Abstract

We propose the optical implementation of diffractive optical elements onto electrically addressed liquid-crystal spatial light modulators. We compare the classic implementations onto amplitude-only or phase-only domains with the implementations onto coupled phase and amplitude (spiral) domains. We demonstrate that the coupling between amplitude and phase provides a trade-off between diffraction efficiency and the signal-to-noise ratio in the reconstruction. Furthermore, when investigating the influence of the maximum dephasing on phase domains and spiral domains through the use of optimal trade-off design, we show that phase-only domains with limited maximum dephasing can provide satisfactory performance. Finally, optical implementations are provided.

© 2001 Optical Society of America

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  1. V. Laude, C. Dirson, “Liquid-crystal active lens: application to image resolution enhancement,” Opt. Commun. 163, 72–78 (1999).
    [CrossRef]
  2. CRL Opto, “Miniatures LCDs,” http://www.crlopto.com/wop/lc-prods.htm (1999).
  3. V. Laude, P. Réfrégier, “Multicriteria characterization of coding domains with optimal Fourier SLM filters,” Appl. Opt. 33, 4465–4471 (1994).
    [CrossRef] [PubMed]
  4. D. A. Gregory, “Real-time pattern recognition using a modified liquid crystal television in a coherent optical correlator,” Appl. Opt. 25, 467–469 (1986).
    [CrossRef] [PubMed]
  5. L. G. Neto, D. Roberge, Y. Sheng, “Full-range, continuous, complex modulation by the use of two coupled-mode liquid-crystal televisions,” Appl. Opt. 35, 4567–4576 (1996).
    [CrossRef] [PubMed]
  6. L. G. Neto, D. Roberge, Y. Sheng, “Programmable optical phase-mostly holograms with coupled-mode modulation liquid crystal television,” Appl. Opt. 34, 1944–1950 (1995).
    [CrossRef] [PubMed]
  7. P. Réfrégier, “Filter design for optical pattern recognition: multicriteria optimization approach,” Opt. Lett. 15, 854–856 (1990).
    [CrossRef] [PubMed]
  8. L. Legeard, P. Réfrégier, P. Ambs, “Multicriteria optimality for iterative encoding of computer-generated holograms,” Appl. Opt. 36, 7444–7449 (1997).
    [CrossRef]
  9. M. A. Seldowitz, J. P. Allebach, D. W. Sweeney, “Synthesis of digital holograms by direct binary search,” Appl. Opt. 26, 2788–2798 (1987).
    [CrossRef] [PubMed]
  10. L. Bigué, P. Ambs, “Optimal multicriteria approach to the iterative Fourier transform algorithm,” Appl. Opt. 40, 5886–5893 (2001).
    [CrossRef]
  11. Z. Zhang, G. Lu, F. T. S. Yu, “Simple method for measuring phase modulation in liquid crystal televisions,” Opt. Eng. 33, 3018–3022 (1994).
    [CrossRef]
  12. M. Yamauchi, T. Eiju, “Optimization of twisted nematic liquid crystal panels for spatial light phase modulation,” Opt. Commun. 115, 19–25 (1995).
    [CrossRef]
  13. J. Colin, “Corrélation optique photoréfractive haute cadence à transformée de Fourier conjointe,” Thesis, Université Paris 6, Paris, France (1998).
  14. C. Soutar, K. Lu, “Determination of the physical properties of an arbitrary twisted-nematic liquid crystal cell,” Opt. Eng. 33, 2704–2712 (1994).
    [CrossRef]
  15. I. Labastida, A. Carnicer, E. Martin-Badosa, S. Vallmitjana, I. Juvells, “Optical correlation by use of partial phase-only modulation with VGA liquid-crystal displays,” Appl. Opt. 39, 766–769 (2000).
    [CrossRef]
  16. K. Lu, B. E. A. Saleh, “Theory and design of the liquid crystal TV as an optical phase modulator,” Opt. Eng. 29, 240–246 (1990).
    [CrossRef]
  17. C. R. Fernández-Pousa, I. Moreno, N. Bennis, C. Gómez-Reino, “Generalized formulation and symmetry properties of reciprocal nonabsorbing polarization devices: application to liquid-crystal displays,” J. Opt. Soc. Am. A 17, 2074–2080 (2000).
    [CrossRef]
  18. S. E. Monroe, M. J. Rollins, R. D. Juday, “Advances in full-face full-complex SLM characterization,” in Optical Pattern Recognition XII, D. P. Casasent, T.-H. Chao, eds., Proc. SPIE4387, 68–77 (2001).
    [CrossRef]
  19. S. E. Broomfield, M. A. A. Neil, E. G. S. Paige, “Programmable multiple-level phase modulation that uses ferroelectric liquid-crystal spatial light modulators,” Appl. Opt. 34, 6652–6665 (1995).
    [CrossRef] [PubMed]
  20. J. A. Davis, P. Tsai, D. M. Cottrell, T. Sonehara, J. Amako, “Transmission variations in liquid crystal spatial light modulators caused by interference and diffraction effects,” Opt. Eng. 38, 1051–1057 (1999).
    [CrossRef]
  21. N. Mukohzaka, N. Yoshida, H. Toyoda, Y. Kobayashi, T. Hara, “Diffraction efficiency analysis of a parallel-aligned nematic-liquid-crystal spatial light modulator,” Appl. Opt. 33, 2804–2811 (1994).
    [CrossRef] [PubMed]
  22. C. Stolz, L. Bigué, P. Ambs, “High-resolution multilevel computer generated holograms on a TN LCD spatial light modulator,” in Diffractive Optics, F. Wyrowski, J. Turunen, eds., Vol. 22 of EOS Topical Meetings Digest Series (European Optical Society, Hanover, Germany), pp. 215–216 (1999).

2001 (1)

2000 (2)

1999 (2)

V. Laude, C. Dirson, “Liquid-crystal active lens: application to image resolution enhancement,” Opt. Commun. 163, 72–78 (1999).
[CrossRef]

J. A. Davis, P. Tsai, D. M. Cottrell, T. Sonehara, J. Amako, “Transmission variations in liquid crystal spatial light modulators caused by interference and diffraction effects,” Opt. Eng. 38, 1051–1057 (1999).
[CrossRef]

1997 (1)

1996 (1)

1995 (3)

1994 (4)

C. Soutar, K. Lu, “Determination of the physical properties of an arbitrary twisted-nematic liquid crystal cell,” Opt. Eng. 33, 2704–2712 (1994).
[CrossRef]

Z. Zhang, G. Lu, F. T. S. Yu, “Simple method for measuring phase modulation in liquid crystal televisions,” Opt. Eng. 33, 3018–3022 (1994).
[CrossRef]

N. Mukohzaka, N. Yoshida, H. Toyoda, Y. Kobayashi, T. Hara, “Diffraction efficiency analysis of a parallel-aligned nematic-liquid-crystal spatial light modulator,” Appl. Opt. 33, 2804–2811 (1994).
[CrossRef] [PubMed]

V. Laude, P. Réfrégier, “Multicriteria characterization of coding domains with optimal Fourier SLM filters,” Appl. Opt. 33, 4465–4471 (1994).
[CrossRef] [PubMed]

1990 (2)

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

P. Réfrégier, “Filter design for optical pattern recognition: multicriteria optimization approach,” Opt. Lett. 15, 854–856 (1990).
[CrossRef] [PubMed]

1987 (1)

1986 (1)

Allebach, J. P.

Amako, J.

J. A. Davis, P. Tsai, D. M. Cottrell, T. Sonehara, J. Amako, “Transmission variations in liquid crystal spatial light modulators caused by interference and diffraction effects,” Opt. Eng. 38, 1051–1057 (1999).
[CrossRef]

Ambs, P.

L. Bigué, P. Ambs, “Optimal multicriteria approach to the iterative Fourier transform algorithm,” Appl. Opt. 40, 5886–5893 (2001).
[CrossRef]

L. Legeard, P. Réfrégier, P. Ambs, “Multicriteria optimality for iterative encoding of computer-generated holograms,” Appl. Opt. 36, 7444–7449 (1997).
[CrossRef]

C. Stolz, L. Bigué, P. Ambs, “High-resolution multilevel computer generated holograms on a TN LCD spatial light modulator,” in Diffractive Optics, F. Wyrowski, J. Turunen, eds., Vol. 22 of EOS Topical Meetings Digest Series (European Optical Society, Hanover, Germany), pp. 215–216 (1999).

Bennis, N.

Bigué, L.

L. Bigué, P. Ambs, “Optimal multicriteria approach to the iterative Fourier transform algorithm,” Appl. Opt. 40, 5886–5893 (2001).
[CrossRef]

C. Stolz, L. Bigué, P. Ambs, “High-resolution multilevel computer generated holograms on a TN LCD spatial light modulator,” in Diffractive Optics, F. Wyrowski, J. Turunen, eds., Vol. 22 of EOS Topical Meetings Digest Series (European Optical Society, Hanover, Germany), pp. 215–216 (1999).

Broomfield, S. E.

Carnicer, A.

Colin, J.

J. Colin, “Corrélation optique photoréfractive haute cadence à transformée de Fourier conjointe,” Thesis, Université Paris 6, Paris, France (1998).

Cottrell, D. M.

J. A. Davis, P. Tsai, D. M. Cottrell, T. Sonehara, J. Amako, “Transmission variations in liquid crystal spatial light modulators caused by interference and diffraction effects,” Opt. Eng. 38, 1051–1057 (1999).
[CrossRef]

Davis, J. A.

J. A. Davis, P. Tsai, D. M. Cottrell, T. Sonehara, J. Amako, “Transmission variations in liquid crystal spatial light modulators caused by interference and diffraction effects,” Opt. Eng. 38, 1051–1057 (1999).
[CrossRef]

Dirson, C.

V. Laude, C. Dirson, “Liquid-crystal active lens: application to image resolution enhancement,” Opt. Commun. 163, 72–78 (1999).
[CrossRef]

Eiju, T.

M. Yamauchi, T. Eiju, “Optimization of twisted nematic liquid crystal panels for spatial light phase modulation,” Opt. Commun. 115, 19–25 (1995).
[CrossRef]

Fernández-Pousa, C. R.

Gómez-Reino, C.

Gregory, D. A.

Hara, T.

Juday, R. D.

S. E. Monroe, M. J. Rollins, R. D. Juday, “Advances in full-face full-complex SLM characterization,” in Optical Pattern Recognition XII, D. P. Casasent, T.-H. Chao, eds., Proc. SPIE4387, 68–77 (2001).
[CrossRef]

Juvells, I.

Kobayashi, Y.

Labastida, I.

Laude, V.

V. Laude, C. Dirson, “Liquid-crystal active lens: application to image resolution enhancement,” Opt. Commun. 163, 72–78 (1999).
[CrossRef]

V. Laude, P. Réfrégier, “Multicriteria characterization of coding domains with optimal Fourier SLM filters,” Appl. Opt. 33, 4465–4471 (1994).
[CrossRef] [PubMed]

Legeard, L.

Lu, G.

Z. Zhang, G. Lu, F. T. S. Yu, “Simple method for measuring phase modulation in liquid crystal televisions,” Opt. Eng. 33, 3018–3022 (1994).
[CrossRef]

Lu, K.

C. Soutar, K. Lu, “Determination of the physical properties of an arbitrary twisted-nematic liquid crystal cell,” Opt. Eng. 33, 2704–2712 (1994).
[CrossRef]

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

Martin-Badosa, E.

Monroe, S. E.

S. E. Monroe, M. J. Rollins, R. D. Juday, “Advances in full-face full-complex SLM characterization,” in Optical Pattern Recognition XII, D. P. Casasent, T.-H. Chao, eds., Proc. SPIE4387, 68–77 (2001).
[CrossRef]

Moreno, I.

Mukohzaka, N.

Neil, M. A. A.

Neto, L. G.

Paige, E. G. S.

Réfrégier, P.

Roberge, D.

Rollins, M. J.

S. E. Monroe, M. J. Rollins, R. D. Juday, “Advances in full-face full-complex SLM characterization,” in Optical Pattern Recognition XII, D. P. Casasent, T.-H. Chao, eds., Proc. SPIE4387, 68–77 (2001).
[CrossRef]

Saleh, B. E. A.

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

Seldowitz, M. A.

Sheng, Y.

Sonehara, T.

J. A. Davis, P. Tsai, D. M. Cottrell, T. Sonehara, J. Amako, “Transmission variations in liquid crystal spatial light modulators caused by interference and diffraction effects,” Opt. Eng. 38, 1051–1057 (1999).
[CrossRef]

Soutar, C.

C. Soutar, K. Lu, “Determination of the physical properties of an arbitrary twisted-nematic liquid crystal cell,” Opt. Eng. 33, 2704–2712 (1994).
[CrossRef]

Stolz, C.

C. Stolz, L. Bigué, P. Ambs, “High-resolution multilevel computer generated holograms on a TN LCD spatial light modulator,” in Diffractive Optics, F. Wyrowski, J. Turunen, eds., Vol. 22 of EOS Topical Meetings Digest Series (European Optical Society, Hanover, Germany), pp. 215–216 (1999).

Sweeney, D. W.

Toyoda, H.

Tsai, P.

J. A. Davis, P. Tsai, D. M. Cottrell, T. Sonehara, J. Amako, “Transmission variations in liquid crystal spatial light modulators caused by interference and diffraction effects,” Opt. Eng. 38, 1051–1057 (1999).
[CrossRef]

Vallmitjana, S.

Yamauchi, M.

M. Yamauchi, T. Eiju, “Optimization of twisted nematic liquid crystal panels for spatial light phase modulation,” Opt. Commun. 115, 19–25 (1995).
[CrossRef]

Yoshida, N.

Yu, F. T. S.

Z. Zhang, G. Lu, F. T. S. Yu, “Simple method for measuring phase modulation in liquid crystal televisions,” Opt. Eng. 33, 3018–3022 (1994).
[CrossRef]

Zhang, Z.

Z. Zhang, G. Lu, F. T. S. Yu, “Simple method for measuring phase modulation in liquid crystal televisions,” Opt. Eng. 33, 3018–3022 (1994).
[CrossRef]

Appl. Opt. (10)

M. A. Seldowitz, J. P. Allebach, D. W. Sweeney, “Synthesis of digital holograms by direct binary search,” Appl. Opt. 26, 2788–2798 (1987).
[CrossRef] [PubMed]

N. Mukohzaka, N. Yoshida, H. Toyoda, Y. Kobayashi, T. Hara, “Diffraction efficiency analysis of a parallel-aligned nematic-liquid-crystal spatial light modulator,” Appl. Opt. 33, 2804–2811 (1994).
[CrossRef] [PubMed]

V. Laude, P. Réfrégier, “Multicriteria characterization of coding domains with optimal Fourier SLM filters,” Appl. Opt. 33, 4465–4471 (1994).
[CrossRef] [PubMed]

I. Labastida, A. Carnicer, E. Martin-Badosa, S. Vallmitjana, I. Juvells, “Optical correlation by use of partial phase-only modulation with VGA liquid-crystal displays,” Appl. Opt. 39, 766–769 (2000).
[CrossRef]

L. G. Neto, D. Roberge, Y. Sheng, “Programmable optical phase-mostly holograms with coupled-mode modulation liquid crystal television,” Appl. Opt. 34, 1944–1950 (1995).
[CrossRef] [PubMed]

S. E. Broomfield, M. A. A. Neil, E. G. S. Paige, “Programmable multiple-level phase modulation that uses ferroelectric liquid-crystal spatial light modulators,” Appl. Opt. 34, 6652–6665 (1995).
[CrossRef] [PubMed]

L. G. Neto, D. Roberge, Y. Sheng, “Full-range, continuous, complex modulation by the use of two coupled-mode liquid-crystal televisions,” Appl. Opt. 35, 4567–4576 (1996).
[CrossRef] [PubMed]

L. Legeard, P. Réfrégier, P. Ambs, “Multicriteria optimality for iterative encoding of computer-generated holograms,” Appl. Opt. 36, 7444–7449 (1997).
[CrossRef]

L. Bigué, P. Ambs, “Optimal multicriteria approach to the iterative Fourier transform algorithm,” Appl. Opt. 40, 5886–5893 (2001).
[CrossRef]

D. A. Gregory, “Real-time pattern recognition using a modified liquid crystal television in a coherent optical correlator,” Appl. Opt. 25, 467–469 (1986).
[CrossRef] [PubMed]

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

Opt. Commun. (2)

V. Laude, C. Dirson, “Liquid-crystal active lens: application to image resolution enhancement,” Opt. Commun. 163, 72–78 (1999).
[CrossRef]

M. Yamauchi, T. Eiju, “Optimization of twisted nematic liquid crystal panels for spatial light phase modulation,” Opt. Commun. 115, 19–25 (1995).
[CrossRef]

Opt. Eng. (4)

C. Soutar, K. Lu, “Determination of the physical properties of an arbitrary twisted-nematic liquid crystal cell,” Opt. Eng. 33, 2704–2712 (1994).
[CrossRef]

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

J. A. Davis, P. Tsai, D. M. Cottrell, T. Sonehara, J. Amako, “Transmission variations in liquid crystal spatial light modulators caused by interference and diffraction effects,” Opt. Eng. 38, 1051–1057 (1999).
[CrossRef]

Z. Zhang, G. Lu, F. T. S. Yu, “Simple method for measuring phase modulation in liquid crystal televisions,” Opt. Eng. 33, 3018–3022 (1994).
[CrossRef]

Opt. Lett. (1)

Other (4)

C. Stolz, L. Bigué, P. Ambs, “High-resolution multilevel computer generated holograms on a TN LCD spatial light modulator,” in Diffractive Optics, F. Wyrowski, J. Turunen, eds., Vol. 22 of EOS Topical Meetings Digest Series (European Optical Society, Hanover, Germany), pp. 215–216 (1999).

S. E. Monroe, M. J. Rollins, R. D. Juday, “Advances in full-face full-complex SLM characterization,” in Optical Pattern Recognition XII, D. P. Casasent, T.-H. Chao, eds., Proc. SPIE4387, 68–77 (2001).
[CrossRef]

J. Colin, “Corrélation optique photoréfractive haute cadence à transformée de Fourier conjointe,” Thesis, Université Paris 6, Paris, France (1998).

CRL Opto, “Miniatures LCDs,” http://www.crlopto.com/wop/lc-prods.htm (1999).

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Figures (11)

Fig. 1
Fig. 1

Typical OCC [i.e., locus of points ( C 1(μ), C 2(μ))] when C 1 and C 2 are to be minimized. μ = 0 corresponds to optimizing only C 2 and μ = 1 corresponds to optimizing only C 1.

Fig. 2
Fig. 2

Optical system used for the characterization of the SLM. P and A, the polarizer and the analyzer, respectively.

Fig. 3
Fig. 3

Six coding domains resulting from the characterization at 633 nm of the SLM, corresponding to six polarizer–analyser configurations.

Fig. 4
Fig. 4

(a) Four eight-level phase domains for different maximum phase modulation and (b) the corresponding OCCs.

Fig. 5
Fig. 5

(a) Simulation of the reconstruction of an eight-level pure-amplitude DOE, difficult to implement in practice. (b) Simulation of the reconstruction of the same DOE when displayed on a SLM with a 2π spiral-coding domain.

Fig. 6
Fig. 6

(a) Ideal spiral domains and (b) their corresponding OCCs.

Fig. 7
Fig. 7

Comparison between the OCCs of the amplitude domains (binary and eight levels) and of the spiral domains.

Fig. 8
Fig. 8

Comparison between the OCCs of some spiral domains with the one of pure π phase domains.

Fig. 9
Fig. 9

(a) Selected experimental domains at 633 nm and (b) their corresponding OCCs compared with theoretical ones.

Fig. 10
Fig. 10

Simulations of DOEs designed with (a) binary-amplitude domain, (b) the (0°, -90°) domain, (c) the (45°, 45°) domain, and (d) the (20°, 80°) configurations.

Fig. 11
Fig. 11

Example of optical reconstructions performed with (a) binary-amplitude domain, (b) the (0°, -90°) domain, (c) the (45°, 45°) domain, and (d) the (20°, 80°) configurations.

Tables (3)

Tables Icon

Table 1 Equation System Used for Amplitude Measurementsa When a Gray-Level Pattern Is Displayed on the SLM

Tables Icon

Table 2 Expression of the Phase Retardation for the Six Considered Configurationsa When a Ronchi Ruling Is Displayed on the SLM

Tables Icon

Table 3 Measurement of Relative Diffraction Efficiency of DOEs Computed with Several Coding Domains

Equations (10)

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

C=μC1+1-μC2.
SNRa=1ERRa=q,r |fq, r|2q,r|fq, r|-ca|gq, r|2,
ca=q,r |fq, r||gq, r|q,r |gq, r|2
η=desired reconstruction energyincident light energy=q,r |gq, r|2MN,
C=μ 1η+1-μERRa.
xoutyout=PψAJPψPxinyin,
xinyin
J=c exp-iβf-ig-h-ijh-ijf+ig,
Pψ=cos2 ψsin ψ cos ψsin ψ cos ψsin2 ψ.
Ap2, 02=N24 a2 sinc2ap2bm12+m22+2m1m2 cosϕ1-ϕ2,

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