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Journal of the Optical Society of America A

Journal of the Optical Society of America A


  • Vol. 16, Iss. 10 — Oct. 1, 1999
  • pp: 2425–2438

Modified minimum-distance criterion for blended random and nonrandom encoding

Markus Duelli, Matthew Reece, and Robert W. Cohn  »View Author Affiliations

JOSA A, Vol. 16, Issue 10, pp. 2425-2438 (1999)

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Two pixel-oriented methods for designing Fourier transform holograms—pseudorandom encoding and minimum-distance encoding—usually produce higher-fidelity reconstructions when combined than those produced by each method individually. In previous studies minimum-distance encoding was defined as the mapping from the desired complex value to the closest value produced by the modulator. This method is compared with a new minimum-distance criterion in which the desired complex value is mapped to the closest value that can be realized by pseudorandom encoding. Simulations and experimental measurements using quantized phase and amplitude modulators show that the modified approach to blended encoding produces more faithful reconstructions than those of the previous method.

© 1999 Optical Society of America

OCIS Codes
(030.6600) Coherence and statistical optics : Statistical optics
(070.2580) Fourier optics and signal processing : Paraxial wave optics
(090.1760) Holography : Computer holography
(230.6120) Optical devices : Spatial light modulators

Original Manuscript: December 7, 1998
Revised Manuscript: May 24, 1999
Manuscript Accepted: May 24, 1999
Published: October 1, 1999

Markus Duelli, Matthew Reece, and Robert W. Cohn, "Modified minimum-distance criterion for blended random and nonrandom encoding," J. Opt. Soc. Am. A 16, 2425-2438 (1999)

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  1. N. C. Gallagher, B. Liu, “Method for computing kinoforms that reduces image reconstruction error,” Appl. Opt. 12, 2328–2335 (1973). [CrossRef] [PubMed]
  2. H. Stark, W. C. Catino, J. L. LoCicero, “Design of phase gratings by generalized projections,” J. Opt. Soc. Am. A 8, 566–571 (1991). [CrossRef]
  3. M. P. Dames, R. J. Dowling, P. McKee, D. Wood, “Efficient optical elements to generate intensity weighted spot arrays: design and fabrication,” Appl. Opt. 30, 2685–2691 (1991). [CrossRef] [PubMed]
  4. J. Bengtsson, “Kinoform design with an optimal-rotation-angle method,” Appl. Opt. 33, 6879–6884 (1994). [CrossRef] [PubMed]
  5. E. G. Johnson, M. A. Abushagur, “Microgenetic-algorithm optimization methods applied to dielectric gratings,” J. Opt. Soc. Am. A 12, 1152–1160 (1995). [CrossRef]
  6. J. N. Mait, “Understanding diffractive optic design in the scalar domain,” J. Opt. Soc. Am. A 12, 2145–2158 (1995). [CrossRef]
  7. J. N. Mait, “Diffractive beauty,” Opt. Photon. News 9, 21–25 (November1998). [CrossRef]
  8. R. W. Cohn, M. Liang, “Pseudorandom phase-only encoding of real-time spatial light modulators,” Appl. Opt. 35, 2488–2498 (1996). [CrossRef] [PubMed]
  9. R. W. Cohn, A. A. Vasiliev, W. Liu, D. L. Hill, “Fully complex diffractive optics via patterned diffuser arrays,” J. Opt. Soc. Am. A 14, 1110–1123 (1997). [CrossRef]
  10. B. R. Brown, A. W. Lohmann, “Complex spatial filter,” Appl. Opt. 5, 967–969 (1966). [CrossRef] [PubMed]
  11. W.-H. Lee, “Computer-generated holograms: techniques and applications,” in Progress in Optics, E. Wolf, ed. (Elsevier, Amsterdam, 1978), Vol. 16, pp. 119–231.
  12. W. J. Dallas, “Computer-generated holograms,” in The Computer in Optical Research, B. R. Frieden, ed. (Springer, Berlin, 1980), Chap. 6, pp. 291–366.
  13. R. W. Cohn, L. G. Hassebrook, “Representations of fully complex functions on real-time spatial light modulators,” in Optical Information Processing, F. T. S. Yu, S. Jutamulia, eds. (Cambridge U. Press, Cambridge, UK, 1998), Chap. 15, pp. 396–432.
  14. R. W. Cohn, W. Liu, “Pseudorandom encoding of fully complex modulation to bi-amplitude phase modulators,” in Diffractive Optics and Micro-optics, Vol. 5 of 1996 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1996), pp. 237–240.
  15. L. G. Hassebrook, M. E. Lhamon, R. C. Daley, R. W. Cohn, M. Liang, “Random phase encoding of composite fully complex filters,” Opt. Lett. 21, 272–274 (1996). [CrossRef] [PubMed]
  16. R. W. Cohn, M. Liang, “Approximating fully complex spatial modulation with pseudorandom phase-only modulation,” Appl. Opt. 33, 4406–4415 (1994). [CrossRef] [PubMed]
  17. R. D. Juday, “Optimal realizable filters and the minimum Euclidean distance principle,” Appl. Opt. 32, 5100–5111 (1993). [CrossRef] [PubMed]
  18. R. W. Cohn, “Pseudorandom encoding of fully complex functions onto amplitude coupled phase modulators,” J. Opt. Soc. Am. A 15, 868–883 (1998). [CrossRef]
  19. J. P. Kirk, A. L. Jones, “Phase-only complex-valued spatial filter,” J. Opt. Soc. Am. 61, 1023–1028 (1971). [CrossRef]
  20. L. B. Lesem, P. M. Hirsch, J. A. Jordon, “The kinoform: a new wavefront reconstruction device,” IBM J. Res. Dev. 13, 150–155 (1969). [CrossRef]
  21. J. L. Horner, P. D. Gianino, “Phase-only matched filtering,” Appl. Opt. 23, 812–816 (1984). [CrossRef] [PubMed]
  22. R. W. Cohn, M. Duelli, “Ternary pseudorandom encoding of Fourier transform holograms,” J. Opt. Soc. Am. A 16, 71–84 (1999). [CrossRef]
  23. M. W. Farn, J. W. Goodman, “Optimal maximum correlation filter for arbitrarily constrained devices,” Appl. Opt. 28, 3362–3366 (1989). [CrossRef]
  24. R. D. Juday, “Correlation with a spatial light modulator having phase and amplitude cross coupling,” Appl. Opt. 28, 4865–4869 (1989). [CrossRef] [PubMed]
  25. M. Montes-Usategui, J. Campos, I. Juvells, “Computation of arbitrarily constrained synthetic discriminant functions,” Appl. Opt. 34, 3904–3914 (1995). [CrossRef] [PubMed]
  26. R. D. Juday, J. Knopp, “HOLOMED—an algorithm for computer generated holograms,” in Optical Pattern Recognition VII, D. P. Casasent, T. Chao, eds., Proc. SPIE2752, 162–172 (1996). [CrossRef]
  27. R. W. Cohn, “Analyzing the encoding range of amplitude-phase coupled spatial light modulators,” Opt. Eng. 38, 361–367 (1999). [CrossRef]
  28. U. Krackhardt, J. N. Mait, N. Streibl, “Upper bound on the diffraction efficiency of phase-only fanout elements,” Appl. Opt. 31, 27–37 (1992). [CrossRef] [PubMed]
  29. D. J. Cho, S. T. Thurman, J. T. Donner, G. M. Morris, “Characteristics of a 128×128 liquid crystal spatial light modulator for wave-front generation,” Opt. Lett. 23, 969–971 (1998). [CrossRef]
  30. A. Bergeron, J. Gauvin, F. Gagnon, D. Gingras, H. H. Arsenault, M. Doucet, “Phase calibration and applications of a liquid-crystal spatial light modulator,” Appl. Opt. 34, 5133–5139 (1995). [CrossRef] [PubMed]
  31. M. Duelli, D. L. Hill, R. W. Cohn, “Frequency swept measurements of coherent diffraction patterns,” Appl. Opt. 37, 8131–8133 (1998). [CrossRef]
  32. The influence that is due to roll-off may at first seem to be surprisingly small, but calculating the effect of this roll-off on the nonuniformity/standard deviation of the ideally uniform spot array gives NU=4.2%. The small influence of the rolloff on NU is further explained by the fact that the simulated values of NU are generally greater than 4% and that standard deviations, rather than being additive, add as the square root of the sum of the squares.

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