Three-Dimensional Optical Diffraction Tomography with Lippmann-Schwinger Model

TL;DR

This paper introduces an accurate and efficient 3D optical diffraction tomography method using the nonlinear Lippmann-Schwinger model, improving image reconstruction quality over traditional approximate models.

Contribution

It presents a novel implementation of the forward model based on the exact Lippmann-Schwinger equation and integrates it into a regularized reconstruction framework.

Findings

Substantially better reconstructions than traditional approximate models.

Effective handling of limited view and large sample size challenges.

Validated on both simulated and real data.

Abstract

A broad class of imaging modalities involve the resolution of an inverse-scattering problem. Among them, three-dimensional optical diffraction tomography (ODT) comes with its own challenges. These include a limited range of views, a large size of the sample with respect to the illumination wavelength, and optical aberrations that are inherent to the system itself. In this work, we present an accurate and efficient implementation of the forward model. It relies on the exact (nonlinear) Lippmann-Schwinger equation. We address several crucial issues such as the discretization of the Green function, the computation of the far field, and the estimation of the incident field. We then deploy this model in a regularized variational-reconstruction framework and show on both simulated and real data that it leads to substantially better reconstructions than the approximate models that are traditionally used in ODT.