Tested two methods for scattering light from an ideal moon. The Ideal image is shown upper left (log scale) with a completely dark sky, narrow BS crescent and ES.
Bottom left is the moon after scattering the light using our current PSF and a brute force method — simply add all the pixels in the ideal image multiplied by the PSF. Bottom right is the same, but using an FFT method instead. The scattered light at the edges of the frame is too high to simply use the 512×512 frame in the FFT, instead the idea moon is placed in the center of a 1536×1536 frame, the FFT carried out, and then clipped back to 512×512. Upper right is the ratio of these two methods. There is a lot of structure at a very low level — the display limits on the ratio are set at 0.9993 to 1.0009, and the ratio is with 0.1% of unity everywhere on the frame. This should be sufficiently accurate for our purposes, but we should double check!
The histogram of pixel values in the ratio image is shown below: