OSA's Digital Library

Applied Optics

Applied Optics


  • Editor: Joseph N. Mait
  • Vol. 51, Iss. 33 — Nov. 20, 2012
  • pp: 7900–7909

Coherent optical three-dimensional spectrum-correlation processing of wave signals based on space–time integration

Vasily Ezhov  »View Author Affiliations

Applied Optics, Vol. 51, Issue 33, pp. 7900-7909 (2012)

View Full Text Article

Enhanced HTML    Acrobat PDF (788 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



The architectures of classical analog coherent optical (ACO) spectrum analyzers and correlators are not designed to process the wave signal as a whole, i.e., simultaneously in three dimensions. In this paper, the theory of ACO three-dimensional direct spectrum-correlation processing of spatial–temporal optical replicas (copies) of wave signals is discussed. In the single-stage and two-stage ACO systems, the spatial power spectrum and spatial correlation function of the wave signal (envelope) are obtained on the basis of space–time integration. The geometry of the final compressed signal in the output plane of either optical system allows one to evaluate the angle of wave arrival. The wave signal to be processed can theoretically have any form (due to autocorrelation properties of the systems) and an unlimited duration (due to time integration of wave energy and possibility of electronic subtraction of the intermediate bias terms of the time integration).

© 2012 Optical Society of America

OCIS Codes
(070.1170) Fourier optics and signal processing : Analog optical signal processing
(070.4550) Fourier optics and signal processing : Correlators
(070.4790) Fourier optics and signal processing : Spectrum analysis

ToC Category:
Fourier Optics and Signal Processing

Original Manuscript: May 29, 2012
Revised Manuscript: October 10, 2012
Manuscript Accepted: October 11, 2012
Published: November 13, 2012

Vasily Ezhov, "Coherent optical three-dimensional spectrum-correlation processing of wave signals based on space–time integration," Appl. Opt. 51, 7900-7909 (2012)

Sort:  Author  |  Year  |  Journal  |  Reset  


  1. J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, 1968).
  2. A. VanderLugt, Optical Signal Processing (Wiley, 2005).
  3. C. S. Weaver and J. W. Goodman, “A technique for optical convolving two functions,” Appl. Opt. 5, 1248–1249 (1966). [CrossRef]
  4. D. C. Beste and E. N. Leith, “An optical technique for simultaneous beamforming and cross-correlation,” IEEE Trans. Aerosp. Electron. Syst. AES-2, 376–381 (1966). [CrossRef]
  5. R. E. Williams and K. VonBieren, “Combined beam forming and cross-correlation of broadband signals from a multidimensional array using coherent optics,” Appl. Opt. 10, 1386–1392 (1971). [CrossRef]
  6. C. E. Thomas, “Optical spectrum analysis of large space bandwidth signals,” Appl. Opt. 5, 1782–1790 (1966). [CrossRef]
  7. R. A. Sprague and Ch. L. Koliopulos, “Time integrating acoustooptic correlator,” Appl. Opt. 15, 89–92 (1976). [CrossRef]
  8. T. M. Turpin, “Time integrating optical processors,” Proc. SPIE 154, 196–203 (1978).
  9. T. R. Bader, “Acoustooptic spectrum analysis: a high performance hybrid technique,” Appl. Opt. 18, 1668–1672 (1979). [CrossRef]
  10. D. Psaltis and D. Casasent, “Time- and space-integrating spectrum analyzer,” Appl. Opt. 18, 3203–3204 (1979). [CrossRef]
  11. V. Ezhov, “The three-dimensional coherent optical correlator with generalized hologram for implementing the time compression of a spatial–temporal spectrum of the wave process,” in Proceedings of the 7th International Conference HOLOEXPO-2010 (Bauman Moscow State Technical University, 2010), pp. 416–421, in Russian.
  12. The discrete aperture leads simply to a spatial multiplication of the spectrum, corresponding to a continuous aperture (without changing the shape of the spectrum).
  13. All necessary information is contained in the (+1)st diffraction order of the light, corresponding to the second term of the input optical signal 1+exp[i2π(…)]+exp[−i2π(…)], which describes a whole real-valued amplitude light modulation.
  14. S. Tay, P.-A. Blanche, R. Voorakaranam, A. Tunc, W. Lin, S. Rokutanda, T. Gu, D. Flores, P. Wang, G. Li, P. Hilaire, J. Thomas, R. Norwood, M. Yamamoto, and N. Peyghambarian, “An updatable holographic 3D display,” Nature 451, 694–698 (2008). [CrossRef]
  15. P. Q. Thai and A. Alphones, “Hybrid optical beam-former in receiver mode,” Opt. Photon. J. 1, 130–136 (2011). [CrossRef]
  16. T. Pertsch, T. Zentgraf, U. Peschel, A. Brauer, and F. Lederer, “Beam steering in waveguide arrays,” Appl. Phys. Lett. 80, 3247–3249 (2002). [CrossRef]
  17. V. Ezhov, “Coherent optical correlator with space–time integration for radio astronomy,” in Proceedings of the 4th All-Union School on Optical Information Processing (Holography Research Council of USSR Academy of Sciences, 1984), pp. 270–271, in Russian.

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.

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited