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

preprint

posted on 2023-07-08, 04:02 authored by Saransh Singh, K. Aditya MohanThe 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.