OSA's Digital Library

Applied Optics

Applied Optics


  • Vol. 37, Iss. 29 — Oct. 10, 1998
  • pp: 6911–6913

Analysis of the fractional Hilbert transform

Jeffrey A. Davis, Dylan E. McNamara, and Don M. Cottrell  »View Author Affiliations

Applied Optics, Vol. 37, Issue 29, pp. 6911-6913 (1998)

View Full Text Article

Enhanced HTML    Acrobat PDF (66 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



The Hilbert transform is of interest for image-processing applications because it forms an image that is edge enhanced relative to an input object. Recently a fractional Hilbert transform was introduced that can select which edges are enhanced and to what degree the edge enhancement occurs. Although experimental results of this selective edge enhancement were presented, there was no explanation of this phenomenon. We analyze a one-dimensional fractional Hilbert transform acting on a one-dimensional rectangle function and show how it produces an output image that is selectively edge enhanced.

© 1998 Optical Society of America

OCIS Codes
(070.0070) Fourier optics and signal processing : Fourier optics and signal processing
(070.2590) Fourier optics and signal processing : ABCD transforms
(070.6110) Fourier optics and signal processing : Spatial filtering
(100.0100) Image processing : Image processing
(100.2980) Image processing : Image enhancement
(100.5010) Image processing : Pattern recognition
(110.6980) Imaging systems : Transforms
(120.2440) Instrumentation, measurement, and metrology : Filters
(200.3050) Optics in computing : Information processing

Original Manuscript: December 8, 1997
Revised Manuscript: June 3, 1998
Published: October 10, 1998

Jeffrey A. Davis, Dylan E. McNamara, and Don M. Cottrell, "Analysis of the fractional Hilbert transform," Appl. Opt. 37, 6911-6913 (1998)

Sort:  Author  |  Year  |  Journal  |  Reset  


  1. R. B. Bracewell, The Fourier Transform and Its Application (McGraw-Hill, New York, 1965), Chap. 12.
  2. A. W. Lohmann, D. Mendlovic, Z. Zalevsky, “Fractional Hilbert transform,” Opt. Lett. 21, 281–283 (1996). [CrossRef] [PubMed]
  3. A. W. Lohmann, E. Tepichin, J. G. Ramirez, “Optical implementation of the fractional Hilbert transform for two-dimensional objects,” Appl. Opt. 36, 6620–6626 (1997). [CrossRef]
  4. J. A. Davis, D. M. Cottrell, R. P. Tiangco, “Analysis of the phase-only filter,” in Optical Pattern Recognition VI, D. P. Casasent, T. H. Chao, eds., Proc. SPIE2490, 77–87 (1994). [CrossRef]

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.


Fig. 1 Fig. 2 Fig. 3

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited