The decomposition of the Mueller matrix of blood films has been carried out using differential matrices with polarized and depolarized parts. The use of a coherent reference wave is applied and the algorithm of digital holographic reconstruction of the field of complex amplitudes is used. On this basis, the 3D Mueller-matrix diffuse tomography method—the reconstruction of distributions of fluctuations of linear and circular birefringence of depolarizing polycrystalline films of human blood is analytically justified and experimentally tested. The dynamics of the change in the magnitude of the statistical moments of the first-fourth order, which characterize layer-by-layer distributions of fluctuations in the phase anisotropy of the blood film, is examined and analyzed. The most sensitive parameters for prostate cancer are the statistical moments of the third and fourth orders, which characterize the asymmetry and kurtosis of fluctuations in the linear and circular birefringence of blood films. The excellent accuracy of differentiation obtained polycrystalline films of blood from healthy donors and patients with cancer patients was achieved.

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We introduce a method of azimuthally invariant 3D Mueller-matrix (MM) layer-by-layer mapping of the phase and amplitude parameters of anisotropy of the partially depolarizing layers of benign (adenoma) and malignant (carcinoma) prostate tumours. The technique is based on the analysis of spatial variations of Mueller matrix invariant (MMI) of histological sections of benign (adenoma) and malignant (carcinoma) tissue samples. The phase dependence of magnitudes of the first-to-fourth order statistical moments is applied to characterize 3D spatial distributions of MMI of linear and circular birefringence and dichroism of prostate tumours. The high order statistical moments and phase sections of the optimal differentiation of the polycrystalline structure of tissue samples are revealed. The obtained results are compared with the results obtained by conventional methods utilizing polarized light, including 2D and 3D Mueller matrix imaging.

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Layered topographic maps of the depolarisation due to diffuse biological tissues are produced using a polarisation-holographic Mueller matrix method approach. Histological sections of myocardial tissue with a spatially structured optically anisotropic fibrillar network, and parenchymal liver tissue with a polycrystalline island structure are successfully mapped. The topography of the myocardium maps relates to the scattering multiplicity within the volume and the specific morphological structures of the biological crystallite networks. The overall depolarisation map is a convolution of the effects of these two factors. Parenchymal liver tissues behave broadly similarly, but the different biological structures present cause the degree of scattering multiplicity to increase more rapidly with increasing phase. Through statistical analysis, the dependences of the magnitudes of the first to fourth order statistical moments are determined. These moments characterise the changing distributions of the depolarisation values through the volume of biological tissues with different morphological structures. Parenchymal liver tissue depolarisation maps are characterised by larger mean and variance, and less skewness and kurtosis, compared to the distributions for the myocardium. This work demonstrates that a polarisation-holographic Mueller matrix method can be applied to the assessment of the 3D morphology of biological tissues, with applications in disease diagnosis.