Monomorphous decomposition method for phase retrieval and phase-contrast tomography

TL;DR

This paper introduces a novel method to decompose complex refractive index distributions into two simpler monomorphous components, enabling more stable phase retrieval in phase-contrast imaging and tomography.

Contribution

It extends the phase-retrieval approach based on the Transport of Intensity Equation to arbitrary objects by decomposing them into monomorphous parts, improving stability.

Findings

Exact representation of complex distributions as sum of two monomorphous distributions

Enhanced stability of phase retrieval methods using this decomposition

Potential applications in quantitative phase-contrast imaging

Abstract

We show that an arbitrary spatial distribution of complex refractive index inside an object can be exactly represented as a sum of two "monomorphous" complex distributions, i.e. the distributions with the ratios of the real part to the imaginary part being constant throughout the object. A priori knowledge of constituent materials can be used to estimate the global lower and upper boundaries for this ratio. This approach can be viewed as an extension of the successful phase-retrieval method, based on the Transport of Intensity equation, that was previously developed for monomorphous (homogeneous) objects, such as e.g. objects consisting of a single material. We demonstrate that the monomorphous decomposition can lead to more stable methods for phase retrieval using the Transport of Intensity Equation. Such methods may find application in quantitative in-line phase-contrast imaging and phase-contrast tomography.