The fundamental component of the work contains a summary of the theoretical foundations of the algorithms of the scale-self-similar approach for the analysis of digital Mueller-matrix images of birefringent architectonics of biological tissues. The theoretical consideration of multifractal analysis and determination of singularity spectra of fractal dimensions of coordinate distributions of matrix elements (Mueller-matrix images - MMI) of biological tissue preparations is based on the method of maxima of amplitude modules of the wavelet transform (WTMM). The applied part of the work is devoted to the comparison of diagnostic capabilities for determining the prescription of mechanical brain injury using algorithms of statistical (central statistical moments of the 1st - 4th orders), fractal (approximating curves to logarithmic dependences of power spectra) and multifractal (WTMM) analysis of MMI linear birefringence of fibrillar networks of neurons of nervous tissue. Excellent (~95%) accuracy of differential diagnosis of the prescription of mechanical injury has been achieved.

Traditional methods of imaging Muller-matrix polarimetry ensure obtaining large arrays of experimental data in the form of 16 Muller-matrix images. Processing and comparative analysis of the received information is quite time-consuming and requires a long time. A new algorithmic polarization-singular approach to the analysis of coordinate distributions of matrix elements (Mueller-matrix maps) of polycrystalline birefringent structure of biological tissues is considered. A Mueller-matrix model for describing the optical anisotropy of biological layers is proposed. Analytical correlations between polarization-singular states of the object field and characteristic values of Mueller-matrix images of birefringence soft tissue objects were found. The proposed algorithmic polarization-singular theory is experimentally verified. Examples of polarization singularities networks of Mueller-matrix maps of histological preparations of real tissues of female reproductive sphere are given. Diagnostic possibilities of the developed polarization-singular algorithms in diagnostics and differentiation of the stages of extragenital endometriosis are illustrated. Another area of biomedical diagnostics has been successfully tested: polarization-singular criteria for forensic Mueller-matrix determination of the age of myocardial injury of the deceased have been defined.

A new local-topological approach to describe the spatial and angular distributions of polarization parameters of multiply scattered optically anisotropic biological layers of laser fields is considered. A new analytical parameter to describe the local polarization structure of a set of points of coherent object fields, the degree of local depolarization (DLD), is introduced for the first time. The experimental scheme and the technique of measuring coordinate distributions (maps) of DLD The new method of local polarimetry was experimentally tested on histological specimens of biopsy sections of operatively extracted breast tumors. The measured DLD maps were processed using statistical, autocorrelation and scale-sampling approaches. Markers for differential diagnosis of benign (fibroadenoma) and malignant (sarcoma) breast tumors were defined.