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)

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)

- Jan04 new stiffer leaf springs installed dome, side roller bearing one side tightened up.
- Turret floor reinforced (weight added).
- 3 compressors added to the top of the dome (upper left side).
- kevlar cables installed.
- alfa installed.
- turret encoder lost index and then recalibrated.
- tiedown 4 jack replaced. position of tiedown re established use tape measure. No time for an az swing to check the 1 az term of the tilt sensors.
- 501 points were used for the model.
- The model data was taken with model14 installed.
- The data was taken with heiles calibration scans rather than the turret scans.

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 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).
- 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).
- 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 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.
- 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.
- Fig. 7 shows the same raw errors plotted versus za. T

Fitting the model. (top)

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 |

- 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 also 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 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)

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).

- Fig 1 top is the azimuth encoder table made by smoothing to 1 through 6 degrees azimuth (bottom to top).
- 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 over plots the azimuth residuals and the az enctable 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)

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:

- 327 Mhz. 3 frequency bands, 1 source were taken.
- 430 Mhz . 3 frequency bands , 1 source were taken.
- 610 Mhz . 3 frequency bands, 1 source were taken.
- lbw. 4 frequencies, 3 sources.
- sbw. 3 frequencies, 2 sources.
- sbh. 4 frequencies, 2 sources.
- cband. 4 frequencies, 2 sources.
- cbandHi. 4 frequencies, 2 sources.
- xband. 4 frequencies, 2 sources.
- Mean(sbn)-mean(rcv) for each source and frequency band. black is the azimuth error and red is the za error.

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.

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.proVariogram 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 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.

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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