EOVSA Wiki - User contributions [en]

Reference Gain Calibration

2017-07-30T21:24:58Z

Ztwang: /* List of Analyzed Reference Calibrations */

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)

<pre>
import refcal_anal as ra
from util import Time
#example time range of the refcal scan that took place BEFORE the observation
trange=Time(['2017-04-08T14:00','2017-04-08T15:00'])
</pre>



Now read the data from that timerange
<pre>
out=ra.rd_refcal(trange)
</pre>
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.

To correct for differential feed rotation (for refcal data after 05:00 UT on 2017-Jul-01), you can use:
<pre>
out_corr = ra.unrot_refcal(out)
</pre>

Take a look at the phases (averaged over each band):
<pre>
ra.graph(out_corr)
</pre>
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).
<pre>
ra.graph(out_corr, bandplt=[5,13,19,25], pol=1)
</pre>



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.

<pre>
refcal=ra.refcal_anal(out_corr,timerange=trange,scanidx=[0])
</pre>

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.

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

<pre>
refcal['flag'][11]=1
</pre>

If satisfied with the results (by looking at the plots), we can go ahead and send them to the SQL database
<pre>
import cal_header as ch
ch.refcal2sql(refcal)
</pre>

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:
<pre>
t=Time('2017-04-07T19:40')
refcal=ra.sql2refcal(t)
</pre>
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.

== Updating the Reference Calibrations Table ==
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:
<pre>
t=Time('2017-06-23T19:40') # retrieves the refcal at 13:07 UT on that day
refcal=ra.sql2refcal(t)
ra.graph_results(refcal, savefigs=True)
</pre>
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.

== List of Analyzed Reference Calibrations ==

{| class="wikitable" style="text-align: center; width: 800px; height: 200px;"
|-
| Date || Timestamp || Source || Obs Trange || Scan Idx || Avg Trange || Bands || Phase Plot || Amp Plot || Comments
|-
| 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.
|-
| 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.
|-
| 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.
|-
| 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.
|-
| 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.
|-
| 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.
|-
| 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.
|-
| 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.
|-
| 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.
|-
| 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.
|-
| 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
|-
| 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
|-
| 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
|-
| 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
|-
| 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
|-
| 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
|-
| 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
|-
| 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
|-
| 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
|-
| 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
|-
| 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
|-
| 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
|-
| 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
|-
| 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
|-
| 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
|-
| 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
|-
| 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] ||
|-
| 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
|-
| 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] ||
|-
| 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] ||
|-
| 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] ||
|-
| 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] ||
|-
| 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] ||
|-
| 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] ||
|-
| 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] ||
|-
| 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] ||
|-
| 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] ||
|-
| 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] ||
|-
| 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] ||
|-
| 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] ||
|-
| 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] ||
|-
| 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] ||
|-
| 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] ||
|-
| 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] ||
|-
| 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
|-
| 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] ||
|-
| 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] ||
|-
| 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] ||
|-
| 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] ||
|-
| 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] ||
|-
| 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] ||
|-
| 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] ||
|-
| 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] ||
|-

Reference Gain Calibration

2017-07-30T21:10:54Z

Ztwang: /* List of Analyzed Reference Calibrations */

Reference Gain Calibration

2017-07-27T19:56:58Z

Ztwang: /* List of Analyzed Reference Calibrations */

2016-09-24T21:08:01Z

Ztwang: /* Linear to Circular Conversion */

== Linear to Circular Conversion ==
[[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.]]
[[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 -π/2. This adjustment automatically makes XY* phases on LCP channels become +π/2.]]
[[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.]]
[[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.]]
[[File:Linear_to_Circular_Conversion_Figure5.jpg|thumb|600px|Figure 4: Same as Fig. 5, but for the Nimiq-5 commun-ications satellite.]]
At EOVSA’s linear feeds, in the electric field the linear polarization, X and Y, relates to RCP and LCP (R and L) as:

:<math>
\begin{align}
R = X + iY \\
L = X - iY
\end{align}
</math>

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

:<math>
\begin{align}
RR^* = (X + iY)(X + iY)^* &= XX^* - iXY^* + iYX^* + YY^* \\
LL^* = (X - iY)(X - iY)^* &= XX^* + iXY^* - iYX^* + YY^* \\
\end{align}
</math>

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,

:<math>
\begin{align}
Stokes \, I &= \frac{RR^* + LL^*}{2} = XX^* + YY^* \\
Stokes \, V &= \frac{RR^* - LL^*}{2} = i(XX^* - YY^*)
\end{align}
</math>

For completeness:

:<math>\begin{align}
Stokes \, Q &= XX^* - YY^* \\
Stokes \, U &= XY^* - YX^* \\
P_{linear} &= \sqrt{U^2 + Q^2} \\
\Theta &= \frac{1}{2}\tan^{-1}{\frac{U}{Q}}
\end{align}
</math>

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.

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 π/2 for both XY* and YX* according to:

:<math>\begin{align}
XY^{*'} &= XY^*e^{-i(\phi(v) + \frac{\pi}{2})} \\
YX^{*'} &= YX^*e^{ i(\phi(v) + \frac{\pi}{2})}
\end{align}
</math>

where φ(v) is the phase fit by the linear function. The corrected phases are shown in the lower panel of Figure 2.

When the corrected (primed) quantities are used in

:<math>\begin{align}
RR^* &= XX^* - iXY^{*'} + iYX^{*'} + YY^* \\
LL^* &= XX^* + iXY^{*'} - iYX^{*'} + YY^*
\end{align}
</math>

the resulting channel separation is shown in Figure 3, which shows pretty much perfect channel separation, with the correct polarity.

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.

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).

Just to show that the approach is general, the results for a different communications satellite, Nimiq-5, is shown in Figure 5.

== Polarization Mixing Correction ==
Due to relative feed rotation between az-al mounted antennas and equatorial mounted antennas

File:Linear to Circular Conversion Figure5.jpg

2016-09-24T21:05:05Z

Ztwang:

File:Linear to Circular Conversion Figure4.jpg

2016-09-24T21:04:44Z

Ztwang:

File:Linear to Circular Conversion Figure3.jpg

2016-09-24T21:04:15Z

Ztwang:

Polarization Calibration

2016-09-24T21:03:55Z

Ztwang: /* Linear to Circular Conversion */

== Linear to Circular Conversion ==
[[File:Linear_to_Circular_Conversion_Figure1.jpg|thumb|600px|]]
[[File:Linear_to_Circular_Conversion_Figure2.jpg|thumb|600px|]]
[[File:Linear_to_Circular_Conversion_Figure3.jpg|thumb|600px|]]
[[File:Linear_to_Circular_Conversion_Figure4.jpg|thumb|600px|]]
[[File:Linear_to_Circular_Conversion_Figure5.jpg|thumb|600px|]]
At EOVSA’s linear feeds, in the electric field the linear polarization, X and Y, relates to RCP and LCP (R and L) as:

:<math>
\begin{align}
R = X + iY \\
L = X - iY
\end{align}
</math>

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

:<math>
\begin{align}
RR^* = (X + iY)(X + iY)^* &= XX^* - iXY^* + iYX^* + YY^* \\
LL^* = (X - iY)(X - iY)^* &= XX^* + iXY^* - iYX^* + YY^* \\
\end{align}
</math>

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,

:<math>
\begin{align}
Stokes \, I &= \frac{RR^* + LL^*}{2} = XX^* + YY^* \\
Stokes \, V &= \frac{RR^* - LL^*}{2} = i(XX^* - YY^*)
\end{align}
</math>

For completeness:

:<math>\begin{align}
Stokes \, Q &= XX^* - YY^* \\
Stokes \, U &= XY^* - YX^* \\
P_{linear} &= \sqrt{U^2 + Q^2} \\
\Theta &= \frac{1}{2}\tan^{-1}{\frac{U}{Q}}
\end{align}
</math>

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.

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 π/2 for both XY* and YX* according to:

:<math>\begin{align}
XY^{*'} &= XY^*e^{-i(\phi(v) + \frac{\pi}{2})} \\
YX^{*'} &= YX^*e^{ i(\phi(v) + \frac{\pi}{2})}
\end{align}
</math>

where φ(v) is the phase fit by the linear function. The corrected phases are shown in the lower panel of Figure 2.

When the corrected (primed) quantities are used in

:<math>\begin{align}
RR^* &= XX^* - iXY^{*'} + iYX^{*'} + YY^* \\
LL^* &= XX^* + iXY^{*'} - iYX^{*'} + YY^*
\end{align}
</math>

the resulting channel separation is shown in Figure 3, which shows pretty much perfect channel separation, with the correct polarity.

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.

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).

Just to show that the approach is general, the results for a different communications satellite, Nimiq-5, is shown in Figure 5.

== Polarization Mixing Correction ==
Due to relative feed rotation between az-al mounted antennas and equatorial mounted antennas

Polarization Calibration

2016-09-24T21:03:36Z

Ztwang: /* Linear to Circular Conversion */

== Linear to Circular Conversion ==
[[File:Linear_to_Circular_Conversion_Figure1.jpg|thumb|500px|]]
[[File:Linear_to_Circular_Conversion_Figure2.jpg|thumb|500px|]]
[[File:Linear_to_Circular_Conversion_Figure3.jpg|thumb|500px|]]
[[File:Linear_to_Circular_Conversion_Figure4.jpg|thumb|500px|]]
[[File:Linear_to_Circular_Conversion_Figure5.jpg|thumb|500px|]]
At EOVSA’s linear feeds, in the electric field the linear polarization, X and Y, relates to RCP and LCP (R and L) as:

:<math>
\begin{align}
R = X + iY \\
L = X - iY
\end{align}
</math>

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

:<math>
\begin{align}
RR^* = (X + iY)(X + iY)^* &= XX^* - iXY^* + iYX^* + YY^* \\
LL^* = (X - iY)(X - iY)^* &= XX^* + iXY^* - iYX^* + YY^* \\
\end{align}
</math>

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,

:<math>
\begin{align}
Stokes \, I &= \frac{RR^* + LL^*}{2} = XX^* + YY^* \\
Stokes \, V &= \frac{RR^* - LL^*}{2} = i(XX^* - YY^*)
\end{align}
</math>

For completeness:

:<math>\begin{align}
Stokes \, Q &= XX^* - YY^* \\
Stokes \, U &= XY^* - YX^* \\
P_{linear} &= \sqrt{U^2 + Q^2} \\
\Theta &= \frac{1}{2}\tan^{-1}{\frac{U}{Q}}
\end{align}
</math>

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.

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 π/2 for both XY* and YX* according to:

:<math>\begin{align}
XY^{*'} &= XY^*e^{-i(\phi(v) + \frac{\pi}{2})} \\
YX^{*'} &= YX^*e^{ i(\phi(v) + \frac{\pi}{2})}
\end{align}
</math>

where φ(v) is the phase fit by the linear function. The corrected phases are shown in the lower panel of Figure 2.

When the corrected (primed) quantities are used in

:<math>\begin{align}
RR^* &= XX^* - iXY^{*'} + iYX^{*'} + YY^* \\
LL^* &= XX^* + iXY^{*'} - iYX^{*'} + YY^*
\end{align}
</math>

the resulting channel separation is shown in Figure 3, which shows pretty much perfect channel separation, with the correct polarity.

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.

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).

Just to show that the approach is general, the results for a different communications satellite, Nimiq-5, is shown in Figure 5.

== Polarization Mixing Correction ==
Due to relative feed rotation between az-al mounted antennas and equatorial mounted antennas

Polarization Calibration

2016-09-24T21:02:49Z

Ztwang: /* Linear to Circular Conversion */

== Linear to Circular Conversion ==
[[File:Linear_to_Circular_Conversion_Figure2.jpg|thumb|800px|]]
At EOVSA’s linear feeds, in the electric field the linear polarization, X and Y, relates to RCP and LCP (R and L) as:

:<math>
\begin{align}
R = X + iY \\
L = X - iY
\end{align}
</math>

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

:<math>
\begin{align}
RR^* = (X + iY)(X + iY)^* &= XX^* - iXY^* + iYX^* + YY^* \\
LL^* = (X - iY)(X - iY)^* &= XX^* + iXY^* - iYX^* + YY^* \\
\end{align}
</math>

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,

:<math>
\begin{align}
Stokes \, I &= \frac{RR^* + LL^*}{2} = XX^* + YY^* \\
Stokes \, V &= \frac{RR^* - LL^*}{2} = i(XX^* - YY^*)
\end{align}
</math>

For completeness:

:<math>\begin{align}
Stokes \, Q &= XX^* - YY^* \\
Stokes \, U &= XY^* - YX^* \\
P_{linear} &= \sqrt{U^2 + Q^2} \\
\Theta &= \frac{1}{2}\tan^{-1}{\frac{U}{Q}}
\end{align}
</math>

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.

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 π/2 for both XY* and YX* according to:

:<math>\begin{align}
XY^{*'} &= XY^*e^{-i(\phi(v) + \frac{\pi}{2})} \\
YX^{*'} &= YX^*e^{ i(\phi(v) + \frac{\pi}{2})}
\end{align}
</math>

where φ(v) is the phase fit by the linear function. The corrected phases are shown in the lower panel of Figure 2.

When the corrected (primed) quantities are used in

:<math>\begin{align}
RR^* &= XX^* - iXY^{*'} + iYX^{*'} + YY^* \\
LL^* &= XX^* + iXY^{*'} - iYX^{*'} + YY^*
\end{align}
</math>

the resulting channel separation is shown in Figure 3, which shows pretty much perfect channel separation, with the correct polarity.

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.

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).

Just to show that the approach is general, the results for a different communications satellite, Nimiq-5, is shown in Figure 5.

== Polarization Mixing Correction ==
Due to relative feed rotation between az-al mounted antennas and equatorial mounted antennas

Polarization Calibration

2016-09-24T21:01:52Z

2016-09-24T20:21:45Z

Ztwang: /* Linear to Circular Conversion */