high-frequency receivers. The low-frequency receiver observations did not have delays adjusted. So we use scans with indices 1, 3, 5, 7, 9, 11, 13 which are associated with the high-frequency receiver scans. <br />
<pre><br />
scanidx=[1, 3, 5, 7, 9, 11, 13]<br />
</pre>,<br />
<br />
Then, we can further determine a finer selection of time range which has clean and stable phases (better to check more bands using ra.graph()). Observations within this time range (after the scanidx selection, if provided) will be used for averaging to get the reference phases/amplitudes. Data will be flagged if the SNR is less than minsnr, which can be supplied. The default minsnr is set to 1.0.<br />
<br />
<pre><br />
timerange=Time(['2017-04-08T05:00','2017-04-08T07:00'])<br />
<br />
refcal=ra.refcal_anal(out_corr,timerange=timerange,scanidx=scanidx)<br />
</pre>--><br />
<br />
Observations within this time range will be used for averaging to get the reference phases/amplitudes. Data will be flagged if the SNR is less than minsnr, which can be supplied. The default minsnr is set to 1.0. We can further determine a finer selection of time range within this scan that has clean and stable phases if needed, by setting the new timerange in "trange" below.<br />
<br />
<pre><br />
refcal=ra.refcal_anal(out_corr,timerange=trange,scanidx=[0])<br />
</pre><br />
<br />
It will generate four plots. First and second are phases and amplitudes of the data similar as those produced by ra.graph(), but with the selected time range for averaging highlighted (one can use "bandplt" and "pol" to choose bands and polarization to display as well). The 3rd plot is the averaged phase vs. frequency and the 4th is the averaged amplitude vs. frequency. Those data will be our "analyzed" reference calibration data saved in the returned dictionary (named "refcal" here). The dictionary contains the actual complex values (refcal['refcal']), a flag array with the same shape (refcal['flag']), and some timestamps, e.g., refcal['t_mid'] is the middle of the time range used for averaging. Both refcal['refcal'] and refcal['flag'] have a shape of (15, 2, 34) -- which corresponds to # of antennas, # of polarizations, and # of bands.<br />
<br />
If you determine some antenna, band, polarization need to be flagged/unflagged, they have to be manually changed in the returned refcal['flag'] array. In this example, Antenna 12 was not tracking, and the algorithm did not pick up all of them, so we have to do this manually -- setting refcal['flag'][11, :, :]=1<br />
<br />
<pre><br />
refcal['flag'][11]=1<br />
</pre><br />
<br />
If satisfied with the results (by looking at the plots), we can go ahead and send them to the SQL database<br />
<pre><br />
import cal_header as ch<br />
ch.refcal2sql(refcal)<br />
</pre><br />
<br />
To retrieve the refcal data back from SQL database based on, e.g., a solar data one wish to calibrate. We can provide a time: <br />
<pre><br />
t=Time('2017-04-07T19:40')<br />
refcal=ra.sql2refcal(t)<br />
</pre><br />
The resulted refcal have three keys: 'amp' (15 x 2 x 34 array), 'pha' (15 x 2 x 34 array), and 'timestamp' (in jd). The refcal data found will be the closest one PRIOR to the supplied observation time.<br />
<br />
== Updating the Reference Calibrations Table ==<br />
The table below lists the known good reference calibrations. To facilitate adding entries to this table, do the following, where the time is after the desired refcal, but before any later refcal:<br />
<pre><br />
t=Time('2017-06-23T19:40') # retrieves the refcal at 13:07 UT on that day<br />
refcal=ra.sql2refcal(t)<br />
ra.graph_results(refcal, savefigs=True)<br />
</pre><br />
This will create summary plots of the amplitude and phase, will write the two corresponding *.png files into the /common/webplots/refcal folder, and will print as a text string the lines needed to add an entry. Just cut from the terminal and paste into the wiki editor at the appropriate place to preserve time order.<br />
<br />
== List of Analyzed Reference Calibrations ==<br />
<br />
{| class="wikitable" style="text-align: center; width: 800px; height: 200px;"<br />
|-<br />
| Date || Timestamp || Source || Obs Trange || Scan Idx || Avg Trange || Bands || Phase Plot || Amp Plot || Comments<br />
|-<br />
| 2017/04/02 || 06:36:50 || 3c273 || 04:20~11:00 || All || 05:47~07:26 || 5, 7, 9, 11, 13, 15, 17, 19, 21, 23 || [[:File:20170402_refcal_pha.png|Phase]] || [[:File:20170402_refcal_amp.png|Amp]] || Ant 12 was not tracking. Delay center change at 11:38:17.<br />
|-<br />
| 2017/04/04 || 09:32:50 || 3c273 || 04:43~10:57 || All || 08:46~10:19 || 5, 7, 9, 11, 13, 15, 17, 19, 21, 23 || [[:File:20170404_refcal_pha.png|Phase]] || [[:File:20170404_refcal_amp.png|Amp]] || Ant 12 was not tracking. Delay center change at 16:43:51.<br />
|-<br />
| 2017/04/05 ||06:44:10 || 3c273 || 04:17~10:30 || All || 04:27~09:34 || 5, 7, 9, 11, 13, 15, 17, 19, 21, 23 || [[:File:20170405_refcal_pha.png|Phase]] || [[:File:20170405_refcal_amp.png|Amp]] || Ant 12 was not tracking.<br />
|-<br />
| 2017/04/06 || 09:54:50|| 3c273 || 04:14~10:49 || All || 05:39~08:11 || 5, 7, 9, 11, 13, 15, 17, 19, 21, 23 || [[:File:20170406_refcal_pha.png|Phase]] || [[:File:20170406_refcal_amp.png|Amp]] || Ant 12 was not tracking.<br />
|-<br />
| 2017/04/07 || 08:30:51|| 3c273 || 04:00~10:30 || 1, 3, 5, 7, 9, 11, 13, 15, 17 || 07:53~09:10 || 5~34 || [[:File:20170407_refcal_pha.png|Phase]] || [[:File:20170407_refcal_amp.png|Amp]] || Ant 12 was not tracking.<br />
|-<br />
| 2017/04/08 || 06:14:51 || 3c273 || 05:00~10:30 || 1, 3, 5, 7, 9, 11, 13 || 05:00~07:00 || 5~34 || [[:File:20170408_refcal_pha.png|Phase]] || [[:File:20170408_refcal_amp.png|Amp]] || Ant 12 was not tracking. Ant 13 not working. Delay center change at 2017-04-08T03:12:26. Another refcal record is added at 2017-04-09T06:14:45.<br />
|-<br />
| 2017/04/10 || 06:57:10 || 3c273 || 04:30~10:30 || 2, 6, 8 || || 5~34 || [[:File:20170410_refcal_pha.png|Phase]] || [[:File:20170410_refcal_amp.png|Amp]] || Ant 12 was not tracking. Delay center change at 2017-04-08 13:20:39. <br />
|-<br />
| 2017/04/16 || 06:36:48 || 3c273 || 03:00~11:00 || || 05:55~07:20 || 5~34 || [[:File:20170416_refcal_pha.png|Phase]] || [[:File:20170416_refcal_amp.png|Amp]] || Ant 12 was not tracking. <br />
|-<br />
| 2017/04/17 || 06:41:51 || 3c273 || 03:29~10:07 || All || 05:55~07:29 || 5~34 || [[:File:20170417_refcal_pha.png|Phase]] || [[:File:20170417_refcal_amp.png|Amp]] || Ant 12 was not tracking. Delay center change at 19:12:58.<br />
|-<br />
| 2017/04/26 || 08:06:52 || 3c273 || 02:50~09:28 || All || 07:21~08:57 || 5~34 || [[:File:20170426_refcal_pha.png|Phase]] || [[:File:20170426_refcal_amp.png|Amp]] || Ant 12 was not tracking. Delay center change at 04:37:28 and 11:51:26.<br />
|-<br />
| 2017/06/11 || 12:56:22 || 2253+161 || || 0 || || 5~34 || [http://ovsa.njit.edu/refcal/20170611_refcal_pha.png Phase] || [http://ovsa.njit.edu/refcal/20170611_refcal_amp.png Amp] || No calibration for: Ant 12<br />
|-<br />
| 2017/06/14 || 02:33:19 || 1229+020 || || 0 || || 5~34 || [http://ovsa.njit.edu/refcal/20170614_refcal_pha.png Phase] || [http://ovsa.njit.edu/refcal/20170614_refcal_amp.png Amp] || No calibration for: Ant 8 Ant 12<br />
|-<br />
| 2017/06/14 || 13:01:19 || 2253+161 || || 0 || || 5~34 || [http://ovsa.njit.edu/refcal/20170614_refcal_pha.png Phase] || [http://ovsa.njit.edu/refcal/20170614_refcal_amp.png Amp] || No calibration for: Ant 12<br />
|-<br />
| 2017/06/15 || 13:05:48 || || || 0 || || 5~34 || [http://ovsa.njit.edu/refcal/20170615_refcal_pha.png Phase] || [http://ovsa.njit.edu/refcal/20170615_refcal_amp.png Amp] || No calibration for: Ant 12<br />
|-<br />
| 2017/06/16 || 13:05:48 || || || 0 || || 5~34 || [http://ovsa.njit.edu/refcal/20170616_refcal_pha.png Phase] || [http://ovsa.njit.edu/refcal/20170616_refcal_amp.png Amp] || No calibration for: Ant 12<br />
|-<br />
| 2017/06/20 || 13:06:26 || || || 0 || || 5~34 || [http://ovsa.njit.edu/refcal/20170620_refcal_pha.png Phase] || [http://ovsa.njit.edu/refcal/20170620_refcal_amp.png Amp] || No calibration for: Ant 1 Ant 12<br />
|-<br />
| 2017/06/21 || 13:06:38 || || || 0 || || 5~34 || [http://ovsa.njit.edu/refcal/20170621_refcal_pha.png Phase] || [http://ovsa.njit.edu/refcal/20170621_refcal_amp.png Amp] || No calibration for: Ant 12<br />
|-<br />
| 2017/06/22 || 13:06:53 || || || 0 || || 5~34 || [http://ovsa.njit.edu/refcal/20170622_refcal_pha.png Phase] || [http://ovsa.njit.edu/refcal/20170622_refcal_amp.png Amp] || No calibration for: Ant 12<br />
|-<br />
| 2017/06/23 || 13:07:09 || || || 0 || || 5~34 || [http://ovsa.njit.edu/refcal/20170623_refcal_pha.png Phase] || [http://ovsa.njit.edu/refcal/20170623_refcal_amp.png Amp] || No calibration for: Ant 12<br />
|-<br />
| 2017/06/24 || 02:25:49 || || || 0 || || 5~34 || [http://ovsa.njit.edu/refcal/20170624_refcal_pha.png Phase] || [http://ovsa.njit.edu/refcal/20170624_refcal_amp.png Amp] || No calibration for: Ant 12<br />
|-<br />
| 2017/06/24 || 13:07:25 || || || 0 || || 5~34 || [http://ovsa.njit.edu/refcal/20170624_refcal_pha.png Phase] || [http://ovsa.njit.edu/refcal/20170624_refcal_amp.png Amp] || No calibration for: Ant 12<br />
|-<br />
| 2017/06/25 || 13:07:43 || || || 0 || || 5~34 || [http://ovsa.njit.edu/refcal/20170625_refcal_pha.png Phase] || [http://ovsa.njit.edu/refcal/20170625_refcal_amp.png Amp] || No calibration for: Ant 10 Ant 12<br />
|-<br />
| 2017/06/26 || 13:15:47 || || || 0 || || 5~34 || [http://ovsa.njit.edu/refcal/20170626_refcal_pha.png Phase] || [http://ovsa.njit.edu/refcal/20170626_refcal_amp.png Amp] || No calibration for: Ant 10 Ant 12<br />
|-<br />
| 2017/06/27 || 13:02:49 || 2253+161 || || 0 || || 5~34 || [http://ovsa.njit.edu/refcal/20170627_refcal_pha.png Phase] || [http://ovsa.njit.edu/refcal/20170627_refcal_amp.png Amp] || No calibration for: Ant 12<br />
|-<br />
| 2017/06/30 || 02:47:50 || 1229+020 || || 0 || || 5~34 || [http://ovsa.njit.edu/refcal/20170630_refcal_pha.png Phase] || [http://ovsa.njit.edu/refcal/20170630_refcal_amp.png Amp] || No calibration for: Ant 12<br />
|-<br />
| 2017/07/01 || 02:44:49 || 1229+020 || || 0 || || 5~34 || [http://ovsa.njit.edu/refcal/20170701_refcal_pha.png Phase] || [http://ovsa.njit.edu/refcal/20170701_refcal_amp.png Amp] || No calibration for: Ant 12<br />
|-<br />
| 2017/07/02 || 03:01:20 || 1229+020 || || 0 || || 5~34 || [http://ovsa.njit.edu/refcal/20170702_refcal_pha.png Phase] || [http://ovsa.njit.edu/refcal/20170702_refcal_amp.png Amp] ||<br />
|-<br />
| 2017/07/03 || 02:47:49 || 1229+020 || || 0 || || 5~34 || [http://ovsa.njit.edu/refcal/20170703_refcal_pha.png Phase] || [http://ovsa.njit.edu/refcal/20170703_refcal_amp.png Amp] || No calibration for: Ant 10<br />
|-<br />
| 2017/07/04 || 02:47:49 || 1229+020 || || 0 || || 5~34 || [http://ovsa.njit.edu/refcal/20170704_refcal_pha.png Phase] || [http://ovsa.njit.edu/refcal/20170704_refcal_amp.png Amp] ||<br />
|-<br />
| 2017/07/05 || 02:55:19 || 1229+020 || || 0 || || 5~34 || [http://ovsa.njit.edu/refcal/20170705_refcal_pha.png Phase] || [http://ovsa.njit.edu/refcal/20170705_refcal_amp.png Amp] ||<br />
|-<br />
| 2017/07/06 || 02:47:49 || 1229+020 || || 0 || || 5~34 || [http://ovsa.njit.edu/refcal/20170706_refcal_pha.png Phase] || [http://ovsa.njit.edu/refcal/20170706_refcal_amp.png Amp] || <br />
|-<br />
| 2017/07/07 || 13:12:49 || 2253+161 || || 0 || || 5~34 || [http://ovsa.njit.edu/refcal/20170707_refcal_pha.png Phase] || [http://ovsa.njit.edu/refcal/20170707_refcal_amp.png Amp] ||<br />
|-<br />
| 2017/07/09 || 02:35:49 || 1229+020 || || 0 || || 5~34 || [http://ovsa.njit.edu/refcal/20170709_refcal_pha.png Phase] || [http://ovsa.njit.edu/refcal/20170709_refcal_amp.png Amp] ||<br />
|-<br />
| 2017/07/09 || 13:16:49 || 2253+161 || || 0 || || 5~34 || [http://ovsa.njit.edu/refcal/20170709_refcal_pha.png Phase] || [http://ovsa.njit.edu/refcal/20170709_refcal_amp.png Amp] ||<br />
|-<br />
| 2017/07/10 || 13:14:17 || 0319+415 || || 0 || || 5~34 || [http://ovsa.njit.edu/refcal/20170710_refcal_pha.png Phase] || [http://ovsa.njit.edu/refcal/20170710_refcal_amp.png Amp] ||<br />
|-<br />
| 2017/07/11 || 13:14:18 || 0319+415 || || 0 || || 5~34 || [http://ovsa.njit.edu/refcal/20170711_refcal_pha.png Phase] || [http://ovsa.njit.edu/refcal/20170711_refcal_amp.png Amp] ||<br />
|-<br />
| 2017/07/12 || 13:14:24 || 0319+415 || || 0 || || 5~34 || [http://ovsa.njit.edu/refcal/20170712_refcal_pha.png Phase] || [http://ovsa.njit.edu/refcal/20170712_refcal_amp.png Amp] ||<br />
|-<br />
| 2017/07/13 || 13:14:59 || 0319+415 || || 0 || || 5~34 || [http://ovsa.njit.edu/refcal/20170713_refcal_pha.png Phase] || [http://ovsa.njit.edu/refcal/20170713_refcal_amp.png Amp] ||<br />
|-<br />
| 2017/07/14 || 13:15:35 || 0319+415 || || 0 || || 5~34 || [http://ovsa.njit.edu/refcal/20170714_refcal_pha.png Phase] || [http://ovsa.njit.edu/refcal/20170714_refcal_amp.png Amp] ||<br />
|-<br />
| 2017/07/16 || 02:48:33 || 1229+020 || || 0 || || 5~34 || [http://ovsa.njit.edu/refcal/20170716_refcal_pha.png Phase] || [http://ovsa.njit.edu/refcal/20170716_refcal_amp.png Amp] ||<br />
|-<br />
| 2017/07/16 || 13:16:48 || 0319+415 || || 0 || || 5~34 || [http://ovsa.njit.edu/refcal/20170716_refcal_pha.png Phase] || [http://ovsa.njit.edu/refcal/20170716_refcal_amp.png Amp] ||<br />
|-<br />
| 2017/07/17 || 13:14:54 || 0319+415 || || 0 || || 5~34 || [http://ovsa.njit.edu/refcal/20170717_refcal_pha.png Phase] || [http://ovsa.njit.edu/refcal/20170717_refcal_amp.png Amp] ||<br />
|-<br />
| 2017/07/18 || 13:15:31 || 0319+415 || || 0 || || 5~34 || [http://ovsa.njit.edu/refcal/20170718_refcal_pha.png Phase] || [http://ovsa.njit.edu/refcal/20170718_refcal_amp.png Amp] ||<br />
|-<br />
| 2017/07/19 || 13:16:16 || 0319+415 || || 0 || || 5~34 || [http://ovsa.njit.edu/refcal/20170719_refcal_pha.png Phase] || [http://ovsa.njit.edu/refcal/20170719_refcal_amp.png Amp] ||<br />
|-<br />
| 2017/07/20 || 13:16:49 || 0319+415 || || 0 || || 5~34 || [http://ovsa.njit.edu/refcal/20170720_refcal_pha.png Phase] || [http://ovsa.njit.edu/refcal/20170720_refcal_amp.png Amp] || No calibration for: Ant 10<br />
|-<br />
| 2017/07/21 || 13:20:57 || 0319+415 || || 0 || || 5~34 || [http://ovsa.njit.edu/refcal/20170721_refcal_pha.png Phase] || [http://ovsa.njit.edu/refcal/20170721_refcal_amp.png Amp] ||<br />
|-<br />
| 2017/07/22 || 13:21:36 || 0319+415 || || 0 || || 5~34 || [http://ovsa.njit.edu/refcal/20170722_refcal_pha.png Phase] || [http://ovsa.njit.edu/refcal/20170722_refcal_amp.png Amp] ||<br />
|-<br />
| 2017/07/23 || 13:34:22 || 0319+415 || || 0 || || 5~34 || [http://ovsa.njit.edu/refcal/20170723_refcal_pha.png Phase] || [http://ovsa.njit.edu/refcal/20170723_refcal_amp.png Amp] ||<br />
|-<br />
| 2017/07/24 || 13:22:58 || 0319+415 || || 0 || || 5~34 || [http://ovsa.njit.edu/refcal/20170724_refcal_pha.png Phase] || [http://ovsa.njit.edu/refcal/20170724_refcal_amp.png Amp] ||<br />
|-<br />
| 2017/07/25 || 13:23:38 || 0319+415 || || 0 || || 5~34 || [http://ovsa.njit.edu/refcal/20170725_refcal_pha.png Phase] || [http://ovsa.njit.edu/refcal/20170725_refcal_amp.png Amp] ||<br />
|-<br />
| 2017/07/26 || 18:00:49 || 0319+415 || || 0 || || 5~34 || [http://ovsa.njit.edu/refcal/20170726_refcal_pha.png Phase] || [http://ovsa.njit.edu/refcal/20170726_refcal_amp.png Amp] ||<br />
|-</div>Ztwanghttp://www.ovsa.njit.edu/wiki/index.php/Reference_Gain_CalibrationReference Gain Calibration2017-07-27T19:52:46Z<p>Ztwang: /* List of Analyzed Reference Calibrations */</p>
<hr />
<div>Reference complex gain calibration refers to determining the "system" amplitude and phase with high precision as a function of IF band (i.e. integrated over each 500 MHz IF band). A typical reference calibration would cover 34 bands, 2 polarizations, and 13 antennas. The routines to retrieve and analyze the data are in the module refcal_anal.py. Start from a time range during which the reference calibration observation occurred (check the [http://ovsa.njit.edu/phasecal/ phasecal results] to see which 1-hr scan had stable phases)<br />
<br />
<pre><br />
import refcal_anal as ra<br />
from util import Time<br />
#example time range of the refcal scan that took place BEFORE the observation<br />
trange=Time(['2017-04-08T14:00','2017-04-08T15:00'])<br />
</pre><br />
<br />
<!--BIN'S PREVIOUS TEXTS<pre><br />
import refcal_anal as ra<br />
from util import Time<br />
trange=Time(['2017-04-08T05:00','2017-04-08T15:30'])<br />
</pre>--><br />
<br />
Now read the data from that timerange<br />
<pre><br />
out=ra.rd_refcal(trange)<br />
</pre><br />
Note that there are optional arguments that can be given, such as projid='PHASECAL' (the default) and srcid='1229+060', but these are generally not needed.<br />
<br />
To correct for differential feed rotation (for refcal data after 05:00 UT on 2017-Jul-01), you can use:<br />
<pre><br />
out_corr = ra.unrot_refcal(out)<br />
</pre><br />
<br />
Take a look at the phases (averaged over each band): <br />
<pre><br />
ra.graph(out_corr)<br />
</pre><br />
By default it displays only bands 5, 11, 17, 23 and polarization XX. To change the bands and polarization to display, use the "bandplt" and 'pol' parameters (better to check more bands).<br />
<pre><br />
ra.graph(out_corr, bandplt=[5,13,19,25], pol=1)<br />
</pre><br />
<br />
<!--BIN'S PREVIOUS TEXTS: From the plot, one can determine which scans are the good ones to use and record the indices of useful scans as "scanidx". In this example, we were alternating between the low- and high-frequency receivers. The low-frequency receiver observations did not have delays adjusted. So we use scans with indices 1, 3, 5, 7, 9, 11, 13 which are associated with the high-frequency receiver scans. <br />
<pre><br />
scanidx=[1, 3, 5, 7, 9, 11, 13]<br />
</pre>,<br />
<br />
Then, we can further determine a finer selection of time range which has clean and stable phases (better to check more bands using ra.graph()). Observations within this time range (after the scanidx selection, if provided) will be used for averaging to get the reference phases/amplitudes. Data will be flagged if the SNR is less than minsnr, which can be supplied. The default minsnr is set to 1.0.<br />
<br />
<pre><br />
timerange=Time(['2017-04-08T05:00','2017-04-08T07:00'])<br />
<br />
refcal=ra.refcal_anal(out_corr,timerange=timerange,scanidx=scanidx)<br />
</pre>--><br />
<br />
Observations within this time range will be used for averaging to get the reference phases/amplitudes. Data will be flagged if the SNR is less than minsnr, which can be supplied. The default minsnr is set to 1.0. We can further determine a finer selection of time range within this scan that has clean and stable phases if needed, by setting the new timerange in "trange" below.<br />
<br />
<pre><br />
refcal=ra.refcal_anal(out_corr,timerange=trange,scanidx=[0])<br />
</pre><br />
<br />
It will generate four plots. First and second are phases and amplitudes of the data similar as those produced by ra.graph(), but with the selected time range for averaging highlighted (one can use "bandplt" and "pol" to choose bands and polarization to display as well). The 3rd plot is the averaged phase vs. frequency and the 4th is the averaged amplitude vs. frequency. Those data will be our "analyzed" reference calibration data saved in the returned dictionary (named "refcal" here). The dictionary contains the actual complex values (refcal['refcal']), a flag array with the same shape (refcal['flag']), and some timestamps, e.g., refcal['t_mid'] is the middle of the time range used for averaging. Both refcal['refcal'] and refcal['flag'] have a shape of (15, 2, 34) -- which corresponds to # of antennas, # of polarizations, and # of bands.<br />
<br />
If you determine some antenna, band, polarization need to be flagged/unflagged, they have to be manually changed in the returned refcal['flag'] array. In this example, Antenna 12 was not tracking, and the algorithm did not pick up all of them, so we have to do this manually -- setting refcal['flag'][11, :, :]=1<br />
<br />
<pre><br />
refcal['flag'][11]=1<br />
</pre><br />
<br />
If satisfied with the results (by looking at the plots), we can go ahead and send them to the SQL database<br />
<pre><br />
import cal_header as ch<br />
ch.refcal2sql(refcal)<br />
</pre><br />
<br />
To retrieve the refcal data back from SQL database based on, e.g., a solar data one wish to calibrate. We can provide a time: <br />
<pre><br />
t=Time('2017-04-07T19:40')<br />
refcal=ra.sql2refcal(t)<br />
</pre><br />
The resulted refcal have three keys: 'amp' (15 x 2 x 34 array), 'pha' (15 x 2 x 34 array), and 'timestamp' (in jd). The refcal data found will be the closest one PRIOR to the supplied observation time.<br />
<br />
== Updating the Reference Calibrations Table ==<br />
The table below lists the known good reference calibrations. To facilitate adding entries to this table, do the following, where the time is after the desired refcal, but before any later refcal:<br />
<pre><br />
t=Time('2017-06-23T19:40') # retrieves the refcal at 13:07 UT on that day<br />
refcal=ra.sql2refcal(t)<br />
ra.graph_results(refcal, savefigs=True)<br />
</pre><br />
This will create summary plots of the amplitude and phase, will write the two corresponding *.png files into the /common/webplots/refcal folder, and will print as a text string the lines needed to add an entry. Just cut from the terminal and paste into the wiki editor at the appropriate place to preserve time order.<br />
<br />
== List of Analyzed Reference Calibrations ==<br />
<br />
{| class="wikitable" style="text-align: center; width: 800px; height: 200px;"<br />
|-<br />
| Date || Timestamp || Source || Obs Trange || Scan Idx || Avg Trange || Bands || Phase Plot || Amp Plot || Comments<br />
|-<br />
| 2017/04/02 || 06:36:50 || 3c273 || 04:20~11:00 || All || 05:47~07:26 || 5, 7, 9, 11, 13, 15, 17, 19, 21, 23 || [[:File:20170402_refcal_pha.png|Phase]] || [[:File:20170402_refcal_amp.png|Amp]] || Ant 12 was not tracking. Delay center change at 11:38:17.<br />
|-<br />
| 2017/04/04 || 09:32:50 || 3c273 || 04:43~10:57 || All || 08:46~10:19 || 5, 7, 9, 11, 13, 15, 17, 19, 21, 23 || [[:File:20170404_refcal_pha.png|Phase]] || [[:File:20170404_refcal_amp.png|Amp]] || Ant 12 was not tracking. Delay center change at 16:43:51.<br />
|-<br />
| 2017/04/05 ||06:44:10 || 3c273 || 04:17~10:30 || All || 04:27~09:34 || 5, 7, 9, 11, 13, 15, 17, 19, 21, 23 || [[:File:20170405_refcal_pha.png|Phase]] || [[:File:20170405_refcal_amp.png|Amp]] || Ant 12 was not tracking.<br />
|-<br />
| 2017/04/06 || 09:54:50|| 3c273 || 04:14~10:49 || All || 05:39~08:11 || 5, 7, 9, 11, 13, 15, 17, 19, 21, 23 || [[:File:20170406_refcal_pha.png|Phase]] || [[:File:20170406_refcal_amp.png|Amp]] || Ant 12 was not tracking.<br />
|-<br />
| 2017/04/07 || 08:30:51|| 3c273 || 04:00~10:30 || 1, 3, 5, 7, 9, 11, 13, 15, 17 || 07:53~09:10 || 5~34 || [[:File:20170407_refcal_pha.png|Phase]] || [[:File:20170407_refcal_amp.png|Amp]] || Ant 12 was not tracking.<br />
|-<br />
| 2017/04/08 || 06:14:51 || 3c273 || 05:00~10:30 || 1, 3, 5, 7, 9, 11, 13 || 05:00~07:00 || 5~34 || [[:File:20170408_refcal_pha.png|Phase]] || [[:File:20170408_refcal_amp.png|Amp]] || Ant 12 was not tracking. Ant 13 not working. Delay center change at 2017-04-08T03:12:26. Another refcal record is added at 2017-04-09T06:14:45.<br />
|-<br />
| 2017/04/10 || 06:57:10 || 3c273 || 04:30~10:30 || 2, 6, 8 || || 5~34 || [[:File:20170410_refcal_pha.png|Phase]] || [[:File:20170410_refcal_amp.png|Amp]] || Ant 12 was not tracking. Delay center change at 2017-04-08 13:20:39. <br />
|-<br />
| 2017/04/16 || 06:36:48 || 3c273 || 03:00~11:00 || || 05:55~07:20 || 5~34 || [[:File:20170416_refcal_pha.png|Phase]] || [[:File:20170416_refcal_amp.png|Amp]] || Ant 12 was not tracking. <br />
|-<br />
| 2017/04/17 || 06:41:51 || 3c273 || 03:29~10:07 || All || 05:55~07:29 || 5~34 || [[:File:20170417_refcal_pha.png|Phase]] || [[:File:20170417_refcal_amp.png|Amp]] || Ant 12 was not tracking. Delay center change at 19:12:58.<br />
|-<br />
| 2017/04/26 || 08:06:52 || 3c273 || 02:50~09:28 || All || 07:21~08:57 || 5~34 || [[:File:20170426_refcal_pha.png|Phase]] || [[:File:20170426_refcal_amp.png|Amp]] || Ant 12 was not tracking. Delay center change at 04:37:28 and 11:51:26.<br />
|-<br />
| 2017/06/11 || 12:56:22 || 2253+161 || || 0 || || 5~34 || [http://ovsa.njit.edu/refcal/20170611_refcal_pha.png Phase] || [http://ovsa.njit.edu/refcal/20170611_refcal_amp.png Amp] || No calibration for: Ant 12<br />
|-<br />
| 2017/06/14 || 02:33:19 || 1229+020 || || 0 || || 5~34 || [http://ovsa.njit.edu/refcal/20170614_refcal_pha.png Phase] || [http://ovsa.njit.edu/refcal/20170614_refcal_amp.png Amp] || No calibration for: Ant 8 Ant 12<br />
|-<br />
| 2017/06/14 || 13:01:19 || 2253+161 || || 0 || || 5~34 || [http://ovsa.njit.edu/refcal/20170614_refcal_pha.png Phase] || [http://ovsa.njit.edu/refcal/20170614_refcal_amp.png Amp] || No calibration for: Ant 12<br />
|-<br />
| 2017/06/15 || 13:05:48 || || || 0 || || 5~34 || [http://ovsa.njit.edu/refcal/20170615_refcal_pha.png Phase] || [http://ovsa.njit.edu/refcal/20170615_refcal_amp.png Amp] || No calibration for: Ant 12<br />
|-<br />
| 2017/06/16 || 13:05:48 || || || 0 || || 5~34 || [http://ovsa.njit.edu/refcal/20170616_refcal_pha.png Phase] || [http://ovsa.njit.edu/refcal/20170616_refcal_amp.png Amp] || No calibration for: Ant 12<br />
|-<br />
| 2017/06/20 || 13:06:26 || || || 0 || || 5~34 || [http://ovsa.njit.edu/refcal/20170620_refcal_pha.png Phase] || [http://ovsa.njit.edu/refcal/20170620_refcal_amp.png Amp] || No calibration for: Ant 1 Ant 12<br />
|-<br />
| 2017/06/21 || 13:06:38 || || || 0 || || 5~34 || [http://ovsa.njit.edu/refcal/20170621_refcal_pha.png Phase] || [http://ovsa.njit.edu/refcal/20170621_refcal_amp.png Amp] || No calibration for: Ant 12<br />
|-<br />
| 2017/06/22 || 13:06:53 || || || 0 || || 5~34 || [http://ovsa.njit.edu/refcal/20170622_refcal_pha.png Phase] || [http://ovsa.njit.edu/refcal/20170622_refcal_amp.png Amp] || No calibration for: Ant 12<br />
|-<br />
| 2017/06/23 || 13:07:09 || || || 0 || || 5~34 || [http://ovsa.njit.edu/refcal/20170623_refcal_pha.png Phase] || [http://ovsa.njit.edu/refcal/20170623_refcal_amp.png Amp] || No calibration for: Ant 12<br />
|-<br />
| 2017/06/24 || 02:25:49 || || || 0 || || 5~34 || [http://ovsa.njit.edu/refcal/20170624_refcal_pha.png Phase] || [http://ovsa.njit.edu/refcal/20170624_refcal_amp.png Amp] || No calibration for: Ant 12<br />
|-<br />
| 2017/06/24 || 13:07:25 || || || 0 || || 5~34 || [http://ovsa.njit.edu/refcal/20170624_refcal_pha.png Phase] || [http://ovsa.njit.edu/refcal/20170624_refcal_amp.png Amp] || No calibration for: Ant 12<br />
|-<br />
| 2017/06/25 || 13:07:43 || || || 0 || || 5~34 || [http://ovsa.njit.edu/refcal/20170625_refcal_pha.png Phase] || [http://ovsa.njit.edu/refcal/20170625_refcal_amp.png Amp] || No calibration for: Ant 10 Ant 12<br />
|-<br />
| 2017/06/26 || 13:15:47 || || || 0 || || 5~34 || [http://ovsa.njit.edu/refcal/20170626_refcal_pha.png Phase] || [http://ovsa.njit.edu/refcal/20170626_refcal_amp.png Amp] || No calibration for: Ant 10 Ant 12<br />
|-<br />
| 2017/06/27 || 13:02:49 || 2253+161 || || 0 || || 5~34 || [http://ovsa.njit.edu/refcal/20170627_refcal_pha.png Phase] || [http://ovsa.njit.edu/refcal/20170627_refcal_amp.png Amp] || No calibration for: Ant 12<br />
|-<br />
| 2017/06/30 || 02:47:50 || 1229+020 || || 0 || || 5~34 || [http://ovsa.njit.edu/refcal/20170630_refcal_pha.png Phase] || [http://ovsa.njit.edu/refcal/20170630_refcal_amp.png Amp] || No calibration for: Ant 12<br />
|-<br />
| 2017/07/01 || 02:44:49 || 1229+020 || || 0 || || 5~34 || [http://ovsa.njit.edu/refcal/20170701_refcal_pha.png Phase] || [http://ovsa.njit.edu/refcal/20170701_refcal_amp.png Amp] || No calibration for: Ant 12<br />
|-<br />
| 2017/07/02 || 03:01:20 || 1229+020 || || 0 || || 5~34 || [http://ovsa.njit.edu/refcal/20170702_refcal_pha.png Phase] || [http://ovsa.njit.edu/refcal/20170702_refcal_amp.png Amp] ||<br />
|-<br />
| 2017/07/03 || 02:47:49 || 1229+020 || || 0 || || 5~34 || [http://ovsa.njit.edu/refcal/20170703_refcal_pha.png Phase] || [http://ovsa.njit.edu/refcal/20170703_refcal_amp.png Amp] || No calibration for: Ant 10<br />
|-<br />
| 2017/07/04 || 02:47:49 || 1229+020 || || 0 || || 5~34 || [http://ovsa.njit.edu/refcal/20170704_refcal_pha.png Phase] || [http://ovsa.njit.edu/refcal/20170704_refcal_amp.png Amp] ||<br />
|-<br />
| 2017/07/05 || 02:55:19 || 1229+020 || || 0 || || 5~34 || [http://ovsa.njit.edu/refcal/20170705_refcal_pha.png Phase] || [http://ovsa.njit.edu/refcal/20170705_refcal_amp.png Amp] ||<br />
|-<br />
| 2017/07/06 || 02:47:49 || 1229+020 || || 0 || || 5~34 || [http://ovsa.njit.edu/refcal/20170706_refcal_pha.png Phase] || [http://ovsa.njit.edu/refcal/20170706_refcal_amp.png Amp] || <br />
|-<br />
| 2017/07/07 || 13:12:49 || 2253+161 || || 0 || || 5~34 || [http://ovsa.njit.edu/refcal/20170707_refcal_pha.png Phase] || [http://ovsa.njit.edu/refcal/20170707_refcal_amp.png Amp] ||<br />
|-<br />
| 2017/07/09 || 02:35:49 || 1229+020 || || 0 || || 5~34 || [http://ovsa.njit.edu/refcal/20170709_refcal_pha.png Phase] || [http://ovsa.njit.edu/refcal/20170709_refcal_amp.png Amp] ||<br />
|-<br />
| 2017/07/09 || 13:16:49 || 2253+161 || || 0 || || 5~34 || [http://ovsa.njit.edu/refcal/20170709_refcal_pha.png Phase] || [http://ovsa.njit.edu/refcal/20170709_refcal_amp.png Amp] ||<br />
|-<br />
| 2017/07/10 || 13:14:17 || 0319+415 || || 0 || || 5~34 || [http://ovsa.njit.edu/refcal/20170710_refcal_pha.png Phase] || [http://ovsa.njit.edu/refcal/20170710_refcal_amp.png Amp] ||<br />
|-<br />
| 2017/07/11 || 13:14:18 || 0319+415 || || 0 || || 5~34 || [http://ovsa.njit.edu/refcal/20170711_refcal_pha.png Phase] || [http://ovsa.njit.edu/refcal/20170711_refcal_amp.png Amp] ||<br />
|-<br />
| 2017/07/12 || 13:14:24 || 0319+415 || || 0 || || 5~34 || [http://ovsa.njit.edu/refcal/20170712_refcal_pha.png Phase] || [http://ovsa.njit.edu/refcal/20170712_refcal_amp.png Amp] ||<br />
|-<br />
| 2017/07/13 || 13:14:59 || 0319+415 || || 0 || || 5~34 || [http://ovsa.njit.edu/refcal/20170713_refcal_pha.png Phase] || [http://ovsa.njit.edu/refcal/20170713_refcal_amp.png Amp] ||<br />
|-<br />
| 2017/07/14 || 13:15:35 || 0319+415 || || 0 || || 5~34 || [http://ovsa.njit.edu/refcal/20170714_refcal_pha.png Phase] || [http://ovsa.njit.edu/refcal/20170714_refcal_amp.png Amp] ||<br />
|-<br />
| 2017/07/16 || 02:48:33 || 1229+020 || || 0 || || 5~34 || [http://ovsa.njit.edu/refcal/20170716_refcal_pha.png Phase] || [http://ovsa.njit.edu/refcal/20170716_refcal_amp.png Amp] ||<br />
|-<br />
| 2017/07/16 || 13:16:48 || 0319+415 || || 0 || || 5~34 || [http://ovsa.njit.edu/refcal/20170716_refcal_pha.png Phase] || [http://ovsa.njit.edu/refcal/20170716_refcal_amp.png Amp] ||<br />
|-<br />
| 2017/07/17 || 13:14:54 || 0319+415 || || 0 || || 5~34 || [http://ovsa.njit.edu/refcal/20170717_refcal_pha.png Phase] || [http://ovsa.njit.edu/refcal/20170717_refcal_amp.png Amp] ||<br />
|-<br />
| 2017/07/18 || 13:15:31 || 0319+415 || || 0 || || 5~34 || [http://ovsa.njit.edu/refcal/20170718_refcal_pha.png Phase] || [http://ovsa.njit.edu/refcal/20170718_refcal_amp.png Amp] ||<br />
|-<br />
| 2017/07/19 || 13:16:16 || 0319+415 || || 0 || || 5~34 || [http://ovsa.njit.edu/refcal/20170719_refcal_pha.png Phase] || [http://ovsa.njit.edu/refcal/20170719_refcal_amp.png Amp] ||<br />
|-<br />
| 2017/07/20 || 13:16:49 || 0319+415 || || 0 || || 5~34 || [http://ovsa.njit.edu/refcal/20170720_refcal_pha.png Phase] || [http://ovsa.njit.edu/refcal/20170720_refcal_amp.png Amp] || No calibration for: Ant 10<br />
|-<br />
| 2017/07/21 || 13:20:57 || 0319+415 || || 0 || || 5~34 || [http://ovsa.njit.edu/refcal/20170721_refcal_pha.png Phase] || [http://ovsa.njit.edu/refcal/20170721_refcal_amp.png Amp] ||<br />
|-<br />
| 2017/07/22 || 13:21:36 || 0319+415 || || 0 || || 5~34 || [http://ovsa.njit.edu/refcal/20170722_refcal_pha.png Phase] || [http://ovsa.njit.edu/refcal/20170722_refcal_amp.png Amp] ||<br />
|-<br />
| 2017/07/23 || 13:34:22 || 0319+415 || || 0 || || 5~34 || [http://ovsa.njit.edu/refcal/20170723_refcal_pha.png Phase] || [http://ovsa.njit.edu/refcal/20170723_refcal_amp.png Amp] ||<br />
|-<br />
| 2017/07/24 || 13:22:58 || 0319+415 || || 0 || || 5~34 || [http://ovsa.njit.edu/refcal/20170724_refcal_pha.png Phase] || [http://ovsa.njit.edu/refcal/20170724_refcal_amp.png Amp] ||<br />
|-<br />
| 2017/07/25 || 13:23:38 || 0319+415 || || 0 || || 5~34 || [http://ovsa.njit.edu/refcal/20170725_refcal_pha.png Phase] || [http://ovsa.njit.edu/refcal/20170725_refcal_amp.png Amp] ||<br />
|-</div>Ztwanghttp://www.ovsa.njit.edu/wiki/index.php/Reference_Gain_CalibrationReference Gain Calibration2017-07-27T19:34:26Z<p>Ztwang: /* List of Analyzed Reference Calibrations */</p>
<hr />
<div>Reference complex gain calibration refers to determining the "system" amplitude and phase with high precision as a function of IF band (i.e. integrated over each 500 MHz IF band). A typical reference calibration would cover 34 bands, 2 polarizations, and 13 antennas. The routines to retrieve and analyze the data are in the module refcal_anal.py. Start from a time range during which the reference calibration observation occurred (check the [http://ovsa.njit.edu/phasecal/ phasecal results] to see which 1-hr scan had stable phases)<br />
<br />
<pre><br />
import refcal_anal as ra<br />
from util import Time<br />
#example time range of the refcal scan that took place BEFORE the observation<br />
trange=Time(['2017-04-08T14:00','2017-04-08T15:00'])<br />
</pre><br />
<br />
<!--BIN'S PREVIOUS TEXTS<pre><br />
import refcal_anal as ra<br />
from util import Time<br />
trange=Time(['2017-04-08T05:00','2017-04-08T15:30'])<br />
</pre>--><br />
<br />
Now read the data from that timerange<br />
<pre><br />
out=ra.rd_refcal(trange)<br />
</pre><br />
Note that there are optional arguments that can be given, such as projid='PHASECAL' (the default) and srcid='1229+060', but these are generally not needed.<br />
<br />
To correct for differential feed rotation (for refcal data after 05:00 UT on 2017-Jul-01), you can use:<br />
<pre><br />
out_corr = ra.unrot_refcal(out)<br />
</pre><br />
<br />
Take a look at the phases (averaged over each band): <br />
<pre><br />
ra.graph(out_corr)<br />
</pre><br />
By default it displays only bands 5, 11, 17, 23 and polarization XX. To change the bands and polarization to display, use the "bandplt" and 'pol' parameters (better to check more bands).<br />
<pre><br />
ra.graph(out_corr, bandplt=[5,13,19,25], pol=1)<br />
</pre><br />
<br />
<!--BIN'S PREVIOUS TEXTS: From the plot, one can determine which scans are the good ones to use and record the indices of useful scans as "scanidx". In this example, we were alternating between the low- and high-frequency receivers. The low-frequency receiver observations did not have delays adjusted. So we use scans with indices 1, 3, 5, 7, 9, 11, 13 which are associated with the high-frequency receiver scans. <br />
<pre><br />
scanidx=[1, 3, 5, 7, 9, 11, 13]<br />
</pre>,<br />
<br />
Then, we can further determine a finer selection of time range which has clean and stable phases (better to check more bands using ra.graph()). Observations within this time range (after the scanidx selection, if provided) will be used for averaging to get the reference phases/amplitudes. Data will be flagged if the SNR is less than minsnr, which can be supplied. The default minsnr is set to 1.0.<br />
<br />
<pre><br />
timerange=Time(['2017-04-08T05:00','2017-04-08T07:00'])<br />
<br />
refcal=ra.refcal_anal(out_corr,timerange=timerange,scanidx=scanidx)<br />
</pre>--><br />
<br />
Observations within this time range will be used for averaging to get the reference phases/amplitudes. Data will be flagged if the SNR is less than minsnr, which can be supplied. The default minsnr is set to 1.0. We can further determine a finer selection of time range within this scan that has clean and stable phases if needed, by setting the new timerange in "trange" below.<br />
<br />
<pre><br />
refcal=ra.refcal_anal(out_corr,timerange=trange,scanidx=[0])<br />
</pre><br />
<br />
It will generate four plots. First and second are phases and amplitudes of the data similar as those produced by ra.graph(), but with the selected time range for averaging highlighted (one can use "bandplt" and "pol" to choose bands and polarization to display as well). The 3rd plot is the averaged phase vs. frequency and the 4th is the averaged amplitude vs. frequency. Those data will be our "analyzed" reference calibration data saved in the returned dictionary (named "refcal" here). The dictionary contains the actual complex values (refcal['refcal']), a flag array with the same shape (refcal['flag']), and some timestamps, e.g., refcal['t_mid'] is the middle of the time range used for averaging. Both refcal['refcal'] and refcal['flag'] have a shape of (15, 2, 34) -- which corresponds to # of antennas, # of polarizations, and # of bands.<br />
<br />
If you determine some antenna, band, polarization need to be flagged/unflagged, they have to be manually changed in the returned refcal['flag'] array. In this example, Antenna 12 was not tracking, and the algorithm did not pick up all of them, so we have to do this manually -- setting refcal['flag'][11, :, :]=1<br />
<br />
<pre><br />
refcal['flag'][11]=1<br />
</pre><br />
<br />
If satisfied with the results (by looking at the plots), we can go ahead and send them to the SQL database<br />
<pre><br />
import cal_header as ch<br />
ch.refcal2sql(refcal)<br />
</pre><br />
<br />
To retrieve the refcal data back from SQL database based on, e.g., a solar data one wish to calibrate. We can provide a time: <br />
<pre><br />
t=Time('2017-04-07T19:40')<br />
refcal=ra.sql2refcal(t)<br />
</pre><br />
The resulted refcal have three keys: 'amp' (15 x 2 x 34 array), 'pha' (15 x 2 x 34 array), and 'timestamp' (in jd). The refcal data found will be the closest one PRIOR to the supplied observation time.<br />
<br />
== Updating the Reference Calibrations Table ==<br />
The table below lists the known good reference calibrations. To facilitate adding entries to this table, do the following, where the time is after the desired refcal, but before any later refcal:<br />
<pre><br />
t=Time('2017-06-23T19:40') # retrieves the refcal at 13:07 UT on that day<br />
refcal=ra.sql2refcal(t)<br />
ra.graph_results(refcal, savefigs=True)<br />
</pre><br />
This will create summary plots of the amplitude and phase, will write the two corresponding *.png files into the /common/webplots/refcal folder, and will print as a text string the lines needed to add an entry. Just cut from the terminal and paste into the wiki editor at the appropriate place to preserve time order.<br />
<br />
== List of Analyzed Reference Calibrations ==<br />
<br />
{| class="wikitable" style="text-align: center; width: 800px; height: 200px;"<br />
|-<br />
| Date || Timestamp || Source || Obs Trange || Scan Idx || Avg Trange || Bands || Phase Plot || Amp Plot || Comments<br />
|-<br />
| 2017/04/02 || 06:36:50 || 3c273 || 04:20~11:00 || All || 05:47~07:26 || 5, 7, 9, 11, 13, 15, 17, 19, 21, 23 || [[:File:20170402_refcal_pha.png|Phase]] || [[:File:20170402_refcal_amp.png|Amp]] || Ant 12 was not tracking. Delay center change at 11:38:17.<br />
|-<br />
| 2017/04/04 || 09:32:50 || 3c273 || 04:43~10:57 || All || 08:46~10:19 || 5, 7, 9, 11, 13, 15, 17, 19, 21, 23 || [[:File:20170404_refcal_pha.png|Phase]] || [[:File:20170404_refcal_amp.png|Amp]] || Ant 12 was not tracking. Delay center change at 16:43:51.<br />
|-<br />
| 2017/04/05 ||06:44:10 || 3c273 || 04:17~10:30 || All || 04:27~09:34 || 5, 7, 9, 11, 13, 15, 17, 19, 21, 23 || [[:File:20170405_refcal_pha.png|Phase]] || [[:File:20170405_refcal_amp.png|Amp]] || Ant 12 was not tracking.<br />
|-<br />
| 2017/04/06 || 09:54:50|| 3c273 || 04:14~10:49 || All || 05:39~08:11 || 5, 7, 9, 11, 13, 15, 17, 19, 21, 23 || [[:File:20170406_refcal_pha.png|Phase]] || [[:File:20170406_refcal_amp.png|Amp]] || Ant 12 was not tracking.<br />
|-<br />
| 2017/04/07 || 08:30:51|| 3c273 || 04:00~10:30 || 1, 3, 5, 7, 9, 11, 13, 15, 17 || 07:53~09:10 || 5~34 || [[:File:20170407_refcal_pha.png|Phase]] || [[:File:20170407_refcal_amp.png|Amp]] || Ant 12 was not tracking.<br />
|-<br />
| 2017/04/08 || 06:14:51 || 3c273 || 05:00~10:30 || 1, 3, 5, 7, 9, 11, 13 || 05:00~07:00 || 5~34 || [[:File:20170408_refcal_pha.png|Phase]] || [[:File:20170408_refcal_amp.png|Amp]] || Ant 12 was not tracking. Ant 13 not working. Delay center change at 2017-04-08T03:12:26. Another refcal record is added at 2017-04-09T06:14:45.<br />
|-<br />
| 2017/04/10 || 06:57:10 || 3c273 || 04:30~10:30 || 2, 6, 8 || || 5~34 || [[:File:20170410_refcal_pha.png|Phase]] || [[:File:20170410_refcal_amp.png|Amp]] || Ant 12 was not tracking. Delay center change at 2017-04-08 13:20:39. <br />
|-<br />
| 2017/04/16 || 06:36:48 || 3c273 || 03:00~11:00 || || 05:55~07:20 || 5~34 || [[:File:20170416_refcal_pha.png|Phase]] || [[:File:20170416_refcal_amp.png|Amp]] || Ant 12 was not tracking. <br />
|-<br />
| 2017/04/17 || 06:41:51 || 3c273 || 03:29~10:07 || All || 05:55~07:29 || 5~34 || [[:File:20170417_refcal_pha.png|Phase]] || [[:File:20170417_refcal_amp.png|Amp]] || Ant 12 was not tracking. Delay center change at 19:12:58.<br />
|-<br />
| 2017/04/26 || 08:06:52 || 3c273 || 02:50~09:28 || All || 07:21~08:57 || 5~34 || [[:File:20170426_refcal_pha.png|Phase]] || [[:File:20170426_refcal_amp.png|Amp]] || Ant 12 was not tracking. Delay center change at 04:37:28 and 11:51:26.<br />
|-<br />
| 2017/06/11 || 12:56:22 || 2253+161 || || 0 || || 5~34 || [http://ovsa.njit.edu/refcal/20170611_refcal_pha.png Phase] || [http://ovsa.njit.edu/refcal/20170611_refcal_amp.png Amp] || No calibration for: Ant 12<br />
|-<br />
| 2017/06/14 || 02:33:19 || 1229+020 || || 0 || || 5~34 || [http://ovsa.njit.edu/refcal/20170614_refcal_pha.png Phase] || [http://ovsa.njit.edu/refcal/20170614_refcal_amp.png Amp] || No calibration for: Ant 8 Ant 12<br />
|-<br />
| 2017/06/14 || 13:01:19 || 2253+161 || || 0 || || 5~34 || [http://ovsa.njit.edu/refcal/20170614_refcal_pha.png Phase] || [http://ovsa.njit.edu/refcal/20170614_refcal_amp.png Amp] || No calibration for: Ant 12<br />
|-<br />
| 2017/06/15 || 13:05:48 || || || 0 || || 5~34 || [http://ovsa.njit.edu/refcal/20170615_refcal_pha.png Phase] || [http://ovsa.njit.edu/refcal/20170615_refcal_amp.png Amp] || No calibration for: Ant 12<br />
|-<br />
| 2017/06/16 || 13:05:48 || || || 0 || || 5~34 || [http://ovsa.njit.edu/refcal/20170616_refcal_pha.png Phase] || [http://ovsa.njit.edu/refcal/20170616_refcal_amp.png Amp] || No calibration for: Ant 12<br />
|-<br />
| 2017/06/20 || 13:06:26 || || || 0 || || 5~34 || [http://ovsa.njit.edu/refcal/20170620_refcal_pha.png Phase] || [http://ovsa.njit.edu/refcal/20170620_refcal_amp.png Amp] || No calibration for: Ant 1 Ant 12<br />
|-<br />
| 2017/06/21 || 13:06:38 || || || 0 || || 5~34 || [http://ovsa.njit.edu/refcal/20170621_refcal_pha.png Phase] || [http://ovsa.njit.edu/refcal/20170621_refcal_amp.png Amp] || No calibration for: Ant 12<br />
|-<br />
| 2017/06/22 || 13:06:53 || || || 0 || || 5~34 || [http://ovsa.njit.edu/refcal/20170622_refcal_pha.png Phase] || [http://ovsa.njit.edu/refcal/20170622_refcal_amp.png Amp] || No calibration for: Ant 12<br />
|-<br />
| 2017/06/23 || 13:07:09 || || || 0 || || 5~34 || [http://ovsa.njit.edu/refcal/20170623_refcal_pha.png Phase] || [http://ovsa.njit.edu/refcal/20170623_refcal_amp.png Amp] || No calibration for: Ant 12<br />
|-<br />
| 2017/06/24 || 02:25:49 || || || 0 || || 5~34 || [http://ovsa.njit.edu/refcal/20170624_refcal_pha.png Phase] || [http://ovsa.njit.edu/refcal/20170624_refcal_amp.png Amp] || No calibration for: Ant 12<br />
|-<br />
| 2017/06/24 || 13:07:25 || || || 0 || || 5~34 || [http://ovsa.njit.edu/refcal/20170624_refcal_pha.png Phase] || [http://ovsa.njit.edu/refcal/20170624_refcal_amp.png Amp] || No calibration for: Ant 12<br />
|-<br />
| 2017/06/25 || 13:07:43 || || || 0 || || 5~34 || [http://ovsa.njit.edu/refcal/20170625_refcal_pha.png Phase] || [http://ovsa.njit.edu/refcal/20170625_refcal_amp.png Amp] || No calibration for: Ant 10 Ant 12<br />
|-<br />
| 2017/06/26 || 13:15:47 || || || 0 || || 5~34 || [http://ovsa.njit.edu/refcal/20170626_refcal_pha.png Phase] || [http://ovsa.njit.edu/refcal/20170626_refcal_amp.png Amp] || No calibration for: Ant 10 Ant 12<br />
|-<br />
| 2017/06/27 || 13:02:49 || 2253+161 || || 0 || || 5~34 || [http://ovsa.njit.edu/refcal/20170627_refcal_pha.png Phase] || [http://ovsa.njit.edu/refcal/20170627_refcal_amp.png Amp] || No calibration for: Ant 12<br />
|-<br />
| 2017/06/30 || 02:47:50 || 1229+020 || || 0 || || 5~34 || [http://ovsa.njit.edu/refcal/20170630_refcal_pha.png Phase] || [http://ovsa.njit.edu/refcal/20170630_refcal_amp.png Amp] || No calibration for: Ant 12<br />
|-<br />
| 2017/07/01 || 02:44:49 || 1229+020 || || 0 || || 5~34 || [http://ovsa.njit.edu/refcal/20170701_refcal_pha.png Phase] || [http://ovsa.njit.edu/refcal/20170701_refcal_amp.png Amp] || No calibration for: Ant 12<br />
|-<br />
| 2017/07/02 || 03:01:20 || 1229+020 || || 0 || || 5~34 || [http://ovsa.njit.edu/refcal/20170702_refcal_pha.png Phase] || [http://ovsa.njit.edu/refcal/20170702_refcal_amp.png Amp] ||<br />
|-<br />
| 2017/07/03 || 02:47:49 || 1229+020 || || 0 || || 5~34 || [http://ovsa.njit.edu/refcal/20170703_refcal_pha.png Phase] || [http://ovsa.njit.edu/refcal/20170703_refcal_amp.png Amp] || No calibration for: Ant 10<br />
|-<br />
| 2017/07/04 || 02:47:49 || 1229+020 || || 0 || || 5~34 || [http://ovsa.njit.edu/refcal/20170704_refcal_pha.png Phase] || [http://ovsa.njit.edu/refcal/20170704_refcal_amp.png Amp] ||<br />
|-<br />
| 2017/07/05 || 02:55:19 || 1229+020 || || 0 || || 5~34 || [http://ovsa.njit.edu/refcal/20170705_refcal_pha.png Phase] || [http://ovsa.njit.edu/refcal/20170705_refcal_amp.png Amp] ||<br />
|-<br />
| 2017/07/06 || 02:47:49 || 1229+020 || || 0 || || 5~34 || [http://ovsa.njit.edu/refcal/20170706_refcal_pha.png Phase] || [http://ovsa.njit.edu/refcal/20170706_refcal_amp.png Amp] || <br />
|-<br />
| 2017/07/07 || 13:12:49 || 2253+161 || || 0 || || 5~34 || [http://ovsa.njit.edu/refcal/20170707_refcal_pha.png Phase] || [http://ovsa.njit.edu/refcal/20170707_refcal_amp.png Amp] ||<br />
|-<br />
| 2017/07/09 || 02:35:49 || 1229+020 || || 0 || || 5~34 || [http://ovsa.njit.edu/refcal/20170709_refcal_pha.png Phase] || [http://ovsa.njit.edu/refcal/20170709_refcal_amp.png Amp] ||<br />
|-<br />
| 2017/07/09 || 13:16:49 || 2253+161 || || 0 || || 5~34 || [http://ovsa.njit.edu/refcal/20170709_refcal_pha.png Phase] || [http://ovsa.njit.edu/refcal/20170709_refcal_amp.png Amp] ||<br />
|-<br />
| 2017/07/10 || 13:14:17 || 0319+415 || || 0 || || 5~34 || [http://ovsa.njit.edu/refcal/20170710_refcal_pha.png Phase] || [http://ovsa.njit.edu/refcal/20170710_refcal_amp.png Amp] ||<br />
|-<br />
| 2017/07/11 || 13:14:18 || 0319+415 || || 0 || || 5~34 || [http://ovsa.njit.edu/refcal/20170711_refcal_pha.png Phase] || [http://ovsa.njit.edu/refcal/20170711_refcal_amp.png Amp] ||<br />
|-<br />
| 2017/07/12 || 13:14:24 || 0319+415 || || 0 || || 5~34 || [http://ovsa.njit.edu/refcal/20170712_refcal_pha.png Phase] || [http://ovsa.njit.edu/refcal/20170712_refcal_amp.png Amp] ||<br />
|-<br />
| 2017/07/13 || 13:14:59 || 0319+415 || || 0 || || 5~34 || [http://ovsa.njit.edu/refcal/20170713_refcal_pha.png Phase] || [http://ovsa.njit.edu/refcal/20170713_refcal_amp.png Amp] ||<br />
|-<br />
| 2017/07/14 || 13:15:35 || 0319+415 || || 0 || || 5~34 || [http://ovsa.njit.edu/refcal/20170714_refcal_pha.png Phase] || [http://ovsa.njit.edu/refcal/20170714_refcal_amp.png Amp] ||<br />
|-<br />
| 2017/07/16 || 02:48:33 || 1229+020 || || 0 || || 5~34 || [http://ovsa.njit.edu/refcal/20170716_refcal_pha.png Phase] || [http://ovsa.njit.edu/refcal/20170716_refcal_amp.png Amp] ||<br />
|-<br />
| 2017/07/16 || 13:16:48 || 0319+415 || || 0 || || 5~34 || [http://ovsa.njit.edu/refcal/20170716_refcal_pha.png Phase] || [http://ovsa.njit.edu/refcal/20170716_refcal_amp.png Amp] ||<br />
|-<br />
| 2017/07/17 || 13:14:54 || 0319+415 || || 0 || || 5~34 || [http://ovsa.njit.edu/refcal/20170717_refcal_pha.png Phase] || [http://ovsa.njit.edu/refcal/20170717_refcal_amp.png Amp] ||<br />
|-<br />
| 2017/07/18 || 13:15:31 || 0319+415 || || 0 || || 5~34 || [http://ovsa.njit.edu/refcal/20170718_refcal_pha.png Phase] || [http://ovsa.njit.edu/refcal/20170718_refcal_amp.png Amp] ||<br />
|-<br />
| 2017/07/19 || 13:16:16 || 0319+415 || || 0 || || 5~34 || [http://ovsa.njit.edu/refcal/20170719_refcal_pha.png Phase] || [http://ovsa.njit.edu/refcal/20170719_refcal_amp.png Amp] ||<br />
|-<br />
| 2017/07/20 || 13:16:49 || 0319+415 || || 0 || || 5~34 || [http://ovsa.njit.edu/refcal/20170720_refcal_pha.png Phase] || [http://ovsa.njit.edu/refcal/20170720_refcal_amp.png Amp] || No calibration for: Ant 10<br />
|-<br />
| 2017/07/21 || 13:20:57 || 0319+415 || || 0 || || 5~34 || [http://ovsa.njit.edu/refcal/20170721_refcal_pha.png Phase] || [http://ovsa.njit.edu/refcal/20170721_refcal_amp.png Amp] ||<br />
|-<br />
| 2017/07/22 || 13:21:36 || 0319+415 || || 0 || || 5~34 || [http://ovsa.njit.edu/refcal/20170722_refcal_pha.png Phase] || [http://ovsa.njit.edu/refcal/20170722_refcal_amp.png Amp] ||<br />
|-<br />
| 2017/07/24 || 13:22:58 || 0319+415 || || 0 || || 5~34 || [http://ovsa.njit.edu/refcal/20170724_refcal_pha.png Phase] || [http://ovsa.njit.edu/refcal/20170724_refcal_amp.png Amp] ||<br />
|-<br />
| 2017/07/25 || 13:23:38 || 0319+415 || || 0 || || 5~34 || [http://ovsa.njit.edu/refcal/20170725_refcal_pha.png Phase] || [http://ovsa.njit.edu/refcal/20170725_refcal_amp.png Amp] ||<br />
|-</div>Ztwanghttp://www.ovsa.njit.edu/wiki/index.php/Reference_Gain_CalibrationReference Gain Calibration2017-07-27T19:26:48Z<p>Ztwang: /* List of Analyzed Reference Calibrations */</p>
<hr />
<div>Reference complex gain calibration refers to determining the "system" amplitude and phase with high precision as a function of IF band (i.e. integrated over each 500 MHz IF band). A typical reference calibration would cover 34 bands, 2 polarizations, and 13 antennas. The routines to retrieve and analyze the data are in the module refcal_anal.py. Start from a time range during which the reference calibration observation occurred (check the [http://ovsa.njit.edu/phasecal/ phasecal results] to see which 1-hr scan had stable phases)<br />
<br />
<pre><br />
import refcal_anal as ra<br />
from util import Time<br />
#example time range of the refcal scan that took place BEFORE the observation<br />
trange=Time(['2017-04-08T14:00','2017-04-08T15:00'])<br />
</pre><br />
<br />
<!--BIN'S PREVIOUS TEXTS<pre><br />
import refcal_anal as ra<br />
from util import Time<br />
trange=Time(['2017-04-08T05:00','2017-04-08T15:30'])<br />
</pre>--><br />
<br />
Now read the data from that timerange<br />
<pre><br />
out=ra.rd_refcal(trange)<br />
</pre><br />
Note that there are optional arguments that can be given, such as projid='PHASECAL' (the default) and srcid='1229+060', but these are generally not needed.<br />
<br />
To correct for differential feed rotation (for refcal data after 05:00 UT on 2017-Jul-01), you can use:<br />
<pre><br />
out_corr = ra.unrot_refcal(out)<br />
</pre><br />
<br />
Take a look at the phases (averaged over each band): <br />
<pre><br />
ra.graph(out_corr)<br />
</pre><br />
By default it displays only bands 5, 11, 17, 23 and polarization XX. To change the bands and polarization to display, use the "bandplt" and 'pol' parameters (better to check more bands).<br />
<pre><br />
ra.graph(out_corr, bandplt=[5,13,19,25], pol=1)<br />
</pre><br />
<br />
<!--BIN'S PREVIOUS TEXTS: From the plot, one can determine which scans are the good ones to use and record the indices of useful scans as "scanidx". In this example, we were alternating between the low- and high-frequency receivers. The low-frequency receiver observations did not have delays adjusted. So we use scans with indices 1, 3, 5, 7, 9, 11, 13 which are associated with the high-frequency receiver scans. <br />
<pre><br />
scanidx=[1, 3, 5, 7, 9, 11, 13]<br />
</pre>,<br />
<br />
Then, we can further determine a finer selection of time range which has clean and stable phases (better to check more bands using ra.graph()). Observations within this time range (after the scanidx selection, if provided) will be used for averaging to get the reference phases/amplitudes. Data will be flagged if the SNR is less than minsnr, which can be supplied. The default minsnr is set to 1.0.<br />
<br />
<pre><br />
timerange=Time(['2017-04-08T05:00','2017-04-08T07:00'])<br />
<br />
refcal=ra.refcal_anal(out_corr,timerange=timerange,scanidx=scanidx)<br />
</pre>--><br />
<br />
Observations within this time range will be used for averaging to get the reference phases/amplitudes. Data will be flagged if the SNR is less than minsnr, which can be supplied. The default minsnr is set to 1.0. We can further determine a finer selection of time range within this scan that has clean and stable phases if needed, by setting the new timerange in "trange" below.<br />
<br />
<pre><br />
refcal=ra.refcal_anal(out_corr,timerange=trange,scanidx=[0])<br />
</pre><br />
<br />
It will generate four plots. First and second are phases and amplitudes of the data similar as those produced by ra.graph(), but with the selected time range for averaging highlighted (one can use "bandplt" and "pol" to choose bands and polarization to display as well). The 3rd plot is the averaged phase vs. frequency and the 4th is the averaged amplitude vs. frequency. Those data will be our "analyzed" reference calibration data saved in the returned dictionary (named "refcal" here). The dictionary contains the actual complex values (refcal['refcal']), a flag array with the same shape (refcal['flag']), and some timestamps, e.g., refcal['t_mid'] is the middle of the time range used for averaging. Both refcal['refcal'] and refcal['flag'] have a shape of (15, 2, 34) -- which corresponds to # of antennas, # of polarizations, and # of bands.<br />
<br />
If you determine some antenna, band, polarization need to be flagged/unflagged, they have to be manually changed in the returned refcal['flag'] array. In this example, Antenna 12 was not tracking, and the algorithm did not pick up all of them, so we have to do this manually -- setting refcal['flag'][11, :, :]=1<br />
<br />
<pre><br />
refcal['flag'][11]=1<br />
</pre><br />
<br />
If satisfied with the results (by looking at the plots), we can go ahead and send them to the SQL database<br />
<pre><br />
import cal_header as ch<br />
ch.refcal2sql(refcal)<br />
</pre><br />
<br />
To retrieve the refcal data back from SQL database based on, e.g., a solar data one wish to calibrate. We can provide a time: <br />
<pre><br />
t=Time('2017-04-07T19:40')<br />
refcal=ra.sql2refcal(t)<br />
</pre><br />
The resulted refcal have three keys: 'amp' (15 x 2 x 34 array), 'pha' (15 x 2 x 34 array), and 'timestamp' (in jd). The refcal data found will be the closest one PRIOR to the supplied observation time.<br />
<br />
== Updating the Reference Calibrations Table ==<br />
The table below lists the known good reference calibrations. To facilitate adding entries to this table, do the following, where the time is after the desired refcal, but before any later refcal:<br />
<pre><br />
t=Time('2017-06-23T19:40') # retrieves the refcal at 13:07 UT on that day<br />
refcal=ra.sql2refcal(t)<br />
ra.graph_results(refcal, savefigs=True)<br />
</pre><br />
This will create summary plots of the amplitude and phase, will write the two corresponding *.png files into the /common/webplots/refcal folder, and will print as a text string the lines needed to add an entry. Just cut from the terminal and paste into the wiki editor at the appropriate place to preserve time order.<br />
<br />
== List of Analyzed Reference Calibrations ==<br />
<br />
{| class="wikitable" style="text-align: center; width: 800px; height: 200px;"<br />
|-<br />
| Date || Timestamp || Source || Obs Trange || Scan Idx || Avg Trange || Bands || Phase Plot || Amp Plot || Comments<br />
|-<br />
| 2017/04/02 || 06:36:50 || 3c273 || 04:20~11:00 || All || 05:47~07:26 || 5, 7, 9, 11, 13, 15, 17, 19, 21, 23 || [[:File:20170402_refcal_pha.png|Phase]] || [[:File:20170402_refcal_amp.png|Amp]] || Ant 12 was not tracking. Delay center change at 11:38:17.<br />
|-<br />
| 2017/04/04 || 09:32:50 || 3c273 || 04:43~10:57 || All || 08:46~10:19 || 5, 7, 9, 11, 13, 15, 17, 19, 21, 23 || [[:File:20170404_refcal_pha.png|Phase]] || [[:File:20170404_refcal_amp.png|Amp]] || Ant 12 was not tracking. Delay center change at 16:43:51.<br />
|-<br />
| 2017/04/05 ||06:44:10 || 3c273 || 04:17~10:30 || All || 04:27~09:34 || 5, 7, 9, 11, 13, 15, 17, 19, 21, 23 || [[:File:20170405_refcal_pha.png|Phase]] || [[:File:20170405_refcal_amp.png|Amp]] || Ant 12 was not tracking.<br />
|-<br />
| 2017/04/06 || 09:54:50|| 3c273 || 04:14~10:49 || All || 05:39~08:11 || 5, 7, 9, 11, 13, 15, 17, 19, 21, 23 || [[:File:20170406_refcal_pha.png|Phase]] || [[:File:20170406_refcal_amp.png|Amp]] || Ant 12 was not tracking.<br />
|-<br />
| 2017/04/07 || 08:30:51|| 3c273 || 04:00~10:30 || 1, 3, 5, 7, 9, 11, 13, 15, 17 || 07:53~09:10 || 5~34 || [[:File:20170407_refcal_pha.png|Phase]] || [[:File:20170407_refcal_amp.png|Amp]] || Ant 12 was not tracking.<br />
|-<br />
| 2017/04/08 || 06:14:51 || 3c273 || 05:00~10:30 || 1, 3, 5, 7, 9, 11, 13 || 05:00~07:00 || 5~34 || [[:File:20170408_refcal_pha.png|Phase]] || [[:File:20170408_refcal_amp.png|Amp]] || Ant 12 was not tracking. Ant 13 not working. Delay center change at 2017-04-08T03:12:26. Another refcal record is added at 2017-04-09T06:14:45.<br />
|-<br />
| 2017/04/10 || 06:57:10 || 3c273 || 04:30~10:30 || 2, 6, 8 || || 5~34 || [[:File:20170410_refcal_pha.png|Phase]] || [[:File:20170410_refcal_amp.png|Amp]] || Ant 12 was not tracking. Delay center change at 2017-04-08 13:20:39. <br />
|-<br />
| 2017/04/16 || 06:36:48 || 3c273 || 03:00~11:00 || || 05:55~07:20 || 5~34 || [[:File:20170416_refcal_pha.png|Phase]] || [[:File:20170416_refcal_amp.png|Amp]] || Ant 12 was not tracking. <br />
|-<br />
| 2017/04/17 || 06:41:51 || 3c273 || 03:29~10:07 || All || 05:55~07:29 || 5~34 || [[:File:20170417_refcal_pha.png|Phase]] || [[:File:20170417_refcal_amp.png|Amp]] || Ant 12 was not tracking. Delay center change at 19:12:58.<br />
|-<br />
| 2017/04/26 || 08:06:52 || 3c273 || 02:50~09:28 || All || 07:21~08:57 || 5~34 || [[:File:20170426_refcal_pha.png|Phase]] || [[:File:20170426_refcal_amp.png|Amp]] || Ant 12 was not tracking. Delay center change at 04:37:28 and 11:51:26.<br />
|-<br />
| 2017/06/11 || 12:56:22 || 2253+161 || || 0 || || 5~34 || [http://ovsa.njit.edu/refcal/20170611_refcal_pha.png Phase] || [http://ovsa.njit.edu/refcal/20170611_refcal_amp.png Amp] || No calibration for: Ant 12<br />
|-<br />
| 2017/06/14 || 02:33:19 || 1229+020 || || 0 || || 5~34 || [http://ovsa.njit.edu/refcal/20170614_refcal_pha.png Phase] || [http://ovsa.njit.edu/refcal/20170614_refcal_amp.png Amp] || No calibration for: Ant 8 Ant 12<br />
|-<br />
| 2017/06/14 || 13:01:19 || 2253+161 || || 0 || || 5~34 || [http://ovsa.njit.edu/refcal/20170614_refcal_pha.png Phase] || [http://ovsa.njit.edu/refcal/20170614_refcal_amp.png Amp] || No calibration for: Ant 12<br />
|-<br />
| 2017/06/15 || 13:05:48 || || || 0 || || 5~34 || [http://ovsa.njit.edu/refcal/20170615_refcal_pha.png Phase] || [http://ovsa.njit.edu/refcal/20170615_refcal_amp.png Amp] || No calibration for: Ant 12<br />
|-<br />
| 2017/06/16 || 13:05:48 || || || 0 || || 5~34 || [http://ovsa.njit.edu/refcal/20170616_refcal_pha.png Phase] || [http://ovsa.njit.edu/refcal/20170616_refcal_amp.png Amp] || No calibration for: Ant 12<br />
|-<br />
| 2017/06/20 || 13:06:26 || || || 0 || || 5~34 || [http://ovsa.njit.edu/refcal/20170620_refcal_pha.png Phase] || [http://ovsa.njit.edu/refcal/20170620_refcal_amp.png Amp] || No calibration for: Ant 1 Ant 12<br />
|-<br />
| 2017/06/21 || 13:06:38 || || || 0 || || 5~34 || [http://ovsa.njit.edu/refcal/20170621_refcal_pha.png Phase] || [http://ovsa.njit.edu/refcal/20170621_refcal_amp.png Amp] || No calibration for: Ant 12<br />
|-<br />
| 2017/06/22 || 13:06:53 || || || 0 || || 5~34 || [http://ovsa.njit.edu/refcal/20170622_refcal_pha.png Phase] || [http://ovsa.njit.edu/refcal/20170622_refcal_amp.png Amp] || No calibration for: Ant 12<br />
|-<br />
| 2017/06/23 || 13:07:09 || || || 0 || || 5~34 || [http://ovsa.njit.edu/refcal/20170623_refcal_pha.png Phase] || [http://ovsa.njit.edu/refcal/20170623_refcal_amp.png Amp] || No calibration for: Ant 12<br />
|-<br />
| 2017/06/24 || 02:25:49 || || || 0 || || 5~34 || [http://ovsa.njit.edu/refcal/20170624_refcal_pha.png Phase] || [http://ovsa.njit.edu/refcal/20170624_refcal_amp.png Amp] || No calibration for: Ant 12<br />
|-<br />
| 2017/06/24 || 13:07:25 || || || 0 || || 5~34 || [http://ovsa.njit.edu/refcal/20170624_refcal_pha.png Phase] || [http://ovsa.njit.edu/refcal/20170624_refcal_amp.png Amp] || No calibration for: Ant 12<br />
|-<br />
| 2017/06/25 || 13:07:43 || || || 0 || || 5~34 || [http://ovsa.njit.edu/refcal/20170625_refcal_pha.png Phase] || [http://ovsa.njit.edu/refcal/20170625_refcal_amp.png Amp] || No calibration for: Ant 10 Ant 12<br />
|-<br />
| 2017/06/26 || 13:15:47 || || || 0 || || 5~34 || [http://ovsa.njit.edu/refcal/20170626_refcal_pha.png Phase] || [http://ovsa.njit.edu/refcal/20170626_refcal_amp.png Amp] || No calibration for: Ant 10 Ant 12<br />
|-<br />
| 2017/06/27 || 13:02:49 || 2253+161 || || 0 || || 5~34 || [http://ovsa.njit.edu/refcal/20170627_refcal_pha.png Phase] || [http://ovsa.njit.edu/refcal/20170627_refcal_amp.png Amp] || No calibration for: Ant 12<br />
|-<br />
| 2017/06/30 || 02:47:50 || 1229+020 || || 0 || || 5~34 || [http://ovsa.njit.edu/refcal/20170630_refcal_pha.png Phase] || [http://ovsa.njit.edu/refcal/20170630_refcal_amp.png Amp] || No calibration for: Ant 12<br />
|-<br />
| 2017/07/01 || 02:44:49 || 1229+020 || || 0 || || 5~34 || [http://ovsa.njit.edu/refcal/20170701_refcal_pha.png Phase] || [http://ovsa.njit.edu/refcal/20170701_refcal_amp.png Amp] || No calibration for: Ant 12<br />
|-<br />
| 2017/07/02 || 03:01:20 || 1229+020 || || 0 || || 5~34 || [http://ovsa.njit.edu/refcal/20170702_refcal_pha.png Phase] || [http://ovsa.njit.edu/refcal/20170702_refcal_amp.png Amp] ||<br />
|-<br />
| 2017/07/03 || 02:47:49 || 1229+020 || || 0 || || 5~34 || [http://ovsa.njit.edu/refcal/20170703_refcal_pha.png Phase] || [http://ovsa.njit.edu/refcal/20170703_refcal_amp.png Amp] || No calibration for: Ant 10<br />
|-<br />
| 2017/07/04 || 02:47:49 || 1229+020 || || 0 || || 5~34 || [http://ovsa.njit.edu/refcal/20170704_refcal_pha.png Phase] || [http://ovsa.njit.edu/refcal/20170704_refcal_amp.png Amp] ||<br />
|-<br />
| 2017/07/05 || 02:55:19 || 1229+020 || || 0 || || 5~34 || [http://ovsa.njit.edu/refcal/20170705_refcal_pha.png Phase] || [http://ovsa.njit.edu/refcal/20170705_refcal_amp.png Amp] ||<br />
|-<br />
| 2017/07/06 || 02:47:49 || 1229+020 || || 0 || || 5~34 || [http://ovsa.njit.edu/refcal/20170706_refcal_pha.png Phase] || [http://ovsa.njit.edu/refcal/20170706_refcal_amp.png Amp] || <br />
|-<br />
| 2017/07/07 || 13:12:49 || 2253+161 || || 0 || || 5~34 || [http://ovsa.njit.edu/refcal/20170707_refcal_pha.png Phase] || [http://ovsa.njit.edu/refcal/20170707_refcal_amp.png Amp] ||<br />
|-<br />
| 2017/07/09 || 02:35:49 || 1229+020 || || 0 || || 5~34 || [http://ovsa.njit.edu/refcal/20170709_refcal_pha.png Phase] || [http://ovsa.njit.edu/refcal/20170709_refcal_amp.png Amp] ||<br />
|-<br />
| 2017/07/09 || 13:16:49 || 2253+161 || || 0 || || 5~34 || [http://ovsa.njit.edu/refcal/20170709_refcal_pha.png Phase] || [http://ovsa.njit.edu/refcal/20170709_refcal_amp.png Amp] ||<br />
|-<br />
| 2017/07/10 || 13:14:17 || 0319+415 || || 0 || || 5~34 || [http://ovsa.njit.edu/refcal/20170710_refcal_pha.png Phase] || [http://ovsa.njit.edu/refcal/20170710_refcal_amp.png Amp] ||<br />
|-<br />
| 2017/07/11 || 13:14:18 || 0319+415 || || 0 || || 5~34 || [http://ovsa.njit.edu/refcal/20170711_refcal_pha.png Phase] || [http://ovsa.njit.edu/refcal/20170711_refcal_amp.png Amp] ||<br />
|-<br />
| 2017/07/12 || 13:14:24 || 0319+415 || || 0 || || 5~34 || [http://ovsa.njit.edu/refcal/20170712_refcal_pha.png Phase] || [http://ovsa.njit.edu/refcal/20170712_refcal_amp.png Amp] ||<br />
|-<br />
| 2017/07/13 || 13:14:59 || 0319+415 || || 0 || || 5~34 || [http://ovsa.njit.edu/refcal/20170713_refcal_pha.png Phase] || [http://ovsa.njit.edu/refcal/20170713_refcal_amp.png Amp] ||<br />
|-<br />
| 2017/07/14 || 13:15:35 || 0319+415 || || 0 || || 5~34 || [http://ovsa.njit.edu/refcal/20170714_refcal_pha.png Phase] || [http://ovsa.njit.edu/refcal/20170714_refcal_amp.png Amp] ||<br />
|-<br />
| 2017/07/16 || 02:48:33 || 1229+020 || || 0 || || 5~34 || [http://ovsa.njit.edu/refcal/20170716_refcal_pha.png Phase] || [http://ovsa.njit.edu/refcal/20170716_refcal_amp.png Amp] ||<br />
|-<br />
| 2017/07/16 || 13:16:48 || 0319+415 || || 0 || || 5~34 || [http://ovsa.njit.edu/refcal/20170716_refcal_pha.png Phase] || [http://ovsa.njit.edu/refcal/20170716_refcal_amp.png Amp] ||<br />
|-<br />
| 2017/07/17 || 13:14:54 || 0319+415 || || 0 || || 5~34 || [http://ovsa.njit.edu/refcal/20170717_refcal_pha.png Phase] || [http://ovsa.njit.edu/refcal/20170717_refcal_amp.png Amp] ||<br />
|-<br />
| 2017/07/18 || 13:15:31 || 0319+415 || || 0 || || 5~34 || [http://ovsa.njit.edu/refcal/20170718_refcal_pha.png Phase] || [http://ovsa.njit.edu/refcal/20170718_refcal_amp.png Amp] ||<br />
|-<br />
| 2017/07/19 || 13:16:16 || 0319+415 || || 0 || || 5~34 || [http://ovsa.njit.edu/refcal/20170719_refcal_pha.png Phase] || [http://ovsa.njit.edu/refcal/20170719_refcal_amp.png Amp] ||<br />
|-<br />
| 2017/07/20 || 13:16:49 || 0319+415 || || 0 || || 5~34 || [http://ovsa.njit.edu/refcal/20170720_refcal_pha.png Phase] || [http://ovsa.njit.edu/refcal/20170720_refcal_amp.png Amp] || No calibration for: Ant 10<br />
|-<br />
| 2017/07/21 || 13:20:57 || 0319+415 || || 0 || || 5~34 || [http://ovsa.njit.edu/refcal/20170721_refcal_pha.png Phase] || [http://ovsa.njit.edu/refcal/20170721_refcal_amp.png Amp] ||<br />
|-<br />
| 2017/07/22 || 13:21:36 || 0319+415 || || 0 || || 5~34 || [http://ovsa.njit.edu/refcal/20170722_refcal_pha.png Phase] || [http://ovsa.njit.edu/refcal/20170722_refcal_amp.png Amp] ||<br />
|-<br />
| 2017/07/24 || 13:22:58 || 0319+415 || || 0 || || 5~34 || [http://ovsa.njit.edu/refcal/20170724_refcal_pha.png Phase] || [http://ovsa.njit.edu/refcal/20170724_refcal_amp.png Amp] ||<br />
|-</div>Ztwanghttp://www.ovsa.njit.edu/wiki/index.php/Polarization_CalibrationPolarization Calibration2016-09-27T18:38:12Z<p>Ztwang: /* Linear to Circular Conversion */</p>
<hr />
<div>== Linear to Circular Conversion ==<br />
<br />
At EOVSA’s linear feeds, in the electric field the linear polarization, X and Y, relates to RCP and LCP (R and L) as:<br />
<center><br />
:<math><br />
\begin{align} <br />
R = X + iY \\<br />
L = X - iY <br />
\end{align}<br />
</math><br />
</center><br />
In terms of autocorrelation powers, we have the 4 polarization products XX*, YY*, XY* and YX*, where the * denotes complex conjugation. The quantities RR* and LL* are then<br />
<center><br />
:<math><br />
\begin{align} <br />
RR^* = (X + iY)(X + iY)^* &= XX^* - iXY^* + iYX^* + YY^* \\<br />
LL^* = (X - iY)(X - iY)^* &= XX^* + iXY^* - iYX^* + YY^* \\<br />
\end{align}<br />
</math><br />
</center><br />
One problem is that there is generally a non-zero delay in Y with respect to X. This creates phase slopes in XY* and YX* from which we can determine the delay very accurately. As a check,<br />
<center><br />
:<math><br />
\begin{align} <br />
Stokes \, I &= \frac{RR^* + LL^*}{2} = XX^* + YY^* \\<br />
Stokes \, V &= \frac{RR^* - LL^*}{2} = i(XX^* - YY^*) <br />
\end{align}<br />
</math><br />
</center><br />
For completeness:<br />
<center><br />
:<math>\begin{align} <br />
Stokes \, Q &= XX^* - YY^* \\<br />
Stokes \, U &= XY^* - YX^* \\<br />
P_{linear} &= \sqrt{U^2 + Q^2} \\<br />
\Theta &= \frac{1}{2}\tan^{-1}{\frac{U}{Q}}<br />
\end{align}<br />
</math><br />
</center><br />
When I plot the quantities I, V, R and L as measured (Figure 1) for geosynchronous satellite Ciel-2, the results look reasonable, except that there are parts of the band where R and L are mis-assigned, and others where they do not separate well.<br />
<br />
[[File:Figure1.jpg|center|thumb|800px|Figure 1: Amplitudes of Stokes I, Stokes V, RCP and LCP for Ciel-2 satellite. The red vertical lines show the center of RCP channels, while the green vertical lines show the center of LCP channels. There is pretty good separation of RCP and LCP at lower and higher frequencies in the range, but around 12.4 GHz the polarization has switched and is mis-assigned.]]<br />
<br />
The problem is that residual phase slope of Y with respect to X, caused by a difference in delay between the two channels. This can be seen in the upper panel of Figure 2, which shows the uncorrected phases of XY* and YX*. To correct the phases, the RCP phase was fit by a linear least-squares routine, and then the phases were offset by &pi;/2 for both XY* and YX* according to:<br />
<center><br />
:<math>\begin{align}<br />
XY^{*'} &= XY^*e^{-i(\phi(v) + \frac{\pi}{2})} \\<br />
YX^{*'} &= YX^*e^{ i(\phi(v) + \frac{\pi}{2})}<br />
\end{align}<br />
</math><br />
</center><br />
where &phi;(v) is the phase fit by the linear function. The corrected phases are shown in the lower panel of Figure 2.<br />
<br />
[[File:Linear_to_Circular_Conversion_Figure2.jpg|center|thumb|800px|Figure 2: Upper panel) Raw phases on XY* (blue) and YX* (green). Lower panel) Phases corrected by removing a delay slope of order 3 ns, and shifting the phase such that the XY* phases on RCP channels is -&pi;/2. This adjustment automatically makes XY* phases on LCP channels become +&pi;/2.]]<br />
<br />
When the corrected (primed) quantities are used in<br />
<center><br />
:<math>\begin{align}<br />
RR^* &= XX^* - iXY^{*'} + iYX^{*'} + YY^* \\<br />
LL^* &= XX^* + iXY^{*'} - iYX^{*'} + YY^*<br />
\end{align}<br />
</math><br />
</center><br />
the resulting channel separation is shown in Figure 3, which shows pretty much perfect channel separation, with the correct polarity.<br />
<br />
[[File:Linear_to_Circular_Conversion_Figure3.jpg|center|thumb|800px|Figure 3: Amplitudes of Stokes I, Stokes V, RCP and LCP for Ciel-2 satellite, after correcting for delay. The red vertical lines show the center of RCP channels, while the green vertical lines show the center of LCP channels. There is now PERFECT correspondence between RCP channels and the plot, and likewise for LCP channels.]]<br />
<br />
This analysis can be performed on all antennas in a completely automated way, to produce the results of Fig. 3. The curves for each antenna are very similar, except that they show differences in amplitude (gain) as a function of frequency. When the curves are scaled to have the same Stokes I levels, the result is shown in Figure 4. Here the 13 antennas are shown in different colors. It is clear that matching Stokes I also causes an excellent match in the other polarizations. Remaining mismatch is likely due to not subtracting a no-signal background prior to scaling the Stokes I curves.<br />
<br />
[[File:Linear_to_Circular_Conversion_Figure4.jpg|center|thumb|800px|Figure 4: Same as Fig. 3, but for all 13 atnennas, with the Stokes I curve for each antenna scaled so that they agree. The beacon frequency in marked in the lower panel.]]<br />
<br />
Also marked in Figure 4 is the location of the beacon signal for Ciel-2, which is at 12.209 GHz. The beacon signal appears in precisely the correct bin (frequency subchannel), indicating that we have precise tuning (certainly not unexpected, but nice to see).<br />
<br />
Just to show that the approach is general, the results for a different communications satellite, Nimiq-5, is shown in Figure 5.<br />
<br />
[[File:Linear_to_Circular_Conversion_Figure5.jpg|center|thumb|800px|Figure 4: Same as Fig. 5, but for the Nimiq-5 commun-ications satellite.]]<br />
<br />
== Polarization Mixing Correction ==<br />
Due to relative feed rotation between az-al mounted antennas and equatorial mounted antennas</div>Ztwanghttp://www.ovsa.njit.edu/wiki/index.php/Polarization_CalibrationPolarization Calibration2016-09-27T18:37:28Z<p>Ztwang: /* Linear to Circular Conversion */</p>
<hr />
<div>== Linear to Circular Conversion ==<br />
<br />
At EOVSA’s linear feeds, in the electric field the linear polarization, X and Y, relates to RCP and LCP (R and L) as:<br />
<center><br />
:<math><br />
\begin{align} <br />
R = X + iY \\<br />
L = X - iY <br />
\end{align}<br />
</math><br />
</center><br />
In terms of autocorrelation powers, we have the 4 polarization products XX*, YY*, XY* and YX*, where the * denotes complex conjugation. The quantities RR* and LL* are then<br />
<br />
:<math><br />
\begin{align} <br />
RR^* = (X + iY)(X + iY)^* &= XX^* - iXY^* + iYX^* + YY^* \\<br />
LL^* = (X - iY)(X - iY)^* &= XX^* + iXY^* - iYX^* + YY^* \\<br />
\end{align}<br />
</math><br />
<br />
One problem is that there is generally a non-zero delay in Y with respect to X. This creates phase slopes in XY* and YX* from which we can determine the delay very accurately. As a check,<br />
<br />
:<math><br />
\begin{align} <br />
Stokes \, I &= \frac{RR^* + LL^*}{2} = XX^* + YY^* \\<br />
Stokes \, V &= \frac{RR^* - LL^*}{2} = i(XX^* - YY^*) <br />
\end{align}<br />
</math><br />
<br />
For completeness:<br />
<br />
:<math>\begin{align} <br />
Stokes \, Q &= XX^* - YY^* \\<br />
Stokes \, U &= XY^* - YX^* \\<br />
P_{linear} &= \sqrt{U^2 + Q^2} \\<br />
\Theta &= \frac{1}{2}\tan^{-1}{\frac{U}{Q}}<br />
\end{align}<br />
</math><br />
<br />
When I plot the quantities I, V, R and L as measured (Figure 1) for geosynchronous satellite Ciel-2, the results look reasonable, except that there are parts of the band where R and L are mis-assigned, and others where they do not separate well.<br />
<br />
[[File:Figure1.jpg|center|thumb|800px|Figure 1: Amplitudes of Stokes I, Stokes V, RCP and LCP for Ciel-2 satellite. The red vertical lines show the center of RCP channels, while the green vertical lines show the center of LCP channels. There is pretty good separation of RCP and LCP at lower and higher frequencies in the range, but around 12.4 GHz the polarization has switched and is mis-assigned.]]<br />
<br />
The problem is that residual phase slope of Y with respect to X, caused by a difference in delay between the two channels. This can be seen in the upper panel of Figure 2, which shows the uncorrected phases of XY* and YX*. To correct the phases, the RCP phase was fit by a linear least-squares routine, and then the phases were offset by &pi;/2 for both XY* and YX* according to:<br />
<br />
:<math>\begin{align}<br />
XY^{*'} &= XY^*e^{-i(\phi(v) + \frac{\pi}{2})} \\<br />
YX^{*'} &= YX^*e^{ i(\phi(v) + \frac{\pi}{2})}<br />
\end{align}<br />
</math><br />
<br />
where &phi;(v) is the phase fit by the linear function. The corrected phases are shown in the lower panel of Figure 2.<br />
<br />
[[File:Linear_to_Circular_Conversion_Figure2.jpg|center|thumb|800px|Figure 2: Upper panel) Raw phases on XY* (blue) and YX* (green). Lower panel) Phases corrected by removing a delay slope of order 3 ns, and shifting the phase such that the XY* phases on RCP channels is -&pi;/2. This adjustment automatically makes XY* phases on LCP channels become +&pi;/2.]]<br />
<br />
When the corrected (primed) quantities are used in<br />
<br />
:<math>\begin{align}<br />
RR^* &= XX^* - iXY^{*'} + iYX^{*'} + YY^* \\<br />
LL^* &= XX^* + iXY^{*'} - iYX^{*'} + YY^*<br />
\end{align}<br />
</math><br />
<br />
the resulting channel separation is shown in Figure 3, which shows pretty much perfect channel separation, with the correct polarity.<br />
<br />
[[File:Linear_to_Circular_Conversion_Figure3.jpg|center|thumb|800px|Figure 3: Amplitudes of Stokes I, Stokes V, RCP and LCP for Ciel-2 satellite, after correcting for delay. The red vertical lines show the center of RCP channels, while the green vertical lines show the center of LCP channels. There is now PERFECT correspondence between RCP channels and the plot, and likewise for LCP channels.]]<br />
<br />
This analysis can be performed on all antennas in a completely automated way, to produce the results of Fig. 3. The curves for each antenna are very similar, except that they show differences in amplitude (gain) as a function of frequency. When the curves are scaled to have the same Stokes I levels, the result is shown in Figure 4. Here the 13 antennas are shown in different colors. It is clear that matching Stokes I also causes an excellent match in the other polarizations. Remaining mismatch is likely due to not subtracting a no-signal background prior to scaling the Stokes I curves.<br />
<br />
[[File:Linear_to_Circular_Conversion_Figure4.jpg|center|thumb|800px|Figure 4: Same as Fig. 3, but for all 13 atnennas, with the Stokes I curve for each antenna scaled so that they agree. The beacon frequency in marked in the lower panel.]]<br />
<br />
Also marked in Figure 4 is the location of the beacon signal for Ciel-2, which is at 12.209 GHz. The beacon signal appears in precisely the correct bin (frequency subchannel), indicating that we have precise tuning (certainly not unexpected, but nice to see).<br />
<br />
Just to show that the approach is general, the results for a different communications satellite, Nimiq-5, is shown in Figure 5.<br />
<br />
[[File:Linear_to_Circular_Conversion_Figure5.jpg|center|thumb|800px|Figure 4: Same as Fig. 5, but for the Nimiq-5 commun-ications satellite.]]<br />
<br />
== Polarization Mixing Correction ==<br />
Due to relative feed rotation between az-al mounted antennas and equatorial mounted antennas</div>Ztwanghttp://www.ovsa.njit.edu/wiki/index.php/Polarization_CalibrationPolarization Calibration2016-09-24T21:23:31Z<p>Ztwang: /* Linear to Circular Conversion */</p>
<hr />
<div>== Linear to Circular Conversion ==<br />
<br />
At EOVSA’s linear feeds, in the electric field the linear polarization, X and Y, relates to RCP and LCP (R and L) as:<br />
<br />
:<math><br />
\begin{align} <br />
R = X + iY \\<br />
L = X - iY <br />
\end{align}<br />
</math><br />
<br />
In terms of autocorrelation powers, we have the 4 polarization products XX*, YY*, XY* and YX*, where the * denotes complex conjugation. The quantities RR* and LL* are then<br />
<br />
:<math><br />
\begin{align} <br />
RR^* = (X + iY)(X + iY)^* &= XX^* - iXY^* + iYX^* + YY^* \\<br />
LL^* = (X - iY)(X - iY)^* &= XX^* + iXY^* - iYX^* + YY^* \\<br />
\end{align}<br />
</math><br />
<br />
One problem is that there is generally a non-zero delay in Y with respect to X. This creates phase slopes in XY* and YX* from which we can determine the delay very accurately. As a check,<br />
<br />
:<math><br />
\begin{align} <br />
Stokes \, I &= \frac{RR^* + LL^*}{2} = XX^* + YY^* \\<br />
Stokes \, V &= \frac{RR^* - LL^*}{2} = i(XX^* - YY^*) <br />
\end{align}<br />
</math><br />
<br />
For completeness:<br />
<br />
:<math>\begin{align} <br />
Stokes \, Q &= XX^* - YY^* \\<br />
Stokes \, U &= XY^* - YX^* \\<br />
P_{linear} &= \sqrt{U^2 + Q^2} \\<br />
\Theta &= \frac{1}{2}\tan^{-1}{\frac{U}{Q}}<br />
\end{align}<br />
</math><br />
<br />
When I plot the quantities I, V, R and L as measured (Figure 1) for geosynchronous satellite Ciel-2, the results look reasonable, except that there are parts of the band where R and L are mis-assigned, and others where they do not separate well.<br />
<br />
[[File:Figure1.jpg|center|thumb|800px|Figure 1: Amplitudes of Stokes I, Stokes V, RCP and LCP for Ciel-2 satellite. The red vertical lines show the center of RCP channels, while the green vertical lines show the center of LCP channels. There is pretty good separation of RCP and LCP at lower and higher frequencies in the range, but around 12.4 GHz the polarization has switched and is mis-assigned.]]<br />
<br />
The problem is that residual phase slope of Y with respect to X, caused by a difference in delay between the two channels. This can be seen in the upper panel of Figure 2, which shows the uncorrected phases of XY* and YX*. To correct the phases, the RCP phase was fit by a linear least-squares routine, and then the phases were offset by &pi;/2 for both XY* and YX* according to:<br />
<br />
:<math>\begin{align}<br />
XY^{*'} &= XY^*e^{-i(\phi(v) + \frac{\pi}{2})} \\<br />
YX^{*'} &= YX^*e^{ i(\phi(v) + \frac{\pi}{2})}<br />
\end{align}<br />
</math><br />
<br />
where &phi;(v) is the phase fit by the linear function. The corrected phases are shown in the lower panel of Figure 2.<br />
<br />
[[File:Linear_to_Circular_Conversion_Figure2.jpg|center|thumb|800px|Figure 2: Upper panel) Raw phases on XY* (blue) and YX* (green). Lower panel) Phases corrected by removing a delay slope of order 3 ns, and shifting the phase such that the XY* phases on RCP channels is -&pi;/2. This adjustment automatically makes XY* phases on LCP channels become +&pi;/2.]]<br />
<br />
When the corrected (primed) quantities are used in<br />
<br />
:<math>\begin{align}<br />
RR^* &= XX^* - iXY^{*'} + iYX^{*'} + YY^* \\<br />
LL^* &= XX^* + iXY^{*'} - iYX^{*'} + YY^*<br />
\end{align}<br />
</math><br />
<br />
the resulting channel separation is shown in Figure 3, which shows pretty much perfect channel separation, with the correct polarity.<br />
<br />
[[File:Linear_to_Circular_Conversion_Figure3.jpg|center|thumb|800px|Figure 3: Amplitudes of Stokes I, Stokes V, RCP and LCP for Ciel-2 satellite, after correcting for delay. The red vertical lines show the center of RCP channels, while the green vertical lines show the center of LCP channels. There is now PERFECT correspondence between RCP channels and the plot, and likewise for LCP channels.]]<br />
<br />
This analysis can be performed on all antennas in a completely automated way, to produce the results of Fig. 3. The curves for each antenna are very similar, except that they show differences in amplitude (gain) as a function of frequency. When the curves are scaled to have the same Stokes I levels, the result is shown in Figure 4. Here the 13 antennas are shown in different colors. It is clear that matching Stokes I also causes an excellent match in the other polarizations. Remaining mismatch is likely due to not subtracting a no-signal background prior to scaling the Stokes I curves.<br />
<br />
[[File:Linear_to_Circular_Conversion_Figure4.jpg|center|thumb|800px|Figure 4: Same as Fig. 3, but for all 13 atnennas, with the Stokes I curve for each antenna scaled so that they agree. The beacon frequency in marked in the lower panel.]]<br />
<br />
Also marked in Figure 4 is the location of the beacon signal for Ciel-2, which is at 12.209 GHz. The beacon signal appears in precisely the correct bin (frequency subchannel), indicating that we have precise tuning (certainly not unexpected, but nice to see).<br />
<br />
Just to show that the approach is general, the results for a different communications satellite, Nimiq-5, is shown in Figure 5.<br />
<br />
[[File:Linear_to_Circular_Conversion_Figure5.jpg|center|thumb|800px|Figure 4: Same as Fig. 5, but for the Nimiq-5 commun-ications satellite.]]<br />
<br />
== Polarization Mixing Correction ==<br />
Due to relative feed rotation between az-al mounted antennas and equatorial mounted antennas</div>Ztwanghttp://www.ovsa.njit.edu/wiki/index.php/Polarization_CalibrationPolarization Calibration2016-09-24T21:22:53Z<p>Ztwang: </p>
<hr />
<div>== Linear to Circular Conversion ==<br />
<br />
At EOVSA’s linear feeds, in the electric field the linear polarization, X and Y, relates to RCP and LCP (R and L) as:<br />
<br />
:<math><br />
\begin{align} <br />
R = X + iY \\<br />
L = X - iY <br />
\end{align}<br />
</math><br />
<br />
In terms of autocorrelation powers, we have the 4 polarization products XX*, YY*, XY* and YX*, where the * denotes complex conjugation. The quantities RR* and LL* are then<br />
<br />
:<math><br />
\begin{align} <br />
RR^* = (X + iY)(X + iY)^* &= XX^* - iXY^* + iYX^* + YY^* \\<br />
LL^* = (X - iY)(X - iY)^* &= XX^* + iXY^* - iYX^* + YY^* \\<br />
\end{align}<br />
</math><br />
<br />
One problem is that there is generally a non-zero delay in Y with respect to X. This creates phase slopes in XY* and YX* from which we can determine the delay very accurately. As a check,<br />
<br />
:<math><br />
\begin{align} <br />
Stokes \, I &= \frac{RR^* + LL^*}{2} = XX^* + YY^* \\<br />
Stokes \, V &= \frac{RR^* - LL^*}{2} = i(XX^* - YY^*) <br />
\end{align}<br />
</math><br />
<br />
For completeness:<br />
<br />
:<math>\begin{align} <br />
Stokes \, Q &= XX^* - YY^* \\<br />
Stokes \, U &= XY^* - YX^* \\<br />
P_{linear} &= \sqrt{U^2 + Q^2} \\<br />
\Theta &= \frac{1}{2}\tan^{-1}{\frac{U}{Q}}<br />
\end{align}<br />
</math><br />
<br />
When I plot the quantities I, V, R and L as measured (Figure 1) for geosynchronous satellite Ciel-2, the results look reasonable, except that there are parts of the band where R and L are mis-assigned, and others where they do not separate well.<br />
<br />
[[File:Figure1.jpg|center|thumb|800px|Figure 1: Amplitudes of Stokes I, Stokes V, RCP and LCP for Ciel-2 satellite. The red vertical lines show the center of RCP channels, while the green vertical lines show the center of LCP channels. There is pretty good separation of RCP and LCP at lower and higher frequencies in the range, but around 12.4 GHz the polarization has switched and is mis-assigned.]]<br />
<br />
The problem is that residual phase slope of Y with respect to X, caused by a difference in delay between the two channels. This can be seen in the upper panel of Figure 2, which shows the uncorrected phases of XY* and YX*. To correct the phases, the RCP phase was fit by a linear least-squares routine, and then the phases were offset by &pi;/2 for both XY* and YX* according to:<br />
<br />
:<math>\begin{align}<br />
XY^{*'} &= XY^*e^{-i(\phi(v) + \frac{\pi}{2})} \\<br />
YX^{*'} &= YX^*e^{ i(\phi(v) + \frac{\pi}{2})}<br />
\end{align}<br />
</math><br />
<br />
where &phi;(v) is the phase fit by the linear function. The corrected phases are shown in the lower panel of Figure 2.<br />
<br />
[[File:Linear_to_Circular_Conversion_Figure2.jpg|center|thumb|800px|Figure 2: Upper panel) Raw phases on XY* (blue) and YX* (green). Lower panel) Phases corrected by removing a delay slope of order 3 ns, and shifting the phase such that the XY* phases on RCP channels is -&pi;/2. This adjustment automatically makes XY* phases on LCP channels become +&pi;/2.]]<br />
<br />
When the corrected (primed) quantities are used in<br />
<br />
:<math>\begin{align}<br />
RR^* &= XX^* - iXY^{*'} + iYX^{*'} + YY^* \\<br />
LL^* &= XX^* + iXY^{*'} - iYX^{*'} + YY^*<br />
\end{align}<br />
</math><br />
<br />
the resulting channel separation is shown in Figure 3, which shows pretty much perfect channel separation, with the correct polarity.<br />
<br />
[[File:Linear_to_Circular_Conversion_Figure3.jpg|center|thumb|400px|Figure 3: Amplitudes of Stokes I, Stokes V, RCP and LCP for Ciel-2 satellite, after correcting for delay. The red vertical lines show the center of RCP channels, while the green vertical lines show the center of LCP channels. There is now PERFECT correspondence between RCP channels and the plot, and likewise for LCP channels.]]<br />
<br />
This analysis can be performed on all antennas in a completely automated way, to produce the results of Fig. 3. The curves for each antenna are very similar, except that they show differences in amplitude (gain) as a function of frequency. When the curves are scaled to have the same Stokes I levels, the result is shown in Figure 4. Here the 13 antennas are shown in different colors. It is clear that matching Stokes I also causes an excellent match in the other polarizations. Remaining mismatch is likely due to not subtracting a no-signal background prior to scaling the Stokes I curves.<br />
<br />
[[File:Linear_to_Circular_Conversion_Figure4.jpg|center|thumb|800px|Figure 4: Same as Fig. 3, but for all 13 atnennas, with the Stokes I curve for each antenna scaled so that they agree. The beacon frequency in marked in the lower panel.]]<br />
<br />
Also marked in Figure 4 is the location of the beacon signal for Ciel-2, which is at 12.209 GHz. The beacon signal appears in precisely the correct bin (frequency subchannel), indicating that we have precise tuning (certainly not unexpected, but nice to see).<br />
<br />
Just to show that the approach is general, the results for a different communications satellite, Nimiq-5, is shown in Figure 5.<br />
<br />
[[File:Linear_to_Circular_Conversion_Figure5.jpg|center|thumb|800px|Figure 4: Same as Fig. 5, but for the Nimiq-5 commun-ications satellite.]]<br />
<br />
== Polarization Mixing Correction ==<br />
Due to relative feed rotation between az-al mounted antennas and equatorial mounted antennas</div>Ztwanghttp://www.ovsa.njit.edu/wiki/index.php/Polarization_CalibrationPolarization Calibration2016-09-24T21:21:57Z<p>Ztwang: /* Linear to Circular Conversion */</p>
<hr />
<div>== Linear to Circular Conversion ==<br />
<br />
At EOVSA’s linear feeds, in the electric field the linear polarization, X and Y, relates to RCP and LCP (R and L) as:<br />
<br />
:<math><br />
\begin{align} <br />
R = X + iY \\<br />
L = X - iY <br />
\end{align}<br />
</math><br />
<br />
In terms of autocorrelation powers, we have the 4 polarization products XX*, YY*, XY* and YX*, where the * denotes complex conjugation. The quantities RR* and LL* are then<br />
<br />
:<math><br />
\begin{align} <br />
RR^* = (X + iY)(X + iY)^* &= XX^* - iXY^* + iYX^* + YY^* \\<br />
LL^* = (X - iY)(X - iY)^* &= XX^* + iXY^* - iYX^* + YY^* \\<br />
\end{align}<br />
</math><br />
<br />
One problem is that there is generally a non-zero delay in Y with respect to X. This creates phase slopes in XY* and YX* from which we can determine the delay very accurately. As a check,<br />
<br />
:<math><br />
\begin{align} <br />
Stokes \, I &= \frac{RR^* + LL^*}{2} = XX^* + YY^* \\<br />
Stokes \, V &= \frac{RR^* - LL^*}{2} = i(XX^* - YY^*) <br />
\end{align}<br />
</math><br />
<br />
For completeness:<br />
<br />
:<math>\begin{align} <br />
Stokes \, Q &= XX^* - YY^* \\<br />
Stokes \, U &= XY^* - YX^* \\<br />
P_{linear} &= \sqrt{U^2 + Q^2} \\<br />
\Theta &= \frac{1}{2}\tan^{-1}{\frac{U}{Q}}<br />
\end{align}<br />
</math><br />
<br />
When I plot the quantities I, V, R and L as measured (Figure 1) for geosynchronous satellite Ciel-2, the results look reasonable, except that there are parts of the band where R and L are mis-assigned, and others where they do not separate well.<br />
<br />
[[File:Figure1.jpg|center|thumb|400px|Figure 1: Amplitudes of Stokes I, Stokes V, RCP and LCP for Ciel-2 satellite. The red vertical lines show the center of RCP channels, while the green vertical lines show the center of LCP channels. There is pretty good separation of RCP and LCP at lower and higher frequencies in the range, but around 12.4 GHz the polarization has switched and is mis-assigned.]]<br />
<br />
The problem is that residual phase slope of Y with respect to X, caused by a difference in delay between the two channels. This can be seen in the upper panel of Figure 2, which shows the uncorrected phases of XY* and YX*. To correct the phases, the RCP phase was fit by a linear least-squares routine, and then the phases were offset by &pi;/2 for both XY* and YX* according to:<br />
<br />
:<math>\begin{align}<br />
XY^{*'} &= XY^*e^{-i(\phi(v) + \frac{\pi}{2})} \\<br />
YX^{*'} &= YX^*e^{ i(\phi(v) + \frac{\pi}{2})}<br />
\end{align}<br />
</math><br />
<br />
where &phi;(v) is the phase fit by the linear function. The corrected phases are shown in the lower panel of Figure 2.<br />
<br />
[[File:Linear_to_Circular_Conversion_Figure2.jpg|center|thumb|400px|Figure 2: Upper panel) Raw phases on XY* (blue) and YX* (green). Lower panel) Phases corrected by removing a delay slope of order 3 ns, and shifting the phase such that the XY* phases on RCP channels is -&pi;/2. This adjustment automatically makes XY* phases on LCP channels become +&pi;/2.]]<br />
<br />
When the corrected (primed) quantities are used in<br />
<br />
:<math>\begin{align}<br />
RR^* &= XX^* - iXY^{*'} + iYX^{*'} + YY^* \\<br />
LL^* &= XX^* + iXY^{*'} - iYX^{*'} + YY^*<br />
\end{align}<br />
</math><br />
<br />
the resulting channel separation is shown in Figure 3, which shows pretty much perfect channel separation, with the correct polarity.<br />
<br />
[[File:Linear_to_Circular_Conversion_Figure3.jpg|center|thumb|400px|Figure 3: Amplitudes of Stokes I, Stokes V, RCP and LCP for Ciel-2 satellite, after correcting for delay. The red vertical lines show the center of RCP channels, while the green vertical lines show the center of LCP channels. There is now PERFECT correspondence between RCP channels and the plot, and likewise for LCP channels.]]<br />
<br />
This analysis can be performed on all antennas in a completely automated way, to produce the results of Fig. 3. The curves for each antenna are very similar, except that they show differences in amplitude (gain) as a function of frequency. When the curves are scaled to have the same Stokes I levels, the result is shown in Figure 4. Here the 13 antennas are shown in different colors. It is clear that matching Stokes I also causes an excellent match in the other polarizations. Remaining mismatch is likely due to not subtracting a no-signal background prior to scaling the Stokes I curves.<br />
<br />
[[File:Linear_to_Circular_Conversion_Figure4.jpg|center|thumb|400px|Figure 4: Same as Fig. 3, but for all 13 atnennas, with the Stokes I curve for each antenna scaled so that they agree. The beacon frequency in marked in the lower panel.]]<br />
<br />
Also marked in Figure 4 is the location of the beacon signal for Ciel-2, which is at 12.209 GHz. The beacon signal appears in precisely the correct bin (frequency subchannel), indicating that we have precise tuning (certainly not unexpected, but nice to see).<br />
<br />
Just to show that the approach is general, the results for a different communications satellite, Nimiq-5, is shown in Figure 5.<br />
<br />
[[File:Linear_to_Circular_Conversion_Figure5.jpg|center|thumb|400px|Figure 4: Same as Fig. 5, but for the Nimiq-5 commun-ications satellite.]]<br />
<br />
== Polarization Mixing Correction ==<br />
Due to relative feed rotation between az-al mounted antennas and equatorial mounted antennas</div>Ztwanghttp://www.ovsa.njit.edu/wiki/index.php/Polarization_CalibrationPolarization Calibration2016-09-24T21:21:08Z<p>Ztwang: </p>
<hr />
<div>== Linear to Circular Conversion ==<br />
<br />
At EOVSA’s linear feeds, in the electric field the linear polarization, X and Y, relates to RCP and LCP (R and L) as:<br />
<br />
:<math><br />
\begin{align} <br />
R = X + iY \\<br />
L = X - iY <br />
\end{align}<br />
</math><br />
<br />
In terms of autocorrelation powers, we have the 4 polarization products XX*, YY*, XY* and YX*, where the * denotes complex conjugation. The quantities RR* and LL* are then<br />
<br />
:<math><br />
\begin{align} <br />
RR^* = (X + iY)(X + iY)^* &= XX^* - iXY^* + iYX^* + YY^* \\<br />
LL^* = (X - iY)(X - iY)^* &= XX^* + iXY^* - iYX^* + YY^* \\<br />
\end{align}<br />
</math><br />
<br />
One problem is that there is generally a non-zero delay in Y with respect to X. This creates phase slopes in XY* and YX* from which we can determine the delay very accurately. As a check,<br />
<br />
:<math><br />
\begin{align} <br />
Stokes \, I &= \frac{RR^* + LL^*}{2} = XX^* + YY^* \\<br />
Stokes \, V &= \frac{RR^* - LL^*}{2} = i(XX^* - YY^*) <br />
\end{align}<br />
</math><br />
<br />
For completeness:<br />
<br />
:<math>\begin{align} <br />
Stokes \, Q &= XX^* - YY^* \\<br />
Stokes \, U &= XY^* - YX^* \\<br />
P_{linear} &= \sqrt{U^2 + Q^2} \\<br />
\Theta &= \frac{1}{2}\tan^{-1}{\frac{U}{Q}}<br />
\end{align}<br />
</math><br />
<br />
When I plot the quantities I, V, R and L as measured (Figure 1) for geosynchronous satellite Ciel-2, the results look reasonable, except that there are parts of the band where R and L are mis-assigned, and others where they do not separate well.<br />
<br />
[[File:Figure1.jpg|center|thumb|400px|Figure 1: Amplitudes of Stokes I, Stokes V, RCP and LCP for Ciel-2 satellite. The red vertical lines show the center of RCP channels, while the green vertical lines show the center of LCP channels. There is pretty good separation of RCP and LCP at lower and higher frequencies in the range, but around 12.4 GHz the polarization has switched and is mis-assigned.]]<br />
<br />
The problem is that residual phase slope of Y with respect to X, caused by a difference in delay between the two channels. This can be seen in the upper panel of Figure 2, which shows the uncorrected phases of XY* and YX*. To correct the phases, the RCP phase was fit by a linear least-squares routine, and then the phases were offset by &pi;/2 for both XY* and YX* according to:<br />
<br />
:<math>\begin{align}<br />
XY^{*'} &= XY^*e^{-i(\phi(v) + \frac{\pi}{2})} \\<br />
YX^{*'} &= YX^*e^{ i(\phi(v) + \frac{\pi}{2})}<br />
\end{align}<br />
</math><br />
<br />
where &phi;(v) is the phase fit by the linear function. The corrected phases are shown in the lower panel of Figure 2.<br />
<br />
[[File:Linear_to_Circular_Conversion_Figure2.jpg|thumb|400px|Figure 2: Upper panel) Raw phases on XY* (blue) and YX* (green). Lower panel) Phases corrected by removing a delay slope of order 3 ns, and shifting the phase such that the XY* phases on RCP channels is -&pi;/2. This adjustment automatically makes XY* phases on LCP channels become +&pi;/2.]]<br />
<br />
When the corrected (primed) quantities are used in<br />
<br />
:<math>\begin{align}<br />
RR^* &= XX^* - iXY^{*'} + iYX^{*'} + YY^* \\<br />
LL^* &= XX^* + iXY^{*'} - iYX^{*'} + YY^*<br />
\end{align}<br />
</math><br />
<br />
the resulting channel separation is shown in Figure 3, which shows pretty much perfect channel separation, with the correct polarity.<br />
<br />
[[File:Linear_to_Circular_Conversion_Figure3.jpg|thumb|400px|Figure 3: Amplitudes of Stokes I, Stokes V, RCP and LCP for Ciel-2 satellite, after correcting for delay. The red vertical lines show the center of RCP channels, while the green vertical lines show the center of LCP channels. There is now PERFECT correspondence between RCP channels and the plot, and likewise for LCP channels.]]<br />
<br />
This analysis can be performed on all antennas in a completely automated way, to produce the results of Fig. 3. The curves for each antenna are very similar, except that they show differences in amplitude (gain) as a function of frequency. When the curves are scaled to have the same Stokes I levels, the result is shown in Figure 4. Here the 13 antennas are shown in different colors. It is clear that matching Stokes I also causes an excellent match in the other polarizations. Remaining mismatch is likely due to not subtracting a no-signal background prior to scaling the Stokes I curves.<br />
<br />
[[File:Linear_to_Circular_Conversion_Figure4.jpg|thumb|400px|Figure 4: Same as Fig. 3, but for all 13 atnennas, with the Stokes I curve for each antenna scaled so that they agree. The beacon frequency in marked in the lower panel.]]<br />
<br />
Also marked in Figure 4 is the location of the beacon signal for Ciel-2, which is at 12.209 GHz. The beacon signal appears in precisely the correct bin (frequency subchannel), indicating that we have precise tuning (certainly not unexpected, but nice to see).<br />
<br />
Just to show that the approach is general, the results for a different communications satellite, Nimiq-5, is shown in Figure 5.<br />
<br />
[[File:Linear_to_Circular_Conversion_Figure5.jpg|thumb|400px|Figure 4: Same as Fig. 5, but for the Nimiq-5 commun-ications satellite.]]<br />
<br />
== Polarization Mixing Correction ==<br />
Due to relative feed rotation between az-al mounted antennas and equatorial mounted antennas</div>Ztwanghttp://www.ovsa.njit.edu/wiki/index.php/Polarization_CalibrationPolarization Calibration2016-09-24T21:17:05Z<p>Ztwang: /* Linear to Circular Conversion */</p>
<hr />
<div>== Linear to Circular Conversion ==<br />
[[File:Figure1.jpg|center|thumb|400px|Figure 1: Amplitudes of Stokes I, Stokes V, RCP and LCP for Ciel-2 satellite. The red vertical lines show the center of RCP channels, while the green vertical lines show the center of LCP channels. There is pretty good separation of RCP and LCP at lower and higher frequencies in the range, but around 12.4 GHz the polarization has switched and is mis-assigned.]]<br />
[[File:Linear_to_Circular_Conversion_Figure2.jpg|thumb|400px|Figure 2: Upper panel) Raw phases on XY* (blue) and YX* (green). Lower panel) Phases corrected by removing a delay slope of order 3 ns, and shifting the phase such that the XY* phases on RCP channels is -&pi;/2. This adjustment automatically makes XY* phases on LCP channels become +&pi;/2.]]<br />
[[File:Linear_to_Circular_Conversion_Figure3.jpg|thumb|400px|Figure 3: Amplitudes of Stokes I, Stokes V, RCP and LCP for Ciel-2 satellite, after correcting for delay. The red vertical lines show the center of RCP channels, while the green vertical lines show the center of LCP channels. There is now PERFECT correspondence between RCP channels and the plot, and likewise for LCP channels.]]<br />
[[File:Linear_to_Circular_Conversion_Figure4.jpg|thumb|400px|Figure 4: Same as Fig. 3, but for all 13 atnennas, with the Stokes I curve for each antenna scaled so that they agree. The beacon frequency in marked in the lower panel.]]<br />
[[File:Linear_to_Circular_Conversion_Figure5.jpg|thumb|400px|Figure 4: Same as Fig. 5, but for the Nimiq-5 commun-ications satellite.]]<br />
At EOVSA’s linear feeds, in the electric field the linear polarization, X and Y, relates to RCP and LCP (R and L) as:<br />
<br />
:<math><br />
\begin{align} <br />
R = X + iY \\<br />
L = X - iY <br />
\end{align}<br />
</math><br />
<br />
In terms of autocorrelation powers, we have the 4 polarization products XX*, YY*, XY* and YX*, where the * denotes complex conjugation. The quantities RR* and LL* are then<br />
<br />
:<math><br />
\begin{align} <br />
RR^* = (X + iY)(X + iY)^* &= XX^* - iXY^* + iYX^* + YY^* \\<br />
LL^* = (X - iY)(X - iY)^* &= XX^* + iXY^* - iYX^* + YY^* \\<br />
\end{align}<br />
</math><br />
<br />
One problem is that there is generally a non-zero delay in Y with respect to X. This creates phase slopes in XY* and YX* from which we can determine the delay very accurately. As a check,<br />
<br />
:<math><br />
\begin{align} <br />
Stokes \, I &= \frac{RR^* + LL^*}{2} = XX^* + YY^* \\<br />
Stokes \, V &= \frac{RR^* - LL^*}{2} = i(XX^* - YY^*) <br />
\end{align}<br />
</math><br />
<br />
For completeness:<br />
<br />
:<math>\begin{align} <br />
Stokes \, Q &= XX^* - YY^* \\<br />
Stokes \, U &= XY^* - YX^* \\<br />
P_{linear} &= \sqrt{U^2 + Q^2} \\<br />
\Theta &= \frac{1}{2}\tan^{-1}{\frac{U}{Q}}<br />
\end{align}<br />
</math><br />
<br />
When I plot the quantities I, V, R and L as measured (Figure 1) for geosynchronous satellite Ciel-2, the results look reasonable, except that there are parts of the band where R and L are mis-assigned, and others where they do not separate well.<br />
<br />
The problem is that residual phase slope of Y with respect to X, caused by a difference in delay between the two channels. This can be seen in the upper panel of Figure 2, which shows the uncorrected phases of XY* and YX*. To correct the phases, the RCP phase was fit by a linear least-squares routine, and then the phases were offset by &pi;/2 for both XY* and YX* according to:<br />
<br />
:<math>\begin{align}<br />
XY^{*'} &= XY^*e^{-i(\phi(v) + \frac{\pi}{2})} \\<br />
YX^{*'} &= YX^*e^{ i(\phi(v) + \frac{\pi}{2})}<br />
\end{align}<br />
</math><br />
<br />
where &phi;(v) is the phase fit by the linear function. The corrected phases are shown in the lower panel of Figure 2.<br />
<br />
When the corrected (primed) quantities are used in<br />
<br />
:<math>\begin{align}<br />
RR^* &= XX^* - iXY^{*'} + iYX^{*'} + YY^* \\<br />
LL^* &= XX^* + iXY^{*'} - iYX^{*'} + YY^*<br />
\end{align}<br />
</math><br />
<br />
the resulting channel separation is shown in Figure 3, which shows pretty much perfect channel separation, with the correct polarity.<br />
<br />
This analysis can be performed on all antennas in a completely automated way, to produce the results of Fig. 3. The curves for each antenna are very similar, except that they show differences in amplitude (gain) as a function of frequency. When the curves are scaled to have the same Stokes I levels, the result is shown in Figure 4. Here the 13 antennas are shown in different colors. It is clear that matching Stokes I also causes an excellent match in the other polarizations. Remaining mismatch is likely due to not subtracting a no-signal background prior to scaling the Stokes I curves.<br />
<br />
Also marked in Figure 4 is the location of the beacon signal for Ciel-2, which is at 12.209 GHz. The beacon signal appears in precisely the correct bin (frequency subchannel), indicating that we have precise tuning (certainly not unexpected, but nice to see).<br />
<br />
Just to show that the approach is general, the results for a different communications satellite, Nimiq-5, is shown in Figure 5.<br />
<br />
== Polarization Mixing Correction ==<br />
Due to relative feed rotation between az-al mounted antennas and equatorial mounted antennas</div>Ztwanghttp://www.ovsa.njit.edu/wiki/index.php/Delay_CalibrationDelay Calibration2016-09-24T21:16:48Z<p>Ztwang: </p>
<hr />
<div>== Delay Center Calibration ==<br />
=== 1. Background ===<br />
[[File:del_centr_f1.png|thumb|800px| Figure 1: EOVSA data in the 12.15-12.55 GHz band on CIEL-2, taken with nearly optimal delay (in this case -7 steps in Y relative to X channel) on Antenna 4 in R (blue) and L (green) polarizations. The channels and their polarizations agree well with the nominal band centers, shown with the blue and green vertical lines. Each channel is relatively flat, and separated by narrow notches, but the R and L bands overlap in an interleaving fashion. The band amplitudes vary because the transmissions are in “spot beams” pointed at different places in North America, not all pointing directly at central California.]]<br />
The signals from each antenna have to reach the correlator with the appropriate delays to compensate for cable length differences. For most interferometers, only relative delays between antennas matters, but because the EOVSA converts X and Y polarization into R and L, it appears that the relative delay requirement between X and Y for a given antenna is even more stringent (see section 2). The problem is especially tricky for EOVSA, because the ROACH boards use the KatADC digitizers, which have a clock speed that is a factor of 4 higher than the FPGA clock, so that four-way multiplexing is done. The initialization of this multiplexing is random on startup of the ROACH boards, so there can be differences of up to 4 coarse delay steps, which has to be calibrated every time the ROACHes are restarted. Thus, we need a delay center calibration procedure that can be done quickly and reliably.<br />
This document describes the use of geostationary satellites for delay center calibration, as well as some lessons learned by using this method. This concerns both interferometric phase on each baseline and polarization purity on each antenna, but both can be accomplished at the same time by choosing a satellite with both R and L polarized channels. <br />
The precise analysis needed depends strongly on the choice of geostationary satellite. The experiments done so far have used the CIEL-2 satellite, which has alternating R- and L-polarized channels that overlap. The transmission bands of CIEL-2 are well demonstrated by the actual EOVSA total power data shown in Figure 1.<br />
The CIEL-2 satellite is located at <math>149^o</math> W longitude, and so is fairly isolated from other satellites, which become close together at more eastern longitudes. It is good to avoid having more than one satellite in the 2.1-m antenna beam at a time. The EOVSA beam is relatively small at this <math>K_u</math> band frequency, which also helps.<br />
[[File:del_centr_f2.png|thumb|800px| Figure 2: R-channel amplitudes taken on CIEL-2 while stepping Y-channel delays relative to X by one step/s. The alternation between R and L on every step is seen at high channel numbers, while it takes two steps to swtich at channel 2048, and four steps at channel 1024. The optimum step is around 0.5.]]<br />
To observe a geostationary satellite with the EOVSA system is quite easy. The system automatically downloads the latest coordinate (two-line element, or TLE) files from http://www.celestrak.com/, finds the satellite name in the file, and converts the TLE coordinates to the required RA and Dec table needed to track the satellite. The satellite name for CIEL-2 is just CIEL-2, but because the names have to match exactly, it is sometimes necessary to manually download the file http://www.celestrak.com/NORAD/elements/geo.txt and find the exact spelling of the satellite name. If there are spaces in the name (e.g. “GALAXY 3C (G-3C)”), replace them with underscores (“GALAXY_3C_(G-3C)”). Because these are geostationary satellites, when the track tables are loaded into the antennas the RA should advance 1 s for each second, in order to keep the actual position fixed. However, the satellites do execute small ellipses on the sky, so RA and Dec do change very slightly.<br />
<br />
=== 2. Delay Centers and R/L Polarization ===<br />
Because the R and L polarization is obtained from X and Y in the digital correlator, the delays between X and Y channels must be kept very close to zero. In fact, for Nyquist sampling of the IF that we use, a single coarse delay step at the high end corresponds to a complete swap of polarization R -> L and L -> R. This is nicely demonstrated by Figure 2, which shows data taken on the Ciel-2 geostationary satellite in R polarization. As shown in Figure 1, the broadcast frequencies on this satellite alternate between R and L polarization. As the delay is swept from -10 steps to +5 steps, the polarization pattern, which nominally should look like the one at delay step +1, instead alternates between R and L polarization on each step at frequency channel 4096, but takes two steps at channel 2048, and four steps at channel 1024, etc. The alternation at lower channels produces a symmetric pattern suggested by the two white curves overlaid on the plot, and helps to show that the best step will be somewhere between steps 1 and 0, but closer to step 1. Unfortunately, to get the correct delay within less than a coarse delay step requires either the insertion of a small length of cable equivalent to the desired partial-step delay, or else an adjustment of the complex number used in the correlator to convert X and Y to R and L. <br />
[[File:del_centr_f3.png|thumb|800px| Figure 3: Plots of the data in Figure 2 at close to the optimal delay and at the adjacent delay offsets above and below it. Note that the color of the channels near 12.5 GHz (180-degrees per step) alternate while those near 12.2 GHz do not. At 12.35 GHz, the top plot is X,Y, middle plot is R,L, and bottom plot is Y,X, etc., as the phase drift caused by the delay is 90-degrees per step.]]<br />
In the case of Figure 2, the optimum delay of Y with respect to X is about +0.5 steps, which can be accomplished by adding an approximately 6-inch cable in the Y-channel, calculated from (0.5 step)*(1.25 ns/step)*(0.85 ft/ns), where the latter factor takes into account the slower propagation of light in cable. Note that only fractional steps need to be adjusted by adding short cables, since whole steps can be adjusted simply by adjusting the coarse delay offsets in the file delay_centers.txt. For example, the data shown in Figure 3 are the same as in Figure 2, but taken at a time when the optimal delay was 7 steps off.<br />
Instead of adding short cables, it is likely that merely adjusting the complex factor used to convert X, Y to R, L in the correlator can be adjusted for the appropriate delay (i.e. instead of a constant, an appropriate slope in phase correction can be introduced), but I think it is best for now to try to get an optimized analog system so that any such phase corrections are either not needed or kept small.<br />
Whenever the ROACH boards are power-cycled or restarted, we can expect the phase of the 4-way multiplexing of the digitized signal to change randomly between 0, 1, 2, and 3 in units of coarse steps. Because the two polarizations of each antenna go through the same digitizer, it may be that the two channels of a given digitizer change their multiplexing phase together, in which case the relative X and Y delay will not change. This remains to be confirmed. If so, an analysis like the above is only needed on an occasional basis in case some analog component or cable changes. If the X and Y multiplexing phases do change independently, then the above analysis will have to be done on each restart.<br />
=== 3. Delay Centers and Cross-Correlation ===<br />
The above considerations affect the relative X vs. Y delays on a given antenna. In addition, the overall delays of X on each antenna relative to X on the others, and likewise for Y, have to be maintained at the optimum value by examining the slope in phase across the band while on a satellite. Note that the cross-correlation measurements are completely independent in X and Y, so optimal delays from cross-correlation do not guarantee optimal delays for the purpose of polarization as described above. In fact, it is probably best to do cross-correlation optimization using the correlator in X and Y mode rather than R and L, to avoid conflating the two.<br />
<br />
== Fine Delay Calibration ==</div>Ztwanghttp://www.ovsa.njit.edu/wiki/index.php/Delay_CalibrationDelay Calibration2016-09-24T21:16:21Z<p>Ztwang: /* 1. Background */</p>
<hr />
<div>== Delay Center Calibration ==<br />
=== 1. Background ===<br />
[[File:del_centr_f1.png|center|thumb|800px| Figure 1: EOVSA data in the 12.15-12.55 GHz band on CIEL-2, taken with nearly optimal delay (in this case -7 steps in Y relative to X channel) on Antenna 4 in R (blue) and L (green) polarizations. The channels and their polarizations agree well with the nominal band centers, shown with the blue and green vertical lines. Each channel is relatively flat, and separated by narrow notches, but the R and L bands overlap in an interleaving fashion. The band amplitudes vary because the transmissions are in “spot beams” pointed at different places in North America, not all pointing directly at central California.]]<br />
The signals from each antenna have to reach the correlator with the appropriate delays to compensate for cable length differences. For most interferometers, only relative delays between antennas matters, but because the EOVSA converts X and Y polarization into R and L, it appears that the relative delay requirement between X and Y for a given antenna is even more stringent (see section 2). The problem is especially tricky for EOVSA, because the ROACH boards use the KatADC digitizers, which have a clock speed that is a factor of 4 higher than the FPGA clock, so that four-way multiplexing is done. The initialization of this multiplexing is random on startup of the ROACH boards, so there can be differences of up to 4 coarse delay steps, which has to be calibrated every time the ROACHes are restarted. Thus, we need a delay center calibration procedure that can be done quickly and reliably.<br />
This document describes the use of geostationary satellites for delay center calibration, as well as some lessons learned by using this method. This concerns both interferometric phase on each baseline and polarization purity on each antenna, but both can be accomplished at the same time by choosing a satellite with both R and L polarized channels. <br />
The precise analysis needed depends strongly on the choice of geostationary satellite. The experiments done so far have used the CIEL-2 satellite, which has alternating R- and L-polarized channels that overlap. The transmission bands of CIEL-2 are well demonstrated by the actual EOVSA total power data shown in Figure 1.<br />
The CIEL-2 satellite is located at <math>149^o</math> W longitude, and so is fairly isolated from other satellites, which become close together at more eastern longitudes. It is good to avoid having more than one satellite in the 2.1-m antenna beam at a time. The EOVSA beam is relatively small at this <math>K_u</math> band frequency, which also helps.<br />
[[File:del_centr_f2.png|thumb|800px| Figure 2: R-channel amplitudes taken on CIEL-2 while stepping Y-channel delays relative to X by one step/s. The alternation between R and L on every step is seen at high channel numbers, while it takes two steps to swtich at channel 2048, and four steps at channel 1024. The optimum step is around 0.5.]]<br />
To observe a geostationary satellite with the EOVSA system is quite easy. The system automatically downloads the latest coordinate (two-line element, or TLE) files from http://www.celestrak.com/, finds the satellite name in the file, and converts the TLE coordinates to the required RA and Dec table needed to track the satellite. The satellite name for CIEL-2 is just CIEL-2, but because the names have to match exactly, it is sometimes necessary to manually download the file http://www.celestrak.com/NORAD/elements/geo.txt and find the exact spelling of the satellite name. If there are spaces in the name (e.g. “GALAXY 3C (G-3C)”), replace them with underscores (“GALAXY_3C_(G-3C)”). Because these are geostationary satellites, when the track tables are loaded into the antennas the RA should advance 1 s for each second, in order to keep the actual position fixed. However, the satellites do execute small ellipses on the sky, so RA and Dec do change very slightly.<br />
<br />
=== 2. Delay Centers and R/L Polarization ===<br />
Because the R and L polarization is obtained from X and Y in the digital correlator, the delays between X and Y channels must be kept very close to zero. In fact, for Nyquist sampling of the IF that we use, a single coarse delay step at the high end corresponds to a complete swap of polarization R -> L and L -> R. This is nicely demonstrated by Figure 2, which shows data taken on the Ciel-2 geostationary satellite in R polarization. As shown in Figure 1, the broadcast frequencies on this satellite alternate between R and L polarization. As the delay is swept from -10 steps to +5 steps, the polarization pattern, which nominally should look like the one at delay step +1, instead alternates between R and L polarization on each step at frequency channel 4096, but takes two steps at channel 2048, and four steps at channel 1024, etc. The alternation at lower channels produces a symmetric pattern suggested by the two white curves overlaid on the plot, and helps to show that the best step will be somewhere between steps 1 and 0, but closer to step 1. Unfortunately, to get the correct delay within less than a coarse delay step requires either the insertion of a small length of cable equivalent to the desired partial-step delay, or else an adjustment of the complex number used in the correlator to convert X and Y to R and L. <br />
[[File:del_centr_f3.png|thumb|800px| Figure 3: Plots of the data in Figure 2 at close to the optimal delay and at the adjacent delay offsets above and below it. Note that the color of the channels near 12.5 GHz (180-degrees per step) alternate while those near 12.2 GHz do not. At 12.35 GHz, the top plot is X,Y, middle plot is R,L, and bottom plot is Y,X, etc., as the phase drift caused by the delay is 90-degrees per step.]]<br />
In the case of Figure 2, the optimum delay of Y with respect to X is about +0.5 steps, which can be accomplished by adding an approximately 6-inch cable in the Y-channel, calculated from (0.5 step)*(1.25 ns/step)*(0.85 ft/ns), where the latter factor takes into account the slower propagation of light in cable. Note that only fractional steps need to be adjusted by adding short cables, since whole steps can be adjusted simply by adjusting the coarse delay offsets in the file delay_centers.txt. For example, the data shown in Figure 3 are the same as in Figure 2, but taken at a time when the optimal delay was 7 steps off.<br />
Instead of adding short cables, it is likely that merely adjusting the complex factor used to convert X, Y to R, L in the correlator can be adjusted for the appropriate delay (i.e. instead of a constant, an appropriate slope in phase correction can be introduced), but I think it is best for now to try to get an optimized analog system so that any such phase corrections are either not needed or kept small.<br />
Whenever the ROACH boards are power-cycled or restarted, we can expect the phase of the 4-way multiplexing of the digitized signal to change randomly between 0, 1, 2, and 3 in units of coarse steps. Because the two polarizations of each antenna go through the same digitizer, it may be that the two channels of a given digitizer change their multiplexing phase together, in which case the relative X and Y delay will not change. This remains to be confirmed. If so, an analysis like the above is only needed on an occasional basis in case some analog component or cable changes. If the X and Y multiplexing phases do change independently, then the above analysis will have to be done on each restart.<br />
=== 3. Delay Centers and Cross-Correlation ===<br />
The above considerations affect the relative X vs. Y delays on a given antenna. In addition, the overall delays of X on each antenna relative to X on the others, and likewise for Y, have to be maintained at the optimum value by examining the slope in phase across the band while on a satellite. Note that the cross-correlation measurements are completely independent in X and Y, so optimal delays from cross-correlation do not guarantee optimal delays for the purpose of polarization as described above. In fact, it is probably best to do cross-correlation optimization using the correlator in X and Y mode rather than R and L, to avoid conflating the two.<br />
<br />
== Fine Delay Calibration ==</div>Ztwanghttp://www.ovsa.njit.edu/wiki/index.php/Polarization_CalibrationPolarization Calibration2016-09-24T21:13:47Z<p>Ztwang: /* Linear to Circular Conversion */</p>
<hr />
<div>== Linear to Circular Conversion ==<br />
[[File:Figure1.jpg|thumb|400px|Figure 1: Amplitudes of Stokes I, Stokes V, RCP and LCP for Ciel-2 satellite. The red vertical lines show the center of RCP channels, while the green vertical lines show the center of LCP channels. There is pretty good separation of RCP and LCP at lower and higher frequencies in the range, but around 12.4 GHz the polarization has switched and is mis-assigned.]]<br />
[[File:Linear_to_Circular_Conversion_Figure2.jpg|thumb|400px|Figure 2: Upper panel) Raw phases on XY* (blue) and YX* (green). Lower panel) Phases corrected by removing a delay slope of order 3 ns, and shifting the phase such that the XY* phases on RCP channels is -&pi;/2. This adjustment automatically makes XY* phases on LCP channels become +&pi;/2.]]<br />
[[File:Linear_to_Circular_Conversion_Figure3.jpg|thumb|400px|Figure 3: Amplitudes of Stokes I, Stokes V, RCP and LCP for Ciel-2 satellite, after correcting for delay. The red vertical lines show the center of RCP channels, while the green vertical lines show the center of LCP channels. There is now PERFECT correspondence between RCP channels and the plot, and likewise for LCP channels.]]<br />
[[File:Linear_to_Circular_Conversion_Figure4.jpg|thumb|400px|Figure 4: Same as Fig. 3, but for all 13 atnennas, with the Stokes I curve for each antenna scaled so that they agree. The beacon frequency in marked in the lower panel.]]<br />
[[File:Linear_to_Circular_Conversion_Figure5.jpg|thumb|400px|Figure 4: Same as Fig. 5, but for the Nimiq-5 commun-ications satellite.]]<br />
At EOVSA’s linear feeds, in the electric field the linear polarization, X and Y, relates to RCP and LCP (R and L) as:<br />
<br />
:<math><br />
\begin{align} <br />
R = X + iY \\<br />
L = X - iY <br />
\end{align}<br />
</math><br />
<br />
In terms of autocorrelation powers, we have the 4 polarization products XX*, YY*, XY* and YX*, where the * denotes complex conjugation. The quantities RR* and LL* are then<br />
<br />
:<math><br />
\begin{align} <br />
RR^* = (X + iY)(X + iY)^* &= XX^* - iXY^* + iYX^* + YY^* \\<br />
LL^* = (X - iY)(X - iY)^* &= XX^* + iXY^* - iYX^* + YY^* \\<br />
\end{align}<br />
</math><br />
<br />
One problem is that there is generally a non-zero delay in Y with respect to X. This creates phase slopes in XY* and YX* from which we can determine the delay very accurately. As a check,<br />
<br />
:<math><br />
\begin{align} <br />
Stokes \, I &= \frac{RR^* + LL^*}{2} = XX^* + YY^* \\<br />
Stokes \, V &= \frac{RR^* - LL^*}{2} = i(XX^* - YY^*) <br />
\end{align}<br />
</math><br />
<br />
For completeness:<br />
<br />
:<math>\begin{align} <br />
Stokes \, Q &= XX^* - YY^* \\<br />
Stokes \, U &= XY^* - YX^* \\<br />
P_{linear} &= \sqrt{U^2 + Q^2} \\<br />
\Theta &= \frac{1}{2}\tan^{-1}{\frac{U}{Q}}<br />
\end{align}<br />
</math><br />
<br />
When I plot the quantities I, V, R and L as measured (Figure 1) for geosynchronous satellite Ciel-2, the results look reasonable, except that there are parts of the band where R and L are mis-assigned, and others where they do not separate well.<br />
<br />
The problem is that residual phase slope of Y with respect to X, caused by a difference in delay between the two channels. This can be seen in the upper panel of Figure 2, which shows the uncorrected phases of XY* and YX*. To correct the phases, the RCP phase was fit by a linear least-squares routine, and then the phases were offset by &pi;/2 for both XY* and YX* according to:<br />
<br />
:<math>\begin{align}<br />
XY^{*'} &= XY^*e^{-i(\phi(v) + \frac{\pi}{2})} \\<br />
YX^{*'} &= YX^*e^{ i(\phi(v) + \frac{\pi}{2})}<br />
\end{align}<br />
</math><br />
<br />
where &phi;(v) is the phase fit by the linear function. The corrected phases are shown in the lower panel of Figure 2.<br />
<br />
When the corrected (primed) quantities are used in<br />
<br />
:<math>\begin{align}<br />
RR^* &= XX^* - iXY^{*'} + iYX^{*'} + YY^* \\<br />
LL^* &= XX^* + iXY^{*'} - iYX^{*'} + YY^*<br />
\end{align}<br />
</math><br />
<br />
the resulting channel separation is shown in Figure 3, which shows pretty much perfect channel separation, with the correct polarity.<br />
<br />
This analysis can be performed on all antennas in a completely automated way, to produce the results of Fig. 3. The curves for each antenna are very similar, except that they show differences in amplitude (gain) as a function of frequency. When the curves are scaled to have the same Stokes I levels, the result is shown in Figure 4. Here the 13 antennas are shown in different colors. It is clear that matching Stokes I also causes an excellent match in the other polarizations. Remaining mismatch is likely due to not subtracting a no-signal background prior to scaling the Stokes I curves.<br />
<br />
Also marked in Figure 4 is the location of the beacon signal for Ciel-2, which is at 12.209 GHz. The beacon signal appears in precisely the correct bin (frequency subchannel), indicating that we have precise tuning (certainly not unexpected, but nice to see).<br />
<br />
Just to show that the approach is general, the results for a different communications satellite, Nimiq-5, is shown in Figure 5.<br />
<br />
== Polarization Mixing Correction ==<br />
Due to relative feed rotation between az-al mounted antennas and equatorial mounted antennas</div>Ztwanghttp://www.ovsa.njit.edu/wiki/index.php/Polarization_CalibrationPolarization Calibration2016-09-24T21:09:33Z<p>Ztwang: </p>
<hr />
<div>== Linear to Circular Conversion ==<br />
[[File:Linear_to_Circular_Conversion_Figure1.jpg|thumb|400px|Figure 1: Amplitudes of Stokes I, Stokes V, RCP and LCP for Ciel-2 satellite. The red vertical lines show the center of RCP channels, while the green vertical lines show the center of LCP channels. There is pretty good separation of RCP and LCP at lower and higher frequencies in the range, but around 12.4 GHz the polarization has switched and is mis-assigned.]]<br />
[[File:Linear_to_Circular_Conversion_Figure2.jpg|thumb|400px|Figure 2: Upper panel) Raw phases on XY* (blue) and YX* (green). Lower panel) Phases corrected by removing a delay slope of order 3 ns, and shifting the phase such that the XY* phases on RCP channels is -&pi;/2. This adjustment automatically makes XY* phases on LCP channels become +&pi;/2.]]<br />
[[File:Linear_to_Circular_Conversion_Figure3.jpg|thumb|400px|Figure 3: Amplitudes of Stokes I, Stokes V, RCP and LCP for Ciel-2 satellite, after correcting for delay. The red vertical lines show the center of RCP channels, while the green vertical lines show the center of LCP channels. There is now PERFECT correspondence between RCP channels and the plot, and likewise for LCP channels.]]<br />
[[File:Linear_to_Circular_Conversion_Figure4.jpg|thumb|400px|Figure 4: Same as Fig. 3, but for all 13 atnennas, with the Stokes I curve for each antenna scaled so that they agree. The beacon frequency in marked in the lower panel.]]<br />
[[File:Linear_to_Circular_Conversion_Figure5.jpg|thumb|400px|Figure 4: Same as Fig. 5, but for the Nimiq-5 commun-ications satellite.]]<br />
At EOVSA’s linear feeds, in the electric field the linear polarization, X and Y, relates to RCP and LCP (R and L) as:<br />
<br />
:<math><br />
\begin{align} <br />
R = X + iY \\<br />
L = X - iY <br />
\end{align}<br />
</math><br />
<br />
In terms of autocorrelation powers, we have the 4 polarization products XX*, YY*, XY* and YX*, where the * denotes complex conjugation. The quantities RR* and LL* are then<br />
<br />
:<math><br />
\begin{align} <br />
RR^* = (X + iY)(X + iY)^* &= XX^* - iXY^* + iYX^* + YY^* \\<br />
LL^* = (X - iY)(X - iY)^* &= XX^* + iXY^* - iYX^* + YY^* \\<br />
\end{align}<br />
</math><br />
<br />
One problem is that there is generally a non-zero delay in Y with respect to X. This creates phase slopes in XY* and YX* from which we can determine the delay very accurately. As a check,<br />
<br />
:<math><br />
\begin{align} <br />
Stokes \, I &= \frac{RR^* + LL^*}{2} = XX^* + YY^* \\<br />
Stokes \, V &= \frac{RR^* - LL^*}{2} = i(XX^* - YY^*) <br />
\end{align}<br />
</math><br />
<br />
For completeness:<br />
<br />
:<math>\begin{align} <br />
Stokes \, Q &= XX^* - YY^* \\<br />
Stokes \, U &= XY^* - YX^* \\<br />
P_{linear} &= \sqrt{U^2 + Q^2} \\<br />
\Theta &= \frac{1}{2}\tan^{-1}{\frac{U}{Q}}<br />
\end{align}<br />
</math><br />
<br />
When I plot the quantities I, V, R and L as measured (Figure 1) for geosynchronous satellite Ciel-2, the results look reasonable, except that there are parts of the band where R and L are mis-assigned, and others where they do not separate well.<br />
<br />
The problem is that residual phase slope of Y with respect to X, caused by a difference in delay between the two channels. This can be seen in the upper panel of Figure 2, which shows the uncorrected phases of XY* and YX*. To correct the phases, the RCP phase was fit by a linear least-squares routine, and then the phases were offset by &pi;/2 for both XY* and YX* according to:<br />
<br />
:<math>\begin{align}<br />
XY^{*'} &= XY^*e^{-i(\phi(v) + \frac{\pi}{2})} \\<br />
YX^{*'} &= YX^*e^{ i(\phi(v) + \frac{\pi}{2})}<br />
\end{align}<br />
</math><br />
<br />
where &phi;(v) is the phase fit by the linear function. The corrected phases are shown in the lower panel of Figure 2.<br />
<br />
When the corrected (primed) quantities are used in<br />
<br />
:<math>\begin{align}<br />
RR^* &= XX^* - iXY^{*'} + iYX^{*'} + YY^* \\<br />
LL^* &= XX^* + iXY^{*'} - iYX^{*'} + YY^*<br />
\end{align}<br />
</math><br />
<br />
the resulting channel separation is shown in Figure 3, which shows pretty much perfect channel separation, with the correct polarity.<br />
<br />
This analysis can be performed on all antennas in a completely automated way, to produce the results of Fig. 3. The curves for each antenna are very similar, except that they show differences in amplitude (gain) as a function of frequency. When the curves are scaled to have the same Stokes I levels, the result is shown in Figure 4. Here the 13 antennas are shown in different colors. It is clear that matching Stokes I also causes an excellent match in the other polarizations. Remaining mismatch is likely due to not subtracting a no-signal background prior to scaling the Stokes I curves.<br />
<br />
Also marked in Figure 4 is the location of the beacon signal for Ciel-2, which is at 12.209 GHz. The beacon signal appears in precisely the correct bin (frequency subchannel), indicating that we have precise tuning (certainly not unexpected, but nice to see).<br />
<br />
Just to show that the approach is general, the results for a different communications satellite, Nimiq-5, is shown in Figure 5.<br />
<br />
== Polarization Mixing Correction ==<br />
Due to relative feed rotation between az-al mounted antennas and equatorial mounted antennas</div>Ztwanghttp://www.ovsa.njit.edu/wiki/index.php/Polarization_CalibrationPolarization Calibration2016-09-24T21:08:49Z<p>Ztwang: </p>
<hr />
<div>== Linear to Circular Conversion ==<br />
[[File:Linear_to_Circular_Conversion_Figure1.jpg|thumb|800px|Figure 1: Amplitudes of Stokes I, Stokes V, RCP and LCP for Ciel-2 satellite. The red vertical lines show the center of RCP channels, while the green vertical lines show the center of LCP channels. There is pretty good separation of RCP and LCP at lower and higher frequencies in the range, but around 12.4 GHz the polarization has switched and is mis-assigned.]]<br />
[[File:Linear_to_Circular_Conversion_Figure2.jpg|thumb|800px|Figure 2: Upper panel) Raw phases on XY* (blue) and YX* (green). Lower panel) Phases corrected by removing a delay slope of order 3 ns, and shifting the phase such that the XY* phases on RCP channels is -&pi;/2. This adjustment automatically makes XY* phases on LCP channels become +&pi;/2.]]<br />
[[File:Linear_to_Circular_Conversion_Figure3.jpg|thumb|800px|Figure 3: Amplitudes of Stokes I, Stokes V, RCP and LCP for Ciel-2 satellite, after correcting for delay. The red vertical lines show the center of RCP channels, while the green vertical lines show the center of LCP channels. There is now PERFECT correspondence between RCP channels and the plot, and likewise for LCP channels.]]<br />
[[File:Linear_to_Circular_Conversion_Figure4.jpg|thumb|800px|Figure 4: Same as Fig. 3, but for all 13 atnennas, with the Stokes I curve for each antenna scaled so that they agree. The beacon frequency in marked in the lower panel.]]<br />
[[File:Linear_to_Circular_Conversion_Figure5.jpg|thumb|800px|Figure 4: Same as Fig. 5, but for the Nimiq-5 commun-ications satellite.]]<br />
At EOVSA’s linear feeds, in the electric field the linear polarization, X and Y, relates to RCP and LCP (R and L) as:<br />
<br />
:<math><br />
\begin{align} <br />
R = X + iY \\<br />
L = X - iY <br />
\end{align}<br />
</math><br />
<br />
In terms of autocorrelation powers, we have the 4 polarization products XX*, YY*, XY* and YX*, where the * denotes complex conjugation. The quantities RR* and LL* are then<br />
<br />
:<math><br />
\begin{align} <br />
RR^* = (X + iY)(X + iY)^* &= XX^* - iXY^* + iYX^* + YY^* \\<br />
LL^* = (X - iY)(X - iY)^* &= XX^* + iXY^* - iYX^* + YY^* \\<br />
\end{align}<br />
</math><br />
<br />
One problem is that there is generally a non-zero delay in Y with respect to X. This creates phase slopes in XY* and YX* from which we can determine the delay very accurately. As a check,<br />
<br />
:<math><br />
\begin{align} <br />
Stokes \, I &= \frac{RR^* + LL^*}{2} = XX^* + YY^* \\<br />
Stokes \, V &= \frac{RR^* - LL^*}{2} = i(XX^* - YY^*) <br />
\end{align}<br />
</math><br />
<br />
For completeness:<br />
<br />
:<math>\begin{align} <br />
Stokes \, Q &= XX^* - YY^* \\<br />
Stokes \, U &= XY^* - YX^* \\<br />
P_{linear} &= \sqrt{U^2 + Q^2} \\<br />
\Theta &= \frac{1}{2}\tan^{-1}{\frac{U}{Q}}<br />
\end{align}<br />
</math><br />
<br />
When I plot the quantities I, V, R and L as measured (Figure 1) for geosynchronous satellite Ciel-2, the results look reasonable, except that there are parts of the band where R and L are mis-assigned, and others where they do not separate well.<br />
<br />
The problem is that residual phase slope of Y with respect to X, caused by a difference in delay between the two channels. This can be seen in the upper panel of Figure 2, which shows the uncorrected phases of XY* and YX*. To correct the phases, the RCP phase was fit by a linear least-squares routine, and then the phases were offset by &pi;/2 for both XY* and YX* according to:<br />
<br />
:<math>\begin{align}<br />
XY^{*'} &= XY^*e^{-i(\phi(v) + \frac{\pi}{2})} \\<br />
YX^{*'} &= YX^*e^{ i(\phi(v) + \frac{\pi}{2})}<br />
\end{align}<br />
</math><br />
<br />
where &phi;(v) is the phase fit by the linear function. The corrected phases are shown in the lower panel of Figure 2.<br />
<br />
When the corrected (primed) quantities are used in<br />
<br />
:<math>\begin{align}<br />
RR^* &= XX^* - iXY^{*'} + iYX^{*'} + YY^* \\<br />
LL^* &= XX^* + iXY^{*'} - iYX^{*'} + YY^*<br />
\end{align}<br />
</math><br />
<br />
the resulting channel separation is shown in Figure 3, which shows pretty much perfect channel separation, with the correct polarity.<br />
<br />
This analysis can be performed on all antennas in a completely automated way, to produce the results of Fig. 3. The curves for each antenna are very similar, except that they show differences in amplitude (gain) as a function of frequency. When the curves are scaled to have the same Stokes I levels, the result is shown in Figure 4. Here the 13 antennas are shown in different colors. It is clear that matching Stokes I also causes an excellent match in the other polarizations. Remaining mismatch is likely due to not subtracting a no-signal background prior to scaling the Stokes I curves.<br />
<br />
Also marked in Figure 4 is the location of the beacon signal for Ciel-2, which is at 12.209 GHz. The beacon signal appears in precisely the correct bin (frequency subchannel), indicating that we have precise tuning (certainly not unexpected, but nice to see).<br />
<br />
Just to show that the approach is general, the results for a different communications satellite, Nimiq-5, is shown in Figure 5.<br />
<br />
== Polarization Mixing Correction ==<br />
Due to relative feed rotation between az-al mounted antennas and equatorial mounted antennas</div>Ztwanghttp://www.ovsa.njit.edu/wiki/index.php/Polarization_CalibrationPolarization Calibration2016-09-24T21:08:01Z<p>Ztwang: /* Linear to Circular Conversion */</p>
<hr />
<div>== Linear to Circular Conversion ==<br />
[[File:Linear_to_Circular_Conversion_Figure1.jpg|thumb|600px|Figure 1: Amplitudes of Stokes I, Stokes V, RCP and LCP for Ciel-2 satellite. The red vertical lines show the center of RCP channels, while the green vertical lines show the center of LCP channels. There is pretty good separation of RCP and LCP at lower and higher frequencies in the range, but around 12.4 GHz the polarization has switched and is mis-assigned.]]<br />
[[File:Linear_to_Circular_Conversion_Figure2.jpg|thumb|600px|Figure 2: Upper panel) Raw phases on XY* (blue) and YX* (green). Lower panel) Phases corrected by removing a delay slope of order 3 ns, and shifting the phase such that the XY* phases on RCP channels is -&pi;/2. This adjustment automatically makes XY* phases on LCP channels become +&pi;/2.]]<br />
[[File:Linear_to_Circular_Conversion_Figure3.jpg|thumb|600px|Figure 3: Amplitudes of Stokes I, Stokes V, RCP and LCP for Ciel-2 satellite, after correcting for delay. The red vertical lines show the center of RCP channels, while the green vertical lines show the center of LCP channels. There is now PERFECT correspondence between RCP channels and the plot, and likewise for LCP channels.]]<br />
[[File:Linear_to_Circular_Conversion_Figure4.jpg|thumb|600px|Figure 4: Same as Fig. 3, but for all 13 atnennas, with the Stokes I curve for each antenna scaled so that they agree. The beacon frequency in marked in the lower panel.]]<br />
[[File:Linear_to_Circular_Conversion_Figure5.jpg|thumb|600px|Figure 4: Same as Fig. 5, but for the Nimiq-5 commun-ications satellite.]]<br />
At EOVSA’s linear feeds, in the electric field the linear polarization, X and Y, relates to RCP and LCP (R and L) as:<br />
<br />
:<math><br />
\begin{align} <br />
R = X + iY \\<br />
L = X - iY <br />
\end{align}<br />
</math><br />
<br />
In terms of autocorrelation powers, we have the 4 polarization products XX*, YY*, XY* and YX*, where the * denotes complex conjugation. The quantities RR* and LL* are then<br />
<br />
:<math><br />
\begin{align} <br />
RR^* = (X + iY)(X + iY)^* &= XX^* - iXY^* + iYX^* + YY^* \\<br />
LL^* = (X - iY)(X - iY)^* &= XX^* + iXY^* - iYX^* + YY^* \\<br />
\end{align}<br />
</math><br />
<br />
One problem is that there is generally a non-zero delay in Y with respect to X. This creates phase slopes in XY* and YX* from which we can determine the delay very accurately. As a check,<br />
<br />
:<math><br />
\begin{align} <br />
Stokes \, I &= \frac{RR^* + LL^*}{2} = XX^* + YY^* \\<br />
Stokes \, V &= \frac{RR^* - LL^*}{2} = i(XX^* - YY^*) <br />
\end{align}<br />
</math><br />
<br />
For completeness:<br />
<br />
:<math>\begin{align} <br />
Stokes \, Q &= XX^* - YY^* \\<br />
Stokes \, U &= XY^* - YX^* \\<br />
P_{linear} &= \sqrt{U^2 + Q^2} \\<br />
\Theta &= \frac{1}{2}\tan^{-1}{\frac{U}{Q}}<br />
\end{align}<br />
</math><br />
<br />
When I plot the quantities I, V, R and L as measured (Figure 1) for geosynchronous satellite Ciel-2, the results look reasonable, except that there are parts of the band where R and L are mis-assigned, and others where they do not separate well.<br />
<br />
The problem is that residual phase slope of Y with respect to X, caused by a difference in delay between the two channels. This can be seen in the upper panel of Figure 2, which shows the uncorrected phases of XY* and YX*. To correct the phases, the RCP phase was fit by a linear least-squares routine, and then the phases were offset by &pi;/2 for both XY* and YX* according to:<br />
<br />
:<math>\begin{align}<br />
XY^{*'} &= XY^*e^{-i(\phi(v) + \frac{\pi}{2})} \\<br />
YX^{*'} &= YX^*e^{ i(\phi(v) + \frac{\pi}{2})}<br />
\end{align}<br />
</math><br />
<br />
where &phi;(v) is the phase fit by the linear function. The corrected phases are shown in the lower panel of Figure 2.<br />
<br />
When the corrected (primed) quantities are used in<br />
<br />
:<math>\begin{align}<br />
RR^* &= XX^* - iXY^{*'} + iYX^{*'} + YY^* \\<br />
LL^* &= XX^* + iXY^{*'} - iYX^{*'} + YY^*<br />
\end{align}<br />
</math><br />
<br />
the resulting channel separation is shown in Figure 3, which shows pretty much perfect channel separation, with the correct polarity.<br />
<br />
This analysis can be performed on all antennas in a completely automated way, to produce the results of Fig. 3. The curves for each antenna are very similar, except that they show differences in amplitude (gain) as a function of frequency. When the curves are scaled to have the same Stokes I levels, the result is shown in Figure 4. Here the 13 antennas are shown in different colors. It is clear that matching Stokes I also causes an excellent match in the other polarizations. Remaining mismatch is likely due to not subtracting a no-signal background prior to scaling the Stokes I curves.<br />
<br />
Also marked in Figure 4 is the location of the beacon signal for Ciel-2, which is at 12.209 GHz. The beacon signal appears in precisely the correct bin (frequency subchannel), indicating that we have precise tuning (certainly not unexpected, but nice to see).<br />
<br />
Just to show that the approach is general, the results for a different communications satellite, Nimiq-5, is shown in Figure 5.<br />
<br />
== Polarization Mixing Correction ==<br />
Due to relative feed rotation between az-al mounted antennas and equatorial mounted antennas</div>Ztwanghttp://www.ovsa.njit.edu/wiki/index.php/File:Linear_to_Circular_Conversion_Figure5.jpgFile:Linear to Circular Conversion Figure5.jpg2016-09-24T21:05:05Z<p>Ztwang: </p>
<hr />
<div></div>Ztwanghttp://www.ovsa.njit.edu/wiki/index.php/File:Linear_to_Circular_Conversion_Figure4.jpgFile:Linear to Circular Conversion Figure4.jpg2016-09-24T21:04:44Z<p>Ztwang: </p>
<hr />
<div></div>Ztwanghttp://www.ovsa.njit.edu/wiki/index.php/File:Linear_to_Circular_Conversion_Figure3.jpgFile:Linear to Circular Conversion Figure3.jpg2016-09-24T21:04:15Z<p>Ztwang: </p>
<hr />
<div></div>Ztwanghttp://www.ovsa.njit.edu/wiki/index.php/Polarization_CalibrationPolarization Calibration2016-09-24T21:03:55Z<p>Ztwang: /* Linear to Circular Conversion */</p>
<hr />
<div>== Linear to Circular Conversion ==<br />
[[File:Linear_to_Circular_Conversion_Figure1.jpg|thumb|600px|]]<br />
[[File:Linear_to_Circular_Conversion_Figure2.jpg|thumb|600px|]]<br />
[[File:Linear_to_Circular_Conversion_Figure3.jpg|thumb|600px|]]<br />
[[File:Linear_to_Circular_Conversion_Figure4.jpg|thumb|600px|]]<br />
[[File:Linear_to_Circular_Conversion_Figure5.jpg|thumb|600px|]]<br />
At EOVSA’s linear feeds, in the electric field the linear polarization, X and Y, relates to RCP and LCP (R and L) as:<br />
<br />
:<math><br />
\begin{align} <br />
R = X + iY \\<br />
L = X - iY <br />
\end{align}<br />
</math><br />
<br />
In terms of autocorrelation powers, we have the 4 polarization products XX*, YY*, XY* and YX*, where the * denotes complex conjugation. The quantities RR* and LL* are then<br />
<br />
:<math><br />
\begin{align} <br />
RR^* = (X + iY)(X + iY)^* &= XX^* - iXY^* + iYX^* + YY^* \\<br />
LL^* = (X - iY)(X - iY)^* &= XX^* + iXY^* - iYX^* + YY^* \\<br />
\end{align}<br />
</math><br />
<br />
One problem is that there is generally a non-zero delay in Y with respect to X. This creates phase slopes in XY* and YX* from which we can determine the delay very accurately. As a check,<br />
<br />
:<math><br />
\begin{align} <br />
Stokes \, I &= \frac{RR^* + LL^*}{2} = XX^* + YY^* \\<br />
Stokes \, V &= \frac{RR^* - LL^*}{2} = i(XX^* - YY^*) <br />
\end{align}<br />
</math><br />
<br />
For completeness:<br />
<br />
:<math>\begin{align} <br />
Stokes \, Q &= XX^* - YY^* \\<br />
Stokes \, U &= XY^* - YX^* \\<br />
P_{linear} &= \sqrt{U^2 + Q^2} \\<br />
\Theta &= \frac{1}{2}\tan^{-1}{\frac{U}{Q}}<br />
\end{align}<br />
</math><br />
<br />
When I plot the quantities I, V, R and L as measured (Figure 1) for geosynchronous satellite Ciel-2, the results look reasonable, except that there are parts of the band where R and L are mis-assigned, and others where they do not separate well.<br />
<br />
The problem is that residual phase slope of Y with respect to X, caused by a difference in delay between the two channels. This can be seen in the upper panel of Figure 2, which shows the uncorrected phases of XY* and YX*. To correct the phases, the RCP phase was fit by a linear least-squares routine, and then the phases were offset by &pi;/2 for both XY* and YX* according to:<br />
<br />
:<math>\begin{align}<br />
XY^{*'} &= XY^*e^{-i(\phi(v) + \frac{\pi}{2})} \\<br />
YX^{*'} &= YX^*e^{ i(\phi(v) + \frac{\pi}{2})}<br />
\end{align}<br />
</math><br />
<br />
where &phi;(v) is the phase fit by the linear function. The corrected phases are shown in the lower panel of Figure 2.<br />
<br />
When the corrected (primed) quantities are used in<br />
<br />
:<math>\begin{align}<br />
RR^* &= XX^* - iXY^{*'} + iYX^{*'} + YY^* \\<br />
LL^* &= XX^* + iXY^{*'} - iYX^{*'} + YY^*<br />
\end{align}<br />
</math><br />
<br />
the resulting channel separation is shown in Figure 3, which shows pretty much perfect channel separation, with the correct polarity.<br />
<br />
This analysis can be performed on all antennas in a completely automated way, to produce the results of Fig. 3. The curves for each antenna are very similar, except that they show differences in amplitude (gain) as a function of frequency. When the curves are scaled to have the same Stokes I levels, the result is shown in Figure 4. Here the 13 antennas are shown in different colors. It is clear that matching Stokes I also causes an excellent match in the other polarizations. Remaining mismatch is likely due to not subtracting a no-signal background prior to scaling the Stokes I curves.<br />
<br />
Also marked in Figure 4 is the location of the beacon signal for Ciel-2, which is at 12.209 GHz. The beacon signal appears in precisely the correct bin (frequency subchannel), indicating that we have precise tuning (certainly not unexpected, but nice to see).<br />
<br />
Just to show that the approach is general, the results for a different communications satellite, Nimiq-5, is shown in Figure 5.<br />
<br />
== Polarization Mixing Correction ==<br />
Due to relative feed rotation between az-al mounted antennas and equatorial mounted antennas</div>Ztwanghttp://www.ovsa.njit.edu/wiki/index.php/Polarization_CalibrationPolarization Calibration2016-09-24T21:03:36Z<p>Ztwang: /* Linear to Circular Conversion */</p>
<hr />
<div>== Linear to Circular Conversion ==<br />
[[File:Linear_to_Circular_Conversion_Figure1.jpg|thumb|500px|]]<br />
[[File:Linear_to_Circular_Conversion_Figure2.jpg|thumb|500px|]]<br />
[[File:Linear_to_Circular_Conversion_Figure3.jpg|thumb|500px|]]<br />
[[File:Linear_to_Circular_Conversion_Figure4.jpg|thumb|500px|]]<br />
[[File:Linear_to_Circular_Conversion_Figure5.jpg|thumb|500px|]]<br />
At EOVSA’s linear feeds, in the electric field the linear polarization, X and Y, relates to RCP and LCP (R and L) as:<br />
<br />
:<math><br />
\begin{align} <br />
R = X + iY \\<br />
L = X - iY <br />
\end{align}<br />
</math><br />
<br />
In terms of autocorrelation powers, we have the 4 polarization products XX*, YY*, XY* and YX*, where the * denotes complex conjugation. The quantities RR* and LL* are then<br />
<br />
:<math><br />
\begin{align} <br />
RR^* = (X + iY)(X + iY)^* &= XX^* - iXY^* + iYX^* + YY^* \\<br />
LL^* = (X - iY)(X - iY)^* &= XX^* + iXY^* - iYX^* + YY^* \\<br />
\end{align}<br />
</math><br />
<br />
One problem is that there is generally a non-zero delay in Y with respect to X. This creates phase slopes in XY* and YX* from which we can determine the delay very accurately. As a check,<br />
<br />
:<math><br />
\begin{align} <br />
Stokes \, I &= \frac{RR^* + LL^*}{2} = XX^* + YY^* \\<br />
Stokes \, V &= \frac{RR^* - LL^*}{2} = i(XX^* - YY^*) <br />
\end{align}<br />
</math><br />
<br />
For completeness:<br />
<br />
:<math>\begin{align} <br />
Stokes \, Q &= XX^* - YY^* \\<br />
Stokes \, U &= XY^* - YX^* \\<br />
P_{linear} &= \sqrt{U^2 + Q^2} \\<br />
\Theta &= \frac{1}{2}\tan^{-1}{\frac{U}{Q}}<br />
\end{align}<br />
</math><br />
<br />
When I plot the quantities I, V, R and L as measured (Figure 1) for geosynchronous satellite Ciel-2, the results look reasonable, except that there are parts of the band where R and L are mis-assigned, and others where they do not separate well.<br />
<br />
The problem is that residual phase slope of Y with respect to X, caused by a difference in delay between the two channels. This can be seen in the upper panel of Figure 2, which shows the uncorrected phases of XY* and YX*. To correct the phases, the RCP phase was fit by a linear least-squares routine, and then the phases were offset by &pi;/2 for both XY* and YX* according to:<br />
<br />
:<math>\begin{align}<br />
XY^{*'} &= XY^*e^{-i(\phi(v) + \frac{\pi}{2})} \\<br />
YX^{*'} &= YX^*e^{ i(\phi(v) + \frac{\pi}{2})}<br />
\end{align}<br />
</math><br />
<br />
where &phi;(v) is the phase fit by the linear function. The corrected phases are shown in the lower panel of Figure 2.<br />
<br />
When the corrected (primed) quantities are used in<br />
<br />
:<math>\begin{align}<br />
RR^* &= XX^* - iXY^{*'} + iYX^{*'} + YY^* \\<br />
LL^* &= XX^* + iXY^{*'} - iYX^{*'} + YY^*<br />
\end{align}<br />
</math><br />
<br />
the resulting channel separation is shown in Figure 3, which shows pretty much perfect channel separation, with the correct polarity.<br />
<br />
This analysis can be performed on all antennas in a completely automated way, to produce the results of Fig. 3. The curves for each antenna are very similar, except that they show differences in amplitude (gain) as a function of frequency. When the curves are scaled to have the same Stokes I levels, the result is shown in Figure 4. Here the 13 antennas are shown in different colors. It is clear that matching Stokes I also causes an excellent match in the other polarizations. Remaining mismatch is likely due to not subtracting a no-signal background prior to scaling the Stokes I curves.<br />
<br />
Also marked in Figure 4 is the location of the beacon signal for Ciel-2, which is at 12.209 GHz. The beacon signal appears in precisely the correct bin (frequency subchannel), indicating that we have precise tuning (certainly not unexpected, but nice to see).<br />
<br />
Just to show that the approach is general, the results for a different communications satellite, Nimiq-5, is shown in Figure 5.<br />
<br />
== Polarization Mixing Correction ==<br />
Due to relative feed rotation between az-al mounted antennas and equatorial mounted antennas</div>Ztwanghttp://www.ovsa.njit.edu/wiki/index.php/Polarization_CalibrationPolarization Calibration2016-09-24T21:02:49Z<p>Ztwang: /* Linear to Circular Conversion */</p>
<hr />
<div>== Linear to Circular Conversion ==<br />
[[File:Linear_to_Circular_Conversion_Figure2.jpg|thumb|800px|]]<br />
At EOVSA’s linear feeds, in the electric field the linear polarization, X and Y, relates to RCP and LCP (R and L) as:<br />
<br />
:<math><br />
\begin{align} <br />
R = X + iY \\<br />
L = X - iY <br />
\end{align}<br />
</math><br />
<br />
In terms of autocorrelation powers, we have the 4 polarization products XX*, YY*, XY* and YX*, where the * denotes complex conjugation. The quantities RR* and LL* are then<br />
<br />
:<math><br />
\begin{align} <br />
RR^* = (X + iY)(X + iY)^* &= XX^* - iXY^* + iYX^* + YY^* \\<br />
LL^* = (X - iY)(X - iY)^* &= XX^* + iXY^* - iYX^* + YY^* \\<br />
\end{align}<br />
</math><br />
<br />
One problem is that there is generally a non-zero delay in Y with respect to X. This creates phase slopes in XY* and YX* from which we can determine the delay very accurately. As a check,<br />
<br />
:<math><br />
\begin{align} <br />
Stokes \, I &= \frac{RR^* + LL^*}{2} = XX^* + YY^* \\<br />
Stokes \, V &= \frac{RR^* - LL^*}{2} = i(XX^* - YY^*) <br />
\end{align}<br />
</math><br />
<br />
For completeness:<br />
<br />
:<math>\begin{align} <br />
Stokes \, Q &= XX^* - YY^* \\<br />
Stokes \, U &= XY^* - YX^* \\<br />
P_{linear} &= \sqrt{U^2 + Q^2} \\<br />
\Theta &= \frac{1}{2}\tan^{-1}{\frac{U}{Q}}<br />
\end{align}<br />
</math><br />
<br />
When I plot the quantities I, V, R and L as measured (Figure 1) for geosynchronous satellite Ciel-2, the results look reasonable, except that there are parts of the band where R and L are mis-assigned, and others where they do not separate well.<br />
<br />
The problem is that residual phase slope of Y with respect to X, caused by a difference in delay between the two channels. This can be seen in the upper panel of Figure 2, which shows the uncorrected phases of XY* and YX*. To correct the phases, the RCP phase was fit by a linear least-squares routine, and then the phases were offset by &pi;/2 for both XY* and YX* according to:<br />
<br />
:<math>\begin{align}<br />
XY^{*'} &= XY^*e^{-i(\phi(v) + \frac{\pi}{2})} \\<br />
YX^{*'} &= YX^*e^{ i(\phi(v) + \frac{\pi}{2})}<br />
\end{align}<br />
</math><br />
<br />
where &phi;(v) is the phase fit by the linear function. The corrected phases are shown in the lower panel of Figure 2.<br />
<br />
When the corrected (primed) quantities are used in<br />
<br />
:<math>\begin{align}<br />
RR^* &= XX^* - iXY^{*'} + iYX^{*'} + YY^* \\<br />
LL^* &= XX^* + iXY^{*'} - iYX^{*'} + YY^*<br />
\end{align}<br />
</math><br />
<br />
the resulting channel separation is shown in Figure 3, which shows pretty much perfect channel separation, with the correct polarity.<br />
<br />
This analysis can be performed on all antennas in a completely automated way, to produce the results of Fig. 3. The curves for each antenna are very similar, except that they show differences in amplitude (gain) as a function of frequency. When the curves are scaled to have the same Stokes I levels, the result is shown in Figure 4. Here the 13 antennas are shown in different colors. It is clear that matching Stokes I also causes an excellent match in the other polarizations. Remaining mismatch is likely due to not subtracting a no-signal background prior to scaling the Stokes I curves.<br />
<br />
Also marked in Figure 4 is the location of the beacon signal for Ciel-2, which is at 12.209 GHz. The beacon signal appears in precisely the correct bin (frequency subchannel), indicating that we have precise tuning (certainly not unexpected, but nice to see).<br />
<br />
Just to show that the approach is general, the results for a different communications satellite, Nimiq-5, is shown in Figure 5.<br />
<br />
== Polarization Mixing Correction ==<br />
Due to relative feed rotation between az-al mounted antennas and equatorial mounted antennas</div>Ztwanghttp://www.ovsa.njit.edu/wiki/index.php/Polarization_CalibrationPolarization Calibration2016-09-24T21:01:52Z<p>Ztwang: /* Linear to Circular Conversion */</p>
<hr />
<div>== Linear to Circular Conversion ==<br />
[[File:Linear_to_Circular_Conversion_Figure2.jpg]]<br />
At EOVSA’s linear feeds, in the electric field the linear polarization, X and Y, relates to RCP and LCP (R and L) as:<br />
<br />
:<math><br />
\begin{align} <br />
R = X + iY \\<br />
L = X - iY <br />
\end{align}<br />
</math><br />
<br />
In terms of autocorrelation powers, we have the 4 polarization products XX*, YY*, XY* and YX*, where the * denotes complex conjugation. The quantities RR* and LL* are then<br />
<br />
:<math><br />
\begin{align} <br />
RR^* = (X + iY)(X + iY)^* &= XX^* - iXY^* + iYX^* + YY^* \\<br />
LL^* = (X - iY)(X - iY)^* &= XX^* + iXY^* - iYX^* + YY^* \\<br />
\end{align}<br />
</math><br />
<br />
One problem is that there is generally a non-zero delay in Y with respect to X. This creates phase slopes in XY* and YX* from which we can determine the delay very accurately. As a check,<br />
<br />
:<math><br />
\begin{align} <br />
Stokes \, I &= \frac{RR^* + LL^*}{2} = XX^* + YY^* \\<br />
Stokes \, V &= \frac{RR^* - LL^*}{2} = i(XX^* - YY^*) <br />
\end{align}<br />
</math><br />
<br />
For completeness:<br />
<br />
:<math>\begin{align} <br />
Stokes \, Q &= XX^* - YY^* \\<br />
Stokes \, U &= XY^* - YX^* \\<br />
P_{linear} &= \sqrt{U^2 + Q^2} \\<br />
\Theta &= \frac{1}{2}\tan^{-1}{\frac{U}{Q}}<br />
\end{align}<br />
</math><br />
<br />
When I plot the quantities I, V, R and L as measured (Figure 1) for geosynchronous satellite Ciel-2, the results look reasonable, except that there are parts of the band where R and L are mis-assigned, and others where they do not separate well.<br />
<br />
The problem is that residual phase slope of Y with respect to X, caused by a difference in delay between the two channels. This can be seen in the upper panel of Figure 2, which shows the uncorrected phases of XY* and YX*. To correct the phases, the RCP phase was fit by a linear least-squares routine, and then the phases were offset by &pi;/2 for both XY* and YX* according to:<br />
<br />
:<math>\begin{align}<br />
XY^{*'} &= XY^*e^{-i(\phi(v) + \frac{\pi}{2})} \\<br />
YX^{*'} &= YX^*e^{ i(\phi(v) + \frac{\pi}{2})}<br />
\end{align}<br />
</math><br />
<br />
where &phi;(v) is the phase fit by the linear function. The corrected phases are shown in the lower panel of Figure 2.<br />
<br />
When the corrected (primed) quantities are used in<br />
<br />
:<math>\begin{align}<br />
RR^* &= XX^* - iXY^{*'} + iYX^{*'} + YY^* \\<br />
LL^* &= XX^* + iXY^{*'} - iYX^{*'} + YY^*<br />
\end{align}<br />
</math><br />
<br />
the resulting channel separation is shown in Figure 3, which shows pretty much perfect channel separation, with the correct polarity.<br />
<br />
This analysis can be performed on all antennas in a completely automated way, to produce the results of Fig. 3. The curves for each antenna are very similar, except that they show differences in amplitude (gain) as a function of frequency. When the curves are scaled to have the same Stokes I levels, the result is shown in Figure 4. Here the 13 antennas are shown in different colors. It is clear that matching Stokes I also causes an excellent match in the other polarizations. Remaining mismatch is likely due to not subtracting a no-signal background prior to scaling the Stokes I curves.<br />
<br />
Also marked in Figure 4 is the location of the beacon signal for Ciel-2, which is at 12.209 GHz. The beacon signal appears in precisely the correct bin (frequency subchannel), indicating that we have precise tuning (certainly not unexpected, but nice to see).<br />
<br />
Just to show that the approach is general, the results for a different communications satellite, Nimiq-5, is shown in Figure 5.<br />
<br />
== Polarization Mixing Correction ==<br />
Due to relative feed rotation between az-al mounted antennas and equatorial mounted antennas</div>Ztwanghttp://www.ovsa.njit.edu/wiki/index.php/File:Linear_to_Circular_Conversion_Figure2.jpgFile:Linear to Circular Conversion Figure2.jpg2016-09-24T21:00:28Z<p>Ztwang: </p>
<hr />
<div></div>Ztwanghttp://www.ovsa.njit.edu/wiki/index.php/Polarization_CalibrationPolarization Calibration2016-09-24T21:00:14Z<p>Ztwang: /* Linear to Circular Conversion */</p>
<hr />
<div>== Linear to Circular Conversion ==<br />
At EOVSA’s linear feeds, in the electric field the linear polarization, X and Y, relates to RCP and LCP (R and L) as:<br />
<br />
:<math><br />
\begin{align} <br />
R = X + iY \\<br />
L = X - iY <br />
\end{align}<br />
</math><br />
<br />
In terms of autocorrelation powers, we have the 4 polarization products XX*, YY*, XY* and YX*, where the * denotes complex conjugation. The quantities RR* and LL* are then<br />
<br />
:<math><br />
\begin{align} <br />
RR^* = (X + iY)(X + iY)^* &= XX^* - iXY^* + iYX^* + YY^* \\<br />
LL^* = (X - iY)(X - iY)^* &= XX^* + iXY^* - iYX^* + YY^* \\<br />
\end{align}<br />
</math><br />
<br />
One problem is that there is generally a non-zero delay in Y with respect to X. This creates phase slopes in XY* and YX* from which we can determine the delay very accurately. As a check,<br />
<br />
:<math><br />
\begin{align} <br />
Stokes \, I &= \frac{RR^* + LL^*}{2} = XX^* + YY^* \\<br />
Stokes \, V &= \frac{RR^* - LL^*}{2} = i(XX^* - YY^*) <br />
\end{align}<br />
</math><br />
<br />
For completeness:<br />
<br />
:<math>\begin{align} <br />
Stokes \, Q &= XX^* - YY^* \\<br />
Stokes \, U &= XY^* - YX^* \\<br />
P_{linear} &= \sqrt{U^2 + Q^2} \\<br />
\Theta &= \frac{1}{2}\tan^{-1}{\frac{U}{Q}}<br />
\end{align}<br />
</math><br />
[[File:Linear_to_Circular_Conversion_Figure2.jpg]]<br />
When I plot the quantities I, V, R and L as measured (Figure 1) for geosynchronous satellite Ciel-2, the results look reasonable, except that there are parts of the band where R and L are mis-assigned, and others where they do not separate well.<br />
<br />
The problem is that residual phase slope of Y with respect to X, caused by a difference in delay between the two channels. This can be seen in the upper panel of Figure 2, which shows the uncorrected phases of XY* and YX*. To correct the phases, the RCP phase was fit by a linear least-squares routine, and then the phases were offset by &pi;/2 for both XY* and YX* according to:<br />
<br />
:<math>\begin{align}<br />
XY^{*'} &= XY^*e^{-i(\phi(v) + \frac{\pi}{2})} \\<br />
YX^{*'} &= YX^*e^{ i(\phi(v) + \frac{\pi}{2})}<br />
\end{align}<br />
</math><br />
<br />
where &phi;(v) is the phase fit by the linear function. The corrected phases are shown in the lower panel of Figure 2.<br />
<br />
When the corrected (primed) quantities are used in<br />
<br />
:<math>\begin{align}<br />
RR^* &= XX^* - iXY^{*'} + iYX^{*'} + YY^* \\<br />
LL^* &= XX^* + iXY^{*'} - iYX^{*'} + YY^*<br />
\end{align}<br />
</math><br />
<br />
the resulting channel separation is shown in Figure 3, which shows pretty much perfect channel separation, with the correct polarity.<br />
<br />
This analysis can be performed on all antennas in a completely automated way, to produce the results of Fig. 3. The curves for each antenna are very similar, except that they show differences in amplitude (gain) as a function of frequency. When the curves are scaled to have the same Stokes I levels, the result is shown in Figure 4. Here the 13 antennas are shown in different colors. It is clear that matching Stokes I also causes an excellent match in the other polarizations. Remaining mismatch is likely due to not subtracting a no-signal background prior to scaling the Stokes I curves.<br />
<br />
Also marked in Figure 4 is the location of the beacon signal for Ciel-2, which is at 12.209 GHz. The beacon signal appears in precisely the correct bin (frequency subchannel), indicating that we have precise tuning (certainly not unexpected, but nice to see).<br />
<br />
Just to show that the approach is general, the results for a different communications satellite, Nimiq-5, is shown in Figure 5.<br />
<br />
== Polarization Mixing Correction ==<br />
Due to relative feed rotation between az-al mounted antennas and equatorial mounted antennas</div>Ztwanghttp://www.ovsa.njit.edu/wiki/index.php/Polarization_CalibrationPolarization Calibration2016-09-24T20:55:14Z<p>Ztwang: /* Linear to Circular Conversion */</p>
<hr />
<div>== Linear to Circular Conversion ==<br />
At EOVSA’s linear feeds, in the electric field the linear polarization, X and Y, relates to RCP and LCP (R and L) as:<br />
<br />
:<math><br />
\begin{align} <br />
R = X + iY \\<br />
L = X - iY <br />
\end{align}<br />
</math><br />
<br />
In terms of autocorrelation powers, we have the 4 polarization products XX*, YY*, XY* and YX*, where the * denotes complex conjugation. The quantities RR* and LL* are then<br />
<br />
:<math><br />
\begin{align} <br />
RR^* = (X + iY)(X + iY)^* &= XX^* - iXY^* + iYX^* + YY^* \\<br />
LL^* = (X - iY)(X - iY)^* &= XX^* + iXY^* - iYX^* + YY^* \\<br />
\end{align}<br />
</math><br />
<br />
One problem is that there is generally a non-zero delay in Y with respect to X. This creates phase slopes in XY* and YX* from which we can determine the delay very accurately. As a check,<br />
<br />
:<math><br />
\begin{align} <br />
Stokes \, I &= \frac{RR^* + LL^*}{2} = XX^* + YY^* \\<br />
Stokes \, V &= \frac{RR^* - LL^*}{2} = i(XX^* - YY^*) <br />
\end{align}<br />
</math><br />
<br />
For completeness:<br />
<br />
:<math>\begin{align} <br />
Stokes \, Q &= XX^* - YY^* \\<br />
Stokes \, U &= XY^* - YX^* \\<br />
P_{linear} &= \sqrt{U^2 + Q^2} \\<br />
\Theta &= \frac{1}{2}\tan^{-1}{\frac{U}{Q}}<br />
\end{align}<br />
</math><br />
[[File:Linear_to_Circular_Conversion_Figure1.jpg]]<br />
When I plot the quantities I, V, R and L as measured (Figure 1) for geosynchronous satellite Ciel-2, the results look reasonable, except that there are parts of the band where R and L are mis-assigned, and others where they do not separate well.<br />
<br />
The problem is that residual phase slope of Y with respect to X, caused by a difference in delay between the two channels. This can be seen in the upper panel of Figure 2, which shows the uncorrected phases of XY* and YX*. To correct the phases, the RCP phase was fit by a linear least-squares routine, and then the phases were offset by &pi;/2 for both XY* and YX* according to:<br />
<br />
:<math>\begin{align}<br />
XY^{*'} &= XY^*e^{-i(\phi(v) + \frac{\pi}{2})} \\<br />
YX^{*'} &= YX^*e^{ i(\phi(v) + \frac{\pi}{2})}<br />
\end{align}<br />
</math><br />
<br />
where &phi;(v) is the phase fit by the linear function. The corrected phases are shown in the lower panel of Figure 2.<br />
<br />
When the corrected (primed) quantities are used in<br />
<br />
:<math>\begin{align}<br />
RR^* &= XX^* - iXY^{*'} + iYX^{*'} + YY^* \\<br />
LL^* &= XX^* + iXY^{*'} - iYX^{*'} + YY^*<br />
\end{align}<br />
</math><br />
<br />
the resulting channel separation is shown in Figure 3, which shows pretty much perfect channel separation, with the correct polarity.<br />
<br />
This analysis can be performed on all antennas in a completely automated way, to produce the results of Fig. 3. The curves for each antenna are very similar, except that they show differences in amplitude (gain) as a function of frequency. When the curves are scaled to have the same Stokes I levels, the result is shown in Figure 4. Here the 13 antennas are shown in different colors. It is clear that matching Stokes I also causes an excellent match in the other polarizations. Remaining mismatch is likely due to not subtracting a no-signal background prior to scaling the Stokes I curves.<br />
<br />
Also marked in Figure 4 is the location of the beacon signal for Ciel-2, which is at 12.209 GHz. The beacon signal appears in precisely the correct bin (frequency subchannel), indicating that we have precise tuning (certainly not unexpected, but nice to see).<br />
<br />
Just to show that the approach is general, the results for a different communications satellite, Nimiq-5, is shown in Figure 5.<br />
<br />
== Polarization Mixing Correction ==<br />
Due to relative feed rotation between az-al mounted antennas and equatorial mounted antennas</div>Ztwanghttp://www.ovsa.njit.edu/wiki/index.php/Polarization_CalibrationPolarization Calibration2016-09-24T20:54:03Z<p>Ztwang: /* Linear to Circular Conversion */</p>
<hr />
<div>== Linear to Circular Conversion ==<br />
At EOVSA’s linear feeds, in the electric field the linear polarization, X and Y, relates to RCP and LCP (R and L) as:<br />
<br />
:<math><br />
\begin{align} <br />
R = X + iY \\<br />
L = X - iY <br />
\end{align}<br />
</math><br />
<br />
In terms of autocorrelation powers, we have the 4 polarization products XX*, YY*, XY* and YX*, where the * denotes complex conjugation. The quantities RR* and LL* are then<br />
<br />
:<math><br />
\begin{align} <br />
RR^* = (X + iY)(X + iY)^* &= XX^* - iXY^* + iYX^* + YY^* \\<br />
LL^* = (X - iY)(X - iY)^* &= XX^* + iXY^* - iYX^* + YY^* \\<br />
\end{align}<br />
</math><br />
<br />
One problem is that there is generally a non-zero delay in Y with respect to X. This creates phase slopes in XY* and YX* from which we can determine the delay very accurately. As a check,<br />
<br />
:<math><br />
\begin{align} <br />
Stokes \, I &= \frac{RR^* + LL^*}{2} = XX^* + YY^* \\<br />
Stokes \, V &= \frac{RR^* - LL^*}{2} = i(XX^* - YY^*) <br />
\end{align}<br />
</math><br />
<br />
For completeness:<br />
<br />
:<math>\begin{align} <br />
Stokes \, Q &= XX^* - YY^* \\<br />
Stokes \, U &= XY^* - YX^* \\<br />
P_{linear} &= \sqrt{U^2 + Q^2} \\<br />
\Theta &= \frac{1}{2}\tan^{-1}{\frac{U}{Q}}<br />
\end{align}<br />
</math><br />
[[File:Linear to Circular Conversion Figure1.jpg]]<br />
When I plot the quantities I, V, R and L as measured (Figure 1) for geosynchronous satellite Ciel-2, the results look reasonable, except that there are parts of the band where R and L are mis-assigned, and others where they do not separate well.<br />
<br />
The problem is that residual phase slope of Y with respect to X, caused by a difference in delay between the two channels. This can be seen in the upper panel of Figure 2, which shows the uncorrected phases of XY* and YX*. To correct the phases, the RCP phase was fit by a linear least-squares routine, and then the phases were offset by &pi;/2 for both XY* and YX* according to:<br />
<br />
:<math>\begin{align}<br />
XY^{*'} &= XY^*e^{-i(\phi(v) + \frac{\pi}{2})} \\<br />
YX^{*'} &= YX^*e^{ i(\phi(v) + \frac{\pi}{2})}<br />
\end{align}<br />
</math><br />
<br />
where &phi;(v) is the phase fit by the linear function. The corrected phases are shown in the lower panel of Figure 2.<br />
<br />
When the corrected (primed) quantities are used in<br />
<br />
:<math>\begin{align}<br />
RR^* &= XX^* - iXY^{*'} + iYX^{*'} + YY^* \\<br />
LL^* &= XX^* + iXY^{*'} - iYX^{*'} + YY^*<br />
\end{align}<br />
</math><br />
<br />
the resulting channel separation is shown in Figure 3, which shows pretty much perfect channel separation, with the correct polarity.<br />
<br />
This analysis can be performed on all antennas in a completely automated way, to produce the results of Fig. 3. The curves for each antenna are very similar, except that they show differences in amplitude (gain) as a function of frequency. When the curves are scaled to have the same Stokes I levels, the result is shown in Figure 4. Here the 13 antennas are shown in different colors. It is clear that matching Stokes I also causes an excellent match in the other polarizations. Remaining mismatch is likely due to not subtracting a no-signal background prior to scaling the Stokes I curves.<br />
<br />
Also marked in Figure 4 is the location of the beacon signal for Ciel-2, which is at 12.209 GHz. The beacon signal appears in precisely the correct bin (frequency subchannel), indicating that we have precise tuning (certainly not unexpected, but nice to see).<br />
<br />
Just to show that the approach is general, the results for a different communications satellite, Nimiq-5, is shown in Figure 5.<br />
<br />
== Polarization Mixing Correction ==<br />
Due to relative feed rotation between az-al mounted antennas and equatorial mounted antennas</div>Ztwanghttp://www.ovsa.njit.edu/wiki/index.php/Polarization_CalibrationPolarization Calibration2016-09-24T20:53:06Z<p>Ztwang: /* Linear to Circular Conversion */</p>
<hr />
<div>== Linear to Circular Conversion ==<br />
At EOVSA’s linear feeds, in the electric field the linear polarization, X and Y, relates to RCP and LCP (R and L) as:<br />
<br />
:<math><br />
\begin{align} <br />
R = X + iY \\<br />
L = X - iY <br />
\end{align}<br />
</math><br />
<br />
In terms of autocorrelation powers, we have the 4 polarization products XX*, YY*, XY* and YX*, where the * denotes complex conjugation. The quantities RR* and LL* are then<br />
<br />
:<math><br />
\begin{align} <br />
RR^* = (X + iY)(X + iY)^* &= XX^* - iXY^* + iYX^* + YY^* \\<br />
LL^* = (X - iY)(X - iY)^* &= XX^* + iXY^* - iYX^* + YY^* \\<br />
\end{align}<br />
</math><br />
<br />
One problem is that there is generally a non-zero delay in Y with respect to X. This creates phase slopes in XY* and YX* from which we can determine the delay very accurately. As a check,<br />
<br />
:<math><br />
\begin{align} <br />
Stokes \, I &= \frac{RR^* + LL^*}{2} = XX^* + YY^* \\<br />
Stokes \, V &= \frac{RR^* - LL^*}{2} = i(XX^* - YY^*) <br />
\end{align}<br />
</math><br />
<br />
For completeness:<br />
<br />
:<math>\begin{align} <br />
Stokes \, Q &= XX^* - YY^* \\<br />
Stokes \, U &= XY^* - YX^* \\<br />
P_{linear} &= \sqrt{U^2 + Q^2} \\<br />
\Theta &= \frac{1}{2}\tan^{-1}{\frac{U}{Q}}<br />
\end{align}<br />
</math><br />
[[File:Figure1.jpg]]<br />
When I plot the quantities I, V, R and L as measured (Figure 1) for geosynchronous satellite Ciel-2, the results look reasonable, except that there are parts of the band where R and L are mis-assigned, and others where they do not separate well.<br />
<br />
The problem is that residual phase slope of Y with respect to X, caused by a difference in delay between the two channels. This can be seen in the upper panel of Figure 2, which shows the uncorrected phases of XY* and YX*. To correct the phases, the RCP phase was fit by a linear least-squares routine, and then the phases were offset by &pi;/2 for both XY* and YX* according to:<br />
<br />
:<math>\begin{align}<br />
XY^{*'} &= XY^*e^{-i(\phi(v) + \frac{\pi}{2})} \\<br />
YX^{*'} &= YX^*e^{ i(\phi(v) + \frac{\pi}{2})}<br />
\end{align}<br />
</math><br />
<br />
where &phi;(v) is the phase fit by the linear function. The corrected phases are shown in the lower panel of Figure 2.<br />
<br />
When the corrected (primed) quantities are used in<br />
<br />
:<math>\begin{align}<br />
RR^* &= XX^* - iXY^{*'} + iYX^{*'} + YY^* \\<br />
LL^* &= XX^* + iXY^{*'} - iYX^{*'} + YY^*<br />
\end{align}<br />
</math><br />
<br />
the resulting channel separation is shown in Figure 3, which shows pretty much perfect channel separation, with the correct polarity.<br />
<br />
This analysis can be performed on all antennas in a completely automated way, to produce the results of Fig. 3. The curves for each antenna are very similar, except that they show differences in amplitude (gain) as a function of frequency. When the curves are scaled to have the same Stokes I levels, the result is shown in Figure 4. Here the 13 antennas are shown in different colors. It is clear that matching Stokes I also causes an excellent match in the other polarizations. Remaining mismatch is likely due to not subtracting a no-signal background prior to scaling the Stokes I curves.<br />
<br />
Also marked in Figure 4 is the location of the beacon signal for Ciel-2, which is at 12.209 GHz. The beacon signal appears in precisely the correct bin (frequency subchannel), indicating that we have precise tuning (certainly not unexpected, but nice to see).<br />
<br />
Just to show that the approach is general, the results for a different communications satellite, Nimiq-5, is shown in Figure 5.<br />
<br />
== Polarization Mixing Correction ==<br />
Due to relative feed rotation between az-al mounted antennas and equatorial mounted antennas</div>Ztwanghttp://www.ovsa.njit.edu/wiki/index.php/File:Figure1.jpgFile:Figure1.jpg2016-09-24T20:47:33Z<p>Ztwang: </p>
<hr />
<div></div>Ztwanghttp://www.ovsa.njit.edu/wiki/index.php/Polarization_CalibrationPolarization Calibration2016-09-24T20:45:18Z<p>Ztwang: /* Linear to Circular Conversion */</p>
<hr />
<div>== Linear to Circular Conversion ==<br />
At EOVSA’s linear feeds, in the electric field the linear polarization, X and Y, relates to RCP and LCP (R and L) as:<br />
<br />
:<math><br />
\begin{align} <br />
R = X + iY \\<br />
L = X - iY <br />
\end{align}<br />
</math><br />
<br />
In terms of autocorrelation powers, we have the 4 polarization products XX*, YY*, XY* and YX*, where the * denotes complex conjugation. The quantities RR* and LL* are then<br />
<br />
:<math><br />
\begin{align} <br />
RR^* = (X + iY)(X + iY)^* &= XX^* - iXY^* + iYX^* + YY^* \\<br />
LL^* = (X - iY)(X - iY)^* &= XX^* + iXY^* - iYX^* + YY^* \\<br />
\end{align}<br />
</math><br />
<br />
One problem is that there is generally a non-zero delay in Y with respect to X. This creates phase slopes in XY* and YX* from which we can determine the delay very accurately. As a check,<br />
<br />
:<math><br />
\begin{align} <br />
Stokes \, I &= \frac{RR^* + LL^*}{2} = XX^* + YY^* \\<br />
Stokes \, V &= \frac{RR^* - LL^*}{2} = i(XX^* - YY^*) <br />
\end{align}<br />
</math><br />
<br />
For completeness:<br />
<br />
:<math>\begin{align} <br />
Stokes \, Q &= XX^* - YY^* \\<br />
Stokes \, U &= XY^* - YX^* \\<br />
P_{linear} &= \sqrt{U^2 + Q^2} \\<br />
\Theta &= \frac{1}{2}\tan^{-1}{\frac{U}{Q}}<br />
\end{align}<br />
</math><br />
[[File:Example.jpg]]<br />
When I plot the quantities I, V, R and L as measured (Figure 1) for geosynchronous satellite Ciel-2, the results look reasonable, except that there are parts of the band where R and L are mis-assigned, and others where they do not separate well.<br />
<br />
The problem is that residual phase slope of Y with respect to X, caused by a difference in delay between the two channels. This can be seen in the upper panel of Figure 2, which shows the uncorrected phases of XY* and YX*. To correct the phases, the RCP phase was fit by a linear least-squares routine, and then the phases were offset by &pi;/2 for both XY* and YX* according to:<br />
<br />
:<math>\begin{align}<br />
XY^{*'} &= XY^*e^{-i(\phi(v) + \frac{\pi}{2})} \\<br />
YX^{*'} &= YX^*e^{ i(\phi(v) + \frac{\pi}{2})}<br />
\end{align}<br />
</math><br />
<br />
where &phi;(v) is the phase fit by the linear function. The corrected phases are shown in the lower panel of Figure 2.<br />
<br />
When the corrected (primed) quantities are used in<br />
<br />
:<math>\begin{align}<br />
RR^* &= XX^* - iXY^{*'} + iYX^{*'} + YY^* \\<br />
LL^* &= XX^* + iXY^{*'} - iYX^{*'} + YY^*<br />
\end{align}<br />
</math><br />
<br />
the resulting channel separation is shown in Figure 3, which shows pretty much perfect channel separation, with the correct polarity.<br />
<br />
This analysis can be performed on all antennas in a completely automated way, to produce the results of Fig. 3. The curves for each antenna are very similar, except that they show differences in amplitude (gain) as a function of frequency. When the curves are scaled to have the same Stokes I levels, the result is shown in Figure 4. Here the 13 antennas are shown in different colors. It is clear that matching Stokes I also causes an excellent match in the other polarizations. Remaining mismatch is likely due to not subtracting a no-signal background prior to scaling the Stokes I curves.<br />
<br />
Also marked in Figure 4 is the location of the beacon signal for Ciel-2, which is at 12.209 GHz. The beacon signal appears in precisely the correct bin (frequency subchannel), indicating that we have precise tuning (certainly not unexpected, but nice to see).<br />
<br />
Just to show that the approach is general, the results for a different communications satellite, Nimiq-5, is shown in Figure 5.<br />
<br />
== Polarization Mixing Correction ==<br />
Due to relative feed rotation between az-al mounted antennas and equatorial mounted antennas</div>Ztwanghttp://www.ovsa.njit.edu/wiki/index.php/Polarization_CalibrationPolarization Calibration2016-09-24T20:38:45Z<p>Ztwang: /* Linear to Circular Conversion */</p>
<hr />
<div>== Linear to Circular Conversion ==<br />
At EOVSA’s linear feeds, in the electric field the linear polarization, X and Y, relates to RCP and LCP (R and L) as:<br />
<br />
:<math><br />
\begin{align} <br />
R = X + iY \\<br />
L = X - iY <br />
\end{align}<br />
</math><br />
<br />
In terms of autocorrelation powers, we have the 4 polarization products XX*, YY*, XY* and YX*, where the * denotes complex conjugation. The quantities RR* and LL* are then<br />
<br />
:<math><br />
\begin{align} <br />
RR^* = (X + iY)(X + iY)^* &= XX^* - iXY^* + iYX^* + YY^* \\<br />
LL^* = (X - iY)(X - iY)^* &= XX^* + iXY^* - iYX^* + YY^* \\<br />
\end{align}<br />
</math><br />
<br />
One problem is that there is generally a non-zero delay in Y with respect to X. This creates phase slopes in XY* and YX* from which we can determine the delay very accurately. As a check,<br />
<br />
:<math><br />
\begin{align} <br />
Stokes \, I &= \frac{RR^* + LL^*}{2} = XX^* + YY^* \\<br />
Stokes \, V &= \frac{RR^* - LL^*}{2} = i(XX^* - YY^*) <br />
\end{align}<br />
</math><br />
<br />
For completeness:<br />
<br />
:<math>\begin{align} <br />
Stokes \, Q &= XX^* - YY^* \\<br />
Stokes \, U &= XY^* - YX^* \\<br />
P_{linear} &= \sqrt{U^2 + Q^2} \\<br />
\Theta &= \frac{1}{2}\tan^{-1}{\frac{U}{Q}}<br />
\end{align}<br />
</math><br />
<br />
When I plot the quantities I, V, R and L as measured (Figure 1) for geosynchronous satellite Ciel-2, the results look reasonable, except that there are parts of the band where R and L are mis-assigned, and others where they do not separate well.<br />
<br />
The problem is that residual phase slope of Y with respect to X, caused by a difference in delay between the two channels. This can be seen in the upper panel of Figure 2, which shows the uncorrected phases of XY* and YX*. To correct the phases, the RCP phase was fit by a linear least-squares routine, and then the phases were offset by &pi;/2 for both XY* and YX* according to:<br />
<br />
:<math>\begin{align}<br />
XY^{*'} &= XY^*e^{-i(\phi(v) + \frac{\pi}{2})} \\<br />
YX^{*'} &= YX^*e^{ i(\phi(v) + \frac{\pi}{2})}<br />
\end{align}<br />
</math><br />
<br />
where &phi;(v) is the phase fit by the linear function. The corrected phases are shown in the lower panel of Figure 2.<br />
<br />
When the corrected (primed) quantities are used in<br />
<br />
:<math>\begin{align}<br />
RR^* &= XX^* - iXY^{*'} + iYX^{*'} + YY^* \\<br />
LL^* &= XX^* + iXY^{*'} - iYX^{*'} + YY^*<br />
\end{align}<br />
</math><br />
<br />
the resulting channel separation is shown in Figure 3, which shows pretty much perfect channel separation, with the correct polarity.<br />
<br />
This analysis can be performed on all antennas in a completely automated way, to produce the results of Fig. 3. The curves for each antenna are very similar, except that they show differences in amplitude (gain) as a function of frequency. When the curves are scaled to have the same Stokes I levels, the result is shown in Figure 4. Here the 13 antennas are shown in different colors. It is clear that matching Stokes I also causes an excellent match in the other polarizations. Remaining mismatch is likely due to not subtracting a no-signal background prior to scaling the Stokes I curves.<br />
<br />
Also marked in Figure 4 is the location of the beacon signal for Ciel-2, which is at 12.209 GHz. The beacon signal appears in precisely the correct bin (frequency subchannel), indicating that we have precise tuning (certainly not unexpected, but nice to see).<br />
<br />
Just to show that the approach is general, the results for a different communications satellite, Nimiq-5, is shown in Figure 5.<br />
<br />
== Polarization Mixing Correction ==<br />
Due to relative feed rotation between az-al mounted antennas and equatorial mounted antennas</div>Ztwanghttp://www.ovsa.njit.edu/wiki/index.php/Polarization_CalibrationPolarization Calibration2016-09-24T20:37:45Z<p>Ztwang: /* Linear to Circular Conversion */</p>
<hr />
<div>== Linear to Circular Conversion ==<br />
At EOVSA’s linear feeds, in the electric field the linear polarization, X and Y, relates to RCP and LCP (R and L) as:<br />
<br />
:<math><br />
\begin{align} <br />
R = X + iY \\<br />
L = X - iY <br />
\end{align}<br />
</math><br />
<br />
In terms of autocorrelation powers, we have the 4 polarization products XX*, YY*, XY* and YX*, where the * denotes complex conjugation. The quantities RR* and LL* are then<br />
<br />
:<math><br />
\begin{align} <br />
RR^* = (X + iY)(X + iY)^* &= XX^* - iXY^* + iYX^* + YY^* \\<br />
LL^* = (X - iY)(X - iY)^* &= XX^* + iXY^* - iYX^* + YY^* \\<br />
\end{align}<br />
</math><br />
<br />
One problem is that there is generally a non-zero delay in Y with respect to X. This creates phase slopes in XY* and YX* from which we can determine the delay very accurately. As a check,<br />
<br />
:<math><br />
\begin{align} <br />
Stokes \, I &= \frac{RR^* + LL^*}{2} = XX^* + YY^* \\<br />
Stokes \, V &= \frac{RR^* - LL^*}{2} = i(XX^* - YY^*) <br />
\end{align}<br />
</math><br />
<br />
For completeness:<br />
<br />
:<math>\begin{align} <br />
Stokes \, Q &= XX^* - YY^* \\<br />
Stokes \, U &= XY^* - YX^* \\<br />
P_{linear} &= \sqrt{U^2 + Q^2} \\<br />
\Theta &= \frac{1}{2}\tan^{-1}{\frac{U}{Q}}<br />
\end{align}<br />
</math><br />
<br />
When I plot the quantities I, V, R and L as measured (Figure 1) for geosynchronous satellite Ciel-2, the results look reasonable, except that there are parts of the band where R and L are mis-assigned, and others where they do not separate well.<br />
<br />
The problem is that residual phase slope of Y with respect to X, caused by a difference in delay between the two channels. This can be seen in the upper panel of Figure 2, which shows the uncorrected phases of XY* and YX*. To correct the phases, the RCP phase was fit by a linear least-squares routine, and then the phases were offset by &pi;/2 for both XY* and YX* according to:<br />
<br />
:<math>\begin{align}<br />
XY^{*'} &= XY^*e^{-i(\phi(v) + \frac{\pi}{2})} \\<br />
YX^{*'} &= YX^*e^{ i(\phi(v) + \frac{\pi}{2})}<br />
\end{align}<br />
</math><br />
<br />
where &phi;(v) is the phase fit by the linear function. The corrected phases are shown in the lower panel of Figure 2.<br />
<br />
When the corrected (primed) quantities are used in<br />
<br />
:<math>\begin{align}<br />
RR^* &= XX^* - iXY^{*'} + iYX^{*'} + YY^* \\<br />
LL^* &= XX^* + iXY^{*'} - iYX^{*'} + YY^*<br />
\end{align}<br />
</math><br />
<br />
== Polarization Mixing Correction ==<br />
Due to relative feed rotation between az-al mounted antennas and equatorial mounted antennas</div>Ztwanghttp://www.ovsa.njit.edu/wiki/index.php/Polarization_CalibrationPolarization Calibration2016-09-24T20:37:25Z<p>Ztwang: /* Linear to Circular Conversion */</p>
<hr />
<div>== Linear to Circular Conversion ==<br />
At EOVSA’s linear feeds, in the electric field the linear polarization, X and Y, relates to RCP and LCP (R and L) as:<br />
<br />
:<math><br />
\begin{align} <br />
R = X + iY \\<br />
L = X - iY <br />
\end{align}<br />
</math><br />
<br />
In terms of autocorrelation powers, we have the 4 polarization products XX*, YY*, XY* and YX*, where the * denotes complex conjugation. The quantities RR* and LL* are then<br />
<br />
:<math><br />
\begin{align} <br />
RR^* = (X + iY)(X + iY)^* &= XX^* - iXY^* + iYX^* + YY^* \\<br />
LL^* = (X - iY)(X - iY)^* &= XX^* + iXY^* - iYX^* + YY^* \\<br />
\end{align}<br />
</math><br />
<br />
One problem is that there is generally a non-zero delay in Y with respect to X. This creates phase slopes in XY* and YX* from which we can determine the delay very accurately. As a check,<br />
<br />
:<math><br />
\begin{align} <br />
Stokes \, I &= \frac{RR^* + LL^*}{2} = XX^* + YY^* \\<br />
Stokes \, V &= \frac{RR^* - LL^*}{2} = i(XX^* - YY^*) <br />
\end{align}<br />
</math><br />
<br />
For completeness:<br />
<br />
:<math>\begin{align} <br />
Stokes \, Q &= XX^* - YY^* \\<br />
Stokes \, U &= XY^* - YX^* \\<br />
P_{linear} &= \sqrt{U^2 + Q^2} \\<br />
\Theta &= \frac{1}{2}\tan^{-1}{\frac{U}{Q}}<br />
\end{align}<br />
</math><br />
<br />
When I plot the quantities I, V, R and L as measured (Figure 1) for geosynchronous satellite Ciel-2, the results look reasonable, except that there are parts of the band where R and L are mis-assigned, and others where they do not separate well.<br />
<br />
The problem is that residual phase slope of Y with respect to X, caused by a difference in delay between the two channels. This can be seen in the upper panel of Figure 2, which shows the uncorrected phases of XY* and YX*. To correct the phases, the RCP phase was fit by a linear least-squares routine, and then the phases were offset by &pi;/2 for both XY* and YX* according to:<br />
<br />
:<math>\begin{align}<br />
XY^{*'} &= XY^*e^{-i(\phi(v) + \frac{\pi}{2})} <br />
YX^{*'} &= YX^*e^{ i(\phi(v) + \frac{\pi}{2})}<br />
\end{align}<br />
</math><br />
<br />
where &phi;(v) is the phase fit by the linear function. The corrected phases are shown in the lower panel of Figure 2.<br />
<br />
When the corrected (primed) quantities are used in<br />
<br />
:<math>\begin{align}<br />
RR^* &= XX^* - iXY^{*'} + iYX^{*'} + YY^*<br />
LL^* &= XX^* + iXY^{*'} - iYX^{*'} + YY^*<br />
\end{align}<br />
</math><br />
<br />
== Polarization Mixing Correction ==<br />
Due to relative feed rotation between az-al mounted antennas and equatorial mounted antennas</div>Ztwanghttp://www.ovsa.njit.edu/wiki/index.php/Polarization_CalibrationPolarization Calibration2016-09-24T20:36:53Z<p>Ztwang: /* Linear to Circular Conversion */</p>
<hr />
<div>== Linear to Circular Conversion ==<br />
At EOVSA’s linear feeds, in the electric field the linear polarization, X and Y, relates to RCP and LCP (R and L) as:<br />
<br />
:<math><br />
\begin{align} <br />
R = X + iY \\<br />
L = X - iY <br />
\end{align}<br />
</math><br />
<br />
In terms of autocorrelation powers, we have the 4 polarization products XX*, YY*, XY* and YX*, where the * denotes complex conjugation. The quantities RR* and LL* are then<br />
<br />
:<math><br />
\begin{align} <br />
RR^* = (X + iY)(X + iY)^* &= XX^* - iXY^* + iYX^* + YY^* \\<br />
LL^* = (X - iY)(X - iY)^* &= XX^* + iXY^* - iYX^* + YY^* \\<br />
\end{align}<br />
</math><br />
<br />
One problem is that there is generally a non-zero delay in Y with respect to X. This creates phase slopes in XY* and YX* from which we can determine the delay very accurately. As a check,<br />
<br />
:<math><br />
\begin{align} <br />
Stokes \, I &= \frac{RR^* + LL^*}{2} = XX^* + YY^* \\<br />
Stokes \, V &= \frac{RR^* - LL^*}{2} = i(XX^* - YY^*) <br />
\end{align}<br />
</math><br />
<br />
For completeness:<br />
<br />
:<math>\begin{align} <br />
Stokes \, Q &= XX^* - YY^* \\<br />
Stokes \, U &= XY^* - YX^* \\<br />
P_{linear} &= \sqrt{U^2 + Q^2} \\<br />
\Theta &= \frac{1}{2}\tan^{-1}{\frac{U}{Q}}<br />
\end{align}<br />
</math><br />
<br />
When I plot the quantities I, V, R and L as measured (Figure 1) for geosynchronous satellite Ciel-2, the results look reasonable, except that there are parts of the band where R and L are mis-assigned, and others where they do not separate well.<br />
<br />
The problem is that residual phase slope of Y with respect to X, caused by a difference in delay between the two channels. This can be seen in the upper panel of Figure 2, which shows the uncorrected phases of XY* and YX*. To correct the phases, the RCP phase was fit by a linear least-squares routine, and then the phases were offset by &pi;/2 for both XY* and YX* according to:<br />
<br />
:<math>\begin{align}<br />
XY^{*}' &= XY^*e^{-i(\phi(v) + \frac{\pi}{2})} <br />
YX^{*}' &= YX^*e^{ i(\phi(v) + \frac{\pi}{2})}<br />
\end{align}<br />
</math><br />
<br />
where &phi;(v) is the phase fit by the linear function. The corrected phases are shown in the lower panel of Figure 2.<br />
<br />
When the corrected (primed) quantities are used in<br />
<br />
:<math>\begin{align}<br />
RR^* &= XX^* - iXY^{*'} + iYX^{*'} + YY^*<br />
LL^* &= XX^* + iXY^{*'} - iYX^{*'} + YY^*<br />
\end{align}<br />
</math><br />
<br />
== Polarization Mixing Correction ==<br />
Due to relative feed rotation between az-al mounted antennas and equatorial mounted antennas</div>Ztwanghttp://www.ovsa.njit.edu/wiki/index.php/Polarization_CalibrationPolarization Calibration2016-09-24T20:36:30Z<p>Ztwang: /* Linear to Circular Conversion */</p>
<hr />
<div>== Linear to Circular Conversion ==<br />
At EOVSA’s linear feeds, in the electric field the linear polarization, X and Y, relates to RCP and LCP (R and L) as:<br />
<br />
:<math><br />
\begin{align} <br />
R = X + iY \\<br />
L = X - iY <br />
\end{align}<br />
</math><br />
<br />
In terms of autocorrelation powers, we have the 4 polarization products XX*, YY*, XY* and YX*, where the * denotes complex conjugation. The quantities RR* and LL* are then<br />
<br />
:<math><br />
\begin{align} <br />
RR^* = (X + iY)(X + iY)^* &= XX^* - iXY^* + iYX^* + YY^* \\<br />
LL^* = (X - iY)(X - iY)^* &= XX^* + iXY^* - iYX^* + YY^* \\<br />
\end{align}<br />
</math><br />
<br />
One problem is that there is generally a non-zero delay in Y with respect to X. This creates phase slopes in XY* and YX* from which we can determine the delay very accurately. As a check,<br />
<br />
:<math><br />
\begin{align} <br />
Stokes \, I &= \frac{RR^* + LL^*}{2} = XX^* + YY^* \\<br />
Stokes \, V &= \frac{RR^* - LL^*}{2} = i(XX^* - YY^*) <br />
\end{align}<br />
</math><br />
<br />
For completeness:<br />
<br />
:<math>\begin{align} <br />
Stokes \, Q &= XX^* - YY^* \\<br />
Stokes \, U &= XY^* - YX^* \\<br />
P_{linear} &= \sqrt{U^2 + Q^2} \\<br />
\Theta &= \frac{1}{2}\tan^{-1}{\frac{U}{Q}}<br />
\end{align}<br />
</math><br />
<br />
When I plot the quantities I, V, R and L as measured (Figure 1) for geosynchronous satellite Ciel-2, the results look reasonable, except that there are parts of the band where R and L are mis-assigned, and others where they do not separate well.<br />
<br />
The problem is that residual phase slope of Y with respect to X, caused by a difference in delay between the two channels. This can be seen in the upper panel of Figure 2, which shows the uncorrected phases of XY* and YX*. To correct the phases, the RCP phase was fit by a linear least-squares routine, and then the phases were offset by &pi;/2 for both XY* and YX* according to:<br />
<br />
:<math>\begin{align}<br />
XY^{*}' &= XY^*e^{-i(\phi(v) + \frac{\pi}{2})} <br />
YX^{*}' &= YX^*e^{ i(\phi(v) + \frac{\pi}{2})}<br />
\end{align}<br />
</math><br />
<br />
where &phi;(v) is the phase fit by the linear function. The corrected phases are shown in the lower panel of Figure 2.<br />
<br />
When the corrected (primed) quantities are used in<br />
<br />
:<math>\begin{align}<br />
RR^* &= XX^* - iXY^{*}' + iYX^{*}' + YY^*<br />
LL^* &= XX^* + iXY^{*}' - iYX^{*}' + YY^*<br />
\end{align}<br />
</math><br />
<br />
== Polarization Mixing Correction ==<br />
Due to relative feed rotation between az-al mounted antennas and equatorial mounted antennas</div>Ztwanghttp://www.ovsa.njit.edu/wiki/index.php/Polarization_CalibrationPolarization Calibration2016-09-24T20:35:58Z<p>Ztwang: /* Linear to Circular Conversion */</p>
<hr />
<div>== Linear to Circular Conversion ==<br />
At EOVSA’s linear feeds, in the electric field the linear polarization, X and Y, relates to RCP and LCP (R and L) as:<br />
<br />
:<math><br />
\begin{align} <br />
R = X + iY \\<br />
L = X - iY <br />
\end{align}<br />
</math><br />
<br />
In terms of autocorrelation powers, we have the 4 polarization products XX*, YY*, XY* and YX*, where the * denotes complex conjugation. The quantities RR* and LL* are then<br />
<br />
:<math><br />
\begin{align} <br />
RR^* = (X + iY)(X + iY)^* &= XX^* - iXY^* + iYX^* + YY^* \\<br />
LL^* = (X - iY)(X - iY)^* &= XX^* + iXY^* - iYX^* + YY^* \\<br />
\end{align}<br />
</math><br />
<br />
One problem is that there is generally a non-zero delay in Y with respect to X. This creates phase slopes in XY* and YX* from which we can determine the delay very accurately. As a check,<br />
<br />
:<math><br />
\begin{align} <br />
Stokes \, I &= \frac{RR^* + LL^*}{2} = XX^* + YY^* \\<br />
Stokes \, V &= \frac{RR^* - LL^*}{2} = i(XX^* - YY^*) <br />
\end{align}<br />
</math><br />
<br />
For completeness:<br />
<br />
:<math>\begin{align} <br />
Stokes \, Q &= XX^* - YY^* \\<br />
Stokes \, U &= XY^* - YX^* \\<br />
P_{linear} &= \sqrt{U^2 + Q^2} \\<br />
\Theta &= \frac{1}{2}\tan^{-1}{\frac{U}{Q}}<br />
\end{align}<br />
</math><br />
<br />
When I plot the quantities I, V, R and L as measured (Figure 1) for geosynchronous satellite Ciel-2, the results look reasonable, except that there are parts of the band where R and L are mis-assigned, and others where they do not separate well.<br />
<br />
The problem is that residual phase slope of Y with respect to X, caused by a difference in delay between the two channels. This can be seen in the upper panel of Figure 2, which shows the uncorrected phases of XY* and YX*. To correct the phases, the RCP phase was fit by a linear least-squares routine, and then the phases were offset by &pi;/2 for both XY* and YX* according to:<br />
<br />
:<math>\begin{align}<br />
XY^{*}' &= XY^*e^{-i(\phi(v) + \frac{\pi}{2})} <br />
YX^{*}' &= YX^*e^{ i(\phi(v) + \frac{\pi}{2})}<br />
\end{align}<br />
</math><br />
<br />
where &phi;(v) is the phase fit by the linear function. The corrected phases are shown in the lower panel of Figure 2.<br />
<br />
When the corrected (primed) quantities are used in<br />
<br />
:<math>\begin{align}<br />
RR^* &= XX^* - iXY^(*)' + iYX^(*)' + YY^*<br />
LL^* &= XX^* + iXY^(*)' - iYX^(*)' + YY^*<br />
\end{align}<br />
</math><br />
<br />
== Polarization Mixing Correction ==<br />
Due to relative feed rotation between az-al mounted antennas and equatorial mounted antennas</div>Ztwanghttp://www.ovsa.njit.edu/wiki/index.php/Polarization_CalibrationPolarization Calibration2016-09-24T20:35:09Z<p>Ztwang: /* Linear to Circular Conversion */</p>
<hr />
<div>== Linear to Circular Conversion ==<br />
At EOVSA’s linear feeds, in the electric field the linear polarization, X and Y, relates to RCP and LCP (R and L) as:<br />
<br />
:<math><br />
\begin{align} <br />
R = X + iY \\<br />
L = X - iY <br />
\end{align}<br />
</math><br />
<br />
In terms of autocorrelation powers, we have the 4 polarization products XX*, YY*, XY* and YX*, where the * denotes complex conjugation. The quantities RR* and LL* are then<br />
<br />
:<math><br />
\begin{align} <br />
RR^* = (X + iY)(X + iY)^* &= XX^* - iXY^* + iYX^* + YY^* \\<br />
LL^* = (X - iY)(X - iY)^* &= XX^* + iXY^* - iYX^* + YY^* \\<br />
\end{align}<br />
</math><br />
<br />
One problem is that there is generally a non-zero delay in Y with respect to X. This creates phase slopes in XY* and YX* from which we can determine the delay very accurately. As a check,<br />
<br />
:<math><br />
\begin{align} <br />
Stokes \, I &= \frac{RR^* + LL^*}{2} = XX^* + YY^* \\<br />
Stokes \, V &= \frac{RR^* - LL^*}{2} = i(XX^* - YY^*) <br />
\end{align}<br />
</math><br />
<br />
For completeness:<br />
<br />
:<math>\begin{align} <br />
Stokes \, Q &= XX^* - YY^* \\<br />
Stokes \, U &= XY^* - YX^* \\<br />
P_{linear} &= \sqrt{U^2 + Q^2} \\<br />
\Theta &= \frac{1}{2}\tan^{-1}{\frac{U}{Q}}<br />
\end{align}<br />
</math><br />
<br />
When I plot the quantities I, V, R and L as measured (Figure 1) for geosynchronous satellite Ciel-2, the results look reasonable, except that there are parts of the band where R and L are mis-assigned, and others where they do not separate well.<br />
<br />
The problem is that residual phase slope of Y with respect to X, caused by a difference in delay between the two channels. This can be seen in the upper panel of Figure 2, which shows the uncorrected phases of XY* and YX*. To correct the phases, the RCP phase was fit by a linear least-squares routine, and then the phases were offset by &pi;/2 for both XY* and YX* according to:<br />
<br />
:<math>\begin{align}<br />
XY^{*}' &= XY^*e^{-i(\phi(v) + \frac{\pi}{2})} <br />
YX^{*}' &= YX^*e^{ i(\phi(v) + \frac{\pi}{2})}<br />
\end{align}<br />
</math><br />
<br />
where &phi;(v) is the phase fit by the linear function. The corrected phases are shown in the lower panel of Figure 2.<br />
<br />
When the corrected (primed) quantities are used in<br />
<br />
:<math>\begin{align}<br />
RR^* &= XX^* - iXY^(*)' + iYX^(*)' + YY^*<br />
LL^* &= XX^* + iXY^(*') - iYX^(*') + YY^*<br />
\end{align}<br />
</math><br />
<br />
== Polarization Mixing Correction ==<br />
Due to relative feed rotation between az-al mounted antennas and equatorial mounted antennas</div>Ztwanghttp://www.ovsa.njit.edu/wiki/index.php/Polarization_CalibrationPolarization Calibration2016-09-24T20:30:35Z<p>Ztwang: /* Linear to Circular Conversion */</p>
<hr />
<div>== Linear to Circular Conversion ==<br />
At EOVSA’s linear feeds, in the electric field the linear polarization, X and Y, relates to RCP and LCP (R and L) as:<br />
<br />
:<math><br />
\begin{align} <br />
R = X + iY \\<br />
L = X - iY <br />
\end{align}<br />
</math><br />
<br />
In terms of autocorrelation powers, we have the 4 polarization products XX*, YY*, XY* and YX*, where the * denotes complex conjugation. The quantities RR* and LL* are then<br />
<br />
:<math><br />
\begin{align} <br />
RR^* = (X + iY)(X + iY)^* &= XX^* - iXY^* + iYX^* + YY^* \\<br />
LL^* = (X - iY)(X - iY)^* &= XX^* + iXY^* - iYX^* + YY^* \\<br />
\end{align}<br />
</math><br />
<br />
One problem is that there is generally a non-zero delay in Y with respect to X. This creates phase slopes in XY* and YX* from which we can determine the delay very accurately. As a check,<br />
<br />
:<math><br />
\begin{align} <br />
Stokes \, I &= \frac{RR^* + LL^*}{2} = XX^* + YY^* \\<br />
Stokes \, V &= \frac{RR^* - LL^*}{2} = i(XX^* - YY^*) <br />
\end{align}<br />
</math><br />
<br />
For completeness:<br />
<br />
:<math>\begin{align} <br />
Stokes \, Q &= XX^* - YY^* \\<br />
Stokes \, U &= XY^* - YX^* \\<br />
P_{linear} &= \sqrt{U^2 + Q^2} \\<br />
\Theta &= \frac{1}{2}\tan^{-1}{\frac{U}{Q}}<br />
\end{align}<br />
</math><br />
<br />
When I plot the quantities I, V, R and L as measured (Figure 1) for geosynchronous satellite Ciel-2, the results look reasonable, except that there are parts of the band where R and L are mis-assigned, and others where they do not separate well.<br />
<br />
The problem is that residual phase slope of Y with respect to X, caused by a difference in delay between the two channels. This can be seen in the upper panel of Figure 2, which shows the uncorrected phases of XY* and YX*. To correct the phases, the RCP phase was fit by a linear least-squares routine, and then the phases were offset by &pi;/2 for both XY* and YX* according to:<br />
<br />
:<math>\begin{align}<br />
XY^{*'} &= XY^*e^{-i(\phi(v) + \frac{\pi}{2})} <br />
<br />
\end{align}<br />
</math><br />
<br />
== Polarization Mixing Correction ==<br />
Due to relative feed rotation between az-al mounted antennas and equatorial mounted antennas</div>Ztwanghttp://www.ovsa.njit.edu/wiki/index.php/Polarization_CalibrationPolarization Calibration2016-09-24T20:26:56Z<p>Ztwang: /* Linear to Circular Conversion */</p>
<hr />
<div>== Linear to Circular Conversion ==<br />
At EOVSA’s linear feeds, in the electric field the linear polarization, X and Y, relates to RCP and LCP (R and L) as:<br />
<br />
:<math><br />
\begin{align} <br />
R = X + iY \\<br />
L = X - iY <br />
\end{align}<br />
</math><br />
<br />
In terms of autocorrelation powers, we have the 4 polarization products XX*, YY*, XY* and YX*, where the * denotes complex conjugation. The quantities RR* and LL* are then<br />
<br />
:<math><br />
\begin{align} <br />
RR^* = (X + iY)(X + iY)^* &= XX^* - iXY^* + iYX^* + YY^* \\<br />
LL^* = (X - iY)(X - iY)^* &= XX^* + iXY^* - iYX^* + YY^* \\<br />
\end{align}<br />
</math><br />
<br />
One problem is that there is generally a non-zero delay in Y with respect to X. This creates phase slopes in XY* and YX* from which we can determine the delay very accurately. As a check,<br />
<br />
:<math><br />
\begin{align} <br />
Stokes \, I &= \frac{RR^* + LL^*}{2} = XX^* + YY^* \\<br />
Stokes \, V &= \frac{RR^* - LL^*}{2} = i(XX^* - YY^*) <br />
\end{align}<br />
</math><br />
<br />
For completeness:<br />
<br />
:<math>\begin{align} <br />
Stokes \, Q &= XX^* - YY^* \\<br />
Stokes \, U &= XY^* - YX^* \\<br />
P_{linear} &= \sqrt{U^2 + Q^2} \\<br />
\Theta &= \frac{1}{2}\tan^{-1}{\frac{U}{Q}}<br />
\end{align}<br />
</math><br />
<br />
When I plot the quantities I, V, R and L as measured (Figure 1) for geosynchronous satellite Ciel-2, the results look reasonable, except that there are parts of the band where R and L are mis-assigned, and others where they do not separate well.<br />
<br />
The problem is that residual phase slope of Y with respect to X, caused by a difference in delay between the two channels. This can be seen in the upper panel of Figure 2, which shows the uncorrected phases of XY* and YX*. To correct the phases, the RCP phase was fit by a linear least-squares routine, and then the phases were offset by &pi;/2 for both XY* and YX* according to:<br />
<br />
== Polarization Mixing Correction ==<br />
Due to relative feed rotation between az-al mounted antennas and equatorial mounted antennas</div>Ztwanghttp://www.ovsa.njit.edu/wiki/index.php/Polarization_CalibrationPolarization Calibration2016-09-24T20:26:23Z<p>Ztwang: /* Linear to Circular Conversion */</p>
<hr />
<div>== Linear to Circular Conversion ==<br />
At EOVSA’s linear feeds, in the electric field the linear polarization, X and Y, relates to RCP and LCP (R and L) as:<br />
<br />
:<math><br />
\begin{align} <br />
R = X + iY \\<br />
L = X - iY <br />
\end{align}<br />
</math><br />
<br />
In terms of autocorrelation powers, we have the 4 polarization products XX*, YY*, XY* and YX*, where the * denotes complex conjugation. The quantities RR* and LL* are then<br />
<br />
:<math><br />
\begin{align} <br />
RR^* = (X + iY)(X + iY)^* = XX^* - iXY^* + iYX^* + YY^* \\<br />
LL^* = (X - iY)(X - iY)^* = XX^* + iXY^* - iYX^* + YY^* \\<br />
\end{align}<br />
</math><br />
<br />
One problem is that there is generally a non-zero delay in Y with respect to X. This creates phase slopes in XY* and YX* from which we can determine the delay very accurately. As a check,<br />
<br />
:<math><br />
\begin{align} <br />
Stokes \, I = \frac{RR^* + LL^*}{2} = XX^* + YY^* \\<br />
Stokes \, V = \frac{RR^* - LL^*}{2} = i(XX^* - YY^*) <br />
\end{align}<br />
</math><br />
<br />
For completeness:<br />
<br />
:<math>\begin{align} <br />
Stokes \, Q &= XX^* - YY^* \\<br />
Stokes \, U &= XY^* - YX^* \\<br />
P_{linear} &= \sqrt{U^2 + Q^2} \\<br />
\Theta &= \frac{1}{2}\tan^{-1}{\frac{U}{Q}}<br />
\end{align}<br />
</math><br />
<br />
When I plot the quantities I, V, R and L as measured (Figure 1) for geosynchronous satellite Ciel-2, the results look reasonable, except that there are parts of the band where R and L are mis-assigned, and others where they do not separate well.<br />
<br />
The problem is that residual phase slope of Y with respect to X, caused by a difference in delay between the two channels. This can be seen in the upper panel of Figure 2, which shows the uncorrected phases of XY* and YX*. To correct the phases, the RCP phase was fit by a linear least-squares routine, and then the phases were offset by &pi;/2 for both XY* and YX* according to:<br />
<br />
== Polarization Mixing Correction ==<br />
Due to relative feed rotation between az-al mounted antennas and equatorial mounted antennas</div>Ztwanghttp://www.ovsa.njit.edu/wiki/index.php/Polarization_CalibrationPolarization Calibration2016-09-24T20:25:20Z<p>Ztwang: /* Linear to Circular Conversion */</p>
<hr />
<div>== Linear to Circular Conversion ==<br />
At EOVSA’s linear feeds, in the electric field the linear polarization, X and Y, relates to RCP and LCP (R and L) as:<br />
<br />
:<math><br />
\begin{align} <br />
R = X + iY \\<br />
L = X - iY <br />
\end{align}<br />
</math><br />
<br />
In terms of autocorrelation powers, we have the 4 polarization products XX*, YY*, XY* and YX*, where the * denotes complex conjugation. The quantities RR* and LL* are then<br />
<br />
:<math><br />
\begin{align} <br />
RR^* = (X + iY)(X + iY)^* = XX^* - iXY^* + iYX^* + YY^* \\<br />
LL^* = (X - iY)(X - iY)^* = XX^* + iXY^* - iYX^* + YY^* \\<br />
\end{align}<br />
</math><br />
<br />
One problem is that there is generally a non-zero delay in Y with respect to X. This creates phase slopes in XY* and YX* from which we can determine the delay very accurately. As a check,<br />
<br />
:<math><br />
\begin{align} <br />
Stokes \, I = \frac{RR^* + LL^*}{2} = XX^* + YY^* \\<br />
Stokes \, V = \frac{RR^* - LL^*}{2} = i(XX^* - YY^*) <br />
\end{align}<br />
</math><br />
<br />
For completeness:<br />
<br />
:<math>\begin{align*} <br />
Stokes \, Q = XX^* - YY^* \\<br />
Stokes \, U = XY^* - YX^* \\<br />
P_{linear} = \sqrt{U^2 + Q^2} \\<br />
\Theta = \frac{1}{2}\tan^{-1}{\frac{U}{Q}}<br />
\end{align*}<br />
</math><br />
<br />
When I plot the quantities I, V, R and L as measured (Figure 1) for geosynchronous satellite Ciel-2, the results look reasonable, except that there are parts of the band where R and L are mis-assigned, and others where they do not separate well.<br />
<br />
The problem is that residual phase slope of Y with respect to X, caused by a difference in delay between the two channels. This can be seen in the upper panel of Figure 2, which shows the uncorrected phases of XY* and YX*. To correct the phases, the RCP phase was fit by a linear least-squares routine, and then the phases were offset by &pi;/2 for both XY* and YX* according to:<br />
<br />
== Polarization Mixing Correction ==<br />
Due to relative feed rotation between az-al mounted antennas and equatorial mounted antennas</div>Ztwanghttp://www.ovsa.njit.edu/wiki/index.php/Polarization_CalibrationPolarization Calibration2016-09-24T20:24:46Z<p>Ztwang: /* Linear to Circular Conversion */</p>
<hr />
<div>== Linear to Circular Conversion ==<br />
At EOVSA’s linear feeds, in the electric field the linear polarization, X and Y, relates to RCP and LCP (R and L) as:<br />
<br />
:<math><br />
\begin{align} <br />
R = X + iY \\<br />
L = X - iY <br />
\end{align}<br />
</math><br />
<br />
In terms of autocorrelation powers, we have the 4 polarization products XX*, YY*, XY* and YX*, where the * denotes complex conjugation. The quantities RR* and LL* are then<br />
<br />
:<math><br />
\begin{align} <br />
RR^* = (X + iY)(X + iY)^* = XX^* - iXY^* + iYX^* + YY^* \\<br />
LL^* = (X - iY)(X - iY)^* = XX^* + iXY^* - iYX^* + YY^* \\<br />
\end{align}<br />
</math><br />
<br />
One problem is that there is generally a non-zero delay in Y with respect to X. This creates phase slopes in XY* and YX* from which we can determine the delay very accurately. As a check,<br />
<br />
:<math><br />
\begin{align} <br />
Stokes \, I = \frac{RR^* + LL^*}{2} = XX^* + YY^* \\<br />
Stokes \, V = \frac{RR^* - LL^*}{2} = i(XX^* - YY^*) <br />
\end{align}<br />
</math><br />
<br />
For completeness:<br />
<br />
:<math>\begin{align} <br />
Stokes \, Q = XX^* - YY^* \\<br />
Stokes \, U = XY^* - YX^* \\<br />
P_{linear} = \sqrt{U^2 + Q^2} \\<br />
\Theta = \frac{1}{2}\tan^{-1}{\frac{U}{Q}}<br />
\end{align}<br />
</math><br />
<br />
When I plot the quantities I, V, R and L as measured (Figure 1) for geosynchronous satellite Ciel-2, the results look reasonable, except that there are parts of the band where R and L are mis-assigned, and others where they do not separate well.<br />
<br />
The problem is that residual phase slope of Y with respect to X, caused by a difference in delay between the two channels. This can be seen in the upper panel of Figure 2, which shows the uncorrected phases of XY* and YX*. To correct the phases, the RCP phase was fit by a linear least-squares routine, and then the phases were offset by &pi;/2 for both XY* and YX* according to:<br />
<br />
== Polarization Mixing Correction ==<br />
Due to relative feed rotation between az-al mounted antennas and equatorial mounted antennas</div>Ztwanghttp://www.ovsa.njit.edu/wiki/index.php/Polarization_CalibrationPolarization Calibration2016-09-24T20:24:26Z<p>Ztwang: /* Linear to Circular Conversion */</p>
<hr />
<div>== Linear to Circular Conversion ==<br />
At EOVSA’s linear feeds, in the electric field the linear polarization, X and Y, relates to RCP and LCP (R and L) as:<br />
<br />
:<math><br />
\begin{align} <br />
R = X + iY \\<br />
L = X - iY <br />
\end{align}<br />
</math><br />
<br />
In terms of autocorrelation powers, we have the 4 polarization products XX*, YY*, XY* and YX*, where the * denotes complex conjugation. The quantities RR* and LL* are then<br />
<br />
:<math><br />
\begin{align} <br />
RR^* = (X + iY)(X + iY)^* = XX^* - iXY^* + iYX^* + YY^* \\<br />
LL^* = (X - iY)(X - iY)^* = XX^* + iXY^* - iYX^* + YY^* \\<br />
\end{align}<br />
</math><br />
<br />
One problem is that there is generally a non-zero delay in Y with respect to X. This creates phase slopes in XY* and YX* from which we can determine the delay very accurately. As a check,<br />
<br />
:<math><br />
\begin{align} <br />
Stokes \, I = \frac{RR^* + LL^*}{2} = XX^* + YY^* \\<br />
Stokes \, V = \frac{RR^* - LL^*}{2} = i(XX^* - YY^*) <br />
\end{align}<br />
</math><br />
<br />
For completeness:<br />
<br />
:<math><br />
Stokes \, Q = XX^* - YY^* \\<br />
Stokes \, U = XY^* - YX^* \\<br />
P_{linear} = \sqrt{U^2 + Q^2} \\<br />
\Theta = \frac{1}{2}\tan^{-1}{\frac{U}{Q}}<br />
</math><br />
<br />
When I plot the quantities I, V, R and L as measured (Figure 1) for geosynchronous satellite Ciel-2, the results look reasonable, except that there are parts of the band where R and L are mis-assigned, and others where they do not separate well.<br />
<br />
The problem is that residual phase slope of Y with respect to X, caused by a difference in delay between the two channels. This can be seen in the upper panel of Figure 2, which shows the uncorrected phases of XY* and YX*. To correct the phases, the RCP phase was fit by a linear least-squares routine, and then the phases were offset by &pi;/2 for both XY* and YX* according to:<br />
<br />
== Polarization Mixing Correction ==<br />
Due to relative feed rotation between az-al mounted antennas and equatorial mounted antennas</div>Ztwanghttp://www.ovsa.njit.edu/wiki/index.php/Polarization_CalibrationPolarization Calibration2016-09-24T20:23:03Z<p>Ztwang: /* Linear to Circular Conversion */</p>
<hr />
<div>== Linear to Circular Conversion ==<br />
At EOVSA’s linear feeds, in the electric field the linear polarization, X and Y, relates to RCP and LCP (R and L) as:<br />
<br />
:<math><br />
\begin{align} <br />
R = X + iY \\<br />
L = X - iY <br />
\end{align}<br />
</math><br />
<br />
In terms of autocorrelation powers, we have the 4 polarization products XX*, YY*, XY* and YX*, where the * denotes complex conjugation. The quantities RR* and LL* are then<br />
<br />
:<math><br />
\begin{align} <br />
RR^* = (X + iY)(X + iY)^* = XX^* - iXY^* + iYX^* + YY^* \\<br />
LL^* = (X - iY)(X - iY)^* = XX^* + iXY^* - iYX^* + YY^* \\<br />
\end{align}<br />
</math><br />
<br />
One problem is that there is generally a non-zero delay in Y with respect to X. This creates phase slopes in XY* and YX* from which we can determine the delay very accurately. As a check,<br />
<br />
:<math><br />
\begin{align} <br />
Stokes \, I = \frac{RR^* + LL^*}{2} = XX^* + YY^* \\<br />
Stokes \, V = \frac{RR^* - LL^*}{2} = i(XX^* - YY^*) <br />
\end{align}<br />
</math><br />
<br />
For completeness:<br />
<br />
:<math><br />
\begin{align} <br />
Stokes \, Q = XX^* - YY^* \\<br />
Stokes \, U = XY^* - YX^* \\<br />
P_{linear} = \sqrt{U^2 + Q^2} \\<br />
\Theta = \frac{1}{2}\tan^{-1}{\frac{U}{Q}}<br />
\end{align}<br />
</math><br />
<br />
When I plot the quantities I, V, R and L as measured (Figure 1) for geosynchronous satellite Ciel-2, the results look reasonable, except that there are parts of the band where R and L are mis-assigned, and others where they do not separate well.<br />
<br />
The problem is that residual phase slope of Y with respect to X, caused by a difference in delay between the two channels. This can be seen in the upper panel of Figure 2, which shows the uncorrected phases of XY* and YX*. To correct the phases, the RCP phase was fit by a linear least-squares routine, and then the phases were offset by &pi;/2 for both XY* and YX* according to:<br />
<br />
== Polarization Mixing Correction ==<br />
Due to relative feed rotation between az-al mounted antennas and equatorial mounted antennas</div>Ztwanghttp://www.ovsa.njit.edu/wiki/index.php/Polarization_CalibrationPolarization Calibration2016-09-24T20:22:41Z<p>Ztwang: /* Linear to Circular Conversion */</p>
<hr />
<div>== Linear to Circular Conversion ==<br />
At EOVSA’s linear feeds, in the electric field the linear polarization, X and Y, relates to RCP and LCP (R and L) as:<br />
<br />
:<math><br />
\begin{align} <br />
R = X + iY \\<br />
L = X - iY <br />
\end{align}<br />
</math><br />
<br />
In terms of autocorrelation powers, we have the 4 polarization products XX*, YY*, XY* and YX*, where the * denotes complex conjugation. The quantities RR* and LL* are then<br />
<br />
:<math><br />
\begin{align} <br />
RR^* = (X + iY)(X + iY)^* = XX^* - iXY^* + iYX^* + YY^* \\<br />
LL^* = (X - iY)(X - iY)^* = XX^* + iXY^* - iYX^* + YY^* \\<br />
\end{align}<br />
</math><br />
<br />
One problem is that there is generally a non-zero delay in Y with respect to X. This creates phase slopes in XY* and YX* from which we can determine the delay very accurately. As a check,<br />
<br />
:<math><br />
\begin{align} <br />
Stokes \, I = \frac{RR^* + LL^*}{2} = XX^* + YY^* \\<br />
Stokes \, V = \frac{RR^* - LL^*}{2} = i(XX^* - YY^*) <br />
\end{align}<br />
</math><br />
<br />
For completeness:<br />
<br />
:<math><br />
\begin{align} <br />
Stokes \, Q = XX^* - YY^* \\<br />
Stokes \, U = XY^* - YX^* \\<br />
P_{linear} = \sqrt{U^2 + Q^2} \\<br />
\Theta = \frac{1}{2}\tan^{-1}{\frac{U}{Q}} \\<br />
\end{align}<br />
</math><br />
<br />
When I plot the quantities I, V, R and L as measured (Figure 1) for geosynchronous satellite Ciel-2, the results look reasonable, except that there are parts of the band where R and L are mis-assigned, and others where they do not separate well.<br />
<br />
The problem is that residual phase slope of Y with respect to X, caused by a difference in delay between the two channels. This can be seen in the upper panel of Figure 2, which shows the uncorrected phases of XY* and YX*. To correct the phases, the RCP phase was fit by a linear least-squares routine, and then the phases were offset by &pi;/2 for both XY* and YX* according to:<br />
<br />
== Polarization Mixing Correction ==<br />
Due to relative feed rotation between az-al mounted antennas and equatorial mounted antennas</div>Ztwanghttp://www.ovsa.njit.edu/wiki/index.php/Polarization_CalibrationPolarization Calibration2016-09-24T20:22:20Z<p>Ztwang: /* Linear to Circular Conversion */</p>
<hr />
<div>== Linear to Circular Conversion ==<br />
At EOVSA’s linear feeds, in the electric field the linear polarization, X and Y, relates to RCP and LCP (R and L) as:<br />
<br />
:<math><br />
\begin{align} <br />
R = X + iY \\<br />
L = X - iY \\<br />
\end{align}<br />
</math><br />
<br />
In terms of autocorrelation powers, we have the 4 polarization products XX*, YY*, XY* and YX*, where the * denotes complex conjugation. The quantities RR* and LL* are then<br />
<br />
:<math><br />
\begin{align} <br />
RR^* = (X + iY)(X + iY)^* = XX^* - iXY^* + iYX^* + YY^* \\<br />
LL^* = (X - iY)(X - iY)^* = XX^* + iXY^* - iYX^* + YY^* \\<br />
\end{align}<br />
</math><br />
<br />
One problem is that there is generally a non-zero delay in Y with respect to X. This creates phase slopes in XY* and YX* from which we can determine the delay very accurately. As a check,<br />
<br />
:<math><br />
\begin{align} <br />
Stokes \, I = \frac{RR^* + LL^*}{2} = XX^* + YY^* \\<br />
Stokes \, V = \frac{RR^* - LL^*}{2} = i(XX^* - YY^*) <br />
\end{align}<br />
</math><br />
<br />
For completeness:<br />
<br />
:<math><br />
\begin{align} <br />
Stokes \, Q = XX^* - YY^* \\<br />
Stokes \, U = XY^* - YX^* \\<br />
P_{linear} = \sqrt{U^2 + Q^2} \\<br />
\Theta = \frac{1}{2}\tan^{-1}{\frac{U}{Q}} \\<br />
\end{align}<br />
</math><br />
<br />
When I plot the quantities I, V, R and L as measured (Figure 1) for geosynchronous satellite Ciel-2, the results look reasonable, except that there are parts of the band where R and L are mis-assigned, and others where they do not separate well.<br />
<br />
The problem is that residual phase slope of Y with respect to X, caused by a difference in delay between the two channels. This can be seen in the upper panel of Figure 2, which shows the uncorrected phases of XY* and YX*. To correct the phases, the RCP phase was fit by a linear least-squares routine, and then the phases were offset by &pi;/2 for both XY* and YX* according to:<br />
<br />
== Polarization Mixing Correction ==<br />
Due to relative feed rotation between az-al mounted antennas and equatorial mounted antennas</div>Ztwanghttp://www.ovsa.njit.edu/wiki/index.php/Polarization_CalibrationPolarization Calibration2016-09-24T20:21:45Z<p>Ztwang: /* Linear to Circular Conversion */</p>
<hr />
<div>== Linear to Circular Conversion ==<br />
At EOVSA’s linear feeds, in the electric field the linear polarization, X and Y, relates to RCP and LCP (R and L) as:<br />
<br />
:<math><br />
\begin{align} <br />
R = X + iY \\<br />
L = X - iY \\<br />
\end{align}<br />
</math><br />
<br />
In terms of autocorrelation powers, we have the 4 polarization products XX*, YY*, XY* and YX*, where the * denotes complex conjugation. The quantities RR* and LL* are then<br />
<br />
:<math><br />
\begin{align} <br />
RR^* = (X + iY)(X + iY)^* = XX^* - iXY^* + iYX^* + YY^* \\<br />
LL^* = (X - iY)(X - iY)^* = XX^* + iXY^* - iYX^* + YY^* \\<br />
\end{align}<br />
</math><br />
<br />
One problem is that there is generally a non-zero delay in Y with respect to X. This creates phase slopes in XY* and YX* from which we can determine the delay very accurately. As a check,<br />
<br />
:<math><br />
\begin{align} <br />
Stokes \, I = \frac{RR^* + LL^*}{2} = XX^* + YY^* \\<br />
Stokes \, V = \frac{RR^* - LL^*}{2} = i(XX^* - YY^*) \\<br />
\end{align}<br />
</math><br />
<br />
For completeness:<br />
<br />
:<math><br />
\begin{align} <br />
Stokes \, Q = XX^* - YY^* \\<br />
Stokes \, U = XY^* - YX^* \\<br />
P_{linear} = \sqrt{U^2 + Q^2} \\<br />
\Theta = \frac{1}{2}\tan^{-1}{\frac{U}{Q}} \\<br />
\end{align}<br />
</math><br />
<br />
When I plot the quantities I, V, R and L as measured (Figure 1) for geosynchronous satellite Ciel-2, the results look reasonable, except that there are parts of the band where R and L are mis-assigned, and others where they do not separate well.<br />
<br />
The problem is that residual phase slope of Y with respect to X, caused by a difference in delay between the two channels. This can be seen in the upper panel of Figure 2, which shows the uncorrected phases of XY* and YX*. To correct the phases, the RCP phase was fit by a linear least-squares routine, and then the phases were offset by &pi;/2 for both XY* and YX* according to:<br />
<br />
== Polarization Mixing Correction ==<br />
Due to relative feed rotation between az-al mounted antennas and equatorial mounted antennas</div>Ztwang