Optical di usion of cw, pulse and density waves in scattering media and comparisons with radiative transfer

Transport theory's equation of transfer is a well-accepted model for wave scattering in a random medium. However, exact solutions are only available for a small class of special cases (isotropic scattering in in nite and semiin nite domains) and thus, analytic solutions for a wide variety of geometries and range of parameters which correspond to more physically relevant situations still remain to be determined. Many have derived di usion approximations using asymptotic analysis1{8. These approximate equations have the advantage of easily obtainable, closed-form solutions. In addition, there has been a signi cant amount of experimental data which agrees well with the solution of the di usion equation. However, the applicability of the di usion approximation to many other physically relevant settings remains questionable. Experimental evidence shows that biological media are highly anisotropic (asymmetry parameter values greater than 0:9), and thus a careful investigation is necessary to determine the di usion approximation's applicability to highly anisotropic media. Furthermore, a question remains as to which of the several di usion equations most closely approximates the solution given by the equation of transfer. In this paper, we address questions pertaining to the di usion approximation of the equation of transfer for applications in biomedical imaging. We numerically solve the equation of transfer for the plane-parallel problem and compare the existing di usion theories in order to determine which of the several theories most closely approximates the equation of transfer. In doing so, we determine the validity of the di usion approximation for optically imaging biological media. Some numerical results have been obtained for the case when the refractive index of the background medium di ers from that of the surrounding medium. In order to evaluate the di usion approximation's validity simply and e ectively, we only consider the idealized case of index-matched boundary conditions. We perform these comparisons for cw, pulse and photon density waves.