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

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.

A novel and practical approach for determination of the acoustic nonlinearity parameter using a pulse-echo method

“…Compared to the TT mode, the total correction of PE mode is very large and changes steeply in thin sample regions. The significance of making total corrections in determining the acoustic nonlinearity parameter in TT mode has been investigated and reported in [10]. …”

“…In Fig. 1 The incident primary beam fields and the generated second harmonic beam fields can be obtained using the approach of Green's function 1 2 and G G [10] 1 (6) Using the MGB models developed in earlier study for the fundamental and second harmonic waves, the reflected beam fields can be expressed as (8) 060006-2 where 1 R and 2 R are the reflection coefficients of the fundamental and the second harmonic, respectively…”

“…These effects are well known for fundamental waves in linear regime, while those for second harmonic waves have not been well addressed and therefore not properly used 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 theory of the KZK equation [8][9][10]. Simulation results are presented for the reflected beam fields of the fundamental and second harmonic 060006-1 waves, the uncorrected behavior and the properties of the total correction that include reflection, attenuation and diffraction effects.…”

Development of attenuation and diffraction corrections for linear and nonlinear Rayleigh surface waves radiating from a uniform line source

“…In case of longitudinal waves, the nonlinearity parameter is based on the plane wave displacement solution of nonlinear wave equation, and is determined from the ratio of amplitudes of the fundamental and that of the second harmonic generated in the medium. 10,11 Herrmann et al 12 derived a relationship between the acoustic nonlinearity parameter β of longitudinal wave and the out-of-plane displacement components of the first (U 1z ) and second harmonic amplitude (U 2z ) when a Rayleigh surface wave propagates in an isotropic infinite half-space with a weak quadratic nonlinearity. The nonlinearity parameter β 11 of Rayleigh wave was defined and introduced in the two-dimensional nonlinear wave equation of fluids.…”

“…Attenuation corrections are obtained from the quasilinear theory of plane Rayleigh wave equations. To obtain the closed form expressions for diffraction corrections, the multi-Gaussian beam (MGB) models 10,19 are employed to represent the integral solutions derived from the quasilinear theory. Diffraction corrections are presented for a couple of transmitter-receiver geometries, and the effects of making these corrections are examined through the simulation of nonlinearity parameter determination in a solid sample.…”