Abstract

Analog Fourier optical processing systems can perform important classes of signal processing operations in parallel, but suffer from limited accuracy. Digital–optical equivalents of such systems could be built that share many features of the analog systems while allowing greater accuracy. We show that the digital equivalent of any system consisting of an arbitrary number of lenses, filters, spatial light modulators, and sections of free space can be constructed. There are many possible applications for such systems as well as many alternative technologies for constructing them; this paper stresses the potential of free-space interconnected active-device-plane-based optoelectronic architectures as a digital signal processing environment. Implementation of the active-device planes through hybridization of optoelectronic components with silicon electronics should allow the realization of systems whose performance exceeds that of purely electronic systems.

© 1996 Optical Society of America

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  1. J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968).
  2. J. W. Goodman, “Four decades of optical information processing,” Opt. Photonics News 2(2), 11–15 (1991).
  3. H. M. Ozaktas, Y. Amitai, J. W. Goodman, “Comparison of system size for some optical interconnection architectures and the folded multi-facet architecture” Opt. Commun. 82, 225–228 (1991).
  4. H. M. Ozaktas, D. Mendlovic, “Multi-stage optical interconnection architectures with least possible growth of system size” Opt. Lett. 18, 296–298 (1993).
  5. D. Mendlovic, H. M. Ozaktas, “Optical-coordinate transformation methods and optical-interconnection architectures,” Appl. Opt. 32, 5119–5124 (1993).
  6. See, for example, the special issue on smart pixels, S. R. Forrest, H. S. Hinton, eds., IEEE J. Quantum Electron.29 (2), (1993).
  7. See, for example, D. A. B. Miller, “Computing with light,” in 1995 Yearbook of Science and the Future (Encyclopedia Britannica, Chicago, 1994), pp. 134–147.
  8. F. B. McCormick, T. J. Cloonan, A. L. Lentine, J. M. Sasian, R. L. Morrison, M. G. Beckman, S. L. Walker, M. J. Wojcik, S. J. Hinterlong, R. J. Crisci, R. A. Novotny, H. S. Hinton, “Five-stage free-space optical switching network with field-effect transistor self-electro-optic-effect-device smart-pixel arrays,” Appl. Opt.33, 1601–1618 (1994);H. S. Hinton, T. J. Cloonan, F. B. McCormick, A. L. Lentine, F. A. P. Tooley, “Free-space digital optical systems” Proc. IEEE 82, 1632–1649 (1994).
  9. K. S. Huang, C. B. Kuznia, B. K. Jenkins, A. A. Sawchuk, “Parallel architectures for digital optical cellular image processing” Proc. IEEE 82, 1711–1723 (1994).
  10. K. W. Goossen, J. E. Cunningham, W. Y. Jan, “GaAs 850 modulators solder-bonded to silicon” IEEE Photonics Tech-nol. Lett. 5, 776–778 (1993);K. W. Goosen, J. E. Cunningham, J. A. Walker, L. A. D’Asaro, S. P. Hui, P. Tseng, R. Leibenguth, D. Kossives, D. Kossives, D. D. Bacon, D. Dahringer, L. M. F. Chirovsky, A. L. Lentine, D. A. B. Miller, “GaAs MQW modulators integrated with silicon CMOS” IEEE Photonics Technol. Lett. 7, 360–362 (1995).
  11. F. Kiamilev, A. Krishnamoorthy, “Smart pixel designs for image processing,” in Photonics for Processors, Neural Networks, and Memories II, J. L. Horner, B. Javidi, S. T. Kowel, eds., Proc. Soc. Photo-Opt. Instrum. Eng.2297, 37 (1994).
  12. A. K. Jain, Fundamentals of Digital Image Processing (Prentice-Hall, Englewood Cliffs, N.J., 1989), p. 505.
  13. S. G. Smith, P. B. Denyer, “Efficient bit-serial complex multiplication and sum-of-products computation using distributed arithmetic,” in Proceedings of the International Conference on Acoustics, Speech, and Signal Processing, 1986 (IEEE, New York, 1986), pp. 2203–2206.
  14. R. F. Lyon, “Two’s complement pipeline multipliers” IEEE Trans. Commun. 24, 418–425 (1976).
  15. H. M. Ozaktas, J. W. Goodman, “Elements of a hybrid interconnection theory,” Appl. Opt. 33, 2968–2987 (1994).
  16. A. V. Krishnamoorthy, P. J. Marchand, F. E. Kiamilev, S. C. Esener, “Grain-size considerations for optoelectronic multistage interconnection networks,” Appl. Opt. 31, 5480–5507 (1992).
  17. M.J. Bastiaans, “Wigner distribution function and its application to first-order optics” J. Opt. Soc. Am. 69, 1710–1716 (1979).
  18. H. M. Ozaktas, D. Mendlovic, “Fractional Fourier optics” J. Opt. Soc. Am. A 12, 743–751 (1995).
  19. A. Papoulis, Signal Analysis (McGraw-Hill, New York, 1977), p. 289.
  20. M. Nazarathy, J. Shamir, “First-order optics—a canonical operator representation: lossless systems” J. Opt. Soc. Am. 72, 356–364 (1982).
  21. H. M. Ozaktas, B. Barshan, D. Mendlovic, L. Onural, “Convolution, filtering, and multiplexing in fractional Fourier domains and their relation to chirp and wavelet transforms” J. Opt. Soc. Am. A 11, 547–559 (1994).
  22. A. W. Lohmann, “Image rotation, Wigner rotation, and the fractional Fourier transform” J. Opt. Soc. Am. A 10, 2181–2186 (1993).
  23. A. W. Lohmann, B. H. Soffer, “Relationships between the Radon–Wigner and fractional Fourier transformations” J. Opt. Soc. Am. A 11, 1798–1801 (1994).
  24. L. B. Almeida, “The fractional Fourier transform and time-frequency representations” IEEE Trans. Signal Process. 42, 3084–3091 (1994).
  25. A. C. McBride, F. H. Kerr, “On Namias’s fractional Fourier transforms” IMA J. Appl. Math. 39, 159–175 (1987).
  26. A. L. Lentine, K. W. Goossen, J. F. Walker, L. M. F. Chirovsky, L. A. D’Asaro, B. Tseng, R. E. Leibenguth, D. Kossives, D. Dahringer, D. D. Bacon, T. K. Woodward, “700 Mb/s operation of optoelectronic switching nodes comprised of flip-chip-bonded GaAs/AlGaAs MQW modulators on silicon CMOS circuitry,” in Conference on Lasers and Electro-Optics, Vol. 15 of 1995 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1995), postdeadline paper CPD11.
  27. M. J. Little, J. Grinberg, “The 3-D computer: an integrated stack of WSI wafers,” in Wafer-Scale Integration (Kluwer, New York, 1988), Chap. 8.

1995 (1)

1994 (5)

1993 (4)

K. W. Goossen, J. E. Cunningham, W. Y. Jan, “GaAs 850 modulators solder-bonded to silicon” IEEE Photonics Tech-nol. Lett. 5, 776–778 (1993);K. W. Goosen, J. E. Cunningham, J. A. Walker, L. A. D’Asaro, S. P. Hui, P. Tseng, R. Leibenguth, D. Kossives, D. Kossives, D. D. Bacon, D. Dahringer, L. M. F. Chirovsky, A. L. Lentine, D. A. B. Miller, “GaAs MQW modulators integrated with silicon CMOS” IEEE Photonics Technol. Lett. 7, 360–362 (1995).

A. W. Lohmann, “Image rotation, Wigner rotation, and the fractional Fourier transform” J. Opt. Soc. Am. A 10, 2181–2186 (1993).

H. M. Ozaktas, D. Mendlovic, “Multi-stage optical interconnection architectures with least possible growth of system size” Opt. Lett. 18, 296–298 (1993).

D. Mendlovic, H. M. Ozaktas, “Optical-coordinate transformation methods and optical-interconnection architectures,” Appl. Opt. 32, 5119–5124 (1993).

1992 (1)

1991 (2)

J. W. Goodman, “Four decades of optical information processing,” Opt. Photonics News 2(2), 11–15 (1991).

H. M. Ozaktas, Y. Amitai, J. W. Goodman, “Comparison of system size for some optical interconnection architectures and the folded multi-facet architecture” Opt. Commun. 82, 225–228 (1991).

1987 (1)

A. C. McBride, F. H. Kerr, “On Namias’s fractional Fourier transforms” IMA J. Appl. Math. 39, 159–175 (1987).

1982 (1)

M. Nazarathy, J. Shamir, “First-order optics—a canonical operator representation: lossless systems” J. Opt. Soc. Am. 72, 356–364 (1982).

1979 (1)

M.J. Bastiaans, “Wigner distribution function and its application to first-order optics” J. Opt. Soc. Am. 69, 1710–1716 (1979).

1976 (1)

R. F. Lyon, “Two’s complement pipeline multipliers” IEEE Trans. Commun. 24, 418–425 (1976).

Almeida, L. B.

L. B. Almeida, “The fractional Fourier transform and time-frequency representations” IEEE Trans. Signal Process. 42, 3084–3091 (1994).

Amitai, Y.

H. M. Ozaktas, Y. Amitai, J. W. Goodman, “Comparison of system size for some optical interconnection architectures and the folded multi-facet architecture” Opt. Commun. 82, 225–228 (1991).

Bacon, D. D.

A. L. Lentine, K. W. Goossen, J. F. Walker, L. M. F. Chirovsky, L. A. D’Asaro, B. Tseng, R. E. Leibenguth, D. Kossives, D. Dahringer, D. D. Bacon, T. K. Woodward, “700 Mb/s operation of optoelectronic switching nodes comprised of flip-chip-bonded GaAs/AlGaAs MQW modulators on silicon CMOS circuitry,” in Conference on Lasers and Electro-Optics, Vol. 15 of 1995 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1995), postdeadline paper CPD11.

Barshan, B.

Bastiaans, M.J.

M.J. Bastiaans, “Wigner distribution function and its application to first-order optics” J. Opt. Soc. Am. 69, 1710–1716 (1979).

Beckman, M. G.

F. B. McCormick, T. J. Cloonan, A. L. Lentine, J. M. Sasian, R. L. Morrison, M. G. Beckman, S. L. Walker, M. J. Wojcik, S. J. Hinterlong, R. J. Crisci, R. A. Novotny, H. S. Hinton, “Five-stage free-space optical switching network with field-effect transistor self-electro-optic-effect-device smart-pixel arrays,” Appl. Opt.33, 1601–1618 (1994);H. S. Hinton, T. J. Cloonan, F. B. McCormick, A. L. Lentine, F. A. P. Tooley, “Free-space digital optical systems” Proc. IEEE 82, 1632–1649 (1994).

Chirovsky, L. M. F.

A. L. Lentine, K. W. Goossen, J. F. Walker, L. M. F. Chirovsky, L. A. D’Asaro, B. Tseng, R. E. Leibenguth, D. Kossives, D. Dahringer, D. D. Bacon, T. K. Woodward, “700 Mb/s operation of optoelectronic switching nodes comprised of flip-chip-bonded GaAs/AlGaAs MQW modulators on silicon CMOS circuitry,” in Conference on Lasers and Electro-Optics, Vol. 15 of 1995 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1995), postdeadline paper CPD11.

Cloonan, T. J.

F. B. McCormick, T. J. Cloonan, A. L. Lentine, J. M. Sasian, R. L. Morrison, M. G. Beckman, S. L. Walker, M. J. Wojcik, S. J. Hinterlong, R. J. Crisci, R. A. Novotny, H. S. Hinton, “Five-stage free-space optical switching network with field-effect transistor self-electro-optic-effect-device smart-pixel arrays,” Appl. Opt.33, 1601–1618 (1994);H. S. Hinton, T. J. Cloonan, F. B. McCormick, A. L. Lentine, F. A. P. Tooley, “Free-space digital optical systems” Proc. IEEE 82, 1632–1649 (1994).

Crisci, R. J.

F. B. McCormick, T. J. Cloonan, A. L. Lentine, J. M. Sasian, R. L. Morrison, M. G. Beckman, S. L. Walker, M. J. Wojcik, S. J. Hinterlong, R. J. Crisci, R. A. Novotny, H. S. Hinton, “Five-stage free-space optical switching network with field-effect transistor self-electro-optic-effect-device smart-pixel arrays,” Appl. Opt.33, 1601–1618 (1994);H. S. Hinton, T. J. Cloonan, F. B. McCormick, A. L. Lentine, F. A. P. Tooley, “Free-space digital optical systems” Proc. IEEE 82, 1632–1649 (1994).

Cunningham, J. E.

K. W. Goossen, J. E. Cunningham, W. Y. Jan, “GaAs 850 modulators solder-bonded to silicon” IEEE Photonics Tech-nol. Lett. 5, 776–778 (1993);K. W. Goosen, J. E. Cunningham, J. A. Walker, L. A. D’Asaro, S. P. Hui, P. Tseng, R. Leibenguth, D. Kossives, D. Kossives, D. D. Bacon, D. Dahringer, L. M. F. Chirovsky, A. L. Lentine, D. A. B. Miller, “GaAs MQW modulators integrated with silicon CMOS” IEEE Photonics Technol. Lett. 7, 360–362 (1995).

D’Asaro, L. A.

A. L. Lentine, K. W. Goossen, J. F. Walker, L. M. F. Chirovsky, L. A. D’Asaro, B. Tseng, R. E. Leibenguth, D. Kossives, D. Dahringer, D. D. Bacon, T. K. Woodward, “700 Mb/s operation of optoelectronic switching nodes comprised of flip-chip-bonded GaAs/AlGaAs MQW modulators on silicon CMOS circuitry,” in Conference on Lasers and Electro-Optics, Vol. 15 of 1995 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1995), postdeadline paper CPD11.

Dahringer, D.

A. L. Lentine, K. W. Goossen, J. F. Walker, L. M. F. Chirovsky, L. A. D’Asaro, B. Tseng, R. E. Leibenguth, D. Kossives, D. Dahringer, D. D. Bacon, T. K. Woodward, “700 Mb/s operation of optoelectronic switching nodes comprised of flip-chip-bonded GaAs/AlGaAs MQW modulators on silicon CMOS circuitry,” in Conference on Lasers and Electro-Optics, Vol. 15 of 1995 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1995), postdeadline paper CPD11.

Denyer, P. B.

S. G. Smith, P. B. Denyer, “Efficient bit-serial complex multiplication and sum-of-products computation using distributed arithmetic,” in Proceedings of the International Conference on Acoustics, Speech, and Signal Processing, 1986 (IEEE, New York, 1986), pp. 2203–2206.

Esener, S. C.

Goodman, J. W.

H. M. Ozaktas, J. W. Goodman, “Elements of a hybrid interconnection theory,” Appl. Opt. 33, 2968–2987 (1994).

H. M. Ozaktas, Y. Amitai, J. W. Goodman, “Comparison of system size for some optical interconnection architectures and the folded multi-facet architecture” Opt. Commun. 82, 225–228 (1991).

J. W. Goodman, “Four decades of optical information processing,” Opt. Photonics News 2(2), 11–15 (1991).

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968).

Goossen, K. W.

K. W. Goossen, J. E. Cunningham, W. Y. Jan, “GaAs 850 modulators solder-bonded to silicon” IEEE Photonics Tech-nol. Lett. 5, 776–778 (1993);K. W. Goosen, J. E. Cunningham, J. A. Walker, L. A. D’Asaro, S. P. Hui, P. Tseng, R. Leibenguth, D. Kossives, D. Kossives, D. D. Bacon, D. Dahringer, L. M. F. Chirovsky, A. L. Lentine, D. A. B. Miller, “GaAs MQW modulators integrated with silicon CMOS” IEEE Photonics Technol. Lett. 7, 360–362 (1995).

A. L. Lentine, K. W. Goossen, J. F. Walker, L. M. F. Chirovsky, L. A. D’Asaro, B. Tseng, R. E. Leibenguth, D. Kossives, D. Dahringer, D. D. Bacon, T. K. Woodward, “700 Mb/s operation of optoelectronic switching nodes comprised of flip-chip-bonded GaAs/AlGaAs MQW modulators on silicon CMOS circuitry,” in Conference on Lasers and Electro-Optics, Vol. 15 of 1995 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1995), postdeadline paper CPD11.

Grinberg, J.

M. J. Little, J. Grinberg, “The 3-D computer: an integrated stack of WSI wafers,” in Wafer-Scale Integration (Kluwer, New York, 1988), Chap. 8.

Hinterlong, S. J.

F. B. McCormick, T. J. Cloonan, A. L. Lentine, J. M. Sasian, R. L. Morrison, M. G. Beckman, S. L. Walker, M. J. Wojcik, S. J. Hinterlong, R. J. Crisci, R. A. Novotny, H. S. Hinton, “Five-stage free-space optical switching network with field-effect transistor self-electro-optic-effect-device smart-pixel arrays,” Appl. Opt.33, 1601–1618 (1994);H. S. Hinton, T. J. Cloonan, F. B. McCormick, A. L. Lentine, F. A. P. Tooley, “Free-space digital optical systems” Proc. IEEE 82, 1632–1649 (1994).

Hinton, H. S.

F. B. McCormick, T. J. Cloonan, A. L. Lentine, J. M. Sasian, R. L. Morrison, M. G. Beckman, S. L. Walker, M. J. Wojcik, S. J. Hinterlong, R. J. Crisci, R. A. Novotny, H. S. Hinton, “Five-stage free-space optical switching network with field-effect transistor self-electro-optic-effect-device smart-pixel arrays,” Appl. Opt.33, 1601–1618 (1994);H. S. Hinton, T. J. Cloonan, F. B. McCormick, A. L. Lentine, F. A. P. Tooley, “Free-space digital optical systems” Proc. IEEE 82, 1632–1649 (1994).

Huang, K. S.

K. S. Huang, C. B. Kuznia, B. K. Jenkins, A. A. Sawchuk, “Parallel architectures for digital optical cellular image processing” Proc. IEEE 82, 1711–1723 (1994).

Jain, A. K.

A. K. Jain, Fundamentals of Digital Image Processing (Prentice-Hall, Englewood Cliffs, N.J., 1989), p. 505.

Jan, W. Y.

K. W. Goossen, J. E. Cunningham, W. Y. Jan, “GaAs 850 modulators solder-bonded to silicon” IEEE Photonics Tech-nol. Lett. 5, 776–778 (1993);K. W. Goosen, J. E. Cunningham, J. A. Walker, L. A. D’Asaro, S. P. Hui, P. Tseng, R. Leibenguth, D. Kossives, D. Kossives, D. D. Bacon, D. Dahringer, L. M. F. Chirovsky, A. L. Lentine, D. A. B. Miller, “GaAs MQW modulators integrated with silicon CMOS” IEEE Photonics Technol. Lett. 7, 360–362 (1995).

Jenkins, B. K.

K. S. Huang, C. B. Kuznia, B. K. Jenkins, A. A. Sawchuk, “Parallel architectures for digital optical cellular image processing” Proc. IEEE 82, 1711–1723 (1994).

Kerr, F. H.

A. C. McBride, F. H. Kerr, “On Namias’s fractional Fourier transforms” IMA J. Appl. Math. 39, 159–175 (1987).

Kiamilev, F.

F. Kiamilev, A. Krishnamoorthy, “Smart pixel designs for image processing,” in Photonics for Processors, Neural Networks, and Memories II, J. L. Horner, B. Javidi, S. T. Kowel, eds., Proc. Soc. Photo-Opt. Instrum. Eng.2297, 37 (1994).

Kiamilev, F. E.

Kossives, D.

A. L. Lentine, K. W. Goossen, J. F. Walker, L. M. F. Chirovsky, L. A. D’Asaro, B. Tseng, R. E. Leibenguth, D. Kossives, D. Dahringer, D. D. Bacon, T. K. Woodward, “700 Mb/s operation of optoelectronic switching nodes comprised of flip-chip-bonded GaAs/AlGaAs MQW modulators on silicon CMOS circuitry,” in Conference on Lasers and Electro-Optics, Vol. 15 of 1995 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1995), postdeadline paper CPD11.

Krishnamoorthy, A.

F. Kiamilev, A. Krishnamoorthy, “Smart pixel designs for image processing,” in Photonics for Processors, Neural Networks, and Memories II, J. L. Horner, B. Javidi, S. T. Kowel, eds., Proc. Soc. Photo-Opt. Instrum. Eng.2297, 37 (1994).

Krishnamoorthy, A. V.

Kuznia, C. B.

K. S. Huang, C. B. Kuznia, B. K. Jenkins, A. A. Sawchuk, “Parallel architectures for digital optical cellular image processing” Proc. IEEE 82, 1711–1723 (1994).

Leibenguth, R. E.

A. L. Lentine, K. W. Goossen, J. F. Walker, L. M. F. Chirovsky, L. A. D’Asaro, B. Tseng, R. E. Leibenguth, D. Kossives, D. Dahringer, D. D. Bacon, T. K. Woodward, “700 Mb/s operation of optoelectronic switching nodes comprised of flip-chip-bonded GaAs/AlGaAs MQW modulators on silicon CMOS circuitry,” in Conference on Lasers and Electro-Optics, Vol. 15 of 1995 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1995), postdeadline paper CPD11.

Lentine, A. L.

A. L. Lentine, K. W. Goossen, J. F. Walker, L. M. F. Chirovsky, L. A. D’Asaro, B. Tseng, R. E. Leibenguth, D. Kossives, D. Dahringer, D. D. Bacon, T. K. Woodward, “700 Mb/s operation of optoelectronic switching nodes comprised of flip-chip-bonded GaAs/AlGaAs MQW modulators on silicon CMOS circuitry,” in Conference on Lasers and Electro-Optics, Vol. 15 of 1995 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1995), postdeadline paper CPD11.

F. B. McCormick, T. J. Cloonan, A. L. Lentine, J. M. Sasian, R. L. Morrison, M. G. Beckman, S. L. Walker, M. J. Wojcik, S. J. Hinterlong, R. J. Crisci, R. A. Novotny, H. S. Hinton, “Five-stage free-space optical switching network with field-effect transistor self-electro-optic-effect-device smart-pixel arrays,” Appl. Opt.33, 1601–1618 (1994);H. S. Hinton, T. J. Cloonan, F. B. McCormick, A. L. Lentine, F. A. P. Tooley, “Free-space digital optical systems” Proc. IEEE 82, 1632–1649 (1994).

Little, M. J.

M. J. Little, J. Grinberg, “The 3-D computer: an integrated stack of WSI wafers,” in Wafer-Scale Integration (Kluwer, New York, 1988), Chap. 8.

Lohmann, A. W.

Lyon, R. F.

R. F. Lyon, “Two’s complement pipeline multipliers” IEEE Trans. Commun. 24, 418–425 (1976).

Marchand, P. J.

McBride, A. C.

A. C. McBride, F. H. Kerr, “On Namias’s fractional Fourier transforms” IMA J. Appl. Math. 39, 159–175 (1987).

McCormick, F. B.

F. B. McCormick, T. J. Cloonan, A. L. Lentine, J. M. Sasian, R. L. Morrison, M. G. Beckman, S. L. Walker, M. J. Wojcik, S. J. Hinterlong, R. J. Crisci, R. A. Novotny, H. S. Hinton, “Five-stage free-space optical switching network with field-effect transistor self-electro-optic-effect-device smart-pixel arrays,” Appl. Opt.33, 1601–1618 (1994);H. S. Hinton, T. J. Cloonan, F. B. McCormick, A. L. Lentine, F. A. P. Tooley, “Free-space digital optical systems” Proc. IEEE 82, 1632–1649 (1994).

Mendlovic, D.

Miller, D. A. B.

See, for example, D. A. B. Miller, “Computing with light,” in 1995 Yearbook of Science and the Future (Encyclopedia Britannica, Chicago, 1994), pp. 134–147.

Morrison, R. L.

F. B. McCormick, T. J. Cloonan, A. L. Lentine, J. M. Sasian, R. L. Morrison, M. G. Beckman, S. L. Walker, M. J. Wojcik, S. J. Hinterlong, R. J. Crisci, R. A. Novotny, H. S. Hinton, “Five-stage free-space optical switching network with field-effect transistor self-electro-optic-effect-device smart-pixel arrays,” Appl. Opt.33, 1601–1618 (1994);H. S. Hinton, T. J. Cloonan, F. B. McCormick, A. L. Lentine, F. A. P. Tooley, “Free-space digital optical systems” Proc. IEEE 82, 1632–1649 (1994).

Nazarathy, M.

M. Nazarathy, J. Shamir, “First-order optics—a canonical operator representation: lossless systems” J. Opt. Soc. Am. 72, 356–364 (1982).

Novotny, R. A.

F. B. McCormick, T. J. Cloonan, A. L. Lentine, J. M. Sasian, R. L. Morrison, M. G. Beckman, S. L. Walker, M. J. Wojcik, S. J. Hinterlong, R. J. Crisci, R. A. Novotny, H. S. Hinton, “Five-stage free-space optical switching network with field-effect transistor self-electro-optic-effect-device smart-pixel arrays,” Appl. Opt.33, 1601–1618 (1994);H. S. Hinton, T. J. Cloonan, F. B. McCormick, A. L. Lentine, F. A. P. Tooley, “Free-space digital optical systems” Proc. IEEE 82, 1632–1649 (1994).

Onural, L.

Ozaktas, H. M.

Papoulis, A.

A. Papoulis, Signal Analysis (McGraw-Hill, New York, 1977), p. 289.

Sasian, J. M.

F. B. McCormick, T. J. Cloonan, A. L. Lentine, J. M. Sasian, R. L. Morrison, M. G. Beckman, S. L. Walker, M. J. Wojcik, S. J. Hinterlong, R. J. Crisci, R. A. Novotny, H. S. Hinton, “Five-stage free-space optical switching network with field-effect transistor self-electro-optic-effect-device smart-pixel arrays,” Appl. Opt.33, 1601–1618 (1994);H. S. Hinton, T. J. Cloonan, F. B. McCormick, A. L. Lentine, F. A. P. Tooley, “Free-space digital optical systems” Proc. IEEE 82, 1632–1649 (1994).

Sawchuk, A. A.

K. S. Huang, C. B. Kuznia, B. K. Jenkins, A. A. Sawchuk, “Parallel architectures for digital optical cellular image processing” Proc. IEEE 82, 1711–1723 (1994).

Shamir, J.

M. Nazarathy, J. Shamir, “First-order optics—a canonical operator representation: lossless systems” J. Opt. Soc. Am. 72, 356–364 (1982).

Smith, S. G.

S. G. Smith, P. B. Denyer, “Efficient bit-serial complex multiplication and sum-of-products computation using distributed arithmetic,” in Proceedings of the International Conference on Acoustics, Speech, and Signal Processing, 1986 (IEEE, New York, 1986), pp. 2203–2206.

Soffer, B. H.

Tseng, B.

A. L. Lentine, K. W. Goossen, J. F. Walker, L. M. F. Chirovsky, L. A. D’Asaro, B. Tseng, R. E. Leibenguth, D. Kossives, D. Dahringer, D. D. Bacon, T. K. Woodward, “700 Mb/s operation of optoelectronic switching nodes comprised of flip-chip-bonded GaAs/AlGaAs MQW modulators on silicon CMOS circuitry,” in Conference on Lasers and Electro-Optics, Vol. 15 of 1995 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1995), postdeadline paper CPD11.

Walker, J. F.

A. L. Lentine, K. W. Goossen, J. F. Walker, L. M. F. Chirovsky, L. A. D’Asaro, B. Tseng, R. E. Leibenguth, D. Kossives, D. Dahringer, D. D. Bacon, T. K. Woodward, “700 Mb/s operation of optoelectronic switching nodes comprised of flip-chip-bonded GaAs/AlGaAs MQW modulators on silicon CMOS circuitry,” in Conference on Lasers and Electro-Optics, Vol. 15 of 1995 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1995), postdeadline paper CPD11.

Walker, S. L.

F. B. McCormick, T. J. Cloonan, A. L. Lentine, J. M. Sasian, R. L. Morrison, M. G. Beckman, S. L. Walker, M. J. Wojcik, S. J. Hinterlong, R. J. Crisci, R. A. Novotny, H. S. Hinton, “Five-stage free-space optical switching network with field-effect transistor self-electro-optic-effect-device smart-pixel arrays,” Appl. Opt.33, 1601–1618 (1994);H. S. Hinton, T. J. Cloonan, F. B. McCormick, A. L. Lentine, F. A. P. Tooley, “Free-space digital optical systems” Proc. IEEE 82, 1632–1649 (1994).

Wojcik, M. J.

F. B. McCormick, T. J. Cloonan, A. L. Lentine, J. M. Sasian, R. L. Morrison, M. G. Beckman, S. L. Walker, M. J. Wojcik, S. J. Hinterlong, R. J. Crisci, R. A. Novotny, H. S. Hinton, “Five-stage free-space optical switching network with field-effect transistor self-electro-optic-effect-device smart-pixel arrays,” Appl. Opt.33, 1601–1618 (1994);H. S. Hinton, T. J. Cloonan, F. B. McCormick, A. L. Lentine, F. A. P. Tooley, “Free-space digital optical systems” Proc. IEEE 82, 1632–1649 (1994).

Woodward, T. K.

A. L. Lentine, K. W. Goossen, J. F. Walker, L. M. F. Chirovsky, L. A. D’Asaro, B. Tseng, R. E. Leibenguth, D. Kossives, D. Dahringer, D. D. Bacon, T. K. Woodward, “700 Mb/s operation of optoelectronic switching nodes comprised of flip-chip-bonded GaAs/AlGaAs MQW modulators on silicon CMOS circuitry,” in Conference on Lasers and Electro-Optics, Vol. 15 of 1995 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1995), postdeadline paper CPD11.

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A. L. Lentine, K. W. Goossen, J. F. Walker, L. M. F. Chirovsky, L. A. D’Asaro, B. Tseng, R. E. Leibenguth, D. Kossives, D. Dahringer, D. D. Bacon, T. K. Woodward, “700 Mb/s operation of optoelectronic switching nodes comprised of flip-chip-bonded GaAs/AlGaAs MQW modulators on silicon CMOS circuitry,” in Conference on Lasers and Electro-Optics, Vol. 15 of 1995 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1995), postdeadline paper CPD11.

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F. B. McCormick, T. J. Cloonan, A. L. Lentine, J. M. Sasian, R. L. Morrison, M. G. Beckman, S. L. Walker, M. J. Wojcik, S. J. Hinterlong, R. J. Crisci, R. A. Novotny, H. S. Hinton, “Five-stage free-space optical switching network with field-effect transistor self-electro-optic-effect-device smart-pixel arrays,” Appl. Opt.33, 1601–1618 (1994);H. S. Hinton, T. J. Cloonan, F. B. McCormick, A. L. Lentine, F. A. P. Tooley, “Free-space digital optical systems” Proc. IEEE 82, 1632–1649 (1994).

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