The paper deals with investigation of the processes of laser radiation transformation by biological crystals networks using the singular optics techniques. The results obtained showed a distinct correlation between the points of “characteristic” values of coordinate distributions of Mueller matrix ( ) elements and polarization singularities (L- and C-points) of laser transformation of biological crystals networks with the following possibility of Mueller-matrix selection of polarization singularity. The technique of Mueller-matrix diagnostics of pathological changes of skin derma is proposed. 1. Introduction Laser polarimetry [1] enabling to obtain information about optical anisotropy [2–5] of biological tissues (BT) is an important direction of noninvasive diagnostics of organic phase-heterogeneous layers. For statistic analysis of such polarimetric information a model approach has been worked out based on the following conditions [1, 2, 6–12]:(i)all the variety of human BT can be represented by four main types—connective, muscular epithelial, and neural tissues; (ii)structure of any BT type is regarded as a two-component amorphous-crystalline one; (iii)the crystalline component or extracellular matrix is formed by the network of optically uniaxial birefringent protein (collagen, myosin, elastine, etc.) fibrils or biological crystals; (iv)the process of transformation of laser radiation polarization state by biological crystal is characterized by Mueller matrix operators of an optically uniaxial crystal Here -direction of optical axis of biological crystal with birefringence index , -phase shift between orthogonal components of the amplitude of a probing laser beam with wave length . A new approach to description of the BT laser images based on the analysis of coordinate distributions of polarization singularities became developed the above-mentioned statistical [13–22]. Linearly (L-points) and circularly (C-points) polarized states of light oscillations belong to them. For L-points the direction of the electric-intensity vector’s rotation is indefinite (singular). For a C-point, the polarization azimuth of the electric intensity vector is indefinite. Investigation of laser images of the connective tissue layers revealed a developed network of polarization singularities [23–26], which was quantitatively estimated in the form of distribution of the amount of L- and C-points. By means of the analysis of the given distribution’s statistical moments of the 1st–4th orders (the technique of polarization mapping) the criteria of diagnostics of oncological
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