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Since recently, a number of innovative polarization-based optical imaging modalities have been introduced and extensively used in various biomedical applications, with an ultimate aim to attain the practical tool for the optical biopsy and functional characterization of biological tissues. The techniques utilize polarization properties of light and Mueller matrix mapping of microscopic images of histological sections of biological tissues or polycrystalline films of biological fluids. The main drawback of currently developed laser polarimetry approaches and Mueller matrix mapping techniques is poor reproducibility of experimental data. This is due to azimuthal dependence of polarization and ellipticity values of most matrix elements to sample orientation in respect to incidence light polarization. Current study aims to generalize the methods of laser polarimetry for diagnosis of partially depolarizing optically anisotropic biological tissues. A method of differential Mueller matrix mapping for reconstruction of linear and circular birefringence and dichroism parameter distributions of partially depolarizing layers of biological tissues of different morphological structure is introduced and practically implemented. The coordinate distributions of the value of the first-order differential matrix elements of histological sections of brain tissue with spatially structured, optically anisotropic fibrillar network, as well as of parenchymatous tissue of the rectum wall with an "islet" polycrystalline structure are determined. Within the statistical analysis of polarization reproduced distributions of the averaged parameters of phase and amplitude anisotropy, the significant sensitivity of the statistical moments of the third and fourth orders to changes in the polycrystalline structure of partially depolarizing layers of biological tissue is observed. The differentiation of female reproductive sphere connective tissue is realized with excellent accuracy. The differential Mueller matrix mapping method for reconstruction of distributions of linear and circular birefringence and dichroism parameters of partially depolarizing layers of biological tissues of different morphological structures is proposed and substantiated. Differential diagnostics of changes in the phase (good balanced accuracy) and amplitude (excellent balanced accuracy) of the anisotropy of the partially depolarizing layers of the vagina wall tissue with prolapse of the genitals is realized. The maximum diagnostic efficiency of the first-order differential matrix method was demonstrated in comparison with the traditional methods of polarization and Mueller matrix mapping of histological sections of light-scattering biological tissues. [ABSTRACT FROM AUTHOR]