Abstract

The inherent distortion of a reflective parallel aligned spatial light modulator (SLM) may need compensation not only for the backplane curvature but also for other possible nonuniformities caused by thickness variations of the liquid crystal layer across the aperture. First, we build a global look-up table (LUT) of phase modulation versus the addressed gray level for the whole device aperture. Second, when a lack of spatial uniformity is observed, we define a grid of cells onto the SLM aperture and develop a multipoint calibration. The relative phase variations between neighboring cells for a uniform gray level lead us to build a multi-LUT for improved compensation. Multipoint calibration can be done using either phase-shift interferometry or Fourier diffraction pattern analysis of binary phase gratings. Experimental results show the compensation progress in diffractive optical elements displayed on two SLMs.

© 2007 Optical Society of America

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References

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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  28. D. J. Cho, S. T. Thurman, J. T. Donner, and G. M. Morris, "Characteristics of a 128 × 128 liquid crystal spatial light modulator for wavefront generation," Opt. Lett. 23, 969-971 (1998).
  29. I. Moreno, C. Iemmi, A. Márquez, J. Campos, and M. J. Yzuel, "Modulation light efficiency of diffractive lenses displayed in a restricted phase-mostly modulation display," Appl. Opt. 43, 6278-6284 (2004).
    [CrossRef]
  30. X. Xun and R. W. Cohn, "Phase calibration of spatially nonuniform spatial light modulators," Appl. Opt. 43, 6400-6406 (2004).
    [CrossRef]
  31. J. Otón and P. Ambs, "Characterization and applications of a pure phase reflective liquid crystal spatial light modulator," Proc. SPIE 6254, 62540N (2006).
  32. P. Grother and D. Casasent, "Optical path difference measurement technique for SLMs," Opt. Commun. 189, 31-38 (2001).
    [CrossRef]
  33. J. D. Downie, B. P. Hine, and M. B. Reid, "Effects and correction of magneto-optic spatial light modulator phase errors in an optical correlator," Appl. Opt. 31, 636-643 (1992).
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    [CrossRef]
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    [CrossRef]
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2006 (3)

2005 (4)

V. Duran, J. Lancis, E. Tajahuerce, and Z. Jaroszewicz, "Univocal determination of the cell parameters of a twisted nematic liquid crystal display by single-wavelength polarimetry," J. Appl. Phys. 97, 043101 (2005).
[CrossRef]

A. Márquez, C. Iemmi, J. Campos, J. Escalera, and M. Yzuel, "Programmable apodizer to compensate chromatic aberration effects using a liquid crystal spatial light modulator," Opt. Express 13, 716-730 (2005).
[CrossRef]

J. Otón, M. S. Millán, and E. Pérez-Cabré, "Programmable lens design in a pixelated screen of twisted-nematic liquid crystal display," Opt. Pura Apl. 38, 47-56 (2005).

W. Osten, C. Kohler, and J. Liesener, "Evaluation and application of spatial light modulators for optical metrology," Opt. Pura Apl. 38, 71-81 (2005).

2004 (7)

A. Michalkiewicz, M. Kujawinska, T. Kozacki, X. Wang, and P. J. Bos, "Holographic three-dimensional displays with liquid crystal on silicon spatial light modulator," Proc. SPIE 5531, 85-94 (2004).
[CrossRef]

M. Stanley, M. A. Smith, A. P. Smith, P. J. Watson, S. D. Coomber, C. D. Cameron, C. W. Slinger, and A. D. Wood, "3D electronic holography display system using a 100 megapixel spatial light modulator," Proc. SPIE 5249, 297-308 (2004).
[CrossRef]

P. M. Prieto, E. J. Fernández, S. Manzanera, and P. Artal, "Adaptive optics with a programmable phase modulator: applications in the human eye," Opt. Express 12, 4059-4071 (2004).
[CrossRef]

D. C. O'Brien, G. E. Faulkner, T. D. Wilkinson, B. Robertson, and D. G. Leyva, "Design and analysis of an adaptive board-to-board dynamic holographic interconnect," Appl. Opt. 43, 3297-3305 (2004).
[CrossRef]

J. Harriman, A. Linnenberger, and S. Serati, "Improving spatial light modulator performance through phase compensation," Proc. SPIE 5553, 58-67 (2004).
[CrossRef]

I. Moreno, C. Iemmi, A. Márquez, J. Campos, and M. J. Yzuel, "Modulation light efficiency of diffractive lenses displayed in a restricted phase-mostly modulation display," Appl. Opt. 43, 6278-6284 (2004).
[CrossRef]

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

2003 (2)

P. J. Rodrigo, R. L. Eriksen, V. R. Daria, and J. Glückstad, "Shack-Hartmann multiple-beam optical tweezers," Opt. Express 11, 208-214 (2003).

S. P. Laut, D. U. Bartsch, and W. R. Freeman, "Experimental approach to the characterization of a micromachined continuous-membrane deformable mirror," Proc. SPIE 5169, 95-103 (2003).
[CrossRef]

2002 (1)

2001 (2)

H. J. Tiziani, T. Haist, J. Liesener, M. Reicherter, and L. Seifert, "Applications of SLMs for optical metrology," Proc. SPIE 4457, 72-81 (2001).
[CrossRef]

P. Grother and D. Casasent, "Optical path difference measurement technique for SLMs," Opt. Commun. 189, 31-38 (2001).
[CrossRef]

2000 (3)

1999 (2)

M. Reicherter, T. Haist, E. U. Wagemann, and H. J. Tiziani, "Optical particle trapping with computer-generated holograms written on a liquid-crystal display," Opt. Lett. 24, 608-610 (1999).

J. A. Davis, D. B. Allison, K. G. D'Nelly, M. L. Wilson, and I. Moreno, "Ambiguities in measuring the physical parameters for twisted-nematic liquid crystal spatial light modulators," Opt. Eng. 38, 705-709 (1999).
[CrossRef]

1998 (4)

D. J. Cho, S. T. Thurman, J. T. Donner, and G. M. Morris, "Characteristics of a 128 × 128 liquid crystal spatial light modulator for wavefront generation," Opt. Lett. 23, 969-971 (1998).

J. A. Davis, I. Moreno, and P. Tsai, "Polarization eigenstates for twisted-nematic liquid crystal displays," Appl. Opt. 37, 937-945 (1998).

I. Moreno, J. A. Davis, K. G. D'Nelly, and D. B. Allison, "Transmission and phase measurement for polarization eigenvectors in twisted-nematic liquid crystal spatial light modulators," Opt. Eng. 37, 3048-3052 (1998).
[CrossRef]

V. Laude, "Twisted-nematic liquid crystal pixelated active lens," Opt. Commun. 153, 134-152 (1998).
[CrossRef]

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)

1994 (3)

Z. Zhang, G. Lu, and F. Yu, "Simple method for measuring phase modulation in liquid crystal television," Opt. Eng. 33, 3018-3022 (1994).
[CrossRef]

D. C. O'Brien, R. J. Mears, T. D. Wilkinson, and W. A. Crossland, "Dynamic holographic interconnects that use ferroelectric liquid crystal spatial light modulators," Appl. Opt. 33, 2795-2803 (1994).

C. Soutar and K. Lu, "Determination of the physical properties of an arbitrary twisted-nematic liquid crystal cell," Opt. Eng. 33, 2704-2712 (1994).
[CrossRef]

1992 (1)

1990 (1)

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

1989 (1)

1988 (1)

Appl. Opt. (9)

D. C. O'Brien, R. J. Mears, T. D. Wilkinson, and W. A. Crossland, "Dynamic holographic interconnects that use ferroelectric liquid crystal spatial light modulators," Appl. Opt. 33, 2795-2803 (1994).

D. C. O'Brien, G. E. Faulkner, T. D. Wilkinson, B. Robertson, and D. G. Leyva, "Design and analysis of an adaptive board-to-board dynamic holographic interconnect," Appl. Opt. 43, 3297-3305 (2004).
[CrossRef]

M. J. Yzuel, J. Campos, A. Marquez, J. C. Escalera, J. A. Davis, C. Lemmi, and S. Ledesma, "Inherent apodization of lenses encoded on liquid crystal spatial light modulators," Appl. Opt. 39, 6034-6039 (2000).

J. Campos, A. Marquez, M. J. Yzuel, J. A. Davis, D. M. Cottrell, and I. Moreno, "Fully complex synthetic discriminant functions written onto phase-only modulators," Appl. Opt. 39, 5965-5970 (2000).

J. A. Davis, I. Moreno, and P. Tsai, "Polarization eigenstates for twisted-nematic liquid crystal displays," Appl. Opt. 37, 937-945 (1998).

I. Moreno, C. Iemmi, A. Márquez, J. Campos, and M. J. Yzuel, "Modulation light efficiency of diffractive lenses displayed in a restricted phase-mostly modulation display," Appl. Opt. 43, 6278-6284 (2004).
[CrossRef]

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

J. D. Downie, B. P. Hine, and M. B. Reid, "Effects and correction of magneto-optic spatial light modulator phase errors in an optical correlator," Appl. Opt. 31, 636-643 (1992).

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

J. Appl. Phys. (1)

V. Duran, J. Lancis, E. Tajahuerce, and Z. Jaroszewicz, "Univocal determination of the cell parameters of a twisted nematic liquid crystal display by single-wavelength polarimetry," J. Appl. Phys. 97, 043101 (2005).
[CrossRef]

J. Opt. Soc. Am. A (2)

Opt. Commun. (2)

V. Laude, "Twisted-nematic liquid crystal pixelated active lens," Opt. Commun. 153, 134-152 (1998).
[CrossRef]

P. Grother and D. Casasent, "Optical path difference measurement technique for SLMs," Opt. Commun. 189, 31-38 (2001).
[CrossRef]

Opt. Eng. (7)

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]

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

C. Soutar and K. Lu, "Determination of the physical properties of an arbitrary twisted-nematic liquid crystal cell," Opt. Eng. 33, 2704-2712 (1994).
[CrossRef]

I. Moreno, J. A. Davis, K. G. D'Nelly, and D. B. Allison, "Transmission and phase measurement for polarization eigenvectors in twisted-nematic liquid crystal spatial light modulators," Opt. Eng. 37, 3048-3052 (1998).
[CrossRef]

J. A. Davis, D. B. Allison, K. G. D'Nelly, M. L. Wilson, and I. Moreno, "Ambiguities in measuring the physical parameters for twisted-nematic liquid crystal spatial light modulators," Opt. Eng. 38, 705-709 (1999).
[CrossRef]

A. Márquez, J. Campos, M. J. Yzuel, I. Moreno, J. A. Davis, C. Iemmi, A. Moreno, and A. Robert, "Characterization of edge effects in twisted nematic liquid crystal displays," Opt. Eng. 39, 3301-3307 (2000).
[CrossRef]

Z. Zhang, G. Lu, and F. Yu, "Simple method for measuring phase modulation in liquid crystal television," Opt. Eng. 33, 3018-3022 (1994).
[CrossRef]

Opt. Express (5)

Opt. Lett. (3)

Opt. Pura Apl. (2)

J. Otón, M. S. Millán, and E. Pérez-Cabré, "Programmable lens design in a pixelated screen of twisted-nematic liquid crystal display," Opt. Pura Apl. 38, 47-56 (2005).

W. Osten, C. Kohler, and J. Liesener, "Evaluation and application of spatial light modulators for optical metrology," Opt. Pura Apl. 38, 71-81 (2005).

Proc. SPIE (6)

A. Michalkiewicz, M. Kujawinska, T. Kozacki, X. Wang, and P. J. Bos, "Holographic three-dimensional displays with liquid crystal on silicon spatial light modulator," Proc. SPIE 5531, 85-94 (2004).
[CrossRef]

M. Stanley, M. A. Smith, A. P. Smith, P. J. Watson, S. D. Coomber, C. D. Cameron, C. W. Slinger, and A. D. Wood, "3D electronic holography display system using a 100 megapixel spatial light modulator," Proc. SPIE 5249, 297-308 (2004).
[CrossRef]

S. P. Laut, D. U. Bartsch, and W. R. Freeman, "Experimental approach to the characterization of a micromachined continuous-membrane deformable mirror," Proc. SPIE 5169, 95-103 (2003).
[CrossRef]

J. Harriman, A. Linnenberger, and S. Serati, "Improving spatial light modulator performance through phase compensation," Proc. SPIE 5553, 58-67 (2004).
[CrossRef]

H. J. Tiziani, T. Haist, J. Liesener, M. Reicherter, and L. Seifert, "Applications of SLMs for optical metrology," Proc. SPIE 4457, 72-81 (2001).
[CrossRef]

J. Otón and P. Ambs, "Characterization and applications of a pure phase reflective liquid crystal spatial light modulator," Proc. SPIE 6254, 62540N (2006).

Other (6)

Holoeye Photonics AG and Holoeye Corporation 〈http://www.holoeye.com〉.

D. Malacara, ed., Optical Shop Testing, 2nd ed. (Wiley, 1992), Chap. 14, p. 501.

Boulder Nonlinear Systems 〈http://www.bnonlinear.com〉.

A. G. Bennett and R. B. Rabbetts, Clinical Visual Optics, 3rd ed. (Butterworth-Heinemann, 1998).

L. N. Thibos, R. A. Applegate, J. T. Schwiegerling, and R. Webb, "Standards for reporting the optical aberrations of eyes," in Vision Science and Its Applications, Vol. 35 of Trends in Optics and Photonics Series, V. Lakshminarayanan, ed. (Optical Society of America, 2000), 232-244.

B. Kress and P. Meyrueis, Digital Diffractive Optics, an Introduction to Planar Diffractive Optics and Related Technology (Wiley, 2000).

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Figures (14)

Fig. 1
Fig. 1

(Color online) Michelson interferometer to measure the spatial uniformity and the phase modulation capability of the SLM: P 1 and P 2 , linear polarizers, L 1 , L 2 , lenses. SF and BS stand for spatial filter and beam splitter, respectively. A halfwave plate (denoted λ / 2 ) is used to adjust the polarization of the incident beam on the SLM. The SLM plane (O) is imaged onto the CCD sensor ( O ) .

Fig. 2
Fig. 2

(a) Image consisting of two sectors with the reference gray level N ref and the varying gray level N v ; (b)–(d) interferograms of the Holoeye modulator obtained with Δ ϕ ( N ) 0 , π , 2 π , respectively; (e)–(g) interferograms of the BNS modulator obtained with Δ ϕ ( N ) 0 , π , 2 π , respectively.

Fig. 3
Fig. 3

(Color online) (a) Phase modulation for the Holoeye HEO 1080 P SLM as a function of the index level range [ 0 , 1471 ] for the illuminating wavelength 633   nm . (b) LUT to map the 8-bit addressed gray levels on the index level range of [ 200, 680 ] that corresponds to a phase modulation of 2π measured in (a). (c) Linear phase modulation obtained using the LUT of (b).

Fig. 4
Fig. 4

(Color online) Setup for the calibration of the BNS SLM, based on the display of binary phase Ronchi gratings on the SLM and the analysis of first order peak intensity of the Fourier diffraction pattern. The gray level values of the grid are N ref and N v .

Fig. 5
Fig. 5

(Color online) Calibration of the BNS SLM based on displaying binary phase Ronchi gratings. (a) Intensity for the first diffraction order I 1 ( Δ ϕ ) as function of the index level N v varying from 0 to 255. (b) Phase shift computed from the data plotted in (a). (c) LUT used to extend the index level range [ 0 , 90 ] to a mapped 8-bit gray level range [ 0 , 255 ] and equivalently map a lineal phase shift range modulation [ 0 , 2 π ] . (d) Intensity of the first diffraction order I 1 ( Δ ϕ ) of (a) as a function of the mapped 8-bit gray level range [ 0 , 255 ] .

Fig. 6
Fig. 6

(Color online) (a) Plots of the phase shift vs. the BNS index level in the central area of SLM aperture (dotted), at a border region (dashed), and that obtained by the phase Ronchi grating method (solid). (b) Phase shift curves plotted in (a) normalized to their maximum values in the index level range [ 0 , 100 ] .

Fig. 7
Fig. 7

(Color online) (a) Interferogram of BNS modulator with superimposed partition of 8 × 8 sectors. (b) Chessboard scheme used to determine N 2 π ( x , y ) in each sector by fringe matching at the surroundings of the vertex. (c) Partial view of the interferogram for N v = 70 . Fringes coincide at the border of the SLM aperture (circle). (d) Partial view of the interferogram for N v = 100 . Fringes match at the central area of the aperture (square). (e) Map of N 2 π ( x , y ) experimentally measured for 9 × 9 vertexes in the modulator aperture. (f) Interpolated map to the 256 × 256 pixels of the modulator aperture.

Fig. 8
Fig. 8

(Color online) (a) Holoeye and (b) BNS SLM aperture interferograms recorded for a constant value of the gray level addressed to the modulator; (c) and (d) Wavefront distribution obtained respectively from (a) and (b).

Fig. 9
Fig. 9

(Color online) WFD computed using different decompositions of Zernike polynomials (coefficients according to single index notation), with no compensation (denoted by NC in the abscissa axis) and after compensation. (a) Holoeye 1080P SLM. In this case, the WFD was computed taking into account both an elliptical aperture and the whole rectangular aperture. (b) BNS SLM. The WFD was computed taking into account both the inscribed circular and the whole square aperture.

Fig. 10
Fig. 10

Interferogram of the Holoeye modulator: (a) parallel reference mirror, without compensation of wavefront distortion; (b) tilted reference mirror, without compensation; (c) parallel mirror, with compensation of wavefront distortion; (d) tilted mirror, with compensation.

Fig. 11
Fig. 11

Interferogram of BNS modulator: (a) parallel reference mirror, without compensation of wavefront distortion; (b) tilted reference mirror, without compensation; (c) parallel mirror, with compensation of wavefront distortion; (d) tilted mirror, with compensation.

Fig. 12
Fig. 12

Interferograms obtained when a phase distribution corresponding to either X astigmatism (3rd Zernike polynomial, column on the left) or XY astigmatism (5th Zernike polynomial, column on the right) is generated by the BNS modulator. Top: ideal phase pattern distributions; Second row: Without compensation, global LUT; Third row: With compensation, global LUT; Fourth row: With compensation, multi-LUT.

Fig. 13
Fig. 13

Reconstruction of a Fresnel hologram of the UPC logo using the Holoeye SLM, with a focal length lens of f = 100   cm included in the hologram design. (a) Overview of image reconstruction; (b) (detail) without compensation; (c) (detail) with compensation.

Fig. 14
Fig. 14

Reconstruction of a Fresnel hologram of the MIPS logo using the BNS SLM, with a focal length lens of f = 13.1   cm included in the hologram design. (a) Overview of image reconstruction; (b) (detail) without compensation of the aberration and using the global LUT; (c) without compensation and using the multi-LUT; (d) with compensation and using the multi-LUT.

Tables (2)

Tables Icon

Table 1 Technical Specifications of the HEO-1080 P SLM from Holoeye

Tables Icon

Table 2 Technical Specifications of the P256 ZTN-LC SLM from BNS

Equations (9)

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

I 1 ( Δ ϕ ) [ 1 cos Δ ϕ ( N ) ] .
Δ ϕ ( x , y , N ) = 2 π λ ( n e ( x , y , N ) n 0 ) d ( x , y ) ,
n e ( x , y , N ) = n e ( N ) ( x , y ) ,
Δ ϕ ( x , y , N ) = 2 π λ [ n e ( N ) n 0 ] d ( x , y ) ,
Δ ϕ Norm ( x , y , N ) = Δ ϕ ( x , y , N ) Δ ϕ Max ( x , y , N ) = n e ( N ) n 0 n e ( N ) n 0
= Δ ϕ Norm ( N ) .
Δ ϕ Max ( x , y ) = 2 π Δ ϕ Norm [ N 2 π ( x , y ) ] ,
Δ ϕ ( x , y , N ) = Δ ϕ Norm ( N ) 2 π Δ ϕ Norm [ N 2 π ( x , y ) ] .
Δ ϕ ( x , y , N ) = Δ ϕ Norm ( N ) π Δ ϕ Norm [ N π ( x , y ) ] .

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