Pointing model 13, jan02
(lastupdate: 12jul02 .. This model only installed sbh, xband)
Main reflector surface adjustments completed on the 38000 panels sep01.
AO9 survey of dome done 09aug01. From the dish photogrammetry we now know
the position of the horizontal offsets of the platform relative to the
dish and theAO9 monument.
Large beam 20 feet from center bearing on azimuth arm used to jack
up the dome is still there.
Model data was taken from sband narrow calibration runs (heiles scans)
sep01 thru dec01 and turret scans dec01,jan02. The calibration runs fit
a 2-d gaussian with coma and sidelobes. The turret scans only fit a 2-d
gaussian. The extra coma fit causes the pointing position to differ by
a few arc seconds between the two methods when the coma is appreciable.
1016 points were used for the model.
The model data was taken with model11 installed (model12 was never used).
Data used to compute the model:
used to compute model 13 (.ps) (.pdf)
was taken using model11 (the previous model). Figures 1-5 show these
errors. Figures 6 and 7 remove the model 11 correction and show the raw
telescope pointing error. All errors are great circle arc seconds.
Fig. 1 is the azimuth/zenith angle coverage for the input data. The closely
spaced * are taken with turret scans while the +'s are taken with calibration
Fig. 2 is the pointing error (za error top, az error bottom) plotted versus
azimuth. This is relative to model 11. The left half of each plot is the
northern portion of the dish (southern sources with declination < 18.2
degrees). The right half of each plot is the southern portion of the dish
(northern sources). Relative to model 11 it looks like the northern part
of the dish has changed more than the southern half. Especially southern
sources after transit (the northeast quadrant). The rms was 7.16 arcseconds
in za and 8.64 arc seconds in azimuth which gives a 11.2 arc seconds pointing
for data taken with model 11. There is also a 3.7 arc second offset in
the azimuth mainly from the northeast quadrant.
Figure 3 is the pointing error (za error top, az error bottom) versus zenith
angle for the input data. There is a ramp in za of the zenith angle error
of .46 arc seconds per degree relative to model 11 (red line). This could
be from weight being added to the dome/feed tower since model 11 (tertiary
Figure 4 is the za and azimuth errors plotted by source order. The sources
are color coded. + are turret scans and * are calibration scans.
The mean and rms are also broken down by turret and calibration scan.
At first I thought the jump in azimuth errors at sample 650 was a problem
with the turret encoder jumping. After looking a little closer, this is
the offset found in both turret and calibration scans for the northeast
Fig. 5 is the magnitude and direction of these errors plotted versus
azimuth and za. 1 tick mark is 10 arc seconds. At the bottom is a table
of the average magnitude and rms for the entire dish and computed for every
5 degrees in za.
Fig. 6 has the raw az, za errors plotted versus azimuth. The model 11 correction
has been removed. Model 13 will be fit to this data set. Fits to 1az, 2az,
and 3az have been over plotted with the amplitude and phase angle of the
maximum. The 1az term of the raw pointing errors agrees with the difference
we found in the theodolite-azencoder
azimuths. So the large encoder offsets are coming from the horizontal
offset of the platform relative to the dish.
Fig. 7 shows the same raw errors plotted versus za.
The model is fit to the raw errors. An encoder table
spaced every .5 degrees in za is computed for azimuth and zenith angle
errors and then removed. The final residuals are great circle errors.
The telescope must move in that direction from the computed position to
point at the source. The model13
fit with residuals (.ps) (.pdf)
||total residuals [asecs]
|mod 13 with Enc Table
|mod13 za & az EncTbl
Fig. 1 plots the residuals versus za for the azimuth and za errors. The
encoder table has not yet been removed. The computed encoder table
is over plotted in red.
Fig. 2 plots the azimuth and za (raw Errors - ( model + encoderTable) )
residuals versus za. The rms errors are are very close to those from
model 12 which was taken after the adjustments of the 3000 tieback
cables were done.
Fig. 3 plots the azimuth and za (raw Errors - (model + encoder table) residuals
versus azimuth. There is more scatter in the northern half of the dish.
The two methods (turret scan, calibration scan) have a difference of 1.2
arc seconds offset for their residuals in the north half of the dish but
the rms's are very close: (5.52,5.62). Maybe this is the azimuth encoder
wrack gear showing up.
Fig. 4 plots the za and azimuth residual errors by source.
Fig. 5 shows the za, az model residuals plotted versus source declination.
Fig. 6 has the residual error plotted versus azimuth and zenith angle.
1 tick mark is 5 arc seconds. A table of the average error and the errors
every 5 degrees za is at the bottom of the plot. Also included is the model
parameters and values.
Variogram of the pointing residuals.
of the raw errors and pointing residuals (.ps) (.pdf)
shows the correlation of the measurements versus separation of the points.
The residual error and raw pointing error difference is computed for all
points on a pair wise basis. A metric is then defined for the point separation
and is used to bin the data. The variance of the pair differences for each
bin is then computed and plotted versus the distance. For each figure the
top plot is the pairwise difference of the pointing residuals (including
the zaencoder table) while the bottom plot has the pairwise difference
of the raw errors input to make the model.
This data can be used to interpolate the residuals
onto an az,za grid (it gives the nugget (y intercept), range (where the
variance increases), and the sill (value where the variance levels
off) for the krigging routine)
Fig. 1 is the variogram using the great circle angular separation of the
points as the metric. The separation was binned to .3 degrees steps. The
correlation increases until za=1.5 and then levels off. There remains some
structure in the az residuals (1.5 degrees is close to the 25 foot spacing
of the main cables ). The large correlation in the bottom plot is the 1az
term of the raw pointing errors.
Fig. 2 projects the points into the xy plane and then measures the distance
(since the kriging would be done in this plane). It looks the same as that
of figure 1.
Azimuth encoder table:
An azimuth encoder table for azimuth residuals was built
by smoothing the great circle azimuth residuals in azimuth and then removing
this from the (model-zaEncTbl) azimuth residuals. I first tried smoothing
the littlc circle errors (azErr/sinza) thinking that the azimuth
encoder wrack gear was the largest culprit and it should give a little
circle error. The residuals didn't get much better. The low za errors were
messing up the averages. This must mean that the azimuth residual errors
are great circle and not little circle.
The table step has 1 degree steps in azimuth. Different
az smoothing was tried. The az
encoder table results (.ps) (.pdf)
are shown in the figure:
Fig 1 top is the azimuth encoder table made by smoothing to 1 through 6
degrees azimuth (bottom to top). There is a 30 degree structure in the
table between azimuths of 70 and 180 degrees.
Fig 1 bottom plots the azimuth encoder residuals (black line) for azimuth
smoothing 1 through 19 degrees. The green line is the azimuth residuals
without the azimuth encoder table. The red line is the total residuals
(za plus az) for the various smoothing.
Fig 2 overplots the azimuth residuals and the az enctbl smoothed to 3 and
6 degrees azimuth.
Fig3 is a fourier transform of the azimuth encoder table (built with 1
degree smoothing). The top plot is plotted versus cycles and the bottom
plot versus period (in degrees). The power is at 4 cycles and 12 cycles
(90 degree spacing and 30 degree spacing). (I think the az encoder rack
gear has 15 degree sections...see
az rack gear)
This model has not yet been installed. We need some observing time to
check each receivers offsets relative to the new model...
following not yet done...
Verifying the model
A few sources not included in the model were tracked
to verify the model. This was done during the day with the sband receiver.
The sources include J0242+110, J0403+260, J2316+040, J0137+331 (3C48),
J0318+164 (CTA21), and J0603+219. The 325 points had an az rms of 6.56,
a za rms of 3.50 giving a total rms of 7.4 asecs.
To compute the azimuth and zenith angle offsets for
the other receivers, CTA21 was tracked with sbn and then with lbn,lbw,cband
and 430. The offsets in azimuth and za were adjusted so that the
average error was the same as that for sband narrow. J0602+219 was
tracked with sband narrow and the 610 and 430 receiver.
Figure 1 shows the az, za coverage for sband (CTA21 was tracked on two
Figure 2 plots the za error, az error versus az.
Figure 3 plots the za error, az error versus za.
Figure 4 plots the za error, az error by source.
Figure 5 is an arrow plot versus az, za of the errors (5 asecs = 1 tick
figure 6 shows the errors for sband, lbn, lbw, and cband. The sbn, cband
zaerror have a large difference rise to set. Lbw az error does not track
lbn very well.