Polarization-Based Optical Imaging
In this study I present polarization effects resulting from the reflection and transmission of a narrow beam of light through biological tissues. This is done numerically with a Monte Carlo method based on a transport equation which takes into account pol
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troduction Optical imaging is proving to be a potentially useful non-invasive technique for the detection of objects in the human body. The ultimate goal is the detection of millimeter-sized cancerous tissue before it spreads into the surrounding healthy tissue [1–3]. Cancerous tissue absorbs more light than healthy tissue due to its higher blood content, giving rise to a perturbation in the measured light intensity. The main problem in using light as a diagnostic tool is that it is strongly scattered by normal tissue, resulting in image blurring. Various techniques have been devised to overcome this difficulty, e.g., time gating, optical coherence, confocal detection, etc. All these techniques distinguish between weakly and strongly scattered photons, i.e., those scattered through small angles and those scattered through large angles. Recently, there has been a considerable interest in the polarization properties of the reflected and transmitted light. Multiple scattering gives rise to diffusion and depolarization. The effectiveness of polarization-sensitive techniques to discriminate between weakly and strongly scattered photons has been demonstrated experimentally by Schmitt et al. [4], Rowe et al. [5], and Demos et al. [6], among others. We have reported numerical evidence for this previously using the theory of radiative transfer taking into account polarization of light [7]. The theory of radiative transfer, employing Stokes parameters, can be used to describe light propagation through a medium. Analytical solutions are not known except in simple particular cases, such as plane parallel atmospheres
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M. Moscoso
with a constant net flux [8]. When the incident laser beam is narrow no solution is known. Therefore we have developed a Monte Carlo method to obtain the spatial distribution of the total intensity and of the polarization components of the transmitted and reflected beams. Other methods for solving the vector radiative transfer equation have been explored in [9]. In [9] we presented a complete discussion of Chebyshev spectral methods for solving radiative transfer problems. In this method, we approximated the spatial dependence of the intensity by an expansion of Chebyshev polynomials. This yields a coupled system of integro-differential equations for the expansion coefficients that depend on angle and time. Next, we approximated the integral operation on the angle variables using a Gaussian quadrature rule resulting in a coupled system of differential equations with respect to time. Using a second order finite-difference approximation, we discretized the time variable. We solved the resultant system of equations with an efficient algorithm that makes Chebyshev spectral methods competitive with other methods for radiative transfer equations. Section 2 contains the theory of radiative transfer employing Stokes parameters. In Sect. 3 we describe our model where we represent a biological tissue as a medium with weak random fluctuations of the dielectric permittivity (r) = 0 [1 + δ(r)], where r denotes position and δ
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