title: Extension of the angular spectrum method to calculate pressure from a spherically curved acoustic source.
abstract: The angular spectrum method is an accurate and computationally efficient method for modeling acoustic wave propagation. The use of the typical 2D fast Fourier transform algorithm makes this a fast technique but it requires that the source pressure (or velocity) be specified on a plane. Here the angular spectrum method is extended to calculate pressure from a spherical transducer-as used extensively in applications such as magnetic resonance-guided focused ultrasound surgery-to a plane. The approach, called the Ring-Bessel technique, decomposes the curved source into circular rings of increasing radii, each ring a different distance from the intermediate plane, and calculates the angular spectrum of each ring using a Fourier series. Each angular spectrum is then propagated to the intermediate plane where all the propagated angular spectra are summed to obtain the pressure on the plane; subsequent plane-to-plane propagation can be achieved using the traditional angular spectrum method. Since the Ring-Bessel calculations are carried out in the frequency domain, it reduces calculation times by a factor of approximately 24 compared to the Rayleigh-Sommerfeld method and about 82 compared to the Field II technique, while maintaining accuracies of better than 96% as judged by those methods for cases of both solid and phased-array transducers.
authors.affiliation: Department of Bioengineering, University of Utah, 72 South Central Campus Drive, Room 2646, Salt Lake City, Utah 84112, USA. urvivyas@gmail.com
authors.forename: Urvi
authors.initials: U
authors.lastname: Vyas
authors.forename: Douglas A
authors.initials: DA
authors.lastname: Christensen
mesh_terms: D000465:Algorithms; D004867:Equipment Design; D005583:Fourier Analysis; D053783:Magnetic Resonance Imaging, Interventional; D008962:Models, Theoretical; D009038:Motion; D011312:Pressure; D012815:Signal Processing, Computer-Assisted; D013016:Sound; D014160:Transducers, Pressure; D059708:Ultrasonic Surgical Procedures; D014465:Ultrasonics / Q000295:instrumentation