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Applied Optics

Applied Optics

APPLICATIONS-CENTERED RESEARCH IN OPTICS

  • Vol. 37, Iss. 5 — Feb. 10, 1998
  • pp: 828–833

Monochromatic electromagnetic wavelets and the Huygens principle

Yunlong Sheng, Sylvain Deschênes, and H. John Caulfield  »View Author Affiliations


Applied Optics, Vol. 37, Issue 5, pp. 828-833 (1998)
http://dx.doi.org/10.1364/AO.37.000828


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Abstract

For the first time, to our knowledge, optical diffraction is shown to be a wavelet transform with the electromagnetic wavelets. We show that the optical wavelets proposed by Onural [ Opt. Lett. 18 , 846 (1993)] are the Huygens wavelets under a Fresnel approximation, and the electromagnetic wavelets proposed by Kaiser [A Friendly Guide to Wavelets (Birkhauser, Boston, Mass., 1994)] reduce to Hyugens wavelets in the case of a monochromatic field.

© 1998 Optical Society of America

OCIS Codes
(050.1940) Diffraction and gratings : Diffraction
(100.7410) Image processing : Wavelets
(110.6980) Imaging systems : Transforms

History
Original Manuscript: June 19, 1997
Revised Manuscript: October 8, 1997
Published: February 10, 1998

Citation
Yunlong Sheng, Sylvain Deschênes, and H. John Caulfield, "Monochromatic electromagnetic wavelets and the Huygens principle," Appl. Opt. 37, 828-833 (1998)
http://www.opticsinfobase.org/ao/abstract.cfm?URI=ao-37-5-828


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References

  1. M. Born, E. Wolf, Principle of Optics, 6th ed. (Pergamon, Oxford, 1980), Chap. 3.
  2. Y. Li, H. Szu, Y. Sheng, H. J. Caulfield, “Wavelet processing and optics,” Proc. IEEE. 84, 720–732 (1996). [CrossRef]
  3. G. Strang, T. Nguyen, Wavelet and Filter Banks (Wellesley-Cambridge, Wellesley, 1996), Chap. 11.
  4. L. Onural, “Diffraction from a wavelet point of view,” Opt. Lett. 18, 846–848 (1993). [CrossRef] [PubMed]
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  6. G. Kaiser, “Wavelet electrodynamics,” Phys. Lett. A 168, 28–34 (1992). [CrossRef]
  7. G. Kaiser, A Friendly Guide to Wavelets (Birkhauser, Boston, Mass., 1994).
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  9. Y. Sheng, D. Roberge, H. Szu, “Optical wavelet transform,” Opt. Eng. 31, 1840–1845 (1992). [CrossRef]
  10. J. Lu, H. Zou, J. F. Greenleaf, “A new approach to obtain limited diffraction beams,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 42, 850–853 (1995). [CrossRef]
  11. G. Kaiser, “Remote sensing with electromagnetic and acoustic wavelets: a variational approach,” in Wavelet Applications II, H. Szu ed., Proc. SPIE2491, 399–410 (1995). [CrossRef]
  12. L. Gross, “Norm invariance of mass-zero equations under the conformal group,” J. Math. Phys. 5, 687–695 (1964). [CrossRef]

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