Direct and inverse problems of weak scattering from quasi-homogeneous biological tissue

The well-established model for the spatial correlation function of the refractive index fluctuations in a statistically stationary biological tissue [Sheppard CJR. Fractal model of light scattering in biological tissue and cells. Opt Lett. 2007;32:142–144] is applied to the direct scattering problem of light within the validity regimes of the first-order Born approximation and the quasi-homogeneous approximation. It is analytically found how the far-zone angular distribution of the scattered spectral density is related to the parameters of the bio-tissues refractive index correlation function. Then the inverse problem of reconstructing the parameters of the bio-tissues correlation function from several measurements of the scattered spectral density is solved analytically. These results are of importance for medical diagnostics in soft tissues.