Wavelet analysis of Fourier polarized images of the human bile Yuriy O. Ushenko,* Olexander V. Dubolazov, Artem O. Karachevtsev, Mykhaylo P. Gorsky, and Yulya F. Marchuk Correlation Optics Department, Chernivtsi National University, 2 Kotsyubinsky St., Chernivtsi, 58012, Ukraine *Corresponding author: yuriyu@gmail.com Received 12 December 2011; revised 2 February 2012; accepted 2 February 2012; posted 2 February 2012 (Doc. ID 159308); published 29 March 2012 The model of generalized optical anisotropy of human bile is suggested, and the method of the polarimetric phase Fourier transform of the image of the laser radiation field that is generated by the mechanisms of linear and circular birefringence of polycrystalline networks with a wavelet-diagnosis of cholelithiasis is analytically substantiated. © 2012 Optical Society of America OCIS codes: 030.0030, 070.0070, 170.0170. 1. Introduction Among diverse optical-physical methods [ 1– 10] of diagnosing the optical-anisotropic component of bio- logical objects a specific trend has separated—laser polarimetry [ 11– 29] of microscopic images of biologi- cal tissues with further statistical [ 17, 21], correlation [ 19, 22– 24], fractal [ 13, 17] wavelet [ 27, 28] and singu- lar [ 26, 29, 30] analysis in an approximation of linear birefringence of polycrystalline protein networks. At the same time, apart from linear birefringence, the mechanisms of transforming the state of laser radiation polarization by optical-anisotropic biologi- cal structures are more diverse and include optical dichroism, circular birefringence [ 7, 8]. The laser polarimetry techniques characterize general mani- festations of such mechanisms in the process of polar- izationally inhomogeneous images formation. At the same time, each of these partial mechanisms is closely connected with transformation of biochem- ical components of the biological layer. Consequently, pathological changes are inevitably accompanied by the changes of various types of optical anisotropy. Thus, the task of optical differentiation of such me- chanisms is important for development of laser polarimetry techniques. Fourier analysis of polariza- tionally inhomogeneous images of biological layers can become one of possible solutions of this task [ 31]. The main idea of such an approach is based on the existence of differences in spatial-frequency spectra of Fourier images of non-uniformly scaled biological crystals with various anisotropy mechan- isms. Methemetically these differences are desctibed by means of the phase of Fourier transform of the two-dimensional (2D) array of polarization asimuths and ellipticity. Physically this approach can be rea- lized using the Fourier transform polarization micro- objective. Thus, Fourier polarimetry consists in measuring the distributions of polarization state of object field in the frequency plane, determining the 2D array of Fourier transform phase with the follow- ing statistical, correlation, fractal and wavelet analyses of the data obtained. Our research is aimed at designing the experimen- tal method of Fourier’ s laser polarimetry of human bile layers for separation of optical manifestations of linear and circular birefringence for early diagnos- tics of cholelithiasis. 2. The Theory Of The Method Geometrically (d ≈ 10 - 15 μm) and optically thin (attenuation coefficient τ  0.081 - 0.087) bile smears, placed on optically homogeneous glass are 1559-128X/12/10C133-07$15.00/0 © 2012 Optical Society of America 1 April 2012 / Vol. 51, No. 10 / APPLIED OPTICS C133