POINTING MODEL

When coordinates are inserted into the TCS (telescope control system) the telescope slews to them, if the telescope were perfect it would slew immediately to this position. However structural imperfections mean that it doesnt end up at the requested coordinates. A pointing model is used to describe these imperfections and correct for them so when a certain position is requested the telescope can point at it to reasonable accuracy.

POINTING LOGS

Each night, pointing data is logged in a file called POINTING.log. This file contains many variable describing the state of the telescope and the source but the key values are;

• Az El coordinates of source
• K-mirror parameters
• UAZ and UEL
• DX and DY

Along with POINTING.log a second file is generated which is formatted to be compatible with TPOINT, this allows the data to be run through TPOINT which is our primary tool for analuysing pointing performance.

MODEL DETERMINATION

The pointing model for the JCMT is determined with RxA with the pointing model for the other receiver assumed to be identical but with an applied offset or collimation.
Seven parameters describe the RxA model which is determined by a dedicated all-sky pointing run. The data acquired is then run through the TPOINT program which calculates the best-fit model to describe the whole sky.

COLLIMATIONS

For each observation uaz and uel are the collimation values for that individual observation. If you were to run it through tpoint you would get a value for ie and ca with zero scatter around it dS and dZ=0. But when considering a whole night you still get 1 value for IE and CA which is now the best fit for the nights data, the ds and dz are the scatter (residuals) around this best fit value (to centre it at 0). The values in pointing.log do not reflect ds and dz at all, they are the offsets including the extra constant bit that gets subtracted in tpoint. small scatter is good (ie small dS and dZ) as it means the average offset is a pretty good fit for all the data so even if you get big offsets fro a pointing they are maintained across the sky and on to the next point source so don't pose a problem, its the random jumps around this that are bad.

In the TCS: These are the permanent values stored for each instrument and are offsets in azimuth and elevation from the current pointing model. Naturally they are 0,0 for RxA but HARP and RXW do not point in the same direction and so have positive values of these collimations.

Nightly collimations: The values are rarely same night to night. The default values in the TCS will get the telescope to the right area of the sky, then local pointing is used to make the final adjustments. this difference between the default and actual collimations gives the residuals from the pointing model - uaz and uel. If you were to update the collimation terms in the TCS you would want to correct them by the mean offsets from the model (For receivers other than RxA this is the RxA model + existing collimation values).

• CA_NEW = CA_default + uaz
• IE_NEW = IE_default - uel

TPOINT

Sky rms - standard rms of the residuals from a pointing model fit
Population standard deviation - The rms weighted by the distribution of measurements over az el.

Pop. SD tends to be larger for datasets with fewer points or poor sky coverage. As N increases pop SD approaches sky rms. Pop. SD is the most honest statistic and reflects the fact that with few observations and many coefficients, the residuals will be smaller than they should be if one uses sky rms.

Pointing data is analysed in TPOINT by fitting the data to the existing model. Two parameters are routinely allowed to change, the collimation values IE and CA. The best fit of these is close to the default value in the TCS, within 0-3" typically. These are adjusted so that the scatter of residuals from the pointing model is now centred around a zero value. The values dS and dZ are calculated which are the offsets from the pointing model (including the collimation adjustment - as offsets from '0') for each observation. The rms of these residuals then describes the pointing performance for a given night. In the equations below you can see that dS is equal to the offset from the original model plus the mean value for uaz which is the collimation correction for this dataset.

• dS = - uaz + uaz
• dZ = - uel + uel

DIFFERENTIAL POINTING FOR RXW

Coming soon!