To show the effect of progressively wider PSFs smearing the ideal image, we apply the standard PSF with alfa set to 1.4, 1.6, 1.8 and 1,9 (close to the limit), and plot a 'slice' across the discs:
Top panel: In red the counts of the ideal image across the lunar disc, along with slices of smeared images for alfa=1.4 (top), 1.6, 1.8, and 1.9 (lowest).
Bottom panel: The absolute-value percentage difference between the slices in the top panel and the ideal image slice.
In the first panel we see that indeed the halo is approximately linear on the DS part of the sky.
We see in the bottom panel that the DS (columns 150-390, approximately) is strongly affected by the smearing by the PSF for values of alfa we have seen on even 'good nights' - alfa~1.6. Occasionally we have seen alfa~1.8 and even there the DS is strongly affected at the extreme edge of the disc, away from the BS, by approximately 10%.