Determined in this work are analytical interrelations between orientations of optical axes and birefringence of biological crystals and characteristic values of Jones-matrix elements corresponding to flat layers of polycrystalline networks, which set the conditions providing formation of polarization singularities in laser images. Performed is the complex statistical, correlation and fractal analysis of distributions for the amount of characteristic values inherent to Jones-matrix elements corresponding to bile layers of healthy and sick patients. Also, offered are the objective criteria for differentiation of optical properties typical to polycrystalline networks of human bile in different physiological states, and realized is the Jones-matrix diagnostics of cholelithiasis.

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