Abstract

Optical computing is a new method to implement signal processing functions. The multiplication between a vector and a matrix is an important arithmetic algorithm in the signal processing domain. The optical vector–matrix multiplier (OVMM) is an optoelectronic system to carry out this operation, which consists of an electronic module and an optical module. In this paper, we propose an optical module for OVMM. To eliminate the cross talk and make full use of the optical elements, an elaborately designed structure that involves spherical lenses and cylindrical lenses is utilized in this optical system. The optical design software package ZEMAX is used to optimize the parameters and simulate the whole system. Finally, experimental data is obtained through experiments to evaluate the overall performance of the system. The results of both simulation and experiment indicate that the system constructed can implement the multiplication between a matrix with dimensions of 16 by 16 and a vector with a dimension of 16 successfully.

© 2013 Optical Society of America

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References

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    [CrossRef]
  3. J. W. Goodman, A. R. Dias, and L. M. Woody, “Fully parallel, high-speed incoherent optical method for performing discrete Fourier transforms,” Opt. Lett. 2, 1–3 (1978).
    [CrossRef]
  4. N. T. Shaked, T. Tabib, G. Simon, S. Messika, S. Dolev, and J. Rosen, “Optical binary-matrix synthesis for solving bounded NP-complete combinatorial problems,” Opt. Eng. 46, 108201 (2007).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  9. P. Le, D. Y. Zang, and Chen S. Tsai, “Integrated electrooptic Bragg modulator modules for matrix-vector and matrix-matrix multiplications,” App. Opt. 27, 1780–1785 (1988).
    [CrossRef]
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  12. J. W. Goodman, Introduction to Fourier Optics, 3rd ed. (Publishing House of Electronics Industry, 2006), Chap. 8, p. 206.
  13. Y. M. Zhang, Applied Optics (Publishing House of Electronics Industry, 2008).
  14. X. C. Yuan, Optical Design (Science, 1983).
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    [CrossRef]

2010 (2)

2007 (1)

N. T. Shaked, T. Tabib, G. Simon, S. Messika, S. Dolev, and J. Rosen, “Optical binary-matrix synthesis for solving bounded NP-complete combinatorial problems,” Opt. Eng. 46, 108201 (2007).
[CrossRef]

2004 (1)

1994 (1)

J. A. Carter, D. R. Pape, P. A. Wasilousky, and T. A. Sunderlin, “High-performance optical vector-matrix coprocessor,” Proc. SPIE 2297, 225–236 (1994).
[CrossRef]

1992 (2)

C. K. Gary, “Comparison of optics and electronics for the calculation of matrix-vector products,” Proc. SPIE 1704, 544–555 (1992).
[CrossRef]

C. K. Gary, “Matrix-vector multiplication using digital partitioning for more accurate optical computing,” Appl. Opt. 31, 6205–6211 (1992).
[CrossRef]

1988 (2)

L. J. Cheng and G. Gheen, “Matrix-vector multiplication in thin photorefractive GaAs crystals,” Appl. Opt. 27, 4236–4238 (1988).
[CrossRef]

P. Le, D. Y. Zang, and Chen S. Tsai, “Integrated electrooptic Bragg modulator modules for matrix-vector and matrix-matrix multiplications,” App. Opt. 27, 1780–1785 (1988).
[CrossRef]

1987 (1)

1986 (1)

1978 (1)

Born, M.

M. Born and E. Wolf, Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light (Cambridge University, 1999).

Carter, J. A.

J. A. Carter, D. R. Pape, P. A. Wasilousky, and T. A. Sunderlin, “High-performance optical vector-matrix coprocessor,” Proc. SPIE 2297, 225–236 (1994).
[CrossRef]

Casasent, D.

Caulfield, H. J.

H. J. Caulfield and S. Dolev, “Why future supercomputing requires optics,” Nat. Photonics 4, 261–263 (2010).
[CrossRef]

Cheng, L. J.

Chiou, A. E. T.

Dias, A. R.

Dolev, S.

H. J. Caulfield and S. Dolev, “Why future supercomputing requires optics,” Nat. Photonics 4, 261–263 (2010).
[CrossRef]

N. T. Shaked, T. Tabib, G. Simon, S. Messika, S. Dolev, and J. Rosen, “Optical binary-matrix synthesis for solving bounded NP-complete combinatorial problems,” Opt. Eng. 46, 108201 (2007).
[CrossRef]

Gary, C. K.

C. K. Gary, “Comparison of optics and electronics for the calculation of matrix-vector products,” Proc. SPIE 1704, 544–555 (1992).
[CrossRef]

C. K. Gary, “Matrix-vector multiplication using digital partitioning for more accurate optical computing,” Appl. Opt. 31, 6205–6211 (1992).
[CrossRef]

Geary, J. M.

J. M. Geary, Introduction to Lens Design with Practical ZEMAX Examples (Willmann-Bell, 2002).

Gheen, G.

Goodman, J. W.

J. W. Goodman, A. R. Dias, and L. M. Woody, “Fully parallel, high-speed incoherent optical method for performing discrete Fourier transforms,” Opt. Lett. 2, 1–3 (1978).
[CrossRef]

J. W. Goodman, Introduction to Fourier Optics, 3rd ed. (Publishing House of Electronics Industry, 2006), Chap. 8, p. 206.

Gruber, M.

Jackson, J.

Kamal, M.

Le, P.

P. Le, D. Y. Zang, and Chen S. Tsai, “Integrated electrooptic Bragg modulator modules for matrix-vector and matrix-matrix multiplications,” App. Opt. 27, 1780–1785 (1988).
[CrossRef]

Messika, S.

N. T. Shaked, T. Tabib, G. Simon, S. Messika, S. Dolev, and J. Rosen, “Optical binary-matrix synthesis for solving bounded NP-complete combinatorial problems,” Opt. Eng. 46, 108201 (2007).
[CrossRef]

Narayanswamy, S.

Packirisamy, M.

Pape, D. R.

J. A. Carter, D. R. Pape, P. A. Wasilousky, and T. A. Sunderlin, “High-performance optical vector-matrix coprocessor,” Proc. SPIE 2297, 225–236 (1994).
[CrossRef]

Rosen, J.

N. T. Shaked, T. Tabib, G. Simon, S. Messika, S. Dolev, and J. Rosen, “Optical binary-matrix synthesis for solving bounded NP-complete combinatorial problems,” Opt. Eng. 46, 108201 (2007).
[CrossRef]

Shaked, N. T.

N. T. Shaked, T. Tabib, G. Simon, S. Messika, S. Dolev, and J. Rosen, “Optical binary-matrix synthesis for solving bounded NP-complete combinatorial problems,” Opt. Eng. 46, 108201 (2007).
[CrossRef]

Simon, G.

N. T. Shaked, T. Tabib, G. Simon, S. Messika, S. Dolev, and J. Rosen, “Optical binary-matrix synthesis for solving bounded NP-complete combinatorial problems,” Opt. Eng. 46, 108201 (2007).
[CrossRef]

Sunderlin, T. A.

J. A. Carter, D. R. Pape, P. A. Wasilousky, and T. A. Sunderlin, “High-performance optical vector-matrix coprocessor,” Proc. SPIE 2297, 225–236 (1994).
[CrossRef]

Tabib, T.

N. T. Shaked, T. Tabib, G. Simon, S. Messika, S. Dolev, and J. Rosen, “Optical binary-matrix synthesis for solving bounded NP-complete combinatorial problems,” Opt. Eng. 46, 108201 (2007).
[CrossRef]

Tsai, Chen S.

P. Le, D. Y. Zang, and Chen S. Tsai, “Integrated electrooptic Bragg modulator modules for matrix-vector and matrix-matrix multiplications,” App. Opt. 27, 1780–1785 (1988).
[CrossRef]

Wasilousky, P. A.

J. A. Carter, D. R. Pape, P. A. Wasilousky, and T. A. Sunderlin, “High-performance optical vector-matrix coprocessor,” Proc. SPIE 2297, 225–236 (1994).
[CrossRef]

Wolf, E.

M. Born and E. Wolf, Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light (Cambridge University, 1999).

Woody, L. M.

Yeh, R.

Yuan, X. C.

X. C. Yuan, Optical Design (Science, 1983).

Zang, D. Y.

P. Le, D. Y. Zang, and Chen S. Tsai, “Integrated electrooptic Bragg modulator modules for matrix-vector and matrix-matrix multiplications,” App. Opt. 27, 1780–1785 (1988).
[CrossRef]

Zhang, Y. M.

Y. M. Zhang, Applied Optics (Publishing House of Electronics Industry, 2008).

App. Opt. (1)

P. Le, D. Y. Zang, and Chen S. Tsai, “Integrated electrooptic Bragg modulator modules for matrix-vector and matrix-matrix multiplications,” App. Opt. 27, 1780–1785 (1988).
[CrossRef]

Appl. Opt. (5)

Nat. Photonics (1)

H. J. Caulfield and S. Dolev, “Why future supercomputing requires optics,” Nat. Photonics 4, 261–263 (2010).
[CrossRef]

Opt. Eng. (1)

N. T. Shaked, T. Tabib, G. Simon, S. Messika, S. Dolev, and J. Rosen, “Optical binary-matrix synthesis for solving bounded NP-complete combinatorial problems,” Opt. Eng. 46, 108201 (2007).
[CrossRef]

Opt. Lett. (2)

Proc. SPIE (2)

J. A. Carter, D. R. Pape, P. A. Wasilousky, and T. A. Sunderlin, “High-performance optical vector-matrix coprocessor,” Proc. SPIE 2297, 225–236 (1994).
[CrossRef]

C. K. Gary, “Comparison of optics and electronics for the calculation of matrix-vector products,” Proc. SPIE 1704, 544–555 (1992).
[CrossRef]

Other (6)

J. W. Goodman, Introduction to Fourier Optics, 3rd ed. (Publishing House of Electronics Industry, 2006), Chap. 8, p. 206.

Y. M. Zhang, Applied Optics (Publishing House of Electronics Industry, 2008).

X. C. Yuan, Optical Design (Science, 1983).

M. Born and E. Wolf, Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light (Cambridge University, 1999).

ZEMAX, Optical Design Program, User’s Guide (ZEMAX, 2007).

J. M. Geary, Introduction to Lens Design with Practical ZEMAX Examples (Willmann-Bell, 2002).

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Figures (14)

Fig. 1.
Fig. 1.

Schematic of the optical system of the OVMM.

Fig. 2.
Fig. 2.

Schematic of the double telecentric lens.

Fig. 3.
Fig. 3.

(a) Schematic of cross talk. (b) Schematic of the strategy to eliminate cross talk.

Fig. 4.
Fig. 4.

Optical layout of design of L1.

Fig. 5.
Fig. 5.

Aberration ray fan plot and line footprint diagram of L1.

Fig. 6.
Fig. 6.

Optical layout of design of L21.

Fig. 7.
Fig. 7.

Aberration ray fan plot and line footprint diagram of L21.

Fig. 8.
Fig. 8.

Optical layout of design of L22.

Fig. 9.
Fig. 9.

(a) Aberration ray fan and (b) line footprint diagram of L22.

Fig. 10.
Fig. 10.

Shaded model of the whole system.

Fig. 11.
Fig. 11.

Illuminance distribution at the imaging plane. (a) The illuminance distribution in the x axis. (b) The illuminance distribution in the y axis.

Fig. 12.
Fig. 12.

Physical map of the system.

Fig. 13.
Fig. 13.

Optical power detected at the imaging plane.

Fig. 14.
Fig. 14.

Estimate of elements of Y.

Tables (1)

Tables Icon

Table 1. Primary Optical Parameters Specification of L1 and L21

Equations (8)

Equations on this page are rendered with MathJax. Learn more.

yi=j=1naijbj,(i=1,2n).
ϕ1/ϕ2=EFL2/EFL1=0.984,
t=(ϕ1+ϕ2)/ϕ1ϕ2.
kϕk/nk,
β=ΔdΔa=500μm250μm=2.
MF2=Wi(ViTi)2/Wi,
Iiyiexp[a(i8.5)2].
yi^=16Iib/Iia,i=1,2,...16,

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