The phase path length is different for polA,B as it comes from the dewar, through the upstairs if/lo, down the fiber optic cables, through the
2nd IF, and into the backends. This phase difference can be measured  by splitting the signal from a cal diode and injecting it into polA and polB (we call this the correlated cal). This is typically done in the dewar before the lna (but after the polarizer).

    In jan2019 p3233 noticed  that the phase difference (measured as MHz/deg across frequency) had changed a bit. To investigate this problem i looked at their historical data (which included P3031, P3139,P3185, and P3233) covering may 2016 through dec 2018. After looking at the data,
p3233 found a problem in their code (so there was no actual problem). Since i had already looked at the data, the results might be interesting for later reference.

Setup used:

    Different if/lo setups can have different  phase differences (depending on the mixer, filters used..). The setup used for this data was:

• lbw in linear mode.
• the 1st mixing stage used the 10GHz upconverter. The if1 was then 1-2GHz.
• the downstairs if/lo used the 1-2 GHz with the 3 500 MHz filters (1000-1500, 1250-1750, and 1500-2000)MHz.
• The mock spectrometer backend  was used.
  
• 4x 86MHz bands typically centered at 1170,1420,1520, and 1620 MHz.
• full stokes data was taken with 32,64, or 128 channels.
• The calibration scans used the 25 Hz hardware winking cal.
• The spectral dump times were around 300 usecs.
• Around 11 seconds of data were taken (11 1 second records).
  

Processing the data:

    The stokes parameters are:

• StokesI: Ea*Ea + Eb*Eb (I've left out the complex * sign)(
• StokesQ: Ea*Ea - Eb*Eb
• StokesU: 2*Ea*Eb*cos(delta)
• StokesV: 2*Ea*Eb *sin(delta)
• where delta is the phase angle between polA and polB

The phase difference delta =Atan(stokesV/stokesU) = Atan(sin(delta)/cos(delta))

•  Since Ea,Eb cancel, it is not necessary to amplitude calibrate the signals to get the correct value of delta.
• Note:
  
• When  using a mixer, a high side lo will flip the sign of stokesV and leave the sign of stokesU unchanged.
• So if the final recorded band has an odd number of high side lo's, then stokesV should be negated before using it (i've done this for the data).
  
• more info
  
  

To find the phase difference (delta) vs frequency :

•  For each 11 second cal scan:
• for each 1 second cal record:
• compute the total power for each 300 usec spectra (stokes I averaged over the bandpass).
  
• compute the median of this total power time series.
  
• separate  out the cal on and cal off samples (greater, less than the median value).
  
• do a linear fit to the calon, caloff samples (separately).
• throw out any points outliers (greater than 3 sigma).
• This was to remove any points close to the cal transitions as well as  rfi.
• average the calOn and calOff spectra (scaling by the number used)
  
• compute calDif=calOn - calOff  (for each stokes parameter) this should only have power from the cal diode.
• compute delta(freq)=atan(stokesV/stokesU) from this cal difference.
  
• scan through delta(freq) unwrapping the phase jumps.
• Do a linear fit to delta(freq)= c0 + Slope*(freq- centerFreq)
• slope is the Degrees/MHz  change in delta.
• For each cal scan, 11 slopes were computed (1 for each 1 second record)
• the average and rms of these 11 numbers were then used as the slope and rms for the calscan.

Plotting the data:

    There were 139 cal scans each with 4 frequency measurements included in this data set (2016-2018).

The plots show the data and Deg/MHz results (.ps) (.pdf)

• Page 1: example of a 1 second integrated calOn - calOff spectra for the 4 frequency bands
• Each frame is a separate frequency band.
• The colors are: black-polA, red-polB, green-stokesU, blue-stokesV.
• Since the cal is injected evenly in polA,B, you would expect the cal power to show up in stokesU (i may have left off a factor of 2 here).
• The upper left of each frame shows which if2 filter was used for the band (1250,1500,1750), as well as the 2nd lo used. The 2nd IF center frequency was 325 MHz).
  
• Page 2: example deltaPhase vs frequency for each band (after the phase jumps were removed).
• Each frame is a separate frequency band.
• bands 2,3,4 are flipped in frequency. I have corrected stokesV for each of these (see above).
• The phase difference decreases as the frequency increases. There is about 600 Degress in the 86 MHz.
  
• Most of this difference is coming from the fiber optic cable difference (index of refraction) for the polA,B cables.
• Page 3: plots of the slope of the phaseDif vs frequency (from the fits)
  
• the fit was: delta = c0 + c1*(freq - cfr) for each band.. c1 is the slope (deg/MHz)
• For each cal scan the 11  1 second (calOn-calOff) slopes vs freq were fit.
• the program then computed the average and the rms for the coef from each fit.
• top: avg calscan slope (deg/MHz) vs freq.
• This is all of the data.
• Bottom: slope (deg/MHz) vs rms.
• The outliers on the upper plot have larger rms's. They were probably contaminated by rfi.
• Page 4: Slope (deg/MHz) vs freq keeping points with rms< .15 deg/MHz.
• the points with larger rms have been excluded. There are still a vew outliers.
  
• The colors show the epoch when the data was taken
• I've added a small offset to the frequency of the different bands so they don't completely overlay each other.
  
• A straight line would do a pretty good job of fitting the 1170, 1520, and 1620 data.
• The data in the 1420 band lay below the line fitting the other frequencies.
• The 1420 band uses the same if1 filter (1500MHz cfr) as the 1520 cfr band, so this difference is a bit of a mystery.

SUMMARY:

•     The deg/MHz phase difference for polA,B  by frequency band:

band Center Freq MHz	phase difference slope (deg/MHz)
1170	-6.51
1420	-7.53
1520	-7.51
1620	-7.67

• There was a small shift in the slope between may16 and may17 (about .1 deg/MHz).
• since 2017 it has been relatively stable.
• The slope at 1420 MHz is a bit low from the line fitting the 1170,1520,1620 data.
  
• Most of this difference is coming from the fiber optic cables (index of refraction difference in the polA,B cables).
  

processing: x101/190207/ caldoall.pro, fitcalphase.pro, proccalfile.pro, plotcalall.pro