Pointing model 13, jan02

(lastupdate: 12jul02 .. This model only installed sbh, xband)

Background:

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:

The data 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 scans.
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 platform, etc..)
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 quadrant.
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.

Model13 fit:

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) are:

	za residuals	az residuals	total residuals [asecs]
mod13 noEncTable	5.89	6.81	9.0
mod 13 with Enc Table	3.54	5.16	6.26
mod12 withEncTbl	3.65	5.61	6.69
mod13 za & az EncTbl	3.54	4.02 (smo3)	5.40

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.

A variogram 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.

Figure 1 shows the az, za coverage for sband (CTA21 was tracked on two separate days).
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 mark).

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 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.

processing: x101/model/jan02/inpsav.pro,pltinp.pro,domodel.pro,pltmodel.pro

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