References to Cite

Continuous Waves with Phased Array Using Angular Spectrum Approach with Rectangular Transducer

R. J. McGough. Rapid calculations of time-harmonic nearfield pressures produced by rectangular pistons. J. Acoust. Soc. Am. 2004;115:1934-1941.

X. Zeng and R. J. McGough. Evaluation of the angular spectrum approach for simulations of near-field pressures. J. Acoust. Soc. Am. 2008;123:68-76.

D. Chen and R. J. McGough. A 2D fast near-field method for calculating near-field pressures generated by apodized rectangular pistons. J. Acoust. Soc. Am. 2006;124:1526-1537.

BibTeX Format

@article{ rect-bibtex,
	  author = "R. J. McGough",
	  title = "Rapid calculations of time-harmonic nearfield pressures produced by rectangular pistons",
	  journal = "Journal of the Acoustical Society of America",
	  volume = "115",
	  number = "5",
	  pages = "1934-1941",
	  year = "2004" }
	  
@article{ asa-bibtex,
	  author = "X. Zeng and R. J. McGough",
	  title = "Evaluation of the angular spectrum approach for simulations of near-field pressures",
	  journal = "Journal of the Acoustical Society of America",
	  volume = "123",
	  number = "1",
	  pages = "68-76",
	  year = "2008" }
	  
@article{ fmn-bibtex,
	  author = "D. Chen and R. J. McGough",
	  title = "A 2D fast near-field method for calculating near-field pressures generated by apodized rectangular pistons",
	  journal = "Journal of the Acoustical Society of America",
	  volume = "124",
	  number = "5",
	  pages = "1526-1537",
	  year = "2008" }

Links to papers

An efficient grid sectoring method for calculations of the near-field pressure generated by a circular piston.

PDF | PubMed

Evaluation of the angular spectrum approach for simulations of near-field pressure.

PDF | PubMed

A 2D fast near-field method for calculating near-field pressures generated by apodized rectangular pistons.

PDF | PubMed

Background Information

Angular Spectrum Approach

The angular spectrum approach describes the diffraction of acoustic waves from finite apertures by superposing plane waves traveling in different directions and propagating these components in the spatial frequency domain. As opposed to integral approaches that calculate the field at each observation point, the angular spectrum approach computes the pressure field in successive planes with a two-dimensional (2D) fast Fourier transform (FFT), which speeds up these calculations significantly. The angular spectru, approach uses either the normal particle velocity or the pressure as the source, and then the spectral propagator function or the 2D Fourier transform of the spatial propagator is multiplied by the source in the spatial frequency domain to simulate the source in the spatial frequency domain to simulate the propagation of acoustic waves. The ASA paper is cited because it exaplains the method of using ASA when analyzing continuos waves.

The Fast Nearfield Method

The fast nearfield method, which converges much more rapidly than the point source superposition method or the impulse response, produces accurate numerical results in a fraction of the time required by other approaches. In addition, the FNM has been adapted to transient problems encountered in imaging applications. For time-domain problems, the FNM avoids the temporal aliasing problems associated with the impulse response approach while also providing a fast and efficient method for computing transient fields. Since the field generated by each element is exact in a linear, homogeneous medium, the user does not have to worry about controlling the error in large acoustic calculations. The FMN paper is cited because it analyzes one plane while the ASA calculates the other planes.