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The derivative-free Fourier shell identity for photoacoustics
In X-ray tomography, the Fourier slice theorem provides a relationship between the Fourier components of the object being imaged and the measured projection data. The Fourier slice theorem is the basis for X-ray Fourier-based tomographic inversion techniques. A similar relationship, referred to as t...
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Formato: | Online Artículo Texto |
Lenguaje: | English |
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Springer International Publishing
2016
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Acceso en línea: | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5028376/ https://www.ncbi.nlm.nih.gov/pubmed/27652170 http://dx.doi.org/10.1186/s40064-016-3294-y |
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author | Baddour, Natalie |
author_facet | Baddour, Natalie |
author_sort | Baddour, Natalie |
collection | PubMed |
description | In X-ray tomography, the Fourier slice theorem provides a relationship between the Fourier components of the object being imaged and the measured projection data. The Fourier slice theorem is the basis for X-ray Fourier-based tomographic inversion techniques. A similar relationship, referred to as the ‘Fourier shell identity’ has been previously derived for photoacoustic applications. However, this identity relates the pressure wavefield data function and its normal derivative measured on an arbitrary enclosing aperture to the three-dimensional Fourier transform of the enclosed object evaluated on a sphere. Since the normal derivative of pressure is not normally measured, the applicability of the formulation is limited in this form. In this paper, alternative derivations of the Fourier shell identity in 1D, 2D polar and 3D spherical polar coordinates are presented. The presented formulations do not require the normal derivative of pressure, thereby lending the formulas directly adaptable for Fourier based absorber reconstructions. |
format | Online Article Text |
id | pubmed-5028376 |
institution | National Center for Biotechnology Information |
language | English |
publishDate | 2016 |
publisher | Springer International Publishing |
record_format | MEDLINE/PubMed |
spelling | pubmed-50283762016-09-20 The derivative-free Fourier shell identity for photoacoustics Baddour, Natalie Springerplus Research In X-ray tomography, the Fourier slice theorem provides a relationship between the Fourier components of the object being imaged and the measured projection data. The Fourier slice theorem is the basis for X-ray Fourier-based tomographic inversion techniques. A similar relationship, referred to as the ‘Fourier shell identity’ has been previously derived for photoacoustic applications. However, this identity relates the pressure wavefield data function and its normal derivative measured on an arbitrary enclosing aperture to the three-dimensional Fourier transform of the enclosed object evaluated on a sphere. Since the normal derivative of pressure is not normally measured, the applicability of the formulation is limited in this form. In this paper, alternative derivations of the Fourier shell identity in 1D, 2D polar and 3D spherical polar coordinates are presented. The presented formulations do not require the normal derivative of pressure, thereby lending the formulas directly adaptable for Fourier based absorber reconstructions. Springer International Publishing 2016-09-19 /pmc/articles/PMC5028376/ /pubmed/27652170 http://dx.doi.org/10.1186/s40064-016-3294-y Text en © The Author(s) 2016 Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. |
spellingShingle | Research Baddour, Natalie The derivative-free Fourier shell identity for photoacoustics |
title | The derivative-free Fourier shell identity for photoacoustics |
title_full | The derivative-free Fourier shell identity for photoacoustics |
title_fullStr | The derivative-free Fourier shell identity for photoacoustics |
title_full_unstemmed | The derivative-free Fourier shell identity for photoacoustics |
title_short | The derivative-free Fourier shell identity for photoacoustics |
title_sort | derivative-free fourier shell identity for photoacoustics |
topic | Research |
url | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5028376/ https://www.ncbi.nlm.nih.gov/pubmed/27652170 http://dx.doi.org/10.1186/s40064-016-3294-y |
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