Information Transfer as a Framework for Optimized Phase Imaging

TL;DR

This paper introduces an information-theoretic framework using Fisher Information to evaluate and optimize phase imaging techniques, especially for strongly scattering samples, proposing generalized methods including Zernike phase contrast and interferometry.

Contribution

It develops a generalized information transfer framework for phase imaging, enabling optimization of imaging schemes for strongly scattering samples with minimal prior knowledge.

Findings

Generalized Zernike phase contrast is efficient with prior sample knowledge.

Random sensing captures significant information without prior knowledge.

Optimized interferometry can target specific sample features.

Abstract

In order to efficiently image a non-absorbing sample (a phase object), dedicated phase contrast optics are required. Typically, these optics are designed with the assumption that the sample is weakly scattering, implying a linear relation between a sample's phase and its transmission function. In the strongly scattering, non-linear case, the standard optics are ineffective and the transfer functions used to characterize them are uninformative. We use the Fisher Information (FI) to assess the efficiency of various phase imaging schemes and to calculate an Information Transfer Function (ITF). We show that a generalized version of Zernike phase contrast is efficient given sufficient foreknowledge of the sample. We show that with no foreknowledge, a random sensing measurement yields a significant fraction of the available information. Finally, we introduce a generalized approach to common path interferometry which can be optimized to prioritize sensitivity to particular sample features. Each of these measurements can be performed using Fourier lenses and phase masks.