Three-dimensional contrast transfer function in phase-contrast tomography

TL;DR

This paper introduces a 3D phase retrieval method for propagation-based X-ray phase-contrast tomography using the contrast transfer function formalism applied after volume reconstruction, enhancing efficiency and applicability.

Contribution

The novel approach performs phase retrieval on the 3D reconstructed volume rather than on 2D projections, extending CTF formalism to partially-coherent illumination and strongly absorbing samples.

Findings

Provides fast and stable phase retrieval comparable to traditional methods.

Allows localized application to specific objects, improving computational efficiency.

Extends CTF validity to larger propagation distances, surpassing transport-of-intensity approaches.

Abstract

A new method is developed for three-dimensional (3D) reconstruction of multi-material objects using propagation-based X-ray phase-contrast tomography (PB-CT) with phase retrieval via the contrast transfer function (CTF) formalism. The approach differs from conventional PB-CT algorithms that apply phase retrieval on individual two-dimensional (2D) projections. Instead, this method involves performing phase retrieval to the CT-reconstructed volume in 3D. The CTF formalism is further extended to the cases of partially-coherent illumination and strongly absorbing samples. Simulated results demonstrate that the proposed post-reconstruction CTF method provides fast and stable phase retrieval, producing results equivalent to conventional pre-reconstruction 2D CTF phase retrieval. Moreover, it is shown that application can be highly localised to isolated objects of interest, without a significant loss of quality, thus leading to increased computational efficiency. Combined with the extended validity of the CTF to greater propagation distances, this method provides additional advantages over approaches based on the transport-of-intensity equation.