Validation of the born approximation in 2-D weakly-scattering biological random media using the FDTD method

In this paper, we present a validation of the Born (or single-scattering) approximation [1] in the electromagnetic scattering analysis of two-dimensional (2-D) weakly-scattering biological random media. We base our validation mostly on data regarding the single biological cell, mainly because of its ubiquity and the amount of previously available data regarding its refractive index properties. We first construct a statistical model for the refractive-index distribution of the biological medium. We then derive an analytical formula for the expected value of the total scattering cross-section of the medium under the Born approximation, and demonstrate that the results are in good agreement with the data obtained from the 2-D finite-difference-time-domain (FDTD) [2] simulation of media with refractive index values based on previous reports for biological cells. This agreement constitutes a proof-of-concept for the use of the Born approximation in weakly-scattering biological media, and suggests future work on its validation in 3-D.