Links to sections:
Intro
Setup
Processing the data
Selecting the good 2d gauss fits
Telescope gain
SEFD
Tsys
xband sidelobes.
Coefficients from fits
Summary

Plots

the time and az, el coverage (.ps) (.pdf)
how the "reasonable crosses" were selected (.ps) (.pdf)
how the data was clipped (.ps) (.pdf):
pointing error after clipping (.ps)  (.pdf)

the fluxes, and gain fits vs frequency (.ps) (.pdf)
the sefd data and the fits (.ps) (.pdf)
the Tsys data and the fits for each frequency band (.ps) (.pdf)
look at the components of the Tsys fit (.ps) (.pdf)

movies of the raw 2d gauss fits

• each movie shows the data and fits to the 7 freq bands for each cross taken
• top frame : azimuth strip and 2d fit to azimuth
• middle frame; elevation strip data and 2d fit to elevation
• bottom: plot azimuth , elevation data vs  elevation offset from center of cross. over plot the fits.
  
• 3C144.avi  (crab) (30Mbytes)
  
•  it had lots of rain and lousy fits.
  
• 3C405.avi  (CygnusA)  (101Mybes)
• 3C461.avi  (CasA)  (128 Mbytes)
• Notes:
• the 8789 and 8931 Mhz bands occasionally show spikes across the strips.
  
• This is a 4 sec periodic rfi in the band.
• If the fit passed the goodness of fit test (bmwidth, pointing error, tsys) then the work include (in yellow) appears in the upper right corner).
  

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Intro

      Crosses were done in jun22 after the s,x receiver was remounted on the telescope (following the  QRFH testing). This was to check the pointing and the telescope gain. The Crab (3C144), CasA (3C461) and CygnusA( 3C405) were the  sources tracked.

    Plots,fits were made for:

• SEFD vs el
• gain vs el
• tsys vs el
• included is the atmospheric contribution to tsys vs elevation.

The plots show the time and az, el coverage (.ps) (.pdf)

•  Top: elevation vs hour of day for the sources
• Each day is a different color: 25,26,27 jun22
• the symbols flag the different sources used.
• The crab data 14:00 to 18:00 had lots of rain.
• Bottom: elevation vs azimuth for crosses
  
• the inner loop is CasA
• the outer loop is CygnusA
  

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Setup

The setup was:

• xband was used.
  
• 7 freq bands of 172.032 MHz each was used.
• cfr of bands:
• 8223. 8363. 8505. 8647. 8789. 8931. 9073.
• 142 MHz between band centers
• total span 1022 MHz
  
• A  10sec cal on,off was fired at the start of each cross.
• 3 sources:
• 3C144 (Crab)
• Most of these were taken during a rainy period and had to be discarded.
  
• 3C405 (cygA) 
  
• 3C461 (CasA)
  
• pointing:
• az, el strips.
• 1.2 deg strips,
•  120 secs/strip,10 Hz sampling ->.06 Amin/sample
  
•  bm FWHM=10amin  -> 166 samples/FWHM,  and 7.2 beams per strip.
• I tried tracking the sources rise to set (in the time available).
  
• mock setup:
• 172.032 bw, 1024 channels , 166KHz/channel, 10Hz sampling
  
• pola,b recorded separately

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Processing the data

• idl was used for the processing.
• mascrossfind(), mascrossinp(), mascrossfit2d()
• The total power was computed from the recorded spectra the steps were:
  
• the spectra and cals were input
• excluded freq range (known rfi)
• 8319.4->8348.3 MHz was always excluded)
• search for rfi in the azimuth spectra (the el spectra had larger Tsys variation during the el strip).
  
• the spectra from the 1st and last 3rd of the azimuth strip were concatenated (exclude the beam)
• the rms/mean by channel was computed
• a robust linear fit vs freq was done on the rms spectra
• any residuals >3sigma were flagged as rfi channels and excluded.
  
• The cals were input
• cnts->kelvins vs freq were computed.
  
• The average value  was computed  using the good channel mask (from above).
• The  total power using the good channel mask was computed and then converted to deg K.
  
• The 2d gauss fitting was done by gsfit2d_12m()
• The fit used:
  
• x=az, y=el
• xm=(x - x0)   .. x0 is az pointing error
• ym=(y- y0)    .. y0 is el pointing error
• in case the beam was elliptical, the az,el direction was rotated to the major, minor axis of the ellipse:
  
• xp=xm*cos(th) + ym*sin(th)
• yp=-xm*sin(th)  = ym*cos(th)
• xp,yp were then used for the fitting.
  
• z=A0 + A1*exp(-xp^2/sigxp^2  - yp^2/sigyp^2) + A7*ElOffset
• note: I've left out the factor of 1/2 by the sigx,sigy..
• this was corrected later when the results are converted to FWHM .
• The fit parameters were then:
• A[0]: Tsys
• A[1]: src Amplitude
• A[2]: x, az offset (pointing error)
• A[3]: y, el  offset (pointing error)
• A[4]: FWHM Az
• A[5]: FWHM El
• A[6]: theta rotation angle az,el to ellipse major,minor axis.
• A[7]: elevation  change during the cross (since Tsys can change with el)
• this is a linear fit to the baseline in elevation.
• the 2d gauss fit was iterated twice.
• 1st: fit all points, find the pointing offset in az, el
• 2nd Fit: exclude the sidelobes from the 2dfit (0 weight) using the pointing offsets to locate them.
  
• The resulting 2d gaussfit  parameters were used to give
• Tsrc/Tsys, Tsys (degK)
  
• az,el pointing error
• sefd
• FWHM of beam in az, and el direction

processing: x101/220625/crosses.pro

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Selecting the good fits:

    Some of the crosses were taken with clouds and rain. The data was examined to see how to separate out the good from the bad fits.When the conditions were really bad, the fit did not converge.  Some fits converged, but they were not fitting the src deflection.
To select "good" crosses:

• The fit had to converge.
• the fit FWHM in az and el had to be reasonable
• Tsys had to be reasonable
• The pointing error had to be reasonable
• the fit sigma should not be too large.

The 1st set of plots show how the "reasonable crosses" were selected (.ps) (.pdf)

• Page 1: FWHM vs cross index for each source:
• Each frequency band is a different color.
• the az and el FWHM are over plotted.
• top: 3C144 (crab)
• very few of the FWHM are good. this is mainly rain.
• middle: 3C405 (cygA)
• points cluster around 10Amin
• bottom:3C461 (CasA)
• points are around 10Amin.
• Page 2: FWHM vs azimuth
• Page 3: FWHM vs Elevation
• Page 4: FWHM vs fit rms (in degK)
• CygA rms's are better than casA's.
• i ended up clipping the rms at .4 K
• Page 5:  FWHM El vs FWHM Az
• Colors are different frequency bands.
• Both cygA and casA show a linear slope in fwhmEl vs fwhmAz
• When the El width is large, the az width is small.
  
• When the az width is large the el width is small.
• if the source was elongated the you would expected this as the parallatic angle rotated around
• But:
• The theta parameter should align the az with the wide axis and the el with the  narrower axis (or visa versa)
• The widths are measured i the rotated coords
• cygnus A has two strong regions so it can be elongated.
• but Casa is (a supernova remnant is spherical
• So I'm not sure why the slope
  
• Page  6: FWHM El,az vs azimuth (left column) and elevation (right column) pointing errors.
• there are two groups of pointing error in az,el for 3C405 (cygA).
  

The 2nd set of plots show how the data was clipped (.ps) (.pdf):

• the Thresholds used for  good data
• FWHM: 8.7Amin < FWHM < 11.3 Amin (in az and el)
• PntError:  abs(azErr), abs(ElErr) < 1amin
• FitRms <.4 degK
• Page 1:   FWHM, pntErr,rms
• top : FWHM El vs  fwhmAz
• red box contains  good crosses
• Middle:  ElPnErr vs AzPntErr
• red box is +/- 1Amin err contains good crosses.
• bottom: rms of 2dfits
• below red line (.4K) are good crosses,
• Page2: FWHM vs Pointing error
• 2968 total points (ncross*Nfreqbands)
• 2460 points after clipping.
  
• red + are excluded points (from all criteria)
  
• top,2nd: FWHM az,el  vs az pointing error
• 3rd,bottom: fwhmaz,el  vs el pointing error
  
• Page 3: az,el coverage.
• the red + are crosses that have >3 freq bands excluded (7 bands/point)
• Page 4: tsys vs el from fits.  before, after clipping
• Each source is a different symbol
• each color is a different freq band.
• top : tsys all data (between 90 and 160 degK)
• bottom: Tsys after clipping.

The pointing error after clipping (.ps)  (.pdf)

• A new pointing model was not made after the receiver was reinstalled.
• Page 1: pointing error vs az,el
  
• Black:az pointing error
• Green: el pointing error
• Red are points that have < 5 good freq bands (7bands /cross)
  
• Each source is a separate symbol
• Top: Pnt error vs azimuth
• Bottom: pnt Err vs elevation
• Page 2: 2-d arrow plot of pointing error.
• Each color is a separate source
• arrow Length: 1 division =30Asecs
• arrow direction: along the radius is el error, perp to radius=az error.
• 
  

• avg,rms pointing error (Asecs)

  azErr Asec		elErr Asec		totalErr Asec sqrt(azerr^2+elErr^2)
  avg	rms	avg	rms	avg	rms
  -5	20.4	-23	18.7	34.7	13.5

• The elevation avg error was closer to 0  (-4.12asec) after the last model was made 
• There may be a small shift in the receiver elevation position after remounting it.   
  

processing: x101/220625/chkfits.pro

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Telescope gain:

    The telescope gain was computed using the 2d gauss fits, the Cal value, and the source fluxes. The source used were:

• 3C144 crab .. only a few good crosses
• 3C405 Cygnus A
• 3C461 CasA .. whose flux varies with time.
  

The fluxes were taken from:

• Perley and butler: An accurate flux density scale 50 MHz to 50 GHz (2017) (.pdf)
• Baars et al: The absolute spectrum of CasA (1977) (.pdf)
• This included a flux yearly rate of change.
• Weiland et al: 7year wmap observations: Planets and Celestial calibration sources. (.pdf
  

The plots show the fluxes, and gain fits vs frequency (.ps) (.pdf)

• I did not do any source size corrections to the fluxes (more info)
• Using a size correction would lower the flux to use so the gains would be a little higher.
• The problem was deciding the size of the objects (more info)
  
• Page 1: source fluxes from the catalogs
• Top: flux vs freq from the 3 catalogs
• Black: perley
• Perley claims his flux equation is good to 4GHz. Probably too extended for higher freq at vla.
• I am using the equation at 8+ GHz.
  
• Red: baars
• I've corrected for the yearly change.
  
• green: wmap
• each symbol is a different source
• all 3 catalogs agree on the flux of cygnusA
• Bottom: Ratio fluxes to Perley flux
• red: Baars/perley
• green: Wmap/perley flux
• The flux(freq) change is larger for baars and wmap for casA and crab
• Page2: measured gain using the different catalogs.
• Each source is a different symbol
• Black: Perley flux, red:baars flux, green: wmap
• top: gain vs elevation
• 3C405(cygnusA) perley and baars agree, wmap gain is lower (flux is higher)
• 3C461(CasA): Perley gain is higher, baars gain close to cygnusA gain
• middle: Compare just Perley and baars gain. vs elevation
• bottom: compare perley, baars gain vs azimuth.
• CasA: it is extended and it changes with time.
• the perley value has no rate correction (it is 5 years old).
• baars has a rate correction (but it may be using a yearly decrease a little larger than more recent values.
• For the gain curves  i ended up using:
• Perley flux for Cygnus A and crab
• baars flux for CasA since it gave a gain that was closer to the gain measured with cygnus A.
• Pages 3-5: gain fits for the 7 frequency bands.
• I tried 3 different fits
• red: fit1: gain=A0 + A1*el
• green:fit2: gain=A0 + A1*sin(el)
• This is the fit i ended up using.
  
• blue: fit3: gain=A0  + A2*el^2
• The purple  symbols were excluded from the fit
• Page 6:the fits
• top: fit sigmas for the freq fits by freq
• each color is a different freq band
• The x axis has the values for fit1, fit2, fit3
• the y axis is the fit sigma in K/Jy
• I ended up selecting fit2 (the dotted line) g=A0+a1*sin(el)
• Bottom: gain fit curves vs elevation.
  
• each color is a different freq band

Processing: x101/220625/fitgain.pro

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SEFD

    The SEFD (System Equivalent Flux Density) was computed at:

•  Tsys/(srcDeflection/srcFlux)
• Since we divide Tsys by the source deflection any errors in the measured calvalue are canceled.
• 3C405 (cygA) and 3C461 (casA) were the main sources used  (with a view crosses on 3C144 (crab)

The plots show the sefd data and the fits (.ps) (.pdf)

• Page 1: srcDeflection/Tsys  vs az,el by freq
• Each color is a different frequency band.
• Each source is a different symbol
• top: srcDeflection/Tsys vs elevation
• + cygnusA is about  4% of Tsys
• * casA is around 10% of Tsys
• Bottom: srcDeflection/Tsys vs azimuth
• Page 2: source Fluxes vs frequency.
  
• top 3C144 (from Perley et al)
• middle: Cygnus A (from perley et al)
• bottom: casA from baars (after correction)
• These fluxes have no size corrections.
• Page 3: SEFD  vs el,az by freq band
• Each color is a separate  frequency band
• each source is a different symbol.
• Top: sefd vs elevation
• bottom: sefd vs azimuth
• The lowest sefd is around 3700 Jy.
• The increase in sefd at low el is from the tsys increase (from the atmosphere.. see below)
• Page 4-6 SEFD vs el data and fits.
• I tried two different fits:
• sefd = A0 + A1*sin(el)^A2
• sefd = A0 + A1*sin(el)^-1
  
• Tsys should  vary by sin(el)-1  ...
  
• there is a small variation of gain with elevation.
  
• Each frame is a separate freq band
• each source is a different symbol
• the values for each fit are printed at the top of each frame.
• There is a larger error in the fit .. mainly from the Tsys changing during the 3 days from clouds.
• Page 7: sefd fits vs freq and el
• Top: sefd fits vs freq for el=60deg
  
• The error bars are the sigmas from the fits.
• There is little difference between the two fits and their errors.l
• I ended up using the fit with sin(el)^(-1)  rather that fitting for the exponent. This mirrors the tsys variation with el.
• Bottom: over plot sefd fit vs el for all freq bands
• This is using sefd=A0 + A1*sin(el)^(-1)

processing: x101/220625/chksefd.pro

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Tsys

    Tsys was taken from the Constant term in the 2d gaussfit.
It will contain contributions from:

• sky, cmb
• atmosphere
• scattered ground radiation
• receiver contributions.

The Tatm  will be a function of elevation. As we go lower in elevation we look through more atmosphere so there is more absorption of the sky signal.
We then get more emission from the  water vapor.

Equation for Tsys: (from Interferometry and synthesis in radio astronomy (Thompson, Moran , and swenson 2016, chapter 13).

Tmeasured= Tconst + Tatm*(1-exp(-tau*sec(za)) + Tcmb*(exp(-tau*sec(za)))

• Tconst is independent of elevation (Trcv..)
• Tcmb = 2.725
• It is reduced by the absorption.
  
• sec(za)= 1/cos(za) = 1/sin(el)
  
• Tatm is the Atmospheric temp contribution (mainly from water vapor at 8GHz).
  
• You should integrate over Tatm as it changes with altitude
• it changes by about -6.5K per Km up till around the tropopause (around 10Km)
• The water vapor scale height is about 2 Km.
• The temperature to use is normally 13 to 20K less than the ground temperature.
• This all works out if you don't have a bunch of clouds. If there are lots of clouds then my guess is that the Tatm to use may be biased to the height of the clouds.
• tau is the opacity.
  

What to fit for:

• -tau*sec(za) is a small value  (< .02)
• The exp() can be approximated by (1- tau*sec(za).
• The Tatm term becomes:
• Tatm*tau*sec(za)
• If you fit for both Tatm and tau then  you can fit the data ok , but only the product of Tatm*tau will be correct.  Tatm and tau can take on any values as long as the product is correct.
  

• While fitting for Tsys. i used:
• Tsys = A0 + A1*(1 - exp(-A2*sec(za))  Tcmb*(exp(-A2*sec(za))
• A0 =Trcv
• A1= Tatm
  
• I tried Tatm as a fit variable
• I also tried Tatm with a fixed value (270K)
  
• A2 = tau (optical depth)
• Noise can also come from ground radiation:
• scattered into the feed
• from sidelobes as you approach el = 0 deg
• When fitting  i tried:
• Fit all the elevation data
• Fit only elevation data above 10Deg
• i then compared the fits to see if excluding the lowest points made a difference.
  

The first set of plots show the Tsys data and the fits for each frequency band (.ps) (.pdf)

• Page 1: Tsys vs el  from the constant term of the 2d gaussfit.
• Each color is a different frequency band
• each symbol  is a different source.
• Points below the yellow line (at el=10deg) were excluded when doing the clipped in elevation fit.
  
• Page 2-8 Tsys fits to el for each freq band
• I tried 4 fits at each freq band
• Fitting using all the data:
• include Tatm as a variable to fit for (red fit)
• fix Tatm at 270K (green fit)
• Fit all points about el=10deg
• include Tatm as a variable to fit for (blue fit)
• fix Tatm at 270K (purple fit)
  
• top: Tsys vs elevation and fits ( in different colors)
• All of the lines lay on top of each other (but the blue and purple lines only extend down to el=10)
  
• bottom:Tsys vs azimuth
  
• CasA (*) deviations
• There were  two separate paths vs elevation
• Plotting vs azimuth shows that 1 side is asymmetric. this is probably caused by changes in the cloud cover when CasA was observed (on multiple days).
• This is pulling the fits higher at low elevation.
• I could have excluded this data and got better fits (but we normally have clouds so i figured i leave them in.
• Page 9: Fit rms's vs freq
• The red (fit for Tatm) and green (Tatm=270) using all the points overlay each other
• The blue(fit for Tatm) and purple(Tatm=270K) using el>10 overlay each other.
• The rms using all the points is larger since there was more scatter in the points below el=10
• But the two fits gave similar results
• So there is not a large contribution from ground radiation being scattered in at low elevation.
  

The 2nd set of plots look at the components of the Tsys fit (.ps) (.pdf)

• I ended up using the fit with all elevations, and a Tatm fixed at 270K.
  
• Page 1: Tsys fits and components
• Top: Fits for Tsys  by freq band
• each color is a different freq band.
• The 2 highest freq bands have the highest Tsys. This may be the receiver, or the rfi in the bands not being completely removed.
  
• 2nd: Tatm contribution to Tsys vs elevation. (Tatm(1-exp*(-tau*sec(za)))
• When looking vertically there is about 5K of temp added looking through the atmosphere.
• At low elevation, the Tatm contribution is up to 40 K
• 3rd: Tconst  vs freq from fits
  
• bottom: tau vs frequency.
• The opacity is about .0175 for the entire frequency range.
• This uses 270K for Tatm. higher values of Tatm would lower the opacity.
• Page 2: Opacity vs Tatm value used
• If we varied the fixed Tatm, then the opacity value tau will change.
• Fits were done changing the Tatm constant value from 200 to 300K using the 8505  MHz band data)
  
• The plot shows the resulting opacity for each Tatm
• The red * is the Tatm that was used for fits.
  

Deriving the Tsys value from the fits could be problematic. As the cloud cover changes, tau and Tatm will change. It's probably better to use the cal value for each observation to get Tsys.

processing: x101/220625/chktsys.pro

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SideLobes

    The crosses on 3C406 (Cygnus) were used to measure the 1st sidelobe level at xband. Cygnus A is a strong source with a relatively small extension (1 to 2 amin). The xband beamwidth is about 10 Amin.

Processing the data

• The 184 azimuth strips of CasA were used (the elevation strips had more variation with el)
• Each strip was 1.2 deg (72 Amin or about 7 beams)
  
• 1200 samples in the strip (.06 Amin /sample or 167 samples per fwhm)
• 7 frequency bands were used.
  
• The 2d gaussfits using az,el strips were first done to get the pointing offsets.
  
• for each az strip of each freq band:
• do a linear fit to get the baseline
• use 200 points on each edge for the fits
• remove the baseline and smooth to 11 points (.6 6amin)
• normalize to the peak value
• compute the average az pointing error (median for the 7 bands)
• shift the data by the pointing error so the peaks of multiple strips will all sit close to an offset of 0
• For each freq band compute the median for the 156 az strips.

Plotting the sidelobe results

    The plots show the sidelobe results (.ps) (.pdf) :

• Top frame: 156 az strips for 3C405.
• This data is from the 8223 Mhz freq Band.
  
• A linear baseline was removed from each strip, it was then smoothed by 11 samples, normalized to the peak value, and shifted to correct for the pointing error.
• The x axis is great circle azimuth offset in Amin.
• The y axis is  linear power.
  
• Middle frame: the median strip for each freq band.
• Each color is a separate freq band.
• the median was over the 156 strips.
• Bottom frame: Median strip in db below the peak for each freq band,
• The 1st sidelobes are at -16 and -14 db below the peak.

processing: x101/220625/sidelobes.pro

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Fit coefficients

    The ASCII  fit coefficients  can be found int the the following files:

fit	file	fit Type	cols in file	Notes
Tsys	tsyscoef.txt	Tsys=Tconst+Tatm*(1-exp(-tau*sec(za))) +Tcmb*(-tau*sec(za))	freqMhz Tconst Tatm Tau	Tcmb=2.725 Tatm=270
gain	gaincoef.txt	G=A0+A1*sin(el)	freqMHz A0 A1
sefd	sefdcoef.txt	SEFD=A0+A1*(sin(el)^-1)	FreqMhz A0 A1

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SUMMARY:

• 424 crosses were done at xband 25-27jun22 after the xb/sb receiver was reinstalled on the 12meter telescope.
• 7  freq Bands covering 8150 to 9150 MHz were used.
• 3C405 (CygnusA), 3C461 (CasA) were used ( crosses on 3C144 (crab) had problems with rain).
  
• 2d cross fits were done on each freq band (424*70=2968 2d gaussfits)
• good fits were selected by:
• 8.7Amin < FWHM < 11.3 Amin
• -1Amin < (pntErr in az or el)< 1Amin
• 2d gaussfit sigma < .4 K
• After selecting, there were 2460 2d gaussfits (about 350 good cross positions).
• Pointing error:
• the rms error was 34 Asecs
• the elevation had larger offset. The may have been a positioning error when the feed was reinstalled.
  
• The Telescope gain was computed  and then fit vs el for each frequency band.
  
• The fit used was:
• gain= A0 + A1*sin(el)
  
• For el > 60 the gain was about .026 K/Jy
• A 12meter telescope area =(!pi *(12/2.)^2= 113.1 m^2
• at 2760 m^2/Kelvin the gain would be 113.1/2760. = .041 K/Jy
• .026/.041 gives an aperture efficiency of about 63%.
• No source size corrections were done to the source Fluxes.
• a size correction for extended sources would decrease the flux and increase the gain.
• Any errors in the cal values would carry over into the gains.
• The SEFD was computed and then fit vs el for each frequency band.
• The fit used was:
• SEFD=A0 + A1*sin(el)^-1
• At el=90 the sefd ranged from 3600 to 3900 Jy.
• Any errors in the cal values are cancelled when computing the SEFD
  
• Tsys was taken from the 2d gaussfits and then fit vs elevation
• The fit used was:
• Tsys= A0 + A1*(1-exp(-A2 * sec(za))) + Tcmb*exp(-A2*sec(za)
  
• A0= Tconst
• A1=Tatm. this was fixed at 270K
  
• A2=tau
• using Tatm of around 270K gave an opacity tau of about .0175
• If we used a different Tatm, then the opacity would change..
• limiting the tsys fits to el  > 10 did not change the fit values
• there is not a lot of ground radiation from the sidelobes getting into the system at low elevations.
  
• Using Fit values for Tsys can be problematic at xband since it can change as the cloud cover changes.
  
• Probably best to measure Tsys with the cal each observation.
  
• The fit coef are available in an ASCII file (more info)