Design of Partial Mueller-Matrix Polarimeters for Application-Specific Sensors

At a particular frequency, most materials and objects of interest exhibit a polarization signature, or Mueller matrix, of limited dimensionality, with many matrix elements either negligibly small or redundant due to symmetry. Robust design of a polarization sensor for a particular material or object of interest, or for an application with a limited set of materials or objects, will adapt to the signature subspace, as well as the available modulators, in order to avoid unnecessary measurements and hardware and their associated budgets, errors, and artifacts. At the same time, measured polarization features should be expressed in the Stokes-Mueller basis to allow use of known phenomenology for data interpretation and processing as well as instrument calibration and troubleshooting. This approach to partial Mueller-matrix polarimeter (pMMP) design begins by defining a vector space of reduced Mueller matrices and an instrument vector representing the polarization modulators and other components of the sensor. The reduced-Mueller vector space is proven to be identical to R15 and to provide a completely linear description constrained to the Mueller cone. The reduced irradiance, the inner product of the reduced instrument and target vectors, is then applied to construct classifiers and tune modulator parameters, for instance to maximize representation of a specific target in a fixed number of measured channels. This design method eliminates the use of pseudo-inverses and reveals the optimal channel compositions to capture a particular signature feature, or a limited set of features, under given hardware constraints. Examples are given for common optical division-of-amplitude (DoA) 2-channel passive and serial/DoT-DoA 4-channel active polarimeters with rotating crystal modulators for classification of targets with diattenuation and depolarization characteristics.