Abstract

Nematic liquid crystal spatial light modulators (SLMs) with fast switching times and high diffraction efficiency are important to various applications ranging from optical beam steering and adaptive optics to optical tweezers. Here we demonstrate the great benefits that can be derived in terms of speed enhancement without loss of diffraction efficiency from two mutually compatible approaches. The first technique involves the idea of overdrive, that is the calculation of intermediate patterns to speed up the transition to the target phase pattern. The second concerns optimization of the target pattern to reduce the required phase change applied to each pixel, which in addition leads to a substantial reduction of variations in the intensity of the diffracted light during the transition. When these methods are applied together, we observe transition times for the diffracted light fields of about 1 ms, which represents up to a tenfold improvement over current approaches. We experimentally demonstrate the improvements of the approach for applications such as holographic image projection, beam steering and switching, and real-time control loops.

© 2013 Optical Society of America

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References

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    [Crossref] [PubMed]
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    [Crossref]
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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
  22. S.-T. Wu, “Phase retardation dependent optical response time of parallel-aligned liquid crystals,” J. Appl. Phys. 60, 1836–1838 (1986).
    [Crossref]
  23. Z. Cao, Q. Mu, L. Hu, D. Li, Z. Peng, Y. Liu, and L. Xuan, “Preliminary use of nematic liquid crystal adaptive optics with a 2.16-meter reflecting telescope,” Opt. Express 17, 2530–2537 (2009).
    [Crossref] [PubMed]
  24. K. D. Wulff, D. G. Cole, and R. L. Clark, “Servo control of an optical trap,” Appl. Opt. 46, 4923–4931 (2007).
    [Crossref] [PubMed]
  25. G. M. Gibson, J. Leach, S. Keen, A. J. Wright, and M. J. Padgett, “Measuring the accuracy of particleposition and force in optical tweezers using high-speed video microscopy,” Opt. Express 16, 14561–14570 (2008).
    [Crossref] [PubMed]
  26. D. Preece, R. Bowman, A. Linnenberger, G. Gibson, S. Serati, and M. Padgett, “Increasing trap stiffness with position clamping in holographic optical tweezers,” Opt. Express 17, 22718–22725 (2009).
    [Crossref]

2012 (1)

2011 (1)

2010 (1)

2009 (3)

2008 (1)

2007 (4)

2006 (2)

2005 (1)

2004 (2)

2001 (1)

1999 (1)

1997 (1)

1994 (1)

1989 (1)

S.-T. Wu and C.-S. Wu, “High-speed liquid-crystal modulators using transient nematic effect,” J. Appl. Phys. 65, 527–532 (1989).
[Crossref]

1986 (1)

S.-T. Wu, “Phase retardation dependent optical response time of parallel-aligned liquid crystals,” J. Appl. Phys. 60, 1836–1838 (1986).
[Crossref]

1984 (1)

P. Bos and K. Koehler, “The pi-cell: a fast liquid-crystal optical-switching device,” Mol. Cryst. Liq. Cryst. 113, 329–339 (1984).
[Crossref]

1974 (1)

H. K. Bucher, R. T. Klingbiel, and J. P. VanMeter, “Frequency-addressed liquid crystal field effect,” Appl. Phys. Lett. 25, 186–188 (1974).
[Crossref]

Ambs, P.

Backsten, J.

Bengtsson, J.

Bernet, S.

Bos, P.

Bowman, R.

Browne, S.

Bucher, H. K.

H. K. Bucher, R. T. Klingbiel, and J. P. VanMeter, “Frequency-addressed liquid crystal field effect,” Appl. Phys. Lett. 25, 186–188 (1974).
[Crossref]

Cao, Z.

Cho, D. J.

Clark, R. L.

Cohn, R. W.

Cole, D. G.

Cooper, J.

Dayton, D.

DiLeonardo, R.

Engström, D.

M. Persson, D. Engström, A. Frank, J. Backsten, J. Bengtsson, and M. Goksör, “Minimizing intensity fluctuations in dynamic holographic optical tweezers by restricted phase change,” Opt. Express 18, 11250–11263 (2010).
[Crossref] [PubMed]

D. Engström, M. Persson, and M. Goksör, “Spatial phase calibration used to improve holographic optical trapping,” in Digital Holography and Three-Dimensional Imaging (Optical Society of America, 2012), p. DSu2C.3.

Fan, Y.-H.

Frank, A.

Fürhapter, S.

Gibson, G.

Gibson, G. M.

Glushchenko, A.

Goksör, M.

M. Persson, D. Engström, A. Frank, J. Backsten, J. Bengtsson, and M. Goksör, “Minimizing intensity fluctuations in dynamic holographic optical tweezers by restricted phase change,” Opt. Express 18, 11250–11263 (2010).
[Crossref] [PubMed]

D. Engström, M. Persson, and M. Goksör, “Spatial phase calibration used to improve holographic optical trapping,” in Digital Holography and Three-Dimensional Imaging (Optical Society of America, 2012), p. DSu2C.3.

Gonglewski, J.

Haist, T.

Hermerschmidt, A.

G. Lazarev, A. Hermerschmidt, S. Krüger, and S. Osten, “LCOS spatial light modulators: Trends and applications,” in Optical Imaging and Metrology: Advanced Technologies, W. Osten and N. Reingand, eds. (Wiley-VCH, 2012), chap. 1, pp. 1–30.
[Crossref]

Hu, H.

Hu, L.

Ianni, F.

Jesacher, A.

Keen, S.

Kirby, A. K.

Klingbiel, R. T.

H. K. Bucher, R. T. Klingbiel, and J. P. VanMeter, “Frequency-addressed liquid crystal field effect,” Appl. Phys. Lett. 25, 186–188 (1974).
[Crossref]

Koehler, K.

P. Bos and K. Koehler, “The pi-cell: a fast liquid-crystal optical-switching device,” Mol. Cryst. Liq. Cryst. 113, 329–339 (1984).
[Crossref]

Krüger, S.

G. Lazarev, A. Hermerschmidt, S. Krüger, and S. Osten, “LCOS spatial light modulators: Trends and applications,” in Optical Imaging and Metrology: Advanced Technologies, W. Osten and N. Reingand, eds. (Wiley-VCH, 2012), chap. 1, pp. 1–30.
[Crossref]

Lazarev, G.

G. Lazarev, A. Hermerschmidt, S. Krüger, and S. Osten, “LCOS spatial light modulators: Trends and applications,” in Optical Imaging and Metrology: Advanced Technologies, W. Osten and N. Reingand, eds. (Wiley-VCH, 2012), chap. 1, pp. 1–30.
[Crossref]

Leach, J.

Leonardo, R. D.

Li, D.

Lin, Y.-H.

Linnenberger, A.

Liu, C.

Liu, Y.

Love, G.

Love, G. D.

Lu, Y.-Q.

Major, J.

Maurer, C.

McManamon, P.

Millán, M. S.

Mu, Q.

Osten, S.

G. Lazarev, A. Hermerschmidt, S. Krüger, and S. Osten, “LCOS spatial light modulators: Trends and applications,” in Optical Imaging and Metrology: Advanced Technologies, W. Osten and N. Reingand, eds. (Wiley-VCH, 2012), chap. 1, pp. 1–30.
[Crossref]

Otón, J.

Padgett, M.

Padgett, M. J.

Peng, Z.

Pérez-Cabré, E.

Persson, M.

M. Persson, D. Engström, A. Frank, J. Backsten, J. Bengtsson, and M. Goksör, “Minimizing intensity fluctuations in dynamic holographic optical tweezers by restricted phase change,” Opt. Express 18, 11250–11263 (2010).
[Crossref] [PubMed]

D. Engström, M. Persson, and M. Goksör, “Spatial phase calibration used to improve holographic optical trapping,” in Digital Holography and Three-Dimensional Imaging (Optical Society of America, 2012), p. DSu2C.3.

Preece, D.

Purvis, A.

Reicherter, M.

Ren, H.

Restaino, S.

Ritsch-Marte, M.

Ruocco, G.

Savage, N.

N. Savage, “Digital spatial light modulators,” Nat. Photonics 3, 170–172 (2009).
[Crossref]

Schwaighofer, A.

Serati, S.

Tiziani, H. J.

VanMeter, J. P.

H. K. Bucher, R. T. Klingbiel, and J. P. VanMeter, “Frequency-addressed liquid crystal field effect,” Appl. Phys. Lett. 25, 186–188 (1974).
[Crossref]

Wagemann, E. U.

Wang, B.

West, J.

Wright, A. J.

Wu, C.-S.

S.-T. Wu and C.-S. Wu, “High-speed liquid-crystal modulators using transient nematic effect,” J. Appl. Phys. 65, 527–532 (1989).
[Crossref]

Wu, J.

Wu, S.-T.

Y.-H. Wu, Y.-H. Lin, Y.-Q. Lu, H. Ren, Y.-H. Fan, J. Wu, and S.-T. Wu, “Submillisecond response variable optical attenuator based on sheared polymer network liquid crystal,” Opt. Express 12, 6382–6389 (2004).
[Crossref] [PubMed]

S.-T. Wu and C.-S. Wu, “High-speed liquid-crystal modulators using transient nematic effect,” J. Appl. Phys. 65, 527–532 (1989).
[Crossref]

S.-T. Wu, “Phase retardation dependent optical response time of parallel-aligned liquid crystals,” J. Appl. Phys. 60, 1836–1838 (1986).
[Crossref]

Wu, Y.-H.

Wulff, K. D.

Xuan, L.

Xun, X.

Yao, L.

Zhang, G.

Zhang, X.

Appl. Opt. (6)

Appl. Phys. Lett. (1)

H. K. Bucher, R. T. Klingbiel, and J. P. VanMeter, “Frequency-addressed liquid crystal field effect,” Appl. Phys. Lett. 25, 186–188 (1974).
[Crossref]

J. Appl. Phys. (2)

S.-T. Wu and C.-S. Wu, “High-speed liquid-crystal modulators using transient nematic effect,” J. Appl. Phys. 65, 527–532 (1989).
[Crossref]

S.-T. Wu, “Phase retardation dependent optical response time of parallel-aligned liquid crystals,” J. Appl. Phys. 60, 1836–1838 (1986).
[Crossref]

Mol. Cryst. Liq. Cryst. (1)

P. Bos and K. Koehler, “The pi-cell: a fast liquid-crystal optical-switching device,” Mol. Cryst. Liq. Cryst. 113, 329–339 (1984).
[Crossref]

Nat. Photonics (1)

N. Savage, “Digital spatial light modulators,” Nat. Photonics 3, 170–172 (2009).
[Crossref]

Opt. Express (9)

K. D. Wulff, D. G. Cole, R. L. Clark, R. DiLeonardo, J. Leach, J. Cooper, G. Gibson, and M. J. Padgett, “Aberration correction in holographic optical tweezers,” Opt. Express 14, 4169–4174 (2006).
[Crossref] [PubMed]

R. D. Leonardo, F. Ianni, and G. Ruocco, “Computer generation of optimal holograms for optical trap arrays,” Opt. Express 15, 1913–1922 (2007).
[Crossref] [PubMed]

A. Jesacher, A. Schwaighofer, S. Fürhapter, C. Maurer, S. Bernet, and M. Ritsch-Marte, “Wavefront correction of spatial light modulators using an optical vortex image,” Opt. Express 15, 5801–5808 (2007).
[Crossref] [PubMed]

A. K. Kirby and G. D. Love, “Fast, large and controllable phase modulation using dual frequency liquid crystals,” Opt. Express 12, 1470–1475 (2004).
[Crossref] [PubMed]

Y.-H. Wu, Y.-H. Lin, Y.-Q. Lu, H. Ren, Y.-H. Fan, J. Wu, and S.-T. Wu, “Submillisecond response variable optical attenuator based on sheared polymer network liquid crystal,” Opt. Express 12, 6382–6389 (2004).
[Crossref] [PubMed]

G. M. Gibson, J. Leach, S. Keen, A. J. Wright, and M. J. Padgett, “Measuring the accuracy of particleposition and force in optical tweezers using high-speed video microscopy,” Opt. Express 16, 14561–14570 (2008).
[Crossref] [PubMed]

Z. Cao, Q. Mu, L. Hu, D. Li, Z. Peng, Y. Liu, and L. Xuan, “Preliminary use of nematic liquid crystal adaptive optics with a 2.16-meter reflecting telescope,” Opt. Express 17, 2530–2537 (2009).
[Crossref] [PubMed]

D. Preece, R. Bowman, A. Linnenberger, G. Gibson, S. Serati, and M. Padgett, “Increasing trap stiffness with position clamping in holographic optical tweezers,” Opt. Express 17, 22718–22725 (2009).
[Crossref]

M. Persson, D. Engström, A. Frank, J. Backsten, J. Bengtsson, and M. Goksör, “Minimizing intensity fluctuations in dynamic holographic optical tweezers by restricted phase change,” Opt. Express 18, 11250–11263 (2010).
[Crossref] [PubMed]

Opt. Lett. (4)

Other (2)

G. Lazarev, A. Hermerschmidt, S. Krüger, and S. Osten, “LCOS spatial light modulators: Trends and applications,” in Optical Imaging and Metrology: Advanced Technologies, W. Osten and N. Reingand, eds. (Wiley-VCH, 2012), chap. 1, pp. 1–30.
[Crossref]

D. Engström, M. Persson, and M. Goksör, “Spatial phase calibration used to improve holographic optical trapping,” in Digital Holography and Three-Dimensional Imaging (Optical Society of America, 2012), p. DSu2C.3.

Supplementary Material (1)

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Figures (10)

Fig. 1
Fig. 1 Schematic diagram illustrating the general idea for improving the response time by using an overdrive voltage. (a) To change the phase from φ0 to φ1 with the standard switching approach, the control voltage is switched to a value U1 value that in the steady state induces the phase φ1. (b) A substantial speedup is achieved with the overdrive method, if for some time the voltage is set to the maximum value Umax until the phase reaches the desired value φ1.

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Fig. 2
Fig. 2 Reduction of phase changes by exploiting an extended accessible range. The speed for switching between phase values φ1 and φ2 near the edge of the conventional range [0, 2π] can be strongly enhanced if one is allowed to access an extended range such that an equivalent phase value φ2 + 2π is targeted instead of φ2.

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Fig. 3
Fig. 3 Effect of the phase change reduction method on the distribution of phase values and phase differences between subsequent patterns. With phase change reduction method the number of pixels that undergo a phase change larger than π is considerably reduced. Top: histograms of phase values. Bottom: histograms of phase difference between subsequent patterns. (a) Results for random, uncorrelated patterns, both without (blue dashed line) and with (red solid line) phase change reduction algorithm. (b) Results for a pattern sequence where the phase change between subsequent patterns (before phase wrapping) is normally distributed with standard deviation σ = π/4.

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Fig. 4
Fig. 4 Effect of phase change reduction on the mean phase difference and on unwanted intensity variations. Top: root mean square phase difference after unwrapping and phase reduction for several extended range margins (see text). Due to phase wrapping the mean phase difference is significantly increased compared to the mean phase difference σ before phase wrapping (dotted line: σ). With phase change reduction on an extended range [−m, 2π + m] the excess phase changes are largely removed. Bottom: reduction of diffraction efficiency during the transition, based on Eq. (4); dotted line: simple approximation 1 − 1 4 σ 2, valid for small σ and large margin m.

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Fig. 5
Fig. 5 Measured dynamic response of SLM phase shift (a) without overdrive (b) with overdrive. The shown 2π range is placed at φ0 = 2.4π within the available phase range of the SLM.

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Fig. 6
Fig. 6 Fast holographic image projection ( Media 1). Sequence of images taken from a video recording (frame rate 1 kHz) of the projected logos of our research institutes, showing the reduced switching time with overdrive and phase change reduction (top row), compared to without these methods (bottom row). The inset of smaller images, which shows the transition at a higher time resolution of 2 kHz frame rate, demonstrates that with overdrive the transition between two different patterns indeed occurs within about 1 ms, whereas it takes about 10 ms until the transition is completed without the overdrive method.

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Fig. 7
Fig. 7 Regular array of blinking spots. Time sequences of the spot intensities for a symmetric arrangement of six spots equidistantly placed along a line, where we sequentially switch off one of the spots (only data for four spots shown). We have normalized the intensities such that I/I0 = 1 in the steady state for the data in (a), using the same I0 for all data. (a) reference measurement without any speed enhancement (b) overdrive and phase change method applied (c) overdrive method only (d) phase change reduction only, no overdrive (e) restricted phase change method (RPC) [19] applied (with threshold α = 0.75), no overdrive (f) RPC and overdrive methods applied together.

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Fig. 8
Fig. 8 Asymmetric array of blinking spots. Similar to Fig. 7 we show time sequences of the spot intensities, but for an asymmetric arrangement of six spots, which leads to reduced intensity variations. (a) reference measurement without any speed enhancement (b) overdrive and phase change method applied (c) overdrive method only (d) phase change reduction only, no overdrive.

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Fig. 9
Fig. 9 Toggling the beam position between two locations at a rate of 200 Hz, left: total intensity, right: position. (a) position change larger than spot diameter ds, (b) position change smaller than spot diameter.

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Fig. 10
Fig. 10 Real-time feedback loop for beam position, running at 200 Hz. Top: Actual and target position with overdrive and phase reduction, bottom: without overdrive and phase reduction.

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Tables (1)

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Table 1 Typical timings for the calculation of phase patterns for creating an array of spots (resolution 512 × 512 pixel).

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Equations (5)

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φ ( t ) = φ 0 + ( φ 1 − φ 0 ) ( 1 − e − ( t − t 0 ) τ )
Δ t 1 = Δ t ( φ 0 , φ 1 ) = t ( φ 1 ) − t ( φ 0 ) ,
Δ t ( φ 0 , φ 1 ) = − τ ln ( φ 1 − φ m φ 0 − φ m ) ,
p 0 = | 1 N ∑ k e i 1 2 Δ φ k | 2 ,
p 0 ≈ 1 − 1 4 〈 Δ φ 2 〉 .

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