• 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	306K	The tabs was 31C when we started the xband absorber measurements. It was 35.5C when we finished with the sband absorber measurements. I used 33C for the sband abs temp.
Tsky	10K	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 13:25  and finished by 13:50 ast.
• We did 3 absorber scans followed  by 3 on sky  scans.
  
• The scan sequence was:

• Loc	ra,dec	az,el	mockFile #	Notes
  abs	..		300
  abs	--		400
  abs	--		500
  sky	07:43:40/25:50:05	40,80	1000
  sky			1100
  sky			1200

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, calOff spectra.
• This total power was then normalized to the average value for the 3 abs or sky scans.
• I used 2210 to 2319 when computing the total power (to stay away from the band edge and rfi).
  
•  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.
  
• What the plots show:
• PolA values vary by < .5% for abs and sky
• polB abs varies by about 1% while sky varies by < .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
  
• On the sky Tcal = .2*TsysSky
• On Abs  Tcal=.05*TsysAbs
• 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.
• If 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
• Looks like the sky ripple might be in front of the horn.
• a 100 MHz ripple is about 1.5 meters in air. It might be the distance from horn to secondary.
  
• 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 (.0032,.0021)*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 [.0006,.0006]*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: 1\0K
• 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.
• The cal values vary from 20 to 24K with polA,B values within a kelvin or 2.
  
• 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 85K to 140K.
  
• polA and polB now have system temps that track each other.
• There is still a large ripple (about 30K) that has about 1 cycle in the band.
  

Summary:

• The single sband  cal diode feeding polA ad polB of the 12meter was measured on 24jun22 in the afternoon.
• the tcl routine /share/megs/phil/svn/aosoft/p12m/x101/220624_meascalsbxb.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 up to a .5% variation  (polB  abs was 1%)
• The calRatio (calDeflection/calOff) vs freq
  
• absorber was pretty flat
• on sky showed a +/- 20% variation. This is probably a standing wave outside the horn (horn to secondary?).
• a 3rd order robust harmonic function was fit to the calRatios vs freq and then  used to compute Tcal
• the fit residuals were: .0025*TsysOnsky, and .0006*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,,polB: 20 to 24K
• 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 bump we saw in polB Tcal (07jun22) at 2280MHz  is no longer present. Tcal polA,polB track one another.
  
• Tsys vs freq.
• using the calOff measurements on sky Tsys was measured.
• It varied 85 to 130 K over the entire freq band with both pols tracking one another.
  
• There is still a large single cycle variation across the Tsys band with an amplitude of about 20K.
  

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