Optoacoustic inversion via convolution kernel reconstruction in the paraxial approximation and beyond

authored by: O. Melchert, M. Wollweber, B. Roth
Abstract: In this article we address the numeric inversion of optoacoustic signals to initial stress profiles. Therefore we study a Volterra integral equation of the second kind that describes the shape transformation of propagating stress waves in the paraxial approximation of the underlying wave-equation. Expanding the optoacoustic convolution kernel in terms of a Fourier-series, a best fit to a pair of observed near-field and far-field signals allows to obtain a sequence of expansion coefficients that describe a given “apparative” setup. The resulting effective kernel is used to solve the optoacoustic source reconstruction problem using a Picard-Lindelöf correction scheme. We verify the validity of the proposed inversion protocol for synthetic input signals and explore the feasibility of our approach to also account for the shape transformation of signals beyond the paraxial approximation including the inversion of experimental data stemming from measurements on melanin doped PVA hydrogel tissue phantoms.
Organisation(s): Hannover Centre for Optical Technologies (HOT)
Type: Article
Journal: Photoacoustics
Volume: 13
Pages: 1-5
No. of pages: 5
ISSN: 2213-5979
Publication date: 03.2019
Publication status: Published
Peer reviewed: Yes
ASJC Scopus subject areas: Atomic and Molecular Physics, and Optics, Radiology Nuclear Medicine and imaging
Electronic version(s): https://doi.org/10.1016/j.pacs.2018.10.004 (Access: Open)
https://doi.org/10.15488/4732 (Access: Open)

BibTeX

@article{29b39276c1f14690b83f5e65c219897e,
title = "Optoacoustic inversion via convolution kernel reconstruction in the paraxial approximation and beyond",
abstract = "In this article we address the numeric inversion of optoacoustic signals to initial stress profiles. Therefore we study a Volterra integral equation of the second kind that describes the shape transformation of propagating stress waves in the paraxial approximation of the underlying wave-equation. Expanding the optoacoustic convolution kernel in terms of a Fourier-series, a best fit to a pair of observed near-field and far-field signals allows to obtain a sequence of expansion coefficients that describe a given “apparative” setup. The resulting effective kernel is used to solve the optoacoustic source reconstruction problem using a Picard-Lindel{\"o}f correction scheme. We verify the validity of the proposed inversion protocol for synthetic input signals and explore the feasibility of our approach to also account for the shape transformation of signals beyond the paraxial approximation including the inversion of experimental data stemming from measurements on melanin doped PVA hydrogel tissue phantoms.",
keywords = "Convolution kernel reconstruction, Optoacoustics, Tissue phantom, Volterra integral equation of the second kind",
author = "O. Melchert and M. Wollweber and B. Roth",
note = "Funding Information: We thank A. Demircan for commenting on an early draft of the manuscript and E. Blumenr{\"o}ther for providing experimental data. This research work received funding from the VolkswagenStiftung within the “Nieders{\"a}chsisches Vorab” program in the framework of the project “Hybrid Numerical Optics” (HYMNOS; Grant ZN 3061). Valuable discussions within the collaboration of projects MeDiOO and HYMNOS at HOT are gratefully acknowledged. The publication of this article was funded by the Open Access Fund of the Leibniz Universit{\"a}t Hannover. ",
year = "2019",
month = mar,
doi = "10.1016/j.pacs.2018.10.004",
language = "English",
volume = "13",
pages = "1--5",
journal = "Photoacoustics",
issn = "2213-5979",
publisher = "Elsevier GmbH",
}