Evolution of Statistic Moments of 2D-Distributions of Biological Liquid Crystal Net Mueller Matrix Elements in the Process of Their Birefringent Structure Changes

Abstract

This research is aimed to investigate the reliability of Mueller-matrix differentiation of birefringence change of optically thick layers of biological liquid crystals at the early stages of the change in their physiological state. This is performed by measuring the set of skewness and kurtosis values of Mueller matrix image of the phase element M 44 in various points of the object under investigation.

Jones-matrix images corresponding to networks of biological crystals for diagnostics and classification of their optical properties

“…Distributions of values inherent to elements ik ℵ of the Jones matrix can be characterized with the set of statistical moments of the 1-st to 4-th orders M; σ; A; E calculated using the following relations [5,6,25,30]: …”

“…The main "information product" of these methods is obtaining the coordinate distributions for elements of Mueller and Jones matrixes corresponding to biological tissues (BT) [1 -5] with the following statistical (statistical moments of the first to fourth orders [5,6,10,14,19,25,26,30]), correlation (auto-and mutual-correlation functions [12,17,18,21,26]), fractal (fractal dimensionalities [5,6,25]), singular (distributions of amounts of linear and circularly polarized states), wavelet (sets of wavelet coefficients for various scales of biological crystals [22,28]) analyses. As a result, one can determine interrelations between a set of these parameters and distributions of optical axis directions as well as the birefringence value inherent to networks of optically single-axis protein (myosin, collagen, elastin, etc.)…”

Fourier-Stokes polarimetry of fields corresponding to linearly and circularly polarized birefringent protein networks

“…In this approach, the analysis of the obtained data is based on approximation of linear birefringence observed in polycrystalline protein networks. Using the above model approach, the authors found interrelation between the set of statistical moments of the first to fourth orders that characterize distributions of azimuths and ellipticity of polarizations in laser images as well as parameters of anisotropy inherent to the layers of biological tissues [6][7]. As a result, developed was the method for polarization mapping and successfully realized was the diagnostics of oncological (malignant) changes in human biological tissue [8,9].…”

Wavelet analysis of polarization maps of polycrystalline biological fluids networks

“…Specifically, the above mentioned model was used for finding and substantiating the interrelations between the ensemble of statistic moments of the 1 st to 4 th orders that characterize the orientation−phase structure (distribution of optical axes and phase shifts for directions of protein fibril networks) of birefringent BT architectonics and that of 2D distributions of azimuths and ellipticities of their laser images [1]. It was determined that the 3 rd and the 4 th statistic moments for coordinate distributions of ellip− ticities are the most sensitive to the change (caused by dystrophic and oncological processes) of optical aniso− tropy inherent to protein crystals [14,15]. On this basis, the criteria for early diagnostics of muscle dystrophy, pre−cancer states of connective tissue, collagenosis, etc.…”