FRD variation for in-focus spectrograph images have been investigated at varying positions. CenterFRD.png and EdgeFRD.png display two in-focus images with varying FRD (up to 30 mrad). Unsurprisingly, the magnitude of the FRD change is largest at low FRD (on the order of 6/2000 ~ 0.3% counts) and decreases for subsequent increases of FRD, decreasing to 0.1% per pixel variation at high FRD. Curiously, the orientation of the residual at increasing FRD seems to rotate. Possibly this is due to a slight difference between the center of illumination and the pupil (see Center_1DCut.png edges; also see for effect of FRD variations in the pupil image). Variation of Zernike coefficient wavefronts and positioning are still ongoing.

The variation of PSF at different FRDs as a function of wavefronts has been lightly explored. Having set all Zernike coefficient values to 0 at the recommendation of Neven, I investigated the residuals between images with the same pupils as those in CenterFRD.png but with zero wavefront. These images are shown in figure Zero_Wavefront.png.

Notably, the structure of the residuals in figure Zero_Wavefront.png are not dominated by a dipole. This is not due to a centroid correction (a la PIPE2D-563) but comes directly from the analysis. In these images, flux from the center of the PSF is redistributed to the wings of the PSF with increasing FRD. This effect is similar to the effect of FRD in the pupil image: central flux is distributed outward (as is vaguely visible in Center_1DCut.png).

Incorporating the centroid alignment insight from PIPE2D-563, new images (CenterFRD_Align.png, CornerFRD_Align.png, EdgeFRD_Align.png) demonstrating the residuals of spectrograph images. These images are organized in the same way as the original CenterFRD.png with pupil and spectrograph images shown to the left of the residual image (between the spectrograph image and oene with 3mrad less FRD) in each row, increasing from a base of 6 mrad to 30 mrad from top to bottom. Notably, the residuals are no longer dominated by dipole residuals. At low FRD (6-12 mrad) residuals are rather complicated, while residuals approach a more bullseye-like shape at higher FRD (>18mrad).

CenterFRD_AlignClose.png, CornerFRD_AlignClose.png, and EdgeFRD_AlignClose.png display the same results as CenterFRD_Align.png, CornerFRD_Align.png, and EdgeFRD_Align.png respectively, but focus on the 20x20 pixel area about the center of the spectrograph to emphasize variation in the PSF.

In order to quantify the fractional variation in PSF with changing FRD, a slice of the spectrograph image with a width of the 5 horizontal pixels nearest the center of the PSF was taken (Boxcar_Slice.png). Then along the vertical wavelength direction a 1D boxcar extraction was taken (CenterFRD_Alignboxcar.png). Variations in PSFs between images of increasing FRD (after flux scaling and centroid alignment) are shown as labeled in the legend. Residuals correspond to the bullseye-like residuals seen in the 2D images and generally correspond to how flux is displaced in the pupil image due to increasing FRD. However, the center of the residuals seems to possibly be slightly different than the center of the PSF, causing an asymmetry in the residual variation.

Below the residuals are two lines of numeric text. The upper line refers to the difference in counts between the 24mrad and 21mrad spectrograph images. The lower line refers to the percent increase in counts from the 21mrad image to the 24mrad image.  Oddly, there is a pixel that features variations of >1%.  This is an especially large variation and currently under investigation.

1D boxcar extractions of the PSFs were taken in each of the centered, edge, and corner obscurations. CenterPercentBoxcar.png, EdgePercentBoxcar.png, and CornerPercentBoxcar.png represent the % variation of the PSF in the wavelength direction for each position, plotted for the 6-9 mrad FRD increase to the 27-30 mrad FRD increase. In each plot, the blue line represents the change from 6 to 9 mrad, with adjacent lines corresponding to increasing increments of FRD. % variation is taken relative to the boxcar extraction at the lower FRD. Notably, the largest percent variations do not occur at the center of the lines but rather ~3-4 pixels away from the centers of the lines.

ComparePercentVariation.png shows the maximum % variation in a pixel for a given initial FRD value (6-27 mrad) after a 3 mrad increase in FRD. Notably the fractional variation decreases at higher FRD, but position on the detector has a strong effect on the variation.

I'm closing the ticket as the work done here because the analysis presented in this ticket quantifies the effect FRD has on the PSF. Future work on detectability of these variations and the best method of extracting this information is being done in PIPE2D-602.