Estimating the polarization of light has been shown to have merit in a wide variety of applications between UV and LWIR wavelengths. These tasks include target identification, estimation of atmospheric aerosol properties, biomedical and other applications. In all of these applications, polarization sensing has been shown to assist in discrimination ability; however, due to the nature of many phenomena, it is difficult to add polarization sensing everywhere. The goal of this dissertation is to decrease the associated penalties of using polarimetry, and thereby broaden its applicability to other areas. First, the class of channeled polarimeter systems is generalized to relate the Fourier domains of applied modulations to the resulting information channels. The quality of reconstruction is maximized by virtue of using linear system manipulations rather than arithmetic derived by hand, while revealing system properties that allow for immediate performance estimation. Besides identifying optimal systems in terms of equally weighted variance (EWV), a way to redistribute the error between all the information channels is presented. The result of this development often leads to superficial changes that can improve signal-to-noise-ration (SNR) by up to a factor of three compared to existing designs in the literature. Second, the class of partial Mueller matrix polarimeters (pMMPs) is inspected in regards to their capacity to match the level of discrimination performance achieved by full systems. The concepts of structured decomposition and the reconstructables matrix are developed to provide insight into Mueller subspace coverage of pMMPs, while yielding a pMMP basis that allows the formation of ten classes of pMMP systems. A method for evaluating such systems while considering a multi-objective optimization of noise resilience and space coverage is provided. An example is presented for which the number of measurements was reduced to half. Third, the novel developments intended for channeled and partial systems are combined to form a previously undiscussed class of channeled partial Mueller matrix polarimeters (c-pMMPs). These systems leverage the gained understanding in manipulating the structure of the measurement to design modulations such that the desired pieces of information are mapped into channels with favorable reconstruction characteristics.