Initial comparisons carried out with respect to astrometric standards published by Stone and co-workers (Stone 1997; Stone et al. 1999) indicated that a large systematic difference in right ascension existed.

Investigation of the raw data showed that no large image asymmetry was present. Further comparisons made with data released from Bordeaux confirmed that the systematic difference was a feature of the CMT data.

It was soon established that this effect was caused by problems with the charge transfer efficiency of the CCD. Detailed investigations of the CTE properties of similar CCD chips were carried out by Copenhagen University Observatory (Sørensen et al. 2000). Contact with other groups revealed that this wasn't an isolated case (Zacharias et al. 2000). Various solutions are available to reduce the magnitude of this effect which include fine tuning the electronics and increasing the temperature of the CCD. However, there is still a need to calibrate this effect since the data originally taken, before the final set-up was in place, could still be used and also the effect isn't fully removed by these changes.

The observed effect of this problem is to cause a systematic shift in RA as a function of magnitude (see Fig. A.1). On top of this, the effect is also a function of the background illumination which reduces the effect the brighter the sky. This is similar to the reasons needed for a preflash with early CCDs which also had CTE problems. A continuous illumination system was considered for the camera to increase the background level and reduce the effect. However, time and resources were not available to carry out this experiment.

Initial work compared data from the Stone standard regions and fitted a 3-parameter function,

Additionally, the CTE characteristics changed on 9 August 1999, thus a new calibration would be needed. This was indicative of a progressive failure of the camera controller circuitry. It failed totally at the beginning of October 1999 and had to be replaced.

Since the equator had already been covered by the survey, it was unclear whether we had enough data, for all periods, to calibrate the problem properly. Although brief comparisons had also been carried out with respect to other telescopes (Bordeaux), there was insufficient data to provide a calibration. It was thus desirable to compare with other data sets.

$\begin{figure} \par\includegraphics[angle=270,width=8.8cm,clip]{MS2801fa1.eps}\end{figure}$

Figure A.1: This plot shows the general trend in RA caused by the charge transfer efficiency problem. This is a comparison, using observations taken during dark conditions, with respect to Stone's standards. A three-parameter model has been fitted to the data.

Table A.1: This table shows the different calibration periods identified along with some of the characteristics of the periods. The data analysed only covers up to the end of September 2000.
Period Start End Controller Temperature Number of %

observations

(1000's)

0 990 331 990 408 1 $-65~\hbox{$^\circ$ }$ C 518 1

1 990 409 990 806 1 $-58~\hbox{$^\circ$ }$ C 10 721 23

2.1 990 809 990 821 1 $-58~\hbox{$^\circ$ }$ C 976 2

2.2 990 823 990 923 1 $-58~\hbox{$^\circ$ }$ C 1630 3.5

2.3 990 924 991 007 1 $-58~\hbox{$^\circ$ }$ C 1199 2.5

3 991 101 991 213 2 $-65~\hbox{$^\circ$ }$ C 1042 2

4 991 214 000 127 2 $-54~\hbox{$^\circ$ }$ C 1741 4

5 000 128 000 930 2 $-30~\hbox{$^\circ$ }$ C 28 626 62

**Table A.1:** This table shows the different calibration periods identified along with some of the characteristics of the periods. The data analysed only covers up to the end of September 2000.
Period	Start	End	Controller	Temperature	Number of	%
					observations
					(1000's)
0	990 331	990 408	1	$-65~\hbox{$^\circ$ }$ C	518	1
1	990 409	990 806	1	$-58~\hbox{$^\circ$ }$ C	10 721	23
2.1	990 809	990 821	1	$-58~\hbox{$^\circ$ }$ C	976	2
2.2	990 823	990 923	1	$-58~\hbox{$^\circ$ }$ C	1630	3.5
2.3	990 924	991 007	1	$-58~\hbox{$^\circ$ }$ C	1199	2.5
3	991 101	991 213	2	$-65~\hbox{$^\circ$ }$ C	1042	2
4	991 214	000 127	2	$-54~\hbox{$^\circ$ }$ C	1741	4
5	000 128	000 930	2	$-30~\hbox{$^\circ$ }$ C	28 626	62

Palomar Observatory Sky Survey II (POSS2) data was obtained for 27 fields. These had been scanned by the APM (Kibblewhite et al. 1984). This data was matched with the CMT CCD data and the residuals plotted as a function of magnitude (cf. Fig. A.1) for various sky brightness ranges. Although this data was less accurate than that of Stone, more data was available.

Initially, the data was split into 5 periods (1-5), depending on which CCD controller was in operation and what the CCD temperature was. The Controller 1 period was split into two due to the change in CTE characteristics mentioned above.

While carrying out the overlap analysis (see later) it was realized that the first data period had different characteristics, so was split into Periods 0 and 1. This corresponds to a change in the CCD temperature caused by vacuum problems within the camera. Also, the calibration was very unstable for Period 2, so it was split into three. Table A.1 shows the different calibration periods finally adopted.

In analysing this data, it became clear that the (a,b,c) model was not good enough. The replacement model eventually chosen was a simple scaled model. In this model the functionality with magnitude was taken directly from the darkest sky bin of the POSS2 data comparison (the one with the largest effect) and then scaled to fit the other sky brightness bins. Thus the parameterization had been reduced from 3 to 1, the scale value, which could then, in turn, be plotted as a function of sky brightness to see if further parameterization could be carried out. The scale value was defined to be equivalent to the RA shift at the faint end (in arcsec).

The results of these calibrations are shown in Fig. A.2. A simple exponential has been fitted to the data:

$\begin{figure} \par\includegraphics[angle=270,width=8.8cm,clip]{MS2801fa2.eps}\end{figure}$

Figure A.2: This plot shows the scale value plotted versus sky brightness for 4 different periods. A simple exponential has been fitted to the data.

These diagrams demonstrate that a simple parameterization exists for the CTE calibration covering the entire survey. They also clearly show the effect of the various changes made to the CCD camera. At the start of the project the maximum size of the CTE shift (z) was about 0.7''. The new controller reduced this down to 0.3'' due to improved voltage settings and finally the increase of the CCD temperature from -65 $\hbox{$^\circ$ }$ C to -30 $\hbox{$^\circ$ }$ C reduced it further to $\sim$ 0.1''.

Work on the UCAC comparisons lead to the implementation of a CTE "problem spotter'' in the catalogue generation programme via the overlaps. If any of the overlap comparisons show an RA trend after the CTE calibrations have been carried out, it indicates a problem in one (or both) of the two frames of the overlap. Many overlap pairs in the survey were flagged as having problems, thus indicating that a four-period scaled model, characterized by Fig. A.2, was too simplistic.

An analysis was then carried out on all the residual CTE shifts. Firstly, all overlaps were determined (14 000 overlaps for 5 600 frames) and the relative CTE shift for each overlap calculated. At this point we only have information on the overlaps and do not know the individual contribution from each frame. Then, for each frame, the median CTE shift for all its overlaps is calculated, taking care with the signs of these overlap shifts. If most of the calibrations for the frames are correct, then the median will give a good approximation to the CTE shift remaining for that frame. We can then use these frame values to correct the overlap values and then improve our original estimates of the frame values by iteration. This process converges after about 5 iterations.

Note that this is all carried out after a standard CTE calibration had been applied. Thus, the presence of outliers or increased scatter in the results indicates a problem with the current calibration.

Figure A.3 shows the residual CTE shifts for each frame as a function of time. Using a figure like this, it was possible to subdivide the original 4 periods, as used for Fig. A.2, into the periods indicated in Table A.1. For each period, by plotting the residual against sky background you can improve the CTE calibration for that period. In addition to using an exponential model, for some periods, it was necessary to use a model of the form ${\rm scale}=a/(b+{\rm sky})$ , cf. Eq. (A.2).

$\begin{figure} \par\includegraphics[angle=270,width=8.8cm,clip]{MS2801fa3.eps}\end{figure}$

Figure A.3: This plot shows the residual CTE shift (after calibration) as a function of time.

Also shown in Fig. A.3 is the scatter for each period. This gives an indication as to how well the calibration has been carried out. The improvement in the calibration as the survey has progressed simply reflects the reduction in the overall level of the CTE problem.

Period 2 has a high scatter because it generally contains poor data. Originally, data from this period had a much higher scatter. Closer analysis showed that a large part of this came from a few nights. Thus, it was decided to delete 4 nights (5, 6, 15 and 18 September 1999) from the survey. Doing this loses about 650 000 observations (about 1% of the data so far).

From the scatters shown, it can be seen that the CTE problem has been solved to about the 100 mas level for the faint end (3 sigma limits), cf. the faint end random errors of approximately 100 mas. Figure A.1 can be used to gauge how this number translates to brighter magnitudes.

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