Joint reconstruction of x-ray fluorescence and transmission tomography.

Zichao Wendy Di,Young Pyo Hong,Sven Leyffer,Stefan M Wild,Si Chen,Chris Jacobsen

doi:10.1364/oe.25.013107

Zichao Wendy Di, Young Pyo Hong + Show 4 more

Open Access

https://doi.org/10.1364/oe.25.013107

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Abstract

X-ray fluorescence tomography is based on the detection of fluorescence x-ray photons produced following x-ray absorption while a specimen is rotated; it provides information on the 3D distribution of selected elements within a sample. One limitation in the quality of sample recovery is the separation of elemental signals due to the finite energy resolution of the detector. Another limitation is the effect of self-absorption, which can lead to inaccurate results with dense samples. To recover a higher quality elemental map, we combine x-ray fluorescence detection with a second data modality: conventional x-ray transmission tomography using absorption. By using these combined signals in a nonlinear optimization-based approach, we demonstrate the benefit of our algorithm on real experimental data and obtain an improved quantitative reconstruction of the spatial distribution of dominant elements in the sample. Compared with single-modality inversion based on x-ray fluorescence alone, this joint inversion approach reduces ill-posedness and should result in improved elemental quantification and better correction of self-absorption.

Highlights

The use of characteristic x-ray emission lines to distinguish between different chemical elements in a specimen goes back to the birth of quantum mechanics [1]
This is usually done in a scanning microscope mode, where a small x-ray beam spot is raster-scanned across the specimen while x-ray photons are collected by an energy dispersive detector that provides a measure of the energy of each emitted photon [5]
Because the x-ray beam from synchrotron light sources is usually linearly polarized in the horizontal direction, the energy dispersive detector is usually located at a position 90◦ in the horizontal from the incident beam so as to be centered on the direction of minimum elastic scattering as shown in Fig. 1

Summary

Introduction

The use of characteristic x-ray emission lines to distinguish between different chemical elements in a specimen goes back to the birth of quantum mechanics [1]. The x-ray transmission signal (absorption or phase contrast) is recorded, and the x-ray fluorescence (XRF) signal is recorded over an angular range of Ωv by using an energy dispersive detector located at 90◦ to the beam, in the direction of the elastic scattering minimum for a horizontally polarized x-ray beam. If one can measure the transmission sinograms of the specimen at the energies of all x-ray fluorescence lines, it is possible to correct for self absorption [22] This approach is exceedingly difficult to realize experimentally, since a large number of x-ray fluorescence lines are present in many specimens (see Fig. 11) and one would need to collect a transmission tomography dataset at each of these energies. We discuss choices of scaling parameters in the numerical implementation of the algorithm and present the performance of our joint inversion compared with existing approaches on real datasets

Mathematical Model

XRT Imaging Model

Optimization-Based Reconstruction Formulations and Algorithms

Experimental Reconstruction

Conclusion