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Probabilistic and Stochastic Methods in Analysis, with Applications pp 383–467Cite as

Quantum holography and neurocomputer architectures

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Part of the book series: NATO ASI Series ((ASIC,volume 372))

Overview

The development of faster and more efficient computers in recent years has been driven by a seemingly unending thirst for communication, interaction, automation, control issues, information availability, and a yearning for new understanding of the self-organization principles of ourselves and our environment.The challenges of the future force us to create and study new concepts of adaptive information processing and to implement for faster communication novel computer architectures based on fundamental quantum theoretical principles.

The digital computer is extremely effective at producing precise answers to well-defined questions. The nervous system accepts fuzzy, poorly conditioned input, performs a computation that is ill-defined, and produces approximate output. The systems are thus different in essential and fundamentally irreconcilable ways. Our struggles with digital computers have taught us much about how neural computation is not done; unfortunately, they have taught us relatively little about how it is done. Part of the reason for this failure is that a large proportion of neural computation is done in an analog rather than in a digital manner.

Carver A. Mead (1989)

The actions of digital computers themselves depend vitally upon quantum effects—effects that are not, in my opinion, entirely free of difficulties inherent in the quantum theory. What is this ’vital’ quantum dependence? In modern electronic computers, the existence of discrete states is needed (say, coding the digits 0 and 1), so that it becomes a clear-cut matter when the computer is in one of these states and when in another. This is the very essence of the ’digital’ nature of computer operation. This discreteness depends ultimately on quantum mechanics.

Roger Penrose (1989)

This research was supported in part by the Institute for Mathematics and its Applications (IMA) at the University of Minnesota, with funds provided by the National Science Foundation. The author is grateful to Professors Avner Friedman, F. Alberto Grunbaum, and Willard Miller, Jr. for inviting him to participate in the IMA Summer Program 1990 on Radar and Sonar, and to Patricia V. Brick and Kaye Smith of IMA for their active assistance in producing the final version of the text.

Moreover, the author has many people to thank for giving him insights from alternate points of view. He especially wants to thank Professors Emmett N. Leith (University of Michigan at Ann Arbor) and Leonid P. Yaroslavsky (Institute of Information Transmission Problems of the Academy of Sciences of the USSR at Moscow) for technical discussions on optical holography, and to Professors Sing H. Lee (University of California at San Diego) and Jun Uozumi (Hokkaido University at Sapporo) for valuable conversations on computer-generated holography and holofractals, respectively. Finally, discussions with Professors Gheorghe Nemes (Central Institute of Physics at Bucharest) and Alexander G. Ramm (Kansas State University at Manhattan) on phase-space optics are greatly appreciated.

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Bibliography

  1. T. Allen, C. Mead, F. Faggin, and G. Gribble. Orientation-selective VLSI retina. In T. Russel Hsing, editor, Visual Communications and Image Processing’88, number 1001 in Proc. SPIE, pages 1040–1046. SPIE, 1988.

    Google Scholar 

  2. D.Z. Anderson. Coherent optical eigenstate memory. Opt Lett., 11:56–58,1986.

    Article  Google Scholar 

  3. D.Z. Anderson. Nonlinear optical neural networks: Dynamic ring oscillators. In R. Eckmiller and C. v.d. Malsburg, editors, Neural Computers,pages 417–424. Springer-Verlag, Berlin, Heidelberg, New York, London, Paris, Tokyo, 1989.

    Chapter  Google Scholar 

  4. D.Z. Anderson. Competitive and cooperative dynamics in nonlinear optical circuits. In S.F. Zornetzer, J.L. Davis, and C. Lau, editors, An Introduction to Neural and Electronic Networks, pages 349–362. Academic Press, San Diego, New York, Berkeley, Boston, London, Sydney, Tokyo, Toronto, 1990.

    Google Scholar 

  5. D.Z. Anderson and M.C. Erie. Resonator memories and optical novelty filters. Opt Eng., 26:434–444,1987. Also [6].

    Article  Google Scholar 

  6. D.Z. Anderson and M.C. Erie. Resonator memories and optical novelty filters. In Caulfield and Gheen [24], pages 585–595.

    Google Scholar 

  7. D.Z. Anderson and D.M. Lininger. Dynamic optical interconnects: Volume holograms as optical two-port operators. Appl. Opt, 26:5031–5038,1987.

    Article  Google Scholar 

  8. A. Aspect. Proposed experiment to test the nonseparability of quantum mechanics. Phys. Rev., D 14:1944–1951,1976. Also in [196], pp. 435–442.

    Google Scholar 

  9. A. Aspect. Le théorème de Bell: vingt cinq ans après. In 51ième Rencontre entre Physiciens Théoriciens et Mathématiciens, Université Louis Pasteur, Strasbourg, 1990. Institut de Recherche Mathématique Avancée.

    Google Scholar 

  10. A. Aspect. Testing quantum mechanics in optics. In 15th Congress of the International Commission for Optics: Optics in Complex Systems. International Commission for Optics, Garmisch-Partenkirchen, 1990.

    Google Scholar 

  11. A. Aspect and P. Grangier. Experiments on einstein-podolsky-rosentype correlations with pairs of visible photons. In R. Penrose and C.J. Isham, editors, Quantum Concepts in Space and Time, pages 1–15. Clarendon Press, Oxford, 1986.

    Google Scholar 

  12. A. Aspect, P. Grangier, and G. Roger. Experimental tests of realistic local theories via Bell’s theorem. Phys. Rev., 47:460–463,1981.

    Google Scholar 

  13. R. Balian. Un principe d’incertitude fort en théorie du signal ou en mécanique quantique. C.R. Acad. Sci. Paris, 292:1357–1362,1981.

    MathSciNet  Google Scholar 

  14. D.A. Baylor, T.D. Lamb, and K.-W. Yau. Responses of retinal rods to single photons. J. Physiol, 288:613–634,1979.

    Google Scholar 

  15. J.J. Benedetto. Uncertainty principle inequalities and spectrum estimation.In J.S. Byrnes and Jennifer L. Byrnes, editors, Recent Advances in Fourier Analysis and its Applications: Proceedings of the NATO Advanced Study Institute, volume 315 of NATO ASI series C: Mathematical and physical sciences, pages 143–182, Dordrecht, Boston, London, 1990. Kluwer Academic Publishers Group. Held at Il Ciocco Resort, Tuscany, Italy.

    Google Scholar 

  16. A. Berthon. Operator groups and ambiguity functions in signal processing.In J.M. Combes, A. Grossmann, and Ph. Tchamitchian, editors,Wavelets, pages 172–180. Springer-Verlag, Berlin, Heidelberg, New York, London, Paris, Tokyo, Hong Kong, 1989.

    Chapter  Google Scholar 

  17. N. Bohr. Foundations of quantum physics (1926–1932). In J. Kalckar, editor, Collected Works, volume 6. North Holland-Elsevier Science Publishers, Amsterdam, New York, Oxford, 1985.

    Google Scholar 

  18. D. Brady, X.-G. Gu, and D. Psaltis. Photorefractive crystals in optical neural computers. In Neural Networks for Optical Computing, volume 882, pages 132–136. SPIE, 1988.

    Chapter  Google Scholar 

  19. V. Braitenberg. Two visions of the cerebral cortex. In G. Palm and A. Aertsen, editors, Brain Theory, pages 81–96. Springer-Verlag, Berlin, Heidelberg, New York, London, Paris, Tokyo, Hong Kong, 1986.

    Chapter  Google Scholar 

  20. V. Braitenberg and C. Braitenberg. Geometry of orientation columns in the visual cortex. Biological Cybernetics, 33:179–186,1979.

    Article  Google Scholar 

  21. J. Brezin. Geometry and the method of Kirillov. In J. Carmona, J. Dixmier, and M. Vergne, editors, Non-Commutative Harmonic Analysis,volume 466 of Lecture Notes in Math., pages 13–25. Springer-Verlag,Berlin, Heidelberg, New York, London, Paris, Tokyo, Hong Kong, 1975.

    Chapter  Google Scholar 

  22. C.D. Cantrell, V.S. Letokhov, and A.A. Makarov. Coherent excitation of multilevel systems by laser light. In M.S. Feld and V.S. Letokhov, editors, Coherent Nonlinear Optics, pages 165–269. Springer-Verlag, Berlin, Heidelberg, New York, London, Paris, Tokyo, Hong Kong, 1980.

    Chapter  Google Scholar 

  23. P. Cartier. Quantum mechanical commutation relations and theta functions.In A. Borel and G.D. Mostow, editors, Algebraic Croups and Discontinuous Subgroups, pages 361–383, Providence, RI, 1966. Symp. in Pure Math. 9, Amer. Math. Soc.

    Chapter  Google Scholar 

  24. H.J. Caulfield and G. Gheen, editors. Optical Computing. SPIE Optical Engineering Press, Bellingham, WA, 1989.

    Google Scholar 

  25. H. Chen, R.R. Hershey, and E.N. Leith. Diffractive optics with incoherent optical systems. In Ivan Cindrich, editor, Holographic Optics: Design and Applications, volume 883, pages 147–154. SPIE, 1988.

    Chapter  Google Scholar 

  26. T.W. Cole. Fourier theory in modern imaging. In J.R Price, editor, Fourier Techniques and Applications, pages 185–199. Plenum Press, New York and London, 1985.

    Chapter  Google Scholar 

  27. G.D.Collins. Temporally and spatially incoherent methods for Fourier transform holography and optical information processing. PhD thesis, University of Michigan, Ann Arbor, MI, 1983.

    Google Scholar 

  28. R.M.J. Cotterill. The brain: An intriguing piece of condensed matter. Physica Scripta, T 13:161–168,1986.

    Article  Google Scholar 

  29. R.M.J. Cotterill. A possible role for coherence in neural networks. In R.M.J. Cotterill, editor, Computer Simulation in Brain Science, pages 164–188. Cambridge University Press, Cambridge, U.K., 1988.

    Chapter  Google Scholar 

  30. A. Cunha and E.N. Leith. One-way phase conjugation with partially coherent light and superresolution. Opt. Lett., 13:1105–1107,1988.

    Article  Google Scholar 

  31. A. Cunha and E.N. Leith. Generalized one-way phase conjugation systems. J. Optical Society of America A, B 6:1803–1812,1989.

    Article  Google Scholar 

  32. L.J. Cutrona, E.N. Leith, C.J. Palermo, and L.J. Porcello. Optical data processing and filtering systems. Trans. IRE, IT-6:386–400,1960.

    MathSciNet  Google Scholar 

  33. L.J. Cutrona, E.N. Leith, L.J. Porcello, and W.E. Vivian. On the application of coherent optical processing techniques to synthetic-aperture radar. Proc. IEEE, 54:1026–1032,1966.

    Article  Google Scholar 

  34. C. Darmet, J.P. Gauthier, and F. Gourd. Elliptic and almost hyperbolic symmetries for the Woodward ambiguity function. To appear.

    Google Scholar 

  35. J.G. Daugman. Two-dimensional spectral analysis of cortical receptive field profiles. Vision Res., 20:847–856,1980.

    Article  Google Scholar 

  36. J.G. Daugman. Uncertainty relation for resolution in space, spatial frequency,and orientation optimized by two-dimensional visual cortical filters. J. Optical Society of America A, A/2.1160–1169,1985.

    Article  Google Scholar 

  37. J.G. Daugman. Complete discrete 2-d Gabor transforms by neural networks for image analysis and compression. IEEE Trans. Acoustics, Speech, Signal Processing, T-ASSP 36:1169–1179,1988.

    Article  MATH  Google Scholar 

  38. J.G. Daugman. Relaxation neural network for complete discrete 2-d Gabor transforms. In T. Russel Hsing, editor,Visual Communications and Image Processing’88, number 1001 in Proc. SPIE, pages 1048–1061. SPIE, 1988.

    Google Scholar 

  39. J.G. Daugman. Entropy reduction and decorrelation in visual cortex by oriented neural receptive fields. IEEE Trans. Biomedical Eng., T-BME 36:107–114,1989.

    Article  Google Scholar 

  40. D.L. Donoho and P.B. Stark. Uncertainty principles and signal recovery.SIAMJ. of Applied Math., 49:906–931,1989.

    Article  MathSciNet  MATH  Google Scholar 

  41. J.E. Dowling. The Retina: An Approachable Part of the Brain. The Belknap Press of Harvard University Press, Cambridge, MA and London, 1987.

    Google Scholar 

  42. J.C. Eccles. New light on the mind-brain problem: How mental events could influence neural events. In H. Haken, editor, Complex Systems: Operational Approaches, pages 81–106. Springer-Verlag, Berlin, Heidelberg,New York, London, Paris, Tokyo, Hong Kong, 1985.

    Chapter  Google Scholar 

  43. J.C. Eccles. Evolution of the Brain: Creation of the Self. Routledge, London and New York, 1989.

    Google Scholar 

  44. E. Elachi, T. Bicknell, R.L. Jordan, and C. Wu. Spaceborne synthetic-aperture imaging radars: Applications, techniques, and technology. Proc. IEEE, 70:1174–1209,1982.

    Article  Google Scholar 

  45. N.H. Farhat, C.L. Werner, and T.H. Chu. Prospects for three-dimensional projective and tomographic imaging radar networks. Radio Science, 19:1347–1355,1984.

    Article  Google Scholar 

  46. G.W. Farnell. Measured phase distribution in the image space of a microwave lens. Can. J. Phys., 36:935–943,1958.

    Article  Google Scholar 

  47. E.J. Farrell. An introduction to matching polynomials. J. Combinat. Theory, B 27:75–86,1979.

    Google Scholar 

  48. E. Feig and C.A. Micchelli. L2-synthesis by ambiguity functions. In C.K. Chui, W. Schempp, and K. Zeller, editors, Multivariate Approximation Theory IV, pages 143–156. Birkhäuser Verlag, Basel, Boston, Berlin, 1989.

    Chapter  Google Scholar 

  49. J. Feinberg. Optical phase conjugation in photorefractive materials. In R.A. Fisher, editor, Optical Phase Conjugation, pages 417–463. Academic Press, Orlando, San Diego, New York, Austin, Boston, London, Sydney, Tokyo, Toronto, 1983.

    Chapter  Google Scholar 

  50. J. Feinberg. Applications of real-time holography. In Lloyd Huff, editor, Holography, volume 532, pages 119–135. SPIE, 1985.

    Chapter  Google Scholar 

  51. D.I. Feinstein. The hexagonal resistive network and the circular approximation.Technical Report Caltech-CS-TR-88-7, California Institute of Technology, Pasadena, CA, 1988.

    Google Scholar 

  52. D.G. Feitelson. Optical Computing. MIT Press, Cambridge, Mass., London, 1988.

    Google Scholar 

  53. M.R. Feldman and C.C. Guest. Holograms for optical interconnects for very large scale integrated circuits fabricated by electron-beam lithography. Opt Eng., 28:915–921,1989.

    Article  Google Scholar 

  54. R. Felix. When is a Kirillov orbit a linear variety? Proc. Amer. Math. Soc., 86:151–152,1982.

    Article  MathSciNet  MATH  Google Scholar 

  55. J.P. Fitch. Synthetic Aperture Radar. Springer-Verlag, Berlin, Heidelberg,New York, London, Paris, Tokyo, Hong Kong, 1988.

    Book  Google Scholar 

  56. G.B. Folland. Harmonic analysis in phase space. Annals of Mathematics Studies, 122,1989.

    Google Scholar 

  57. D. Gabor. Theory of communication. J. Inst. Elec. Eng., 93:429–457, 1946.

    Google Scholar 

  58. D. Gabor. Associative holographic memories. IBM J. Res. Develop., 13:156–159,1969.

    Article  Google Scholar 

  59. I. Gertner and R. Tolimieri. The group theoretic approach to image representation. J. Visual Communication and Image Representation, 1:67–82,1990.

    Article  Google Scholar 

  60. C.D. Godsil and I. Gutman. On the theory of the matching polynomial. J. Graph Theory, 5:137–144,1981.

    Article  MathSciNet  MATH  Google Scholar 

  61. J.W. Goodman. Optics as an interconnect technology. In H.H. Arsenault,T. Szoplik, and B. Macukow, editors, Optical Processing and Computing, pages 1–32. Academic Press, Orlando, San Diego, New York, Austin, Boston, London, Sydney, Tokyo, Toronto, 1989.

    Chapter  Google Scholar 

  62. J.W. Goodman. A short history of the field of optical computing. In B.S. Wherett and F.A.P. Tooley, editors, Optical Computing, pages 7–21. Scottish Universities Summer School in Physics Publications, Edinburgh, 1989.

    Google Scholar 

  63. P. Greguss. Manifestation of Gabor’s holographic principle in various evolutionary stages of living material. In Jingtang Ke and Ryszard J. Pryputniewicz, editors, International Conference on Holography Applications,volume 673, pages 402–411. SPIE, 1987.

    Google Scholar 

  64. P. Greguss. Nature and the holographic principle. In G. von Bally, editor, Optics in Life Sciences. Springer-Verlag, Berlin, Heidelberg, New York, London, Paris, Tokyo, Hong Kong, To appear.

    Google Scholar 

  65. A. Grossmann and J. Morlet. Decomposition of functions into wavelets of constant shape, and related transforms. In L. Streit, editor, Mathematics and Physics: Lectures on Recent Results, volume 11, pages 135–165. World Scientific, Singapore, Philadelphia, 1985.

    Google Scholar 

  66. J. Harrison. An introduction to fractals. In R.L. Devaney and L. Keen, editors, Chaos and Fractals, number 39 in Proc. Symp. in Appl. Math., pages 107–126, Providence, RI, 1989. American Mathematical Society.

    Google Scholar 

  67. M.J. Hayford. Holographic optical design using CODE V. In Ivan Cindrich,editor, Holographic Optics: Design and Applications, volume 883, pages 2–7. SPIE, 1988.

    Chapter  Google Scholar 

  68. C. Heil and D. Walnut. Gabor and wavelet expansions. In J.S. Byrnes and Jennifer L. Byrnes, editors, Recent Advances in Fourier Analysis and its Applications: Proceedings of the NATO Advanced Study Institute, volume 315 of NATO ASI series C: Mathematical and physical sciences, pages 441–454, Dordrecht, Boston, London, 1990. Kluwer Academic Publishers Group. Held at Il Ciocco Resort, Tuscany, Italy.

    Google Scholar 

  69. W. Heisenberg. Physikalische Prinzipien der Quantenmechanik. BI-Wissenschaftsverlag,Mannheim, Wien, Zürich, 1958.

    Google Scholar 

  70. J.R. Higgins. Five short stories about the cardinal series. Bull. (New Series) AMS, 12:45–89,1985.

    Article  MathSciNet  MATH  Google Scholar 

  71. J. Hilgevoord and J. Uffink. A new view on the uncertainty principle. International School of History of Science, Second Course: Sixty-Two Years of Uncertainty: Historical Philosophical and Physical Inquiries into the Foundations of Quantum Mechanics, 1989. Erice, Sicily.

    Google Scholar 

  72. J. Hilgevoord and J.B.M. Uffink. The mathematical expression of the uncertainty principle. In A. van der Merwe, F. Selleri, and G. Tarozzi, editors, Microphysical Reality and Quantum Formalism, pages 91–114.Kluwer Academic Publishers Group, Dordrecht, Boston, London, 1988.

    Chapter  Google Scholar 

  73. J. Hirsch and R. Hylton. Limits of spatial-frequency discrimination as evidence of neural interpolation. J. Optical Society of America A, 72:1367–1374,1982.

    Article  Google Scholar 

  74. J. Hirsch and R. Hylton. Orientation dependence of visual hyperacuity contains a component with hexagonal symmetry. J. Optical Society of America A, A/1:300–308,1984.

    Article  Google Scholar 

  75. J. Hirsch and R. Hylton. Quality of the primate photoreceptor lattice and limits of spatial vision. Vision Res., 24:347–355,1984.

    Article  Google Scholar 

  76. R.B. Holmes. Mathematical foundations of signal processing, ii: The role of group theory. Technical Report 781, Massachusetts Institute of Technology, Lincoln Laboratory, Lexington, MA, 1987.

    Google Scholar 

  77. H. Hosoya. Matching and symmetry of graphs. Comp. and Maths. with Appls., 12 B:271–290,1986.

    Article  MathSciNet  Google Scholar 

  78. R. Howe. Dual pairs in physics: Harmonic oscillators, photons, electrons,and singletons. In M. Flato, P. Sally, and G. Zuckerman, editors, Applications of Group Theory in Physics and Mathematical Physics, pages 179–207. American Mathematical Society, Providence, RI, 1985.

    Google Scholar 

  79. A. Huang. Towards a digital optics platform. In F. Lanzl, H.-J. Preuss, and G. Weigelt, editors, Optics in Complex Systems, volume 1319 of Proc. SPIE, pages 156–160. SPIE, 1990.

    Google Scholar 

  80. D.M. Hunten, L. Colin, T.M. Donahue, and V.I. Moroz. Venus. University of Arizona Press, Tucson, AZ, 1983.

    Google Scholar 

  81. J. Jahns. Planar packaging of complex optical systems. In F. Lanzl, H.-J. Preuss, and G. Weigelt, editors, Optics in Complex Systems, volume 1319 of Proc. SPIE, pages 681–682. SPIE, 1990.

    Google Scholar 

  82. J. Jahns, M.M. Downs, M.E. Prise, N. Streibl, and S.J. Walker. Dammann gratings for laser beam shaping. Opt Eng., 28:1267–1275,1989.

    Article  Google Scholar 

  83. J.L. Jewell, Y.H. Lee, A. Scherer, S.L. McCall, N.A. Olsson, J.P. Harbison, and L.T. Florez. Surface-emitting microlasers for photonic switching and interchip connections. Opt Eng., pages 210–214,1990.

    Google Scholar 

  84. J.P. Jones and L.A. Palmer. An evaluation of the two-dimensional Gabor filter model of simple receptive fields in cat striate cortex. J. Neurophysiology, 58:1233–1258,1987.

    Google Scholar 

  85. J.P. Jones and L.A. Palmer. The two-dimensional spatial structure of simple receptive fields in cat striate cortex. J. Neurophysiology, 58:1187–1211,1987.

    Google Scholar 

  86. J.P. Jones, A. Stepnoski, and L.A. Palmer. The two-dimensional spectral structure of simple receptive fields in cat striate cortex. J. Neurophysiology,58:1212–1232,1987.

    Google Scholar 

  87. F. Kiamilev, S.C. Esener, R. Paturi, Y. Fainman, P. Mercier, C.C. Guest, and S.H. Lee. Programmable optoelectronic multiprocessors and their comparison with symbolic substitution for digital optical computing. Opt Eng., 28:396–409,1989.

    Article  Google Scholar 

  88. M. King. Fourier optics and radar signal processing. In H. Stark, editor, Applications of Optical Fourier Transforms, pages 209–251. Academic Press, Orlando, San Diego, New York, Austin, Boston, London, Sydney, Tokyo, Toronto, 1982.

    Chapter  Google Scholar 

  89. V.P. Koronkevich. Computer synthesis of diffraction optical elements. In H.H. Arsenault, T. Szoplik, and B. Macukow, editors, Optical Processing and Computing, pages 277–313. Academic Press, Orlando, San Diego, New York, Austin, Boston, London, Sydney, Tokyo, Toronto, 1989.

    Chapter  Google Scholar 

  90. A. Kozma, E.N. Leith, and N.G. Massey. Tilted-plane optical processor. Appl. Opt, 11:1766–1777,1972.

    Article  Google Scholar 

  91. R.E. Kronauer and Y.Y. Zeevi. Reorganization and diversification of signals in vision. IEEE Trans. Systems, Man, and Cybernetics, SMC-15:91–101,1985.

    Article  Google Scholar 

  92. J. Lazzaro and C.A. Mead. A silicon model of auditory localization. Neural Computation, 1:47–57,1989.

    Article  Google Scholar 

  93. E.N. Leith. Quasi-holographic techniques in the microwave region. Proc. IEEE, 59:1305–1318,1971.

    Article  Google Scholar 

  94. E.N. Leith. Synthetic aperature radar. In D. Casasent, editor, Optical Data Processing, pages 89–117. Springer-Verlag, Berlin, Heidelberg, New York, London, Paris, Tokyo, Hong Kong, 1978.

    Chapter  Google Scholar 

  95. E.N. Leith. Incoherent optical processing and holography. In H.H. Arsenault, T. Szoplik, and B. Macukow, editors, Optical Processing and Computing, pages 421–440. Academic Press, Orlando, San Diego, New York, Austin, Boston, London, Sydney, Tokyo, Toronto, 1989.

    Chapter  Google Scholar 

  96. E.N. Leith. Fundamentals of modern holography. In Annual International Symposium on Optical and Optoelectronic Applied Science and Engineering, San Diego, CA, 1990. SPIE.

    Google Scholar 

  97. E.N. Leith and D.K. Angell. Generalization of some incoherent spatial filtering techniques. Appl. Opt, 25:499–502,1986.

    Article  Google Scholar 

  98. E.N. Leith and A. Cunha. Holographic methods for imaging through an inhomogeneity. Opt Eng., 28:574–579,1989.

    Article  Google Scholar 

  99. E.N. Leith and A.L. Inglis. Synthetic antenna data processing by wave-front reconstruction. Appl. Opt, 7:539–544,1968.

    Article  Google Scholar 

  100. E.N. Leith and C.-P. Kuei. Interferometric method for imaging through inhomogeneities. Opt Lett., 12:149–151,1987.

    Article  Google Scholar 

  101. E.N. Leith and J. Upatnieks. Reconstructed wavefronts and communication theory. J. Opt Soc. Amer., 52:1123–1130,1962.

    Article  Google Scholar 

  102. E.N. Leith and J. Upatnieks. Holography with achromatic-fringe systems.J. Opt Soc. Amer, 57:975–980,1967.

    Article  Google Scholar 

  103. A.L. Lentine, H.S. Hinton, D.A.B. Miller, J.E. Henry, J.E. Cunningham, and L.M.F. Chirovsky. Symmetric self-electro-optic effect device: Optical set-reset latch. Appl. Phys. Lett., 52:1419–1421,1988.

    Article  Google Scholar 

  104. H. Lichte. Electron holography approaching atomic resolution. Ultramicroscopy,20:293–304,1986.

    Article  Google Scholar 

  105. E.H. Linfoot and E. Wolf. Phase distribution near focus in an aberration-free diffraction image. Proc. Phys. Soc, B 69:823–832,1956.

    Google Scholar 

  106. R. Linsker. From basic network principles to neural architecture: Emergence of orientation-selective cells. Proc. Natl. Acad. Sci. USA, 83:8390–8394,1986.

    Article  Google Scholar 

  107. R. Linsker. From basic network principles to neural architecture: Emergence of orientation columns. Proc. Natl. Acad. Sci. USA, 83:8779–8783, 1986.

    Article  Google Scholar 

  108. R. Linsker. From basic network principles to neural architecture: Emergence of spatial-opponent cells. Proc. Natl. Acad. Sci. USA, 83:7508–7512,1986.

    Article  Google Scholar 

  109. R. Linsker. Development of feature-analyzing cells and their columnar organization in a layered self-adaptive network. In R.M.J. Cotterill, editor,Computer Simulation in Brain Science, pages 416–431. Cambridge University Press, Cambridge, U.K., 1988.

    Chapter  Google Scholar 

  110. R. Linsker. Self-organization in a perceptual network. Computer, 21:105–117,1988.

    Article  Google Scholar 

  111. S. Marčelja. Mathematical description of the responses of simple cortical cells. J. Opt Soc. Amer., 70:1297–1300,1980.

    Article  MathSciNet  Google Scholar 

  112. W. Martienssen. Experiments on single photons. In 15th Congress of the International Commission for Optics: Optics in Complex Systems. International Commission for Optics, Garmisch-Partenkirchen, 1990.

    Google Scholar 

  113. B.R. Masters. Fractal analysis of human retinal blood vessel patterns:Developmental and diagnostic aspects. In B.R. Masters, editor, Noninvasive Diagnostic Techniques in Opthalmology, pages 515–527. Springer-Verlag, Berlin, Heidelberg, New York, London, Paris, Tokyo, Hong Kong, 1990.

    Chapter  Google Scholar 

  114. F.B. McCormick. Generation of large spot arrays from single laser beam by multiple imaging with binary phase gratings. Opt. Eng., 28:299–304,1989.

    Article  Google Scholar 

  115. C.Mead. Analog VLSI and Neural Systems. Addison-Wesley, Reading, MA, 1989.

    Book  MATH  Google Scholar 

  116. C. Mead and M. Ismail. Analog VLSI Implementation of Neural Systems.Kluwer Academic Publishers Group, Dordrecht, Boston, London,1989.

    Book  Google Scholar 

  117. C.A. Mead and M.A. Mahowald. A silicon model of early visual processing. Neural Networks, 1:91–97,1988.

    Article  Google Scholar 

  118. Y. Meyer. Principe d’incertitude, bases hilbertiennes et algèbres d’opérateurs, 1987.

    Google Scholar 

  119. C.C. Moore and J.A. Wolf. Square integrable representations of nilpotent groups. Trans. Amer. Math. Soc, 185:445–462,1973.

    Article  MathSciNet  Google Scholar 

  120. H. Moscovici. Coherent state representations of nilpotent lie groups. Commun. Math Phys., 54:63–68,1977.

    Article  MathSciNet  MATH  Google Scholar 

  121. D.C Munson, J.D. O’Brien, and W.K. Jenkins. A tomographic formulation of spotlight-mode synthetic aperture radar. Proc. IEEE, 71:917–925,1983.

    Article  Google Scholar 

  122. H.L. Naparst. Radar signal choice and processing for a dense target environment PhD thesis, University of California, Berkeley, CA, 1988.

    Google Scholar 

  123. R. Nobili. Schrödinger wave holography in brain cortex. Phys. Rev., 32:3618–3626,1985.

    Article  Google Scholar 

  124. J. Ohta, M. Takahashi, Y. Nitta, S. Tai, K. Mitsunaga, and K. Kjuma. A new approach to a GaAs/AlGaAs optical neurochip with three layered structure. In Proc. IJCNN International Joint Conference on Neural Networks, volume II, pages 477–482,1989.

    Chapter  Google Scholar 

  125. M. Ould-Beziou. PhD thesis, Université d’Orléans, 1989.

    Google Scholar 

  126. Y. Owechko. Optoelectronic resonator neural networks. Appl. Opt, 26:5104–5114,1987. Also in [24], pp. 577–584.

    Article  Google Scholar 

  127. Y. Owechko. Holographic associative memories. In Uzi Efron, editor, Spatial Light Modulators and Applications III, volume 1150 of Critical Reviews of Optical Science and Technology, pages 164–176. SPIE, 1990.

    Chapter  Google Scholar 

  128. Y Owechko, G.J. Dunning, E. Marom, and B.H. Soffer. Holographic associative memory with nonlinearities in the correlation domain. Appl. Opt, 25:1900–1910,1987. Also in [24], pp. 566–576.

    Article  Google Scholar 

  129. Y. Owechko, E. Marom, B.H. Soffer, and G. Dunning. Associative memory in a phase conjugate resonator cavity utilizing a hologram. In J. Shamir, A.A. Friesem, and E. Marom, editors, Proc. SPIE, volume 700, pages 296–300. IOCC-1986 International Optical Computing Conference, 1986.

    Google Scholar 

  130. E.G. Paek, J.R. Wullert II, M. Jain, A. Von Lehmen, A. Scherer, J.Harbison, L.T. Florez, H.J. Yoo, J.L. Jewel, and Y.H. Lee. Compact and ultrafast holographic memory using a surface-emitting microlaser diode array. Opt Lett., 15:341–343,1990.

    Article  Google Scholar 

  131. E.G. Paek, J.R. Wullert II, A. Von Lehmen, J.S. Patel, M. Jain, A. Scherer, J. Harbison, L.T. Florez, H.J. Yoo, and R. Martin. Implementation of neural network models by using coherent optics. In Uzi Efron, editor, Spatial Light Modulators and Applications III, volume 1150 of Critical Reviews of Optical Science and Technology, pages 192–203. SPIE, 1990.

    Chapter  Google Scholar 

  132. J.C. Pearson, L.H. Finkel, and G.M. Edelman. Plasticity in the organization of adult cerebral cortical maps: A computer simulation based on neuronal group selection. J. Neurosci., 7:4209–4223,1987.

    Google Scholar 

  133. D.M. Pepper. Nonlinear optical phase conjugation. Opt. Eng., 21:156–183,1982.

    Article  Google Scholar 

  134. A. Peremolov. Generalized Coherent States and Their Applications. Springer-Verlag, Berlin, Heidelberg, New York, London, Paris, Tokyo, Hong Kong, 1986.

    Book  Google Scholar 

  135. R.L. Pfleegor and L. Mandel. Interference effects at the single photon level. Phys. Lett., 24 A:766–767,1967.

    Google Scholar 

  136. J. Phillips. A note on square-integrable representations. J. Functional Analysis, 20:83–92,1975.

    Article  MathSciNet  MATH  Google Scholar 

  137. D.A. Pollen and S.F. Ronner. Phase relationships between adjacent simple cells in the visual cortex. Science, 212:1409–1411,1981.

    Article  Google Scholar 

  138. K.H. Pribram, M. Nuwer, and R.J. Baron. The holographic hypothesis of memory structure in brain function and perception. In D.H. Krantz, R.C. Atkinson, R.D. Luce, and P. Suppes, editors, Measurement,Psychophysics, and Neural Information Processing, volume II of Contemporary Developments in Mathematical Psychology, pages 416–457. W.H. Freeman, San Francisco, New York, 1974.

    Google Scholar 

  139. J.F. Price. Uncertainty principles and interference patterns. Proc. Centre for Mathematical Analysis of the Australian National University, 9:241–258,1985.

    Google Scholar 

  140. J.F. Price. Uncertainty principles and sampling theorems. In J.F. Price, editor, Fourier Techniques and Applications, pages 25–44. Plenum Press, New York and London, 1985.

    Chapter  Google Scholar 

  141. J.F. Price and A. Sitaram. Local uncertainty inequalities for locally compact groups. Trans. Amer. Math. Soc, 308:105–114,1988.

    Article  MathSciNet  MATH  Google Scholar 

  142. D. Psaltis. Two-dimensional optical processing using one-dimensional input devices. Proc. IEEE, 72:962–974,1984.

    Article  Google Scholar 

  143. D. Psaltis, D. Brady, X. Gu, and K. Hsu. Optical implementation of neural computers. In H.H. Arsenault, T. Szoplik, and B. Macukow, editors, Optical Processing and Computing, pages 251–276. Academic Press, Orlando, San Diego, New York, Austin, Boston, London, Sydney, Tokyo, Toronto, 1989.

    Chapter  Google Scholar 

  144. D. Psaltis, D. Brady, and K. Wagner. Adaptive optical networks using photorefractive crystals. Appl. Opt, 27:1752–1759,1988. Also in [24], pp. 603–610.

    Article  Google Scholar 

  145. D. Psaltis and N. Farhat. Optical information processing based on an associative-memory model of neural nets with thresholding and feedback. Opt. Lett., 10:98–100,1985. Also in [24], pp. 515–517.

    Article  Google Scholar 

  146. D. Psaltis, C.H. Park, and J. Hong. Higher order associative memories and their optical implementations. Neural Networks, 1:149–163,1988.

    Article  Google Scholar 

  147. G. Ries. Rotationssymmetrische radar ambiguityfunktion. Manuskript,Lehrstuhl für Elektrotechnik VIII-Hochfrequenztechnik, Universität Siegen, 1989.

    Google Scholar 

  148. B. Roberts, M.R. Taghizadeh, J. Turunen, and A. Vasara. Fabrication of space invariant fanout components in dichromatic gelatin. Appl. Opt., 29:1134–1141,1990.

    Article  Google Scholar 

  149. H.R Robertson. The uncertainty principle. Phys. Rev, 34:163–164, 1929.

    Article  Google Scholar 

  150. W. Schempp. Holographic fractals. To appear.

    Google Scholar 

  151. W. Schempp. Phase anomalies in optical neural networks. To appear.

    Google Scholar 

  152. W. Schempp. Gruppentheoretische aspekte der signalübertragung und der kardinalen interpolationssplines I. Math. Meth. in the Appl. Sci., 5:195–215,1983.

    Article  MathSciNet  MATH  Google Scholar 

  153. W. Schempp. Radar ambiguity functions, the Heisenberg group, and holomorphic theta series. Proc. Amer. Math. Soc, 92:103–110,1984.

    Article  MathSciNet  MATH  Google Scholar 

  154. W. Schempp. Group theoretical methods in approximation theory, elementary number theory, and computational signal geometry. J. Approx. Th., V:129–171,1986.

    MathSciNet  Google Scholar 

  155. W. Schempp. Harmonic analysis on the Heisenberg nilpotent Lie group, with applications to signal theory. Pitman Research Notes in Math., 147,1986. Second edition under preparation.

    Google Scholar 

  156. W. Schempp. Elementary holograms and 3-orbifolds. C.R. Math. Rep. Acad. Sci. Canada, 10:155–160,1988.

    MathSciNet  MATH  Google Scholar 

  157. W. Schempp. Holographic grids. In T. Russel Hsing, editor, Visual Communications and Image Processing’88, number 1001 in Proc. SPIE, pages 116–120. SPIE, 1988.

    Google Scholar 

  158. W. Schempp. The holographic transform. In G.V. Milovanovič, editor, Numerical Methods and Approximation Theory, volume III, pages 67–91. University of Niš, Niš, 1988.

    Google Scholar 

  159. W. Schempp. The oscillator representation of the metaplectic group applied to quantum electronics and computerized tomography. In S. Albeverio, Ph. Blanchard, M. Hazewinkel, and L. Streit, editors, Stochastic Processes in Physics and Engineering, pages 305–344. D. Reidel, Dordrecht, Boston, Lancaster, Tokyo, 1988.

    Chapter  Google Scholar 

  160. W. Schempp. Extensions of the Heisenberg group and coaxial coupling of transverse eigenmodes. Rocky Mountain J. Math., pages 383–394, 1989.

    Google Scholar 

  161. W. Schempp. Holographic image processing, coherent optical computing,and neural computer architecture for pattern recognition. In K.B. Wolf, editor, Lie Methods in Optics II, volume 352 of Lecture Notes in Physics, pages 19–45. Springer-Verlag, Berlin, Heidelberg, New York, London, Paris, Tokyo, Hong Kong, 1989.

    Google Scholar 

  162. W. Schempp. Neurocomputer architectures. Results in Math., 16:345–382,1989.

    MathSciNet  MATH  Google Scholar 

  163. D. Schreier. Synthetische Holografie. Fachbuchverlag, Leipzig, 1984.

    Google Scholar 

  164. E.A. Schwartz. Phototransduction in vertebrate rods. Annual. Rev. Neurosci., 8:339–367,1985.

    Article  Google Scholar 

  165. I.E. Segal. Transforms for operators and symplectic automorphisms over locally compact abelian groups. Math. Scand., 13:31–43,1963.

    MathSciNet  MATH  Google Scholar 

  166. J. Shamir, H.J. Caulfield, and R.B. Johnson. Massive holographic interconnection networks and their limitations. Appl. Opt, 28:311–324, 1989. Also in [24], pp. 546–559.

    Article  Google Scholar 

  167. A. Shimony. Recent quantum-mechanically significant optical experiments.In Fundamental Aspects of Quantum Theory, University of South Carolina, Columbia, SC, 1989. Conference on Foundations of Quantum Mechanics to Celebrate 30 Years of the Aharanov-Bohm Effect.

    Google Scholar 

  168. D.S. Shucker. Square integrable representations of unimodular groups. Proc. Amer. Math. Soc., 89:169–172,1983.

    Article  MathSciNet  MATH  Google Scholar 

  169. B.H. Soffer, G.J. Dunning, Y. Owechko, and E. Marom. Associative holographic memory with feedback using phase-conjugate mirrors. Opt Lett., 11:118–120,1986.

    Article  Google Scholar 

  170. B.H. Soffer, Y. Owechko, and G.J. Dunning. A photorefractive optical neural network. In F. Lanzl, H.-J. Preuss, and G. Weigelt, editors, Optics in Complex Systems, volume 1319 of Proc. SPIE, pages 196–197. SPIE, 1990.

    Google Scholar 

  171. C.T. Stansberg. Surface roughness measurements by means of polychromatic speckle patterns. Appl. Opt, 18:4051–4060,1979.

    Article  Google Scholar 

  172. C.T. Stansberg. On the first-order probability density function of integrated laser speckle. Optica Acta, 28:917–932,1981.

    Article  MathSciNet  Google Scholar 

  173. N. Streibl. Beam shaping with optical array generators. J. Mod. Opt, 36:1559–1573,1989.

    Article  Google Scholar 

  174. R.S. Strichartz. Sub-Riemannian geometry. J. Diff. Geom., 24:221–263, 1986.

    MathSciNet  MATH  Google Scholar 

  175. G.J. Swanson. Binary optics technology: The theory and design of multi-level diffractive optical elements. Technical Report 854, Massachusetts Institute of Technology, Lincoln Laboratory, Lexington, MA, 1989.

    Google Scholar 

  176. G.J. Swanson and W.B. Veldkamp. Diffractive optical elements for use in infrared systems. Opt. Eng., 28:605–608,1989.

    Google Scholar 

  177. J.A. Titleer. Elementary quantum phenomenon as building unit. In P. Meystre and M.O. Scully, editors, Quantum Optics, Experimental Gravity, and Measurement Theory, pages 141–143. Plenum Press, New York and London, 1983.

    Google Scholar 

  178. H.J. Tiziani. Real-time meteorology with bso crystals. Optica Acta, 29:463–470,1982.

    Article  Google Scholar 

  179. A. Tonomura. Applications of electron holography. Rev. Mod. Phys., 59:639–669,1987.

    Article  Google Scholar 

  180. J. Uffink and J. Hilgevoord. Interference and distinguishability in quantum mechanics. Physica, B 151:309–313,1988.

    Google Scholar 

  181. J.B.M. Uffink and J. Hilgevoord. New bounds for the uncertainty principle. Phys. Lett., 105 A:176–178,1984.

    Google Scholar 

  182. J. Uozumi, H. Kimura, and T. Asakura. Fraunhofer diffraction by Koch fractals. J. Mod. Opt, 37:1011–1031,1990.

    Article  MathSciNet  MATH  Google Scholar 

  183. J. Uozumi, H. Kimura, and T. Asakura. Optical diffraction by regular and random Koch fractals. In F. Lanzl, H.-J. Preuss, and G. Weigelt, editors, Optics in Complex Systems, volume 1319 of Proc. SPIE, pages 11–12. SPIE, 1990.

    Google Scholar 

  184. J.C. Várilly, J.M. Gracia-Bondía, and W. Schempp. The Moyal representation of quantum mechanics and special function theory. Acta Applicandae Math., 11:225–250,1990.

    Article  Google Scholar 

  185. W.B. Veldkamp, J.R. Leger, and G.J. Swanson. Coherent summation of laser beams using binary phase gratings. Opt Lett., 11:303–305,1986.

    Article  Google Scholar 

  186. Jr. W. Miller. Topics in Harmonic Analysis with Applications to Radar and Sonar. Number 657 in Lecture Notes in Radar/Sonar. IMA Preprint Series, Minneapolis, MN, 1990.

    Google Scholar 

  187. A. Weil. Sur certains groupes d’opérateurs unitaires. Acta Math, 111:143–211,1964. Also in [188], pp. 1–69.

    Article  MathSciNet  MATH  Google Scholar 

  188. A. Weil. Collected Papers, volume III. Springer-Verlag, Berlin, Heidelberg,New York, London, Paris, Tokyo, Hong Kong, 1980.

    Google Scholar 

  189. N. Weste and K. Eshraghian. Principles of CMOS VLSI Design. Addison-Wesley, Reading, MA, 1985.

    Google Scholar 

  190. J.A. Wheeler. The “past” and the “delayed-choice” double-slit experiment.In A.R. Mariow, editor, Mathematical Foundations of Quantum Theory, pages 9–48. Academic Press, Orlando, San Diego, New York, Austin, Boston, London, Sydney, Tokyo, Toronto, 1978.

    Chapter  Google Scholar 

  191. J.A. Wheeler. Frontiers of time. In G. Toraldo di Francia, editor, Problems in the Foundations of Physics, pages 395–497. Inter. School of Physics “Enrico Fermi”, North Holland-Elsevier Science Publishers, 1979.

    Google Scholar 

  192. J.A. Wheeler. Beyond the black hole. In H. Woolf, editor, Some Strangeness in the Proportion: A Centennial Symposium to Celebrate the Achievements of Albert Einstein, pages 341–375, Reading, MA, 1980. Addison-Wesley.

    Google Scholar 

  193. J.A. Wheeler. The computer and the universe. Int. J. Theor. Phys., 21:557–572,1982.

    Article  Google Scholar 

  194. J.A. Wheeler. Particles and geometry. In Unified Theories of Elementary Particles, volume 160 of Lecture Notes in Phys., pages 189–217, Berlin, Heidelberg, New York, London, Paris, Tokyo, Hong Kong, 1982. Heisenberg Symposium, Springer-Verlag.

    Chapter  Google Scholar 

  195. J.A. Wheeler. Law without law. In Wheeler and Zurek [196], pages 182–213.

    Google Scholar 

  196. J.A. Wheeler and W.H. Zurek, editors. Quantum Theory and Measurement.Princeton University Press, Princeton, 1983.

    Google Scholar 

  197. K. Wilber. Das holographische Weltbild. Scherz Verlag, Bern, München, Wien, 1986.

    Google Scholar 

  198. R. Wilson and G.H. Granlund. The uncertainty principle in image processing. IEEE Trans. on Pattern Anal. and Machine Intel., 6:758–767,1984.

    Article  Google Scholar 

  199. W.K. Wooters and W.H. Zurek. Complementarity in the double-slit experiment: Quantum nonseparability and a quantitative statement of Bohr’s principle. Phys. Rev., D 19:473–484, 1979. Also in [196], pp. 443–454.

    Google Scholar 

  200. A. Yariv. Phase conjugate optics and real-time holography. IEEE J. Quantum Electronics, QE 14:650–660,1978.

    Article  Google Scholar 

  201. T. Yatagai. Cellular logic architectures for optical computers. Appl Opt, 25:1571–1577,1986.

    Article  Google Scholar 

  202. J.A. Yeazell and C.R. Stroud. Rydberg-atom wave packets localized in the angular variables. Phys. Rev., A 35:2806–2809,1987.

    Google Scholar 

  203. J.A. Yeazell and C.R. Stroud. Observation of spatially localized atomic electron wave packets. Phys. Rev. Lett., 60:1494–1497,1988.

    Article  Google Scholar 

  204. A.L. Yuille, D.M. Kammen, and D.S. Cohen. Quadrature and the development of orientation selective cortical cells by Hebb rules. Biological Cybernetics, 61:183–194,1989.

    Article  MATH  Google Scholar 

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Schempp, W. (1992). Quantum holography and neurocomputer architectures. In: Byrnes, J.S., Byrnes, J.L., Hargreaves, K.A., Berry, K. (eds) Probabilistic and Stochastic Methods in Analysis, with Applications. NATO ASI Series, vol 372. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-2791-2_20

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