Encyclopedia of Complexity and Systems Science

Living Edition
| Editors: Robert A. Meyers

Optical Computing

  • Thomas J. Naughton
  • Damien Woods
Living reference work entry
DOI: https://doi.org/10.1007/978-3-642-27737-5_377-3

Definition of the Subject

An optical computer is a physical information processing device that uses photons to transport data from one memory location to another and processes the data while it is in this form. In contrast, a conventional digital electronic computer uses electric fields (traveling along conductive paths) for this task. The optical data paths in an optical computer are effected by refraction (such as the action of a lens) or reflection (such as the action of a mirror). A principal advantage of an optical data path over an electrical data path is that optical data paths can intersect and even completely overlap without corrupting the data in either path. Optical computers make use of this property to efficiently transform the optically encoded data from one representation to another, for example, to shuffle or reverse the order of an array of parallel paths or to convolve the data in several arrays of parallel paths. Other advantages of optical computers include inherent...

Keywords

Turing Machine Optical Computer Optical Computing Optical Algorithm Optical Information Processing 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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Bibliography

  1. Abushagur MAG, Caulfield HJ (1987) Speed and convergence of bimodal optical computers. Opt Eng 26(1):22–27CrossRefGoogle Scholar
  2. Adleman LM (1994) Molecular computation of solutions to combinatorial problems. Science 266:1021–1024ADSCrossRefGoogle Scholar
  3. Alhazov A, de Jesús Pérez-Jiménez M (2007) Uniform solution to QSAT using polarizationless active membranes. In: Durand-Lose J, Margenstern M (eds) Machines, Computations and Universality (MCU), vol 4664, LNCS. Springer, Orléans, pp 122–133CrossRefGoogle Scholar
  4. Armitage JD, Lohmann AW (1965) Character recognition by incoherent spatial filtering. Appl Opt 4(4):461–467ADSCrossRefGoogle Scholar
  5. Arsenault HH, Sheng Y (1992) An introduction to optics in computers, vol TT8, Tutorial texts in optical engineering. SPIE Press, BellinghamGoogle Scholar
  6. Arsenault HH, Hsu YN, Chalasinska-Macukow K (1984) Rotation-invariant pattern recognition. Opt Eng 23(6):705–709ADSCrossRefGoogle Scholar
  7. Balcázar JL, Díaz J, Gabarró J (1988) Structural complexity, vol I and II, EATCS monographs on theoretical computer science. Springer, BerlinzbMATHCrossRefGoogle Scholar
  8. Beyette FR Jr, Mitkas PA, Feld SA, Wilmsen CW (1994) Bitonic sorting using an optoelectronic recirculating architecture. Appl Opt 33(35):8164–8172ADSCrossRefGoogle Scholar
  9. Borodin A (1977) On relating time and space to size and depth. SIAM J Comput 6(4):733–744MathSciNetzbMATHCrossRefGoogle Scholar
  10. Bracewell RN (1978) The Fourier transform and its applications, 2nd edn, Electrical and electronic engineering series. McGraw-Hill, New YorkzbMATHGoogle Scholar
  11. Brenner KH, Huang A, Streibl N (1986) Digital optical computing with symbolic substitution. Appl Opt 25(18):3054–3060ADSCrossRefGoogle Scholar
  12. Brenner KH, Kufner M, Kufner S (1990) Highly parallel arithmetic algorithms for a digital optical processor using symbolic substitution logic. Appl Opt 29(11):1610–1618ADSCrossRefGoogle Scholar
  13. Casasent DP (1984) Unified synthetic discriminant function computational formulation. Appl Opt 23:1620–1627ADSCrossRefGoogle Scholar
  14. Casasent DP, House GP (1994a) Comparison of coherent and noncoherent optical correlators. In: Optical pattern recognition V. Proceedings of SPIE, vol 2237. SPIE, Bellingham, pp 170–178Google Scholar
  15. Casasent DP, House GP (1994b) Implementation issues for a noncoherent optical correlator. In: Optical pattern recognition V. Proceedings of SPIE, vol 2237. SPIE, Bellingham, pp 179–188Google Scholar
  16. Casasent DP, Psaltis D (1976a) Position, rotation, and scale invariant optical correlation. Appl Opt 15(7):1795–1799ADSCrossRefGoogle Scholar
  17. Casasent DP, Psaltis D (1976b) Scale invariant optical transforms. Opt Eng 15(3):258–261ADSCrossRefGoogle Scholar
  18. Casasent DP, Jackson J, Neuman CP (1983) Frequency-multiplexed and pipelined iterative optical systolic array processors. Appl Opt 22:115–124ADSCrossRefGoogle Scholar
  19. Caulfield HJ (ed) (1979) Handbook of optical holography. Academic, New YorkGoogle Scholar
  20. Caulfield HJ (1989a) Computing with light. Byte 14:231–237Google Scholar
  21. Caulfield HJ (1989b) The energetic advantage of analog over digital computing, vol 9, OSA optical computing technical digest series. Optical Society of America, Washington, DC, pp 180–183Google Scholar
  22. Caulfield HJ (1990) Space-time complexity in optical computing. In: Javidi B (ed) Optical information-processing systems and architectures II, vol 1347, SPIE. SPIE Press, Bellingham, pp 566–572CrossRefGoogle Scholar
  23. Caulfield HJ, Abushagur MAG (1986) Hybrid analog-digital algebra processors. In: Optical and hybrid computing II. Proceedings of SPIE, vol 634. SPIE Press, Bellingham, pp 86–95Google Scholar
  24. Caulfield HJ, Haimes R (1980) Generalized matched filtering. Appl Opt 19(2):181–183ADSCrossRefGoogle Scholar
  25. Caulfield HJ, Horvitz S, Winkle WAV (1977) Introduction to the special issue on optical computing. Proc IEEE 65(1):4–5CrossRefGoogle Scholar
  26. Caulfield HJ, Rhodes WT, Foster MJ, Horvitz S (1981) Optical implementation of systolic array processing. Opt Commun 40:86–90ADSCrossRefGoogle Scholar
  27. Caulfield HJ, Kinser JM, Rogers SK (1989) Optical neural networks. Proc IEEE 77:1573–1582CrossRefGoogle Scholar
  28. Cerf NJ, Adami C, Kwiat PG (1998) Optical simulation of quantum logic. Phys Rev A 57(3):R1477–R1480ADSMathSciNetCrossRefGoogle Scholar
  29. Chandra AK, Stockmeyer LJ (1976) Alternation. In: 17th annual symposium on foundations of computer science, IEEE, Houston, pp 98–108Google Scholar
  30. Chandra AK, Kozen DC, Stockmeyer LJ (1981) Alternation. J ACM 28(1):114–133MathSciNetzbMATHCrossRefGoogle Scholar
  31. Chang S, Arsenault HH, Garcia-Martinez P, Grover CP (2000) Invariant pattern recognition based on centroids. Appl Opt 39(35):6641–6648ADSCrossRefGoogle Scholar
  32. Chen FS, LaMacchia JT, Fraser DB (1968) Holographic storage in lithium niobate. Appl Phys Lett 13(7):223–225ADSCrossRefGoogle Scholar
  33. Chiou AE (1999) Photorefractive phase-conjugate optics for image processing, trapping, and manipulation of microscopic objects. Proc IEEE 87(12):2074–2085CrossRefGoogle Scholar
  34. Clavero R, Ramos F, Martí J (2005) All-optical flip-flop based on an active Mach-Zehnder interferometer with a feedback loop. Opt Lett 30(21):2861–2863ADSCrossRefGoogle Scholar
  35. Cutrona LJ, Leith EN, Palermo CJ, Porcello LJ (1960) Optical data processing and filtering systems. IRE Trans Inf Theory 6(3):386–400MathSciNetCrossRefGoogle Scholar
  36. Cutrona LJ, Leith EN, Porcello LJ, Vivian WE (1966) On the application of coherent optical processing techniques to synthetic-aperture radar. Proc IEEE 54(8):1026–1032CrossRefGoogle Scholar
  37. Desmulliez MPY, Wherrett BS, Waddie AJ, Snowdon JF, Dines JAB (1996) Performance analysis of self-electro-optic-effect-device-based (seed-based) smart-pixel arrays used in data sorting. Appl Opt 35(32):6397–6416ADSCrossRefGoogle Scholar
  38. Dolev S, Fitoussi H (2007) The traveling beam: optical solution for bounded NP-complete problems. In: Crescenzi P, Prencipe G, Pucci G (eds) The fourth international conference on fun with algorithms (FUN). Springer, Heidelberg, pp 120–134CrossRefGoogle Scholar
  39. Dorren HJS, Hill MT, Liu Y, Calabretta N, Srivatsa A, Huijskens FM, de Waardt H, Khoe GD (2003) Optical packet switching and buffering by using all-optical signal processing methods. J Lightwave Technol 21(1):2–12ADSCrossRefGoogle Scholar
  40. Durand-Lose J (2006) Reversible conservative rational abstract geometrical computation is Turing-universal. In: Logical approaches to computational barriers, second conference on computability in Europe, (CiE). vol 3988, Lecture notes in computer science. Springer, Swansea, pp 163–172Google Scholar
  41. Efron U, Grinberg J, Braatz PO, Little MJ, Reif PG, Schwartz RN (1985) The silicon liquid crystal light valve. J Appl Phys 57(4):1356–1368ADSCrossRefGoogle Scholar
  42. Esteve-Taboada JJ, García J, Ferreira C (2000) Extended scale-invariant pattern recognition with white-light illumination. Appl Opt 39(8):1268–1271ADSCrossRefGoogle Scholar
  43. Farhat NH, Psaltis D (1984) New approach to optical information processing based on the Hopfield model. J Opt Soc Am A 1:1296ADSGoogle Scholar
  44. Feitelson DG (1988) Optical computing: a survey for computer scientists. MIT Press, Cambridge, MAGoogle Scholar
  45. Feng JH, Chin GF, Wu MX, Yan SH, Yan YB (1995) Multiobject recognition in a multichannel joint- transform correlator. Opt Lett 20(1):82–84ADSCrossRefGoogle Scholar
  46. Fortune S, Wyllie J (1978) Parallelism in random access machines. In: Proceedings 10th annual ACM symposium on theory of computing. ACM, New York, pp 114–118Google Scholar
  47. Gabor D (1948) A new microscopic principle. Nature 161(4098):777–778ADSCrossRefGoogle Scholar
  48. Gara AD (1979) Real time tracking of moving objects by optical correlation. Appl Opt 18(2):172–174ADSCrossRefGoogle Scholar
  49. Geldenhuys R, Liu Y, Calabretta N, Hill MT, Huijskens FM, Khoe GD, Dorren HJS (2004) All-optical signal processing for optical packet switching. J Opt Netw 3(12):854–865CrossRefGoogle Scholar
  50. Ghosh AK, Casasent DP, Neuman CP (1985) Performance of direct and iterative algorithms on an optical systolic processor. Appl Opt 24(22):3883–3892ADSCrossRefGoogle Scholar
  51. Goldberg L, Lee SH (1979) Integrated optical half adder circuit. Appl Opt 18:2045–2051ADSCrossRefGoogle Scholar
  52. Goldschlager LM (1977) Synchronous parallel computation. PhD thesis, University of Toronto, Computer Science DepartmentGoogle Scholar
  53. Goldschlager LM (1978) A unified approach to models of synchronous parallel machines. In: Proceedings 10th annual ACM symposium on theory of computing. ACM, New York, pp 89–94Google Scholar
  54. Goldschlager LM (1982) A universal interconnection pattern for parallel computers. J ACM 29(4):1073–1086MathSciNetzbMATHCrossRefGoogle Scholar
  55. Goodman JW (1977) Operations achievable with coherent optical information processing systems. Proc IEEE 65(1):29–38CrossRefGoogle Scholar
  56. Goodman JW (2005) Introduction to fourier optics, 3rd edn. Roberts & Company, EnglewoodGoogle Scholar
  57. Grinberg J, Jacobson AD, Bleha WP, Miller L, Fraas L, Boswell D, Myer G (1975) A new real-time noncoherent to coherent light image converter: the hybrid field effect liquid crystal light valve. Opt Eng 14(3):217–225ADSCrossRefGoogle Scholar
  58. Grover LK (1996) A fast quantum mechanical algorithm for database search. In: Proceedings 28th annual ACM symposium on theory of computing. ACM, New York, pp 212–219Google Scholar
  59. Guilfoyle PS, Hessenbruch JM, Stone RV (1998) Free-space interconnects for high-performance optoelectronic switching. IEEE Comput 31(2):69–75CrossRefGoogle Scholar
  60. Haist T, Osten W (2007) An optical solution for the travelling salesman problem. Opt Express 15(16):10473–10482ADSCrossRefGoogle Scholar
  61. Hartmanis J, Simon J (1974) On the power of multiplication in random access machines. In: Proceedings of the 15th annual symposium on switching and automata theory. IEEE, The University of New Orleans, pp 13–23Google Scholar
  62. Head T (1987) Formal language theory and DNA: an analysis of the generative capacity of specific recombinant behaviors. Bull Math Biol 49(6):737–759MathSciNetzbMATHCrossRefGoogle Scholar
  63. Horner JL (ed) (1987) Optical signal processing. Academic, San DiegoGoogle Scholar
  64. Hough PVC (1962) Methods and measures for recognising complex patterns. US Patent No. 3,069,654Google Scholar
  65. Hsu YN, Arsenault HH (1982) Optical pattern recognition using circular harmonic expansion. Appl Opt 21(22):4016–4019ADSCrossRefGoogle Scholar
  66. Hsu KY, Li HY, Psaltis D (1990) Holographic implementation of a fully connected neural network. Proc IEEE 78(10):1637–1645ADSCrossRefGoogle Scholar
  67. Huang A (1984) Architectural considerations involved in the design of an optical digital computer. Proc IEEE 72(7):780–786CrossRefGoogle Scholar
  68. Huang A, Tsunoda Y, Goodman JW, Ishihara S (1979) Optical computation using residue arithmetic. Appl Opt 18(2):149–162ADSCrossRefGoogle Scholar
  69. Jacobson AD, Beard TD, Bleha WP, Morgerum JD, Wong SY (1972) The liquid crystal light value, an optical-to-optical interface device. In: Proceedings of the conference on parallel image processing, document X-711-72-308, Goddard Space Flight Center. NASA, Washington, DC, pp 288–299Google Scholar
  70. Javidi B (1989) Nonlinear joint power spectrum based optical correlation. Appl Opt 28(12):2358–2367ADSCrossRefGoogle Scholar
  71. Javidi B (1990) Generalization of the linear matched filter concept to nonlinear matched filters. Appl Opt 29(8):1215–1217ADSCrossRefGoogle Scholar
  72. Javidi B, Wang J (1995) Optimum distortion-invariant filter for detecting a noisy distorted target in nonoverlapping background noise. J Opt Soc Am A 12(12):2604–2614ADSCrossRefGoogle Scholar
  73. Karim MA, Awwal AAS (1992) Optical computing: an introduction. Wiley, New YorkGoogle Scholar
  74. Karp RM, Ramachandran V (1990) Parallel algorithms for shared memory machines. In: van Leeuwen J (ed) Handbook of theoretical computer science, vol A. Elsevier, Amsterdam, pp 869–941Google Scholar
  75. Knill E, LaFlamme R, Milburn GJ (2001) A scheme for efficient quantum computation with linear optics. Nature 409:46–52ADSzbMATHCrossRefGoogle Scholar
  76. Lee JN (ed) (1995) Design issues in optical processing. Cambridge studies in modern optics. Cambridge University Press, CambridgeGoogle Scholar
  77. Leith EN (1977) Complex spatial filters for image deconvolution. Proc IEEE 65(1):18–28CrossRefGoogle Scholar
  78. Lenslet Labs (2001) Optical digital signal processing engine. White paper report, Lenslet Ltd., 12 Hachilazon St., Ramat-Gan, Israel 52522Google Scholar
  79. Lipton RJ (1995) Using DNA to solve NP-complete problems. Science 268:542–545ADSCrossRefGoogle Scholar
  80. Lohmann AW (1993) Image rotation, Wigner rotation, and the fractional Fourier transform. J Opt Soc Am A 10(10):2181–2186ADSMathSciNetCrossRefGoogle Scholar
  81. Louri A, Post A (1992) Complexity analysis of optical-computing paradigms. Appl Opt 31(26):5568–5583ADSCrossRefGoogle Scholar
  82. Louri A, Hatch JA Jr, Na J (1995) Constant-time parallel sorting algorithm and its optical implementation using smart pixels. Appl Opt 34(17):3087–3097ADSCrossRefGoogle Scholar
  83. Lu XJ, Yu FTS, Gregory DA (1990) Comparison of Vander lugt and joint transform correlators. Appl Phys B 51:153–164ADSCrossRefGoogle Scholar
  84. McAulay AD (1991) Optical computer architectures: the application of optical concepts to next generation computers. Wiley, New YorkzbMATHGoogle Scholar
  85. Mead C (1989) Analog VLSI and neural systems. Addison-Wesley, ReadingzbMATHCrossRefGoogle Scholar
  86. Miller DA (2000) Rationale and challenges for optical interconnects to electronic chips. Proc IEEE 88(6):728–749CrossRefGoogle Scholar
  87. Moore C (1991) Generalized shifts: undecidability and unpredictability in dynamical systems. Nonlinearity 4:199–230ADSMathSciNetzbMATHCrossRefGoogle Scholar
  88. Moore C (1997) Majority-vote cellular automata, Ising dynamics and P-completeness. J Stat Phys 88(3/4):795–805ADSMathSciNetzbMATHCrossRefGoogle Scholar
  89. Naughton TJ (2000a) Continuous-space model of computation is Turing universal. In: Bains S, Irakliotis LJ (eds) Critical technologies for the future of computing. Proc SPIE, vol 4109. SPIE Press, San Diego, pp 121–128Google Scholar
  90. Naughton TJ (2000b) A model of computation for Fourier optical processors. In: Lessard RA, Galstian T (eds) Optics in computing 2000. Proc SPIE, vol 4089. SPIE Press, Quebec, pp 24–34Google Scholar
  91. Naughton TJ, Woods D (2001) On the computational power of a continuous-space optical model of computation. In: Margenstern M, Rogozhin Y (eds) Machines, computations and universality: third international conference (MCU’01), vol 2055, LNCS. Springer, Heidelberg, pp 288–299CrossRefGoogle Scholar
  92. Naughton T, Javadpour Z, Keating J, Klíma M, Rott J (1999) General-purpose acousto-optic connectionist processor. Opt Eng 38(7):1170–1177ADSCrossRefGoogle Scholar
  93. O’Neill EL (1956) Spatial filtering in optics. IRE Trans Inf Theory 2:56–65CrossRefGoogle Scholar
  94. Oltean M (2006) A light-based device for solving the Hamiltonian path problem. In: Fifth international conference on unconventional computation (UC’06). LNCS, vol 4135. Springer, New York, pp 217–227Google Scholar
  95. Paek EG, Choe JY, Oh TK, Hong JH, Chang TY (1997) Nonmechanical image rotation with an acousto-optic dove prism. Opt Lett 22(15):1195–1197ADSCrossRefGoogle Scholar
  96. Papadimitriou CH (1995) Computational complexity. Addison-Wesley, ReadingzbMATHGoogle Scholar
  97. Parberry I (1987) Parallel complexity theory. Wiley, New YorkzbMATHGoogle Scholar
  98. Păun G (2002) Membrane computing: an introduction. Springer, HeidelbergzbMATHCrossRefGoogle Scholar
  99. Pe’er A, Wang D, Lohmann AW, Friesem AA (1999) Optical correlation with totally incoherent light. Opt Lett 24(21):1469–1471ADSCrossRefGoogle Scholar
  100. Pittman TB, Fitch MJ, Jacobs BC, Franson JD (2003) Experimental controlled-NOT logic gate for single photons in the coincidence basis. Phys Rev A 68:032316–3ADSCrossRefGoogle Scholar
  101. Pratt VR, Stockmeyer LJ (1976) A characterisation of the power of vector machines. J Comput Syst Sci 12:198–221MathSciNetzbMATHCrossRefGoogle Scholar
  102. Pratt VR, Rabin MO, Stockmeyer LJ (1974) A characterisation of the power of vector machines. In: Proceedings of 6th annual ACM symposium on theory of computing. ACM, New York, pp 122–134Google Scholar
  103. Psaltis D, Farhat NH (1985) Optical information processing based on an associative-memory model of neural nets with thresholding and feedback. Opt Lett 10(2):98–100ADSCrossRefGoogle Scholar
  104. Pu A, Denkewalter RF, Psaltis D (1997) Real-time vehicle navigation using a holographic memory. Opt Eng 36(10):2737–2746ADSCrossRefGoogle Scholar
  105. Reif JH, Tyagi A (1997) Efficient parallel algorithms for optical computing with the discrete Fourier transform (DFT) primitive. Appl Opt 36(29):7327–7340ADSCrossRefGoogle Scholar
  106. Reif J, Tygar D, Yoshida A (1990) The computability and complexity of optical beam tracing. In: 31st annual IEEE symposium on Foundations of Computer Science (FOCS). IEEE, St. Louis, pp 106114Google Scholar
  107. Rhodes WT (1981) Acousto-optic signal processing: convolution and correlation. Proc IEEE 69(1):65–79ADSMathSciNetCrossRefGoogle Scholar
  108. Sawchuk AA, Strand TC (1984) Digital optical computing. Proc IEEE 72(7):758–779CrossRefGoogle Scholar
  109. Shaked NT, Simon G, Tabib T, Mesika S, Dolev S, Rosen J (2006) Optical processor for solving the traveling salesman problem (TSP). In: Javidi B, Psaltis D, Caulfield HJ (eds) Proceedings of SPIE, optical information systems IV, vol 63110G. SPIE, BellinghamGoogle Scholar
  110. Shaked NT, Messika S, Dolev S, Rosen J (2007) Optical solution for bounded NP-complete problems. Appl Opt 46(5):711–724ADSCrossRefGoogle Scholar
  111. Shor P (1994) Algorithms for quantum computation: discrete logarithms and factoring. In: Proceedings 35th annual symposium on foundations computer science. ACM, New York, pp 124–134Google Scholar
  112. Sosik P (2003) The computational power of cell division in P systems: beating down parallel computers? Nat Comput 2(3):287–298MathSciNetzbMATHCrossRefGoogle Scholar
  113. Sosik P, Rodriguez-Paton A (2007) Membrane computing and complexity theory: a characterization of PSPACE. J Comput Syst Sci 73(1):137–152MathSciNetzbMATHCrossRefGoogle Scholar
  114. Stirk CW, Athale RA (1988) Sorting with optical compare-and-exchange modules. Appl Opt 27(9):1721–1726ADSCrossRefGoogle Scholar
  115. Stone RV (1994) Optoelectronic processor is programmable and flexible. Laser Focus World 30(8):77–79Google Scholar
  116. Stone RV, Zeise FF, Guilfoyle PS (1991) DOC II 32-bit digital optical computer: optoelectronic hardware and software. In: Optical enhancements to computing technology, Proc SPIE, vol 1563. SPIE, Bellingham, pp 267–278Google Scholar
  117. Stroke GW, Halioua M, Thon F, Willasch DH (1974) Image improvement in high-resolution electron microscopy using holographic image deconvolution. Optik 41(3):319–343Google Scholar
  118. Sullivan DL (1972) Alignment of rotational prisms. Appl Opt 11(9):2028–2032ADSCrossRefGoogle Scholar
  119. Tromp J, van Emde Boas P (1993) Associative storage modification machines. In: Ambos-Spies K, Homer S, Schoning U (eds) Complexity theory: current research. Cambridge University Press, Cambridge, UK, pp 291–313Google Scholar
  120. Turin GL (1960) An introduction to matched filters. IRE Trans Inf Theory 6(3):311–329MathSciNetCrossRefGoogle Scholar
  121. Upatnieks J (1983) Portable real-time coherent optical correlator. Appl Opt 22(18):2798–2803ADSCrossRefGoogle Scholar
  122. van Emde Boas P (1990) Machine models and simulations, chap 1. In: van Leeuwen J (ed) Handbook of theoretical computer science, vol A. Elsevier, AmsterdamGoogle Scholar
  123. van Leeuwen J, Wiedermann J (1987) Array processing machines. BIT 27:25–43MathSciNetzbMATHCrossRefGoogle Scholar
  124. VanderLugt A (1964) Signal detection by complex spatial filtering. IEEE Trans Inf Theory 10(2):139–145CrossRefGoogle Scholar
  125. VanderLugt A (1974) Coherent optical processing. Proc IEEE 62(10):1300–1319ADSCrossRefGoogle Scholar
  126. VanderLugt A (1992) Optical signal processing. Wiley, New YorkGoogle Scholar
  127. Wang CH, Jenkins BK (1990) Subtracting incoherent optical neuron model – analysis, experiment and applications. Appl Opt 29(14):2171–2186ADSCrossRefGoogle Scholar
  128. Wang PY, Saffman M (1999) Selecting optical patterns with spatial phase modulation. Opt Lett 24(16):1118–1120ADSCrossRefGoogle Scholar
  129. Weaver CS, Goodman JW (1966) A technique for optically convolving two functions. Appl Opt 5(7):1248–1249ADSCrossRefGoogle Scholar
  130. Woods D (2005a) Computational complexity of an optical model of computation. PhD thesis, National University of Ireland, MaynoothGoogle Scholar
  131. Woods D (2005b) Upper bounds on the computational power of an optical model of computation. In: Deng X, Du D (eds) 16th international symposium on algorithms and computation (ISAAC 2005). LNCS, vol 3827. Springer, Heidelberg, pp 777–788Google Scholar
  132. Woods D (2006) Optical computing and computational complexity. In: Fifth international conference on unconventional computation (UC’06). LNCS, vol 4135. Springer, pp 27–40Google Scholar
  133. Woods D, Gibson JP (2005a) Complexity of continuous space machine operations. In: Cooper SB, Löewe B, Torenvliet L (eds) New computational paradigms, first conference on computability in Europe (CiE 2005), vol 3526, LNCS. Springer, Amsterdam, pp 540–551Google Scholar
  134. Woods D, Gibson JP (2005b) Lower bounds on the computational power of an optical model of computation. In: Calude CS, Dinneen MJ, Păun G, Pérez-Jiménez MJ, Rozenberg G (eds) Fourth international conference on unconventional computation (UC’05), vol 3699, LNCS. Springer, Heidelberg, pp 237–250CrossRefGoogle Scholar
  135. Woods D, Naughton TJ (2005) An optical model of computation. Theor Comput Sci 334(1-3):227–258MathSciNetzbMATHCrossRefGoogle Scholar
  136. Woods D, Naughton TJ (2008) Parallel and sequential optical computing. In: International workshop on optical supercomputing. LNCS. Springer, HeidelbergGoogle Scholar
  137. Yamaguchi I, Zhang T (1997) Phase-shifting digital holography. Opt Lett 22(16):1268–1270ADSCrossRefGoogle Scholar
  138. Yokomori T (2002) Molecular computing paradigm – toward freedom from Turing’s charm. Nat Comput 1(4):333–390MathSciNetzbMATHCrossRefGoogle Scholar
  139. Yu FTS (1996) Garden of joint transform correlators: an account of recent advances. In: Second international conference on optical information processing. Proc SPIE, vol 2969. SPIE, Bellingham, pp 396–401Google Scholar
  140. Yu FTS, Lu T, Yang X, Gregory DA (1990) Optical neural network with pocket-sized liquid-crystal televisions. Opt Lett 15(15):863–865ADSCrossRefGoogle Scholar
  141. Yu FTS, Jutamulia S, Yin S (eds) (2001) Introduction to information optics. Academic, San DiegoGoogle Scholar
  142. Zhai H, Mu G, Sun J, Zhu X, Liu F, Kang H, Zhan Y (1999) Color pattern recognition in white-light, joint transform correlation. Appl Opt 38(35):7238–7244ADSCrossRefGoogle Scholar

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Authors and Affiliations

  1. 1.Department of Computer ScienceNational University of IrelandMaynooth County KildareIreland
  2. 2.Computer ScienceCalifornia Institute of TechnologyPasadenaUSA