Summary
This paper presents a theoretical model based on wave mechanics for the reflection of focused and parallel ultrasonic beams from a liquid-solid interface. The incident beam is defined by a Gaussian velocity distribution along a plane emitter, and the reflected beam is described through its pressure field by means of asymptotic analysis based on the short wave hypothesis. In the case of a focused reflected beam, nonspecular phenomena are observed for any angle of incidence. However, in the case of a parallel reflected beam, nonspecular reflection only occurs if the incidence of the beam is in the neighborhood of the Rayleigh angle. The objective of this paper is to discuss in detail the physical mechanisms of nonspecular reflection for both focused and unfocused beams and to provide an understanding of the complex phenomena related to nonspecular reflection of ultrasonic beams, which plays an important role in scanning acustic microscopy for materials nondestructive characterization.
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References
Breazeale, M. A., Adler, L., Scott, G. W.: Interaction of ultrasonic waves incident at the Rayleigh angle onto a liquid-solid interface. J. A. P.48, 530–537 (1977).
Bertoni, H. L., Tamir, T.: Unified theory of Rayleigh-angle phenomena for acoustic beams at liquid-solid interfaces. Appl. Phys.2, 157–172 (1973).
Ngoc, T. D. K., Mayer, W. G.: Numerical integration method for reflected beam profiles near Rayleigh angle. J. Acoust. Soc. Am.67, 1149–1152 (1980).
Rousseau, M., Gatignol, P.: Short wave analysis for the reflection of bounded acoustic beams onto liquid-solid interfaces at the Rayleigh incidence. J. Acoust. Soc. Am.78, 1859–1867 (1985).
Bertoni, H. L., Hsue, C. W., Tamir, T.: Nonspecular reflection of convergent beams form liquid-solid interface. Trait. Sign.2, 201–205 (1985).
Nagy, P. B., Cho, C., Adler, L., Chimeriti, D.: Focal shift of convergent ultrasonic beams reflected from a liquid-solid interface. J. Acoust. Soc. Am.81, 835–839 (1987).
Matikas, T. E., Rousseau, M., Gatignol, P.: Experimental study of focused ultrasonic beams reflected at a fluid-solid interface in the neighborhood of the Rayleigh augle. IEEE Trans. on Ultrasonics, Ferroelectrics and Frequency Control39, 737–744 (1992).
Matikas, T. E., Rousseau, M., Gatignol, P.: Theoretical analysis for the reflection of a focused ultrasonic beam from a fluid-solid interface. J. Acoust. Soc. Am.93, 1407–1416 (1993).
Roseau, M.: Asymptotic wave theory. North-Holland Series in Applied Mathematics and Mechanics, Vol. 20. Amsterdam: North-Holland 1976.
Copson, E. T.: Asymptotic expansions. Cambridge: Cambridge University Press 1967.
Ludwig, D.: Uniform asymptotic expansions at a caustic. Comm. Pure Appl. Math.XIX, 215–250 (1966).
Rousseau, M., Gatignol, P.: Etude asymptotique d'un faisceau Gaussien focalise. J. Acoustique1, 95–99 (1988).
Matikas, T. E.: Theoretical and experimental study of the interaction of focused ultrasonic beams with plane fluid-solid interfaces. Application at the analysis of the state of material surfaces. Universite de Technologie de Compiegne, France 1991.
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Matikas, T.E. Unified theory for parallel and focused beam nonspecular reflection at liquid-solid interfaces. Acta Mechanica 155, 27–43 (2002). https://doi.org/10.1007/BF01170838
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DOI: https://doi.org/10.1007/BF01170838