• the cal Deflection total power vs time (.pdf)
• the calRatio vs freq plotted for each scan (.pdf)
• a fit to the CalRatio measurements (.pdf)
• computed Tcal and tsys in K using the new cal values (.pdf)

Links to SECTIONS:
Why the cals were remeasured.
The model used to compute the cal values
The parameter values used in the computation
Taking the data
Processing the data
Results
    Total power vs time by freq band.
     calRatio (caldif/caloff) vs freq
     Fitting to calRatio vs freq
     Computed Tcal and  tsys vs freq
Summary

Why the cals were remeasured.

Parameters used for Tcal computation

    The values i ended up using for the computations (see below for explanations) were:
 

	value	Notes
Tabsorber	310K	The tabs was 89.5F when we started the xband abs. For the last xb abs measurement, the sun hit the absorber. The 3 sband abs measurements were done and then we measured the abs temp to be 99F.  I ended up used 99F (310K)
Tsky	15K	includes any scattered energy. see below
Treceiver	60,65K	polA,B  see below
Tomt	300k	omt temperature.. a guess.
g	.05	reflection coef for horn/omt see below
alpha	(.07,.09)	omt absorption (polA,B)

 Taking the data:

• The hardware winking cal was used:
• 20 millisecond on
• 20 millisecond off
• the cycle started on a hardware 1 second tick.
• The mock spectrometer was set up to measure the spectra.
  
• 1 mock box was used  with the following setup:
• 172.032 MHz bandwidth
• 2048 spectral channels
• polA,B  measured
• data  sampled at 2 milliseconds (winking cal was 20 ms on , 20ms off).
• each scan (sky or absorber) took 2 minutes of data.
  
• The rf center freq was 2278 MHz .
  
• 2205 to 2245 was used from the computation (the rest of mock band lay outside of the rf filter.
  
• The measurement started at 11:05  and finished by 11:51 ast.
• We did 3 absorber scans followed  by 3 on sky  scans.
  
• The scan sequence was:

• Loc	ra,dec	az,el	mockFile #	Notes
  abs	..		500
  abs	--		600
  abs	--		700
  sky	03:39:45/25:25:18	-40,80	1100
  sky			1200
  sky			1300

Processing the data:

    For each scan the following is done:

• Input the winking cal spectra and compute the ratio of calDeflection(freq)/Caloff(freq)
  
• Average the 20 ms of calon, caloff, giving bCalOn[25*120], and bcalOff[25*120]
  
• exclude the 2 ms spectra before and after each cal transition. This gives 16ms of data after the average
• Compute the rms by chan for the bCalon and bCalOff data (for debugging)
  
• Compute the  avg calOn, calOff: bonAvg,boffAvg using the median for averaging
• compute the caldeflection and then the calRatio (by Tsys)
• bcalDef= bcalOn - bcalOff
• bcalRatio=bcalDefl/ bcaloff
• this removes the IF bandpass.
  
• This is then the cal value in units of Tsys (with cal off).
• Average calRatio for the 3 sky scans and the 3 absorber scans.
• Fit a curve to the calRatio for sky and abs.
  
• Compute Tcal using:
• Just the RatioAbs, RatioSky, and the combined RatioSky,RatioAbs (to remove Trcv).
• play around adjusting gamma, alpha, and Trcv to try and get the 3 different Tcal measurements to agree.
  

The Results

Total power vs time by freq band

    Plotting the calOn,calOff  total power vs time (.pdf)

• The total power is computed for each 20ms calOn, caolOff spectra.
• This total power was then normalized to its median value
• The absorber scans were normalized to the median value of the 3 abs scans
  
• the sky scans were normalized to the median value of the 3 sky scans.
•  This shows the gain variation during the abs and sky scans.
  
• The two frames are:(top polA, lower: polB).
• In a single frame there are 6 scans (horizontally):
• abs,abs,abs, sky,sky,sky
  
• blue lines separate the scans. (there is a time lag between each set of  scans).
• this is probably why you see a jumps in the polA sky scans.
  
• What the plots show:
• The abs values vary by about .5%
  
• the sky values change by about 2%.
  

Calratio (calDif/calOff) vs frequency

    The 2nd set of plots shows the calRatio vs freq plotted for each scan (.pdf)

• compute the median spectra for the calon, caloffs
• compute  (calOn-calOff)/calOff  spectra
• The division by calOff should remove the IF bandpass.
• Page 1: average spectra for each 2 minute scan
• top: polA
• bottom: polB
• each color is a different scan
  
• This shows the gain variation across the bandpass.
  
• Page 2: calRatio vs frequency (calOn - calOff)/calOff spectra.
  
• Each color is a different scan:
• black, red, green: abs
• blue,pink, lighter red: sky
  
• The cal is .5 to .7  ( Tsys on sky)
• the cal is .15  * Tsys on absorber
• PolA and polB show  a ripple in frequency (stronger in polA).
  
• This could be a part of a standing wave.  if so it would be about 80MHz or 1.8m with n=1
  
• this is not seen in polB  sky.
  
• Page 3: Normalize each calRatio scan to their median value. see if sky, absorber fractional amplitudes are the same.
  
• top frame: polA
• bottom frame: polB
• Since the calRatio is divided by CalOff
• any frequency variation after the cal injection is cancelled.
• any frequency variation before the cal injection will cause a ripple in the cal deflection.
  
• If it is a standing wave in the cal cable, then the fractional amplitudes should have the Tabs/Tsky ratio.
• It it is a standing wave in the horn, omt, then the fractional amplitudes should be similar (if the reflection happens before the horn mouth.
• If it is a standing wave with one end beyond the horn, then you should see it in the sky and not in the absorber
• this will be hard to differentiate from the 1st since Tabs/Tsky may be up to 20. This would put the sky ripple in the abs noise.
  
• You see the oscillation in sky and abs.
• For polA :
• You don't see the oscillation in abs.
• For polB:
• You see the ripple in the abs,  but it looks to be out of phase with the sky.
  
• a cal ripple should probably be in phase.
  
• Page 4: Look at on sky spectra
• Top: the average calon,caloff spectra (black:polA, red: polB)
• middle: calOn - calOff spectra
• black in polA , red is polB
• bottom: (calOn  - calOff)/calOff
• PolB has a bump in the spectra and the calOn - off
• when you divide by the off, the cal deflection flattens out
• The bump in polA looks like it is coming from a negative dip in the spectra
• when we divide by the calOff this kicks up the center.
• Page 4:  rms/mean by channel for the calon, calOff  spectra
• black polA, red: polB
• top frame: on sky
• bottom frame on absorber
• The rms by channel is computed for the 3000 calOn and calOff cycles for a 2 minute scan.
• The 3 sky calon,off rms' are over plotted in the top frame
• the 3 abs calon, caloff rms' are over plotted in the bottom frame.
• This shows the location of the rfi  in the sky scans.
• The expected rms (from the radiometer equation is plotted on the blue line (.027).
  
• The measured values are close to this. The gain  variation during the 120sec scan will increase the rms.
  

Fitting a curve to the calRatios.

The plots show a fit to the CalRatio measurements (.pdf)

• The 3 sky measurements and 3 absorber measurements were averaged to give a sky and absorber calratio vs freq.
• A robust harmonic fit was then fit to the calRatios vs freq
• the fit included:
• a linear term
• A 3rd order harmonic fit (fitting ripples down to 135/3=45MHz).
• If i used a higher order fit, then it would start to deflect in the rfi regions (where the the robust fit rejected the points).
  
• The fit was iterated throwing out outliers and then redoing the fit.
• Page 1: calratio vs freq and fit
  
• black is polA , red is polB, green is the fit
• the blue * points were excluded from the fit.
• Top: On sky calratio vs freq and fit
• Lots of blue rfi points were rejected on the right side.
  
• 2nd frame: on sky fit residuals
• The residual rms was (.0045,0064)*TsysSky for (polA,polB)
  
• 3rd frame: fit to calRatio on absorber.
• the rfi was not present on absorber
• bottom: absorber fit residuals
• the residual rms was around [.0008,.0012]*TsysAbs
  

Computed Tcal and Tsys using the cal values.

    The  plots show the computed Tcal and tsys in deg K using the new cal values (.pdf)

• Page 1 Tcal vs frequency
• Tcal was  computed using the calRatio from the y factor as well as  just calRatioAbs and calRatioSky.
• the values of Trcv, alpha, and gamma were modified to get the closest agreement with the 3 methods.
• PolA       top frame, polB bottom frame.
  
• black  line: used Y factor calRatio
  
• red line  used calRatioAbs
• blue line used calRatioSky
• We ended up using:
• Tsky + Tscattered: 15K
• Trcv(a,b): (60,65K) .. when computing using just Abs or just Sky.
  
• gamma=.05,alpha=(.07,.09) (polA,polB)
• using Sky by itself does not come very close to the Yfactor or Abs values
• Since the sky input is much less that Tabs, Trcv will have a larger affect
• I've used a  constant value for Trcv.  there is probably some Frequency dependence.
  
• Page 2: Tcal  vs freq and Tsys vs freq
• Top:  Tcal vs freq
• this is from the y factor measurement after adjusting gamma and alpha.
• TcalPolA is 57 to 65K
  
• TcalPolB  is 76 to 92K
  
• The + are the cal values sampled every 5 MHz.
  
• they are entered in the cal table that users will use for the cal value
• routines will then linearly interpolate the cal value between these 5 MHz points.
• Bottom Tsys vs freq
• the cal off data was averaged, divided by the cal deflection and then multiplied by Tcal to get the system temperature on Sky.
• Tsys ranges from 90K to 160K with polb being a little higher than  polA
• between 2240 and 2300 Tsys polA and polB move in opposite directions.
  
• I'm not quite sure i believe these values. It would be really nice to separately measure Trcv on the sky to see how much frequency dependence it has.
  

Summary:

• The single sband  cal diode feeding polA ad polB of the 12meter was measured on 07jun22 in the morning.
• the tcl routine /share/megs/phil/svn/aosoft/p12m/x101/220607_meascal.proc was used to take the data.
  
• The hardware winking cal data was taken for 2 minutes on each scan.
• There were 3 2 minute scans on  abs and 3 2minute scans on sky.
  
• there were few clouds and the elevation was around 80deg for the sky measurement.
  
• Looking at the total power vs time we saw a  1 to 2% variation in the 2 minute measurement
• this is probably a temperature dependent gain variation of the electronics.
• note: the cal diode was  temperature stabilized.
• The calRatio (calDeflection/calOff) vs freq showed frequency variation (especially in polA).
• this was seen on sky and absorber(polB).
• a 3rd order robust harmonic function was fit to the calRatios vs freq and then  used to compute Tcal
• the fit residuals were: .005*TsysOnsky, and .001*TsysOnAbs
• The Tcal was then computed using:
• the Y factor (abs hot load, sky cold load)
• this removes Trcv but needs gamma(reflection coef horn,omt) and alpha (absorption in omt).
• Using just calRatioAbs (this needs Trcv)
  
• using just calRatioSky (this also needs trcv)
  
• Trcv, alpha, gamma were adjusted to get the 3 measurements as close as possible.
• Tcal values
• Tcal polA about 57 to 65K
• Tcal polB about  76 to 92K
  
• a table of values spaced every 5MHz is stored in a file
• /share/megs/phil/svn/aosoft/idl/data/cal12m.datR7
• the idl routines:
• calinpdata.pro will input the entire table
• calget1.pro will input a value at  a single freq.
• the large ripple in PolB value  looks like a problem somewhere
  
• Tsys vs freq.
• using the calOff measurements on sky Tsys was measured.
• It varied 90 to 140 K over the entire freq band with polB being higher than polA.
• PolA , PolB ripple are 180 deg out of phase.
• The attenuators that were installed (3,2)db were supposed to be (7,7)db . This is why the cal values are so high.
  

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