# Clarification on Generalized Lau condition for X-ray interferometers based on dual phase gratings

## TL;DR

This paper corrects misconceptions about the Lau-condition in dual phase grating x-ray interferometry, deriving a new generalized condition through geometrical analysis to improve design and implementation.

## Contribution

It provides a new generalized Lau-condition specific to dual phase grating interferometry, correcting previous assumptions and aiding practical design.

## Key findings

- The traditional Lau-condition does not directly apply to dual phase grating interferometry.
- A new generalized Lau-condition was derived based on geometrical analysis.
- The new condition improves the design accuracy for x-ray interferometers.

## Abstract

To implement dual phase grating x-ray interferometry with x-ray tubes, one needs to incorporate an absorbing source grating. In order to attain good fringe visibility, the period of a source grating should be subject to a stringent condition. In literature some authors claim that the Lau-condition in Talbot-Lau interferometry can be literally transferred to dual phase grating interferometry. In this work we show that this statement in literature is incorrect. Instead, through an intuitive geometrical analysis of fringe formation, we derived a new generalized Lau-condition that provides a useful design tool for implementation of dual phase grating interferometry.