Physics-based basis functions for low-dimensional representation of the refractive index in the high energy limit

TL;DR

This paper introduces a physics-based polynomial model for the refractive index decrement in x-ray energies, simplifying the representation and improving efficiency in phase-contrast tomography.

Contribution

It derives a simple, physics-motivated polynomial form for the refractive index decrement that accurately fits theoretical and experimental data, aiding modeling and inverse problem formulation.

Findings

Excellent agreement with theoretical and experimental data

Reduces dimensionality for efficient modeling

Facilitates well-posed inverse problems in tomography

Abstract

The relationship between the refractive index decrement, $\delta$, and the real part of the atomic form factor, $f^\prime$, is used to derive a simple polynomial functional form for $\delta(E)$ far from the K-edge of the element. The functional form, motivated by the underlying physics, follows an infinite power sum, with most of the energy dependence captured by a single term, $1/E^2$. The derived functional form shows excellent agreement with theoretical and experimentally recorded values. This work helps reduce the dimensionality of the refractive index across the energy range of x-ray radiation for efficient forward modeling and formulation of a well-posed inverse problem in propagation-based polychromatic phase-contrast computed tomography.