Intro

The 2d gauss fit

Examples of the fit using 3C405

Summary

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

- 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.

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

- the cross arms were 4.8 degrees.
- the beamwidth is about .66 degrees.
- the SEFD at sband is about 4100Jy... So the source was about 25% of Tsys.
- I tried doing the linear elevation fit using the elevation offset, and using the just the elevation.
- Bad fits (rfi, etc..) were excluded using:
- fit sigma > .005 when el > 20 degrees
- fit width outside of ( .66 +/- .04)degrees

The plots show the results of the 2d gauss fits (.ps) (.pdf)

**Page 1: examples of strips and fits**- green is the measured strip data, black is the fit using the elevation offset for the linear term, red is the fit using the elevation for the linear term.
- The cross was done at 14.9 deg elevation (rising)

- frame 1,2. azimuth strip.
- frame 1 full strip
- frame 2 showing blowup of baseline fit. The black elOffset fit is flat (since it has no el offset)
- frame 3,4 elevation strip
- frame 3 full strips
- frame 4 blowup showing baseline.
**Page 2: Tsys, src amplitude, sefd fit results:**

- black shows fit using C*ElevationOffset, red shows C*Elevation fits
- + is when the source is rising, * is source setting.
- Frame 1: Tsys fit
- black (elOffset): shows little difference between rising
and setting

- red (el): shows a 10 or 20% difference in rise and set
- Frame 2: Src amplitude fit
- both black and red show the same rise, set variation.
- Frame 3: change in elevation for the azimuth strips (vs el)
- rising the el changes by .35 degrees during each az strip
- setting: the el changes by -.35 degrees for each az strip
- The elOffset fits will assume that this change is 0.
- Frame 4: change in elevation for the elevation strips (vs el)
- the elevation strips move +/- 2.4 degrees from the center of the source.
- rising the el changes by 5.2 degrees, setting it changes by 4.4 degrees.
- Frame 5: SEFD vs elevation for the two types of fits
- The black (elOffset*C ) fit shows a 15 -20%difference rise to set
- the red (el*C) fits track rising, setting pretty well.
- Page 3: fit sigma, tsys/degEl, az error, el error.
- frame 1: the fit sigmas are the same for the two fits
- frame 2: the Tsys/degEl (C*el) coef.. the red (C*elevation) has a little less difference than the black C*elOffset.
- frame 3,4: Az,El pointing error fit vs el
- these are with the model removed.
- both the red and black fits track each other.
- Page 4: FWHM fits for az and el
- both fits give similar results.

- the average is around .67 degrees.

- Using the elevation offsets for the linear term (C*el) in the fit gives SEFD values that show a rise,set variation.
- This is probably caused by forcing the elevation change in the azimuth strip to be 0 (since it used elevation offsets).
- Using the actual elevation for the linear term gives an SEFD that does not depend on rise set.
- The elevation liner fit does show:
- both Tsys and the srcStrength show a rise,set difference this cancels with the SEFD
- My guess is that this is a fitting problem.. not a real
problem with the telescope.

- The rise set difference is probably related to the C*el linear fit

*processing:
aosoft/p12m/model/model3A/chk2dfit.pro*

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