Optical Diffraction Tomography for the Refractive Index Profiling of Objects with Large Space-Bandwidth product

Abstract

The primary goal of this work is to arrive at direction tomography (DT) algorithms freed from the severe linearization in the formulation, and as-assumptions on variation of the refractive index distribution (RID), involved in the earlier approaches based on Born and Royton approximations and the Fourier di reaction theorem (FDT). To start with, a direct single-step re-covery of RID from intensity measurements is demonstrated, replacing the common two-step procedure involving, rest the recovery of phase from in-density followed by the inversion of scattered led for the RID. The information loss, unavoidable in a two-step procedure is thus successfully addressed. Secondly, an iterative method which works with a forward model obtained directly from the Helmholtz equation is developed. This forward model, though has simplifying assumptions, is more general and can accommodate larger variations in RID than that allowed in the previous linear models. The iterative procedure has an update step which uses a linearization of the forward model and a re-linearization step at the updated RID. The procedure which directly employs the measured intensities is used as part of a deterministic Gauss-Newton algorithm and a stochastic optimization algorithm which uses the ensemble Kalman lter to arrive at the recursive update. The stochastic method is found to be more noise-tolerant and efficient to take care of process model inaccuracies. The proof is seen in better reconstructions from experimental data for two example objects, namely, a graded-index optical bre and a photonic-crystal bre. It is further ob-served that the reconstructions from photonic crystal bre are blurred, noisy and less accurate. Identifying the inaccurate implementation of the modemed Helmholtz equation for large k values employing the current sampling rate as the shortcoming, a new procedure, which splits the bandwidth into smaller components using short-time Fourier Transform is developed. The set of equations arrived at, each t for a narrow frequency band, is solved and the solutions are reassembled to obtain the scattered led for the original problem. The simulated di rated intensities so obtained are better matched to their measured experimental counterparts. However, the impel-mentation of the mode end procedure is computation-intensive, for which a parallel-processing machine can be a good solution. The recovery of RID with this mode cation is not attempted in this work and is left for future implementation.