Multidimensional laser microscopy polarization-singular structure of phase-inhomogeneous layers to diagnose and classify their optical properties

Abstract

Yu.O. Ushenko, O.V.Dubolazov Chernivtsi National University, Correlation Optics Dept., Chernivtsi, Ukraine, 58002 Abstract: Presented in this work are the results of investigations aimed at analysis of coordinate distributions of the fourth Stokes vector parameter in laser images of two types of biological phase-inhomogeneous layers, namely: rough and bulk scattering layers. To characterize this parameter for all the types of phase-inhomogeneous layers, the authors have offered to use three groups of parameters: statistic moments of the first to the fourth orders, autocorrelation functions, logarithmic dependences for power spectra. Ascertained are the criteria for diagnostics and classification of phase-inhomogeneous layers optical properties. Keywords: polarization, birefringence, statistical optics, medical and biological imaging, wavelet-analysis, blood plasma 1. Introduction By tradition, the processes of transforming optical radiation of phase-inhomogeneous objects and media are considered, as a rule, in a statistic approach (theory of radiation transfer [1], Monte-Carlo modeling [2-4]). In parallel with traditional statistic inve stigations, formed in recen t 10 to 15 years is the new optical approach to describe a structure of polarizationally inhomogeneous fields in the case of scattered coherent radiation. The main feature of this approach is the analysis of definite polarization stat es to determine the whole structure of coordinate distributions for azimuths and ellipticities of polarization. The so-called polarization singularities are commonly used as these states [5-10]. Among the most spread traditional methods for studying the scattered light fiel ds, one can separate the following independent directions: “scalar” (photometry and spectrophot ometry) and “vector” (polari zation nephelometry, Mueller-matrix optics) [11-42]. Using th ese approaches, determined are interrelations between the sets of statistic moments of the 1-st to the 4-th orders [ 11, 15, 20, 26, 27, 31], correlation functions [13, 18, 19, 22, 27], fractal dimensions [18, 26, 34, 40] that characterize phase-inhomogeneous or rough surfaces and coordinate distributions for phases [15, 16, 19, 28, 39, 42], azimuths and ellipticity of polarization in their laser images [13, 18, 26, 33, 38]. This work is aimed at ascertaining the possibilities to di agnose and classify phase-inhomogeneous layers (PhIL) of various types (surface-scattering and bulk-scattering ones) by determination va lues and ranges for changing the statistic (moments of the 1-st to the 4-th orders), correlation (autocorrelation functions) and fractal (logarithmic dependences for power spectra) parameters that characterize coordinate distributions for polarization-singular states in PhIL laser images. 2. Model conceptions and analytical relations As a base for analytical description of processes providing formation of polarization-inhomogeneous images for various types of PhIL, we have used the model conceptions developed in the works [13-15, 16, 19, 20, 28]: x surface-scattering PhIL is a rough surface (superficial layer of the skin epithelium) consisting of an ensemble of quasi-plane, chaotically oriented micro-areas with optical dimensions