Intro:

• let gIF(f) be the normalized IF bandpass function. I'll pretty much ignore the Tsys and Tsrc frequency dependence.
  
• Bposon_cnts(f)= (Tsrc_cnts(f) + Tsys_cnts(f) )*gIF
• Bposoff_cnts(f)=(Tsys_cnts(f) )*gIF
• Bsrc_tsys(f) = (Bposon_cnts(f)- BposOff_cnts(f))/BposOff_cnts(f) = Tsrc_cnts(f)/Tsys_cnts(f)
• where Bsrc_tsys is now in units of Tsys.
• Bsrc_k(f) = Bsrc_tsys(f) * mean(BposOff_cnts(f)) * CalInK(avg)/Caldif_cnts(avg)
• The 2nd term (mean..) converts the Bsrc_tsys in tsys units back to spectrometer counts.
• CalInK(avg) is the measured cal value averaged over the entire 172 Mhz band of the spectra.
• CalDifCnts(avg) is calOn-calOff averaged over the 172 Mhz spectra.
  

Averaging over spectra.

•  The data for these averages are taken at different times.
• If there is rfi in any of the spectra then the averages will be biased by the rfi.

Example spectra: 3C48.

• Track 3 minutes on and 3 minutes off position
• fire the calon,caloff for 10 seconds in the position off position.
• Use lband wide in linear polarization mode (3C48 .4% polarized at lband .. from nvss).
  
• The data was taken near: az=201, za=16. This is close to transit for the 33 deg dec source.
  
• Use the mock spectrometer.
• 1 second integrations
• 4*172 Mhz bands covering 1115 to 1735 Mhz (this is the entire lbw band). band center frequencies were:
• 1200, 1350, 1500, and 1650 Mhz.
  
• a/d blanking enabled.

• The idl routine masposonoff() was used to reduce the data
• Black is polA, red is polB.
• Vertical dashes show the edges of the 4 bands (there is only about 20Mhz overlap).
  
• The first page used the mean when averaging the 1 second records. The 2nd page used the median.
• Page 1: mean to average the 1 second records:
• Top: When computing the averages, use the entire spectra (no mask).
• the 1200 Mhz polB band is off scale (it is negative).
• Middle: use calOn/calOff to compute frequency channels with rfi to be excluded. The mask was then applied to all averages.
• the 1200 Mhz polB is not on scale, but it is offset from the 1350 Mhz band
• Bottom: Compute the rfi mask from the calon,off and well as the position on,off data.
• the 1200 Mhz band now has a smaller offset from the 1350 Band.
• Page 2: same data as page 1 but the median rather than the mean was used when averaging 1 second spectra.

Summary:

• Large offsets can occur when the rfi is strong.
• Using no mask in the 1200 Mhz band, the source strength for PolB was negative.
  
• the aerostat radar was (1242,1256Mhz) was stronger in the calOff than the calOn.
• <calOn -calOff> then became negative so the cntsToKelvins conversion factor became negative.
• Using calOn/calOff and the data records to compute the rfi mask did the best job.
• There is still an offset between the 1200 Mhz and 1350 Mhz  bands.
• The jump between the 1350 and 1500 Mhz band around 1400 Mhz may related to the resonance in the feed around 1398.
• If the cal values used are wrong, then there can also be a jump between bands. We average the cal value over the entire 172 Mhz band.
• It wouldn't surprise me if the lbw cal values for the 1125-1270 Mhz band were off since the radars were present in the band when the cals were measured (although 20K/170K= 10% is a bit much..)
  

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