After two sets of iterations, I created solution which have:

1. illumination properties of the fiber is the same for all spots in the fiber
2. Zernike components are continuous polynomial functions across the detector

Few concerns/thoughts:
1. When I was doing my iterative process I made a mistake when applying interpolated Zernike values. At one place instead of x,y I wrote y,y so the Zernike polynomials were wrong for good portion of the plane. The algorithm is quite good in recovering the correct solutions for the invidiual spots, but perhaps rerun should be in order?
2. There are problems in the quality of solutions, seen at a) edges of defocus fit, b) center of focused fits
3. Some parameters still need to be extended to areas where I do not have data (e.g., Lorentzian spread due to grating.)

Few figures (with insufficient explanation!)

This figure shows the ``quality'' of fits, as a function of total chi measured in the image. The dotted lines are the interpolation results, while the full lines are fits to singular spots.

The improvement, i.e., chi/chi_max in 2d

Example of 2d fit in focus, center of the detector:

Example of 1d residual in focus, center of the detector: