Ultrasonic field modeling: A comparison of analytical, semi-analytical, and numerical techniques

Tribikram Kundu, Dominique Placko, Ehsan Kabiri Rahani, Tamaki Yanagita, Cac Minh Dao

Research output: Contribution to journalArticlepeer-review

62 Scopus citations


Modeling ultrasonic fields in front of a transducer in the presence and absence of a scatterer is a fundamental problem that has been attempted by different techniques: analytical, semi-analytical, and numerical. However, a comprehensive comparison study among these techniques is currently missing in the literature. The objective of this paper is to make this comparison for different ultrasonic field modeling problems with various degrees of difficulty. Four fundamental problems are considered: a flat circular transducer, a flat square transducer, a circular concave transducer, and a point focused transducer (concave lens) in the presence of a cavity. The ultrasonic field in front of a finite-sized transducer can be obtained by Huygens-Fresnel superposition principle that integrates the contributions of several point sources distributed on the transducer face. This integral which is also known as the Rayleigh integral or Rayleigh-Sommerfeld integral (RSI) can be evaluated analytically for obtaining the pressure field variation along the central axis of the transducer for simple geometries, such as a flat circular transducer. The semi-analytical solution is a newly developed mesh-free technique called the distributed point source method (DPSM). The numerical solution is obtained from finite element analysis. Note that the first three problems study the effect of the transducer size and shape, whereas the fourth problem computes the field in presence of a scatterer.

Original languageEnglish (US)
Article number5610565
Pages (from-to)2795-2807
Number of pages13
JournalIEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control
Issue number12
StatePublished - Dec 2010

ASJC Scopus subject areas

  • Instrumentation
  • Acoustics and Ultrasonics
  • Electrical and Electronic Engineering


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