Optical diffraction tomography in an inhomogeneous background medium

The filtered back-propagation algorithm (FBP algorithm) is a computationally fast and efficient inversion algorithm for reconstructing the 3D index of refraction distribution of weak scattering samples in free space from scattered field data collected in a set of coherent optical scattering experiments. This algorithm is readily derived using classical Fourier analysis applied to the Born or Rytov weak scattering models appropriate to scatterers embedded in a non-attenuating uniform background. In this paper, the inverse scattering problem for optical diffraction tomography (ODT) is formulated using the so-called distorted wave Born and Rytov approximations and a generalized version of the FBP algorithm is derived that applies to weakly scattering samples that are embedded in realistic, multiple scattering ODT experimental configurations. The new algorithms are based on the generalized linear inverse of the linear transformation relating the scattered field data to the complex index of refraction distribution of the scattering samples and are in the form of a superposition of filtered data, computationally back propagated into the ODT experimental configuration. The paper includes a computer simulation comparing the generalized Born and Rytov based FBP inversion algorithms as well as reconstructions generated using the generalized Born based FBP algorithm of a step index optical fiber from experimental ODT data.