Linear algorithms for phase retrieval in the Fresnel region: validity conditions

TL;DR

This paper analyzes linearized models for X-ray phase retrieval in the Fresnel region, establishing validity conditions that enable simplified, non-iterative algorithms suitable for practical applications.

Contribution

It introduces new validity conditions that allow for simplified linear algorithms for phase retrieval, improving computational efficiency without sacrificing accuracy.

Findings

Simplified linear expressions are valid under certain conditions.

Modified validity conditions are practical for many real-world cases.

Non-iterative algorithms achieve accurate phase retrieval.

Abstract

We describe the relationship between different forms of linearized expressions for the spatial distribution of intensity of X-ray projection images obtained in the Fresnel region. We prove that under the natural validity conditions some of the previously published expressions can be simplified without a loss of accuracy. We also introduce modified validity conditions which are likely to be fulfilled in many relevant practical cases, and which lead to a further significant simplification of the expression for the image-plane intensity, permitting simple non-iterative linear algorithms for the phase retrieval.