# Single-shot x-ray speckle-based imaging of a single-material object

## TL;DR

This paper introduces a single-shot x-ray speckle-based imaging method for measuring the projected thickness of single-material objects using a novel approach that requires only one image and leverages speckle deformation and the transport-of-intensity equation.

## Contribution

It presents a new single-shot speckle-based phase imaging technique that simplifies the process by avoiding explicit speckle tracking and uses a closed-form solution for inverse problem solving.

## Key findings

- Method is robust and efficient with noise
- Applicable to x-ray phase--amplitude radiography and tomography
- Suitable for dynamic and radiation-sensitive samples

## Abstract

We develop a means for speckle-based phase imaging of the projected thickness of a single-material object, under the assumption of illumination by spatially random time-independent x-ray speckles. These speckles are generated by passing x rays through a suitable spatially random mask. The method makes use of a single image obtained in the presence of the object, which serves to deform the illuminating speckle field relative to a reference speckle field (which only needs to be measured once) obtained in the presence of the mask and the absence of the object. The method implicitly rather than explicitly tracks speckles, and utilizes the transport-of-intensity equation to give a closed-form solution to the inverse problem of determining the complex transmission function of the object. Implementation using x-ray synchrotron data shows the method to be robust and efficient with respect to noise. Applications include x-ray phase--amplitude radiography and tomography, as well as time-dependent imaging of dynamic and radiation-sensitive samples using low-flux sources.