Abstract
A scalar theory of the propagation of Gaussian ultrasonic beams through lenses and interfaces is presented. For radiation into a fluid, the Fresnel approximation is employed to derive the laws of propagation of Guassian beams (previously employed in the analysis of coherent optical systems). These are then generalized to situations commonly found in nondestructive evaluation by treating the effects of propagation through lenses and through curved interfaces at oblique incidence. A numerical example illustrates the ease with which insight into diffraction phenomena for complex geometries can be gained by this approach. The limitations imposed on the theory by aberrations and the scalar assumption are discussed, and the relationship of the Gaussian theory to the radiation of piston transducers is explored.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
R. T. Beyer and S. V. Letcher,Physical Ultrasonics (Academic Press, New York, 1969), chap. 1.
E. Cavanagh and B. D. Cook, Gaussian-Laguerre description of ultrasonic fields—numerical example: circular piston.J. Acoust. Soc. Am. 67(4):1136–1140 (1980).
J. N. Tjøtta and S. Tjøtta, An analytical model for the near field of a baffled piston transducer.J. Acoust. Soc. Am. 68(1):334–339 (1980).
R. New, R. I. Becker, and P. Wilhelmij, A limiting form for the near field of the baffled piston.J. Acoust. Soc. Am. 70(5):1518–1526 (1981).
G. R. Harris, Review of the transient theory for a baffled planar piston.J. Acoust. Soc. Am. 70(1):10–20 (1981).
R. B. Thompson and T. A. Gray, Analytical diffraction corrections to ultrasonic scattering measurements, inReview of Progress in Quantitative Nondestructive Evaluation 2, D. O. Thompson and D. E. Chimenti, eds. (Plenum Press, New York, 1983), pp. 567–586.
J. Frohly, C. Bruneel, and E. Bridoux, Quantitative study of the aberrations for focussed acoustic plane waves obliquely incident upon a plane interface.J. Appl. Phys. 54:6234–6239 (1983).
R. K. Elsley, R. C. Addison, and L. J. Graham, Detection of flaws below curved surfaces, in ref. 6, in pp. 113–128.
J. Pott and J. G. Harris, Scattering of an acoustic Gaussian beam from a fluid-solid interface,J. Acoust. Soc. Am. 76:S64-S65(A) (1984).
F. D. Martin and M. A. Breazeale, A simple way to eliminate diffraction lobes emitted by ultrasonic transducers.J. Acoust. Soc. Am. 49:1668 (1971).
M. A. Breazeale, F. D. Martin, and B. Blackburn, Reply to ‘radiation pattern of partially electroded piezoelectric transducer.’”J. Acoust. Soc. Am. 70:1791 (1981).
R. O. Claus and P. S. Zerwekh, Ultrasonic transducer with a two-dimensional Gaussian field profile.IEEE Trans. Sonics Ultrasonics SU-30:36–39 (1983).
G. Du and M. A. Breazeale, The sound field of a Gaussian transducer.J. Acoust. Soc. Am. 76:S23(A) (1984).
I. M. Mason, Two-dimensional surface-wave diffraction from an arbitrary source in an anisotropic medium,Electronics Lett. 7:344–345 (1971).
I. M. Mason and E. A. Ash, Acoustic surface wave beam diffraction on anisotropic substrates.J. Appl. Phys. 42:5354–5361 (1971).
I. M. Mason, Anisotropy, diffraction, scaling, surface wave lenses and focussing,J. Acoust. Soc. Am. 53:1123–1128 (1973).
I. M. Mason, E. Papadofrangakis, J. Chambers, and R. Ulrich, Optics of propagation in the anisotropic space of an acoustic surface wave disc delay line,Electronics Lett. 11:348–349 (1975).
A. E. Siegman,An Introduction to Lasers and Masers (McGraw-Hill, New York, 1971).
A. Yariv,Introduction to Optical Electronics (Holt, Rinehart and Winston, New York, 1971).
J. Goodman,Introduction to Fourier Optics (McGraw-Hill, New York, 1968).
I. S. Gradsthein and I. M. Ryzhik,Tables of Integrals, Series, and Products (Academic Press, New York, 1965).
B. D. Cook and W. J. Arnoult III, Gaussian-Laguerre/Hermite formulation for the near field of an ultrasonic transducer.J. Acoust. Soc. Am. 59:9–11 (1976).
E. Cavanagh and B. D. Cook, Lens in the near field of a circular transducer: Gaussian-Laguerre formulation.J. Acoust. Soc. Am. 69:345–351 (1981).
J. M. Coffey and R. K. Chapman, Applications of elastic scattering theory for smooth flat cracks to the quantitative prediction of ultrasonic defect detection and sizing.Nucl. Energy 22:319–333 (1983).
T. A. Gray, R. B. Thompson, and B. P. Newberry, Improvements in ultrasonic measurement modeling with applications to ultrasonic reliability, inReview of Progress in Quantitative NDE 4, D. O. Thompson and D. E. Chimenti, eds. (Plenum Press, New York, in press).
R. B. Thompson, V. G. Kogan, J. M. Rose, T. A. Gray, and E. Lopes, A comparison of the axial fields of Gaussian and piston transducer radiation after passage through cylindrical surfaces at oblique incidence,1983 Ultrasonics Symposium Proceedings (IEEE, New York, 1983), pp. 905–908.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Thompson, R.B., Lopes, E.F. The effects of focusing and refraction on Gaussian ultrasonic beams. J Nondestruct Eval 4, 107–123 (1984). https://doi.org/10.1007/BF00566401
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF00566401