OSA's Digital Library

Applied Optics

Applied Optics


  • Vol. 27, Iss. 21 — Nov. 1, 1988
  • pp: 4431–4437

Optimal binary phase-only matched filters

Michael W. Farn and Joseph W. Goodman  »View Author Affiliations

Applied Optics, Vol. 27, Issue 21, pp. 4431-4437 (1988)

View Full Text Article

Enhanced HTML    Acrobat PDF (877 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



Many spatial light modulators and computer-generated hologram techniques can very efficiently implement binary phase-only filters. At present, almost all binary phase-only filters are designed by first designing a matched spatial filter and then binarizing it. There is no theoretical basis to expect that such a filter will be optimal. This paper first develops a theory for optimal binary phase-only filters and then presents a numerical algorithm which designs the optimal binary phase-only matched filter for a given image. The filter is optimal in the matched filter sense of maximizing SNR at the output origin. Characteristics of the optimal filter compared to conventional binary phase-only filters are discussed.

© 1988 Optical Society of America

Original Manuscript: March 7, 1988
Published: November 1, 1988

Michael W. Farn and Joseph W. Goodman, "Optimal binary phase-only matched filters," Appl. Opt. 27, 4431-4437 (1988)

Sort:  Author  |  Year  |  Journal  |  Reset  


  1. A. VanderLugt, “Signal Detection by Complex Spatial Filtering,” IEEE Trans. Inf. Theory IT-10, 139 (1964). [CrossRef]
  2. G. G. Lendaris, G. L. Stanley, “Diffraction-Pattern Sampling for Automatic Pattern Recognition,” Proc. IEEE 58, 198 (1979). [CrossRef]
  3. K. Johnson, A Review of Spatial Light Modulators and Their Applications, Short Course at O-E/Lase ’88 SPIE Conference, Los Angeles (1988).
  4. H. Farhoosh, M. R. Feldman, S. H. Lee, C. C. Guest, Y. Fainman, R. Eschbach, “Comparison of Binary Encoding Schemes for Electron-Beam Fabrication of Computer Generated Holograms,” Appl. Opt. 26, 4361 (1987). [CrossRef] [PubMed]
  5. S. H. Lee, “Computer Generated Holography: An Introduction,” Appl. Opt. 26, 4350 (1987). [CrossRef] [PubMed]
  6. S. M. Arnold, “Electron Beam Fabrication of Computer-Generated Holograms,” Opt. Eng. 24, 803 (1985). [CrossRef]
  7. H. Dammann, “Synthetic Digital-Phase Gratings—Design, Features, Applications,” Proc. Soc. Photo-Opt. Instrum. Eng. 437, 72 (1983).
  8. A. V. Oppenheim, J. S. Lim, “The Importance of Phase in Signals,” Proc. IEEE 69, 529 (1981). [CrossRef]
  9. R. R. Kallman, “Direct Construction of Phase-Only Filters,” Appl. Opt. 26, 5200 (1987). [CrossRef] [PubMed]
  10. R. R. Kallman, “Optimal Low-Noise Phase-Only and Binary Phase-Only Optical Correlation Filters for Threshold Detectors,” Appl. Opt. 25, 4216 (1986). [CrossRef] [PubMed]
  11. D. Casasent, W. A. Rozzi, “Computer-Generated and Phase-Only Synthetic Discriminant Function Filters,” Appl. Opt. 25, 3767 (1986). [CrossRef] [PubMed]
  12. X. Y. Su, G. S. Zhang, L. R. Guo, “Phase-Only Composite Filter,” Opt. Eng. 26, 520 (1987). [CrossRef]
  13. J. Rosen, J. Shamir, “Distortion Invariant Pattern Recognition with Phase Filters,” Appl. Opt. 26, 2315 (1987). [CrossRef] [PubMed]
  14. H. O. Bartelt, “Applications of the Tandem Component: an Element with Optimum Light Efficiency,” Appl. Opt. 24, 3811 (1985). [CrossRef] [PubMed]
  15. J. L. Horner, H. O. Bartelt, “Two-Bit Correlation,” Appl. Opt. 24, 2889 (1985). [CrossRef] [PubMed]
  16. J. L. Horner, P. D. Gianino, “Applying the Phase-Only Filter Concept to the Synthetic Discriminant Function Correlation Filter,” Appl. Opt. 24, 851 (1985). [CrossRef] [PubMed]
  17. J. L. Horner, P. D. Gianino, “Additional Properties of the Phase-Only Correlation Filter,” Opt. Eng. 23, 695 (1984).
  18. J. L. Horner, P. D. Gianino, “Phase-Only Matched Filtering,” Appl. Opt. 23, 812 (1984). [CrossRef] [PubMed]
  19. J. L. Horner, J. R. Leger, “Pattern Recognition with Binary Phase-Only Filters,” Appl. Opt. 24, 609 (1985). [CrossRef] [PubMed]
  20. D. M. Cottrell, J. A. Davis, M. P. Schamschula, R. A. Lilly, “Multiplexing Capabilities of the Binary Phase-Only Filter,” Appl. Opt. 26, 934 (1987). [CrossRef] [PubMed]
  21. D. M. Cottrell, R. A. Lilly, J. A. Davis, T. Day, “Optical Correlator Performance of Binary Phase-Only Filters Using Fourier and Hartley Transforms,” Appl. Opt. 26, 3755 (1987). [CrossRef] [PubMed]
  22. J. A. Davis, G. M. Heissenberger, R. A. Lilly, D. M. Cottrell, M. F. Brownell, “High Efficiency Optical Reconstruction of Binary Phase-Only Filters using the Hughes Liquid Crystal Light Valve,” Appl. Opt. 26, 929 (1987). [CrossRef] [PubMed]
  23. D. Psaltis, E. G. Paek, S. S. Venkatesh, “Optical Image Correlation with a Binary Spatial Light Modulator,” Opt. Eng. 23, 698 (1984). [CrossRef]
  24. F. T. S. Yu, Optical Information Processing (Wiley, New York, 1983).
  25. B. V. K. Vijaya Kumar, Z. Bahri, “Optimality of Phase-Only Filters,” Proc. Soc. Photo-Opt. Instrum Eng. 884, (1988).
  26. R. N. Bracewell, The Fourier Transform and Its Applications (McGraw-Hill, New York, 1986).

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