Cargando…

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...

Descripción completa

Detalles Bibliográficos
Autor principal: Baddour, Natalie
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Springer International Publishing 2016
Materias:
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
_version_ 1782454358027272192
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
work_keys_str_mv AT baddournatalie thederivativefreefouriershellidentityforphotoacoustics
AT baddournatalie derivativefreefouriershellidentityforphotoacoustics