The propagation of light in tissue may be calculated by exact transport theory, or the approximate diffusion theory, provided the optical properties are known at the source wavelength. Optical properties for the exact methods are the absorption coefficient, scattering coefficient, and angular distribution of scattering. Appropriate properties for diffusion theory are the diffusion length and diffusion coefficient (corrected for anisotropic scattering). Computer programs and analytical solutions (for some simple geometries) exist, but the optical properties have to be determined experimentally and are not well defined as yet. The radiant energy fluence rate and the diffuse transmittance and reflectance have been measured in several tissues and in a few geometries, but there are gaps in the data as a function of wavelength. Calculations and measurements reveal that very large errors can result if the optical properties (for example, the diffusion length) are inaccurate, if anisotropic scattering is neglected, or if the finite size of the irradiating light beam is not taken into account. Furthermore, the radiant energy fluence and transmittance are perturbed by local regions of lesser or greater absorption, although recovery of the fluence and transmittance occurs beyond some three diffusion lengths.

Light transport in tissue

The radiative transfer equation in nonemitting media is solved using a four-flux model in the case of Lorenz-Mie scatter centers embedded in a slab. The various coefficients of absorption and scattering appearing in the theory are nonphenomenological but expressed in terms of quantities available from the Lorenz-Mie framework. Formulas for the various transmittances and reflectances are established. Special cases are then discussed, and (potential or actual) applications reported.

Four-flux models to solve the scattering transfer equation in terms of Lorenz-Mie parameters

Publisher Summary This chapter describes enhanced backscattering in optics. The chapter considers backscatter enhancement in light scattered from a body embedded in a random medium. A similar phenomenon occurs in multiple scattering of light in a randomly inhomogeneous medium where there are no clear-cut scatterers that stand out against a background. The effects of backscatter enhancement and weak localization are phenomena, in which coherent paths of the Watson-Ruffine type are essential. The chapter describes multiple new manifestations of coherent effects in backscattering. These include the effects of long-distance correlations, the partial reversal of the phase front in a random medium, the magic cap effect, antispecular scattering by very rough random surfaces, and backscattering involving surface waves. The chapter also discusses the opposite case of a small number of scatterers, in which summation cannot be replaced with integration.

II Enhanced Backscattering in Optics

A method for solving the three-dimensional equation of transfer for a vertically inhomogeneous atmosphere bounded by a reflecting surface of non-uniform bidirectional reflectance is presented. The technique incorporates a two-dimensional spatial Fourier transform of the transfer equation and solution of the resulting expressions for each Fourier component of the radiation field using the method of Gauss-Seidel iteration. The intensity field in the spatial domain, which is calculated for a variety of altitudes, zenith angles, and azimuths, is reconstructed using the inverse Fourier transform. An empirical surface bidirectional reflectance function is employed, permitting the consideration of non-Lambertian reflective properties.

Atmospheric transfer of radiation above an inhomogeneous non-Lambertian reflective ground—I. Theory

The theoretical foundation for solution of the three-dimensional radiative transfer problem described in the preceding paper is reviewed Practical considerations involved in implementing the Fourier transform/Gauss-Seidel method on a minicomputer are discussed, along with derivations of symmetry relations and approximations which can be used to enhance the computational efficiency Model results for a surface whose albedo varies as a step function are presented and compared with published solutions obtained by using the Monte Carlo method

Atmospheric transfer of radiation above an inhomogeneous non-Lambertian reflective ground. II. Computational considerations and results.

A solution to Chandrasekhar's searchlight problem with isotropic scattering is presented for semi-infinite and finite geometries. The scattering and transmission functions for the Fourier components of intensity are given by expressions analogous to those of the plane-parallel case, except that the physical domain of the variable ζ, which replaces the usual direction cosine, is now the circular region |ζ 1 2 | ≤ 1 2 in the complex plane, and also that the corresponding H-, X-, and Y-functions now depend on a scalar wave number. Nonlinear integral equations for H, X and Y are derived, and numerical methods for computing these functions are given by means of the kernel approximation method.

The searchlight problem with isotropic scattering

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The searchlight problem with isotropic scattering