Abstract

In this paper we experimentally analyze the performance of a twisted nematic liquid crystal on silicon (LCoS) display as a function of the angle of incidence of the incoming beam. These are reflective displays that can be configured to produce amplitude or phase modulation by properly aligning external polarization elements. But we demonstrate that the incident angle plays an important role in the selection of the polarization configuration. We performed a Mueller matrix polarimetric analysis of the display that demonstrates that the recently reported depolarization effect observed in this type of displays is also dependant on the incident angle.

© 2009 Optical Society of America

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  1. P. J. Turunen and F. Wyrowski eds., Diffractive Optics for Industrial and Commercial Applications, (Akademie Verlag, Berlin, 1997).
  2. H. J. Coufal, D. Psaltis and B. T. Sincerbox, eds., Holographic Data Storage, (Springer-Verlag, Berlin, 2000).
  3. W. Osten, C. Kohler, and J. Liesener, "Evaluation and application of spatial light modulators for optical metrology," Opt. Pura Apl. 38, 71-81 (2005).
  4. R. Dou and M. K. Giles, "Closed-loop adaptative optics system with a liquid crystal television as a phase retarder," Opt. Lett. 20, 1583-1585 (1995).
    [CrossRef] [PubMed]
  5. J. Campos, A. Márquez, J. Nicolas, I. Moreno, C. Iemmi, J. C. Escalera, J. A. Davis and J. M. Yzuel, "Optimization of liquid crystals displays behaviour in optical image processing and in diffractive optics", in Optoelectronic information processing: Optics for information systems, (SPIE Press, Critical Reviews) Vol. CR81, 335-364 (2001).
  6. J. A. Davis, I. Moreno and P. Tsai, "Polarization eigenstates for twisted-nematic liquid-crystal displays," Appl. Opt. 37, 937-945 (1998).
    [CrossRef]
  7. A. Márquez, I. Moreno, C. Iemmi, A. Lizana, J. Campos and M. J. Yzuel, "Mueller-Stokes characterization and optimization of a liquid crystal on silicon display showing depolarization," Opt. Express 16, 1669-1685 (2008).
    [CrossRef] [PubMed]
  8. J. E. Wolfe and R. A. Chipman, "Polarimetric characterization of liquid-crystal-on-silicon panels," Appl. Opt. 45, 1688-1703 (2006).
    [CrossRef] [PubMed]
  9. A. Lizana, I. Moreno, C. Iemmi, A. Márquez, J. Campos and M. J. Yzuel, "Time-resolved Mueller matrix analysis of a liquid crystal on silicon display," Appl Opt. 47, 4267-4274 (2008).
    [CrossRef] [PubMed]
  10. A. Lizana, I. Moreno, A. Márquez, C. Iemmi, E. Fernández, J. Campos and M. J. Yzuel, " Time fluctuations of the phase modulation in a liquid crystal on silicon display: characterization and effects in diffractive optics," Opt. Express 16, 16711-16722 (2008).
    [CrossRef] [PubMed]
  11. I. Moreno, A. Lizana, J. Campos, A. Márquez, C. Iemmi, and M. J. Yzuel, "Combined Mueller and Jones matrix method for the evaluation of the complex modulation in a liquid-crystal-on-silicon display," Opt. Lett. 33, 627-629 (2008).
    [CrossRef] [PubMed]
  12. A. Lizana, A. Márquez, I. Moreno, C. Iemmi, J. Campos, and M. J. Yzuel, "Wavelength dependence of polarimetric and phase-shift characterization of a liquid crystal on silicon display," J. Eur. Opt. Soc. - Rapid Pub. 3, 08011 1-6 (2008).
  13. E. Martín-Badosa, M. Montes-Usategui, A. Carnicer, J. Andilla, E. Pleguezuelos, and I. Juvells, "Design strategies for optimizing holographic optical tweezers set-ups," J. Opt. A - Pure Appl. Op. 9, S267-S277 (2007).
    [CrossRef]
  14. D. Goldstein, Polarized Light, (Marcel Dekker, NY, 2003).
    [CrossRef]
  15. J. L. Pezzaniti, S. C. McClain, R. A. Chipman and S.-Y. Lu, "Depolarization in liquid-crystal televisions," Opt. Lett. 18, 2071-2073 (1993).
    [CrossRef] [PubMed]
  16. S. Y. Lu and R. A. Chipman, "Interpretation of Mueller matrices based on polar decomposition," J. Opt. Soc. Am. A 13, 1106-1113 (1996).
    [CrossRef]
  17. P. Lancaster and M Tismenetsky, The Theory of Matrices, 2nd Ed. (Academic, San Diego, 1985).
  18. A. Marquez, I. Moreno, J. Campos, and M. J. Yzuel, "Analisis of Fabry-Perot interference effects on the modulation properties of liquid crystal displays," Opt. Commun. 265, 84-94 (2006).
    [CrossRef]
  19. S. Y. Lu and R. A. Chipman, "Homogeneous and inhomogeneous Jones matrices," J. Opt. Soc. Am. A 11, 766-773 (1994).
    [CrossRef]
  20. S. Huard, Polarisation de la lumière, (Masson, Paris, 1993), pg. 109.
  21. S. Stallinga, "Equivalent retarder approach to reflective liquid crystal displays," J. Appl. Phys. 86, 4756-4766 (1999).
    [CrossRef]
  22. J. Nicolas, 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]
  23. C. Glasenapp, W. Mönch, H. Krause and H. Zappe, "Biochip reader with dynamic holographic excitation and hyperspectral fluorescence detection," J. Biomed. Opt. 2, 014038 (2007).
    [CrossRef]

2008 (4)

2007 (1)

C. Glasenapp, W. Mönch, H. Krause and H. Zappe, "Biochip reader with dynamic holographic excitation and hyperspectral fluorescence detection," J. Biomed. Opt. 2, 014038 (2007).
[CrossRef]

2006 (2)

A. Marquez, I. Moreno, J. Campos, and M. J. Yzuel, "Analisis of Fabry-Perot interference effects on the modulation properties of liquid crystal displays," Opt. Commun. 265, 84-94 (2006).
[CrossRef]

J. E. Wolfe and R. A. Chipman, "Polarimetric characterization of liquid-crystal-on-silicon panels," Appl. Opt. 45, 1688-1703 (2006).
[CrossRef] [PubMed]

2005 (1)

W. Osten, C. Kohler, and J. Liesener, "Evaluation and application of spatial light modulators for optical metrology," Opt. Pura Apl. 38, 71-81 (2005).

2002 (1)

1999 (1)

S. Stallinga, "Equivalent retarder approach to reflective liquid crystal displays," J. Appl. Phys. 86, 4756-4766 (1999).
[CrossRef]

1998 (1)

1996 (1)

1995 (1)

1994 (1)

1993 (1)

Campos, J.

Chipman, R. A.

Davis, J. A.

Dou, R.

Fernández, E.

Giles, M. K.

Glasenapp, C.

C. Glasenapp, W. Mönch, H. Krause and H. Zappe, "Biochip reader with dynamic holographic excitation and hyperspectral fluorescence detection," J. Biomed. Opt. 2, 014038 (2007).
[CrossRef]

Iemmi, C.

Kohler, C.

W. Osten, C. Kohler, and J. Liesener, "Evaluation and application of spatial light modulators for optical metrology," Opt. Pura Apl. 38, 71-81 (2005).

Krause, H.

C. Glasenapp, W. Mönch, H. Krause and H. Zappe, "Biochip reader with dynamic holographic excitation and hyperspectral fluorescence detection," J. Biomed. Opt. 2, 014038 (2007).
[CrossRef]

Liesener, J.

W. Osten, C. Kohler, and J. Liesener, "Evaluation and application of spatial light modulators for optical metrology," Opt. Pura Apl. 38, 71-81 (2005).

Lizana, A.

Lu, S. Y.

Lu, S.-Y.

Marquez, A.

A. Marquez, I. Moreno, J. Campos, and M. J. Yzuel, "Analisis of Fabry-Perot interference effects on the modulation properties of liquid crystal displays," Opt. Commun. 265, 84-94 (2006).
[CrossRef]

Márquez, A.

McClain, S. C.

Mönch, W.

C. Glasenapp, W. Mönch, H. Krause and H. Zappe, "Biochip reader with dynamic holographic excitation and hyperspectral fluorescence detection," J. Biomed. Opt. 2, 014038 (2007).
[CrossRef]

Moreno, I.

Nicolas, J.

Osten, W.

W. Osten, C. Kohler, and J. Liesener, "Evaluation and application of spatial light modulators for optical metrology," Opt. Pura Apl. 38, 71-81 (2005).

Pezzaniti, J. L.

Stallinga, S.

S. Stallinga, "Equivalent retarder approach to reflective liquid crystal displays," J. Appl. Phys. 86, 4756-4766 (1999).
[CrossRef]

Tsai, P.

Wolfe, J. E.

Yzuel, M. J.

Zappe, H.

C. Glasenapp, W. Mönch, H. Krause and H. Zappe, "Biochip reader with dynamic holographic excitation and hyperspectral fluorescence detection," J. Biomed. Opt. 2, 014038 (2007).
[CrossRef]

Appl Opt. (1)

A. Lizana, I. Moreno, C. Iemmi, A. Márquez, J. Campos and M. J. Yzuel, "Time-resolved Mueller matrix analysis of a liquid crystal on silicon display," Appl Opt. 47, 4267-4274 (2008).
[CrossRef] [PubMed]

Appl. Opt. (2)

J. Appl. Phys. (1)

S. Stallinga, "Equivalent retarder approach to reflective liquid crystal displays," J. Appl. Phys. 86, 4756-4766 (1999).
[CrossRef]

J. Biomed. Opt. (1)

C. Glasenapp, W. Mönch, H. Krause and H. Zappe, "Biochip reader with dynamic holographic excitation and hyperspectral fluorescence detection," J. Biomed. Opt. 2, 014038 (2007).
[CrossRef]

J. Opt. Soc. Am. A (3)

Opt. Commun. (1)

A. Marquez, I. Moreno, J. Campos, and M. J. Yzuel, "Analisis of Fabry-Perot interference effects on the modulation properties of liquid crystal displays," Opt. Commun. 265, 84-94 (2006).
[CrossRef]

Opt. Express (2)

Opt. Lett. (3)

Opt. Pura Apl. (1)

W. Osten, C. Kohler, and J. Liesener, "Evaluation and application of spatial light modulators for optical metrology," Opt. Pura Apl. 38, 71-81 (2005).

Other (8)

J. Campos, A. Márquez, J. Nicolas, I. Moreno, C. Iemmi, J. C. Escalera, J. A. Davis and J. M. Yzuel, "Optimization of liquid crystals displays behaviour in optical image processing and in diffractive optics", in Optoelectronic information processing: Optics for information systems, (SPIE Press, Critical Reviews) Vol. CR81, 335-364 (2001).

P. J. Turunen and F. Wyrowski eds., Diffractive Optics for Industrial and Commercial Applications, (Akademie Verlag, Berlin, 1997).

H. J. Coufal, D. Psaltis and B. T. Sincerbox, eds., Holographic Data Storage, (Springer-Verlag, Berlin, 2000).

P. Lancaster and M Tismenetsky, The Theory of Matrices, 2nd Ed. (Academic, San Diego, 1985).

A. Lizana, A. Márquez, I. Moreno, C. Iemmi, J. Campos, and M. J. Yzuel, "Wavelength dependence of polarimetric and phase-shift characterization of a liquid crystal on silicon display," J. Eur. Opt. Soc. - Rapid Pub. 3, 08011 1-6 (2008).

E. Martín-Badosa, M. Montes-Usategui, A. Carnicer, J. Andilla, E. Pleguezuelos, and I. Juvells, "Design strategies for optimizing holographic optical tweezers set-ups," J. Opt. A - Pure Appl. Op. 9, S267-S277 (2007).
[CrossRef]

D. Goldstein, Polarized Light, (Marcel Dekker, NY, 2003).
[CrossRef]

S. Huard, Polarisation de la lumière, (Masson, Paris, 1993), pg. 109.

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Figures (11)

Fig. 1.
Fig. 1.

Set up used to obtain the experimental LCoS Mueller matrix.

Fig. 2.
Fig. 2.

Degree of polarization as a function of the gray level and for an angle of incidence equal to: a) α=2°, b) α=12.5°, c) α=23°, d) α=34° and e) α=45°.

Fig. 3.
Fig. 3.

DOP as a function of different incident SoPs and with an incident angle equal to: a) 2°; b) 45°. The LCoS display is switched off.

Fig. 4.
Fig. 4.

First row and column Mueller coefficients as a function of the gray level for an incident angle of: a, b) α=2°; c, d) α=45°.

Fig. 5.
Fig. 5.

Mueller matrix third row coefficients as a function of the gray level and an incident angle equal to: a) α=2°; b) α=12.5°; c) α=23°; d) α=34° and e) a=45°.

Fig. 6.
Fig. 6.

Retardance as a function of the gray level and different incident angles.

Fig. 7.
Fig. 7.

Equivalent retarder eigenvectors as a function of the gray level for the incident angle α=2°.

Fig. 8.
Fig. 8.

Equivalent retarder eigenvectors as a function of the gray level for the incident angles α=12.5°, α=23°, α=34° and α=45°.

Fig. 9.
Fig. 9.

Theoretical (lines) and experimental (spots) intensity and phase values, when using an incident angle equal to: a) 2°; b) 12.5°; c) 45°. The rotation angle values of polarizers and waveplates used at the PSG and PSD systems are: P1=88° and WP1=7°; P2=90° and WP2=-15°.

Fig. 10.
Fig. 10.

Phase modulation optimization when using an incident angle equal to: a) α=12.5°; b) α=45°.

Fig. 11.
Fig. 11.

(a). Experimental set-up. (b). Optimized phase modulation response obtained when using the beam splitter set-up. On one hand, the intensity values are represented in continuous line (simulation) and black circles (experimental values). On the other hand, the phase values are represented with a dotted line (simulation) and squares (experimental values). The rotation angle values of polarizers and waveplates used at the PSG and PSD systems are: P1=105° and WP1=94°; P2=105° and WP2=82°.

Equations (8)

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I(π2,θ2)=12[S0+S12+S12cos(4θ2)+S22sin(4θ2)S3sin(2θ2)],
2Nr=1Nsin(2πriN)·sin(2πrjN)=2Nr=1Ncos(2πriN)·cos(2πrjN)=δij,
r=1Nsin(2πriN)·cos(2πrjN)=0,
r=1Nsin(2πriN)=r=1Ncos(2πriN)=0.
(S0S1S2S3)=1N((2·r=1NI(π2,θ2,r)4r=1NI(π2,θ2,r)·cos(4θ2,r))8r=1NI(π2,θ2,r)·cos(4θ2,r)8r=1NI(π2,θ2,r)·sin(4θ2,r)4r=1NI(π2,θ2,r)·sin(2θ2,r))
Sinput=(1cos2(2θ1)12sin(4θ1)sin(2θ1)).
Skr(θ1)output=mk0+mk12+mk12cos(4θ1)+mk22sin(4θ1)+mk3sin(2θ1),
M=1N(r=1NS0r2r=1NSr0cos(4θ1,r)4r=1NSr0cos(4θ1,r)4r=1NSr0sin(4θ1,r)2r=1NSr0sin(2θ1,r)r=1NS1r2r=1NSr1cos(4θ1,r)4r=1NSr1cos(4θ1,r)4r=1NSr1sin(4θ1,r)2r=1NSr1sin(2θ1,r)r=1NS2r2r=1NSr2cos(4θ1,r)4r=1NSr2cos(4θ1,r)4r=1NSr2sin(4θ1,r)2r=1NSr2sin(2θ1,r)r=1NS3r2r=1NSr3cos(4θ1,r)4r=1NSr3cos(4θ1,r)4r=1NSr3sin(4θ1,r)2r=1NSr3sin(2θ1,r)),

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