title: Some extensions of the Gaussian beam expansion: radiation fields of the rectangular and the elliptical transducer.
abstract: A straightforward extension of Gaussian beam expansion is presented for calculation of the Fresnel field integral [J. J. Wen and M. A. Breazeale, J. Acoust. Soc. Am. 83, 1752-1756 (1988)]. The source distribution function is expanded into the superposition of a series of two-dimensional Gaussian functions. The corresponding radiation field is expressed as the superposition of these two-dimensional Gaussian beams and is then reduced to the computation of these simple functions. This treatment overcomes the limit that the shape of source is of circular axial-symmetry. The numerical examples are presented for the field of the (uniform) elliptical and the rectangular piston transducers and agree well with the results given by complicated computation.
authors.affiliation: Department of Electronic Engineering, Southeast University, Nanjing 210096, People's Republic of China. dds@seu.edu.cn
authors.forename: Desheng
authors.initials: D
authors.lastname: Ding
authors.forename: Yu
authors.initials: Y
authors.lastname: Zhang
authors.forename: Jinqiu
authors.initials: J
authors.lastname: Liu
mesh_terms: D004867:Equipment Design; D006801:Humans; D008432:Mathematical Computing; D016011:Normal Distribution; D014159:Transducers / Q000706:statistics & numerical data*; D014463:Ultrasonography / Q000295:instrumentation*