http://ovsa.njit.edu//wiki/index.php?title=Calibration_Overview&feed=atom&action=historyCalibration Overview - Revision history2024-03-29T08:04:49ZRevision history for this page on the wikiMediaWiki 1.38.1http://ovsa.njit.edu//wiki/index.php?title=Calibration_Overview&diff=297&oldid=prevBchen at 18:02, 26 September 20162016-09-26T18:02:56Z<p></p>
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<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>!colspan="7" | Table <del style="font-weight: bold; text-decoration: none;">4</del>: Summary of Delay Calibration</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>!colspan="7" | Table <ins style="font-weight: bold; text-decoration: none;">3</ins>: Summary of Delay Calibration</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>|-</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>|-</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>!Calibration Type</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>!Calibration Type</div></td></tr>
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<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>=== Observational Procedure ===</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>=== Observational Procedure ===</div></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>Given the speed with which a bandpass calibration (section <del style="font-weight: bold; text-decoration: none;">3</del>) can be obtained, and the basic similarity between that and the reference calibration, the same basic observational approach can be taken, and only the analysis differs in some details. For integration over 500 MHz, the entire reference calibration can be done on 3C84 in 34 bands, at 50:1 signal to noise ratio, in less than 60 s on large-small baselines. However, it is wise to measure the reference complex gain on all baselines and seek a traditional gain solution. </div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>Given the speed with which a bandpass calibration (section <ins style="font-weight: bold; text-decoration: none;">5</ins>) can be obtained, and the basic similarity between that and the reference calibration, the same basic observational approach can be taken, and only the analysis differs in some details. For integration over 500 MHz, the entire reference calibration can be done on 3C84 in 34 bands, at 50:1 signal to noise ratio, in less than 60 s on large-small baselines <ins style="font-weight: bold; text-decoration: none;">(c.f., sensitivity equations in section 5)</ins>. However, it is wise to measure the reference complex gain on all baselines and seek a traditional gain solution. </div></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div> </div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><span style="color:red">[BC 9/24/2016: However, optimum delay and bandpass corrections should be applied prior to averaging over these channels.] </span></div></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del style="font-weight: bold; text-decoration: none;">The sensitivity per polarization of a single baseline is given by </del></div></td><td colspan="2" class="diff-side-added"></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div> </div></td><td colspan="2" class="diff-side-added"></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del style="font-weight: bold; text-decoration: none;"><center><math>\sigma_{ij}=\frac{4.97\sqrt{T_{\rm sys,i}T_{\rm sys,j}}}{D_{i}D_{j}\sqrt{\Delta t_{\rm s} \Delta \nu_{\rm MHz}}}~{\rm Jy}</math>,</center></del></div></td><td colspan="2" class="diff-side-added"></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div> </div></td><td colspan="2" class="diff-side-added"></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del style="font-weight: bold; text-decoration: none;">where <math>T_{\rm sys, i}</math> and <math>D_i</math> are the system temperature (K) and diameter (m) of the i<sup>th</sup> element, and an antenna efficiency of 0.5 has been assumed. If the system temperature of the cooled 27-m receivers is 30 K, and that of the 2-m receivers is 400 K, the sensitivity on baselines between a 27m-2m pair is:</del></div></td><td colspan="2" class="diff-side-added"></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div> </div></td><td colspan="2" class="diff-side-added"></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del style="font-weight: bold; text-decoration: none;"><center><math>\sigma_{l, s}=\frac{9.6}{\sqrt{\Delta t_{\rm s} \Delta \nu_{\rm MHz}}}~{\rm Jy}</math>,</center></del></div></td><td colspan="2" class="diff-side-added"></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div> </div></td><td colspan="2" class="diff-side-added"></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del style="font-weight: bold; text-decoration: none;">it will take about 23 s with 10:1 signal to noise ratio on 3C84 on each 1-MHz-wide channel (assuming ~20 Jy flux density). This integration time can be further reduced if we combining multiple frequency channels. </del><span style="color:red">[BC 9/24/2016: However, optimum delay and bandpass corrections should be applied prior to averaging over these channels.] </span></div></td><td colspan="2" class="diff-side-added"></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>For small-small (2m-2m) baselines, it becomes:</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>For small-small (2m-2m) baselines, it becomes:</div></td></tr>
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<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>! colspan="7" | Table <del style="font-weight: bold; text-decoration: none;">3</del>: Summary of Reference Gain Calibration</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>! colspan="7" | Table <ins style="font-weight: bold; text-decoration: none;">5</ins>: Summary of Reference Gain Calibration</div></td></tr>
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<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>! colspan="7" | Table <del style="font-weight: bold; text-decoration: none;">3</del>: Summary of Daily Gain Calibration</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>! colspan="7" | Table <ins style="font-weight: bold; text-decoration: none;">6</ins>: Summary of Daily Gain Calibration</div></td></tr>
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</table>Bchenhttp://ovsa.njit.edu//wiki/index.php?title=Calibration_Overview&diff=296&oldid=prevBchen: /* Analysis Procedure */2016-09-26T17:57:58Z<p><span dir="auto"><span class="autocomment">Analysis Procedure</span></span></p>
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<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 17:57, 26 September 2016</td>
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<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>| Full spectrum bandpass calibration || No || Amplitude and phase on each large-small baseline over each spectral channel || Determine the antenna-based complex gain variations across each IF band || <del style="font-weight: bold; text-decoration: none;">Longer </del>integration time on each IF band to obtain adequate SNR || Miriad task mfcal may work, CASA task bandpass may work || Needed for detailed science investigations, could be deferred</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>| Full spectrum bandpass calibration || No || Amplitude and phase on each large-small baseline over each spectral channel || Determine the antenna-based complex gain variations across each IF band || <ins style="font-weight: bold; text-decoration: none;">Relatively longer </ins>integration time on each IF band to obtain adequate SNR || Miriad task mfcal may work, CASA task bandpass may work || Needed for detailed science investigations, could be deferred</div></td></tr>
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</table>Bchenhttp://ovsa.njit.edu//wiki/index.php?title=Calibration_Overview&diff=295&oldid=prevBchen: /* Analysis Procedure */2016-09-26T17:57:12Z<p><span dir="auto"><span class="autocomment">Analysis Procedure</span></span></p>
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<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 17:57, 26 September 2016</td>
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<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>=== Analysis Procedure ===</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>=== Analysis Procedure ===</div></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>The Data are calibrated to correct for pointing offsets vs. frequency (obtained from Pointing Calibration, see 1 above), and the set of amplitudes and phases on each large-small baseline are obtained. Denoting the large antennas as a, b, and the <del style="font-weight: bold; text-decoration: none;">nth </del>small antenna as n, the antenna-based bandpass amplitude as a function of subchannel k for antenna n is</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>The Data are calibrated to correct for pointing offsets vs. frequency (obtained from Pointing Calibration, see 1 above), and the set of amplitudes and phases on each large-small baseline are obtained. Denoting the large antennas as a, b, and the <ins style="font-weight: bold; text-decoration: none;">n<sup>th</sup> </ins>small antenna as n, the antenna-based bandpass amplitude as a function of subchannel k for antenna n is</div></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del style="font-weight: bold; text-decoration: none;"> , (3) </del></div></td><td colspan="2" class="diff-side-added"></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del style="font-weight: bold; text-decoration: none;">where is the square of the amplitude measured on baseline I, j. There appears to be no way to measure the bandpass of the large dishes separately (without small-small baselines), but perhaps they are never needed.</del></div></td><td colspan="2" class="diff-side-added"></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>Assuming we take one of the large antennas (denoted antenna a) as the reference antenna, which we can do without loss of generality, the antenna-based bandpass phase is just that measured on the a-n baseline, <del style="font-weight: bold; text-decoration: none;">n</del>(k) = <del style="font-weight: bold; text-decoration: none;">an</del>(k). Note that <del style="font-weight: bold; text-decoration: none;">bn</del>(k) is useful primarily to verify phase closure. The deviation from closure phase would be used as a measure of the uncertainty in <del style="font-weight: bold; text-decoration: none;">n</del>(k). Given sufficient signal to noise, the bandpass amplitude and phase can be determined for each subchannel k, but if that is not possible, it is sufficient to determine this calibration for each science subband. The product of this analysis is the normalized shape and relative phase variation across the band, which should change slowly (assuming thermal variations of standing waves is well controlled). The overall complex gain will be determined by more frequent measurements integrated over each entire IF band (both reference <del style="font-weight: bold; text-decoration: none;">[section 4] </del>and daily <del style="font-weight: bold; text-decoration: none;">[section 5] amplitude and phase </del>calibration). Note that the Miriad task mfcal performs the required analysis, but no doubt assumes data for all baselines, whereas we have only a small subset of baselines. It is worthwhile to try mfcal on simulated data with some very noisy baselines to see if it comes up with a correct solution. Note also that the total power bandpass response for each antenna, obtained from section 1, could be relevant to compare with the amplitude bandpass response.</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;"><center><math>A_n(k) = \sqrt{\frac{A_{an}^2(k)A_{bn}^2(k)}{A_{ab}^2(k)}}</math></center></ins></div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;"> </ins></div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">where <math>A_{ij}^2=A_{ij}A_{ij}^*</math> is the square of the amplitude measured on baseline i, j. There appears to be no way to measure the bandpass of the large dishes separately (without small-small baselines), but perhaps they are never needed.</ins></div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div> </div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>Assuming we take one of the large antennas (denoted antenna a) as the reference antenna, which we can do without loss of generality, the antenna-based bandpass phase is just that measured on the a-n baseline, <ins style="font-weight: bold; text-decoration: none;"><math>\phi_n</ins>(k) = <ins style="font-weight: bold; text-decoration: none;">\phi_{an}</ins>(k)<ins style="font-weight: bold; text-decoration: none;"></math></ins>. Note that <ins style="font-weight: bold; text-decoration: none;"><math>\phi_{bn}</ins>(k)<ins style="font-weight: bold; text-decoration: none;"></math> </ins>is useful primarily to verify phase closure. The deviation from closure phase <ins style="font-weight: bold; text-decoration: none;"><math>\delta\phi_{cl}(k)=\phi_{ab}(k) + \phi_{bn}(k) - \phi_{an}(k)</math> </ins>would be used as a measure of the uncertainty in <ins style="font-weight: bold; text-decoration: none;"><math>\phi_n</ins>(k)<ins style="font-weight: bold; text-decoration: none;"></math></ins>. Given sufficient signal to noise, the bandpass amplitude and phase can be determined for each subchannel k, but if that is not possible, it is sufficient to determine this calibration for each science subband. The product of this analysis is the normalized shape and relative phase variation across the band, which should change slowly (assuming thermal variations of standing waves is well controlled). The overall complex gain will be determined by more frequent measurements integrated over each entire IF band (both reference and daily <ins style="font-weight: bold; text-decoration: none;">gain </ins>calibration). Note that the Miriad task mfcal performs the required analysis, but no doubt assumes data for all baselines, whereas we have only a small subset of baselines. It is worthwhile to try mfcal on simulated data with some very noisy baselines to see if it comes up with a correct solution. Note also that the total power bandpass response for each antenna, obtained from section 1, could be relevant to compare with the amplitude bandpass response. <ins style="font-weight: bold; text-decoration: none;"><span style='color:orange'>[BC 2016-Sep-26: CASA's bandpass task may work on a subset of baselines. Need to be tested for only using baselines of one antenna, though.]</span></ins></div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div> </div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;"><span style='color:red'>[BC 2016-Sep-26: Now that we only have one 27-m antenna. It means that we need to solve for the complex gain for each channel on each 2-m antenna, totaling 13 x n<sub>ch</sub> solutions (where n<sub>ch</sub> is # of spectral channels), from 13 x n<sub>ch</sub> measurements of complex visibilities on all 13 small-large baselines. The measured visibilities can be described as: </span></ins></div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div> </div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;"><center><math>G_{an}(k)=G_a(k)G_n^*(k)=A_a(k)A_n(k)A_{an}(k)e^{i(\phi_n(k)-\phi_a(k)+\phi_{an}(k))}</math></center></ins></div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div> </div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;"><span style='color:red'>where <math>A_i(k)</math> and <math>\phi_i(k)</math> are amplitude and phase of each antenna at a given spectral channel k, and <math>A_{an}(k)</math> and <math>\phi_{an}(k)</math> are the corresponding baseline error, or closure error. There is no over-determined measurements, unfortunately, so we have to assume no closure error and solve for the antenna-based amplitudes and phases. We also need to use the 27-m antenna as the reference and set its amplitude to unity and phase to zero for all channels.]</span></ins></div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div> </div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">{| class="wikitable"</ins></div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">!colspan="7" | Table 4: Summary of Bandpass Calibration</ins></div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">|-</ins></div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">!Calibration Type</ins></div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">!Impacts Solar Observing?</ins></div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">!Products</ins></div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">!Uses</ins></div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">!Control Requirements</ins></div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">!Analysis Requirements</ins></div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">!Priority</ins></div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">|-</ins></div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">| Full spectrum bandpass calibration || No || Amplitude and phase on each large-small baseline over each spectral channel || Determine the antenna-based complex gain variations across each IF band || Longer integration time on each IF band to obtain adequate SNR || Miriad task mfcal may work, CASA task bandpass may work || Needed for detailed science investigations, could be deferred</ins></div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">|}</ins></div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>== Reference Gain Calibration ==</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>== Reference Gain Calibration ==</div></td></tr>
</table>Bchenhttp://ovsa.njit.edu//wiki/index.php?title=Calibration_Overview&diff=293&oldid=prevBchen: /* Observational Procedure */2016-09-26T13:47:16Z<p><span dir="auto"><span class="autocomment">Observational Procedure</span></span></p>
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<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">← Older revision</td>
<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 13:47, 26 September 2016</td>
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<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>=== Observational Procedure === </div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>=== Observational Procedure === </div></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>The entire array tracks a bright cosmic source, one IF band at a time, integrating on each band until good signal-to-noise is achieved. The procedure is repeated for each of the 34 bands. The sensitivity per polarization of a single baseline is given by</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>The entire array tracks a bright cosmic source, one IF band at a time, integrating on each band until good signal-to-noise is achieved. The procedure is repeated for each of the 34 bands. </div></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>, <del style="font-weight: bold; text-decoration: none;"> (1) </del></div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div> </div></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>where <del style="font-weight: bold; text-decoration: none;">Tsys</del>,i and <del style="font-weight: bold; text-decoration: none;">Di </del>are the system temperature (K) and diameter (m) of the <del style="font-weight: bold; text-decoration: none;">ith </del>element, and an antenna efficiency of 0.5 has been assumed. <del style="font-weight: bold; text-decoration: none;"> </del>If the system temperature of the cooled 27-m receivers is 30 K, and that of the 2-m receivers is 400 K, <del style="font-weight: bold; text-decoration: none;">this </del>is</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>The sensitivity per polarization of a single baseline is given by </div></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>. <del style="font-weight: bold; text-decoration: none;"> (2) </del></div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div> </div></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del style="font-weight: bold; text-decoration: none;">Using 1 </del>MHz <del style="font-weight: bold; text-decoration: none;">subchannel width</del>, it will take about 23 s <del style="font-weight: bold; text-decoration: none;">to do single IF bandpass calibration </del>with 10:1 signal to noise ratio on 3C84 (assuming 20 Jy flux density). <del style="font-weight: bold; text-decoration: none;"> </del>Probably the higher frequency bands will have lower signal to noise, so will take longer, but these are also the bands with the wider science bandwidths. A 50:1 signal to noise ratio measurement (rms phase error about 1.1 degree) on all 34 bands can be done in 6 hours. </div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;"><center><math>\sigma_{ij}=\frac{4.97\sqrt{T_{\rm sys</ins>,<ins style="font-weight: bold; text-decoration: none;">i}T_{\rm sys,j}}}{D_{i}D_{j}\sqrt{\Delta t_{\rm s} \Delta \nu_{\rm MHz}}}~{\rm Jy}</math>,</center></ins></div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div> </div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>where <ins style="font-weight: bold; text-decoration: none;"><math>T_{\rm sys</ins>, i<ins style="font-weight: bold; text-decoration: none;">}</math> </ins>and <ins style="font-weight: bold; text-decoration: none;"><math>D_i</math> </ins>are the system temperature (K) and diameter (m) of the <ins style="font-weight: bold; text-decoration: none;">i<sup>th</sup> </ins>element, and an antenna efficiency of 0.5 has been assumed. If the system temperature of the cooled 27-m receivers is 30 K, and that of the 2-m receivers is 400 K, <ins style="font-weight: bold; text-decoration: none;">the sensitivity on baselines between a 27m-2m pair </ins>is<ins style="font-weight: bold; text-decoration: none;">:</ins></div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div> </div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;"><center><math>\sigma_{l, s}=\frac{9</ins>.<ins style="font-weight: bold; text-decoration: none;">6}{\sqrt{\Delta t_{\rm s} \Delta \nu_{\rm </ins>MHz<ins style="font-weight: bold; text-decoration: none;">}}}~{\rm Jy}</math></ins>,<ins style="font-weight: bold; text-decoration: none;"></center></ins></div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div> </div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>it will take about 23 s with 10:1 signal to noise ratio on 3C84 <ins style="font-weight: bold; text-decoration: none;">on each 1-MHz-wide channel </ins>(assuming <ins style="font-weight: bold; text-decoration: none;">~</ins>20 Jy flux density). Probably the higher frequency bands will have lower signal to noise, so will take longer, but these are also the bands with the wider science bandwidths. A 50:1 signal to noise ratio measurement (rms phase error about 1.1 degree) on all 34 bands can be done in 6 hours.</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>=== Analysis Procedure ===</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>=== Analysis Procedure ===</div></td></tr>
</table>Bchenhttp://ovsa.njit.edu//wiki/index.php?title=Calibration_Overview&diff=289&oldid=prevBchen: /* Observational Procedure */2016-09-26T13:07:01Z<p><span dir="auto"><span class="autocomment">Observational Procedure</span></span></p>
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<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 13:07, 26 September 2016</td>
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<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>=== Observational Procedure ===</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>=== Observational Procedure ===</div></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>The procedure for taking delay center calibration data is to track any strong interferometric point source and sweep the coarse delays in a TBD manner (i.e. track the geometric delay and apply a delay offset, and sweep the offset over some window &Delta;&tau;, from – &Delta;&tau;/2 to +&Delta;&tau;/2) so that the phase slope across an IF band (after the corrections described above for nominal phase slope and fringe rotation) can be obtained. The delay that results in the flattest slope is the correct one. An alternative is to vector average the data over the IF band and maximize the amplitude, which would be a more sensitive measure, but could be adversely affected by RFI. This works for any band, so it should be possible to find an RFI-free band where the chosen point source is strongest. Note that the delays are antenna-based, so they have to be swept differentially (it is the difference in delay between antennas that matters). When using a cosmic source, it is enough to set one of the 27-m antennas as the reference antenna and sweep the delays of each of the others simultaneously, but an alternative is to sweep the two 27-m delays in opposite directions so that all large-small baselines can be examined separately. It is probably worthwhile to check the delays on an isolated solar active region, when available, so that small-small baseline delays can be examined. No doubt there is a clever algorithm to make sweeping of delays most efficient, so that multiple delay centers can be determined simultaneously. The duration of the calibration observation will be set by the integration time needed for an acceptable RMS deviation for the individual measurements at each delay step, and the number of steps over which the delay is swept. The delay center should be very stable, and once determined only changes to hardware or physical cables should occasion the need for remeasuring the delays. UPDATE: We have learned that on restarting a ROACH board it comes up with an indeterminate 4&tau;<sub>s</sub> ambiguity in delay due to the sampling (ADC) clock being 4 times the FPGA clock. This means that WHENEVER A ROACH IS REBOOTED a new delay calibration is needed. A suggested methodology is to go to the Sirius XM Blues geosynchronous satellite at 115 W longitude and observe its S band (2332.5-2345.0 MHz) transmission, to determine the optimum delay by minimizing the phase slope. It will not be necessary to sweep the delay for this, however. The phase slope over 12.5 MHz will be 3.75&Delta;n degrees, where &Delta;n (ranging from -3 to 3 in units of &tau;<sub>s</sub>) is the number of steps by which the delay center has changed since the previous measurement. A special pipeline procedure would be created to do the analysis and update the delay center tables. <span style=color:orange>[BC 9/25/2016: We can also use strong cosmic calibrators to <del style="font-weight: bold; text-decoration: none;">do </del>the delay <del style="font-weight: bold; text-decoration: none;">solution</del>.] </span></div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>The procedure for taking delay center calibration data is to track any strong interferometric point source and sweep the coarse delays in a TBD manner (i.e. track the geometric delay and apply a delay offset, and sweep the offset over some window &Delta;&tau;, from – &Delta;&tau;/2 to +&Delta;&tau;/2) so that the phase slope across an IF band (after the corrections described above for nominal phase slope and fringe rotation) can be obtained. The delay that results in the flattest slope is the correct one. An alternative is to vector average the data over the IF band and maximize the amplitude, which would be a more sensitive measure, but could be adversely affected by RFI. This works for any band, so it should be possible to find an RFI-free band where the chosen point source is strongest. Note that the delays are antenna-based, so they have to be swept differentially (it is the difference in delay between antennas that matters). When using a cosmic source, it is enough to set one of the 27-m antennas as the reference antenna and sweep the delays of each of the others simultaneously, but an alternative is to sweep the two 27-m delays in opposite directions so that all large-small baselines can be examined separately. It is probably worthwhile to check the delays on an isolated solar active region, when available, so that small-small baseline delays can be examined. No doubt there is a clever algorithm to make sweeping of delays most efficient, so that multiple delay centers can be determined simultaneously. The duration of the calibration observation will be set by the integration time needed for an acceptable RMS deviation for the individual measurements at each delay step, and the number of steps over which the delay is swept. The delay center should be very stable, and once determined only changes to hardware or physical cables should occasion the need for remeasuring the delays. UPDATE: We have learned that on restarting a ROACH board it comes up with an indeterminate 4&tau;<sub>s</sub> ambiguity in delay due to the sampling (ADC) clock being 4 times the FPGA clock. This means that WHENEVER A ROACH IS REBOOTED a new delay calibration is needed. A suggested methodology is to go to the Sirius XM Blues geosynchronous satellite at 115 W longitude and observe its S band (2332.5-2345.0 MHz) transmission, to determine the optimum delay by minimizing the phase slope. It will not be necessary to sweep the delay for this, however. The phase slope over 12.5 MHz will be 3.75&Delta;n degrees, where &Delta;n (ranging from -3 to 3 in units of &tau;<sub>s</sub>) is the number of steps by which the delay center has changed since the previous measurement. A special pipeline procedure would be created to do the analysis and update the delay center tables. <span style=color:orange>[BC 9/25/2016: We can also use strong cosmic calibrators to <ins style="font-weight: bold; text-decoration: none;">obtain </ins>the delay <ins style="font-weight: bold; text-decoration: none;">solutions</ins>.] </span></div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>=== Analysis Procedure ===</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>=== Analysis Procedure ===</div></td></tr>
</table>Bchenhttp://ovsa.njit.edu//wiki/index.php?title=Calibration_Overview&diff=288&oldid=prevBchen: /* System Gain Calibration (incomplete) */2016-09-26T13:04:49Z<p><span dir="auto"><span class="autocomment">System Gain Calibration (incomplete)</span></span></p>
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<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>[[File:Eovsa_gain_controls.png|thumb|600px|EOVSA Gain Control "Knobs"]]</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>[[File:Eovsa_gain_controls.png|thumb|600px|EOVSA Gain Control "Knobs"]]</div></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del style="font-weight: bold; text-decoration: none;"></del></div></td><td colspan="2" class="diff-side-added"></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del style="font-weight: bold; text-decoration: none;"><span style="color:red">[BC 9/24/2016: Things below are probably outdated]</span></del></div></td><td colspan="2" class="diff-side-added"></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>This attenuation scheme uses the Day/Night calibrator as a single setting, while the others are variable in 1 dB steps. The Day/Night attenuator difference of 17 dB is probably too much. The solar variation attenuator in the front end applies to the entire 1-18 GHz RF band, and sets the overall power level to keep the optical link in its linear range. Note that strong fluctuations in a narrow band (e.g. spike bursts) will have less effect when integrated over the entire RF band, so changes to this attenuator should normally be slow and steady during solar bursts. In the back end, the attenuation is applied in the IF (650-1150 MHz) chain. The first attenuator is for leveling the receiver in the absence of bursts. Once leveled, the settings for each receiver will vary with IF band, but will be fixed in time. The second attenuator is for maintaining the output level during solar bursts, and it is this attenuator that will need to be controlled on a relatively fast timescale. Each attenuator will need to have each of its steps calibrated. The two back end attenuators will be in a single integrated assembly, and are best measured offline using test equipment. Assuming adequate temperature control, they should be stable, and changes would indicate a failure of the assembly. Thus, a maintenance test can be conducted periodically to check their values, but it should not be necessary to have a daily gain calibration procedure that checks every IF attenuation setting.</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>This attenuation scheme uses the Day/Night calibrator as a single setting, while the others are variable in 1 dB steps. The Day/Night attenuator difference of 17 dB is probably too much. The solar variation attenuator in the front end applies to the entire 1-18 GHz RF band, and sets the overall power level to keep the optical link in its linear range. Note that strong fluctuations in a narrow band (e.g. spike bursts) will have less effect when integrated over the entire RF band, so changes to this attenuator should normally be slow and steady during solar bursts. In the back end, the attenuation is applied in the IF (650-1150 MHz) chain. The first attenuator is for leveling the receiver in the absence of bursts. Once leveled, the settings for each receiver will vary with IF band, but will be fixed in time. The second attenuator is for maintaining the output level during solar bursts, and it is this attenuator that will need to be controlled on a relatively fast timescale. Each attenuator will need to have each of its steps calibrated. The two back end attenuators will be in a single integrated assembly, and are best measured offline using test equipment. Assuming adequate temperature control, they should be stable, and changes would indicate a failure of the assembly. Thus, a maintenance test can be conducted periodically to check their values, but it should not be necessary to have a daily gain calibration procedure that checks every IF attenuation setting.</div></td></tr>
</table>Bchenhttp://ovsa.njit.edu//wiki/index.php?title=Calibration_Overview&diff=240&oldid=prevBchen: /* Analysis Procedure */2016-09-25T12:51:52Z<p><span dir="auto"><span class="autocomment">Analysis Procedure</span></span></p>
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<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>=== Analysis Procedure ===</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>=== Analysis Procedure ===</div></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>In the case of delay calibration on a cosmic source with the 27-m antennas, a full delay calibration will result in 2(N <del style="font-weight: bold; text-decoration: none;">2</del>) + 1 measurements (27 for N = 15) to determine N <del style="font-weight: bold; text-decoration: none;">1 </del>(14 for N = 15) delays (one reference antenna is set to zero delay). The set of over-determined measurements can be used to find a least-squares solution. <del style="font-weight: bold; text-decoration: none;"> </del>If only one delay needs to be determined (due, for example, to a hardware change affecting only one antenna), then a subarray with the one 2-m antenna and two 27-m antennas can be used, and only the affected antenna needs to be swept, resulting in 2 measurements to determine one delay. Nevertheless, it is probably good practice to measure all of the delays on some periodic schedule. In the case of delay calibration on a solar active region, with no 27-m antennas, both the delay control and analysis are more complicated.</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>In the case of delay calibration on a cosmic source with the 27-m antennas, a full delay calibration will result in 2(N <ins style="font-weight: bold; text-decoration: none;">- 2</ins>) + 1 measurements (27 for N = 15) to determine N <ins style="font-weight: bold; text-decoration: none;">- 1 </ins>(14 for N = 15) delays (one reference antenna is set to zero delay). The set of over-determined measurements can be used to find a least-squares solution. If only one delay needs to be determined (due, for example, to a hardware change affecting only one antenna), then a subarray with the one 2-m antenna and two 27-m antennas can be used, and only the affected antenna needs to be swept, resulting in 2 measurements to determine one delay. Nevertheless, it is probably good practice to measure all of the delays on some periodic schedule. In the case of delay calibration on a solar active region, with no 27-m antennas, both the delay control and analysis are more complicated. <ins style="font-weight: bold; text-decoration: none;"><span style='color:orange'>[BC 9/25/2016: Now that we only have one 27-m antenna, so our measurements are no longer over-determined: 13 measurements to determine 13 delays (it would be convenient to just set the 27-m antenna to zero delay). In practice, we can still yield plausible solutions based on observation of a strong cosmic source (e.g., 3C84).]</span> </ins></div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div> </div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">{| class="wikitable"</ins></div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">!colspan="7" | Table 4: Summary of Delay Calibration</ins></div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">|-</ins></div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">!Calibration Type</ins></div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">!Impacts Solar Observing?</ins></div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">!Products</ins></div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">!Uses</ins></div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">!Control Requirements</ins></div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">!Analysis Requirements</ins></div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">!Priority</ins></div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">|-</ins></div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">| Full array delay calibration on cosmic source || No || Delay pattern for each large- small baseline over an IF band || Determine optimum delay centers || Control 27-m delays in correlator (separately from geometric delay tracking) || Special analysis routine to find/solve for optimum delay solution || Essential</ins></div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">|-</ins></div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">| Single antenna delay calibration on cosmic source || No || Delay pattern for baselines A- n and B-n,* where n is the small antenna || Determine optimum delay center for one antenna || Control 27-m delays in correlator (separately from geometric delay tracking) || Simple analysis routine to find optimum delay || Needed, could be deferred</ins></div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">|-</ins></div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">| Full solar array delay calibration on solar active region || Yes || Delay pattern for each small- small baseline over an IF band || Verify delay centers on small-small baselines || Control all delays in correlator (separately from geometric delay tracking) || Special analysis routine to find/solve for optimum delay solution || Good to have, can be deferred</ins></div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">|}</ins></div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>== Bandpass Calibration ==</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>== Bandpass Calibration ==</div></td></tr>
</table>Bchenhttp://ovsa.njit.edu//wiki/index.php?title=Calibration_Overview&diff=239&oldid=prevBchen: /* Observational Procedure */2016-09-25T12:47:37Z<p><span dir="auto"><span class="autocomment">Observational Procedure</span></span></p>
<table style="background-color: #fff; color: #202122;" data-mw="interface">
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<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">← Older revision</td>
<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 12:47, 25 September 2016</td>
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<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>=== Observational Procedure ===</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>=== Observational Procedure ===</div></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>The procedure for taking delay center calibration data is to track any strong interferometric point source and sweep the coarse delays in a TBD manner (i.e. track the geometric delay and apply a delay offset, and sweep the offset over some window &Delta;&tau;, from – &Delta;&tau;/2 to +&Delta;&tau;/2) so that the phase slope across an IF band (after the corrections described above for nominal phase slope and fringe rotation) can be obtained. The delay that results in the flattest slope is the correct one. An alternative is to vector average the data over the IF band and maximize the amplitude, which would be a more sensitive measure, but could be adversely affected by RFI. This works for any band, so it should be possible to find an RFI-free band where the chosen point source is strongest. Note that the delays are antenna-based, so they have to be swept differentially (it is the difference in delay between antennas that matters). When using a cosmic source, it is enough to set one of the 27-m antennas as the reference antenna and sweep the delays of each of the others simultaneously, but an alternative is to sweep the two 27-m delays in opposite directions so that all large-small baselines can be examined separately. It is probably worthwhile to check the delays on an isolated solar active region, when available, so that small-small baseline delays can be examined. No doubt there is a clever algorithm to make sweeping of delays most efficient, so that multiple delay centers can be determined simultaneously. The duration of the calibration observation will be set by the integration time needed for an acceptable RMS deviation for the individual measurements at each delay step, and the number of steps over which the delay is swept. The delay center should be very stable, and once determined only changes to hardware or physical cables should occasion the need for remeasuring the delays. UPDATE: We have learned that on restarting a ROACH board it comes up with an indeterminate 4&tau;<sub>s</sub> ambiguity in delay due to the sampling (ADC) clock being 4 times the FPGA clock. This means that WHENEVER A ROACH IS REBOOTED a new delay calibration is needed. A suggested methodology is to go to the Sirius XM Blues geosynchronous satellite at 115 W longitude and observe its S band (2332.5-2345.0 MHz) transmission, to determine the optimum delay by minimizing the phase slope. It will not be necessary to sweep the delay for this, however. The phase slope over 12.5 MHz will be 3.75&Delta;n degrees, where <del style="font-weight: bold; text-decoration: none;">\</del>Delta;n (ranging from -3 to 3 in units of &tau;<sub>s</sub>) is the number of steps by which the delay center has changed since the previous measurement. A special pipeline procedure would be created to do the analysis and update the delay center tables. <span style=color:orange>[BC 9/25/2016: <del style="font-weight: bold; text-decoration: none;">I </del>also <del style="font-weight: bold; text-decoration: none;">got pretty good delay solutions based on observation of a </del>strong cosmic <del style="font-weight: bold; text-decoration: none;">source (3C84) using only large-small baselines</del>.] </span></div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>The procedure for taking delay center calibration data is to track any strong interferometric point source and sweep the coarse delays in a TBD manner (i.e. track the geometric delay and apply a delay offset, and sweep the offset over some window &Delta;&tau;, from – &Delta;&tau;/2 to +&Delta;&tau;/2) so that the phase slope across an IF band (after the corrections described above for nominal phase slope and fringe rotation) can be obtained. The delay that results in the flattest slope is the correct one. An alternative is to vector average the data over the IF band and maximize the amplitude, which would be a more sensitive measure, but could be adversely affected by RFI. This works for any band, so it should be possible to find an RFI-free band where the chosen point source is strongest. Note that the delays are antenna-based, so they have to be swept differentially (it is the difference in delay between antennas that matters). When using a cosmic source, it is enough to set one of the 27-m antennas as the reference antenna and sweep the delays of each of the others simultaneously, but an alternative is to sweep the two 27-m delays in opposite directions so that all large-small baselines can be examined separately. It is probably worthwhile to check the delays on an isolated solar active region, when available, so that small-small baseline delays can be examined. No doubt there is a clever algorithm to make sweeping of delays most efficient, so that multiple delay centers can be determined simultaneously. The duration of the calibration observation will be set by the integration time needed for an acceptable RMS deviation for the individual measurements at each delay step, and the number of steps over which the delay is swept. The delay center should be very stable, and once determined only changes to hardware or physical cables should occasion the need for remeasuring the delays. UPDATE: We have learned that on restarting a ROACH board it comes up with an indeterminate 4&tau;<sub>s</sub> ambiguity in delay due to the sampling (ADC) clock being 4 times the FPGA clock. This means that WHENEVER A ROACH IS REBOOTED a new delay calibration is needed. A suggested methodology is to go to the Sirius XM Blues geosynchronous satellite at 115 W longitude and observe its S band (2332.5-2345.0 MHz) transmission, to determine the optimum delay by minimizing the phase slope. It will not be necessary to sweep the delay for this, however. The phase slope over 12.5 MHz will be 3.75&Delta;n degrees, where <ins style="font-weight: bold; text-decoration: none;">&</ins>Delta;n (ranging from -3 to 3 in units of &tau;<sub>s</sub>) is the number of steps by which the delay center has changed since the previous measurement. A special pipeline procedure would be created to do the analysis and update the delay center tables. <span style=color:orange>[BC 9/25/2016: <ins style="font-weight: bold; text-decoration: none;">We can </ins>also <ins style="font-weight: bold; text-decoration: none;">use </ins>strong cosmic <ins style="font-weight: bold; text-decoration: none;">calibrators to do the delay solution</ins>.] </span></div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>=== Analysis Procedure ===</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>=== Analysis Procedure ===</div></td></tr>
</table>Bchenhttp://ovsa.njit.edu//wiki/index.php?title=Calibration_Overview&diff=238&oldid=prevBchen: /* Observational Procedure */2016-09-25T11:35:50Z<p><span dir="auto"><span class="autocomment">Observational Procedure</span></span></p>
<table style="background-color: #fff; color: #202122;" data-mw="interface">
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<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">← Older revision</td>
<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 11:35, 25 September 2016</td>
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<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>=== Observational Procedure ===</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>=== Observational Procedure ===</div></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>The procedure for taking delay center calibration data is to track any strong interferometric point source and sweep the coarse delays in a TBD manner (i.e. track the geometric delay and apply a delay offset, and sweep the offset over some window <del style="font-weight: bold; text-decoration: none;"></del>, from <del style="font-weight: bold; text-decoration: none;">– </del>/2 to <del style="font-weight: bold; text-decoration: none;"> </del>/2) so that the phase slope across an IF band (after the corrections described above for nominal phase slope and fringe rotation) can be obtained. The delay that results in the flattest slope is the correct one. An alternative is to vector average the data over the IF band and maximize the amplitude, which would be a more sensitive measure, but could be adversely affected by RFI. This works for any band, so it should be possible to find an RFI-free band where the chosen point source is strongest. Note that the delays are antenna-based, so they have to be swept differentially (it is the difference in delay between antennas that matters). When using a cosmic source, it is enough to set one of the 27-m antennas as the reference antenna and sweep the delays of each of the others simultaneously, but an alternative is to sweep the two 27-m delays in opposite directions so that all large-small baselines can be examined separately. It is probably worthwhile to check the delays on an isolated solar active region, when available, so that small-small baseline delays can be examined. No doubt there is a clever algorithm to make sweeping of delays most efficient, so that multiple delay centers can be determined simultaneously. The duration of the calibration observation will be set by the integration time needed for an acceptable RMS deviation for the individual measurements at each delay step, and the number of steps over which the delay is swept. The delay center should be very stable, and once determined only changes to hardware or physical cables should occasion the need for remeasuring the delays. UPDATE: We have learned that on restarting a ROACH board it comes up with an indeterminate <del style="font-weight: bold; text-decoration: none;">4s </del>ambiguity in delay due to the sampling (ADC) clock being 4 times the FPGA clock. This means that WHENEVER A ROACH IS REBOOTED a new delay calibration is needed. A suggested methodology is to go to the Sirius XM Blues geosynchronous satellite at 115 W longitude and observe its S band (2332.5-2345.0 MHz) transmission, to determine the optimum delay by minimizing the phase slope. It will not be necessary to sweep the delay for this, however. The phase slope over 12.5 MHz will be 3.<del style="font-weight: bold; text-decoration: none;">75n </del>degrees, where <del style="font-weight: bold; text-decoration: none;">n </del>(ranging from -3 to 3 in units of <del style="font-weight: bold; text-decoration: none;">s</del>) is the number of steps by which the delay center has changed since the previous measurement. A special pipeline procedure would be created to do the analysis and update the delay center tables. </div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>The procedure for taking delay center calibration data is to track any strong interferometric point source and sweep the coarse delays in a TBD manner (i.e. track the geometric delay and apply a delay offset, and sweep the offset over some window <ins style="font-weight: bold; text-decoration: none;">&Delta;&tau;</ins>, from <ins style="font-weight: bold; text-decoration: none;">– &Delta;&tau;</ins>/2 to <ins style="font-weight: bold; text-decoration: none;">+&Delta;&tau;</ins>/2) so that the phase slope across an IF band (after the corrections described above for nominal phase slope and fringe rotation) can be obtained. The delay that results in the flattest slope is the correct one. An alternative is to vector average the data over the IF band and maximize the amplitude, which would be a more sensitive measure, but could be adversely affected by RFI. This works for any band, so it should be possible to find an RFI-free band where the chosen point source is strongest. Note that the delays are antenna-based, so they have to be swept differentially (it is the difference in delay between antennas that matters). When using a cosmic source, it is enough to set one of the 27-m antennas as the reference antenna and sweep the delays of each of the others simultaneously, but an alternative is to sweep the two 27-m delays in opposite directions so that all large-small baselines can be examined separately. It is probably worthwhile to check the delays on an isolated solar active region, when available, so that small-small baseline delays can be examined. No doubt there is a clever algorithm to make sweeping of delays most efficient, so that multiple delay centers can be determined simultaneously. The duration of the calibration observation will be set by the integration time needed for an acceptable RMS deviation for the individual measurements at each delay step, and the number of steps over which the delay is swept. The delay center should be very stable, and once determined only changes to hardware or physical cables should occasion the need for remeasuring the delays. UPDATE: We have learned that on restarting a ROACH board it comes up with an indeterminate <ins style="font-weight: bold; text-decoration: none;">4&tau;<sub>s</sub> </ins>ambiguity in delay due to the sampling (ADC) clock being 4 times the FPGA clock. This means that WHENEVER A ROACH IS REBOOTED a new delay calibration is needed. A suggested methodology is to go to the Sirius XM Blues geosynchronous satellite at 115 W longitude and observe its S band (2332.5-2345.0 MHz) transmission, to determine the optimum delay by minimizing the phase slope. It will not be necessary to sweep the delay for this, however. The phase slope over 12.5 MHz will be 3.<ins style="font-weight: bold; text-decoration: none;">75&Delta;n </ins>degrees, where <ins style="font-weight: bold; text-decoration: none;">\Delta;n </ins>(ranging from -3 to 3 in units of <ins style="font-weight: bold; text-decoration: none;">&tau;<sub>s</sub></ins>) is the number of steps by which the delay center has changed since the previous measurement. A special pipeline procedure would be created to do the analysis and update the delay center tables. <ins style="font-weight: bold; text-decoration: none;"><span style=color:orange>[BC 9/25/2016: I also got pretty good delay solutions based on observation of a strong cosmic source (3C84) using only large-small baselines.] </span></ins></div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>=== Analysis Procedure ===</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>=== Analysis Procedure ===</div></td></tr>
</table>Bchenhttp://ovsa.njit.edu//wiki/index.php?title=Calibration_Overview&diff=237&oldid=prevBchen: /* Delay Tracking */2016-09-25T11:16:01Z<p><span dir="auto"><span class="autocomment">Delay Tracking</span></span></p>
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<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 11:16, 25 September 2016</td>
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<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>=== Delay Tracking === </div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>=== Delay Tracking === </div></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>It is useful to look at some issues related to delay tracking (ref. the A. R. Thompson FASR memo, “FASR_Delay_Fringe_Phsw.pdf”). For the currently considered design, the ADCs will operate at a clock rate of 1200 MHz, or sample time <del style="font-weight: bold; text-decoration: none;">s </del>= 0.833 ns, so coarse delays of that step-size will be trivial to implement using a shift register. In tracking the delay, we would change the delay when the delay error is, say, +<del style="font-weight: bold; text-decoration: none;">½ s</del>, making it then <del style="font-weight: bold; text-decoration: none;">½ s</del>, so this is the maximum delay error. It is interesting that the bandwidth and the sample time are not independent, but rather obey the Nyquist criterion <del style="font-weight: bold; text-decoration: none;">s = </del>1/<del style="font-weight: bold; text-decoration: none;">(2)</del>, so that <del style="font-weight: bold; text-decoration: none;">s </del>= <del style="font-weight: bold; text-decoration: none;">½</del>. Assuming that the IF band ranges from 0 to <del style="font-weight: bold; text-decoration: none;"> </del>(600 MHz in our case) the maximum phase slope across the band, for delay error <del style="font-weight: bold; text-decoration: none;"></del>, is <del style="font-weight: bold; text-decoration: none;"> </del>= <del style="font-weight: bold; text-decoration: none;">2 </del>= <del style="font-weight: bold; text-decoration: none;"></del>/2, where <del style="font-weight: bold; text-decoration: none;"> </del>= <del style="font-weight: bold; text-decoration: none;">½s </del>was used. Therefore, the highest IF frequency channel’s phase will vary linearly with time between <del style="font-weight: bold; text-decoration: none;"></del>/2 and <del style="font-weight: bold; text-decoration: none;"></del>/2. The rate of delay obeys the equation</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>It is useful to look at some issues related to delay tracking (ref. the A. R. Thompson FASR memo, “FASR_Delay_Fringe_Phsw.pdf”). For the currently considered design, the ADCs will operate at a clock rate of 1200 MHz, or sample time <ins style="font-weight: bold; text-decoration: none;">&tau;<sub>s</sub> </ins>= 0.833 ns, so coarse delays of that step-size will be trivial to implement using a shift register. In tracking the delay, we would change the delay when the delay error is, say, +<ins style="font-weight: bold; text-decoration: none;">1/2 &tau;<sub>s</sub></ins>, making it then <ins style="font-weight: bold; text-decoration: none;">-1/2 &tau;<sub>s</sub></ins>, so this is the maximum delay error. It is interesting that the bandwidth and the sample time are not independent, but rather obey the Nyquist criterion 1/<ins style="font-weight: bold; text-decoration: none;">&tau;<sub>s</sub> = 2&Delta;&nu;</ins>, so that <ins style="font-weight: bold; text-decoration: none;">&Delta;&nu;&tau;<sub>s</sub> </ins>= <ins style="font-weight: bold; text-decoration: none;">1/2</ins>. Assuming that the IF band ranges from 0 to <ins style="font-weight: bold; text-decoration: none;">&Delta;&nu; </ins>(600 MHz in our case) the maximum phase slope across the band, for delay error <ins style="font-weight: bold; text-decoration: none;">&tau;</ins>, is <ins style="font-weight: bold; text-decoration: none;">&Delta;&phi; </ins>= <ins style="font-weight: bold; text-decoration: none;">2&pi;&tau;&Delta;&nu; </ins>= <ins style="font-weight: bold; text-decoration: none;">&pi;</ins>/2, where <ins style="font-weight: bold; text-decoration: none;">&tau;</ins>=<ins style="font-weight: bold; text-decoration: none;">1/2&tau;<sub>s</sub> </ins>was used. Therefore, the highest IF frequency channel’s phase will vary linearly with time between <ins style="font-weight: bold; text-decoration: none;">-&pi;</ins>/2 and <ins style="font-weight: bold; text-decoration: none;">+&pi;</ins>/2. The rate of delay obeys the equation</div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div> </div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;"><center><math>\frac{d\tau}{dt} = \Omega B \cos(h)/c </math></center></ins></div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div> </div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div> </div></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>where <del style="font-weight: bold; text-decoration: none;"> </del>= 7.<del style="font-weight: bold; text-decoration: none;">27×105 </del>rad/s is the rotation rate of the Earth, B is the baseline length (maximum about 1.5 km), and h is the hour angle. The maximum rate is then about 0.364 ns/s, so for <del style="font-weight: bold; text-decoration: none;">s </del>= 0.833 ns we would have to step the delay once every 2.29 s for the worst case. To keep the phase of the highest channel within 1 degree, the phase correction must be updated every 2.29 s/90 = 25 ms. It appears that this worst case can be adequately handled by correcting the phase at the output of the correlator, after the 20 ms accumulation. Note also that inserting the delays in the IF causes fringe rotation (natural fringes) at a maximum fringe rate <del style="font-weight: bold; text-decoration: none;">f </del>= (0.364 ns/s)(18 GHz) = 6.6 Hz. Averaging over a time <del style="font-weight: bold; text-decoration: none;">av </del>= 20 ms results in an amplitude given by sinc(<del style="font-weight: bold; text-decoration: none;">fav</del>) = 0.97 in the worst case (18 GHz, at noon, on the longest baseline). This suggests that we might get away with applying fringe stopping at the output of the correlator as well, with a possible small amplitude correction applied. UPDATE: The correlator coarse delays will be set only on a 1 s tick, therefore the delay can be an extra ½ s early or late, giving an error in the worst case of ±0.598 ns (this is ±0.416 ns ± (½ s) (0.364 ns/s), or ±0.<del style="font-weight: bold; text-decoration: none;">72s</del>).</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>where <ins style="font-weight: bold; text-decoration: none;">&Omega; </ins>= 7.<ins style="font-weight: bold; text-decoration: none;">27×10<sup>-5</sup> </ins>rad/s is the rotation rate of the Earth, B is the baseline length (maximum about 1.5 km), and h is the hour angle. The maximum rate is then about 0.364 ns/s, so for <ins style="font-weight: bold; text-decoration: none;">sample time &tau;<sub>s</sub> </ins>= 0.833 ns we would have to step the delay once every 2.29 s for the worst case. To keep the phase of the highest channel within 1 degree, the phase correction must be updated every 2.29 s/90 = 25 ms. It appears that this worst case can be adequately handled by correcting the phase at the output of the correlator, after the 20 ms accumulation. Note also that inserting the delays in the IF causes fringe rotation (natural fringes) at a maximum fringe rate <ins style="font-weight: bold; text-decoration: none;">&nu;<sub>f</sub> </ins>= (0.364 ns/s)(18 GHz) = 6.6 Hz. Averaging over a time <ins style="font-weight: bold; text-decoration: none;">&tau;<sub>av</sub> </ins>= 20 ms results in an amplitude given by sinc(<ins style="font-weight: bold; text-decoration: none;">&nu;<sub>f</sub>&tau;<sub>av</sub></ins>) = 0.97 in the worst case (18 GHz, at noon, on the longest baseline). This suggests that we might get away with applying fringe stopping at the output of the correlator as well, with a possible small amplitude correction applied. UPDATE: The correlator coarse delays will be set only on a 1 s tick, therefore the delay can be an extra ½ s early or late, giving an error in the worst case of ±0.598 ns (this is ±0.416 ns ± (½ s) (0.364 ns/s), or ±0.<ins style="font-weight: bold; text-decoration: none;">72&tau;<sub>s</sub></ins>).</div></td></tr>
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<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>=== Observational Procedure ===</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>=== Observational Procedure ===</div></td></tr>
</table>Bchen