Modeling the azimuth pointing errors
The pointing model residuals have
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:
See if the azimuth encoder rack gear runout error corresponds to
Look at the tilt sensor roll residuals to see if they correlate
with the pointing errors.
Take into consideration the za dependence in the mapping of the platform
tilt to the error on the sky.
- 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
- Fit for some basic terms that have physical significance and then
remove them from the raw data:
The Measurements top
A simple fit to the raw errors was done to remove
the large scale errors. The fit in azimuth was:
The plots show various steps in fitting the model
15 input errors (.ps) (.pdf)
- 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
- The fitted values for the coefs:
|This is an offset in the
|fit a 13 order polynmial to
the fit residuals vs za.
- 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
- There is a lot more dispersion in the az errors vs za than the
- The az error dispersion is smallest around 12-13 degrees za.
- The 1az and 3az terms, and
- 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
- Az Fit residuals with 3az term
- 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
- 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
- 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
in the azimuth encoder rack gear was measured back i n 2000.
- 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.
- write program to compute pointing errors for various physical
motions of the telescope (rotating platform, translating in x,y, etc..)
- Using program in 1, see where the 1 az and 3az terms
from. Should there be a za dependence in the 1, 3az terms for az errors?
- look at the tilt sensor data. Use program in 1 to see if the
pointing residual errors correlate with them