# Sample phase gradient and fringe phase shift in dual phase grating X-ray interferometry

## TL;DR

This paper derives formulas linking sample phase gradients to fringe phase shifts in dual phase grating X-ray interferometry, aiding accurate phase retrieval and system design optimization.

## Contribution

The authors provide the first explicit mathematical relationship between sample phase gradients and fringe phase shifts in dual phase grating X-ray interferometry.

## Key findings

- Derived formulas for phase gradient and fringe phase shift relationship
- Provided a design optimization tool for dual phase grating systems
- Enhanced accuracy in local phase gradient retrieval

## Abstract

One of the key tasks in grating based x-ray phase contrast imaging is to accurately retrieve local phase gradients of a sample from measured intensity fringe shifts. To fulfill this task in dual phase grating interferometry, one needs to know the exact mathematical relationship between the two. In this work, using intuitive analysis of the sample-generated fringe shifts based on the beat pattern formation mechanism, the authors derived the formulas relating sample's phase gradients to fringe phase shifts. These formulas provide also a design optimization tool for dual phase grating interferometry.