DOI: 10.1063/1.1729798. Representation of a Function by Its Line Integrals, with Some Radiological Applications

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

10.1063/1.1729798

Crossref journal-article

AIP Publishing

Journal of Applied Physics (317)

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.

Bibliography

Cormack, A. M. (1963). Representation of a Function by Its Line Integrals, with Some Radiological Applications. Journal of Applied Physics, 34(9), 2722â2727.

Authors 1

A. M. Cormack (first)

References 6 Referenced 1,000

10.1126/science.113.2940.525 / Science (1951)
{'key': '2024020207085353700_r1a', 'first-page': '40', 'volume': '11', 'year': '1953', 'journal-title': 'Nucleonics'} / Nucleonics (1953)
10.1148/47.5.487 / Radiology (1946)
10.1038/1821222a0 / Nature (1958)
{'key': '2024020207085353700_r3'}
10.1103/PhysRev.81.404 / Phys. Rev. (1951)

Dates

Type	When
Created	20 years, 4 months ago (April 22, 2005, 12:31 p.m.)
Deposited	1 year, 6 months ago (Feb. 2, 2024, 2:14 a.m.)
Indexed	2 days, 12 hours ago (Aug. 23, 2025, 9:56 p.m.)
Issued	61 years, 11 months ago (Sept. 1, 1963)
Published	61 years, 11 months ago (Sept. 1, 1963)
Published Print	61 years, 11 months ago (Sept. 1, 1963)

Funders 0

None

BibTeX

@article{Cormack_1963, title={Representation of a Function by Its Line Integrals, with Some Radiological Applications}, volume={34}, ISSN={1089-7550}, url={http://dx.doi.org/10.1063/1.1729798}, DOI={10.1063/1.1729798}, number={9}, journal={Journal of Applied Physics}, publisher={AIP Publishing}, author={Cormack, A. M.}, year={1963}, month=sep, pages={2722–2727} }

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