Abstract

A direct quantitative phase measurement method to characterize intrinsic phase modulation from an entire active area of transmissive twisted-nematic liquid-crystal spatial light modulator (TN-LCSLM) is presented using digital holography (DH). The change in birefringence of liquid crystal material with respect to addressed gray scale produces phase modulation of wavefront transmitted through TN-LCSLM. Existing methods for phase modulation characterization of LCSLM mainly provides point measurement on its total active region. In this paper, the DH method is evolved to extract quantitative phase information of an entire active area from a single digital hologram formed using the complex wavefront transmitted through TN-LCSLM.

© 2011 Optical Society of America

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References

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2009 (2)

C. Kohler, F. Zhang, and W. Osten, “Characterization of a spatial light modulator and its application in phase retrieval,” Appl. Opt. 48, 4003–4008 (2009).
[CrossRef] [PubMed]

M. Agour, E. Kolenovic, C. Falldorf, and C. von Kopylow, “Suppression of higher diffraction orders and intensity improvement of optically reconstructed holograms from a spatial light modulator,” J. Opt. A: Pure Appl. Opt. 11105405(2009).
[CrossRef]

2008 (1)

C. Cheng, Y. Lin, M. Hsieh, and H. Tu, “Complex modulation characterization of liquid crystal spatial light modulators by digital holographic microscopy,” Jpn. J. Appl. Phys. 47, 3527–3529 (2008).
[CrossRef]

2006 (1)

2004 (1)

P. Ferraro, S. D. Nicola, A. Finizio, G. Pierattini, and G. Coppola, “Recovering image resolution in reconstructing digital off-axis holograms by Fresnel-transform method,” Appl. Phys. Lett. 85, 2709–2711 (2004).
[CrossRef]

2002 (2)

T. M. Kreis, “Frequency analysis of digital holography with reconstruction by convolution,” Opt. Eng. 41, 1829–1839 (2002).
[CrossRef]

U. Schnars and W. P. O. Jüptner, “Digital recording and numerical reconstruction of holograms,” Meas. Sci. Technol. 13, R85–R101 (2002).
[CrossRef]

1998 (1)

1996 (1)

R. Dou and M. K. Giles, “Simple technique for measuring the phase property of a twisted nematic liquid crystal television,” Opt. Eng. 35, 808–812 (1996).
[CrossRef]

1995 (1)

1990 (1)

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

1989 (1)

1988 (1)

1983 (1)

Agour, M.

M. Agour, E. Kolenovic, C. Falldorf, and C. von Kopylow, “Suppression of higher diffraction orders and intensity improvement of optically reconstructed holograms from a spatial light modulator,” J. Opt. A: Pure Appl. Opt. 11105405(2009).
[CrossRef]

Arsenault, H. H.

Asundi, A.

Barnes, T. H.

Bergeron, A.

Cheng, C.

C. Cheng, Y. Lin, M. Hsieh, and H. Tu, “Complex modulation characterization of liquid crystal spatial light modulators by digital holographic microscopy,” Jpn. J. Appl. Phys. 47, 3527–3529 (2008).
[CrossRef]

Coppola, G.

P. Ferraro, S. D. Nicola, A. Finizio, G. Pierattini, and G. Coppola, “Recovering image resolution in reconstructing digital off-axis holograms by Fresnel-transform method,” Appl. Phys. Lett. 85, 2709–2711 (2004).
[CrossRef]

Davis, J. A.

Dou, R.

R. Dou and M. K. Giles, “Simple technique for measuring the phase property of a twisted nematic liquid crystal television,” Opt. Eng. 35, 808–812 (1996).
[CrossRef]

Doucet, M.

Eiju, T.

Falldorf, C.

M. Agour, E. Kolenovic, C. Falldorf, and C. von Kopylow, “Suppression of higher diffraction orders and intensity improvement of optically reconstructed holograms from a spatial light modulator,” J. Opt. A: Pure Appl. Opt. 11105405(2009).
[CrossRef]

Ferraro, P.

P. Ferraro, S. D. Nicola, A. Finizio, G. Pierattini, and G. Coppola, “Recovering image resolution in reconstructing digital off-axis holograms by Fresnel-transform method,” Appl. Phys. Lett. 85, 2709–2711 (2004).
[CrossRef]

Finizio, A.

P. Ferraro, S. D. Nicola, A. Finizio, G. Pierattini, and G. Coppola, “Recovering image resolution in reconstructing digital off-axis holograms by Fresnel-transform method,” Appl. Phys. Lett. 85, 2709–2711 (2004).
[CrossRef]

Gagnon, F.

Gauvin, J.

Giles, M. K.

R. Dou and M. K. Giles, “Simple technique for measuring the phase property of a twisted nematic liquid crystal television,” Opt. Eng. 35, 808–812 (1996).
[CrossRef]

Gingras, D.

Hsieh, M.

C. Cheng, Y. Lin, M. Hsieh, and H. Tu, “Complex modulation characterization of liquid crystal spatial light modulators by digital holographic microscopy,” Jpn. J. Appl. Phys. 47, 3527–3529 (2008).
[CrossRef]

Jüptner, W. P. O.

U. Schnars and W. P. O. Jüptner, “Digital recording and numerical reconstruction of holograms,” Meas. Sci. Technol. 13, R85–R101 (2002).
[CrossRef]

Kohler, C.

Kolenovic, E.

M. Agour, E. Kolenovic, C. Falldorf, and C. von Kopylow, “Suppression of higher diffraction orders and intensity improvement of optically reconstructed holograms from a spatial light modulator,” J. Opt. A: Pure Appl. Opt. 11105405(2009).
[CrossRef]

Konforti, N.

Kreis, T. M.

T. M. Kreis, “Frequency analysis of digital holography with reconstruction by convolution,” Opt. Eng. 41, 1829–1839 (2002).
[CrossRef]

Lin, Y.

C. Cheng, Y. Lin, M. Hsieh, and H. Tu, “Complex modulation characterization of liquid crystal spatial light modulators by digital holographic microscopy,” Jpn. J. Appl. Phys. 47, 3527–3529 (2008).
[CrossRef]

Lu, K.

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

Marom, E.

Matusda, K.

Moreno, I.

Mutoh, K.

Nicola, S. D.

P. Ferraro, S. D. Nicola, A. Finizio, G. Pierattini, and G. Coppola, “Recovering image resolution in reconstructing digital off-axis holograms by Fresnel-transform method,” Appl. Phys. Lett. 85, 2709–2711 (2004).
[CrossRef]

Ooyama, N.

Osten, W.

Pierattini, G.

P. Ferraro, S. D. Nicola, A. Finizio, G. Pierattini, and G. Coppola, “Recovering image resolution in reconstructing digital off-axis holograms by Fresnel-transform method,” Appl. Phys. Lett. 85, 2709–2711 (2004).
[CrossRef]

Saleh, B. E. A.

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

Schnars, U.

U. Schnars and W. P. O. Jüptner, “Digital recording and numerical reconstruction of holograms,” Meas. Sci. Technol. 13, R85–R101 (2002).
[CrossRef]

Singh, V. R.

Takeda, M.

Tsai, P.

Tu, H.

C. Cheng, Y. Lin, M. Hsieh, and H. Tu, “Complex modulation characterization of liquid crystal spatial light modulators by digital holographic microscopy,” Jpn. J. Appl. Phys. 47, 3527–3529 (2008).
[CrossRef]

von Kopylow, C.

M. Agour, E. Kolenovic, C. Falldorf, and C. von Kopylow, “Suppression of higher diffraction orders and intensity improvement of optically reconstructed holograms from a spatial light modulator,” J. Opt. A: Pure Appl. Opt. 11105405(2009).
[CrossRef]

Wu, S.-T.

Zhang, F.

Appl. Opt. (5)

Appl. Phys. Lett. (1)

P. Ferraro, S. D. Nicola, A. Finizio, G. Pierattini, and G. Coppola, “Recovering image resolution in reconstructing digital off-axis holograms by Fresnel-transform method,” Appl. Phys. Lett. 85, 2709–2711 (2004).
[CrossRef]

J. Opt. A: Pure Appl. Opt. (1)

M. Agour, E. Kolenovic, C. Falldorf, and C. von Kopylow, “Suppression of higher diffraction orders and intensity improvement of optically reconstructed holograms from a spatial light modulator,” J. Opt. A: Pure Appl. Opt. 11105405(2009).
[CrossRef]

Jpn. J. Appl. Phys. (1)

C. Cheng, Y. Lin, M. Hsieh, and H. Tu, “Complex modulation characterization of liquid crystal spatial light modulators by digital holographic microscopy,” Jpn. J. Appl. Phys. 47, 3527–3529 (2008).
[CrossRef]

Meas. Sci. Technol. (1)

U. Schnars and W. P. O. Jüptner, “Digital recording and numerical reconstruction of holograms,” Meas. Sci. Technol. 13, R85–R101 (2002).
[CrossRef]

Opt. Eng. (3)

R. Dou and M. K. Giles, “Simple technique for measuring the phase property of a twisted nematic liquid crystal television,” Opt. Eng. 35, 808–812 (1996).
[CrossRef]

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

T. M. Kreis, “Frequency analysis of digital holography with reconstruction by convolution,” Opt. Eng. 41, 1829–1839 (2002).
[CrossRef]

Opt. Lett. (2)

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Figures (8)

Fig. 1
Fig. 1

Orientation of the polarizer and the analyzer with respect to the LC molecule director axis at the input face of the TN-LCSLM.

Fig. 2
Fig. 2

DH experimental setup for the HOLOEYE 2002 TN-LCSLM phase-modulation characterization. (BS, beam splitter; P, polarizer; A, analyzer; L, collimation lens; and CCD, charge coupling device).

Fig. 3
Fig. 3

Fourier spectrum of a digitally recorded reference hologram. (Red squares indicate diffraction from the SLM, while the yellow circles are the diffraction from the holographic interference fringes).

Fig. 4
Fig. 4

Young’s double-slit principle to evaluate the polarizer and analyzer orientation in phase-mostly mode. (P, polarizer; A, analyzer; L, converging lens; NDF, neutral density filter; MO, microscopic objective; and CCD, charge coupling device).

Fig. 5
Fig. 5

Numerically reconstructed (a) amplitude image, (b) phase image, (c) 3D phase map, and (d) phase step height measured from a digitally recorded hologram with the TN-LCSLM addressed with 0 and 255 gray scales in two equally separated regions.

Fig. 6
Fig. 6

Phase-modulation characterization of the HOLOEYE LC2002 SLM with respect to addressed gray scale in the modulation region using DH.

Fig. 7
Fig. 7

Amplitude-modulation characterization of the HOLOEYE LC2002 SLM in phase-mostly mode with respect to addressed gray scale in the modulation region using DH.

Fig. 8
Fig. 8

(a) Diffractive lens array simulated using IFTA algorithm, (b) intensity (c) phase distribution from the lens array using the DH system, and (d) line profile of distribution along the diameter of a typical microlens from the array.

Equations (11)

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Δ ϕ = β tan 1 [ β γ sin γ cos ( θ 1 + θ 2 α ) cos γ cos ( θ 1 θ 2 + α ) + α γ sin γ sin ( θ 1 θ 2 + α ) ] ,
β ( λ , θ ) = π D λ [ n e ( θ ) n o ] ,
γ = α 2 + β 2 .
O ( x , y ) = e i k z i λ z t ( x , y ) exp [ i 2 π λ z { ( x x ) 2 + ( y y ) 2 } ] d x d y ,
t ( x , y ) = a ( x , y ) { rect ( x d , y d ) q ( x , y ) } ,
q ( x , y ) = exp { i Δ ϕ ( x , y ) } . m , n = 0 M 1 , N 1 δ ( x m Δ d , y n Δ d ) ,
a ( x , y ) = rect ( x M Δ d , y N Δ d ) .
H ( n x , n y ) = | O ( n x , n y ) | 2 + | R ( n x , n y ) | 2 + O * ( n x , n y ) R ( n x , n y ) + O ( n x , n y ) R * ( n x , n y ) .
U real ( n x , n y ) = I 1 [ I { H ( n x , n y ) × R ( n x , n y ) } × I { g ( n x , n y ) } ] .
g ( n x , n y ) = exp ( i 2 π z / λ ) i λ z exp { i π λ z ( n x 2 Δ x 2 + n y 2 Δ y 2 ) } .
Δ ϕ ( n x , n y ) = arctan [ Im { U real ( n x , n y ) } / Re { U real ( n x , n y ) } ] .

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