Appendix B: Flat-fielding

No multiplicative flat field is applied to the raw frame data in the image analysis because of the difficulty in separating multiplicative (flat field) and additive (bias) components and because of the small size (1%) of the effect (see Fig. B.1). Additive (bias and sky) corrections are carried out and the image analysis programme removes the bias as a one-dimensional function in y, combined with a one-dimensional function in x to remove background variations.

Although the raw image data is not kept, the flat-field information is archived every night. Since the CCD camera takes drift-scan observations, the flat fields are one dimensional. Not all the frames will have a flat field since if the sky level is too low then no reliable flat field can be calculated. About two thirds of the frames do not have any flat-field information.

Figure B.1: This plot shows a typical flat field for high sky brightness conditions (noisy solid line). Also shown is the systematic effect in magnitude from Fig. 3 (solid line).

Figure B.1 shows a typical flat field from a frame with a high sky level. Monitoring of the flat fields shows that the main variation seems to be as a function of sky level. If the sky level is high, then the flat field is fairly flat ($\pm$1% level). If the sky level is low, then there is about a 10% variation at one edge of the CCD, most likely caused by just a change in the y-dependent bias level. Over time there is hardly any change in the general flat field shape, however, occasionally a flat field shows a significant difference of a few percent over the 2000 pixels. Closer investigation has shown that these changes are caused by changes in the background and not the sensitivity of the CCD.

Various investigations were carried out to determine whether the measured flat fields represent a multiplicative correction or not due to the problem of disentangling bias and sky.

One experiment was to apply the flat fields during the initial calibration after the preliminary data reduction. Normally, each column would be scaled by the corresponding one in the flat field. For this test, the appropriate column used was the average y value of an image and the corresponding scaling factor was applied to the whole image. Since this was already an approximation, a median filter was applied to the flat field data in order to reduce the level of noise.

After re-reducing the data, a comparison was made with respect to Tycho 2 This showed that the flat fields were not appropriate to use since extra systematic effects at the level of $\sim$5% were now visible. This implies that what is measured as the flat field has at least an additive component, as pointed out above.

As mentioned before, gradients are seen in some of the flat field comparisons. These are of order a few percent over the width of the CCD chip. These tend to happen during periods of bad weather, possibly indicating partially illuminated cloud causing a real gradient in the background and hence an additive effect.

To check this, a comparison was carried out on one particular frame, which has a 5% variation, and a number of overlapping frames. No variation could be seen in the photometry as a function of y for $r'_{\rm CMT}<14$. This indicated that the sensitivity was not varying across the chip. A variation is seen for a sample of faint images. This is consistent with background levels varying with y causing problems with the isophotal correction.

Also shown in Fig. B.1 is the magnitude systematic from Fig. 3. The obvious feature of this plot is that one side matches up reasonably well, while the other doesn't.

Considering the significant differences between the measured flat fields and the photometric corrections derived from the external standards, it was decided that there was no point in using the flat field information in the photometric calibration.