The uncertainty in the calculation of the x-scan psf correction using DMAGCOR is dependent on the number of sources in a cross scan bin. For low density calibration scans the source count can be significantly low resulting in an unreliable correction factor. Another method of interpolating the x-scan psf correction for the low density calibration scans is needed. A proposal was made to use the corrections from the surrounding science (or calibration) scans to assist in determining the corrections for the low density calibration scans. The following plots demonstrate the accuracy of this proposed solution as well as assist in determining the threshold for switching from the corrections in the DMAGCOR file to using the in-scan interpolation approach.

A brief description of the algorithm used in calculating the interpolated correction for the low density x-scan bins follows. The assumption is that the surrounding scans would probably be science or calibration scans which would contain a larger number of sources per x-scan bin. The DMAGCOR correction assigned to the appropriate x-scan bin from the preceding and succeeding scans would be averaged to get an interpolated correction for the low density scan. Prior to averaging the corrections from the adjacent scan-set, the corrections would be normalized to remove any bias present in the adjacent scan corrections. The normalized, average correction for the x-scan bin would finally be adjusted by the weighted average of low density scan corrections. This step would add the appropriate bias for the low density scans in question.

After examination of the plots, we propose identifying low density x-scan bins based on number of sources per bin. The proposed cut would be at 40 sources per bin. Any bins with counts less than 40 would obtain an interpolated psf correction as described above.

Please note that the proposed estimation technique is NOT perfect and may over/under estimate the psf correction when the psf-aperature error in a particular x-scan bin is changing within the time frame of the surrounding scan sets. This is particularly true for the last x-scan bin (10). Note the outliers (> 0.02 and > 200 counts) in the second group of plots below where the counts per bin are plotted verses the difference in the actual and interpolated x-scan correction. In these cases, the actual correction would be used since the counts per bin are > 40. But if the interpolated values were used they would give a correction which would be off by 0.02 to 0.04 magnitudes.

Some additional issues to address are:

DMAGCOR was run on the following nights:
980219s, 980321s, 980322s, 980323s, 980328s, 980330s, 980331s, 980402s, 980514s

Please note also that for the analysis the night of 980801s was not included due to the temperature variations throughout the night.

The following plots were made
Each plot has 10 sub-plots, one plot for each x-scan bin (1 to 10) . The top left plot represents the left most x-scan bin while the bottom right plot represents the right most x-scan bin. Only calibration sets are shown.

Counts in x-scan bin vs. uncertainty in x-scan correction

( Lines on the plot are drawn to mark 0.02 uncertainty and bin counts of 40)

Counts in x-scan bin vs. (actual - interpolated) x-scan correction

( Lines on the plot are drawn to mark 0.02 uncertainty)

Correction uncertainty in x-scan bin vs. (actual - interpolated) x-scan correction

( Lines on the plot are drawn to mark 0.02 uncertainty)