I created a radial profile for many spots across the detector (see radial_profile.png and 2d_of_spot_from_which_radial_profile.png for typical examples). In radial_profile.png there are two lines, where maroon has been done by excluding the 6 pixels along the fiber which might larger flux and for sure do not influence other fibers. The thick lines are ``next fiber'', where I assumed that fibers are 6.5 pixels wide. Dashed lines are denoting centers of these fibers (3.25 pixel from the edge of the fiber). 

In frac_reduction_across_fibers.png I am showing the log ration of the flux between the center and the spot that is 6.5 pixels away from the center (i.e., the maroon flux at the position of the first dashed line in radial_profile.png). The median value for all of the spots is 3.1, i.e, the flux in the center of the next fiber is 10**-3.1 lower than in the center of the original fiber. The result are quite uniform except towards the red end and seemingly bottom right part - where the point spread function is starting to be very elongated.

I also did a small exp where I simulated a spot assuming isotropic flux distribution (so, not full modeling, just making an isotropic model that has the same flux behavior as the median spot taken from data) and calculated what amount of flux ends up in the neighboring fibers. I placed the original spot in the center of the 6-pixel wide fiber, between two central pixels. I have investigated two cases, shown in mask_cases.png = the difference is if the next fiber starts at 3 or 4 pixels from the center of the original fiber. In each case, I assume that the trace width of all fibers is 6 pixels. I then calculated the fraction of flux that ended up in the neighboring fiber as compared in the original fiber. 

In case 1 (larger separation):
0.88% in first neighbor, 0.24% in second neighbor

In case 2 (smaller separation):
1.28% in first neighbor, 0.31% in second neighbor 0.13% in third neighbor.

As discussed on PFS-telecon March 22, 2021, I need to check what is the reason for the outlier in the 2d detector plot.

 The outliers in the original ``frac_reduction_across_fibers.png'' were due to wrong centering of the image. This happened for possible two reasons: 

1. the centering algorithm did not take mask into account, so strong cosmic changed the center of the flux in the image significantly
2. in case that another arc line is present in the image (smaller effect than case 1)

I have changed the algorithm to correctly take masks in to account and removed blues Neon lines which are bunched together.  The updated result is shown in ``frac_reduction_across_fibers_fix_to_outliers.png''.

The possible outliers at y position of roughly 1300 (reddish circles) are due to poor flux in that particular line which makes the estimate uncertain, and as such I believe those are correct.

The median value of decrease has remained virtually unchanged (log10 change at 6.5 pixel from the center was 3.1, and is now  3.13), so I do not find that the rest of the analysis needs to be updated.

During the meeting on Monday, it was mentioned that we should inform Jenny about these results. I am not sure who and how this will be done, so I am keeping the ticket open as a reminded until Jenny is informed.

As discussed on PFS Princeton meeting on April 5, Robert has talked with Jenny. No further action is required at this point.