Structured decomposition of a multi-snapshot nine-reconstructables Mueller matrix polarimeter

Snapshot channeled polarimeters forgo temporal modulation in favor of modulating polarization information in either space or wavenumber. We have recently introduced methodologies for describing both channeled and partial polarimeters. In this paper, we focus on the nine-reconstructables design, which limits the resolution loss by reducing the number of carriers. The architecture offers a number of favorable trade-offs: a factor of 5.44 increase in spatial bandwidth or a factor of 3.67 increase in spectral bandwidth, for a smaller amount of temporal bandwidth loss as dictated by the number of snapshots taken. The multi-snapshot structured decomposition given here allows one to analytically shape the measured space with optimal noise characteristics and minimum system complexity. A two-snapshot system can measure a premeditated set of 14 reconstructables; we provide the null space for the subset of optimal systems that also achieve better SNR than the baseline single-snapshot system. A three-snapshot system can measure all 16 Mueller elements while offering an overall 26.3% or 50.4% better bandwidth-SNR figure of merit for the spectral and spatial systems, respectively. Finally, four-snapshot systems provide diminishing returns, but may be more implementable.