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Applied Optics

Applied Optics

APPLICATIONS-CENTERED RESEARCH IN OPTICS

  • Vol. 39, Iss. 11 — Apr. 10, 2000
  • pp: 1731–1742

Information-based optical design for binary-valued imagery

Wu-Chun Chou, Mark A. Neifeld, and Ruozhong Xuan  »View Author Affiliations


Applied Optics, Vol. 39, Issue 11, pp. 1731-1742 (2000)
http://dx.doi.org/10.1364/AO.39.001731


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Abstract

Applications such as optical data storage, optical computing, and optical interconnects require optical systems that manipulate binary-valued images. Such an optical system can be viewed as a two-dimensional array of binary communication channels. This perspective is used to motivate the use of pagewise mutual information as a metric for optical system analysis and design. Fresnel propagation and coherent imaging both are analyzed in terms of mutual-information transmission. An information-based space–bandwidth product is used to analyze the trade-off between the numerical aperture and the number of image pixels in a coherent 4f system. We propose a new merit function to facilitate information-based optical system design. Information maximization and bit-error-rate minimization both are possible with the new radially weighted encircled-energy merit function. We demonstrate the use of this new merit function through a design example and show that the information throughput is increased by 8% and the bit-error rate is reduced by 36% when compared with systems designed with traditional criteria.

© 2000 Optical Society of America

OCIS Codes
(100.2960) Image processing : Image analysis
(110.2990) Imaging systems : Image formation theory
(200.3050) Optics in computing : Information processing
(220.4830) Optical design and fabrication : Systems design

History
Original Manuscript: February 3, 1999
Revised Manuscript: July 26, 1999
Published: April 10, 2000

Citation
Wu-Chun Chou, Mark A. Neifeld, and Ruozhong Xuan, "Information-based optical design for binary-valued imagery," Appl. Opt. 39, 1731-1742 (2000)
http://www.opticsinfobase.org/ao/abstract.cfm?URI=ao-39-11-1731


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References

  1. I. McMichael, W. Christian, D. Pletcher, T. Y. Chang, J. H. Hong, “Compact holographic storage demonstration with rapid access,” Appl. Opt. 35, 2375–2379 (1996). [CrossRef] [PubMed]
  2. A. Pu, D. Psaltis, “High-density recording in photopolymer-based holographic three-dimensional disks,” Appl. Opt. 35, 2389–2398 (1996). [CrossRef] [PubMed]
  3. P. R. Haugen, S. Rychnovsky, A. Husain, L. D. Hutcheson, “Optical interconnects for high speed computing,” Opt. Eng. 25, 1076–1085 (1986). [CrossRef]
  4. L. A. Bergman, W. H. Wu, A. R. Johnston, R. Nixon, S. C. Esener, C. C. Guest, P. Yu, T. J. Drabik, M. Feldman, S. H. Lee, “Holographic optical interconnects for VLSI,” Opt. Eng. 25, 1109–1118 (1986). [CrossRef]
  5. A. A. Sawchuk, T. C. Strand, “Digital optical computing,” Proc. IEEE 72, 758–779 (1984). [CrossRef]
  6. Y. Ichioka, T. Iwaki, K. Matsuoka, “Optical information processing and beyond,” Proc. IEEE 84, 694–719 (1996). [CrossRef]
  7. D. Gabor, “Theory of communication,” Proc. IEEE 93, 429–457 (1946).
  8. D. Gabor, “Information and light,” in Progress in Optics, E. Wolf, ed. (North-Holland, Amsterdam, The Netherlands, 1961), Vol. 1. [CrossRef]
  9. D. Gabor, “Information processing with coherent light,” Opt. Acta 16, 519–533 (1969). [CrossRef]
  10. D. Gabor, “The transmission of information by coherent light. Parts I–III. Classical theory,” J. Phys. 8, 73–78, 161–163, 253–255 (1975).
  11. D. Slepian, H. O. Pollak, “Prolate spheroidal wave functions, Fourier analysis and uncertainty. I,” Bell Syst. Tech. J. 40, 43–63 (1961). [CrossRef]
  12. H. J. Landau, H. O. Pollak, “Prolate spheroidal wave functions, Fourier analysis and uncertainty. II,” Bell Syst. Tech. J. 40, 65–84 (1961). [CrossRef]
  13. H. J. Landau, H. O. Pollak, “Prolate spheroidal wave functions, Fourier analysis and uncertainty. III,” Bell Syst. Tech. J. 41, 1295–1336 (1962). [CrossRef]
  14. H. M. Ozaktas, K.-H. Brenner, A. W. Lohmann, “Interpretation of the space–bandwidth product as the entropy of distinct connection patterns in multifacet optical inter-connection architectures,” J. Opt. Soc. Am. 10, 418–422 (1997). [CrossRef]
  15. M. A. Neifeld, “Information, resolution, and space–bandwidth product,” Opt. Lett. 23, 1477–1479 (1998). [CrossRef]
  16. E. H. Linfoot, “Information theory and optical images,” J. Opt. Soc. Am. 45, 808–819 (1955). [CrossRef]
  17. B. R. Frieden, “How well can a lens system transmit entropy?” J. Opt. Soc. Am. 58, 1105–1112 (1968). [CrossRef]
  18. C. L. Fales, F. O. Huck, R. W. Samms, “Imaging system design for improved information capacity,” Appl. Opt. 23, 872–888 (1984). [CrossRef] [PubMed]
  19. F. O. Huck, C. L. Fales, N. Halyo, R. W. Samms, K. Stacy, “Image gathering and processing: information and fidelity,” J. Opt. Soc. Am. A 2, 1644–1666 (1985). [CrossRef] [PubMed]
  20. I. J. Cox, C. J. R. Sheppard, “Information capacity and resolution in an optical system,” J. Opt. Soc. Am. A 3, 1152–1158 (1986). [CrossRef]
  21. F. O. Huck, C. L. Fales, J. A. McCormick, S. K. Park, “Image-gathering system design for information and fidelity,” J. Opt. Soc. Am. A 5, 285–299 (1988). [CrossRef]
  22. C. L. Fales, “An information theory of image gathering,” Inf. Sci. (New York) 57–58, 245–285 (1991).
  23. R. Torroba, H. Rabal, B. Ruiz, “An entropy approach to light propagation,” J. Mod. Opt. 39, 1939–1946 (1992). [CrossRef]
  24. L. Carretero, A. Fimia, A. Beléndez, “Entropy-based study of imaging quality in holographic optical elements,” Opt. Lett. 19, 1355–1357 (1994). [CrossRef] [PubMed]
  25. F. O. Huck, C. L. Fales, Z. ur Rahman, Visual Communication: An Information Theory Approach (Kluwer Academic, Boston, Mass., 1997).
  26. M. A. Neifeld, W.-C. Chou, “Information-theoretic limits to the capacity of volume holographic optical memory,” Appl. Opt. 36, 514–517 (1997). [CrossRef] [PubMed]
  27. F. O. Huck, C. L. Fales, R. Alter-Gartenberg, S. K. Park, Z. ur Rahman, “Information-theoretic assessment of sampled imaging systems,” Opt. Eng. 38, 742–762 (1999). [CrossRef]
  28. S. K. Park, Z. ur Rahman, “Fidelity analysis of sampled imaging systems,” Opt. Eng. 38, 786–800 (1999). [CrossRef]
  29. C. Le Brun, E. Guillard, J. Citerne, “Communication systems interactive software (comsis): modeling of components and its application to the simulation of optical communication systems,” Appl. Opt. 37, 6059–6065 (1998). [CrossRef]
  30. S. P. Levitan, T. P. Kurzweg, P. J. Marchand, M. A. Rempel, D. M. Chiarulli, J. A. Martinez, J. M. Bridgen, C. Fan, F. B. McCormick, “Chatoyant: a computer-aided-design tool for free-space optoelectronic systems,” Appl. Opt. 37, 6078–6092 (1998). [CrossRef]
  31. G. A. Betzos, M. S. Porter, J. F. Hutton, P. A. Mitkas, “Optical storage interactive simulator (oasis): an interactive tool for the analysis of page-oriented optical memory,” Appl. Opt. 37, 6115–6126 (1998). [CrossRef]
  32. R. Alter-Gartenberg, S. K. Park, “Information as a quality metric for high-resolution imaging,” in Very High Resolution and Quality Imaging III, V. R. Algazi, A. G. Tescher, eds., Proc. SPIE3308, 16–27 (1998). [CrossRef]
  33. J. Jahns, “Concepts of optical digital computing—a survey,” Optik 57, 429–449 (1980).
  34. D. Psaltis, D. Casasent, “Optical residue arithmetic: a correlation approach,” Appl. Opt. 18, 163–171 (1979). [CrossRef] [PubMed]
  35. C. W. Stirk, “Bit error rate of optical logic: fan-in, threshold, and contrast,” Appl. Opt. 31, 5632–5641 (1992). [CrossRef] [PubMed]
  36. C. E. Shannon, “A mathematical theory of communication,” Bell Syst. Tech. J. 27, 379–423, 623–656 (1948).
  37. T. M. Cover, J. A. Thomas, Elements of Information Theory, 2nd ed. (Wiley, New York, 1991). [CrossRef]
  38. J. W. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw-Hill, New York, 1996).
  39. M.-P. Bernal, G. W. Burr, H. Coufal, M. Quintanilla, “Balancing interpixel cross talk and detector noise to optimize areal density in holographic storage systems,” Appl. Opt. 37, 5377–5385 (1998). [CrossRef]
  40. B. V. Michael, “Entropy-based depth from focus,” J. Opt. Soc. Am. A 10, 561–566 (1993). [CrossRef]
  41. B. R. Frieden, “Restoring with maximum likelihood and maximum entropy,” J. Opt. Soc. Am. 62, 511–518 (1972). [CrossRef] [PubMed]
  42. B. R. Frieden, “Restoring with maximum entropy. II. Superresolution of photographs of diffraction-blurred impulses,” J. Opt. Soc. Am. 62, 1202–1210 (1972). [CrossRef]
  43. Focus Software, ZEMAX Optical Design Program, User’s Guide, 5th ed. (Focus Software, Inc., P.O. Box 18228, Tucson, Ariz. 85731, 1996).
  44. G. W. Burr, W.-C. Chou, M. A. Neifeld, H. Coufal, J. A. Hoffnagle, C. M. Jefferson, “Experimental evaluation of user capacity in holographic data-storage systems,” Appl. Opt. 37, 5431–5443 (1998). [CrossRef]
  45. W.-C. Chou, M. A. Neifeld, “Interleaving and error correction in volume holographic memory systems,” Appl. Opt. 37, 6951–6968 (1998). [CrossRef]
  46. C. Berrou, A. Glavieux, P. Thitimajshima, “Near Shannon limit error-correcting coding and decoding: turbo-codes(1),” in IEEE International Conference on Communications, Geneva, Switzerland (Institute of Electrical and Electronics Engineers, Piscataway, N.J., 1993), pp. 1064–1070.
  47. C. Berrou, A. Glavieux, “Near optimum error correcting coding and decoding: turbo-codes,” IEEE Trans. Commun. 44, 1261–1271 (1996). [CrossRef]
  48. J. Hagenauer, E. Offer, L. Papke, “Iterative decoding of binary block and convolutional codes,” IEEE Trans. Inf. Theory 42, 429–445 (1996). [CrossRef]
  49. X. Chen, K. M. Chugg, M. A. Neifeld, “Near-optimal parallel distributed data detection for page-oriented optical memories,” IEEE J. Select. Top. Quantum Electron. 4, 866–879 (1998). [CrossRef]

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