# X-ray optics and beam characterization using random modulation: Theory

## TL;DR

This paper provides a comprehensive theoretical review of speckle-based X-ray phase-sensing methods, generalizing the concept and discussing their applicability for optical element characterization in various scenarios.

## Contribution

It introduces a generalized theoretical framework for speckle-based X-ray phase-sensing methods, enabling better selection and implementation for different metrology applications.

## Key findings

- Theoretical generalization of speckle methods
- Applicability across different beams and optics
- Guidance for choosing optimal methods for specific scenarios

## Abstract

X-ray near-field speckle-based phase-sensing approaches provide efficient means to characterise optical elements. Here, we present a theoretical review of several of these speckle methods in the frame of optical characterisation and provide a generalization of the concept. As we also demonstrate experimentally in another paper, the methods theoretically developed here can be applied with different beams and optics and within a variety of situations where at-wavelength metrology is desired. By understanding the differences between the various processing methods, it is possible to find and implement the best suited approach for each metrology scenario.