To characterize the degree of consistency of parameters of the optically uniaxial birefringent liquid crystals (protein fibrils) nets of biological tissues a new parameter-complex degree of mutual anisotropy is suggested. The technique of polarization measuring the coordinate distributions of the complex degree of mutual anisotropy of biological tissues is developed. It is shown that statistic approach to the analysis of complex degree of mutual anisotropy distributions of biological tissues of various morphological and physiological states and optical thicknesses appears to be more sensitive and efficient in differentiation of physiological state in comparison with investigations of complex degree of mutual polarization of the corresponding laser images. 1. Introduction In [1, 2] for characterizing the consistency between the polarization states the laser object field in the points with the intensities , a new parameter-complex degree of mutual polarization (CDMP) in the next form This “two-point” theoretical approach was extended to the analysis of polarization-inhomogeneous laser images of human BT with the aim of experimental diagnostics of optical anisotropic structure [3]. In [4] a method of direct polarization measurement of the real part of CDMP for different points ( ) of optically thin image (attenuation coefficient ) of BT layers is proposed where and are the phase shifts between the orthogonal components , of laser amplitude in object field. The ranges of changes of the 1st–4th distribution order statistic moments of the corresponding laser images, important for diagnostics of the human connective tissue oncologic state were determined in [5, 6]. On the other hand, such analysis techniques of lead to disregarding the BT extracellular matrix birefringence, which is a principal physical mechanism of their polarization-heterogeneous images formation [7–11]. That is why it appears to be important to search for new diagnostic parameters directly characterizing the degree of consistency of optical axes and birefringence orientations of various points of protein fibrils network forming the BT extracellular matrix [3]. This paper is aimed on investigation of diagnostic possibilities of optical-anisotropic structure of biological tissues extracellular matrix of different morphology and physiological state by means of statistic analysis of a new parameter-CDMA coordinate distribution. 2. Theoretical Analysis of Laser Radiation Parameters Transformation by the Network of Optically Uniaxial Birefringent Liquid Crystals The processes of laser beam
References
[1]
M. Mujat, A. Dogariu, and G. S. Agarwal, “Interferometric measurement of the degree of polarization and control of the contrast of intensity fluctuations,” Optics Letters, vol. 29, no. 13, pp. 1539–1541, 2004.
[2]
J. Ellis and A. Dogariu, “Complex degree of mutual polarization,” Optics Letters, vol. 29, no. 6, pp. 536–538, 2004.
[3]
S. C. Cowin, “How is a tissue built?” Journal of Biomechanical Engineering, vol. 122, no. 6, pp. 553–569, 2000.
[4]
O. V. Angelsky, A. G. Ushenko, and Y. G. Ushenko, “Complex degree of mutual polarization of biological tissue coherent images for the diagnostics of their physiological state,” Journal of Biomedical Optics, vol. 10, no. 6, Article ID 060502, 2005.
[5]
Y. G. Ushenko, “Complex degree of mutual polarization of Biotissue's Speckle-images,” Ukrainian Journal of Physics, vol. 6, pp. 104–113, 2005.
[6]
M. Mujat and A. Dogariu, “Polarimetric and spectral changes in random electromagnetic fields,” Optics Letters, vol. 28, no. 22, pp. 2153–2155, 2003.
[7]
O. V. Angelsky, A. G. Ushenko, V. P. Pishak, et al., “Polarizing-correlative processing of images of statistic objects in the problem of visualization and topology reconstruction of their phase heterogeneity,” in Photonics, Devices, and Systems, vol. 4016 of Proceedings of SPIE, pp. 419–424, 1999.
[8]
S. P. Morgan, M. P. Khong, and M. G. Somekh, “Effects of polarization state and scatterer concentration on optical imaging through scattering media,” Applied Optics, vol. 36, no. 7, pp. 1560–1565, 1997.
[9]
S. G. Demos and R. R. Alfano, “Optical polarization imaging,” Applied Optics, vol. 36, no. 1, pp. 150–155, 1997.
[10]
S. L. Jacques, J. R. Roman, and K. Lee, “Imaging superficial tissues with polarized light,” Lasers in Surgery & Medicine, vol. 26, no. 2, pp. 119–129, 2000.
[11]
A.G. Ushenko and V. P. Pishak, Coherent-Domain Optical Methods, Biomedical Diagnostics, Environmental and Material Science, Kluwer Academic Publishers, Dordrecht, The Netherlands, 2004.
[12]
Y. A. Ushenko, “Statistical structure of polarization-inhomogeneous images of biotissues with different morphological structures,” Ukrainian Journal of Physics, vol. 6, pp. 63–70, 2005.
[13]
O. V. Angelsky, D. N. Burkovets, V. P. Pishak, and Y. A. Ushenko, “Polarization-correlation investigations of biotissue multifractal structures and their pathological changes diagnostics,” Laser Physics, vol. 10, pp. 1136–1142, 2000.
[14]
A. G. Ushenko, “The vector structure of laser biospeckle fields and polarization diagnostics of collagen skin structures,” Laser Physics, vol. 10, no. 5, pp. 1143–1149, 2000.
[15]
O. V. Angelsky, P. P. Maksimyak, and T. O. Perun, “Optical correlation method for measuring spatial complexity in optical fields,” Optics Letters, vol. 18, no. 2, pp. 90–92, 1993.
[16]
O. V. Angel'ski？, A. G. Ushenko, S. B. Ermolenko, et al., “Polarization-based visualization of multifractal structures for the diagnostics of pathological changes in biological tissues,” Optics and Spectroscopy, vol. 89, no. 5, pp. 799–804, 2000.
[17]
M. Born and E. Wolf, Principles of Optics, Cambridge University Press, Cambridge, UK, 1999.
[18]
R. R. Alfano and J. G. Fujimoto, Advances in Optical Imaging and Photon Migration, vol. 2 of Topics in Optics and Photonics Series, Optical Society of America, Washington, DC, USA, 1996.
[19]
S. Bartel and A. H. Hielscher, “Monte Carlo simulations of the diffuse backscattering Mueller matrix for highly scattering media,” Applied Optics, vol. 39, no. 10, pp. 1580–1588, 2000.
