We generalize an existing algebraic procedure for the polar decomposition of Mueller matrices with negative determinants [Opt. Commun.281, 2406 (2008)OPCOB80030-401810.1016/j.optcom.2007.12.076] to the case of nondiagonal depolarizer matrix factors. The generalized procedure is applied to experimental Mueller matrices illustrating its potential for the phenomenological interpretation of complex polarimetric data.
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Optical polarization is three-dimensional (3-D). Its complete information is described by the nine-component generalized Stokes vector (GSV). However, existing Stokes polarimetry and its design theory are primarily based on the paraxial four-component Stokes vector and 4 × 4 Mueller matrices.
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Mueller matrices provide a complete description of a medium's response to excitation by polarized light, and their characterization is important across a broad range of applications from ellipsometry in material science to polarimetry in biochemistry, medicine and astronomy. Here we introduce single-shot Mueller matrix polarimetry based on generalized measurements performed with a Poincaré beam. We determine the Mueller matrix of a homogeneous medium with unknown optical activity by detecting its optical response to a Poincaré beam, which across its profile contains all polarization states, and analyze the resulting polarization pattern in terms of four generalized measurements, which are implemented as a path-displaced Sagnac interferometer.
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Bioinformatics
June 2024
Department of Biomedical Engineering, Florida International University, West Flagler Street, Miami, FL 33174, USA.
Motivation: Imaging Mueller polarimetry has already proved its potential for biomedicine, remote sensing and metrology. The real-time applications of this modality require both video rate image acquisition and fast data post-processing algorithms. First, one must check the physical realizability of the experimental Mueller matrices in order to filter out non-physical data, ie to test the positive semi-definiteness of the 4 × 4 Hermitian coherency matrix calculated from the elements of corresponding Mueller matrix pixel-wise.
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