links:
Intro
The 2d gauss fit
Examples of the fit using 3C405
Summary

Intro:

    We use crosses on sources for the system performance and pointing model. For the 12 meter they are:

• Each leg of the cross can be 6 or 8 beams long.
• We take 2 minutes for each leg.
• The lengths in great circle arc minutes are:
• sband beam:40' .. in the computations i used .6 degrees or 36'
  
• 6bms*40'= 240' or  4.0 degrees ..  used 3.6 degrees
  
• 8bms*40'= 320' or  5.3 degrees ..   used 4.8 deg
  
• xband beam: 10' .. i used .15 deg or 9'
  
• 6bms*10' = 1.0 degrees .. used  .9 degrees
  
• 8bms*10' = 1.3 degrees .. used 1.2 degrees
  

    For model 3A i just fit 1d gaussians to each az and el strip.

• This gives the pointing offsets and beam widths correctly.
  
• But the peaks are less than the actual values (unless the pointing error is 0).

    Using a 2d gaussian fit will:

• Give the peak with 0 pointing error.
• It also allows us to discriminate against bad crosses (rfi, rain, etc..) since it requires both strips to fit the same 2d gaussian.
• If the source is extended asymmetrically , it will fit for each width, and the rotation angle as the telescope receiver probes undergo parallatic angle rotation.

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The 2d gauss fit:

    The 2d gauss fit is:

• it uses the great circle offsets from the center of the strip for the fit.
• let x=az and y= el.
• The 8 parameter fit  coefficients are:
  
• C0 = Tsys
• C1 = Gaussian amplitude
• C2 = azimuth pointing offset
• C3 = elevation pointing offset
• C4 = Azimuth gaussian width (in sigmas)
• C5 = elevation gaussian width (in sigmas)
• C6 = is the angle (th) that rotates x,y axis into the major,minor axis of the 2d gaussian
• C7 = change in Tsys with elevation offset (or with elevation)
  
• The equation is:
• xp,yp are the az,el rotated to the major,minor axis of the gaussian, with the error offsets removed.
  
• xp= (x - C2)*costh + (y-C3)*sinth
• yp=-(x - C2)*sinth  + (y-C3)*costh
  
• zfit= C0    + C1*exp(- ( xp^2/C4^2 + yp^2/C5^2) ) + C7*elOffset (or el)

• Coefficient C7 (change in tsys with eloffset or el)
• This coef  is needed because the system temperature can change with elevation (do to ground radiation, atmosphere, etc..).
• For the 305meter,
  
• we've always used the elevation (or za) offset for this fit.
• so only the elevation strip would contribute (the elevation offset for the az strip is 0).
• But.. the elevation does change during the azimuth strip because we are tracking the source.
• For 1 minute strips, and elevations that never get below 70deg, the change in tsys for the delEl in the az strip was small.
• For the 12 meter telescope:
• the strips are 2 minutes long (to get better signal to noise).
• The elevation goes all the way down to about 6 deg.
• For 3C405 (dec=60) the change in el during an azimuth strip is:
• rising  :  .3 deg
  
• setting: -.3 deg   
  

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