X-Ray Tomographic Reconstruction

TLDR: In this article, a program employing iterative methods based on the inverse Radon transform was written to correct the data in order to obtain the most accurate images from which element concentrations and internal structure can be determined.

Abstract: Tomographic scans have revolutionized imaging techniques used in medical and biological research by resolving individual sample slices instead of several superimposed images that are obtained from regular x-ray scans. X-Ray fluorescence computed tomography, a more specific tomography technique, bombards the sample with synchrotron x-rays and detects the fluorescent photons emitted from the sample. However, since x-rays are attenuated as they pass through the sample, tomographic scans often produce images with erroneous low densities in areas where the x-rays have already passed through most of the sample. To correct for this and correctly reconstruct the data in order to obtain the most accurate images, a program employing iterative methods based on the inverse Radon transform was written. Applying this reconstruction method to a tomographic image recovered some of the lost densities, providing a more accurate image from which element concentrations and internal structure can be determined.

Figures

Figure 2: Simulated iron and calcium distributions. (a) Iron without correction for attenuation. (b) Iron with correction for attenuation. (c) Calcium without correction for attenuation. (d) Calcium with correction for attenuation. [1]

Figure 3: Diagram of fluorescence tomography [5].

Full text

Work supported in part by US Department of Energy contract DE-AC02-76SF00515.
X-Ray Tomographic Reconstruction
Bonnie Schmittberger
Science Undergraduate Laboratory Internship Program
Bryn Mawr College
SLAC National Accelerator Laboratory
Menlo Park, California
August 14, 2009
Prepared in partial fulfillment of the requirement of the Department of Energy's Science
Undergraduate Laboratory Internship program under the direction of Samuel Webb at the
Stanford Synchrotron Radiation Lightsource at SLAC National Accelerator Laboratory.
Participant: _______________________________
Signature
Project Advisor: ______________________________
Signature
SLAC-TN-10-015

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Table of Contents
Abstract……………………………………………………………………………………3
Introduction………………………………………………………………………………..4
Materials and Methods……………………………………………………………………5
Results……………………………………………………………………………………10
Discussion…………………………………………………………………………….….10
Conclusion……………………………..………………………………………………...12
Acknowledgments………………………………………………………………………..12
References………………………………………………………………………………..13
Figure 1: Schematic of Detector Setup…………………………………………………..14
Figure 2: Calcium and Iron Tomographic Scans……………………………………...…15
Figure 3: Schematic of Axis Setup………………………………………………………16
Figure 4: Tomographic Scan and Reconstruction of Arabidopsis Thaliana………….….17
Appendix: Copy of Reconstruction Code…………………...……………...……………18

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ABSTRACT
X-Ray Tomographic Reconstruction. BONNIE SCHMITTBERGER (Bryn Mawr
College, Bryn Mawr, PA, 19010) DR. SAMUEL WEBB (Stanford Synchrotron
Radiation Laboratory at SLAC National Acceleratory Laboratory, Menlo Park, CA
94025)
Tomographic scans have revolutionized imaging techniques used in medical and
biological research by resolving individual sample slices instead of several superimposed
images that are obtained from regular x-ray scans. X-Ray fluorescence computed
tomography, a more specific tomography technique, bombards the sample with
synchrotron x-rays and detects the fluorescent photons emitted from the sample.
However, since x-rays are attenuated as they pass through the sample, tomographic scans
often produce images with erroneous low densities in areas where the x-rays have already
passed through most of the sample. To correct for this and correctly reconstruct the data
in order to obtain the most accurate images, a program employing iterative methods
based on the inverse Radon transform was written. Applying this reconstruction method
to a tomographic image recovered some of the lost densities, providing a more accurate
image from which element concentrations and internal structure can be determined.

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1. INTRODUCTION
X-Ray fluorescence computed tomography (XFCT) is a synchrotron-based
imaging technique used for mapping the distribution of elements within a sample. In
XFCT, a sample is bombarded with x-rays that excite k-shell electrons. When these
atoms return to their stable state, they emit fluorescent x-rays at energies characteristic of
the element. These photons are collected by a solid state silicon detector that records
multiple energies simultaneously. The total number of photons recorded is a function of
the sum of the various element concentrations along the line of the incident beam. By
rotating the object and compiling horizontal scans, it is possible to obtain a complete
tomographic reconstruction of the distribution of the elements within a sample.
Since the incident beam is attenuated through the sample and part of the emission
is absorbed by the sample, attenuation correction is necessary in order to obtain accurate
results. If reconstruction techniques are not employed, the image of the center of the
sample is blurred, and its density, as recorded by the scan, is much lower than its true
density. Previous reconstruction techniques required a known attenuation at each
fluorescence energy, which necessitated the time-consuming process of rescanning the
sample at all the relevant energies [1]. Tomographic reconstruction is also possible by a
series of mathematical corrections based on the inverse Radon transform, which is a
faster and simpler method.
These reconstruction techniques have attracted numerous scientific disciplines to
XFCT. In particular, the high sensitivity and sub-micrometer resolution of this method is
useful in medicine [2]. The presence of metals and other trace elements drastically affect
intracellular processes in any organism [3]. XFCT is the only sub-micrometer technique

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that can map these elements within cells and search for abnormal quantities and
distributions accompanying the development of certain diseases [3].
2. MATERIALS AND METHODS
i. Data Collection
Once the code was completed, data was collected at the Stanford Synchrotron
Radiation Lightsource. X-Rays obtained from the synchrotron are sent through an ion
chamber to measure the energy of the incident beam. The x-rays are then directed into a
helium-purged chamber where they are focused down to a 2 µm diameter by two
elliptical mirrors. This focused beam is then sent out to the sample, which is scanned by
moving completely across the incident beam, then rotating by a certain small angle,
typically 1 to 3 degrees, and repeating until 180 degrees are covered. This is called a full
translation, half rotation tomographic scan. If the scan were to cover a full rotation, the
amount of attenuation correction would be minimized because the image would only
contain artifacts towards the center of the sample, but that process doubles the scanning
time, generally requiring three to four extra hours.
The detector is placed behind the sample to collect the transmitted x-rays, and
another is placed at 90 degrees to the incident beam to collect the fluorescent photons, as
depicted in Figure 1. A uniform fluorescence around the sample is assumed, so that one
fluorescent photon detector is sufficient. Because elements have signature fluorescence
energies, a fluorescent photon detector that can distinguish different photon energy levels
is used. This detector counts the number of photons that it receives at each energy level,
so the concentrations of different elements in the sample can be determined.