Intro:(top)

    Data for model3A was taken in  Feb16 and mar16.  The setup was:

• crosses were done (az end el strips) while the source was tracked.
• Model2A was installed during data taking.
  
• sband data was taken centered at 2270 MHz
• xband data was taken centered at 8600 MHz
• the mock spectrometers took 1 second spectra with a bandwidth of 172MHz about each center frequency.
• Only 1 pol was available for each frequency band.
  
• The single pol dual frequency data could be taken simultaneously.
• Different strip lengths were tried (since the beam widths  differed by a factor of 4.
  

• strip lengths, strips times tried

  striplen beams	stripTm secs	smps/beam (fwhm)	Notes
  10 beams	60	6	tried with sband, but not enough samples/beam. Did not use this data
  8beams	120	15	did this with sband and sband (separately)
  2beams	120	60	when xband data was taken at 8bms/strip, sband data was taken simultaneously. 8bms/strip in xband gave about 2bms/strip in sband

•  
• When 8 beams strips at sband were taken, the xband data was ignored (there weren't enough samples across the beam).
• I've defined 4 separate pointing datasets
• sband 120 second 8 bm strips (4.8 degree strips)
  
• xband 120 second 8 bm strips (1.2 degree strips)
• sband 120 second 2 bm strips (1.2 degree strips. this data was taken concurrently with the xband data).
• All strips.
  
• More info on modles are made.
  

Taking the data: (top)

The sources used:

Examples of spectra and total power strips:

• Page 1: spectra averaged over 1000 seconds and  rms by channel
  
• the are 8192 channels over the 172.032 Mhz
• The spectra are an average of 1000 seconds
• the rms plots show rms/mean for each frequency channel. 1000 1 sec records were used.
• Top: sband average spectra.
• 2nd frame: sband rms by channel
• the rfi at 2315 - 2332 is probably digital audio.. (although they should start at 2320).
• 2315 -2320 could also be aws band C
  
• the birdie at the center of the band is from the digitizers.
  
• 3rd frame: average xband spectra
• bottom frame: rms/mean for xband
• the birdie at the center of the band is from the digitizers.
• Page 2: total power azimuth strips across sources.
• The total power was computed from each spectra.
• To exclude frequency channels with rfi:
• i fit a polynomial to the rms/mean, and then excluded > 3sigma outliers when computing the total power.
• I overplotted 5 azimuth strips (each strips took 120 secs). Each strip was separated by 240 secs in time.
  
• Top: sband strips across 3C405 (flux: about 785 Jy)
  
• The baselines are relatively stable
• 2nd frame: xband strips across 3C405. (flux: about 214 Jy)
  
• the baseline varied between strips. part of this was weather, part was a gain instability in xband (see below).
• 3rd frame: sband strips across 3C273
• The vertical scale is exanded.
• bottom frame: xband strips across 3C273
• Gaussian fits were then done to these strips:
• y=A0*exp((x-A1)/A2)^2/2.) + A3 + A4*x
  

Problems encountered while taking data:

• Sband had lots of interference.
• I fit a polynomial to rms/mean by channel and then excluded 3sigma outliers.
• The xband total power baselines have lots of variation
• part of this is from the weather.
• We also found a connector problem in the xband system (more info)
  
• most of the sources are extended (especially for xband). If the extent is not spherically symmetric, then we will get an  error that is a function of the az,el orientation of the feed probes.
  

The raw pointing errors: (top)

• extract data for each az, el strip.
• for each spectra compute total power (excluding rfi channels)
• for sband we typically excluded 30 to 40% of the band
• fit a guassian to the data in each strip:
• y=A0*exp({(x - A1)/A2}^2/2.)  + A3 + A4*x
• x is the offset from the center of the strip in great circle units.
  
• A1 is the error Offset.
• remove the pointing model correction that was in use when the data was taken.
  

    We had three  separate data sets:

• sband data taken with 8 beams/strip. The concurrent xband data was ignored
• xband data taken with 8 beams/strip.
• sband data taken with 2 beams/strip. this was taken concurrently with the xband data.

    The first plots show the raw pointing errrors  for the combined data set (.ps) (.pdf):

• Page 1: az, el coverage of the all the sources
• sources used at both long sband strips and xband are traversed twice.
• Page 2: raw az, el errors by cross number.
  
• Model2A has been removed, so this is the telescope error with no model.
• The errors are great circle Arcminutes.
• crosses with errors < -30 arcMinutes or > 6 arcMinutes have been excluded (probably rfi or rain)
  
• Top: az errors vs sample
• This is the order the data was taken.
• Sources that repeat are the concurrent sband,xband data (sband first, then xband)
• Bottom: el errors vs cross number
• Page 3: Az errors vs az and el.
• Top: az errors vs azimuth
• bottom: az errors vs el.
• Some of  the outliers will be removed prior to fitting (see below)
• Page 4: El errors vs az and el.
  
• Top: el errors vs az
• bottom: el errors vs el.

    The 2nd set of plots  show the combined raw errors as an arrow plot (.ps) (.pdf):

• The length of the arrow is proportional to the error.
• 1 tick mark is 3 arcminutes.
• The direction of the arrow shows the direction of the combined error.
• Page 1: Error plot with all data sets included
• Page 2: error plot for xband sources
• Page 3: error plot for sband sources (with 8 beams/strip).

Comparing the different raw data sets:

    The 3rd set of plots look at the differences in the raw errors for the 3 data  sets (.ps) (.pdf)

• Page 1: The beamwidth fits (FWHM) for the three data sets.
  
• The beam width (at a given frequency) should be independent of the pointing error
•  (as long as we are within say 1/2 a beam and the amplitude does not get too low..).
• beam width outliers could be excluded because of bad fits (independent of the pointing error).
• A colored horizontal line shows the median beam width for each  data set:
• Black: sband 8 bm strips
• red    : sband 2 bm strips
• green: xband 8 bm strips.
• Top frame: beam width fit for azimuth strips
• you can see lots of scatter in the weaker sources (3C123, 3C273).
• Bottom frame: beam width fits for elevation strips.
• It's not surprising that the sband 8bm and 2bm strip beamwidths differ.
  
• The 2bm strips do not get down to the baseline...
  
• Page 2: Az, el Errors vs beam width fits.
• To test if the beamwidth fit could be used to exclude pointing outliers , the pointing error was plotted vs the beamwidth fit
• Vertical lines are plotted at the median beamwidth for each dataset.
  
• Top frame: az errors vs az bmwidth fit.
• Bottom frame: el errors vs el bmwidth fit.
• Unfortunately there is no obvious slope to the errors.
• Page 3: fitting a 4th order polynomial to raw errors vs elevation
• To compare the different data sets, a robust 4th order polynomial fit was done vs elevation.
• We can then plot the errors of the dataset relative to this fit.
• Top frame: az errors vs el with fit.
  
• The green line is the fit
• the red crosses are 3 sigma outliers from the fit
• Bottom frame: el errors vs el with fit
• Page 4,5: Residual raw errors by source for the 3 datasets:
• The polynomial fit was subtracted from all of the raw fit errors.
• The residual errors were then plotted vs elevation for each source separately
• Colors were used for the different data sets.
• At the top of each frame, the median error for the data set is printed (in amin).
  
• Page4:
  
• frame 1,2 : residual az,el errors for 3C144 (crab):
• you can see an offset in the sband 8bm and xband 8bm errors.
• The el errors below 45el (for rise) are wandering. I wonder if this was rain?
• but the sband 8bm errors are also elevated.. so maybe something is wrong here?
  
• Frame 3,4: errors for 3C273
• more scatter (but this is a weaker source).
  
• Page 5:
• frame 1,2 :residual az,el errors for 3C405
• frame 3,4: residual az,el errors for 3C461.
• this has more scatter than 3C405 even though it is stronger.
• The scatter may come from it being more extended.
• Page 6: The median residual errors by data set for common sources.
• Top frame: median az error residuals
• xband az errors are  15 to 30 amin below the sband errors
  
• bottom frame: median el error residuals
• the xband el errors are less than 15 aminutes
• I was expecting the that median offset for az and el would be similar....
  
• To do this correctly i should probably make sure that each frequency covered the same az, el range.

Fitting the model: (top)

• all the data.
  
• the xband data
• the sband data 2 bm strips (taken simultaneously with xband).
• the sband data 8bm strips

• All points with az,el errors outside of [-30, + 6] arcminutes were excluded.
• from the raw error plots, these were mainly outliers
• a robust 4th order fit was done to the az,el errors vs elevation (separately)
• any points 3 sigma from the fit were excluded.

•  The residuals for each source are plotted in a different color.
• Page 1 plots the residuals vs sample (this is the order the data was taken).
• the top of the plot shows the rms error in az, el, and the combined error (added in quadrature).
  
• the source table shows the mean and rms error for each source
• the leftmost 2 cols are for az error, the right most 2 cols are for elevation.
• Page 2: plots the az errs by az,el and the el errors by az,el for all sources.
• Page 3: lists the model fit values:
• azF is the azfit, elF is the elfit
• 1az: shows the 1 az term from the az ,el fits (this is the tilt of the telescope)
• The parameter values in degrees, followed by the params in asecs (this is what is loaded in the model).
  

• Fit residuals for all data sets combined (.ps) (.pdf)
• Fit residuals for the xband data (.ps) (.pdf)
• Fit residuals for the sband data 2bm strips (taken with xband) (.ps) (.pdf)
• Fit residuals for the sband data 8bm strips (.ps) (.pdf)

Notes:

• the xband, and sband short strips were limited to the 4 strongest sources..
  
• This may be why they are less than the sband long strips.
  

Summary:

• We will use the xband fit.
• the combined error is  .537 Minutes
• the xband fwhm is 10.1 amin
• the sband fwhm is 39.9 amin
• there was an offset in the sband ,xband pointing errors
• az : 15 to 30 amin
• el : < 15 amin
  

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