Abstract

A new 512 × 512 pixel phase-only spatial light modulator (SLM) has been found to deviate from being flat by several wavelengths. Also, the retardation of the SLM relative to voltage varies across the device by as much as 0.25 wavelength. The birefringence of each pixel as a function of address voltage is measured from the intensity of the SLM between crossed polarizers. To these responses are added a reference spatial phase measured by phase shifting interferometry for a single address voltage. Fits to the measured data facilitate the compensation of the SLM to a root-mean-square wave-front error of 0.06 wavelength. The application of these corrections to flatten the full aperture of the SLM sharpens the focal plane spot and reduces the distortion of computer-designed diffraction patterns.

© 2004 Optical Society of America

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References

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2004

1999

1998

1997

1995

1989

1988

1985

1983

G. Newgebauer, R. Hauck, O. Bryndahl, “Computer-generated circular carrier Fourier holograms,” Opt. Commun. 48, 89–92 (1983).
[CrossRef]

Arsenault, H. H.

Barnes, T. H.

Bergeron, A.

Bryndahl, O.

G. Newgebauer, R. Hauck, O. Bryndahl, “Computer-generated circular carrier Fourier holograms,” Opt. Commun. 48, 89–92 (1983).
[CrossRef]

Chang, X.

Cho, D. J.

Cohn, R. W.

Davis, J. A.

de Bougrenet de la Tocnaye, J. L.

Donner, J. T.

Doucet, M.

Duelli, M.

Dupont, L.

Eiju, T.

Gagnon, F.

Gauvin, J.

Gingras, D.

Goncalves Neto, L.

Hauck, R.

G. Newgebauer, R. Hauck, O. Bryndahl, “Computer-generated circular carrier Fourier holograms,” Opt. Commun. 48, 89–92 (1983).
[CrossRef]

Jay Stockley,

Jay Stockley, Boulder Nonlinear Systems, Inc., 450 Courtney Way, Lafayatte, Colo. 80026 (personal communication, 2003).

Jifang, L.

Konforti, N.

Lilly, R. A.

Liu, H. K.

Marom, E.

Matusda, K.

Morris, G. M.

Newgebauer, G.

G. Newgebauer, R. Hauck, O. Bryndahl, “Computer-generated circular carrier Fourier holograms,” Opt. Commun. 48, 89–92 (1983).
[CrossRef]

Ooyama, N.

Reece, M.

Roberge, D.

Serati, S.

J. Stockley, S. Serati, X. Xun, R. W. Cohn, “Liquid crystal spatial light modulator for multispot beam steering,” in Free Space Laser Communication and Active Laser Illumination III, D. G. Voelz, J. C. Ricklin, eds., Proc. SPIE5160, 208–215 (2004).
[CrossRef]

Sheng, Y.

Stockley, J.

J. Stockley, S. Serati, X. Xun, R. W. Cohn, “Liquid crystal spatial light modulator for multispot beam steering,” in Free Space Laser Communication and Active Laser Illumination III, D. G. Voelz, J. C. Ricklin, eds., Proc. SPIE5160, 208–215 (2004).
[CrossRef]

Thurman, S. T.

Wu, S. T.

Xun, X.

X. Xun, X. Chang, R. W. Cohn, “System for demonstrating arbitrary multi-spot beam steering from spatial light modulators,” Opt. Express 12, 260–268 (2004), http://www.opticsexpress.org .
[CrossRef] [PubMed]

J. Stockley, S. Serati, X. Xun, R. W. Cohn, “Liquid crystal spatial light modulator for multispot beam steering,” in Free Space Laser Communication and Active Laser Illumination III, D. G. Voelz, J. C. Ricklin, eds., Proc. SPIE5160, 208–215 (2004).
[CrossRef]

Yulin, L.

Zhengquan, H.

Zhisheng, Y.

Appl. Opt.

J. Opt. Soc. Am. A

Opt. Commun.

G. Newgebauer, R. Hauck, O. Bryndahl, “Computer-generated circular carrier Fourier holograms,” Opt. Commun. 48, 89–92 (1983).
[CrossRef]

Opt. Express

Opt. Lett.

Other

J. Stockley, S. Serati, X. Xun, R. W. Cohn, “Liquid crystal spatial light modulator for multispot beam steering,” in Free Space Laser Communication and Active Laser Illumination III, D. G. Voelz, J. C. Ricklin, eds., Proc. SPIE5160, 208–215 (2004).
[CrossRef]

Jay Stockley, Boulder Nonlinear Systems, Inc., 450 Courtney Way, Lafayatte, Colo. 80026 (personal communication, 2003).

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

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Figures (9)

Fig. 1
Fig. 1

Intensity images of the SLM illuminated by a collimated laser beam. (a)–(c) The SLM is addressed with a constant gray-scale voltage; (d)–(f) the SLM is calibrated to produce a spatially uniform phase. (a), (d) Intensity images of the SLM. Intensity variations are due to interference between the liquid-crystal layer and the cover glass, to nonuniform intensity of the collimated beam, and to high spatial frequency of the SLM phase modulation. (b), (e) Interferograms of the SLM with a flat reference mirror. (c), (f) SLM viewed through crossed polarizers at ±45° to the extraordinary axis of the SLM. The small blocks in the center of each image have been experimentally adjusted to provide references for maximum and minimum brightness.

Fig. 2
Fig. 2

Schematic of the SLM phase-measurement system (top view). The desired interferogram between the SLM and the piezo mirror is formed on the camera when both polarizers and the laser are polarized along the extraordinary axis of the SLM [e.g., as in Fig. 1(b)]. Ideally, no intensity variation is seen when the shutter is closed in front of the piezo mirror [e.g., as in Fig. 1(a)]. With the shutter closed, the intensity variations that are due to spatially varying birefringence are seen when the polarizers are at ±45° to the extraordinary axis [e.g., as in Fig. 1(f)]. NDF, neutral-density filter; BS, beam splitter; IP, image plane.

Fig. 3
Fig. 3

Measurements of the SLM’s change in birefringence as a function of gray-scale voltage at selected SLM pixels: corner (1, 1), halfway to the center (128, 128), and the center (256, 256). (a) Intensities recorded by the camera of the SLM between crossed polarizers. (b) Phase retardation calculated from (a).

Fig. 4
Fig. 4

Map of spatially varying phase responsiveness across the SLM. Depending on the location across the SLM, 20–25 gray-scale levels produce a 1λ retardation.

Fig. 5
Fig. 5

(a) Measured and (b) smoothed phase distributions, and (c) the phase difference between (a) and (b) for gray-scale address voltage V 0 = 44. The rms phase difference for the entire image in (c) is 0.003λ. (d) Residual phase measured with the calibration in Figs. 4 and 5(b). The rms residual phase error in (d) is 0.06λ. (a)–(d) Black denotes 0λ and white denotes 1λ optical thickness.

Fig. 6
Fig. 6

Intensity images of the SLM loaded with a binary image (a)–(c) without and (d)–(f) with calibration. The SLM is illuminated identically as for Fig. 1, and the images are arranged identically to the images in Fig. 1. The designed retardations for the binary image are 0 and λ/2.

Fig. 7
Fig. 7

Measured surface curvature of the cover glass. The cross section is that of the diagonal indicated by the two arrows.

Fig. 8
Fig. 8

Intensity distributions of the focal spot from the SLM (a) without and (b) with calibration. (c) Diffraction pattern from a mirror of the same aperture as the reflective SLM used in place of the SLM to estimate the diffraction limit. (d) Cross sections along the vertical center lines of (a)–(c). Spots in (a) and (b) were generated off axis to prevent on-axis reflection from the cover glass of the SLM. The lightest white in images in (a), (b), and (c) corresponds to 5%, 5%, and 2.5%, respectively, of the respective peak intensities of the spots.

Fig. 9
Fig. 9

Diffraction pattern of two rings produced by the SLM (a) without calibration and (b) with calibration.

Equations (7)

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ϕ=tan-1I4-I2I1-I3.
I=I01+cos ϕ/2,
ϕ=2πne-nol/λ
t=ϕ/2π,
tx, y=t0x, y+δtx, yVx, y-V0,
Vx, y=V0+tx, y-t0x, y/δtx, y.
E=expi2πrr1+x+yS1+expi2πrr2+x+yS2,

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