# Optimal birefringence distributions for star test polarimetry

## TL;DR

This paper uses variational calculus to determine the optimal birefringence distribution for star test polarimetry, enhancing resolution by encoding polarization information efficiently in the PSF.

## Contribution

It introduces a novel variational approach to optimize birefringence distributions, linking theoretical design to practical implementations in star test polarimetry.

## Key findings

- Optimal birefringence distribution minimizes PSF size.
- The solution aligns with stress-induced birefringence from three edge stress points.
- Enhanced resolution in polarization imaging achieved.

## Abstract

Star test polarimetry is an imaging polarimetry technique in which an element with spatially-varying birefringence is placed in the pupil plane to encode polarization information into the point-spread function (PSF) of an imaging system. In this work, a variational calculation is performed to find the optimal birefringence distribution that effectively encodes polarization information while producing the smallest possible PSF, thus maximizing the resolution for imaging polarimetry. This optimal solution is found to be nearly equivalent to the birefringence distribution that results from a glass window being subjected to three uniformly spaced stress points at its edges, which has been used in previous star test polarimetry setups.