Multi-Gaussian Ultrasonic Beam Modeling for Multiple Curved Interfaces—an ABCD Matrix Approach

ABSTRACT A multi-Gaussian beam model uses a superposition of Gaussian beams to simulate the waves radiated from an ultrasonic transducer. We show that propagation and reflection/transmission laws for Gaussian beams in fluids and elastic solids can be written in the form of A , B , C , D matrices that are analogous to the A, B, C, D scalars used in Gaussian optics. This representation leads to simple expressions for a Gaussian beam even after that beam has been transmitted or reflected at multiple curved interfaces and produces a highly modular multi-Gaussian beam model that is also computationally very efficient. Some examples of the use of this model for both planar and curved interfaces are given.

[1]  F. Walte,et al.  Application-Directed Modeling of Radiation and Propagation of Elastic Waves in Anisotropic Media: GPSS and OPOSSM , 1995 .

[2]  Yu Zhang,et al.  Some extensions of the Gaussian beam expansion: radiation fields of the rectangular and the elliptical transducer. , 2003, The Journal of the Acoustical Society of America.

[3]  E. F. Lopes,et al.  The effects of focusing and refraction on Gaussian ultrasonic beams , 1984 .

[4]  Cleve Moler,et al.  Mathematical Handbook for Scientists and Engineers , 1961 .

[5]  L. Schmerr.  Fundamentals of Ultrasonic Nondestructive Evaluation , 1998 .

[6]  Woon-Seng Gan,et al.  A complex virtual source approach for calculating the diffraction beam field generated by a rectangular planar source. , 2003, IEEE transactions on ultrasonics, ferroelectrics, and frequency control.

[7]  Alan Jeffrey.  CHAPTER 14 – Fresnel Integrals , 1995 .

[8]  D. O. Thompson,et al.  Review of Progress in Quantitative Nondestructive Evaluation , 1985 .

[9]  L. W. Schmerr,et al.  A multigaussian ultrasonic beam model for high performance simulations on a personal computer , 2000 .

[10]  Byron Newberry,et al.  A paraxial theory for the propagation of ultrasonic beams in anisotropic solids , 1989 .

[11]  R. Roberts.  Ultrasonic beam transmission at the interface between an isotropic and a transversely isotropic solid half-space , 1988 .

[12]  D. Thompson,et al.  Review of Progress in Quantitative Nondestructive Evaluation , 1982 .

[13]  Reconstruction of a Piston Transducer Beam Using Multi-Gaussian Beams (MGB) and Its Applications , 1998 .

[14]  Pierre Calmon,et al.  Calculation of Wideband Ultrasonic Fields Radiated by Immersed Transducers into Solids Through Curved Interfaces , 1997 .

[15]  Ieee Microwave Theory,et al.  Quasioptical systems : Gaussian beam quasioptical propagation and applications , 1998 .

[16]  Alan Jeffrey,et al.  Handbook of mathematical formulas and integrals , 1995 .

[17]  V. Červený,et al.  Seismic Ray Theory , 2001, Encyclopedia of Solid Earth Geophysics.

[18]  Lester W. Schmerr,et al.  Ultrasonic beam models: An edge element approach , 1998 .