[1] Bostrom, A., and Wirdelius, H., "Ultrasonic Probe Modeling and Nondestructive Crack
Detection", J. Acoust. Soc. Am., Vol. 97, No. 5, pp. 2836-2848, (1995).
[2] Wen, J.J., and Breazeale, M.A., "A Diffraction Beam Field Expressed as the Superposition
of Gaussian Beams", J. Acoust. Soc. Am., Vol. 83, pp. 1752–1756, (1988).
[3] Ding, D.S., Zhang, Y., and Liu, J.Q., "Some Extensions of the Gaussian Beam Expansion:
Radiation Fields of the Rectangular and the Elliptical Transducer", J. Acoust. Soc. Am.,
Vol. 113, pp. 3043–3048, (2003).
[4] Kim, H.J., Schmerr, L.W., and Sedov, A., "Generation of the Basis Sets for Multi-
Gaussian Ultrasonic Beam Models – An Overview", J. Acoust. Soc. Am., Vol. 119, pp.
1971–1978, (2006).
[5] Spies, M., "Modeling of Transducer Fields in Inhomogeneous Anisotropic Materials using
Gaussian Beam Superposition", NDT&E International, Vol. 33, pp. 155–162 (2000).
[6] Kim, H.J, Song, S.J., and Schmerr, L.W., "An Ultrasonic Measurement Model using a
Multi-Gaussian Beam Model for a Rectangular Transducer", Ultrasonics, Vol. 44, pp.
969–974, (2006).
[7] Spies, M., "Transducer Field Modeling in Anisotropic Media by Superposition of
Gaussian Base Functions", J. Acoust. Soc. Am., Vol. 105, No. 2, Pt. 1, February, pp. 633-
638, (1999).
[8] Spies, M., "Modeling of Transducer Fields in Inhomogeneous Anisotropic Materials using
Gaussian Beam Superposition", NDT&E Int., Vol. 33, pp. 155–162, (2000).
[9] Kim, H.J., Park, J.S., Song, S.J., and Schmerr, L.W., "Modeling Angle Beam Ultrasonic
Testing Using Multi-Gaussian Beams", Journal of Nondestructive Evaluation, Vol. 23,
No. 3, pp. 81-93, (2004).
[10] Schmerr, L.W., and Song, S.J., "Ultrasonic Nondestructive Evaluation Systems: Models
and Measurements", Springer, (2007)
[11] Kim, H.J., Song, S.J. and Schmerr, L.W., " Modeling Ultrasonic Pulse-echo Signals from
a Flat-bottom Hole in Immersion Testing using a Multi-Gaussian Beam " Journal of
Nondestructive Evaluation, Vol. 23, No. 1, (2004).
[12] Zhao, X., and Gang, T., "Nonparaxial Multi-Gaussian Beam Models and Measurement
Models for Phased Array Transducers", Ultrasonics, Vol. 49, pp. 126-130, (2009).
[13] Charlesworth, J.P., and Temple, J.A.G, "Engineering Applications of Ultrasonic Time-offlight
Diffraction", Research Studies Press, 2nd Ed, England, (2001).
[14] Schemerr, L.W., "Fundamentals of Ultrasonic Nondestructive Evaluation", Plenum
Press, (1998).