Abstract

Liquid crystal spatial light modulators (SLMs) are usually configured and calibrated for phase modulation. However, as they are variable retarders, they also have application as polarization modulators. We show that conventional phase-only calibrations are insufficient for this purpose, and a separate retardance calibration is needed. To overcome this shortcoming we report a simple Twyman-Green interferometer-based setup to realize SLM phase and retardance calibration. For phase calibration, we identify the non-linear, spatially variant response to the drive voltage of the SLM using fringe analysis and both horizontally and vertically polarized incident light. For retardance calibration, we use incident light polarized at 45° and assess the intensity variation. The methods presented are compatible with in situ calibration of SLMs.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

Full Article  |  PDF Article
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2019 (4)

2018 (7)

S. Rothau, K. Mantel, and N. Lindlein, “Simultaneous measurement of phase transmission and birefringence of an object under test,” Appl. Opt. 57(17), 4849–4856 (2018).
[Crossref] [PubMed]

Z. Zhao, Z. Xiao, Y. Zhuang, H. Zhang, and H. Zhao, “An interferometric method for local phase modulation calibration of LC-SLM using self-generated phase grating,” Rev. Sci. Instrum. 89(8), 083116 (2018).
[Crossref] [PubMed]

D. K. Gupta, B. V. R. Tata, and T. R. Ravindran, “Optimization of a spatial light modulator driven by digital video interface graphics to generate holographic optical traps,” Appl. Opt. 57(28), 8374–8384 (2018).
[Crossref] [PubMed]

H. Wang, Z. Dong, F. Fan, Y. Feng, Y. Lou, and X. Jiang, “Characterization of Spatial Light Modulator Based on the Phase in Fourier Domain of the Hologram and Its Applications in Coherent Imaging,” Appl. Sci. (Basel) 8(7), 1146 (2018).
[Crossref]

B. Sun, P. S. Salter, C. Roider, A. Jesacher, J. Strauss, J. Heberle, M. Schmidt, and M. J. Booth, “Four-dimensional light shaping: manipulating ultrafast spatiotemporal foci in space and time,” Light Sci. Appl. 7(1), 17117 (2018).
[Crossref] [PubMed]

A. D. Corbett, M. Shaw, A. Yacoot, A. Jefferson, L. Schermelleh, T. Wilson, M. Booth, and P. S. Salter, “Microscope calibration using laser written fluorescence,” Opt. Express 26(17), 21887–21899 (2018).
[Crossref] [PubMed]

N. Matsumoto, A. Konno, T. Inoue, and S. Okazaki, “Aberration correction considering curved sample surface shape for non-contact two-photon excitation microscopy with spatial light modulator,” Sci. Rep. 8(1), 9252 (2018).
[Crossref] [PubMed]

2017 (5)

B. Ndagano, B. Perez-Garcia, F. S. Roux, M. McLaren, C. Rosales-Guzman, Y. Zhang, O. Mouane, R. I. Hernandez-Aranda, T. Konrad, and A. Forbes, “Characterizing quantum channels with non-separable states of classical light,” Nat. Phys. 13(4), 397–402 (2017).
[Crossref]

K. H. Kagalwala, G. Di Giuseppe, A. F. Abouraddy, and B. E. A. Saleh, “Single-photon three-qubit quantum logic using spatial light modulators,” Nat. Commun. 8(1), 739 (2017).
[Crossref] [PubMed]

J. Chen, L. Kong, and Q. Zhan, “Demonstration of a vectorial optical field generator with adaptive close loop control,” Rev. Sci. Instrum. 88(12), 125111 (2017).
[Crossref] [PubMed]

T. Zhao, J. Liu, X. Duan, Q. Gao, J. Duan, X. Li, Y. Wang, W. Wu, and R. Zhang, “Multi-region phase calibration of liquid crystal SLM for holographic display,” Appl. Opt. 56(22), 6168–6174 (2017).
[Crossref] [PubMed]

S. McDermott, P. Li, G. Williams, and A. Maiden, “Characterizing a spatial light modulator using ptychography,” Opt. Lett. 42(3), 371–374 (2017).
[Crossref] [PubMed]

2016 (4)

J. L. M. Fuentes, E. J. Fernández, P. M. Prieto, and P. Artal, “Interferometric method for phase calibration in liquid crystal spatial light modulators using a self-generated diffraction-grating,” Opt. Express 24(13), 14159–14171 (2016).
[Crossref] [PubMed]

T. H. Lu, T. D. Huang, J. G. Wang, L. W. Wang, and R. R. Alfano, “Generation of flower high-order Poincaré sphere laser beams from a spatial light modulator,” Sci. Rep. 6(1), 39657 (2016).
[Crossref] [PubMed]

D. Naidoo, F. S. Roux, A. Dudley, I. Litvin, B. Piccirillo, L. Marrucci, and A. Forbes, “Controlled generation of higher-order Poincaré sphere beams from a laser,” Nat. Photonics 10(5), 327–332 (2016).
[Crossref]

R. Bruck, K. Vynck, P. Lalanne, B. Mills, D. J. Thomson, G. Z. Mashanovich, G. T. Reed, and O. L. Muskens, “All-optical spatial light modulator for reconfigurable silicon photonic circuits,” Optica 3(4), 396–402 (2016).
[Crossref]

2015 (2)

J. Carpenter, B. J. Eggleton, and J. Schröder, “Observation of Eisenbud–Wigner–Smith states as principal modes in multimode fibre,” Nat. Photonics 9(11), 751–757 (2015).
[Crossref]

T.-H. Tsai, X. Yuan, and D. J. Brady, “Spatial light modulator based color polarization imaging,” Opt. Express 23(9), 11912–11926 (2015).
[Crossref] [PubMed]

2014 (2)

2013 (5)

W. Han, Y. Yang, W. Cheng, and Q. Zhan, “Vectorial optical field generator for the creation of arbitrarily complex fields,” Opt. Express 21(18), 20692–20706 (2013).
[Crossref] [PubMed]

D. Engström, M. Persson, J. Bengtsson, and M. Goksör, “Calibration of spatial light modulators suffering from spatially varying phase response,” Opt. Express 21(13), 16086–16103 (2013).
[Crossref] [PubMed]

S. Reichelt, “Spatially resolved phase-response calibration of liquid-crystal-based spatial light modulators,” Appl. Opt. 52(12), 2610–2618 (2013).
[Crossref] [PubMed]

S. Mukhopadhyay, S. Sarkar, K. Bhattacharya, and L. Hazra, “Polarization phase shifting interferometric technique for phase calibration of a reflective phase spatial light modulator,” Opt. Eng. 52(3), 035602 (2013).
[Crossref]

C. Calderon-Hermosillo, N. A. Ochoa, E. N. Arias, and J. García-Márquez, “Inspection of complex amplitudes of spatial light modulators using moiré techniques,” Opt. Lasers Eng. 51(5), 610–615 (2013).
[Crossref]

2012 (2)

2011 (1)

C. Maurer, A. Jesacher, S. Bernet, and M. Ritsch‐Marte, “What spatial light modulators can do for optical microscopy,” Laser Photonics Rev. 5(1), 81–101 (2011).
[Crossref]

2010 (1)

2009 (1)

L. Martínez-León, Z. Jaroszewicz, A. Kołodziejczyk, V. Durán, E. Tajahuerce, and J. Lancis, “Phase calibration of spatial light modulators by means of Fresnel images,” J. Opt. A, Pure Appl. Opt. 11(12), 125405 (2009).
[Crossref]

2007 (1)

H. Zhang, J. Zhang, and L. Wu, “Evaluation of phase-only liquid crystal spatial light modulator for phase modulation performance using a Twyman–Green interferometer,” Meas. Sci. Technol. 18(6), 1724–1728 (2007).
[Crossref]

2006 (2)

K. L. Baker and E. A. Stappaerts, “A single-shot pixellated phase-shifting interferometer utilizing a liquid-crystal spatial light modulator,” Opt. Lett. 31(6), 733–735 (2006).
[Crossref] [PubMed]

K. I. Willig, R. R. Kellner, R. Medda, B. Hein, S. Jakobs, and S. W. Hell, “Nanoscale resolution in GFP-based microscopy,” Nat. Methods 3(9), 721–723 (2006).
[Crossref] [PubMed]

2004 (1)

2002 (1)

2000 (1)

M. Yamauchi, A. Marquez, J. A. Davis, and D. J. Franich, “Interferometric phase measurements for polarization eigenvectors in twisted nematic liquid crystal spatial light modulators,” Opt. Commun. 181(1–3), 1–6 (2000).
[Crossref]

1998 (1)

1982 (1)

M. Takeda, H. Ina, and S. Kobayashi, “Fourier-transform method of fringe-pattern analysis for computer-based topography and interferometry,” J. Opt. Soc. Am. A 72(1), 156–160 (1982).
[Crossref]

Abouraddy, A. F.

K. H. Kagalwala, G. Di Giuseppe, A. F. Abouraddy, and B. E. A. Saleh, “Single-photon three-qubit quantum logic using spatial light modulators,” Nat. Commun. 8(1), 739 (2017).
[Crossref] [PubMed]

Adler, R.

Alfano, R. R.

T. H. Lu, T. D. Huang, J. G. Wang, L. W. Wang, and R. R. Alfano, “Generation of flower high-order Poincaré sphere laser beams from a spatial light modulator,” Sci. Rep. 6(1), 39657 (2016).
[Crossref] [PubMed]

Antonello, J.

Arias, E. N.

C. Calderon-Hermosillo, N. A. Ochoa, E. N. Arias, and J. García-Márquez, “Inspection of complex amplitudes of spatial light modulators using moiré techniques,” Opt. Lasers Eng. 51(5), 610–615 (2013).
[Crossref]

Artal, P.

Baker, K. L.

Belsley, M. S.

Bengtsson, J.

Bernet, S.

C. Maurer, A. Jesacher, S. Bernet, and M. Ritsch‐Marte, “What spatial light modulators can do for optical microscopy,” Laser Photonics Rev. 5(1), 81–101 (2011).
[Crossref]

Bewersdorf, J.

Bhattacharya, K.

S. Mukhopadhyay, S. Sarkar, K. Bhattacharya, and L. Hazra, “Polarization phase shifting interferometric technique for phase calibration of a reflective phase spatial light modulator,” Opt. Eng. 52(3), 035602 (2013).
[Crossref]

Booth, M.

Booth, M. J.

Brady, D. J.

Bruck, R.

Burke, D.

Burton, D. R.

Calderon-Hermosillo, C.

C. Calderon-Hermosillo, N. A. Ochoa, E. N. Arias, and J. García-Márquez, “Inspection of complex amplitudes of spatial light modulators using moiré techniques,” Opt. Lasers Eng. 51(5), 610–615 (2013).
[Crossref]

Carpenter, J.

J. Carpenter, B. J. Eggleton, and J. Schröder, “Observation of Eisenbud–Wigner–Smith states as principal modes in multimode fibre,” Nat. Photonics 9(11), 751–757 (2015).
[Crossref]

Chen, J.

J. Chen, L. Kong, and Q. Zhan, “Demonstration of a vectorial optical field generator with adaptive close loop control,” Rev. Sci. Instrum. 88(12), 125111 (2017).
[Crossref] [PubMed]

Chen, Q.

Cheng, W.

Cohn, R. W.

Corbett, A. D.

Dainty, C.

Davis, I.

Davis, J. A.

M. Yamauchi, A. Marquez, J. A. Davis, and D. J. Franich, “Interferometric phase measurements for polarization eigenvectors in twisted nematic liquid crystal spatial light modulators,” Opt. Commun. 181(1–3), 1–6 (2000).
[Crossref]

Deng, H.

Z. Yu, M. Xia, H. Li, T. Zhong, F. Zhao, H. Deng, Z. Li, D. Li, D. Wang, and P. Lai, “Implementation of digital optical phase conjugation with embedded calibration and phase rectification,” Sci. Rep. 9(1), 1537 (2019).
[Crossref] [PubMed]

Di Giuseppe, G.

K. H. Kagalwala, G. Di Giuseppe, A. F. Abouraddy, and B. E. A. Saleh, “Single-photon three-qubit quantum logic using spatial light modulators,” Nat. Commun. 8(1), 739 (2017).
[Crossref] [PubMed]

Dobbie, I. M.

Dong, Z.

H. Wang, Z. Dong, F. Fan, Y. Feng, Y. Lou, and X. Jiang, “Characterization of Spatial Light Modulator Based on the Phase in Fourier Domain of the Hologram and Its Applications in Coherent Imaging,” Appl. Sci. (Basel) 8(7), 1146 (2018).
[Crossref]

Duan, J.

Duan, X.

Dudley, A.

D. Naidoo, F. S. Roux, A. Dudley, I. Litvin, B. Piccirillo, L. Marrucci, and A. Forbes, “Controlled generation of higher-order Poincaré sphere beams from a laser,” Nat. Photonics 10(5), 327–332 (2016).
[Crossref]

Durán, V.

L. Martínez-León, Z. Jaroszewicz, A. Kołodziejczyk, V. Durán, E. Tajahuerce, and J. Lancis, “Phase calibration of spatial light modulators by means of Fresnel images,” J. Opt. A, Pure Appl. Opt. 11(12), 125405 (2009).
[Crossref]

Eggleton, B. J.

J. Carpenter, B. J. Eggleton, and J. Schröder, “Observation of Eisenbud–Wigner–Smith states as principal modes in multimode fibre,” Nat. Photonics 9(11), 751–757 (2015).
[Crossref]

Engström, D.

Fan, F.

H. Wang, Z. Dong, F. Fan, Y. Feng, Y. Lou, and X. Jiang, “Characterization of Spatial Light Modulator Based on the Phase in Fourier Domain of the Hologram and Its Applications in Coherent Imaging,” Appl. Sci. (Basel) 8(7), 1146 (2018).
[Crossref]

Feng, Y.

H. Wang, Z. Dong, F. Fan, Y. Feng, Y. Lou, and X. Jiang, “Characterization of Spatial Light Modulator Based on the Phase in Fourier Domain of the Hologram and Its Applications in Coherent Imaging,” Appl. Sci. (Basel) 8(7), 1146 (2018).
[Crossref]

Fernández, E. J.

Ferreira, F. P.

Forbes, A.

B. Ndagano, B. Perez-Garcia, F. S. Roux, M. McLaren, C. Rosales-Guzman, Y. Zhang, O. Mouane, R. I. Hernandez-Aranda, T. Konrad, and A. Forbes, “Characterizing quantum channels with non-separable states of classical light,” Nat. Phys. 13(4), 397–402 (2017).
[Crossref]

D. Naidoo, F. S. Roux, A. Dudley, I. Litvin, B. Piccirillo, L. Marrucci, and A. Forbes, “Controlled generation of higher-order Poincaré sphere beams from a laser,” Nat. Photonics 10(5), 327–332 (2016).
[Crossref]

Franich, D. J.

M. Yamauchi, A. Marquez, J. A. Davis, and D. J. Franich, “Interferometric phase measurements for polarization eigenvectors in twisted nematic liquid crystal spatial light modulators,” Opt. Commun. 181(1–3), 1–6 (2000).
[Crossref]

Fuentes, J. L. M.

Gao, Q.

García-Márquez, J.

C. Calderon-Hermosillo, N. A. Ochoa, E. N. Arias, and J. García-Márquez, “Inspection of complex amplitudes of spatial light modulators using moiré techniques,” Opt. Lasers Eng. 51(5), 610–615 (2013).
[Crossref]

Gdeisat, M. A.

Gerritsen, H. C.

Göhler, A.

Goksör, M.

Gould, T. J.

Gupta, D. K.

Haist, T.

Han, W.

Harriman, J. L.

J. L. Harriman, A. Linnenberger, and S. A. Serati, “Improving spatial light modulator performance through phase compensation,” in Proceedings of Advanced Wavefront Control: Methods, Devices, and ApplicationsII, 58–68 (2004).

Hazra, L.

S. Mukhopadhyay, S. Sarkar, K. Bhattacharya, and L. Hazra, “Polarization phase shifting interferometric technique for phase calibration of a reflective phase spatial light modulator,” Opt. Eng. 52(3), 035602 (2013).
[Crossref]

Heberle, J.

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Figures (12)

Fig. 1
Fig. 1 (a) Schematic of the SLM calibration: Twyman-Green interferometer. The analyzer was inserted when doing the retardance calibration. HWP: half wave plate. BS: 50:50 beam splitter; SLM: spatial light modulator. (b) Interferogram obtained when the SLM was replaced with a flat mirror.
Fig. 2
Fig. 2 Blue circles: mean value of the phase measured with the interferometer when the SLM was replaced with a flat mirror; Red crosses: remaining phase after removing εi. After removing εi the phase becomes stationary as expected for a flat mirror.
Fig. 3
Fig. 3 Schematic of the measurement process. The sets of reference (R) and normal (N) measurements were interleaved in time as shown to subsequently apply interpolation and detrending.
Fig. 4
Fig. 4 Decomposition of the phase in the terms outlined in Eq. (11). (a) Г’i varying as a function of PGV at the center point of the SLM; (b) εi varying with the measurement i (c) calculated Φi varying as a function of PGV. For the SLM calibration, the values Φi shown in (c) are of interest.
Fig. 5
Fig. 5 Flow chart of the data processing and analysis method.
Fig. 6
Fig. 6 Step 1: Phase extraction results from the SLM center point (a) Гi (b) Г’i after removal of the piston offset 2kiπ introduced by the phase unwrapping algorithm.
Fig. 7
Fig. 7 Comparison of phase varying as PGV before and after Step 2 and 3. Red circle: Г’i in Eq. (11); yellow cross: Φi in Eq. (11); blue line: ΦS, 3rd order polynomial fit in Eq. (12).
Fig. 8
Fig. 8 (a) The phase map at PGV = 0, SLM was divided into 30 × 40 sub-regions for phase response analysis. (b) ΦS variation along the SLM x direction at y = 15, PGV = 0; the x axis represents the x coordinate of the SLM sub-region (c) ΦS variation with PGV at region (3,15). (d) ΦS variation with PGV at center region.
Fig. 9
Fig. 9 Results after Step 4: subtraction of the phase at PGV = 0 for visualizing the polynomial coefficient differences at SLM different regions (a) The relative phase map, ΦS − d, at PGV = 155 (b) ΦS − d variation along y direction at x = 20, PGV = 155; the y axis represents the y coordinates of the SLM sub-region (c) ΦS − d variation along x direction, at y = 20, PGV = 155 (d) ΦS − d variation as PGV at the center region.
Fig. 10
Fig. 10 Calibration for y polarized incident light. (a) Phase varying as a function of PGV before and after removing phase disturbance ε. Blue circle: before step 2: removing the phase disturbance; Red Cross: after step 2: removing the disturbance. (b) Phase variation along x direction at y = 15, PGV = 0.
Fig. 11
Fig. 11 Retardance calibration: intensity profile recorded by the camera with 45° linearly polarized input light and viewed after the analyzer at (a) PGV = 3 (b) PGV = 56 (c) PGV = 187.
Fig. 12
Fig. 12 Retardance calibration. (a) Red Dot: intensity change with PGV at region (19,18) recorded by camera. Blue Line: Fit obtained. (b) Retardance variation with PGV at (19,18) according to fitting result. (c) Red Dot: intensity change with PGV at region (4,17). Blue Line: fit obtained. (d) Retardance variation with PGV at (4,17).

Tables (1)

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Table 1 Diffraction efficiency comparison with different SLM calibration and different blazed grating periods

Equations (22)

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Θ x ( x,y )= ζ v (x,y)+ Φ x ( x,y )
Θ x ( x,y )=Ψ(x,y)+ Φ x ( x,y )
Θ y ( x,y )= Φ y ( x,y )
Φ x ( x,y )= 2π λ L x ( x,y )= 4π n e λ t(x,y)
Φ y ( x,y )= 2π λ L y ( x,y )= 4π n o λ t(x,y)
Φ x ( x,y )= n e n o Φ y ( x,y )
Θ y (x,y)= Φ y ( x,y )= n o n e Φ x ( x,y )
ΔΘ(x,y)= Θ x (x,y) Θ y (x,y)=( 1 n o n e ) Φ x ( x,y )+Ψ(x,y)= n o n e Φ x ( x,y )+c
I(x,y)= | A e i Φ s (x,y) +B e i Φ R (x,y) | 2 = A 2 + B 2 +AB e i( Φ s (x,y) Φ R (x,y )) +AB e i( Φ R (x,y) Φ s (x,y ))
Γ i = Φ i +2 k i π+ ε i
Γ ' i = Φ i + ε i
Φ S (x,y)= a x,y V 3 + b x,y V 2 + c x,y V+ d x,y
I= | e i Φ x + e i Φ y | 2 =2+2cos( Φ x + Φ y )=4 cos 2 ( Φ x Φ y 2 )
I= cos 2 ( a V 3 +b V 2 +cV+d )
E out (x)=(1γ) e i Φ x (x)
E refl (x)=γ e iF(x)
E ' out (x)= E out + E refl =(1γ) e i Φ x (x) +γ e iF(x)
E ' out (x)= e i Φ x (x) [ 1+γ( e iξ(x) 1 ) ]=A(x) e i Φ x (x)
arg(A)=arctan( γsinξ 1γ+γcosξ )arctan( γsinξ )γsinξ
E int (x)=E ' out (x)+ E refl =1+A e i Φ x (x) 1+ e i( Φ x (x)+γsinξ(x) )
I(x)= | E int (x) | 2 | 1+ e i( Φ x (x)+γsinξ(x)) | 2 =4 cos 2 ( Φ x (x)+γsinξ(x) 2 )
Φ measured Φ x +γsinξ= Φ x +γsin( F Φ x )

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