Green functions for diffuse light in a medium comprising two turbid half-spaces

Abstract

A review of Green functions for diffuse light in two semi-infinite scattering and absorbing half-spaces separated by a plane interface is presented. The frequency-domain Green functions for an intensity-modulated point source are derived within the diffusion approximation by the Hankel transform with respect to the variable in the plane of the interface. Green functions for a line source and a plane source parallel to the interface are obtained from the three-dimensional Green functions by the method of descent. Green functions for a steady state are obtained as a limit of zero modulation frequency. Connection of the frequency-domain Green functions with the time-domain Green functions is shown by use of the Fourier transform in time. The influence of the relative optical parameters, namely, the ratios of diffusion coefficients, absorption coefficients, and refractive indices of the two media on the shape of the contour lines of the specific intensity, is shown for the continuous and intensity-modulated point sources.