9.6.2 Illumination Correction

Even though we use (twilight) sky flats, there still seems to be a large-scale difference between the (sky) flat field and the sky background in the science frames. Since the color of the morning sky (where the sky flats are taken) and of the night sky is different, a large-scale gradient in the quotient of the flat field at different wavelengths (colors) will give an effect that behaves like the above mentioned illumination effect. The problem might be accentuated by a red leak in the Gunn r filter that we used, see Stetson (1989) for a discussion of read leaks.

To determine the illumination correction, one could observe parts of the sky without (or with few) objects. Indeed, two such empty fields were observed; the field SPKS04 was observed in GR and JB (dfsc2413 and 2414), and SPKS10 was observed in GR (dfsc2487). Unfortunately (and surprisingly), these images were not useful since a) the large-scale variation in the two GR empty fields did not match (relative difference on their quotient was up to $\pm$ 1.5%), and b) the large-scale variation in the empty fields did not match that in the science frames. It was checked that the moon was not up when these images were taken (the moon could have caused scattered light problems).

Instead it was tried to determine the illumination correction directly from the science images. A number (48 out of 118) of the GR and JB science images were read from tape and corrected for bias, fat zero, dark, shutter, and flat field (the sky flat fields without any illumination correction were used). The images with few bright objects were found; which was images of the following fields: 214, 21 (two exposures), 22, 36, and 44.

The objects (stars and galaxies) in the images were now removed in the following two step procedure: First all values outside $\pm 5\sigma$ from the median were replaced by the median value, with $\sigma$ calculated from equation (). The median was estimated as the midpt from imstat in two steps, first with no cuts, and then with cuts $\pm 5\sigma$, calculating $\sigma$ from the first midpt. Second, imsurfit was used to fit a legendre polynomial in x and y (with cross terms) of order 4 in x and 3 in y (using the IRAF definition of order), and applying a sigma rejection with a lower sigma of 3 and an upper sigma of 2, using 3 iterations.

The agreement between the large-scale sky background variation in the above mentioned 6 science frames was not that good. In some cases objects had not been totally removed, and in some cases there was no straightforward explanation.

It was decided to use the derived large-scale sky background variation in the two field 21 frames and the field 44 frame (i.e. the mean of the 3) as the illumination correction. These two illumination images (one in GR and one in JB) were normalized using the same section as for the sky flats, [25:800,25:925].

The size of the illumination can be characterized as follows (values for the entire frame): (min,max) is (0.9807,1.013) for GR and (0.9869,1.012) for JB. The standard deviation is 0.62% for GR and 0.47% for JB.

How well the illumination correction is determined is hard to say. If we look at the abovementioned 7 or 8 images (that is, 6 science frames with all objects removed, and 2 (for JB 1) empty field(s)), and we exclude the field 36 science frame because there is an unremoved object in it, and the SPKS10 (GR only) empty field because it is just strange, we can get an estimate of how well we do. The mean standard deviation of the 6 individual GR large-scale patterns is 0.62%. When making the quotient with the decided final illumination correction mentioned above (which is the mean of 3 of the 6 images), the mean standard deviation of the 6 quotients is 0.42%. For JB the numbers are 0.50% and 0.34%

So far, no remaining large-scale pattern has been noticed in the science frames reduced with the abovementioned illumination correction.

For JU, where we only have 5 science frames and no empty fields (though they did not prove useful for GR and JB), no illumination correction could be established, since the 5 frames were full of objects, and the background levels were low.