Kota Hayashi analyzed the data during his stay at Princeton in June/July 2022.

The procedure was as follows:
1. Identify ``background'' defocused image, containing flux from fibers we were not able to hide (78760)
2. Identify ``data'' defocused image, after we exposed fibers (78760)
3. Subtract ``background'' from the ``data'' to get clean PFI image
4. For fibers that are avaliable for both DCB and PFI data, cutout poststamp images of spots taken with PFI, that correpond to the ones already avaliable in DCB data.
5. Center PFI images so that they have same center of lights as DCB images, interpolating with Lanczos5 kernel.
6. Construct radial profile
7. Normalize so that the peak of PFI radial profile matches the peak of DCB radial profile

The result is here: vignetting1.pdf or here (with overlaid theoretical prediction) vignetting2.pdf .

Example of a ``good fiber'', where PFI has less flux at the outer edges of the pupil, compared to DCB:

Example of a ``bad fiber'', where PFI has more flux at the outer edges of the pupil, compared to DCB

1. Based on Jim's theoretical model (figure "theoretical_illumination_jeg.png"), the effect of these illumination patterns is implemented in a module creating model PFI donuts.

2. For each of the available spots, model DCB and PFI images are created.

3. These model images are compared to DCB and PFI images of the same spot in real data. Some examples are shown on the right four panels for each spot (figure "pfi_dcb_division_summary.pdf").

4. In this comparison, pixels with an extremely small value are masked, and then images are normalized so that the total flux would be the same.

5. 1d radial profiles of these images are divided between PFI and DCB for each spot, and then averaged for each fiber (fibers have several spots each).

6. PFI/DCB profiles of the model and real data are shown on the leftmost panel for each of some fibers (figure "pfi_dcb_division_summary.pdf").

pfi_dcb_division_summary.pdf

7. Analysis here cannot be directly compared with Jim's theoretical model. Figure "model_division_profiles.pdf" shows how his model behaves in this analysis.

model_division_profiles.pdf

Those are interesting, although rather hard to interpret as the scaling seems to be (min, max) with things like cosmic rays affecting what we seen. Can you scale all the displays to use e.g. vmin, max = 0, 99th percentile? I'm not sure that's quite the right prescription, but something consistent. Actually, it'd probably be better to scale the images to have the same 99th percentile and use the same scaling. The same comment applies to the plots in the first column; please use the same y-limits for all of them. The goal is to see if e.g. the spot 173 pupil illumination really is different between DCB and PFI.

I'd also like to see the ratios DCB/model_DCB and PFI/model_PFI compared. I suspect that, except for the pupil illumination, the model is the same for the DCB and PFI data. I'm not sure what model is used for the DCB illumination, but Jim's calculations of the PFI illumination (including vignetting and non-telecentricity) should be pretty good. It'd be nice to see a direct comparison of the two models.

Kota Hayashi, Kiyoto Yabe and I just finished our meeting.

1. We agree with your (Robert) comments and Kota will make modifications to the plots.
2. DCB illumination is to be uniform across the entrance pupil, i.e., a uniform disk illuminating a large part of the entrance pupil.
3. I believe that we now have enough insight that we should talk with Jim/Robert/Hassan and ``present'' our findings. I will get in touch on Slack to see what would be the best time to organize this.

The outcome of this presentation was that we need to be super sure that what we are saying is right. In most obvious example, for fiber 360 in model_division_profiles.pdf there is obvious difference in the illumination that is so obvious that one does not need to actually do analysis - it is clear by naked eye that PFI image is more widely illuminated which is different from what is expected.

The actions items are:
1. Make sure that our image, normalization and similare are correct
2. https://pfspipe.ipmu.jp/jira/browse/PIPE2D-1152 (Verify shape of DCB donuts with fresh data, to make sure there are not temporal variations)

JEG made a valid point that PFI images might have a lot more FRD in them, which would spread out the illumination of the donut. This is something we can test.

JFY, measured FRD of cable A, B, are C ~10, 13 and 10 mRad on average, respectively. Additional FRD by cross-mated MTP connection was estimated 2.45 (outer rows, mtp hole 1-8 and 2532), or 6.98 (inner rows, mtp hole 9-24) mRad, respectively.