Abstract

An optimization technique determining the configuration of optical components in a spatial light modulator is proposed. We study a spatial light modulator composed of a twisted nematic liquid crystal, a polarization state generator, and a polarization state detector. To obtain the desired phase and amplitude modulations, four parameters of the polarization state generator and detector should be optimized. A genetic algorithm is applied in searching the configurations suitable to a given twisted nematic li quid crystal. By embodying the proposed technique, the evolution of the designed cost functions is proved.

© 2008 Optical Society of America

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References

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  1. A. Lien, “A detailed derivation of extended Jones matrix representation for twisted nematic liquid crystal displays,” Liq. Cryst. 22, 171-175 (1997).
    [CrossRef]
  2. P. Yeh and C. Gu, Optics of Liquid Crystal Display (Wiley, 1999).
  3. B. E. A. Saleh and K. Lu, “Theory and design of the liquid crystal TV as an optical spatial phase modulator,” Opt. Eng. 29, 240-246 (1990).
    [CrossRef]
  4. J. A. Coy, M. Zaldarriaga, D. F. Grosz, and O. E. Martínez, “Characterization of a liquid crystal television as a programmable spatial light modulator,” Opt. Eng. 35, 15-19 (1996).
    [CrossRef]
  5. A. Márquez, J. Campos, M. J. Yzuel, I. Moreno, J. A. Davis, C. Iemmi, A. Moreno, and A. Robert, “Characterization of edge effects in twisted nematic liquid crystal displays,” Opt. Eng. 39, 3301-3307 (2000).
    [CrossRef]
  6. Q. Wang and S. He, “A new effective model for the director distribution of a twisted nematic liquid crystal cell,” J. Opt. A: Pure Appl. Opt. 7, 438-444 (2005).
    [CrossRef]
  7. J. A. Davis, D. B. Allison, K. G. D'Nelly, M. L. Wilson, and I. Moreno, “Ambiguities in measuring the physical parameters for twisted-nematic liquid crystal spatial light modulators,” Opt. Eng. 38, 705-709 (1999).
    [CrossRef]
  8. J. A. Davis, I. Moreno, and P. Tsai, “Polarization eigenstates for twisted-nematic liquid-crystal displays,” Appl. Opt. 37, 937-945 (1998).
    [CrossRef]
  9. I. Moreno, J. A. Davis, K. G. D'Nelly, and D. B. Allison, “Transmission and phase measurement for polarization eigenvectors in twisted-nematic liquid crystal spatial light modulators,” Opt. Eng. 37, 3048-3052 (1998).
    [CrossRef]
  10. A. Márquez, C. Iemmi, I. Moreno, J. A. Davis, J. Campos, and M. J. Yzuel, “Quantitative prediction of the modulation behavior of twisted nematic liquid crystal displays based on a simple physical model,” Opt. Eng. 40, 2558-2564 (2001).
    [CrossRef]
  11. J. Nicolás, J. Campos, and M. J. Yzuel, “Phase and amplitude modulation of elliptic polarization states by nonabsorbing anisotropic elements: application to liquid-crystal devices,” J. Opt. Soc. Am. A 19, 1013-1020 (2002).
    [CrossRef]
  12. V. Durán, J. Lancis, E. Tajahuerce, and Z. Jaroszewicz, “Equivalent retarder-rotator approach to on-state twisted nematic liquid crystal displays,” J. Appl. Phys. 99, 113101(2006).
    [CrossRef]
  13. V. Durán, J. Lancis, E. Tajahuerce, and M. Fernández-Alonso, “Phase-only modulation with a twisted nematic liquid crystal display by means of equi-azimuth polarization states,” Opt. Express 14, 5607-5616 (2006).
    [CrossRef] [PubMed]
  14. H. Kim and B. Lee, “Optimal nonmonotonic convergence of iterative Fourier-transform algorithm,” Opt. Lett. 30, 296-298 (2005).
    [CrossRef] [PubMed]
  15. J. Hahn, H. Kim, K. Choi, and B. Lee, “Real-time digital holographic beam-shaping system with a genetic feedback tuning loop,” Appl. Opt. 45, 915-924 (2006).
    [CrossRef] [PubMed]
  16. M. C. Gardner, R. E. Kilpatrick, S. E. Day, R. E. Renton, and D. R. Selviah, “Experimental verification of a computer model for optimizing a liquid crystal display for spatial phase modulation,” J. Opt. A: Pure Appl. Opt. 1, 299-303 (1999).
    [CrossRef]
  17. A. Márquez, M. Yamauchi, J. A. Davis, and D. J. Franich, “Phase measurements of a twisted nematic liquid crystal spatial light modulator with a common-path interferometer,” Opt. Commun. 190, 129-133 (2001).
    [CrossRef]
  18. J. Reményi, P. Várhegyi, L. Domjan, P. Koppa, and E. Lorincz, “Amplitude, phase, and hybrid ternary modulation modes of a twisted-nematic liquid-crystal display at ~400 nm,” Appl. Opt. 42, 3428-3434 (2003).
    [CrossRef] [PubMed]
  19. H. Kim and B. Lee, “Optimal design of diffractive optical elements with functional relationship between phase and amplitude modulations using nonlinear optimization methods,” Proc. SPIE 5876, 587611 (2005).
    [CrossRef]

2006 (3)

2005 (3)

H. Kim and B. Lee, “Optimal design of diffractive optical elements with functional relationship between phase and amplitude modulations using nonlinear optimization methods,” Proc. SPIE 5876, 587611 (2005).
[CrossRef]

Q. Wang and S. He, “A new effective model for the director distribution of a twisted nematic liquid crystal cell,” J. Opt. A: Pure Appl. Opt. 7, 438-444 (2005).
[CrossRef]

H. Kim and B. Lee, “Optimal nonmonotonic convergence of iterative Fourier-transform algorithm,” Opt. Lett. 30, 296-298 (2005).
[CrossRef] [PubMed]

2003 (1)

2002 (1)

2001 (2)

A. Márquez, C. Iemmi, I. Moreno, J. A. Davis, J. Campos, and M. J. Yzuel, “Quantitative prediction of the modulation behavior of twisted nematic liquid crystal displays based on a simple physical model,” Opt. Eng. 40, 2558-2564 (2001).
[CrossRef]

A. Márquez, M. Yamauchi, J. A. Davis, and D. J. Franich, “Phase measurements of a twisted nematic liquid crystal spatial light modulator with a common-path interferometer,” Opt. Commun. 190, 129-133 (2001).
[CrossRef]

2000 (1)

A. Márquez, J. Campos, M. J. Yzuel, I. Moreno, J. A. Davis, C. Iemmi, A. Moreno, and A. Robert, “Characterization of edge effects in twisted nematic liquid crystal displays,” Opt. Eng. 39, 3301-3307 (2000).
[CrossRef]

1999 (2)

J. A. Davis, D. B. Allison, K. G. D'Nelly, M. L. Wilson, and I. Moreno, “Ambiguities in measuring the physical parameters for twisted-nematic liquid crystal spatial light modulators,” Opt. Eng. 38, 705-709 (1999).
[CrossRef]

M. C. Gardner, R. E. Kilpatrick, S. E. Day, R. E. Renton, and D. R. Selviah, “Experimental verification of a computer model for optimizing a liquid crystal display for spatial phase modulation,” J. Opt. A: Pure Appl. Opt. 1, 299-303 (1999).
[CrossRef]

1998 (2)

I. Moreno, J. A. Davis, K. G. D'Nelly, and D. B. Allison, “Transmission and phase measurement for polarization eigenvectors in twisted-nematic liquid crystal spatial light modulators,” Opt. Eng. 37, 3048-3052 (1998).
[CrossRef]

J. A. Davis, I. Moreno, and P. Tsai, “Polarization eigenstates for twisted-nematic liquid-crystal displays,” Appl. Opt. 37, 937-945 (1998).
[CrossRef]

1997 (1)

A. Lien, “A detailed derivation of extended Jones matrix representation for twisted nematic liquid crystal displays,” Liq. Cryst. 22, 171-175 (1997).
[CrossRef]

1996 (1)

J. A. Coy, M. Zaldarriaga, D. F. Grosz, and O. E. Martínez, “Characterization of a liquid crystal television as a programmable spatial light modulator,” Opt. Eng. 35, 15-19 (1996).
[CrossRef]

1990 (1)

B. E. A. Saleh and K. Lu, “Theory and design of the liquid crystal TV as an optical spatial phase modulator,” Opt. Eng. 29, 240-246 (1990).
[CrossRef]

Allison, D. B.

J. A. Davis, D. B. Allison, K. G. D'Nelly, M. L. Wilson, and I. Moreno, “Ambiguities in measuring the physical parameters for twisted-nematic liquid crystal spatial light modulators,” Opt. Eng. 38, 705-709 (1999).
[CrossRef]

I. Moreno, J. A. Davis, K. G. D'Nelly, and D. B. Allison, “Transmission and phase measurement for polarization eigenvectors in twisted-nematic liquid crystal spatial light modulators,” Opt. Eng. 37, 3048-3052 (1998).
[CrossRef]

Campos, J.

J. Nicolás, J. Campos, and M. J. Yzuel, “Phase and amplitude modulation of elliptic polarization states by nonabsorbing anisotropic elements: application to liquid-crystal devices,” J. Opt. Soc. Am. A 19, 1013-1020 (2002).
[CrossRef]

A. Márquez, C. Iemmi, I. Moreno, J. A. Davis, J. Campos, and M. J. Yzuel, “Quantitative prediction of the modulation behavior of twisted nematic liquid crystal displays based on a simple physical model,” Opt. Eng. 40, 2558-2564 (2001).
[CrossRef]

A. Márquez, J. Campos, M. J. Yzuel, I. Moreno, J. A. Davis, C. Iemmi, A. Moreno, and A. Robert, “Characterization of edge effects in twisted nematic liquid crystal displays,” Opt. Eng. 39, 3301-3307 (2000).
[CrossRef]

Choi, K.

Coy, J. A.

J. A. Coy, M. Zaldarriaga, D. F. Grosz, and O. E. Martínez, “Characterization of a liquid crystal television as a programmable spatial light modulator,” Opt. Eng. 35, 15-19 (1996).
[CrossRef]

Davis, J. A.

A. Márquez, C. Iemmi, I. Moreno, J. A. Davis, J. Campos, and M. J. Yzuel, “Quantitative prediction of the modulation behavior of twisted nematic liquid crystal displays based on a simple physical model,” Opt. Eng. 40, 2558-2564 (2001).
[CrossRef]

A. Márquez, M. Yamauchi, J. A. Davis, and D. J. Franich, “Phase measurements of a twisted nematic liquid crystal spatial light modulator with a common-path interferometer,” Opt. Commun. 190, 129-133 (2001).
[CrossRef]

A. Márquez, J. Campos, M. J. Yzuel, I. Moreno, J. A. Davis, C. Iemmi, A. Moreno, and A. Robert, “Characterization of edge effects in twisted nematic liquid crystal displays,” Opt. Eng. 39, 3301-3307 (2000).
[CrossRef]

J. A. Davis, D. B. Allison, K. G. D'Nelly, M. L. Wilson, and I. Moreno, “Ambiguities in measuring the physical parameters for twisted-nematic liquid crystal spatial light modulators,” Opt. Eng. 38, 705-709 (1999).
[CrossRef]

J. A. Davis, I. Moreno, and P. Tsai, “Polarization eigenstates for twisted-nematic liquid-crystal displays,” Appl. Opt. 37, 937-945 (1998).
[CrossRef]

I. Moreno, J. A. Davis, K. G. D'Nelly, and D. B. Allison, “Transmission and phase measurement for polarization eigenvectors in twisted-nematic liquid crystal spatial light modulators,” Opt. Eng. 37, 3048-3052 (1998).
[CrossRef]

Day, S. E.

M. C. Gardner, R. E. Kilpatrick, S. E. Day, R. E. Renton, and D. R. Selviah, “Experimental verification of a computer model for optimizing a liquid crystal display for spatial phase modulation,” J. Opt. A: Pure Appl. Opt. 1, 299-303 (1999).
[CrossRef]

D'Nelly, K. G.

J. A. Davis, D. B. Allison, K. G. D'Nelly, M. L. Wilson, and I. Moreno, “Ambiguities in measuring the physical parameters for twisted-nematic liquid crystal spatial light modulators,” Opt. Eng. 38, 705-709 (1999).
[CrossRef]

I. Moreno, J. A. Davis, K. G. D'Nelly, and D. B. Allison, “Transmission and phase measurement for polarization eigenvectors in twisted-nematic liquid crystal spatial light modulators,” Opt. Eng. 37, 3048-3052 (1998).
[CrossRef]

Domjan, L.

Durán, V.

V. Durán, J. Lancis, E. Tajahuerce, and Z. Jaroszewicz, “Equivalent retarder-rotator approach to on-state twisted nematic liquid crystal displays,” J. Appl. Phys. 99, 113101(2006).
[CrossRef]

V. Durán, J. Lancis, E. Tajahuerce, and M. Fernández-Alonso, “Phase-only modulation with a twisted nematic liquid crystal display by means of equi-azimuth polarization states,” Opt. Express 14, 5607-5616 (2006).
[CrossRef] [PubMed]

Fernández-Alonso, M.

Franich, D. J.

A. Márquez, M. Yamauchi, J. A. Davis, and D. J. Franich, “Phase measurements of a twisted nematic liquid crystal spatial light modulator with a common-path interferometer,” Opt. Commun. 190, 129-133 (2001).
[CrossRef]

Gardner, M. C.

M. C. Gardner, R. E. Kilpatrick, S. E. Day, R. E. Renton, and D. R. Selviah, “Experimental verification of a computer model for optimizing a liquid crystal display for spatial phase modulation,” J. Opt. A: Pure Appl. Opt. 1, 299-303 (1999).
[CrossRef]

Grosz, D. F.

J. A. Coy, M. Zaldarriaga, D. F. Grosz, and O. E. Martínez, “Characterization of a liquid crystal television as a programmable spatial light modulator,” Opt. Eng. 35, 15-19 (1996).
[CrossRef]

Gu, C.

P. Yeh and C. Gu, Optics of Liquid Crystal Display (Wiley, 1999).

Hahn, J.

He, S.

Q. Wang and S. He, “A new effective model for the director distribution of a twisted nematic liquid crystal cell,” J. Opt. A: Pure Appl. Opt. 7, 438-444 (2005).
[CrossRef]

Iemmi, C.

A. Márquez, C. Iemmi, I. Moreno, J. A. Davis, J. Campos, and M. J. Yzuel, “Quantitative prediction of the modulation behavior of twisted nematic liquid crystal displays based on a simple physical model,” Opt. Eng. 40, 2558-2564 (2001).
[CrossRef]

A. Márquez, J. Campos, M. J. Yzuel, I. Moreno, J. A. Davis, C. Iemmi, A. Moreno, and A. Robert, “Characterization of edge effects in twisted nematic liquid crystal displays,” Opt. Eng. 39, 3301-3307 (2000).
[CrossRef]

Jaroszewicz, Z.

V. Durán, J. Lancis, E. Tajahuerce, and Z. Jaroszewicz, “Equivalent retarder-rotator approach to on-state twisted nematic liquid crystal displays,” J. Appl. Phys. 99, 113101(2006).
[CrossRef]

Kilpatrick, R. E.

M. C. Gardner, R. E. Kilpatrick, S. E. Day, R. E. Renton, and D. R. Selviah, “Experimental verification of a computer model for optimizing a liquid crystal display for spatial phase modulation,” J. Opt. A: Pure Appl. Opt. 1, 299-303 (1999).
[CrossRef]

Kim, H.

Koppa, P.

Lancis, J.

V. Durán, J. Lancis, E. Tajahuerce, and Z. Jaroszewicz, “Equivalent retarder-rotator approach to on-state twisted nematic liquid crystal displays,” J. Appl. Phys. 99, 113101(2006).
[CrossRef]

V. Durán, J. Lancis, E. Tajahuerce, and M. Fernández-Alonso, “Phase-only modulation with a twisted nematic liquid crystal display by means of equi-azimuth polarization states,” Opt. Express 14, 5607-5616 (2006).
[CrossRef] [PubMed]

Lee, B.

Lien, A.

A. Lien, “A detailed derivation of extended Jones matrix representation for twisted nematic liquid crystal displays,” Liq. Cryst. 22, 171-175 (1997).
[CrossRef]

Lorincz, E.

Lu, K.

B. E. A. Saleh and K. Lu, “Theory and design of the liquid crystal TV as an optical spatial phase modulator,” Opt. Eng. 29, 240-246 (1990).
[CrossRef]

Márquez, A.

A. Márquez, M. Yamauchi, J. A. Davis, and D. J. Franich, “Phase measurements of a twisted nematic liquid crystal spatial light modulator with a common-path interferometer,” Opt. Commun. 190, 129-133 (2001).
[CrossRef]

A. Márquez, C. Iemmi, I. Moreno, J. A. Davis, J. Campos, and M. J. Yzuel, “Quantitative prediction of the modulation behavior of twisted nematic liquid crystal displays based on a simple physical model,” Opt. Eng. 40, 2558-2564 (2001).
[CrossRef]

A. Márquez, J. Campos, M. J. Yzuel, I. Moreno, J. A. Davis, C. Iemmi, A. Moreno, and A. Robert, “Characterization of edge effects in twisted nematic liquid crystal displays,” Opt. Eng. 39, 3301-3307 (2000).
[CrossRef]

Martínez, O. E.

J. A. Coy, M. Zaldarriaga, D. F. Grosz, and O. E. Martínez, “Characterization of a liquid crystal television as a programmable spatial light modulator,” Opt. Eng. 35, 15-19 (1996).
[CrossRef]

Moreno, A.

A. Márquez, J. Campos, M. J. Yzuel, I. Moreno, J. A. Davis, C. Iemmi, A. Moreno, and A. Robert, “Characterization of edge effects in twisted nematic liquid crystal displays,” Opt. Eng. 39, 3301-3307 (2000).
[CrossRef]

Moreno, I.

A. Márquez, C. Iemmi, I. Moreno, J. A. Davis, J. Campos, and M. J. Yzuel, “Quantitative prediction of the modulation behavior of twisted nematic liquid crystal displays based on a simple physical model,” Opt. Eng. 40, 2558-2564 (2001).
[CrossRef]

A. Márquez, J. Campos, M. J. Yzuel, I. Moreno, J. A. Davis, C. Iemmi, A. Moreno, and A. Robert, “Characterization of edge effects in twisted nematic liquid crystal displays,” Opt. Eng. 39, 3301-3307 (2000).
[CrossRef]

J. A. Davis, D. B. Allison, K. G. D'Nelly, M. L. Wilson, and I. Moreno, “Ambiguities in measuring the physical parameters for twisted-nematic liquid crystal spatial light modulators,” Opt. Eng. 38, 705-709 (1999).
[CrossRef]

J. A. Davis, I. Moreno, and P. Tsai, “Polarization eigenstates for twisted-nematic liquid-crystal displays,” Appl. Opt. 37, 937-945 (1998).
[CrossRef]

I. Moreno, J. A. Davis, K. G. D'Nelly, and D. B. Allison, “Transmission and phase measurement for polarization eigenvectors in twisted-nematic liquid crystal spatial light modulators,” Opt. Eng. 37, 3048-3052 (1998).
[CrossRef]

Nicolás, J.

Reményi, J.

Renton, R. E.

M. C. Gardner, R. E. Kilpatrick, S. E. Day, R. E. Renton, and D. R. Selviah, “Experimental verification of a computer model for optimizing a liquid crystal display for spatial phase modulation,” J. Opt. A: Pure Appl. Opt. 1, 299-303 (1999).
[CrossRef]

Robert, A.

A. Márquez, J. Campos, M. J. Yzuel, I. Moreno, J. A. Davis, C. Iemmi, A. Moreno, and A. Robert, “Characterization of edge effects in twisted nematic liquid crystal displays,” Opt. Eng. 39, 3301-3307 (2000).
[CrossRef]

Saleh, B. E. A.

B. E. A. Saleh and K. Lu, “Theory and design of the liquid crystal TV as an optical spatial phase modulator,” Opt. Eng. 29, 240-246 (1990).
[CrossRef]

Selviah, D. R.

M. C. Gardner, R. E. Kilpatrick, S. E. Day, R. E. Renton, and D. R. Selviah, “Experimental verification of a computer model for optimizing a liquid crystal display for spatial phase modulation,” J. Opt. A: Pure Appl. Opt. 1, 299-303 (1999).
[CrossRef]

Tajahuerce, E.

V. Durán, J. Lancis, E. Tajahuerce, and Z. Jaroszewicz, “Equivalent retarder-rotator approach to on-state twisted nematic liquid crystal displays,” J. Appl. Phys. 99, 113101(2006).
[CrossRef]

V. Durán, J. Lancis, E. Tajahuerce, and M. Fernández-Alonso, “Phase-only modulation with a twisted nematic liquid crystal display by means of equi-azimuth polarization states,” Opt. Express 14, 5607-5616 (2006).
[CrossRef] [PubMed]

Tsai, P.

Várhegyi, P.

Wang, Q.

Q. Wang and S. He, “A new effective model for the director distribution of a twisted nematic liquid crystal cell,” J. Opt. A: Pure Appl. Opt. 7, 438-444 (2005).
[CrossRef]

Wilson, M. L.

J. A. Davis, D. B. Allison, K. G. D'Nelly, M. L. Wilson, and I. Moreno, “Ambiguities in measuring the physical parameters for twisted-nematic liquid crystal spatial light modulators,” Opt. Eng. 38, 705-709 (1999).
[CrossRef]

Yamauchi, M.

A. Márquez, M. Yamauchi, J. A. Davis, and D. J. Franich, “Phase measurements of a twisted nematic liquid crystal spatial light modulator with a common-path interferometer,” Opt. Commun. 190, 129-133 (2001).
[CrossRef]

Yeh, P.

P. Yeh and C. Gu, Optics of Liquid Crystal Display (Wiley, 1999).

Yzuel, M. J.

J. Nicolás, J. Campos, and M. J. Yzuel, “Phase and amplitude modulation of elliptic polarization states by nonabsorbing anisotropic elements: application to liquid-crystal devices,” J. Opt. Soc. Am. A 19, 1013-1020 (2002).
[CrossRef]

A. Márquez, C. Iemmi, I. Moreno, J. A. Davis, J. Campos, and M. J. Yzuel, “Quantitative prediction of the modulation behavior of twisted nematic liquid crystal displays based on a simple physical model,” Opt. Eng. 40, 2558-2564 (2001).
[CrossRef]

A. Márquez, J. Campos, M. J. Yzuel, I. Moreno, J. A. Davis, C. Iemmi, A. Moreno, and A. Robert, “Characterization of edge effects in twisted nematic liquid crystal displays,” Opt. Eng. 39, 3301-3307 (2000).
[CrossRef]

Zaldarriaga, M.

J. A. Coy, M. Zaldarriaga, D. F. Grosz, and O. E. Martínez, “Characterization of a liquid crystal television as a programmable spatial light modulator,” Opt. Eng. 35, 15-19 (1996).
[CrossRef]

Appl. Opt. (3)

J. Appl. Phys. (1)

V. Durán, J. Lancis, E. Tajahuerce, and Z. Jaroszewicz, “Equivalent retarder-rotator approach to on-state twisted nematic liquid crystal displays,” J. Appl. Phys. 99, 113101(2006).
[CrossRef]

J. Opt. A: Pure Appl. Opt. (2)

M. C. Gardner, R. E. Kilpatrick, S. E. Day, R. E. Renton, and D. R. Selviah, “Experimental verification of a computer model for optimizing a liquid crystal display for spatial phase modulation,” J. Opt. A: Pure Appl. Opt. 1, 299-303 (1999).
[CrossRef]

Q. Wang and S. He, “A new effective model for the director distribution of a twisted nematic liquid crystal cell,” J. Opt. A: Pure Appl. Opt. 7, 438-444 (2005).
[CrossRef]

J. Opt. Soc. Am. A (1)

Liq. Cryst. (1)

A. Lien, “A detailed derivation of extended Jones matrix representation for twisted nematic liquid crystal displays,” Liq. Cryst. 22, 171-175 (1997).
[CrossRef]

Opt. Commun. (1)

A. Márquez, M. Yamauchi, J. A. Davis, and D. J. Franich, “Phase measurements of a twisted nematic liquid crystal spatial light modulator with a common-path interferometer,” Opt. Commun. 190, 129-133 (2001).
[CrossRef]

Opt. Eng. (6)

B. E. A. Saleh and K. Lu, “Theory and design of the liquid crystal TV as an optical spatial phase modulator,” Opt. Eng. 29, 240-246 (1990).
[CrossRef]

J. A. Coy, M. Zaldarriaga, D. F. Grosz, and O. E. Martínez, “Characterization of a liquid crystal television as a programmable spatial light modulator,” Opt. Eng. 35, 15-19 (1996).
[CrossRef]

A. Márquez, J. Campos, M. J. Yzuel, I. Moreno, J. A. Davis, C. Iemmi, A. Moreno, and A. Robert, “Characterization of edge effects in twisted nematic liquid crystal displays,” Opt. Eng. 39, 3301-3307 (2000).
[CrossRef]

J. A. Davis, D. B. Allison, K. G. D'Nelly, M. L. Wilson, and I. Moreno, “Ambiguities in measuring the physical parameters for twisted-nematic liquid crystal spatial light modulators,” Opt. Eng. 38, 705-709 (1999).
[CrossRef]

I. Moreno, J. A. Davis, K. G. D'Nelly, and D. B. Allison, “Transmission and phase measurement for polarization eigenvectors in twisted-nematic liquid crystal spatial light modulators,” Opt. Eng. 37, 3048-3052 (1998).
[CrossRef]

A. Márquez, C. Iemmi, I. Moreno, J. A. Davis, J. Campos, and M. J. Yzuel, “Quantitative prediction of the modulation behavior of twisted nematic liquid crystal displays based on a simple physical model,” Opt. Eng. 40, 2558-2564 (2001).
[CrossRef]

Opt. Express (1)

Opt. Lett. (1)

Proc. SPIE (1)

H. Kim and B. Lee, “Optimal design of diffractive optical elements with functional relationship between phase and amplitude modulations using nonlinear optimization methods,” Proc. SPIE 5876, 587611 (2005).
[CrossRef]

Other (1)

P. Yeh and C. Gu, Optics of Liquid Crystal Display (Wiley, 1999).

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Figures (10)

Fig. 1
Fig. 1

Schematic of the SLM composed of TNLC, a polarization state generator, and a polarization state detector: θ P 1 and θ P 2 are rotation angles of input and output polarizers; θ W 1 and θ W 2 are rotation angles of input and output wave plates.

Fig. 2
Fig. 2

Elliptic polarization state (a) in the x y plane and (b) its position on the Poincaré sphere.

Fig. 3
Fig. 3

Twist angles and birefringences as a function of TNLC depth: (a), (b) Lu and Saleh model; (c), (d) Coy et al. model.

Fig. 4
Fig. 4

Input and output negative eigenstates E λ ( ) on the Poincaré sphere, and their traces according to the applied voltage (a) without and (b) with the edge effect.

Fig. 5
Fig. 5

Elliptic polarization states of (a) PSG and (b) PSD on the Poincaré sphere.

Fig. 6
Fig. 6

Schematic of the system optimizing the SLM with genetic algorithm.

Fig. 7
Fig. 7

Flow chart of the genetic algorithm implemented with Labview and Matlab.

Fig. 8
Fig. 8

Picture of the experimental setup.

Fig. 9
Fig. 9

Characteristics of SLM during evolution and at stagnated state: (a) phase modulation and (b) amplitude transmission during evolution, and (c) phase modulation and (d) amplitude transmission at stagnated state.

Fig. 10
Fig. 10

Diffraction images using the SLM (a) at the first generation and (b) at the stagnated state after the genetic optimization.

Tables (1)

Tables Icon

Table 1 Optimized Configuration Parameters of the Spatial Light Modulator

Equations (32)

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( δ , ψ ) ( cos ψ e i δ sin ψ ) .
sin 2 ε sin 2 ψ sin δ ,
tan 2 ϕ tan 2 ψ cos δ .
M TNLC = R ( α ) W ( 2 π t Δ n / λ ) R ( α ) M bulk   TNLC W ( 2 π t Δ n / λ ) = exp ( i β ) R ( α ) W ( 2 π t Δ n / λ ) M ( α , β ) W ( 2 π t Δ n / λ ) ,
M bulk   TNLC = exp ( i β ) R ( α ) M ( α , β ) .
R ( θ ) = [ cos θ sin θ sin θ cos θ ] ,
W ( φ ) = [ 1 0 0 exp ( i φ ) ] .
M ( α , β ) = [ cos γ i β sin γ / γ α sin γ / γ α sin γ / γ cos γ + i β sin γ / γ ] .
β = π ( d 2 t ) Δ n eff / λ ,
E λ ( + ) = [ α / ( 2 γ 2 + 2 β γ ) 1 / 2 i ( β + γ ) / ( 2 γ 2 + 2 β γ ) 1 / 2 ] ,
E λ ( ) = [ ( β + γ ) / ( 2 γ 2 + 2 β γ ) 1 / 2 i α / ( 2 γ 2 + 2 β γ ) 1 / 2 ] .
λ ( ± ) = exp ( i β ) exp ( ± i γ ) .
δ = π / 2 ,
ψ = tan 1 [ α / ( β + γ ) ] .
Δ n eff = n e 2 n o 2 n e 2 sin 2 θ tilt ( V ) + n o 2 cos 2 θ tilt ( V ) n o .
θ tilt ( V i ) θ tilt ( V j ) if     V i > V j .
sin 2 ( θ W 1 θ P 1 ) = sin 2 ψ sin δ ,
tan 2 θ W 1 = tan 2 ψ cos δ .
sin 2 ( θ P 2 θ W 2 ) = sin 2 ψ sin δ ,
tan 2 θ W 2 = tan 2 ψ cos δ .
max F [ θ P 1 , θ W 1 , θ P 2 , θ W 2 ] for     0 θ P 1 , θ W 1 , θ P 2 , and θ W 2 π .
I int ( p j ) = I int , 0 cos ( 2 π p j / Λ + M Phase ) .
Λ = f λ / Δ ,
p j = p CCD × ( j 1 ) .
X ( k ) = j = 1 N I int , 0 cos ( 2 π p j / Λ + M Phase ) ω N ( j 1 ) ( k 1 ) ,
ω N = exp ( 2 π i / N ) .
M Phase = unwrap { angle [ X ( p CCD N / Λ + 1 ) ] } .
Δ = 4 f λ / p CCD N .
F ( x i ) = min ( M Phase , i ) max ( M Phase , i ) .
j = 0 16 [ M Amp ( 16 j 1 ) ] 2 10 5 ( watt ) ,
4 j = 0 16 [ M Amp ( 16 j 1 ) ] 2 j = 0 16 { [ M Amp ( 16 j 1 ) ] 2 M Amp 2 ¯ } 2 > 20 .
M Amp 2 ¯ = j = 0 16 [ M Amp ( 16 j 1 ) ] 2 / 17 .

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