Angular spectrum method: Difference between revisions

Revision as of 05:35, 16 August 2019

Revision as of 23:57, 10 June 2020

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The '''angular spectrum method''' is a technique for modeling the propagation of a wave field. This technique involves expanding a complex wave field into a summation of infinite number of [[plane wave]]s. Its mathematical origins lie in the field of [[Fourier Opticsoptics]]<ref>''Digital Picture Processing'', 2nd edition 1982, Azriel Rosenfeld, Avinash C. Kak, {{ISBN|0-12-597302-0}}, Academic Press, Inc.</ref><ref>''Linear Systems, Fourier Transforms, and Optics'' (Wiley Series in Pure and Applied Optics) Jack D. Gaskill</ref><ref>''Introduction to Fourier Optics'', Joseph W. Goodman.</ref> but it has been applied extensively in the field of [[ultrasound]]. The technique can predict an acoustic pressure field distribution over a plane, based upon knowledge of the pressure field distribution at a parallel plane. Predictions in both the forward and backward propagation directions are possible.<ref>[http://www.egr.msu.edu/~fultras-web/background/asa.php ''Angular Spectrum Approach'', Robert J. McGough]</ref>

Modeling the diffraction of a CW (continuous wave), monochromatic (single frequency) field involves the following steps:

# Sampling the complex (real and imaginary) components of a pressure field over a grid of points lying in a cross-sectional plane within the field.

# Taking the 2D-[[Fast Fourier transform|FFT]] (two dimensional [[Fourier Transformtransform]]) of the pressure field contour - this will decompose the field into a 2D "angular spectrum" of component plane waves each traveling in a unique direction.

# Multiplying each point in the 2D-FFT by a propagation term which accounts for the phase change that each plane wave will undergo on its journey to the prediction plane.

# Taking the 2D-IFFT (two dimensional inverse [[Fourier transform]]) of the resulting data set to yield the field contour over the prediction plane.

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Backward propagation predictions can be used to analyze the surface vibration patterns of acoustic radiators such as [[ultrasonic transducer]]s.<ref>''Transducer Characterization using the Angular Spectrum Method'', M.E. Schafer and P.A. Lewin, J. Acoust. Soc. Am. 85:5, 2202-2214, 1989.</ref> Forward propagation can be used to predict the influence of inhomogeneous, nonlinear media on acoustic transducer performance.<ref>''Prediction of ultrasonic field propagation through layered media using the extended angular spectrum method'', Chris Vecchio, Mark Schafer, Peter Lewin, Ultrasound Med Biol. 1994;20(7):611-22.</ref>

==See also==

* [[Weyl expansion]]

==References==

{{reflist}}