Task-specific snapshot Mueller matrix channeled spectropolarimeter optimization

We have developed a tool to simulate reconstruction behavior of a snapshot Mueller matrix channeled spectropolarimeter in presence of noise. A shortcoming of channeled spectropolarimeters is that with a large number of channels, each channel has to be narrow, which limits the reconstruction accuracy and provides a bandlimit constraint on the object. The concept of making partial Mueller matrix measurements can be extended to a channeled system by considering polarimeter designs that make irrelevant Mueller matrix elements unreconstructable, while decreasing the number of channels and subsequently increasing the bandwidth available to each channel. This tool optimizes the distribution of the available bandwidth towards the polarization elements that we care about most. A generic linear systems model of a spectropolarimeter with four variable retarders allows us to construct a matrix that maps Mueller matrix elements into corresponding channels. A pseudo-inverse of that matrix enables the reconstruction of Mueller matrix elements from channels. By specifying a mask vector, we can control the subjective importance of each of the reconstructed elements and weigh their error contribution accordingly. Finally, searching the design space allows us to find a design that maximizes the Signal-to-Noise-Ratio (SNR) for a specific partial Mueller matrix measurement task.