OSA's Digital Library

Applied Optics

Applied Optics

APPLICATIONS-CENTERED RESEARCH IN OPTICS

  • Vol. 39, Iss. 32 — Nov. 10, 2000
  • pp: 5929–5935

Sampling of the diffraction field

Levent Onural  »View Author Affiliations


Applied Optics, Vol. 39, Issue 32, pp. 5929-5935 (2000)
http://dx.doi.org/10.1364/AO.39.005929


View Full Text Article

Enhanced HTML    Acrobat PDF (665 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

Abstract

When optical signals, like diffraction patterns, are processed by digital means the choice of sampling density and geometry is important during analog-to-digital conversion. Continuous band-limited signals can be sampled and recovered from their samples in accord with the Nyquist sampling criteria. The specific form of the convolution kernel that describes the Fresnel diffraction allows another, alternative, full-reconstruction procedure of an object from the samples of its diffraction pattern when the object is space limited. This alternative procedure is applicable and yields full reconstruction even when the diffraction pattern is undersampled and the Nyquist criteria are severely violated. Application of the new procedure to practical diffraction-related phenomena, like in-line holography, improves the processing efficiency without creating any associated artifacts on the reconstructed-object pattern.

© 2000 Optical Society of America

OCIS Codes
(050.1940) Diffraction and gratings : Diffraction
(070.6020) Fourier optics and signal processing : Continuous optical signal processing
(090.1760) Holography : Computer holography
(100.2000) Image processing : Digital image processing

History
Original Manuscript: February 18, 2000
Revised Manuscript: July 20, 2000
Published: November 10, 2000

Citation
Levent Onural, "Sampling of the diffraction field," Appl. Opt. 39, 5929-5935 (2000)
http://www.opticsinfobase.org/ao/abstract.cfm?URI=ao-39-32-5929


Sort:  Author  |  Year  |  Journal  |  Reset  

References

  1. D. E. Dudgeon, R. M. Mersereau, Multidimensional Digital Signal Processing (Prentice-Hall, New York, 1984), Sec. 1.4.
  2. M. Born, E. Wolf, Principles of Optics, 6th ed. (Pergamon, New York, 1980), Chap. 8.
  3. K. Nishihara, S. Hatano, K. Nagayama, “New method of obtaining particle diameter by the fast fourier transform pattern of the in-line hologram,” Opt. Eng. 36, 2429–2439 (1997). [CrossRef]
  4. S. Belaid, D. Lebrun, C. Ozkul, “Application of two-dimensional wavelet transform to hologram analysis—visualization of glass fibers in a turbulent flame,” Opt. Eng. 36, 1947–1951 (1997). [CrossRef]
  5. L. Onural, P. D. Scott, “Digital decoding of in-line holograms,” Opt. Eng. 26, 1124–1132 (1987). [CrossRef]
  6. H. M. Ozaktas, O. Arikan, M. A. Kutay, G. Bozdaği, “Digital computation of the fractional Fourier transform,” IEEE Trans. Sig. Process. 44, 2141–2150 (1996). [CrossRef]
  7. H. M. Ozaktas, M. A. Kutay, D. Mendlovic, “Introduction to the fractional Fourier transform and its applications,” in Advances in Imaging and Electron Physics, P. W. Hawkes, ed. (Academic, San Diego, Calif., 1999), Vol. 106, Chap. 4, pp. 239–291. [CrossRef]
  8. H. M. Ozaktas, B. Barshan, D. Mendlovic, L. Onural, “Convolution, filtering, and multiplexing in fractional Fourier domains and their relation to chirp and wavelet transforms,” J. Opt. Soc. Am. A 11, 547–559 (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.

Figures

Fig. 1 Fig. 2 Fig. 3
 
Fig. 4
 

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited