OSA's Digital Library

Applied Optics

Applied Optics


  • Vol. 28, Iss. 12 — Jun. 15, 1989
  • pp: 2358–2367

Nonlinear joint power spectrum based optical correlation

Bahram Javidi  »View Author Affiliations

Applied Optics, Vol. 28, Issue 12, pp. 2358-2367 (1989)

View Full Text Article

Enhanced HTML    Acrobat PDF (1410 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



A nonlinear joint transform image correlator is investigated. The Fourier transform interference intensity is thresholded to provide higher correlation peak intensity and a better defined correlation spot. Analytical expressions for the thresholded joint power spectrum are provided. The effects of nonlinearity at the Fourier plane on the correlation signals at the output plane are investigated. The correlation signals are determined in terms of nonlinear characteristics of the spatial light modulator (SLM) at the Fourier plane. We show that thresholding the interference intensity results in a sum of infinite harmonic terms. Each harmonic term is envelope modulated due to the nonlinear characteristics of the device and phase modulated by m times the phase modulation of the nonthresholded joint power spectrum. The correct phase information about the correlation signal is recovered from the first-order harmonic of the thresholded interference intensity. We show that various types of autocorrelation signal can be produced simply by varying the severity of the nonlinearity and without the need to synthesize the specific matched filter. For example, the autocorrelation signal produced by a phase-only matched filter can be obtained by selecting the appropriate nonlinearity.

© 1989 Optical Society of America

Original Manuscript: July 18, 1988
Published: June 15, 1989

Bahram Javidi, "Nonlinear joint power spectrum based optical correlation," Appl. Opt. 28, 2358-2367 (1989)

Sort:  Author  |  Year  |  Journal  |  Reset  


  1. H. K. Liu, Ed., Optical and Digital Pattern Recognition, Proc. Soc. Photo-Opt. Instrum. Eng.754, (1987).
  2. H. J. Caulfield, “Role of the Horner Efficiency in the Optimization of Spatial Filters for Optical Pattern Recognition,” Appl. Opt. 21, 4391–4392 (1982). [CrossRef] [PubMed]
  3. J. L. Horner, H. O. Bartelt, “Two-Bit Correlation,” Appl. Opt. 24, 2889–2893 (1985). [CrossRef] [PubMed]
  4. D. Psaltis, E. G. Paek, S. S. Venkatesh, “Optical Image Correlation with a Binary Spatial Light Modulator,” Opt. Eng. 23, 698–704 (1984). [CrossRef]
  5. D. Flannery et al., “Application of Binary Phase-Only Correlation to Machine Vision,” Opt. Eng. 27, 309–320 (1988). [CrossRef]
  6. D. A. Gregory, “Review of Compact Optical Correlators,” Proc. Soc. Photo-Opt. Instrum. Eng. 960, 66–85 (1988).
  7. H. Arsenault, “Performance of the Tandem Component Matched Filter for Pattern Recognition,” Opt. Commun. 65, 334–339 (1988). [CrossRef]
  8. B. Javidi, C. J. Kuo, “Joint Transform Image. Correlation Using a Binary Spatial Light Modulator at the Fourier Plane,” Appl. Opt. 27, 663–665 (1988); J. Opt. Soc. Am. A 4(13), P86 (1987). [CrossRef] [PubMed]
  9. B. Javidi, “Multifunction Nonlinear Optical Processor,” Opt. Eng. 28, August1989, Vol. 8 (1989).
  10. B. Javidi, J. L. Horner, “Single Spatial Light Modulator Joint Transform Correlator,” Appl. Opt. 28, 1027–1032 (1989). [CrossRef] [PubMed]
  11. B. Javidi, “Comparison of Binary Joint Transform Correlators and Phase-Only Matched Filter Based Correlators,” Opt. Eng. 28, 267–272 (1989). [CrossRef]
  12. C. S. Weaver, J. W. Goodman, “A Technique for Optically Convolving Two Functions,” Appl. Opt. 5, 1248–1249 (1966). [CrossRef] [PubMed]
  13. J. E. Rau, “Detection of Differences in Real Distributions,” J. Opt. Soc. Am. 56, 1490–1494 (1966). [CrossRef]
  14. W. R. Bennett, “Spectra of Quantized Signals,” Bell Syst. Tech. J. 27, 446–451 (1948).
  15. D. Middleton, “Some General Results in the Theory of Noise Through Nonlinear Devices,” Q. Appl. Math. 5, 445–498 (1948).
  16. A. Kozma, D. L. Kelly, “Spatial Filtering for Detection of Signals Submerged in Noise,” Appl. Opt. 4, 387–392 (1965). [CrossRef]
  17. A. Kozma, “Photographic Recording of Spatially Modulated Coherent Light,” J. Opt. Soc. Am. 56, 428–432 (1966). [CrossRef]
  18. J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1967).

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
Fig. 4 Fig. 5

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited