Bounds on the microanalyzer array assumption

Micropolarizer arrays are occasionally used in partial Stokes, full Stokes, and Mueller matrix polarimeters. When treating modulated polarimeters as linear systems, specific assumptions are made about the Dirac delta functional forms generated in the channel space by micropolarizer arrays. These assumptions are 1) infinitely fine sampling both spatially and temporally and 2) infinite array sizes. When these assumptions are lifted and the physical channel shapes are computed, channel shapes become dependent on both the physical pixel area and shape, as well as the array size. We show that under certain circumstances the Dirac delta function approximation is not valid, and give some bounding terms to compute when the approximation is valid, i.e., which array and pixel sizes must be used for the Dirac delta function approximation to hold. Additionally, we show how the physical channel shape changes as a function of array and pixel size, for a conventional 0°, 45°,-45°, 90° superpixel micropolarizer array configuration.