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Journal ArticleDOI

Representation of a Function by Its Line Integrals, with Some Radiological Applications

A. M. Cormack
- 01 Sep 1963 - 
- Vol. 34, Iss: 9, pp 2722-2727
TLDR
In this paper, a method for finding a real function in a finite region of a plane given its line integrals along all straight lines intersecting the region was given, and the solution found is applicable to three problems of interest for precise radiology and radiotherapy: (1) the determination of a variable x-ray absorption coefficient in two dimensions, (2) the distribution of positron annihilations when there is an inhomogeneous distribution of the positron emitter in matter, and (3) a variable density of matter with constant chemical composition, using the energy loss
Abstract
A method is given of finding a real function in a finite region of a plane given its line integrals along all straight lines intersecting the region. The solution found is applicable to three problems of interest for precise radiology and radiotherapy: (1) the determination of a variable x‐ray absorption coefficient in two dimensions; (2) the determination of the distribution of positron annihilations when there is an inhomogeneous distribution of the positron emitter in matter; and (3) the determination of a variable density of matter with constant chemical composition, using the energy loss of charged particles in the matter.

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Citations
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Journal ArticleDOI

3D electron microscopy in the physical sciences: the development of Z-contrast and EFTEM tomography

TL;DR: Examples of how STEM dark-field imaging and energy-filtered TEM can be used successfully to examine nearly all types of specimens likely to be encountered by the physical scientist are presented.
Journal ArticleDOI

X-ray computed tomography

TL;DR: This review of CT will proceed in chronological order focussing on technology, image quality and clinical applications, and briefly allude to novel uses of CT such as dual-source CT, C-arm flat-panel-detector CT and micro-CT.
Journal ArticleDOI

Electron tomography and holography in materials science

TL;DR: An overview of the techniques of electron tomography and electron holography is presented and their capabilities with the aid of case studies that span materials science and the interface between the physical sciences and the life sciences are demonstrated.
Journal ArticleDOI

Principles of computer assisted tomography (CAT) in radiographic and radioisotopic imaging.

TL;DR: In this paper, the limitations of present techniques, and new developments and trends are outlined, compared with conventional focal plane tomography, and methods of reconstruction-back projection, iterative reconstruction and analytic reconstruction are described.
Journal ArticleDOI

Three-Dimensional X-ray Microtomography

TL;DR: The new technique of x-ray microtomography nondestructively generates three-dimensional maps of the x-rays attenuation coefficient inside small samples with approximately 1 percent accuracy and with resolution approaching 1 micrometer.
References
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Book

Principles of Optics

Max Born, +1 more
TL;DR: In this paper, the authors discuss various topics about optics, such as geometrical theories, image forming instruments, and optics of metals and crystals, including interference, interferometers, and diffraction.

Principles of Optics

Max Born, +1 more
TL;DR: In this article, the authors discuss various topics about optics, such as geometrical theories, image forming instruments, and optics of metals and crystals, including interference, interferometers, and diffraction.
Journal ArticleDOI

Beugungstheorie des schneidenver-fahrens und seiner verbesserten form, der phasenkontrastmethode

TL;DR: In this paper, ausammenfassung auf Grundlage der A b b eschen Beugungstheorie der optischen Abbildung wird das Aussehen eines Hohlspiegels mit willkurlich verlaufenden kleinen Abweichungen beim Foucaul tschen Schneidenverfahren and beim neuen Phasenkontrastverfhren berechnet.