Currently I've been trying to extract out FRD with a given input PSF. I've plotted the sum of the squares of the residuals in each pixel between a model I'm fitting and the input, finding a plot that looks like Residual_vs_FRD.png. Two things that immediately become apparent are that there are some particularly low values relative to a more apparently upper-limit curve, and that the minimum of the curve doesn't quite match up with the minimum (blue dashed line) or more importantly, the input FRD (orange dot-dash line).
 
I've looked at the fits in 2D and found that for a small number of FRD values, the centering from the algorithm seems to be off. FRD_difference_0_93750.png demonstrates the residuals between each image I generate and the input PSF. Both are slightly misaligned, notable due to a dipole-like structure in each residual, but notably in different directions. All points along the upper curve-like points have the same centering to a much , even with just a small change in FRD (FRD_difference_0_93749.png).
 
The absolute difference in PSF center for each image compared to the input science image is shown in PSFCenterChange.png. Again, most points are the same (non-zero) distance away from the center of the input PSF, which may explain why the input FRD is not matching up with minimum FRD. The sudden jumps in centering for small changes in FRD additionally seems to be a problem restricting current progress.

I've rerun the analysis for the code using Neven's work on PIPE2D-643. Now the code is consistent with its centering and the residuals have a minimum at the input FRD, as seen in v034b_Recenetering.png (blue dotted line is the old minimum, orange dot-dashed line is input FRD). This is extremely promising for the completion of this ticket!