Polarized light interaction with media can reveal the microstructure and anisotropy of complex media beyond what can be obtained from scalar light interaction. Here, we present reciprocal polar decomposition for the backscattering Mueller matrices, a new Mueller matrix decomposition method for analyzing chiral and nonchiral complex media measured in reflection geometry. Reciprocal polar decomposition uniquely accounts for the reciprocity of the optical wave in forward and backward scattering paths. We demonstrate the superiority of the reciprocal polar decomposition against Lu-Chipman and differential Mueller matrix decompositions in various applications of backscattering polarimetry for birefringent targets, tissue sections, and chiral media. We also report examples where Lu-Chipman and differential decompositions produce incorrect media properties, whereas reciprocal polar decomposition succeeds. Reciprocal polar decomposition will open up diverse applications of backscattering polarimetry for biomedicine.
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