New approaches to the linear propagation of acoustic fields

Abstract

New algorithms are described that provide insight into linear field propagation and offer significant reductions in computational complexity. The developments presented here include the usage of a recently developed discrete Hankel transform to implement two single step, planar propagation algorithms for baffled, radially symmetric, acoustic pressure or velocity fields; an update on the single step approaches that reduce computational complexity through geometrically determined spatial frequency limitations; and algorithms for extending to multistep propagation. Two equivalent means of introducing arbitrary medium attenuation into the above schemes are presented. Finally, a planar boundary crossing algorithm that accounts for refraction and reflection (but not multiple reflections) is added to one of the multistep propagating algorithms. The resulting algorithm is then used to examine the differences between the corresponding fields of a focused piston source operating in water and in a layered fat/liver (biomedical imaging) medium. The results yield computationally efficient algorithms that can be used for linear propagation of focused or unfocused beams in attenuating, multilayer media, and also provide the basis for a novel nonlinear propagation algorithm.

Nonlinear acoustic wave equations with fractional loss operators

“…In this section, we use the fractional versions of Euler's equation (18) and the entropy equation (29), to obtain a wave equation with fractional derivatives. Following the approximations to the second order 42 of Hamilton and Morfey 32 the fractional Euler's equation (18), can be simplified as follows:…”

“…This is the case for the BERGEN code, 13,14 the KZKTEXAS code, [15][16][17] and the angular spectrum method of Christopher and Parker. 18,19 In the case of the angular spectrum approach, the attenuation is modeled as proportional to x y , with x the angular frequency and y non-integer, allowing one to simulate attenuation in media like biological tissue. Time domain simulators can use multiple relaxation processes to approximate such attenuation both in the linear case 20 and in the nonlinear case.…”

Ultrasonic oil-film thickness measurement: An angular spectrum approach to assess performance limits

“…These plane waves, which propagate at different angles, can then be analysed separately and eventually recomposed into an ultrasonic field by an inverse angular spectrum. The use of the angular spectrum to model the propagation of acoustic fields and the output of transducers has been widely considered [6][7][8][9][10]. A number of authors have also used the angular spectrum approach in conjunction with multilayered system models.…”

Simulation of ultrasound nonlinear propagation on GPU using a generalized angular spectrum method

“…The great interest in nonlinear propagation and its applications has stimulated the development of simulation programs, capable of predicting the behavior of a large class of ultrasound waves in different tissues. The main strategies to simulate the distortion of a propagating wave are based on the finite difference approach [2] and the angular spectrum method (ASM) [3]. The former is more accurate, but requires a very long time to converge.…”