Pointing model 15, may04

Links to plots:

The input data used to compute model 15 (.ps)  (.pdf)
The model15 fit with residuals (.ps)  (.pdf)
Checking the model by removing a source at a time and recomputing the model (.ps)  (.pdf)
The azimuth encoder table results (.ps)  (.pdf)
Measuring the constant offset terms for the other receivers (.ps)  (.pdf)
Variogram of the raw errors and pointing residuals (.ps)  (.pdf)

Links to sections:

Data used to compute the model.
Fitting the model.
Checking the validity of the model.
Azimuth encoder table.
Measuring the constant offsets for the "other" receivers.
Variogram of the pointing residuals.

Background.   (top)

Data used to compute the model.  (top)

    The data used to compute model 15 (.ps) (.pdf) was taken using model14  (the previous model). Figures 1-5 show these errors. Figures 6 and 7 remove the model 14 correction and show the raw telescope pointing error. All errors are great circle arc seconds.
  1. Fig. 1 is the azimuth/zenith angle coverage for the input data.
  2. Fig. 2 is the pointing error (za error top, az error bottom) plotted versus azimuth. This is relative to model 14. 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).
  3. Figure 3 is the pointing error (za error top, az error bottom) versus zenith angle for the input data. There is a linear ramp in za error of .83 asecs/degZa relative to model14. The feed tower used to sag downhill as the dome went up in za. model14 would then compensate for it. We have now added kevlar cables so the feed tower doesn't sag as much. On the other hand, there is more weight on the dome so the platform is tilting more as you go up in za. Both of these are probably contributing (in opposite directions) to this tilt (it looks like the weight is winning).
  4. Figure 4 is the za and azimuth errors plotted by source order. The sources are color coded.
  5. Fig. 5 is the magnitude and direction  of these errors plotted versus azimuth and za. 1 tick mark is 5 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.
  6. Fig. 6 has the raw az, za errors plotted versus azimuth. The model 14 correction has been removed. Model 15 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.
  7. Fig. 7 shows  the same raw errors plotted versus za. T

Fitting the model.   (top)

    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 model15 fit with residuals (.ps) (.pdf) are:
za residuals az residuals total residuals [asecs]
mod15 noEncTable 6.07 7.08 9.33
mod 15 with Enc Table 2.41 4.20 4.84
  1. 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.
  2. Fig. 2 plots the azimuth and za (raw Errors - ( model + encoderTable) ) residuals versus za.
  3. Fig. 3 plots the azimuth and za (raw Errors - (model + encoder table) residuals versus azimuth. There is more scatter in the azimuth residuals that the za. The tilt sensor measurements show a 6az term over part of the  dish. The encoder rack gear for the azimuth also has some runout. It will cause a azimuth scatter (with a za dependence since these are great circle errors).
  4. Fig. 4 plots the za and azimuth residual errors by source.
  5. Fig. 5 shows the za, az model residuals plotted versus source declination.
  6. 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.
    These residuals are the 2nd best residuals we've measured. The best set of residuals was the first model in may98 (see pointing residuals for a complete list).  The dome side roller bearings on both rails were adjusted to a small tolerance in may98. After that the roller bearings started to break (since the distance between the two rails was not a constant distance as you went up in za).  After tmay98, the bearings on both sides were loosened up leaving slop in the horizontal motion as the dome went up and down in za.  In jan04 of this year the bearings for a single elevation rail were tightened. The other end  was left loose. This forced the dome to follow the path of the right elevation rail. Since the bearings were adjusted to a small tolerance, the motion was repeatable and the model encoder table could take the motion out. The bearing on the other side did not break since it was left with lots of clearance.

Checking the validity of the model.   (top)

    The validity of the model is tested by removing a source at a time from the data set and recomputing the model (.ps)  (.pdf). This was done for all 24 sources in the model.
  • Fig 1 has the model residuals removing one source at a time. 0 is J1041+027, 1=J1150=003.. to 23=2253+161. The black line is the total rms residuals while the red it the azimuth and the green is the zenith angle. The top plot does not include the encoder table while the bottom plot includes it.  Removing the 10th source J0137+331 makes the largest improvement in the model. This source was taken 9:30 am to 11:30 am. At the edges, the tiedown cables had lost tension.
  • Figure 2 plots the mean pointing error and its rms for each source track that was not included in the model. The model was evaluated without source i, then the mean and rms of the pointing model along the az,za track for source i was computed.

  • Azimuth encoder table.   (top)

        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 little 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: (the azimuth encoder table has not been installed).
    1. Fig 1 top is the azimuth encoder table made by smoothing to 1 through 6 degrees azimuth (bottom to top).
    2. 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.
    3. Fig 2 over plots the azimuth residuals and the az enctable smoothed to 3 and 6 degrees azimuth.
    4. 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)

    Measuring the constant offsets for the "other" receivers.   (top)

    The model includes constant terms (great circle) in azimuth and zenith angle for each receiver. These terms can differ receiver to receiver because of positioning error of the horn on the rotary floor. The model is made with sband narrow. After the model we need to compute what the constant offsets for the other receivers are (ideally it would remain constant).

        On 21may04 8 sources were tracked with sbn and the new model 15 installed. 3 of these sources had been used in making the model (J1021+219, J1737+063, and J1925+211). The offsets for the other receivers (not sband narrow) were measured on 15/16
    may04 tracking these same sources (typically 2 sources per receiver).  Before each receiver was used, an offset was included to get the receiver close to where it was supposed to be. The mean offset in the pointing errors between sbn and the "other" receiver is then added to the constant terms used to track these sources.
        The plots show the tracking error for sbn and the other receivers. (.ps)  (.pdf).
    The first 9 plots show the sbn error and the  other receiver error (one per page). Black is the sbn measurement. Red, green, blue, purple are the up to 4 frequency bands of the "other" receiver. The left column has azimuth errors while the right column is za errors.  The numbers printed are the mean(sbnErr) - mean(rcvrErr) in arcseconds. The figures are:

    1. 327 Mhz.  3 frequency bands, 1 source were taken.
    2. 430 Mhz . 3 frequency bands , 1 source were taken.
    3. 610 Mhz . 3 frequency bands, 1 source were taken.
    4. lbw. 4 frequencies, 3 sources.
    5. sbw. 3 frequencies, 2 sources.
    6. sbh. 4 frequencies, 2 sources.
    7. cband. 4 frequencies, 2 sources.
    8. cbandHi. 4 frequencies, 2 sources.
    9. xband. 4 frequencies, 2 sources.
    10. Mean(sbn)-mean(rcv) for each source and frequency band. black is the azimuth error and red is the za error.
        Ideally the (sbn-rcv) value should be the same for all sources and frequencies of a receiver.  Lbw and sbw have 1 source  (J1737+063) that sticks out from the other measurements for that receiver. This is probably because the sbn track for this source had some trouble. It was not included in computing the offset for the receivers.
        Figure 9 also shows that cband high has a za pointing offset that is a function of frequency. This is probably because the coma for the receiver is a function of frequency and it is changing the pointing offset. For cband hi the first 3 frequencies (6600,6900, 7200) were used to compute the pointing offset since they were similar and close to the methanol line.
        The offsets for the individual receivers as calculated from the above data is shown in the table below.
    model 15 receiver offsets.
    rcvr azOffset asecs za offsets asecs
    sbn -40 -102.55
    327 -106.17 25.22
    430 -35.48 -97.48
    610 -45.35 -15.65
    lbw -45.53 -116.21
    sbw -38.77 -89.56
    sbh -44.09 -86.12
    cb -42.45 -80.32
    cbh -40.89 -87.14
    xb -38.97 -85.85

    The azimuth offset is similar for all receivers but 327 (327,430, and 610 were not surveyed into position). The receivers: sbw,sbh,cb,cbh,xb  all have similar za offsets. sbn and lbw differ from this mean value (85.8) by 16 and 30 arc seconds. These two receivers were not moved in the za direction after the survey because there was no room in the hole in the floor to move the receiver.

    processing: x101/model/may04/verify.pro

    Variogram of the pointing residuals.   (top)

        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 pair wise difference of the pointing residuals (including the zaencoder table) while the bottom plot has the pair wise 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)
    1. 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 za correlation increases until za=2. degrees  and then levels off. The az residuals variance increases till about 5 degrees. The 25 foot spacing of the north south main cables is about 1.6 degrees (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.

    2. 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.
    processing: x101/model/may04/doall.pro