Spatiotemporal Deconvolution of Hydrophone Response for Linear and Nonlinear Beams - Part II: Experimental Validation

Keith A. Wear; Anant Shah; Christian Baker

doi:10.1109/TUFFC.2022.3150179

Spatiotemporal Deconvolution of Hydrophone Response for Linear and Nonlinear Beams - Part II: Experimental Validation

Keith A. Wear^*, Anant Shah, Christian Baker

^*Corresponding author for this work

Surgical & Interventional Engineering

Research output: Contribution to journal › Article › peer-review

7 Citations (Scopus)

Abstract

This article reports experimental validation for spatiotemporal deconvolution methods and simple empirical formulas to correct pressure and beamwidth measurements for spatial averaging across a hydrophone sensitive element. The method was validated using linear and nonlinear beams transmitted by seven single-element spherically focusing transducers (2-10 MHz; ${F}$ /#: 1-3) and measured with five hydrophones (sensitive element diameters ${d}_{g}$ : 85-1000 $\mu \text{m}$ ), resulting in 35 transducer/hydrophone combinations. Exponential functions, exp( $-\alpha {x}$ ), where ${x} = {d}_{g}$ /( $\lambda _{{1}}{F}$ /#) and $\lambda _{{1}}$ is the fundamental wavelength, were used to model focal pressure ratios ${p}'/{p}$ (where ${p}'$ is the measured value subjected to spatial averaging and ${p}$ is the true axial value that would be obtained with a hypothetical point hydrophone). Spatiotemporal deconvolution reduced $\alpha $ (followed by root mean squared difference between data and fit) from 0.29-0.30 (7%) to 0.01 (8%) (linear signals) and from 0.29-0.40 (8%) to 0.04 (14%) (nonlinear signals), indicating successful spatial averaging correction. Linear functions, Cx + 1, were used to model FWHM'/FWHM, where FWHM is full-width half-maximum. Spatiotemporal deconvolution reduced ${C}$ from 9% (4%) to -0.6% (1%) (linear signals) and from 30% (10%) to 6% (5%) (nonlinear signals), indicating successful spatial averaging correction. Spatiotemporal deconvolution resulted in significant improvement in accuracy even when the hydrophone geometrical sensitive element diameter exceeded the beam FWHM. Responsible reporting of hydrophone-based pressure measurements should always acknowledge spatial averaging considerations.

Original language	English
Pages (from-to)	1257-1267
Number of pages	11
Journal	IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control
Volume	69
Issue number	4
DOIs	https://doi.org/10.1109/TUFFC.2022.3150179
Publication status	Published - 1 Apr 2022

Keywords

Beamwidth measurement
deconvolution
hydrophone
membrane
pressure measurement
spatial averaging

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10.1109/TUFFC.2022.3150179

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title = "Spatiotemporal Deconvolution of Hydrophone Response for Linear and Nonlinear Beams - Part II: Experimental Validation",

abstract = "This article reports experimental validation for spatiotemporal deconvolution methods and simple empirical formulas to correct pressure and beamwidth measurements for spatial averaging across a hydrophone sensitive element. The method was validated using linear and nonlinear beams transmitted by seven single-element spherically focusing transducers (2-10 MHz; ${F}$ /#: 1-3) and measured with five hydrophones (sensitive element diameters ${d}_{g}$ : 85-1000 $\mu \text{m}$ ), resulting in 35 transducer/hydrophone combinations. Exponential functions, exp( $-\alpha {x}$ ), where ${x} = {d}_{g}$ /( $\lambda _{{1}}{F}$ /#) and $\lambda _{{1}}$ is the fundamental wavelength, were used to model focal pressure ratios ${p}'/{p}$ (where ${p}'$ is the measured value subjected to spatial averaging and ${p}$ is the true axial value that would be obtained with a hypothetical point hydrophone). Spatiotemporal deconvolution reduced $\alpha $ (followed by root mean squared difference between data and fit) from 0.29-0.30 (7%) to 0.01 (8%) (linear signals) and from 0.29-0.40 (8%) to 0.04 (14%) (nonlinear signals), indicating successful spatial averaging correction. Linear functions, Cx + 1, were used to model FWHM'/FWHM, where FWHM is full-width half-maximum. Spatiotemporal deconvolution reduced ${C}$ from 9% (4%) to -0.6% (1%) (linear signals) and from 30% (10%) to 6% (5%) (nonlinear signals), indicating successful spatial averaging correction. Spatiotemporal deconvolution resulted in significant improvement in accuracy even when the hydrophone geometrical sensitive element diameter exceeded the beam FWHM. Responsible reporting of hydrophone-based pressure measurements should always acknowledge spatial averaging considerations.",

keywords = "Beamwidth measurement, deconvolution, hydrophone, membrane, pressure measurement, spatial averaging",

author = "Wear, {Keith A.} and Anant Shah and Christian Baker",

note = "Publisher Copyright: {\textcopyright} 1986-2012 IEEE.",

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doi = "10.1109/TUFFC.2022.3150179",

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AB - This article reports experimental validation for spatiotemporal deconvolution methods and simple empirical formulas to correct pressure and beamwidth measurements for spatial averaging across a hydrophone sensitive element. The method was validated using linear and nonlinear beams transmitted by seven single-element spherically focusing transducers (2-10 MHz; ${F}$ /#: 1-3) and measured with five hydrophones (sensitive element diameters ${d}_{g}$ : 85-1000 $\mu \text{m}$ ), resulting in 35 transducer/hydrophone combinations. Exponential functions, exp( $-\alpha {x}$ ), where ${x} = {d}_{g}$ /( $\lambda _{{1}}{F}$ /#) and $\lambda _{{1}}$ is the fundamental wavelength, were used to model focal pressure ratios ${p}'/{p}$ (where ${p}'$ is the measured value subjected to spatial averaging and ${p}$ is the true axial value that would be obtained with a hypothetical point hydrophone). Spatiotemporal deconvolution reduced $\alpha $ (followed by root mean squared difference between data and fit) from 0.29-0.30 (7%) to 0.01 (8%) (linear signals) and from 0.29-0.40 (8%) to 0.04 (14%) (nonlinear signals), indicating successful spatial averaging correction. Linear functions, Cx + 1, were used to model FWHM'/FWHM, where FWHM is full-width half-maximum. Spatiotemporal deconvolution reduced ${C}$ from 9% (4%) to -0.6% (1%) (linear signals) and from 30% (10%) to 6% (5%) (nonlinear signals), indicating successful spatial averaging correction. Spatiotemporal deconvolution resulted in significant improvement in accuracy even when the hydrophone geometrical sensitive element diameter exceeded the beam FWHM. Responsible reporting of hydrophone-based pressure measurements should always acknowledge spatial averaging considerations.

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KW - pressure measurement

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SN - 0885-3010

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EP - 1267

JO - IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control

JF - IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control

IS - 4

ER -

Spatiotemporal Deconvolution of Hydrophone Response for Linear and Nonlinear Beams - Part II: Experimental Validation

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