Nonlinear estimation of pressure projection of ultrasound fields in background-oriented schlieren imaging

Eero Koponen; Jarkko Leskinen; Tanja Tarvainen; Aki Pulkkinen

doi:10.1364/JOSAA.433762

Journal of the Optical Society of America A
Vol. 39,
Issue 4,
pp. 552-562
(2022)
•https://doi.org/10.1364/JOSAA.433762

Nonlinear estimation of pressure projection of ultrasound fields in background-oriented schlieren imaging

Eero Koponen, Jarkko Leskinen, Tanja Tarvainen, and Aki Pulkkinen

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Eero Koponen, Jarkko Leskinen, Tanja Tarvainen, and Aki Pulkkinen, "Nonlinear estimation of pressure projection of ultrasound fields in background-oriented schlieren imaging," J. Opt. Soc. Am. A 39, 552-562 (2022)

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Abstract

Background-oriented schlieren imaging is a recently proposed method for measuring projections of ultrasound fields. The method is based on observing deflection of light in a heterogeneous refractive index field that is induced by ultrasound via an acousto-optic effect. The deflection of light manifests as apparent perturbations in an imaged target, forming a potential flow estimation problem. In this work, the potential flow approach is formulated as a nonlinear regularized least-squares approach to alleviate limitations of approaches that linearize the problem. The nonlinear approach is shown to outperform the linear one when estimating projections of medically relevant ultrasound fields.

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Data availability

Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.

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Equations (24)

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	${\hat{Ψ}}_{1}$	${\hat{Ψ}}_{2}$	${\hat{Ψ}}_{3}$	${\hat{Ψ}}_{4}$
Linear	10.4	16.7	28.3	27.1
Nonlinear	5.6	5.8	7.6	23.0
HS-Brox2011	30.5	26.8	102.8	111.6
HS-Cai2018	41.9	52.5	84.3	70.4

	${\hat{Ψ}}_{1}$	${\hat{Ψ}}_{2}$	${\hat{Ψ}}_{3}$	${\hat{Ψ}}_{4}$
Linear $Ψ^{+}$	11.1	13.5	30.4	40.5
Nonlinear $Ψ^{+}$	3.1	2.4	7.7	35.7
Linear $Ψ^{-}$	2.3	15.4	27.9	20.4
Nonlinear $Ψ^{-}$	5.7	2.2	1.6	9.9

	${\hat{Ψ}}_{1}$	${\hat{Ψ}}_{2}$	${\hat{Ψ}}_{3}$	${\hat{Ψ}}_{4}$
Linear	10.4	16.7	28.3	27.1
Nonlinear	5.6	5.8	7.6	23.0
HS-Brox2011	30.5	26.8	102.8	111.6
HS-Cai2018	41.9	52.5	84.3	70.4

	${\hat{Ψ}}_{1}$	${\hat{Ψ}}_{2}$	${\hat{Ψ}}_{3}$	${\hat{Ψ}}_{4}$
Linear $Ψ^{+}$	11.1	13.5	30.4	40.5
Nonlinear $Ψ^{+}$	3.1	2.4	7.7	35.7
Linear $Ψ^{-}$	2.3	15.4	27.9	20.4
Nonlinear $Ψ^{-}$	5.7	2.2	1.6	9.9

Abstract

Data availability

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Equations (24)

Journal of the Optical Society of America A