Sections
Intro
Measurements
Conclusions
Plots

# Intro  top

The pointing model residuals have coherent errors in the azimuth axis. We should be able to remove them and improve the fit by:
This page looks for other terms to add to the current model fit. The steps were:
1. Use the raw pointing errors that were used as inputs for model 15 (apr04). They are great circle errors on the sky in units of arc seconds.
2. Fit for some basic terms that have physical significance and then remove them from the raw data:
3. See if the azimuth encoder rack gear runout error corresponds to the errors.
4. Look at the tilt sensor roll residuals to see if they correlate with the pointing errors.
5. Take into consideration the za dependence in the mapping of the platform tilt to the error on the sky.

# The Measurements   top

A simple fit to the raw errors was done to remove the large scale errors. The fit in azimuth  was:
• c0 + c1*az + c2*cos(az) + c3*sin(az) + c4*cos(3az) + c5*sin(3az) + c6*sin(za) + zaEncTblFit
• 1az term (from tilt of the platform)
• 3az term (from 3 fold symetry of the triangle... deformations in the beams).
• za encoder table (the elevation rails are not perfectly aligned).
• The fitted values for the coefs:
•  coef value (asecs) Notes c0:constant -7.4 c1:az -.002 azInDeg c2:cos(az) 91.848 ampl:92.02 c3:sin(az) -5.635 phMax:93.51 deg c4:cos(3az) -5.250 ampl:23.96 c5:sin(3az) -23.378 phMax:64.219 deg c6:sin(za) -1129.124 This is an offset in the azimuth encoder. zaEncTblFit fit a 13 order polynmial to the fit residuals vs za.

The plots show various steps in fitting the model 15 input errors (.ps) (.pdf) :
• Raw az,za Errors: These are the raw pointing errors used to build model 15 (apr04).  Black is the raw data, red is after the  fit (see table above).  The top two pictures are az errors vs az,za. The bottom two plots are za errors vs az,za. There is a linear za dependence in the az,za errors (from the addition of alfa and the rotary floor re enforcing). There is also a large 1 azimuth term (from platform tilt or using the wrong declination for ao).
• Fit residuals and EncTblFit: These are the residuals after the above fit. The top two plots are azErrors while the bottom two plots are za Errors. The red points are the 13th order polynmial fit to the residuals vs za.
• When plotted versus za the errors group together. This is coming from the elevation rail alignment  changing as you move up in za.
• There is a lot more dispersion in the az errors vs za than the za errors.
• The az error dispersion is smallest around 12-13 degrees za.
• The 1az and 3az terms, and fit-encTblFit residuals.:
• The top plot has the 1az fit for az and za errors. The az,za amplitude are about the same.
• The center plot is the 3az fit. The az amplitued is almost twice the za amplitude.
• The bottom plot shows the az,za residuals after removing the zaEncTbl fit. The scatter in the az errors is much bigger than the za errors.
• Az Fit residuals with 3az term overplotted:
• top plot: az fit residuals with 3 az term overplotted.
• 2nd plot: az fit residuals plotted every 2degrees in za with 3 az term overplotted. There is a residual 3 az term at low za.
• 3rd plot. Az fit residuals in az encoder units with the az term overplotted. The errors have been divided by sin(za). If the error occurred at the encoder (azimuth runout or az encoder problem) then the errors should group better with the sin(za) included.
• 4th plot. Plotting the az residuals *sin(za) every two degrees of za.
• Fitting the 3 az term every 2deg in za: The previous page showed that a single 3az fit over all za was not doing a good job of removing the 3az term at low za.  to test this,  a copy of the az fit residuals was made that did not have the 3 az fit included. 3az fits were then done using data every 2 degrees in za. The surprising result is that the 3 az  amplitude is  larger at  low za then at  high za.  As you go up in za the load on the wheels increases.  Part of this depends on the position of the dome when the azimuth rails were shimmed (I assume this was done with the dome close to 10 deg za .. although i don't really know that).
• Fitting 3az term every 2degrees in za: The colored + group az errors every 2 degrees in za. (black line is za=2 to 54deg, red line is za=4 to 6 deg ...). The phase of the 3az term is changing as we go up in za.
• 2nd plot shows the az fit residuals:
• Black triangles: no 3 az fit included
• green *: single 3az fit for all za's
• red: + : fitting 3az term every 2 degrees in za.
• Amplitude of 3az fit vs za: The amplitude of the 3az fit decreases as we go up to za=13 degrees and then it flattens out.
• Phase of 3 az term peak  vs za: There is a linear ramp in the phase of the 3az peak.
• When za=15, the 3az peaks is at az=60 degrees. The azimuth arm is perpendicular to a side of the triangle.
• Az you move down in za, the peak moves clockwise to 75 degrees when za=3 deg.
• Az rms fit residuals every two degrees in za:
• The red * are the az residuals from the fit using a single 3 az term. The rms is computed separately for the za points every two degrees. It has a minimum at za=13
• The black * are the fit residuals for the 3az fits every 2 degrees in za. The single 3az fit does as  good as the 2 deg za fits only az za=13.
• Azimuth encoder runout error: The runout in the azimuth encoder rack gear was measured back i n 2000.

# Conclusions  top

• The 3az term for the az errors is a function of za. The sin(za-balance)*cos(3az) that we are currently including in the model will only approximate the za dependence since there is also a phase dependence of the peak.
• The az encoder runout only matches the pointing errors close to the maximum runout error. Overall, including all of the runout makes the az residuals a little worse.

# To do:

1. write program to compute pointing errors for various physical motions of the telescope (rotating platform, translating in x,y, etc..)
2. Using program in 1, see where the 1 az  and 3az terms  really come from. Should there be a za dependence in the 1, 3az terms for az errors?
3. look at the tilt sensor data. Use program in 1 to see if the pointing residual errors correlate with them

processing: x101/model/azenctbl/aztbl.pro