Diffraction of intensity-modulated light in strongly scattering media in the presence of a 'semi-infinite' absorbing or reflecting plane bounded by a straight edge

摘要

A simple model is developed, based on the diffusion approximation to the linear transport equation, which gives analytic expressions that describe the coherent propagation of sinusoidally intensity-modulated light through a strongly scattering, low absorbing, homogeneous, infinite medium in terms of the interaction coefficients of the medium. Previously, the analytical multiform solutions to Laplace's equation and the Helmholtz equation were derived respectively by Sommerfeld and Carslaw in their studies of electrostatics, sound, and heat to model intensity modulated light in the presence of an absorbing or reflecting `semi-infinite' plane bounded by a straight edge that is immersed in an infinite, strongly scattering, low absorbing, homogeneous medium. The model predictions are in good agreement with the present results of experiments performed on media consisting of Intralipid$+TM$/ and skim milk emulsions containing minute quantities of black India ink and with Monte Carlo simulations. These studies provide a theoretical basis for the understanding of photon diffusion in tissues and allow the determination of conditions to obtain maximum resolution and penetration.