Theory of dichroic X-ray tomography and laminography

TL;DR

This paper develops a theoretical framework for dichroic X-ray tomography and laminography, highlighting the limitations in reconstructing magnetic and optical properties and discussing the necessary conditions and constraints for accurate imaging.

Contribution

It provides a comprehensive theory for dichroic X-ray tomography and laminography, analyzing the reconstruction challenges and proposing conditions for accurate property recovery.

Findings

Reconstruction of magnetic moments requires multiple tilt angles or constraints.

Three polarizations or tilt angles are needed for linear dichroism without constraints.

The common assumption of absorption as a volume integral fails under strong dichroism or birefringence.

Abstract

Dichroic tomography is a 3D imaging technique in which the polarization of the incident beam is used to induce contrast due to the magnetization or orientation of a sample. The aim is to reconstruct not only the optical density but the dichroism of the sample. The theory of dichroic tomographic and laminographic imaging in the parallel-beam case is discussed as well as the problem of reconstruction of the sample's optical properties. The set of projections resulting from a tomographic/laminographic measurement is not sufficient to reconstruct the magnetic moment for magnetic circular dichroism unless additional constraints are applied or data are taken at two or more tilt angles. For linear dichroism, three polarizations or three tilt angles are required to provide enough information to reconstruct without constraints. Possible means of applying constraints are discussed. Furthermore, it is shown that for linear dichroism, the basic assumption that the absorption through a ray path is the integral of the absorption coefficient, defined on the volume of the sample, along the ray path, is not correct when dichroism or birefringence is strong. This assumption is fundamental to tomographic methods.