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Light Transport in Tissue Contents Contents Introduction and Background Motivation General assumptions Definitions and nomenclature Dimensional quantities Dimensionless quantities Phase functions The transport equation Goals Monte Carlo Methods Fixed stepsize method Variable stepsize method Variance reduction techniques Mechanics of photon propagation Phase function Photon absorption Internal reflection Convolution Verification Conclusions The Adding-Doubling Method Definition of reflection and transmission operators Derivation of the adding-doubling method The redistribution function Reflection and transmission of thin layers Boundary conditions Implementation Tabulated values Conclusions The Delta-Eddington Approximation Derivation of the diffusion equation Boundary conditions Index matching, no incident diffuse light Index matching, diffuse light incident Index mismatch, no incident diffuse light Index mismatch, diffuse light incident Glass slide -- no incident diffuse light Glass slide -- diffuse light incident Index matching, no incident diffuse light, both media scattering Index mismatch, no incident diffuse light, both media scattering Dimensionless form of the diffusion equation Solution of the one-dimensional diffusion equation Non-conservative scattering (a'<1), finite slab Non-conservative scattering (a' <1), semi-infinite slab Conservative scattering a=1, finite slab Conservative scattering (a=1), semi-infinite slab Reflection, transmission, and fluence rates in one-dimension Three-dimensional solution of the diffusion equation Formal solution of in terms of Green's functions The Green's Function for an Infinite Slab Explicit Expressions for Flux, Reflection, and Transmission in Three Dimensions Evaluation of the Delta-Eddington Approximation Comparison of total reflection and transmission Comparison of Fluence Rates Conclusions Goniophotometry Single scattering approximation Experimental apparatus Tissue preparation Data reduction Corrections for internal reflection and refraction Least squares fit Evaluation of the method Experimental results Conclusions Spectrophotometry Inverse method Uniqueness of inverse procedure Details of the iteration procedure Evaluation of the inverse method Experimental measurements Bloodless human dermis as a function of wavelength Aorta during moderate power argon irradiation Conclusions Conclusions Discussion Random Variables with Non-Uniform Density Functions Analytic Method Monte Carlo Method Discrete form of the Analytic Method Internal Reflection Basic Reflection Formulas Fresnel Reflection in a Glass Slide Reflection Moments R0, R1, and R2 Star's Approximation Keijzer's Approximation Walsh's Analytic Solution for R1 Egan Polynomial Approximation for R1 Polynomial Approximations to R0, R1, and R2 Approximations for the Boundary Coefficient A The Boundary Condition Parameter in the Presence of a Glass Slide Solid Angle Integrals and Dirac-Delta Functions Integrals over entire spheres Integrals over hemispheres Delta functions Examples of Delta Functions Numerical Details of the 3D Diffusion Solution Eigenvalues One eigenvalue less than More than one eigenvalue less than Summation of series Bibliography

S. A. Prahl."Light Transport in Tissue," PhD thesis, University of Texas at Austin, 1988.