The optical properties of biological tissue are important for photodynamic therapy and diagnostic techniques. Typically, optical properties are obtained using solutions of the radiative transport equation that express the optical properties in terms of readily measurable quantities. These solutions are either exact or approximate and correspond to the direct or indirect methods described by Wilson et al. Direct methods place stringent constraints on the sample to match the assumptions made for exact solution. For example, the direct method used by Flock et al. required very thin samples in which multiple scattering could be ignored. Indirect methods relax the sample constraints but require approximations that are often invalid for tissue samples (e.g., nearly isotropic scattering or no internal reflection at the boundaries). The theory used in indirect methods usually falls into one of three categories: Beer's law, Kubelka-Munk, or the diffusion approximation.
Beer's law neglects scattering and is inappropriate for thick scattering materials. The Kubelka-Munk method and variants are still used, but are limited in their accuracy. Methods based on the diffusion approximation or a similar approximation (e.g., uniform radiances over the forward and backward hemispheres) tend to be more accurate than Kubleka-Munk. Techniques using the diffusion approximation include pulsed photothermal radiometry, time resolved spectroscopy, radial reflectance spectroscopy, weak localization, and an iterative technique that uses reflection and transmission measurements. These methods remain popular because they are easy to use, place relatively minor constraints on the type of sample, and are amenable to analytic manipulation. However, the diffusion approximation assumes that the internal radiance is nearly isotropic and consequently it is a poor approximation when scattering is comparable to absorption.
The IAD method consists of the following steps (1) Guess a set of optical properties; (2) Calculate the reflection and transmission using the adding-doubling method; (3) Compare the calculated values with the measured reflection and transmissions; and then (4) Repeat until a match is made. The set of optical properties that generates reflection and transmission values matching the measured values is taken as the optical properties of the sample. The results obtained using the IAD method are accurate for all optical properties and can be made arbitrarily precise at the cost of increased computation time. Furthermore, by avoiding an analytical solution, it is possible to incorporate the necessary corrections for measurements made with integrating spheres directly. Such corrections are usually quite awkward to implement analytically because the magnitude of the correction depends on the optical properties of the sample measured.
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