Geometrical Optics Formalism to Model Contrast in Dark-Field X-ray Microscopy

TL;DR

This paper introduces a geometrical optics-based formalism for modeling contrast in dark-field X-ray microscopy, enabling improved simulation, design, and interpretation of experiments involving crystalline structures and strain mapping.

Contribution

It provides a general, crystallographic space group-independent formalism for diffraction image simulation, facilitating tailored experimental design and multi-scale imaging in DFXM.

Findings

Demonstrated the formalism's ability to simulate strain fields around dislocations.

Showed how to modify experimental design for specific deformation components.

Validated the model with experimental images of strain in crystals.

Abstract

Dark-field X-ray microscopy is a new full-field imaging technique that nondestructively maps the structure and local strain inside deeply embedded crystalline elements in three dimensions. Placing an objective lens in the diffracted beam generates a magnified projection image of a local volume. We provide a general formalism based on geometrical optics for the diffraction imaging, valid for any crystallographic space group. This allows simulation of diffraction images based on micro-mechanical models. We present example simulations with the formalism, demonstrating how it may be used to design new experiments or interpret existing ones. In particular, we show how modifications to the experimental design may tailor the reciprocal-space resolution function to map specific components of the deformation gradient tensor. The formalism supports multi-length scale experiments, as it enables DFXM to be interfaced with 3DXRD. The formalism is demonstrated by comparison to experimental images of the strain field around a straight dislocation.