Abstract

Spatial light modulators (SLMs) based on liquid crystals are widely used for wavefront shaping. Their large number of pixels allows one to create complex wavefronts. The crosstalk between neighboring pixels, also known as fringing field effect, however, can lead to strong deviations. The realized wavefront may deviate significantly from the prediction based on the idealized assumption that the response across a pixel is uniform and independent of its neighbors. Detailed numerical simulations of the SLM response based on a full 3D physical model accurately match the measured response and properly model the pixel crosstalk. The full model is then used to validate a simplified model that enables much faster crosstalk evaluation and pattern optimization beyond standard performance. General conclusions on how to minimize crosstalk in liquid crystal on silicon (LCoS) SLM systems are derived, as well as a readily accessible estimation of the amount of fringing in a given SLM.

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References

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2019 (1)

2018 (1)

D. Barredo, V. Lienhard, S. de Léséleuc, T. Lahaye, and A. Browaeys, “Synthetic three-dimensional atomic structures assembled atom by atom,” Nature 561, 79–82 (2018).
[Crossref] [PubMed]

2017 (2)

E. Ronzitti, C. Ventalon, M. Canepari, B. C. Forget, E. Papagiakoumou, and V. Emiliani, “Recent advances in patterned photostimulation for optogenetics,” J. Opt. 19, 113001 (2017).
[Crossref]

M. Nakajima, N. Nemoto, K. Yamaguchi, H. Kudo, J. Yamaguchi, K. Suzuki, and T. Hashimoto, “Analysis and suppression of high-order diffractions in liquid-crystal-based spatial light modulator for photonic switch application,” Jpn. J. Appl. Phys. 56, 09NC01 (2017).
[Crossref]

2016 (1)

A. Jesacher and M. Ritsch-Marte, “Synthetic holography in microscopy: opportunities arising from advanced wavefront shaping,” Contemp. Phys. 57, 46–59 (2016).
[Crossref]

2015 (4)

2014 (2)

2013 (2)

2012 (3)

2010 (2)

A. Jesacher, G. D. Marshall, T. Wilson, and M. J. Booth, “Adaptive optics for direct laser writing with plasma emission aberration sensing,” Opt. Express 18, 656–661 (2010).
[Crossref] [PubMed]

C. Maurer, A. Jesacher, S. Bernet, and M. Ritsch-Marte, “What spatial light modulators can do for optical microscopy,” Laser Photonics Rev. 5, 81–101 (2010).
[Crossref]

2005 (1)

2004 (3)

1982 (1)

Anderson, J. E.

Apter, B.

Bahat-Treidel, E.

Barredo, D.

D. Barredo, V. Lienhard, S. de Léséleuc, T. Lahaye, and A. Browaeys, “Synthetic three-dimensional atomic structures assembled atom by atom,” Nature 561, 79–82 (2018).
[Crossref] [PubMed]

Bernet, S.

Booth, M. J.

Bos, P. J.

Bowman, R. W.

Browaeys, A.

D. Barredo, V. Lienhard, S. de Léséleuc, T. Lahaye, and A. Browaeys, “Synthetic three-dimensional atomic structures assembled atom by atom,” Nature 561, 79–82 (2018).
[Crossref] [PubMed]

Canepari, M.

E. Ronzitti, C. Ventalon, M. Canepari, B. C. Forget, E. Papagiakoumou, and V. Emiliani, “Recent advances in patterned photostimulation for optogenetics,” J. Opt. 19, 113001 (2017).
[Crossref]

Chen, P.-J.

Chichkov, B. N.

L. Yang, A. El-Tamer, U. Hinze, J. Li, Y. Hu, W. Huang, J. Chu, and B. N. Chichkov, “Parallel direct laser writing of micro-optical and photonic structures using spatial light modulator,” Opt. Lasers Eng. 70, 26–32 (2015).
[Crossref]

Chu, D.

Chu, J.

L. Yang, A. El-Tamer, U. Hinze, J. Li, Y. Hu, W. Huang, J. Chu, and B. N. Chichkov, “Parallel direct laser writing of micro-optical and photonic structures using spatial light modulator,” Opt. Lasers Eng. 70, 26–32 (2015).
[Crossref]

de Léséleuc, S.

D. Barredo, V. Lienhard, S. de Léséleuc, T. Lahaye, and A. Browaeys, “Synthetic three-dimensional atomic structures assembled atom by atom,” Nature 561, 79–82 (2018).
[Crossref] [PubMed]

Efron, U.

El-Tamer, A.

L. Yang, A. El-Tamer, U. Hinze, J. Li, Y. Hu, W. Huang, J. Chu, and B. N. Chichkov, “Parallel direct laser writing of micro-optical and photonic structures using spatial light modulator,” Opt. Lasers Eng. 70, 26–32 (2015).
[Crossref]

Emiliani, V.

E. Ronzitti, C. Ventalon, M. Canepari, B. C. Forget, E. Papagiakoumou, and V. Emiliani, “Recent advances in patterned photostimulation for optogenetics,” J. Opt. 19, 113001 (2017).
[Crossref]

E. Ronzitti, M. Guillon, V. d. Sars, and V. Emiliani, “LCoS nematic SLM characterization and modeling for diffraction efficiency optimization, zero and ghost orders suppression,” Opt. Express 20, 17843–17855 (2012).
[Crossref] [PubMed]

Engström, D.

Fienup, J. R.

Fontaine, N.

Forbes, A.

Forget, B. C.

E. Ronzitti, C. Ventalon, M. Canepari, B. C. Forget, E. Papagiakoumou, and V. Emiliani, “Recent advances in patterned photostimulation for optogenetics,” J. Opt. 19, 113001 (2017).
[Crossref]

Goksör, M.

Guillon, M.

Haist, T.

Hällstig, E.

E. Hällstig, J. Stigwall, T. Martin, L. Sjöqvist, and M. Lindgren, “Fringing fields in a liquid crystal spatial light modulator for beam steering,” J. Mod. Opt. 51, 1233–1247 (2004).
[Crossref]

Harm, W.

Hashimoto, T.

M. Nakajima, N. Nemoto, K. Yamaguchi, H. Kudo, J. Yamaguchi, K. Suzuki, and T. Hashimoto, “Analysis and suppression of high-order diffractions in liquid-crystal-based spatial light modulator for photonic switch application,” Jpn. J. Appl. Phys. 56, 09NC01 (2017).
[Crossref]

Hinze, U.

L. Yang, A. El-Tamer, U. Hinze, J. Li, Y. Hu, W. Huang, J. Chu, and B. N. Chichkov, “Parallel direct laser writing of micro-optical and photonic structures using spatial light modulator,” Opt. Lasers Eng. 70, 26–32 (2015).
[Crossref]

Hu, Y.

L. Yang, A. El-Tamer, U. Hinze, J. Li, Y. Hu, W. Huang, J. Chu, and B. N. Chichkov, “Parallel direct laser writing of micro-optical and photonic structures using spatial light modulator,” Opt. Lasers Eng. 70, 26–32 (2015).
[Crossref]

Huang, W.

L. Yang, A. El-Tamer, U. Hinze, J. Li, Y. Hu, W. Huang, J. Chu, and B. N. Chichkov, “Parallel direct laser writing of micro-optical and photonic structures using spatial light modulator,” Opt. Lasers Eng. 70, 26–32 (2015).
[Crossref]

Jesacher, A.

Jurling, A. S.

Kudo, H.

M. Nakajima, N. Nemoto, K. Yamaguchi, H. Kudo, J. Yamaguchi, K. Suzuki, and T. Hashimoto, “Analysis and suppression of high-order diffractions in liquid-crystal-based spatial light modulator for photonic switch application,” Jpn. J. Appl. Phys. 56, 09NC01 (2017).
[Crossref]

Lahaye, T.

D. Barredo, V. Lienhard, S. de Léséleuc, T. Lahaye, and A. Browaeys, “Synthetic three-dimensional atomic structures assembled atom by atom,” Nature 561, 79–82 (2018).
[Crossref] [PubMed]

Lazarev, G.

Lee, M. P.

M. P. Lee and M. J. Padgett, “Optical tweezers: a light touch,” J. Microsc. 248, 219–222 (2012).
[Crossref] [PubMed]

Li, J.

L. Yang, A. El-Tamer, U. Hinze, J. Li, Y. Hu, W. Huang, J. Chu, and B. N. Chichkov, “Parallel direct laser writing of micro-optical and photonic structures using spatial light modulator,” Opt. Lasers Eng. 70, 26–32 (2015).
[Crossref]

Lienhard, V.

D. Barredo, V. Lienhard, S. de Léséleuc, T. Lahaye, and A. Browaeys, “Synthetic three-dimensional atomic structures assembled atom by atom,” Nature 561, 79–82 (2018).
[Crossref] [PubMed]

Lindgren, M.

E. Hällstig, J. Stigwall, T. Martin, L. Sjöqvist, and M. Lindgren, “Fringing fields in a liquid crystal spatial light modulator for beam steering,” J. Mod. Opt. 51, 1233–1247 (2004).
[Crossref]

Lingel, C.

Love, G. D.

Lu, T.

Marshall, G. D.

Martin, T.

E. Hällstig, J. Stigwall, T. Martin, L. Sjöqvist, and M. Lindgren, “Fringing fields in a liquid crystal spatial light modulator for beam steering,” J. Mod. Opt. 51, 1233–1247 (2004).
[Crossref]

Maurer, C.

C. Maurer, A. Jesacher, S. Bernet, and M. Ritsch-Marte, “What spatial light modulators can do for optical microscopy,” Laser Photonics Rev. 5, 81–101 (2010).
[Crossref]

Miranda, F. A.

Nakajima, M.

M. Nakajima, N. Nemoto, K. Yamaguchi, H. Kudo, J. Yamaguchi, K. Suzuki, and T. Hashimoto, “Analysis and suppression of high-order diffractions in liquid-crystal-based spatial light modulator for photonic switch application,” Jpn. J. Appl. Phys. 56, 09NC01 (2017).
[Crossref]

Nemoto, N.

M. Nakajima, N. Nemoto, K. Yamaguchi, H. Kudo, J. Yamaguchi, K. Suzuki, and T. Hashimoto, “Analysis and suppression of high-order diffractions in liquid-crystal-based spatial light modulator for photonic switch application,” Jpn. J. Appl. Phys. 56, 09NC01 (2017).
[Crossref]

Nesterov, Y.

Y. Nesterov, Introductory Lectures on Convex Optimization, vol. 87 of Applied Optimization (Springer, 2004).
[Crossref]

Nocedal, J.

J. Nocedal and S. J. Wright, Numerical optimization, Springer series in operations research (Springer, 1999).

Osten, W.

Padgett, M. J.

Papagiakoumou, E.

E. Ronzitti, C. Ventalon, M. Canepari, B. C. Forget, E. Papagiakoumou, and V. Emiliani, “Recent advances in patterned photostimulation for optogenetics,” J. Opt. 19, 113001 (2017).
[Crossref]

Persson, M.

Pivnenko, M.

Pouch, J. J.

Ritsch-Marte, M.

Robertson, B.

Roider, C.

Ronzitti, E.

E. Ronzitti, C. Ventalon, M. Canepari, B. C. Forget, E. Papagiakoumou, and V. Emiliani, “Recent advances in patterned photostimulation for optogenetics,” J. Opt. 19, 113001 (2017).
[Crossref]

E. Ronzitti, M. Guillon, V. d. Sars, and V. Emiliani, “LCoS nematic SLM characterization and modeling for diffraction efficiency optimization, zero and ghost orders suppression,” Opt. Express 20, 17843–17855 (2012).
[Crossref] [PubMed]

Sars, V. d.

Sjöqvist, L.

E. Hällstig, J. Stigwall, T. Martin, L. Sjöqvist, and M. Lindgren, “Fringing fields in a liquid crystal spatial light modulator for beam steering,” J. Mod. Opt. 51, 1233–1247 (2004).
[Crossref]

Stigwall, J.

E. Hällstig, J. Stigwall, T. Martin, L. Sjöqvist, and M. Lindgren, “Fringing fields in a liquid crystal spatial light modulator for beam steering,” J. Mod. Opt. 51, 1233–1247 (2004).
[Crossref]

Strauss, J.

Suzuki, K.

M. Nakajima, N. Nemoto, K. Yamaguchi, H. Kudo, J. Yamaguchi, K. Suzuki, and T. Hashimoto, “Analysis and suppression of high-order diffractions in liquid-crystal-based spatial light modulator for photonic switch application,” Jpn. J. Appl. Phys. 56, 09NC01 (2017).
[Crossref]

Thalhammer, G.

Ventalon, C.

E. Ronzitti, C. Ventalon, M. Canepari, B. C. Forget, E. Papagiakoumou, and V. Emiliani, “Recent advances in patterned photostimulation for optogenetics,” J. Opt. 19, 113001 (2017).
[Crossref]

Wang, B.

Wang, X.

Wilson, T.

Wright, S. J.

J. Nocedal and S. J. Wright, Numerical optimization, Springer series in operations research (Springer, 1999).

Wu, S.-T.

S.-T. Wu and D.-K. Yang, Fundamentals of Liquid Crystal Devices (Wiley, 2006).

Yamaguchi, J.

M. Nakajima, N. Nemoto, K. Yamaguchi, H. Kudo, J. Yamaguchi, K. Suzuki, and T. Hashimoto, “Analysis and suppression of high-order diffractions in liquid-crystal-based spatial light modulator for photonic switch application,” Jpn. J. Appl. Phys. 56, 09NC01 (2017).
[Crossref]

Yamaguchi, K.

M. Nakajima, N. Nemoto, K. Yamaguchi, H. Kudo, J. Yamaguchi, K. Suzuki, and T. Hashimoto, “Analysis and suppression of high-order diffractions in liquid-crystal-based spatial light modulator for photonic switch application,” Jpn. J. Appl. Phys. 56, 09NC01 (2017).
[Crossref]

Yang, D.-K.

S.-T. Wu and D.-K. Yang, Fundamentals of Liquid Crystal Devices (Wiley, 2006).

Yang, L.

L. Yang, A. El-Tamer, U. Hinze, J. Li, Y. Hu, W. Huang, J. Chu, and B. N. Chichkov, “Parallel direct laser writing of micro-optical and photonic structures using spatial light modulator,” Opt. Lasers Eng. 70, 26–32 (2015).
[Crossref]

Appl. Opt. (4)

Contemp. Phys. (1)

A. Jesacher and M. Ritsch-Marte, “Synthetic holography in microscopy: opportunities arising from advanced wavefront shaping,” Contemp. Phys. 57, 46–59 (2016).
[Crossref]

J. Microsc. (1)

M. P. Lee and M. J. Padgett, “Optical tweezers: a light touch,” J. Microsc. 248, 219–222 (2012).
[Crossref] [PubMed]

J. Mod. Opt. (1)

E. Hällstig, J. Stigwall, T. Martin, L. Sjöqvist, and M. Lindgren, “Fringing fields in a liquid crystal spatial light modulator for beam steering,” J. Mod. Opt. 51, 1233–1247 (2004).
[Crossref]

J. Opt. (1)

E. Ronzitti, C. Ventalon, M. Canepari, B. C. Forget, E. Papagiakoumou, and V. Emiliani, “Recent advances in patterned photostimulation for optogenetics,” J. Opt. 19, 113001 (2017).
[Crossref]

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

Jpn. J. Appl. Phys. (1)

M. Nakajima, N. Nemoto, K. Yamaguchi, H. Kudo, J. Yamaguchi, K. Suzuki, and T. Hashimoto, “Analysis and suppression of high-order diffractions in liquid-crystal-based spatial light modulator for photonic switch application,” Jpn. J. Appl. Phys. 56, 09NC01 (2017).
[Crossref]

Laser Photonics Rev. (1)

C. Maurer, A. Jesacher, S. Bernet, and M. Ritsch-Marte, “What spatial light modulators can do for optical microscopy,” Laser Photonics Rev. 5, 81–101 (2010).
[Crossref]

Nature (1)

D. Barredo, V. Lienhard, S. de Léséleuc, T. Lahaye, and A. Browaeys, “Synthetic three-dimensional atomic structures assembled atom by atom,” Nature 561, 79–82 (2018).
[Crossref] [PubMed]

Opt. Express (7)

Opt. Lasers Eng. (1)

L. Yang, A. El-Tamer, U. Hinze, J. Li, Y. Hu, W. Huang, J. Chu, and B. N. Chichkov, “Parallel direct laser writing of micro-optical and photonic structures using spatial light modulator,” Opt. Lasers Eng. 70, 26–32 (2015).
[Crossref]

Opt. Lett. (1)

Other (4)

J. Chen, W. Cranton, and M. Fihn, eds., Handbook of visual display technology, Springer references (Springer, 2012).
[Crossref]

S.-T. Wu and D.-K. Yang, Fundamentals of Liquid Crystal Devices (Wiley, 2006).

J. Nocedal and S. J. Wright, Numerical optimization, Springer series in operations research (Springer, 1999).

Y. Nesterov, Introductory Lectures on Convex Optimization, vol. 87 of Applied Optimization (Springer, 2004).
[Crossref]

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Figures (11)

Fig. 1
Fig. 1 Schematic cross section of a liquid crystal on silicon (LCoS) spatial light modulator: The phase of the reflected wavefront is controlled by applying a voltage across the liquid crystal layer, which changes the orientation of the molecules. The interaction in the transition region leads to smoothing and crosstalk between neighboring pixels.
Fig. 2
Fig. 2 Comparison of measured diffraction efficiency versus phase stroke with simulations based on an idealized response ignoring crosstalk: (a) Ronchi phase grating (period of 2 pixels) in the asymmetric direction, where the ’grooves’ of the grating are oriented orthogonally to the alignment direction of the liquid crystal molecules, and (b) for a grating along the symmetric direction. Especially for large phase strokes large deviations between the idealized and the real behavior are observed.
Fig. 3
Fig. 3 Experimental setup used for characterization of the SLM response: (a) setup for interferometric SLM calibration of phase shift for uniform patterns, (b) setup for diffraction efficiency measurements.
Fig. 4
Fig. 4 Phase shift versus control voltage for a uniform pattern.
Fig. 5
Fig. 5 Diffraction efficiencies into the lowest orders for a binary phase grating (with two levels φ1 and φ2): (a) grating in x-direction, (b) grating in y direction. Since the response depends both on φ1 and φ2, we varied φ1 across the available range, and repeated the experiment with φ2/2π set to 0.1 and 1.3. The obtained results are plotted against the phase difference Δφ = φ1φ2.
Fig. 6
Fig. 6 Result of model calculation for a binary grating oriented along the x-direction, with control voltages corresponding to a phase shift of X waves and Y waves, respectively. Black arrows depict the director configuration, while the electric field is represented by the equipotential lines of the electric potential (blue lines) and electric field lines (red lines with arrow heads).
Fig. 7
Fig. 7 Approximation of the phase response for period 2 gratings by simplified analytic expressions of Eq. (12).
Fig. 8
Fig. 8 Comparison of phase response between (a) full simulations and (b) simplified model for a checkerboard pattern (period 2) with contour lines. (c, d) comparison of diffraction efficiency measurements, full simulations and simplified model.
Fig. 9
Fig. 9 Compensation of pixel crosstalk for a blazed grating with period of 5 pixels. Shown is a comparison of the expected (dotted bars) and measured (striped bars) diffraction efficiency for a simple blazed grating without compensation (blue), and optimized patterns that minimize the root mean square difference of the actual phase to the ideal phase (orange) or the difference of the diffraction intensity to the target values (green).
Fig. 10
Fig. 10 Result of crosstalk compensation for different cost functions. Shown is the (simulated) SLM response for optimized patterns. Overall, all methods yield phase distributions that are closer to the ideal blazed grating. This is achieved by increasing the phase stroke of the control pattern near the large jump.
Fig. 11
Fig. 11 Relative strength of phase modulation needed to maximize or minimize diffraction efficiency for a period 2 checkerboard pattern. The maximum diffraction efficiency is encoded by the color.

Tables (1)

Tables Icon

Table 1 Parameter Values Used for Numerical Simulations.

Equations (18)

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

f d V minimal ,
f = 1 2 K 11 ( n ) 2 + 1 2 K 22 ( n ( × n ) ) 2 + 1 2 K 33 ( n × × n ) 2 1 2 ε E E
ε i j = ε δ i j + ( ε + ε ) n i n j ,
( ε E ) = ( ε Φ ) = 0
F i = f n i j = 1 3 x j ( f n i , j ) = 0 for i { 1 , 2 , 3 }
F i = ( K 11 K 22 ) j = 1 3 2 n j x i x j + K 22 j = 1 3 2 n i x j 2 + ( K 33 K 22 ) j = 1 3 k = 1 3 n j n k 2 n i x k x j + ( K 33 K 22 ) j = 1 3 k = 1 3 ( n j n i x k n k x j + n k n i x k n j x j n j n k x i n k x j ) + ε 0 Δ ε E i j = 1 3 E j n j .
Φ ( k + 1 ) = Φ ( k ) + α ( ε ( Φ ) ) n ( k + 1 ) = n ( k ) + α F
Δ φ ( x ) = 2 π 2 d LC λ 0 d n e n o n o 2 + ( n e 2 n o 2 ) sin 2 ( θ ( x , y ) ) d z .
k ( x ) = { e ( x x 0 ξ + ) n x > x 0 e ( x x 0 ξ ) n x < x 0 ,
K ( x ) = 2 E n ( ) ( ξ + ξ + ) { ξ E n ( x x 0 ξ ) if x < x 0 ξ ξ + 2 + ξ + E n ( x x 0 ξ + ) else
E n ( x ) = x exp ( | x | n ) d x .
φ ^ ( x ) = k = 2 2 ( φ 1 φ 0 ) K up ( x ( 2 k + 1 ) d ) + ( φ 0 φ 1 ) K down ( x ( 2 k + 1 ) d )
φ ( x , y ) = φ 00 + ( φ 10 φ 00 ) ϑ ( x ) + ( φ 01 φ 00 ) Θ ( y ) + ( φ 11 ( φ 10 + φ 01 φ 00 ) ) Θ ( x ) Θ ( y )
φ ^ ( x , y ) = φ 00 + ( φ 10 φ 00 ) K 00 , 10 ( x ) + ( φ 01 φ 00 ) K 00 , 01 ( y ) + ( φ 11 ( φ 10 + φ 01 φ 00 ) ) K 00 , 10 ( x ) K 00 , 01 ( y ) .
α ( y ) = { 0 if y < 2 3 d 1 4 ( 5 3 y d ) ( 3 y d 2 ) if 2 3 d < y < 4 3 d 1 if y > 4 3 d
R = w ( I I 0 ) 2 minimal .
φ crosstalk φ ^ modulation f = e i φ ^ propagation F = ( f ) detector I = | F | 2 cost function R = | I I 0 | 2 2 ,
R φ 00 = φ ¯ 00 k , l [ φ ^ ¯ 00 ( x k , y l ) + ( φ ^ ¯ 10 ( x k , y l ) φ ^ ¯ 00 ( x k , y l ) ) K 00 , 10 ( x k ) + ( φ ^ ¯ 01 ( x k , y l ) φ ^ ¯ 00 ( x k , y l ) ) K 00 , 01 ( y 1 ) + ( φ ^ ¯ 11 ( x k , y l ) ( φ ^ ¯ 10 ( x k , y l ) + φ ^ ¯ 01 ( x k , y l ) φ ^ ¯ 00 ( x k , y l ) ) ) K 00 , 01 ( x k ) K 00 , 01 ( y l ) ]

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