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Methods and Algorithms for the Measurement of the Optical Parameters of Tissues

Methods and algorithms for solving the inverse problem of finding tissue and blood optical parameters such as absorption and scattering coefficients, anisotropy factor, and refractive index are presented. Advantages and drawbacks of these methods are analyzed. Widespread measuring techniques such as integrating sphere, spatially, time-, and angular-resolved, and OCT, as well as inverse methods, such as Kubelka-Munk, multiflux, adding-doubling and inverse Monte Carlo, are overviewed. Exhaustive data on optical properties of human tissue and blood measured in vitro, ex vivo, and in vivo are presented.

2.1 Basic principles

Methods for determining the optical parameters of tissues can be divided into two large groups, direct and indirect methods. Direct methods include those based on some fundamental concepts and rules such as the Bouguer-Beer-Lambert law [see Eq. (1.1)], the single-scattering phase function [see Eqs. (1.13) and (1.15)] for thin samples, or the effective light penetration depth for slabs. The parameters measured are the collimated light transmission Tc and the scattering indicatrix I(I¸) (angular dependence of the scattered light intensity, Wâcm2 sr) for thin samples or the fluence rate inside a slab. The normalized scattering indicatrix is equal to the scattering phase function I(I¸)âI(0) âi p(I¸), 1âsr. These methods are advantageous in that they use very simple analytic expressions for data processing. Their disadvantages are related to the necessity to strictly fulfill experimental conditions dictated by the selected model (single scattering in thin samples, exclusion of the effects of light polarization and refraction at cuvette edges, etc.); in the case of slabs with multiple scattering, the recording detector (usually a fiber light guide with an isotropically scattering ball at the tip end) must be placed far from both the light source and the medium boundaries.

Indirect methods obtain the solution of the inverse scattering problem using a theoretical model of light propagation in a medium. They are in turn divided into iterative and noniterative models. The former use equations in which the optical properties are defined through parameters directly related to the quantities being evaluated. The latter are based on the two-flux Kubelka-Munk model and multiflux models.