OSA's Digital Library

Applied Optics

Applied Optics

APPLICATIONS-CENTERED RESEARCH IN OPTICS

  • Vol. 39, Iss. 35 — Dec. 10, 2000
  • pp: 6573–6586

Interferometric optical Fourier-transform processor for calculation of selected spatial frequencies

Pierre M. Lane and Michael Cada  »View Author Affiliations


Applied Optics, Vol. 39, Issue 35, pp. 6573-6586 (2000)
http://dx.doi.org/10.1364/AO.39.006573


View Full Text Article

Enhanced HTML    Acrobat PDF (184 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

Abstract

A novel interferometric optical Fourier-transform processor is presented that calculates the complex-valued Fourier transform of an image at preselected points on the spatial-frequency plane. The Fourier spectrum of an arbitrary input image is interfered with that of a reference image in a common-path interferometer. Both the real and the imaginary parts of the complex-valued spectrum are determined. The source and the reference images are easily matched to guarantee good fringe visibility. At least six interferograms are postprocessed to extract the real and the imaginary parts of the Fourier spectrum at preselected points. The proposed hybrid optical–digital technique is computationally appropriate when the number of desired spatial frequencies is small compared with the number of pixels in the image. When the number of desired points is comparable with the number of image pixels, a conventional or pruned two-dimensional fast Fourier transform is more appropriate. The number of digital operations required by the hybrid optical–digital Fourier processor is proportional to the number of desired spatial frequencies rather than the number of pixels in the image. The points may be regularly distributed over the spatial-frequency plane or concentrated in one or several irregularly shaped regions of interest. The interferometric optical Fourier processor is demonstrated in a moving-object trajectory estimation system. The system successfully estimates the trajectory of multiple objects moving over both stationary and white-noise backgrounds. A comparison of performance was made with all-digital computation. With everything else equal, our hybrid optical–digital calculation was more than 3 orders of magnitude faster.

© 2000 Optical Society of America

OCIS Codes
(070.0070) Fourier optics and signal processing : Fourier optics and signal processing

History
Original Manuscript: March 27, 2000
Revised Manuscript: August 22, 2000
Published: December 10, 2000

Citation
Pierre M. Lane and Michael Cada, "Interferometric optical Fourier-transform processor for calculation of selected spatial frequencies," Appl. Opt. 39, 6573-6586 (2000)
http://www.opticsinfobase.org/ao/abstract.cfm?URI=ao-39-35-6573


Sort:  Author  |  Year  |  Journal  |  Reset  

References

  1. J. W. Cooley, J. W. Tukey, “An algorithm for the machine calculation of complex Fourier series,” Math. Comput. 19, 297–301 (1965). [CrossRef]
  2. J. D. Markel, “FFT pruning,” IEEE Trans. Acoust. Speech Signal Process. AU-19, 305–311 (1971).
  3. T. Smit, M. R. Smith, S. T. Nichols, “Efficient sinc function interpolation technique for center padded data,” IEEE Trans. Acoust. Speech Signal Process. 38, 1512–1517 (1990). [CrossRef]
  4. K. S. Knudsen, L. T. Bruton, “Moving object detection and trajectory estimation in the transform/spatiotemporal mixed domain,” in Proceedings of the 1992 IEEE International Conference on Acoustics, Speech, and Signal Processing, San Francisco, March 1992 (Institute of Electrical and Electronic Engineers, New York, 1992), Vol. 3, pp. 505–508.
  5. K. S. Knudsen, L. T. Bruton, “Moving object nonlinear trajectory estimation in the transform/spatiotemporal mixed domain,” in Proceedings of the 1992 IEEE Custom Integrated Circuits Conference, San Diego, May 1992 (Institute of Electrical and Electronic Engineers, New York, 1992), Vol. 5, pp. 2481–2484.
  6. T. M. Turpin, “Spectrum analysis using optical processing,” Proc. IEEE 69, 79–92 (1981). [CrossRef]
  7. M. King, W. R. Bennett, L. B. Lambert, M. Arm, “Real-time electro-optical signal processors with coherent detection,” Appl. Opt. 6, 1367–1375 (1967). [CrossRef] [PubMed]
  8. H. R. Carleton, W. T. Maloney, G. Meltz, “Collinear heterodyning in optical processors,” Proc. IEEE 57, 769–775 (1969). [CrossRef]
  9. A. VanderLugt, “Interferometric spectrum analyzer,” Appl. Opt. 33, 2770–2779 (1981).
  10. C. C. Aleksoff, N. S. Subotic, “Compact real-time interferometric Fourier transform processors,” in Optical Information Processing Systems and Architectures II, B. Javidi, ed., Proc. SPIE1347, 427–440 (1990). [CrossRef]
  11. A. VanderLugt, Optical Signal Processing (Wiley, New York, 1992).
  12. W. P. Linnik, “A simple interferometer for the investigation of optical systems,” C. R. Acad. Sci. URSS 5, 208–210 (1933) (in Russian).
  13. E. C. Tam, S. W. Tannone, F. T. S. Yu, D. A. Gregory, “Closed-loop binary phase correction of an LCTV using a point diffraction interferometer,” IEEE Photon. Technol. Lett. 2, 143–146 (1990). [CrossRef]
  14. Y. Zhang, E. Kanterakis, A. Katz, J.-M. Wang, “Optoelectronic wavelet processors based on Smartt interferometry,” Appl. Opt. 33, 5279–5286 (1994). [CrossRef] [PubMed]
  15. P. M. Lane, M. Cada, “An optical Fourier processor and point-diffraction interferometer for moving object trajectory estimation,” Appl. Opt. 38, 4306–4315 (1999). [CrossRef]
  16. D. Malacara, Optical Shop Testing, 2nd ed. (Wiley, New York, 1991).
  17. H. Kadono, M. Ogusu, S. Toyooka, “Phase shifting common path interferometer using a liquid-crystal phase modulator,” Opt. Commun. 110, 391–400 (1994). [CrossRef]
  18. C. R. Mercer, K. Creath, “Liquid-crystal point-diffraction interferometer,” Opt. Lett. 19, 916–918 (1994). [CrossRef] [PubMed]
  19. C. R. Mercer, K. Creath, “Liquid-crystal point-diffraction interferometer for wave-front measurements,” Appl. Opt. 35, 1633–1642 (1996). [CrossRef] [PubMed]
  20. P. M. Lane, “The complex-valued optical Fourier transform and its application to moving-object trajectory estimation,” Ph.D. dissertation (Dalhousie University, Halifax, N.S., 1999).
  21. A. V. Oppenheim, R. W. Schafer, Digital Signal Processing (Prentice-Hall, Englewood Cliffs, N.J., 1975).
  22. G. Strang, T. Nguyen, Wavelets and Filter Banks (Wellesley-Cambridge Press, Wellesley, Mass., 1996).
  23. K. S. Knudsen, L. T. Bruton, “Recursive pruning of the 2-D DFT with 3-D signal processing applications,” IEEE Trans. Signal Process. 41, 1340–1356 (1993). [CrossRef]
  24. K. S. Knudsen, “Multidimensional mixed domain signal processing,” Ph.D. dissertation (University of Calgary, Calgary, Al., 1992).
  25. K. S. Knudsen, L. T. Bruton, “Mixed domain filtering of multidimensional signals,” IEEE Trans. Circuits Syst. Video Technol. 1, 260–268 (1991). [CrossRef]
  26. K. S. Knudsen, L. T. Bruton, “Transform/spatiotemporal mixed domain moving object tracking and enhancement,” in Proceedings of the 1993 European Conference on Circuit Theory and Design, Davos, Switzerland, August 1993 (Elsevier, Amsterdam, 1993), pp. 589–594.
  27. P. M. Lane, K. S. Knudsen, M. Cada, “Moving object trajectory estimation using an optical Fourier processor,” in 1998 International Conference on Applications of Photonic Technology, G. A. Lampropoulos, ed., Proc. SPIE3491, 939–943 (1998).
  28. L. J. Hornbeck, “Digital light processing and MEMS: timely convergence for a bright future (invited plenary paper),” in Micromaching and Microfabrication Process Technology, K. W. Markus, ed., Proc. SPIE2639, p. 2 (abstract only), full paper available from Texas Instruments, Dallas, Tex., 1995.

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