Methods for Efficient Computation of the Image Field of Holographic Lenses for Sound Waves
Methods for efficient computation of the image field of acoustical holographic lenses are presented. The methods are valid for large field angles and large relative apertures and apply at short as well as at long wavelengths. Some of the techniques are based on the Kirchhoff diffraction integral, others on the boundary-diffraction-wave integral. For rapid computation of these integrals we employ three different techniques for different positions of the object and observation points: In the case in which the integrand has small variations we employ the technique of phase and amplitude approximations; in shadow boundary regions we use a uniform asymptotic technique; and in other regions we use a second order asymptotic method.
KeywordsObservation Point Phase Function Sound Wave Local Phase Amplitude Function
Unable to display preview. Download preview PDF.
- 1.H. Heier and J.J. Stamnes, Acoustical Cameras for Underwater Surveillance and Inspection, Proc. Underwater Technology Conference, Bergen, Pergamon Press (1980).Google Scholar
- 2.H. Heier, A Wide-Angle Diffraction Limited Holographic Lens System for Acoustical Imaging, in A.F. Metherell (ed.), Acoustical ImagingVol. 10, Plenum Press.Google Scholar
- 3.J.J. Stamnes and T. Gravelsæter, Image Quality and Diffraction Efficiency of Holographic Lenses for Sound Waves, in A.F. Metherell (ed.), Acoustical Imaging, Vol 10, Plenum Press.Google Scholar
- 4.Weiss and C. Scherg, An Ultrasonic Fresnel Lens Imaging System with High Lateral Resolution, Proc. Ultrasonics International, 534–539 (1979).Google Scholar
- 7.M. Born and E. Wolf, Principles of Optics, 4th ed., Pergamon, New York, Sec. 8.3.2. (1970).Google Scholar
- 8.M. Born and E. Wolf, Principles of Optics, 4th ed., Pergamon, New York, Sec. 8.9 (1970).Google Scholar
- 9.H.M. Pedersen and J.J. Stamnes, Evaluation of diffraction integrals using local phase and amplitude approximations (in preparation).Google Scholar
- 10.J.J. Stamnes, New Methods and Results in Focusing, Proc. ICO Conference on Optics in Four Dimensions, Ensenada, Mexico, American Institute of Physics, (1980).Google Scholar
- 11.J. Focke, Asymptotische Entwicklungen Mittels der Methode der Stationären Phase, Ber. Verh. Saechs. Akad. Wiss., Leipzig, 101:1–48 (1954); G. Braun, Zur Methode der Stationâ en Phase, Acta Phys. Austriaca 10:8–33 (1956); D.S. Jones and M. Kline, Asymptotic Expansion of Multiple Integrals and the Method of Stationary Phase, J. Math. Phys. 37:1–28 (1958); N. Chako, Asymptotic Expansions of Double and Multiple Integrals Occurring in Diffraction Theory, J. Inst. Maths Applics 1: 372–422 (1965).Google Scholar
- 12.J.J. Stamnes and T. Gravelsmter (in preparation).Google Scholar
- 13.L.B. Felsen and N. Marcuwitz, Radiation and Scattering of Waves, Chap. 4, Prenticesss-Hall, Inc., New Jersey (1973).Google Scholar