Abstract

This study presents what is to our knowledge a new and efficient method for the design of an optical finite impulse response (FIR) filter by employing a particle swarm optimization technique. With the method proposed, the design of an optical FIR filter, which is able to provide an arbitrary spectrum output based on crystal birefringence, could be implemented with good performance and high efficiency. The design procedure is discussed. A typical example of a green/magenta filter used in a liquid crystal on silicon projection display is included to demonstrate the feasibility and efficiency of this method in this design process as compared with simulated annealing.

© 2003 Optical Society of America

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  1. A. M. Titile, W. J. Rosenberg, “Tunable birefringent filters,” Opt. Eng. 20, 815–823 (1981).
  2. J. W. Evans, “Solc birefringent filter,” J. Opt. Soc. Am. 48, 142–146 (1958).
    [CrossRef]
  3. Y. Kong, G. H. Li, M. J. Yun, X. Y. Fan, Y. T. Pang, N. Wang, “A research on multiple tunable liquid crystal filter,” Journal of Optoelectronics · Laser 12, 474–476 (2001).
  4. Y. Zhou, F. H. Yu, H. S. Kwok, “Optical FIR filter design based on crystal birefringence,” Opto-Electronic Engineering, to be published (2002).
  5. Z. Y. He, Digital Signal Processing: Theory and Application (People’s Posts Telecommunications Press, Beijing, 1983) pp. 189–333.
  6. S. E. Harris, E. O. Ammann, I. C. Chang, “Optical network synthesis using birefringent crystals. I. Synthesis of lossless network of equal-length crystals,” J. Opt. Soc. Am. 54, 1267–1279 (1964).
    [CrossRef]
  7. G. D. Sharp, J. R. Birge, “Retard Stack Technology for Color Manipulation,” SID Symposium 30, 1072–1075 (1999).
    [CrossRef]
  8. Y. Zhou, G. Z. Wu, F. H. Yu, “Applications of memory simulated annealing for optical FIR filter design,” Acta Optica Sinica, to be published, (2002).
  9. R. C. Eberhart, J. Kennedy, “A new optimizer using particle swarm theory,” in Proceedings of the Sixth International Symposium on Micro Machine and Human Science. (Piscataway, NJ: IEEE Service Center, 1995), pp. 39–43.
    [CrossRef]
  10. J. Kennedy, R. C. Eberhart, “Particle swarm optimization,” in Proceedings of the IEEE International Conference on Neural Networks, IV. (Piscataway, NJ: IEEE Service Center, 1995), pp. 1942–1948.
    [CrossRef]
  11. Y. H. Shi, R. C. Eberhart, “Empirical study of particle swarm optimization,” in Proceedings of the 1999 Congress on Evolutionary Computation. (Piscataway, NJ: IEEE Service Center, 1999), pp. 1945–1950.
  12. Y. H. Shi, R. C. Eberhart, “A modified particle swarm optimizer,” in Proceedings of the IEEE International Conference on Evolutionary Computation. (Piscataway, NJ: IEEE Service Center, 1998b), pp. 69–73.
  13. Y. B. He, J. Y. Xiong, W. Zheng, G. J. Zeng, F. H. Yu, “Technology and applications of LCOS projector,” Optical Instruments 24, 38–46 (2002).

2002

Y. B. He, J. Y. Xiong, W. Zheng, G. J. Zeng, F. H. Yu, “Technology and applications of LCOS projector,” Optical Instruments 24, 38–46 (2002).

2001

Y. Kong, G. H. Li, M. J. Yun, X. Y. Fan, Y. T. Pang, N. Wang, “A research on multiple tunable liquid crystal filter,” Journal of Optoelectronics · Laser 12, 474–476 (2001).

1999

G. D. Sharp, J. R. Birge, “Retard Stack Technology for Color Manipulation,” SID Symposium 30, 1072–1075 (1999).
[CrossRef]

1981

A. M. Titile, W. J. Rosenberg, “Tunable birefringent filters,” Opt. Eng. 20, 815–823 (1981).

1964

1958

Ammann, E. O.

Birge, J. R.

G. D. Sharp, J. R. Birge, “Retard Stack Technology for Color Manipulation,” SID Symposium 30, 1072–1075 (1999).
[CrossRef]

Chang, I. C.

Eberhart, R. C.

R. C. Eberhart, J. Kennedy, “A new optimizer using particle swarm theory,” in Proceedings of the Sixth International Symposium on Micro Machine and Human Science. (Piscataway, NJ: IEEE Service Center, 1995), pp. 39–43.
[CrossRef]

Y. H. Shi, R. C. Eberhart, “Empirical study of particle swarm optimization,” in Proceedings of the 1999 Congress on Evolutionary Computation. (Piscataway, NJ: IEEE Service Center, 1999), pp. 1945–1950.

Y. H. Shi, R. C. Eberhart, “A modified particle swarm optimizer,” in Proceedings of the IEEE International Conference on Evolutionary Computation. (Piscataway, NJ: IEEE Service Center, 1998b), pp. 69–73.

J. Kennedy, R. C. Eberhart, “Particle swarm optimization,” in Proceedings of the IEEE International Conference on Neural Networks, IV. (Piscataway, NJ: IEEE Service Center, 1995), pp. 1942–1948.
[CrossRef]

Evans, J. W.

Fan, X. Y.

Y. Kong, G. H. Li, M. J. Yun, X. Y. Fan, Y. T. Pang, N. Wang, “A research on multiple tunable liquid crystal filter,” Journal of Optoelectronics · Laser 12, 474–476 (2001).

Harris, S. E.

He, Y. B.

Y. B. He, J. Y. Xiong, W. Zheng, G. J. Zeng, F. H. Yu, “Technology and applications of LCOS projector,” Optical Instruments 24, 38–46 (2002).

He, Z. Y.

Z. Y. He, Digital Signal Processing: Theory and Application (People’s Posts Telecommunications Press, Beijing, 1983) pp. 189–333.

Kennedy, J.

R. C. Eberhart, J. Kennedy, “A new optimizer using particle swarm theory,” in Proceedings of the Sixth International Symposium on Micro Machine and Human Science. (Piscataway, NJ: IEEE Service Center, 1995), pp. 39–43.
[CrossRef]

J. Kennedy, R. C. Eberhart, “Particle swarm optimization,” in Proceedings of the IEEE International Conference on Neural Networks, IV. (Piscataway, NJ: IEEE Service Center, 1995), pp. 1942–1948.
[CrossRef]

Kong, Y.

Y. Kong, G. H. Li, M. J. Yun, X. Y. Fan, Y. T. Pang, N. Wang, “A research on multiple tunable liquid crystal filter,” Journal of Optoelectronics · Laser 12, 474–476 (2001).

Kwok, H. S.

Y. Zhou, F. H. Yu, H. S. Kwok, “Optical FIR filter design based on crystal birefringence,” Opto-Electronic Engineering, to be published (2002).

Li, G. H.

Y. Kong, G. H. Li, M. J. Yun, X. Y. Fan, Y. T. Pang, N. Wang, “A research on multiple tunable liquid crystal filter,” Journal of Optoelectronics · Laser 12, 474–476 (2001).

Pang, Y. T.

Y. Kong, G. H. Li, M. J. Yun, X. Y. Fan, Y. T. Pang, N. Wang, “A research on multiple tunable liquid crystal filter,” Journal of Optoelectronics · Laser 12, 474–476 (2001).

Rosenberg, W. J.

A. M. Titile, W. J. Rosenberg, “Tunable birefringent filters,” Opt. Eng. 20, 815–823 (1981).

Sharp, G. D.

G. D. Sharp, J. R. Birge, “Retard Stack Technology for Color Manipulation,” SID Symposium 30, 1072–1075 (1999).
[CrossRef]

Shi, Y. H.

Y. H. Shi, R. C. Eberhart, “Empirical study of particle swarm optimization,” in Proceedings of the 1999 Congress on Evolutionary Computation. (Piscataway, NJ: IEEE Service Center, 1999), pp. 1945–1950.

Y. H. Shi, R. C. Eberhart, “A modified particle swarm optimizer,” in Proceedings of the IEEE International Conference on Evolutionary Computation. (Piscataway, NJ: IEEE Service Center, 1998b), pp. 69–73.

Titile, A. M.

A. M. Titile, W. J. Rosenberg, “Tunable birefringent filters,” Opt. Eng. 20, 815–823 (1981).

Wang, N.

Y. Kong, G. H. Li, M. J. Yun, X. Y. Fan, Y. T. Pang, N. Wang, “A research on multiple tunable liquid crystal filter,” Journal of Optoelectronics · Laser 12, 474–476 (2001).

Wu, G. Z.

Y. Zhou, G. Z. Wu, F. H. Yu, “Applications of memory simulated annealing for optical FIR filter design,” Acta Optica Sinica, to be published, (2002).

Xiong, J. Y.

Y. B. He, J. Y. Xiong, W. Zheng, G. J. Zeng, F. H. Yu, “Technology and applications of LCOS projector,” Optical Instruments 24, 38–46 (2002).

Yu, F. H.

Y. B. He, J. Y. Xiong, W. Zheng, G. J. Zeng, F. H. Yu, “Technology and applications of LCOS projector,” Optical Instruments 24, 38–46 (2002).

Y. Zhou, G. Z. Wu, F. H. Yu, “Applications of memory simulated annealing for optical FIR filter design,” Acta Optica Sinica, to be published, (2002).

Y. Zhou, F. H. Yu, H. S. Kwok, “Optical FIR filter design based on crystal birefringence,” Opto-Electronic Engineering, to be published (2002).

Yun, M. J.

Y. Kong, G. H. Li, M. J. Yun, X. Y. Fan, Y. T. Pang, N. Wang, “A research on multiple tunable liquid crystal filter,” Journal of Optoelectronics · Laser 12, 474–476 (2001).

Zeng, G. J.

Y. B. He, J. Y. Xiong, W. Zheng, G. J. Zeng, F. H. Yu, “Technology and applications of LCOS projector,” Optical Instruments 24, 38–46 (2002).

Zheng, W.

Y. B. He, J. Y. Xiong, W. Zheng, G. J. Zeng, F. H. Yu, “Technology and applications of LCOS projector,” Optical Instruments 24, 38–46 (2002).

Zhou, Y.

Y. Zhou, F. H. Yu, H. S. Kwok, “Optical FIR filter design based on crystal birefringence,” Opto-Electronic Engineering, to be published (2002).

Y. Zhou, G. Z. Wu, F. H. Yu, “Applications of memory simulated annealing for optical FIR filter design,” Acta Optica Sinica, to be published, (2002).

J. Opt. Soc. Am.

Journal of Optoelectronics · Laser

Y. Kong, G. H. Li, M. J. Yun, X. Y. Fan, Y. T. Pang, N. Wang, “A research on multiple tunable liquid crystal filter,” Journal of Optoelectronics · Laser 12, 474–476 (2001).

Opt. Eng.

A. M. Titile, W. J. Rosenberg, “Tunable birefringent filters,” Opt. Eng. 20, 815–823 (1981).

Optical Instruments

Y. B. He, J. Y. Xiong, W. Zheng, G. J. Zeng, F. H. Yu, “Technology and applications of LCOS projector,” Optical Instruments 24, 38–46 (2002).

SID Symposium

G. D. Sharp, J. R. Birge, “Retard Stack Technology for Color Manipulation,” SID Symposium 30, 1072–1075 (1999).
[CrossRef]

Other

Y. Zhou, G. Z. Wu, F. H. Yu, “Applications of memory simulated annealing for optical FIR filter design,” Acta Optica Sinica, to be published, (2002).

R. C. Eberhart, J. Kennedy, “A new optimizer using particle swarm theory,” in Proceedings of the Sixth International Symposium on Micro Machine and Human Science. (Piscataway, NJ: IEEE Service Center, 1995), pp. 39–43.
[CrossRef]

J. Kennedy, R. C. Eberhart, “Particle swarm optimization,” in Proceedings of the IEEE International Conference on Neural Networks, IV. (Piscataway, NJ: IEEE Service Center, 1995), pp. 1942–1948.
[CrossRef]

Y. H. Shi, R. C. Eberhart, “Empirical study of particle swarm optimization,” in Proceedings of the 1999 Congress on Evolutionary Computation. (Piscataway, NJ: IEEE Service Center, 1999), pp. 1945–1950.

Y. H. Shi, R. C. Eberhart, “A modified particle swarm optimizer,” in Proceedings of the IEEE International Conference on Evolutionary Computation. (Piscataway, NJ: IEEE Service Center, 1998b), pp. 69–73.

Y. Zhou, F. H. Yu, H. S. Kwok, “Optical FIR filter design based on crystal birefringence,” Opto-Electronic Engineering, to be published (2002).

Z. Y. He, Digital Signal Processing: Theory and Application (People’s Posts Telecommunications Press, Beijing, 1983) pp. 189–333.

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Figures (7)

Fig. 1
Fig. 1

Basic structure of optical FIR filter.

Fig. 2
Fig. 2

Basic process of particle swarm optimization.

Fig. 3
Fig. 3

Desired spectrum of G/M broadband filter.

Fig. 4
Fig. 4

Comparison of G/M filter design in PSO and SA, six order.

Fig. 5
Fig. 5

Comparison of design with dispersion and without dispersion.

Fig. 6
Fig. 6

Decrease process of PSO.

Fig. 7
Fig. 7

Decrease process of SA.

Equations (13)

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Ct=C0δt+C1δt-a+C2δt-2a++Cnδt-na =k=0n Ckδt-ka,
a=ts-tf= LΔηc.
Δη=ne-no.
Γ=2πΔηLλ.
Cω=C0+C1 exp-iaω+C2 exp-i2aω++Cn exp-inaω =k=0n CK exp-ikaω,
Cλ=C0+C1 exp-i2πΔηL1λ+C2 exp-i4πΔηL1λ++Cn exp-in2πΔηL1λ=k=0n Ck exp-ik2πΔηL1λ=k=0n Ck exp-ikΓ.
Dλ=k=0n Dk exp-ik2πΔηL1λ.
vid=wnvid+C1randpid-xid+C2Randpgd-xid,
xid=xid+vid,  d=1, 2,, D.
wn= 0.5n1-N+ 0.4-0.9N1-N
FobjCK=i=0i=M Pω˜iWω˜iCactualω˜i, CK-Cdesiredω˜i2,
ω˜i= iM, i=0, 1, 2M.
Wω˜i=w1,within pass bandw2,within stop bandw3,within trans_band

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