The model14 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)

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)

- New dome trolleys installed nov02=>feb03.
- Shimming of elevation rails feb03.
- shim pack bolt replacement feb03 (and continuing).
- Dome lifted 1.65 inches , realigned 27 feb03
- 28feb03 2400 lbs added T12,T4 corners, 1400 lbs T8 (in preparation for hairpin replacement).
- survey run 01mar03 -> 03mar03 sbn. 2380Mhz 5Mhz bw, .02 timeconstant.
- 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.
- 1371 points were used for the model.
- The model data was taken with model11 installed.

Data used to compute the model. (top)

- Fig. 1 is the azimuth/zenith angle coverage for the input data.
- 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 there is an offset in azimuth and zenith angle (caused by the shimming).
- 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 error above za of 10. This is from the pitch shimming 10 to 20 za.
- Figure 4 is the za and azimuth errors plotted by source order. The sources are color coded.
- Fig. 5 is the magnitude and direction of these errors plotted versus azimuth and za. 1 tick mark is 30 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 14 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. There is now a large za dependence of the raw azimuth errors. This was not here in jan02. We changed the roll with the shimming and this will move the raw az pointing errors vs za. You'd think that if the collimation was correct, the raw pointing az residuals would not be a function of za. Either there is a residual roll as you go out in za, or the azimuth arm is not along a true radii of the dish. The azimuth position as a function of za did change by a large amount for the 04feb03, 12feb03 surveys, but not for the final 17feb03 survey. This difference was attributed to the uncertainty in the theodolite position for the first two surveys.

Fitting the model. (top)

za residuals | az residuals | total residuals [asecs] | |

mod13 noEncTable | 6.65 | 8.98 | 11.18 |

mod 13 with Enc Table | 3.48 | 5.38 | 6.41 |

- 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.
- 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 has some runout. It will cause a azimuth scatter (with a za dependence since these are great circle errors).
- 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.

Checking the validity of the model. (top)

Fig 1 has the model residuals removing one source at a time. 0 is J2101+036, 1=J2312+-93.. to 23=J0804+302. 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 20th source J1924+334 makes the largest improvement in the model. 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)

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)

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

The offsets for the other receivers (not sband narrow) were measured on 4mar03 and 5mar03. Normally new sources (not in the model) are tracked by sbn and then these same sources are tracked on succeeding nights with the other receivers. The mean offset in the pointing errors between sbn and the other reciever is then added to the sbn constant terms in the model for each receiver.

There was not enough time on the schedule use "new" sources to measure the receiver offsets. Sources that were used in making model14 were tracked by the other receivers using model 14 with the same offsets that the receiver had relative to sbn in model11. The pointing errors that were measured with sbn were converted to model14 errors (remove model 11, add model14) and then the differences were computed between sbn and the other receivers. This looked like it worked ok for the low frequency receivers. For xband I also remeasured the source using model14. This did a better job of matching the sbn track with that of xband. The plots compare the sbn residuals with the other receivers (before and after the new constant terms) (.ps) (.pdf). The colors are:

- Black: This is source residuals measured using sband narrow during the model. They have been corrected to model14.
- Red : This is the same source tracked by the "other" receiver using model 14. The receiver offsets from sbn for model11 were used.
- Green: This is the "other" receiver residuals after computing the new constant offet for this receiver.
- Blue: For xband the source was also retracked using sbn and model14.

The offsets subtracted were:

rcvr | azOffset asecs | za offsets asecs |

lbn | 7.30 | 4.59 |

lbw | 6.19 | .34 |

sbw | 12.97 | -3.80 |

sbh | 1.57 | -1.64 |

cb | 11.60 | -3.72 |

xb | -1.22 | 3.14 |

Variogram of the pointing residuals. (top)

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.

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