Significance of accurate diffraction corrections for the second harmonic wave in determining the acoustic nonlinearity parameter

Hyunjo Jeong,Shuzeng Zhang,Dan Barnard,Xiongbing Li

doi:10.1063/1.4932145

Hyunjo Jeong, Shuzeng Zhang + Show 2 more

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https://doi.org/10.1063/1.4932145

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Abstract

The accurate measurement of acoustic nonlinearity parameter β for fluids or solids generally requires making corrections for diffraction effects due to finite size geometry of transmitter and receiver. These effects are well known in linear acoustics, while those for second harmonic waves have not been well addressed and therefore not properly considered in previous studies. In this work, we explicitly define the attenuation and diffraction corrections using the multi-Gaussian beam (MGB) equations which were developed from the quasilinear solutions of the KZK equation. The effects of making these corrections are examined through the simulation of β determination in water. Diffraction corrections are found to have more significant effects than attenuation corrections, and the β values of water can be estimated experimentally with less than 5% errors when the exact second harmonic diffraction corrections are used together with the negligible attenuation correction effects on the basis of linear frequency dependence between attenuation coefficients, α2 ≃ 2α1.

Highlights

Nonlinear ultrasonic methods have been widely used in recent decades as a nondestructive evaluation tool for biological tissues and damaged solids.1,2 The measurement of nonlinearity parameter, β, receives significant attention
The second term in the right-hand side is defined as the total attenuation correction, MT(z), and the third term is defined as the total diffraction correction, DT(z), respectively: MT(z) =
A more precise approach to determine the acoustic nonlinearity parameter β using the quasilinear theory was proposed based on the attenuation and diffraction corrections of fundamental and second harmonic waves

Summary

Introduction

Nonlinear ultrasonic methods have been widely used in recent decades as a nondestructive evaluation tool for biological tissues and damaged solids. The measurement of nonlinearity parameter, β, receives significant attention. The nonlinearity parameter β is based on the plane wave solution of the nonlinear wave equation, and can be determined from the ratio of amplitudes of the fundamental and that of the second harmonic.. One needs to adjust the amplitudes of the actual acoustic fields to their plane-wave values before they are used to determine β This is the effect referred to as the diffraction correction. An approximate diffraction correction to the second harmonic wave was presented by several authors based on the average velocity potential of Ingenito and Williams, and used in later studies for estimating the nonlinearity parameter of solids and fluids. The plane wave assumption does not hold when it propagates through an attenuating medium The amplitudes of both fundamental and second harmonic waves will decrease due to material absorption.

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