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{{Short description|Technique for modeling the propagation of a wave field}}
{{distinguish|Angular spectrum expansion}}
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In addition to predicting the effects of diffraction,<ref>{{cite journal | last1=Waag | first1=R.C. | last2=Campbell | first2=J.A. | last3=Ridder | first3=J. | last4=Mesdag | first4=P.R. | title=Cross-Sectional Measurements and Extrapolations of Ultrasonic Fields | journal=IEEE Transactions on Sonics and Ultrasonics | publisher=Institute of Electrical and Electronics Engineers (IEEE) | volume=32 | issue=1 | year=1985 | issn=0018-9537 | doi=10.1109/t-su.1985.31566 | pages=26–35| bibcode=1985ITSU...32...26W }}</ref><ref>{{cite journal | last1=Stepanishen | first1=Peter R. | last2=Benjamin | first2=Kim C. | title=Forward and backward projection of acoustic fields using FFT methods | journal=The Journal of the Acoustical Society of America | publisher=Acoustical Society of America (ASA) | volume=71 | issue=4 | year=1982 | issn=0001-4966 | doi=10.1121/1.387606 | pages=803–812| bibcode=1982ASAJ...71..803S }}</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>{{cite journal | last1=Vecchio | first1=Christopher J. | last2=Lewin | first2=Peter A. | title=Finite amplitude acoustic propagation modeling using the extended angular spectrum method | journal=The Journal of the Acoustical Society of America | publisher=Acoustical Society of America (ASA) | volume=95 | issue=5 | year=1994 | issn=0001-4966 | doi=10.1121/1.409849 | pages=2399–2408| bibcode=1994ASAJ...95.2399V }}</ref><ref>{{cite conference |conference=14th Annual International Conference of the IEEE Engineering in Medicine and Biology Society| last1=Vecchio | first1=Chris | last2=Lewin | first2=Peter A. | title=Acoustic propagation modeling using the extended angular spectrum method | publisher=IEEE | year=1992 | isbn=0-7803-0785-2 | doi=10.1109/iembs.1992.5762211 }}</ref><ref>{{cite journal | last1=Christopher | first1=P. Ted | last2=Parker | first2=Kevin J. | title=New approaches to nonlinear diffractive field propagation | journal=The Journal of the Acoustical Society of America | publisher=Acoustical Society of America (ASA) | volume=90 | issue=1 | year=1991 | issn=0001-4966 | doi=10.1121/1.401274 | pages=488–499| pmid=1880298 | bibcode=1991ASAJ...90..488C }}</ref><ref>{{cite journal | last1=Zemp | first1=Roger J. | last2=Tavakkoli | first2=Jahangir | last3=Cobbold | first3=Richard S. C. | title=Modeling of nonlinear ultrasound propagation in tissue from array transducers | journal=The Journal of the Acoustical Society of America | publisher=Acoustical Society of America (ASA) | volume=113 | issue=1 | year=2003 | issn=0001-4966 | doi=10.1121/1.1528926 | pages=139–152| pmid=12558254 | bibcode=2003ASAJ..113..139Z }}</ref><ref>{{cite thesis|bibcode=1992PhDT........59V|title= Finite Amplitude Acoustic Propagation Modeling Using the Extended Angular Spectrum Method|last=Vecchio|first=Christopher John|year=1992|type=PhD|publisher=Dissertation Abstracts International}}</ref>
Backward propagation predictions can be used to analyze the surface vibration patterns of acoustic radiators such as [[ultrasonic transducer]]s.<ref>{{cite journal | last1=Schafer | first1=Mark E. | last2=Lewin | first2=Peter A. | title=Transducer characterization using the angular spectrum method | journal=The Journal of the Acoustical Society of America | publisher=Acoustical Society of America (ASA) | volume=85 | issue=5 | year=1989 | issn=0001-4966 | doi=10.1121/1.397869 | pages=2202–2214| bibcode=1989ASAJ...85.2202S | doi-access=free }}</ref> Forward propagation can be used to predict the influence of inhomogeneous, nonlinear media on acoustic transducer performance.<ref>{{cite journal | last1=Vecchio | first1=Christopher J. | last2=Schafer | first2=Mark E. | last3=Lewin | first3=Peter A. | title=Prediction of ultrasonic field propagation through layered media using the extended angular spectrum method | journal=Ultrasound in Medicine & Biology | publisher=Elsevier BV | volume=20 | issue=7 | year=1994 | issn=0301-5629 | doi=10.1016/0301-5629(94)90109-0 | pages=611–622| pmid=7810021 }}</ref>
==See also==
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