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Applied Optics

Applied Optics

APPLICATIONS-CENTERED RESEARCH IN OPTICS

  • Vol. 41, Iss. 29 — Oct. 10, 2002
  • pp: 6182–6186

Wavelet transforming characteristic of a lens

Liying Tan, Jing Ma, Qi Wang, and Qiwen Ran  »View Author Affiliations


Applied Optics, Vol. 41, Issue 29, pp. 6182-6186 (2002)
http://dx.doi.org/10.1364/AO.41.006182


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Abstract

Based on the wave-front filtering concept of wavelet optics, which we proposed, here we consider that the wave fronts of a light wave are filtered by the lens when the wave fronts pass through the lens. After filtering, the weight of the light field is redistributed, and a Gaussian frequency-modulated complex-valued wavelet function is introduced with the weight function. Subsequent analysis indicates that the lens has a wavelet-transforming characteristic and that the introduction of a Gaussian frequency-modulated complex-valued wavelet function conforms to the actual lens.

© 2002 Optical Society of America

OCIS Codes
(070.2580) Fourier optics and signal processing : Paraxial wave optics
(070.2590) Fourier optics and signal processing : ABCD transforms
(070.4560) Fourier optics and signal processing : Data processing by optical means

History
Original Manuscript: November 28, 2001
Published: October 10, 2002

Citation
Liying Tan, Jing Ma, Qi Wang, and Qiwen Ran, "Wavelet transforming characteristic of a lens," Appl. Opt. 41, 6182-6186 (2002)
http://www.opticsinfobase.org/ao/abstract.cfm?URI=ao-41-29-6182


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References

  1. C. K. Chui, An Introduction to Wavelets (Academic, San Diego, Calif., 1992), pp. 16–22.
  2. W. L. Wang, G. F. Jin, Y. B. Yan, M. X. Wu, “Image feature extraction with optical Harr wavelet transform,” Opt. Eng. 34, 1238–1242 (1995). [CrossRef]
  3. Y. Li, H. H. Szu, Y. Sheng, H. J. Caufield, “Wavelet processing and optics,” Proc. IEEE 84, 720–732 (1996). [CrossRef]
  4. P. G. Block, S. K. Rogers, D. W. Ruck, Optical wavelet transform from computer-generated holography,” Appl. Opt. 33, 5275–5278 (1994). [CrossRef] [PubMed]
  5. L. Tan, J. Ma, Q. Ran, “The elementary theory of wavelet optical diffraction,” in Conference on Lasers and Electro-Optics/Quantum Electronics and Laser Science Conference (CLEO/QELS ’99), Vol. 6 of 1999 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 2000), pp. 113–114.
  6. L. Tan, J. Ma, Q. Wang, Q. Ran, “Filtering theory and application of wavelet optics at the spatial-frequency domain,” Appl. Opt. 40, 257–260 (2001). [CrossRef]

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