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#Taking the 2D-IFFT (two dimensional inverse [[Fourier transform]]) of the resulting data set to yield the field contour over the prediction plane.
In addition to predicting the effects of diffraction,<ref>''Cross-Sectional Measurements and Extrapolations of Ultrasonic Fields'', Waag, R.C. Campbell, J.A. Ridder, J. Mesdag, P.R., Sonics and Ultrasonics, IEEE Transactions on, Jan 1985, Volume: 32, Issue: 1, pp. 26- 35.</ref><ref>''Forward and backward projection of acoustic fields using FFT methods'', Stepanishen, P. R.; Benjamin, K. C., Acoustical Society of America, Journal, vol. 71, Apr. 1982, p. 803-812.</ref>, the model has been extended to apply to non-monochromatic cases (acoustic pulses) and to include the effects of attenuation, refraction, and dispersion. Several researchers have also extended the model to include the nonlinear effects of finite amplitude acoustic propagation (propagation in cases where sound speed is not constant but is dependent upon the instantaneous acoustic pressure).<ref>''Finite amplitude acoustic propagation modeling using the extended angular spectrum method'', Chris Vecchio and Peter Lewin, Journal of the Acoustical Society of America, JASA 95 (5), pp. 2399-2408, 1994.</ref><ref>''Acoustic Propagation Modeling Using the Extended Angular Spectrum Method'', Chris Vecchio and Peter Lewin, Proceedings of the 14th Annual International Conference IEEE Engineering in Medicine and Biology Society, 1992.</ref><ref>''New approaches to nonlinear diffractive field propagation'', P. Ted Christopher and Kevin J. Parker, Journal of the Acoustical Society of America, July 1991, Volume 90, Issue 1, pp. 488-499.</ref><ref>Modeling of nonlinear ultrasound propagation in tissue from array transducers, Roger J. Zemp, Jahangir Tavakkoli, and Richard S. C. Cobbold, Journal of the Acoustical Society of America, January 2003, Volume 113, Issue 1, pp. 139-152.</ref><ref>[http://adsabs.harvard.edu/abs/1992PhDT........59V| Finite Amplitude Acoustic Propagation Modeling Using the Extended Angular Spectrum Method]</ref>.
Backward propagation predictions can be used to analyze the surface vibration patterns of acoustic radiators such as [[ultrasonic]] [[transducers]].<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>.
==References==
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[[Category:Optics]]
[[Category:physics]]
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