Diffraction Corrections for Second Harmonic Beam Fields and Effects on the Nonlinearity Parameter Evaluation

Title & Authors
Diffraction Corrections for Second Harmonic Beam Fields and Effects on the Nonlinearity Parameter Evaluation
Jeong, Hyunjo; Cho, Sungjong; Nam, Kiwoong; Lee, Janghyun;

Abstract
The nonlinearity parameter is frequently measured as a sensitive indicator in damaged material characterization or tissue harmonic imaging. Several previous studies have employed the plane wave solution, and ignored the effects of beam diffraction when measuring the non-linearity parameter $\small{{\beta}}$. This paper presents a multi-Gaussian beam approach to explicitly derive diffraction corrections for fundamental and second harmonics under quasilinear and paraxial approximation. Their effects on the nonlinearity parameter estimation demonstrate complicated dependence of $\small{{\beta}}$ on the transmitter-receiver geometries, frequency, and propagation distance. The diffraction effects on the non-linearity parameter estimation are important even in the nearfield region. Experiments are performed to show that improved $\small{{\beta}}$ values can be obtained by considering the diffraction effects.
Keywords
Diffraction Correction;Multi-Gaussian Beam;Nonlinearity Parameter;
Language
English
Cited by
References
1.
H. Jeong, S. Zhang, D. Barnard and X. Li, "Significance of accurate diffraction corrections for the second harmonic wave in determining the acoustic nonlinearity parameter," AIP ADVANCES, Vol. 5, 097179 (2015)

2.
A. O. Williams Jr., "The piston source at high frequencies," J. Acoust. Soc. Am., Vol. 23, pp. 1-6 (1951)

3.
P. H. Rogers and A. L. Van Buren, "An exact expression for the Lommel-diffraction correction integral," J. Acoust. Soc. Am., Vol. 55, pp. 724-728 (1974)

4.
A. S. Khimunin, "Numerical calculation of the diffraction corrections for the precise measurement of ultrasound absorption," Acustica, Vol. 27, pp. 173-181 (1972)

5.
A. S. Khimunin, "Numerical calculation of the diffraction corrections for the precise measurement of ultrasound phase velocity," Acustica, Vol. 32, pp. 192-200 (1975)

6.
A. S. Khimunin, "Ultrasonic parameter measurements incorporating exact diffraction corrections," Acta Acustica united with Acustica, Vol. 39, 87-95 (1978)

7.
K. Yamada and Y. Fujii, "Acoustic response of a circular receiver to a circular source of different radius," J. Acoust. Soc. Am., Vol. 40, pp. 1193-1194 (1966)

8.
K. Beissner, "Exact integral expression for the diffraction loss of a circular piston source," Acta Acustica united with Acustica Vol. 49, pp. 212-217 (1981)

9.
T. L. Szabo, "Aperture size effects in wideband attenuation measurements," IEEE Ultrasonics Symposium Proceeding, pp. 675-678 (1991)

10.
F. Ingenito and A. O. Williams Jr., "Calculation of second-harmonic generation in a piston beam," J. Acoust. Soc. Am., Vol. 49, pp. 319-328 (1971)

11.
W. N. Cobb, "Finite amplitude method for the determination of the acoustic nonlinearity parameter B/A," J. Acoust. Soc. Am., Vol. 73, pp. 1525-1531 (1983)

12.
D. C. Hurley and C. M. Fortunko, "Determination of the nonlinear ultrasonic parameter beta using a Michelson interferometer," Meas. Sci. Technol., Vol. 8, pp. 634-642 (1997)

13.
C. Pantea, C. F. Osterhoudt and D. N. Sinha, "Determination of acoustical nonlinear parameter of water using the finite amplitude method," Ultrasonics, Vol. 53, pp. 1012-1019 (2013)

14.
F. Dunn, W. K. Law and L. A. Frizzel, "Nonlinear ultrasonic wave propagation in biological media," IEEE Ultrason. Symp., pp. 527-532 (1981)

15.
H. Jeong, S. Cho, K. Nam and J. Lee, "An efficient and accurate method for calculating nonlinear diffraction beam fields," Journal of the Korean Society for Nondestructive Testing, Vol. 36, No. 2, pp. 102-111 (2016)

16.
H.-J. Kim, L. W. Schmerr, Jr. and A. Sedov, "Generation of the basis sets for multi-Gaussian ultrasonic beam models-An overview," J. Acoust. Soc. Am., Vol. 119, pp. 1971-1978 (2006)

17.
K. D. Wallace, C. W. Lloyd, M. R. Holland and J. G. Miller, "Finite amplitude measurements of the nonlinear parameter B/A for liquid mixtures spanning a range relevant to tissue harmonic mode," Ultrasound Med. Biol., Vol. 33, pp. 620- 629 (2007)

18.
H. Jeong, S. Zhang and X. Li, "A novel method for extracting acoustic nonlinearity parameters with diffraction corrections," Journal of Mechanical Science and Technology, Vol. 30, pp. 643-652 (2016)