Abstract

Methods for measuring and compensating the nonlinear electro-optical effect of transmissive, parallel-aligned liquid crystal (LC)-based spatial light modulators (SLMs) are presented. Particularly, the analysis is focused on the spatial nonuniformity of the voltage versus phase modulation characteristics for an active-matrix-driven, electrically controlled birefringence type LC-SLM. A high-quality reconstruction from phase-only modulating SLMs requires a well-calibrated phase addressing across the entire SLM panel. I discuss how the commonly inherent phase-response inhomogeneity of LC-SLM is characterized by purposeful localized measurement techniques. This phase-response inhomogeneity is efficiently compensated by utilizing a Legendre polynomial representation in combination with a remapping of an 8 bit gray level addressing. The calibration procedure is corroborated by measurement data. The LC-SLM’s experimental demonstration finally verifies the resultant improvement in holographic imaging.

© 2013 Optical Society of America

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  1. C. Kohler, X. Schwab, and W. Osten, “Optimally tuned spatial light modulators for digital holography,” Appl. Opt. 45, 960–967 (2006).
    [CrossRef]
  2. D. Engström, G. Milewski, J. Bengtsson, and S. Galt, “Diffraction-based determination of the phase modulation for general spatial light modulators,” Appl. Opt. 45, 7195–7204 (2006).
    [CrossRef]
  3. A. Hermerschmidt, S. Osten, S. Krüger, and T. Blümel, “Wave front generation using a phase-only modulating liquid-crystal-based micro-display with HDTV resolution,” Proc. SPIE 6584, 65840E (2007).
    [CrossRef]
  4. A. Bergeron, J. Gauvin, F. Gagnon, D. Gingras, H. H. Arsenault, and M. Doucet, “Phase calibration and applications of a liquid-crystal spatial light modulator,” Appl. Opt. 34, 5133–5139 (1995).
    [CrossRef]
  5. K. Dev, V. R. Singh, and A. Asundi, “Full-field phase modulation characterization of liquid-crystal spatial light modulator using digital holography,” Appl. Opt. 50, 1593–1600 (2011).
    [CrossRef]
  6. J. W. Tay, M. A. Taylor, and W. P. Bowen, “Sagnac-interferometer-based characterization of spatial light modulators,” Appl. Opt. 48, 2236–2242 (2009).
    [CrossRef]
  7. J. Otón, P. Ambs, M. S. Millán, and E. Pérez-Cabré, “Dynamic calibration for improving the speed of a parallel-aligned liquid-crystal-on-silicon display,” Appl. Opt. 48, 4616–4624 (2009).
    [CrossRef]
  8. Z. Zhang, H. Yang, B. Robertson, M. Redmond, M. Pivnenko, N. Collings, W. A. Crossland, and D. Chu, “Diffraction based phase compensation method for phase-only liquid crystal on silicon devices in operation,” Appl. Opt. 51, 3837–3846 (2012).
    [CrossRef]
  9. 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, 722 (2008).
  10. J. B. Bentley, J. A. Davis, J. Albero, and I. Moreno, “Self-interferometric technique for visualization of phase patterns encoded onto a liquid-crystal display,” Appl. Opt. 45, 7791–7794 (2006).
    [CrossRef]
  11. F. P. Ferreira and M. S. Belsley, “Direct calibration of a spatial light modulator by lateral shearing interferometry,” Opt. Express 18, 7899–7904 (2010).
    [CrossRef]
  12. X. Xun and R. W. Cohn, “Phase calibration of spatially nonuniform spatial light modulators,” Appl. Opt. 43, 6400–6406 (2004).
    [CrossRef]
  13. J. Otón, P. Ambs, M. S. Millán, and E. Pérez-Cabré, “Multipoint phase calibration for improved compensation of inherent wavefront distortion in parallel aligned liquid crystal on silicon displays,” Appl. Opt. 46, 5667–5679 (2007).
    [CrossRef]
  14. M. Rose, “Active matrix liquid crystal displays (AMLCDs),” in Handbook of Visual Display Technology, J. Chen, W. Cranton, and M. Fihn, eds. (Springer, 2012), pp. 1589–1606.
  15. P. Yeh and C. Gu, Optics of Liquid Crystal Displays, 2nd ed. (Wiley, 2010).
  16. MathWorks, “2D cross-correlation,” http://www.mathworks.de/de/help/signal/ref/xcorr2.html .
  17. K. Blankenbach, “Active matrix driving,” in Handbook of Visual Display Technology, J. Chen, W. Cranton, and M. Fihn, eds. (Springer, 2012), pp. 441–458.
  18. R. Gerchberg and W. Saxton, “A practical algorithm for the determination of phase from image and diffraction plane pictures,” Optik 35, 237–246 (1972).
  19. S. Reichelt, R. Häussler, N. Leister, G. Fütterer, and A. Schwerdtner, “Large holographic 3D displays for tomorrow’s TV and monitors—solutions, challenges, and prospects,” in Proceedings of 21st Annual Meeting of the IEEE Lasers and Electro-Optics Society LEOS 2008 (IEEE, 2008), pp. 194–195.
  20. S. Reichelt and N. Leister, “Computational hologram synthesis and representation on spatial light modulators for real-time 3D holographic imaging,” J. Phys. 415, 012038 (2013).
    [CrossRef]

2013 (1)

S. Reichelt and N. Leister, “Computational hologram synthesis and representation on spatial light modulators for real-time 3D holographic imaging,” J. Phys. 415, 012038 (2013).
[CrossRef]

2012 (1)

2011 (1)

2010 (1)

2009 (2)

2008 (1)

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, 722 (2008).

2007 (2)

A. Hermerschmidt, S. Osten, S. Krüger, and T. Blümel, “Wave front generation using a phase-only modulating liquid-crystal-based micro-display with HDTV resolution,” Proc. SPIE 6584, 65840E (2007).
[CrossRef]

J. Otón, P. Ambs, M. S. Millán, and E. Pérez-Cabré, “Multipoint phase calibration for improved compensation of inherent wavefront distortion in parallel aligned liquid crystal on silicon displays,” Appl. Opt. 46, 5667–5679 (2007).
[CrossRef]

2006 (3)

2004 (1)

1995 (1)

1972 (1)

R. Gerchberg and W. Saxton, “A practical algorithm for the determination of phase from image and diffraction plane pictures,” Optik 35, 237–246 (1972).

Albero, J.

Ambs, P.

Arsenault, H. H.

Asundi, A.

Belsley, M. S.

Bengtsson, J.

Bentley, J. B.

Bergeron, A.

Blankenbach, K.

K. Blankenbach, “Active matrix driving,” in Handbook of Visual Display Technology, J. Chen, W. Cranton, and M. Fihn, eds. (Springer, 2012), pp. 441–458.

Blümel, T.

A. Hermerschmidt, S. Osten, S. Krüger, and T. Blümel, “Wave front generation using a phase-only modulating liquid-crystal-based micro-display with HDTV resolution,” Proc. SPIE 6584, 65840E (2007).
[CrossRef]

Bowen, W. P.

Campos, J.

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, 722 (2008).

Chu, D.

Cohn, R. W.

Collings, N.

Crossland, W. A.

Davis, J. A.

Dev, K.

Doucet, M.

Engström, D.

Fernández, E.

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, 722 (2008).

Ferreira, F. P.

Fütterer, G.

S. Reichelt, R. Häussler, N. Leister, G. Fütterer, and A. Schwerdtner, “Large holographic 3D displays for tomorrow’s TV and monitors—solutions, challenges, and prospects,” in Proceedings of 21st Annual Meeting of the IEEE Lasers and Electro-Optics Society LEOS 2008 (IEEE, 2008), pp. 194–195.

Gagnon, F.

Galt, S.

Gauvin, J.

Gerchberg, R.

R. Gerchberg and W. Saxton, “A practical algorithm for the determination of phase from image and diffraction plane pictures,” Optik 35, 237–246 (1972).

Gingras, D.

Gu, C.

P. Yeh and C. Gu, Optics of Liquid Crystal Displays, 2nd ed. (Wiley, 2010).

Häussler, R.

S. Reichelt, R. Häussler, N. Leister, G. Fütterer, and A. Schwerdtner, “Large holographic 3D displays for tomorrow’s TV and monitors—solutions, challenges, and prospects,” in Proceedings of 21st Annual Meeting of the IEEE Lasers and Electro-Optics Society LEOS 2008 (IEEE, 2008), pp. 194–195.

Hermerschmidt, A.

A. Hermerschmidt, S. Osten, S. Krüger, and T. Blümel, “Wave front generation using a phase-only modulating liquid-crystal-based micro-display with HDTV resolution,” Proc. SPIE 6584, 65840E (2007).
[CrossRef]

Iemmi, C.

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, 722 (2008).

Kohler, C.

Krüger, S.

A. Hermerschmidt, S. Osten, S. Krüger, and T. Blümel, “Wave front generation using a phase-only modulating liquid-crystal-based micro-display with HDTV resolution,” Proc. SPIE 6584, 65840E (2007).
[CrossRef]

Leister, N.

S. Reichelt and N. Leister, “Computational hologram synthesis and representation on spatial light modulators for real-time 3D holographic imaging,” J. Phys. 415, 012038 (2013).
[CrossRef]

S. Reichelt, R. Häussler, N. Leister, G. Fütterer, and A. Schwerdtner, “Large holographic 3D displays for tomorrow’s TV and monitors—solutions, challenges, and prospects,” in Proceedings of 21st Annual Meeting of the IEEE Lasers and Electro-Optics Society LEOS 2008 (IEEE, 2008), pp. 194–195.

Lizana, A.

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, 722 (2008).

Márquez, A.

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, 722 (2008).

Milewski, G.

Millán, M. S.

Moreno, I.

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, 722 (2008).

J. B. Bentley, J. A. Davis, J. Albero, and I. Moreno, “Self-interferometric technique for visualization of phase patterns encoded onto a liquid-crystal display,” Appl. Opt. 45, 7791–7794 (2006).
[CrossRef]

Osten, S.

A. Hermerschmidt, S. Osten, S. Krüger, and T. Blümel, “Wave front generation using a phase-only modulating liquid-crystal-based micro-display with HDTV resolution,” Proc. SPIE 6584, 65840E (2007).
[CrossRef]

Osten, W.

Otón, J.

Pérez-Cabré, E.

Pivnenko, M.

Redmond, M.

Reichelt, S.

S. Reichelt and N. Leister, “Computational hologram synthesis and representation on spatial light modulators for real-time 3D holographic imaging,” J. Phys. 415, 012038 (2013).
[CrossRef]

S. Reichelt, R. Häussler, N. Leister, G. Fütterer, and A. Schwerdtner, “Large holographic 3D displays for tomorrow’s TV and monitors—solutions, challenges, and prospects,” in Proceedings of 21st Annual Meeting of the IEEE Lasers and Electro-Optics Society LEOS 2008 (IEEE, 2008), pp. 194–195.

Robertson, B.

Rose, M.

M. Rose, “Active matrix liquid crystal displays (AMLCDs),” in Handbook of Visual Display Technology, J. Chen, W. Cranton, and M. Fihn, eds. (Springer, 2012), pp. 1589–1606.

Saxton, W.

R. Gerchberg and W. Saxton, “A practical algorithm for the determination of phase from image and diffraction plane pictures,” Optik 35, 237–246 (1972).

Schwab, X.

Schwerdtner, A.

S. Reichelt, R. Häussler, N. Leister, G. Fütterer, and A. Schwerdtner, “Large holographic 3D displays for tomorrow’s TV and monitors—solutions, challenges, and prospects,” in Proceedings of 21st Annual Meeting of the IEEE Lasers and Electro-Optics Society LEOS 2008 (IEEE, 2008), pp. 194–195.

Singh, V. R.

Tay, J. W.

Taylor, M. A.

Xun, X.

Yang, H.

Yeh, P.

P. Yeh and C. Gu, Optics of Liquid Crystal Displays, 2nd ed. (Wiley, 2010).

Yzuel, M. J.

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, 722 (2008).

Zhang, Z.

Appl. Opt. (10)

A. Bergeron, J. Gauvin, F. Gagnon, D. Gingras, H. H. Arsenault, and M. Doucet, “Phase calibration and applications of a liquid-crystal spatial light modulator,” Appl. Opt. 34, 5133–5139 (1995).
[CrossRef]

K. Dev, V. R. Singh, and A. Asundi, “Full-field phase modulation characterization of liquid-crystal spatial light modulator using digital holography,” Appl. Opt. 50, 1593–1600 (2011).
[CrossRef]

J. W. Tay, M. A. Taylor, and W. P. Bowen, “Sagnac-interferometer-based characterization of spatial light modulators,” Appl. Opt. 48, 2236–2242 (2009).
[CrossRef]

J. Otón, P. Ambs, M. S. Millán, and E. Pérez-Cabré, “Dynamic calibration for improving the speed of a parallel-aligned liquid-crystal-on-silicon display,” Appl. Opt. 48, 4616–4624 (2009).
[CrossRef]

Z. Zhang, H. Yang, B. Robertson, M. Redmond, M. Pivnenko, N. Collings, W. A. Crossland, and D. Chu, “Diffraction based phase compensation method for phase-only liquid crystal on silicon devices in operation,” Appl. Opt. 51, 3837–3846 (2012).
[CrossRef]

C. Kohler, X. Schwab, and W. Osten, “Optimally tuned spatial light modulators for digital holography,” Appl. Opt. 45, 960–967 (2006).
[CrossRef]

D. Engström, G. Milewski, J. Bengtsson, and S. Galt, “Diffraction-based determination of the phase modulation for general spatial light modulators,” Appl. Opt. 45, 7195–7204 (2006).
[CrossRef]

J. B. Bentley, J. A. Davis, J. Albero, and I. Moreno, “Self-interferometric technique for visualization of phase patterns encoded onto a liquid-crystal display,” Appl. Opt. 45, 7791–7794 (2006).
[CrossRef]

X. Xun and R. W. Cohn, “Phase calibration of spatially nonuniform spatial light modulators,” Appl. Opt. 43, 6400–6406 (2004).
[CrossRef]

J. Otón, P. Ambs, M. S. Millán, and E. Pérez-Cabré, “Multipoint phase calibration for improved compensation of inherent wavefront distortion in parallel aligned liquid crystal on silicon displays,” Appl. Opt. 46, 5667–5679 (2007).
[CrossRef]

J. Phys. (1)

S. Reichelt and N. Leister, “Computational hologram synthesis and representation on spatial light modulators for real-time 3D holographic imaging,” J. Phys. 415, 012038 (2013).
[CrossRef]

Opt. Express (2)

F. P. Ferreira and M. S. Belsley, “Direct calibration of a spatial light modulator by lateral shearing interferometry,” Opt. Express 18, 7899–7904 (2010).
[CrossRef]

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, 722 (2008).

Optik (1)

R. Gerchberg and W. Saxton, “A practical algorithm for the determination of phase from image and diffraction plane pictures,” Optik 35, 237–246 (1972).

Proc. SPIE (1)

A. Hermerschmidt, S. Osten, S. Krüger, and T. Blümel, “Wave front generation using a phase-only modulating liquid-crystal-based micro-display with HDTV resolution,” Proc. SPIE 6584, 65840E (2007).
[CrossRef]

Other (5)

S. Reichelt, R. Häussler, N. Leister, G. Fütterer, and A. Schwerdtner, “Large holographic 3D displays for tomorrow’s TV and monitors—solutions, challenges, and prospects,” in Proceedings of 21st Annual Meeting of the IEEE Lasers and Electro-Optics Society LEOS 2008 (IEEE, 2008), pp. 194–195.

M. Rose, “Active matrix liquid crystal displays (AMLCDs),” in Handbook of Visual Display Technology, J. Chen, W. Cranton, and M. Fihn, eds. (Springer, 2012), pp. 1589–1606.

P. Yeh and C. Gu, Optics of Liquid Crystal Displays, 2nd ed. (Wiley, 2010).

MathWorks, “2D cross-correlation,” http://www.mathworks.de/de/help/signal/ref/xcorr2.html .

K. Blankenbach, “Active matrix driving,” in Handbook of Visual Display Technology, J. Chen, W. Cranton, and M. Fihn, eds. (Springer, 2012), pp. 441–458.

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Figures (10)

Fig. 1.
Fig. 1.

Schematic drawing of an ECB cell in off and on states. The LC director is rotated to the tilt angle θ when an electric field is applied. Light propagation is in the positive z direction.

Fig. 2.
Fig. 2.

Determination of the ECB-mode LC-SLM phase response by intensity modulation measurement. (a) Optical scheme for transmittance measurement with a photodiode (PD) or an optical power meter (OPM). (b) Measured normalized transmittance T norm , determined discontinuous phase shift ϕ discont . , and continuous phase shift ϕ cont . with ambiguities eliminated over applied voltage (from top to bottom).

Fig. 3.
Fig. 3.

Mach–Zehnder interferometer for measuring the phase response.

Fig. 4.
Fig. 4.

Details of the interferogram analysis for phase-response determination. (a) Captured interferogram for a certain voltage level with marked reference and measurement areas I R and I M . (b) Cross correlation of I R and I M . (c) Determined phase response for a series of interferogram pairs I R and I M at different voltage levels.

Fig. 5.
Fig. 5.

Graph of the inverse phase response, that is, the voltage-phase calibration curve V ( ϕ ) .

Fig. 6.
Fig. 6.

V ( ϕ , x , y ) curves and their 2D interpolation plotted as phase responsiveness maps. (a) Set of V ( ϕ ) curves acquired at 12 SLM positions. (b) Selected 4 of 256 voltage maps V ( ϕ , x , y ) interpolated by Legendre polynomials.

Fig. 7.
Fig. 7.

Gray-level remapping at the example of a checkerboard pattern with original gray levels of 0 and 255. Shown are the patterns and their corresponding histograms.

Fig. 8.
Fig. 8.

Photographed intensity modulation when gray-scale wedges are addressed onto the SLM. The SLM is white backlight illuminated and viewed through crossed ± 45 ° linear polarizers.

Fig. 9.
Fig. 9.

2D image reconstruction of Fourier transform holograms (a) without and (b) with consideration of the local phase calibration.

Fig. 10.
Fig. 10.

Holographic reconstruction from iterative phase-only encoded holograms displayed at the LC-SLM (a) without and (b) with local phase calibration. In the upper images the camera focus was set to + 100 mm (in front of display); in the lower images the focus was at 250 mm (behind display).

Equations (10)

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Γ = k 0 d [ n e ( θ ) n o ] d z = k d ( n eff n o ) ,
J ECB = ( 1 0 0 e i ϕ y ( V ) )
J AM = J L 45 P · J ECB · J L + 45 P = 1 2 ( 1 1 1 1 ) ( 1 0 0 e i ϕ y ( V ) ) 1 2 ( 1 1 1 1 ) .
J PM = J ECB = ( 1 0 0 e i ϕ y ( V ) ) .
T ( V ) = sin 2 [ Γ ( V ) 2 ] ,
ϕ ( V ) = 2 arcsin [ T ( V ) 1 2 ] .
I XC ( k , l ) = i = 1 m j = 1 n I R ( i , j ) · conj [ I M ( i + k , j + l ) ] ,
ϕ ( V ) = 2 π f c Δ k 2 ( V ) + Δ l 2 ( V ) .
V ( ϕ ) = n = 0 m a n ( ϕ ϕ 0 ) n ,
B = uint 8 { 255 V max V min [ V ( ϕ , x , y ) V min ] } ,

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