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Optics Letters

| RAPID, SHORT PUBLICATIONS ON THE LATEST IN OPTICAL DISCOVERIES

  • Vol. 23, Iss. 15 — Aug. 1, 1998
  • pp: 1158–1160

Deriving the integral representation of a fractional Hankel transform from a fractional Fourier transform

Li Yu, Yingyang Lu, Xiaoming Zeng, Meichun Huang, Mouzhi Chen, Wenda Huang, and Zizhong Zhu  »View Author Affiliations


Optics Letters, Vol. 23, Issue 15, pp. 1158-1160 (1998)
http://dx.doi.org/10.1364/OL.23.001158


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Abstract

We derive the integral representation of a fractional Hankel transform (FRHT) from a fractional Fourier transform. Some basic properties of the FRHT such as Parseval's theorem and its optical implementation are discussed qualitatively.

© 1998 Optical Society of America

OCIS Codes
(070.4690) Fourier optics and signal processing : Morphological transformations

Citation
Li Yu, Yingyang Lu, Xiaoming Zeng, Meichun Huang, Mouzhi Chen, Wenda Huang, and Zizhong Zhu, "Deriving the integral representation of a fractional Hankel transform from a fractional Fourier transform," Opt. Lett. 23, 1158-1160 (1998)
http://www.opticsinfobase.org/ol/abstract.cfm?URI=ol-23-15-1158


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References

  1. V. Namias, J. Inst. Math. Its Appl. 25, 241 (1980).
  2. Y. B. Karasik, Opt. Lett. 19, 769 (1993).
  3. A. W. Lohmann, J. Opt. Soc. Am. A 10, 2181 (1993).
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  9. J. Hua, L. Liu, and G. Li, Opt. Commun. 137, 11 (1997).
  10. After writing this Letter, we were informed that the FRHT had been studied by Namias.11 Using some unusual relations, Namias derived the integral representations of the FRHT directly from the eigenvalue equation of the ordinary HT.
  11. V. Namias, J. Inst. Math. Its Appl. 26, 187 (1980).
  12. L. Yu, M. Huang, M. Chen, W. Chen, W. Huang, and Z. Zhu, Opt. Lett. 23, 409 (1998).
  13. A. E. Siegman, Opt. Lett. 1, 13 (1977).
  14. W. Magnus and F. Oberhettinger, Formulas and Theorems for the Functions of Mathematical Physics (Chelsea, New York, 1954).

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