Abstract

We consider the use of a ferroelectric liquid-crystal spatial light modulator (FLC SLM) to control the transmittance of a telescope pupil to compensate for the effects of scintillation. Our aim here is to prove the necessary and physically interesting result that it is possible to control the intensity of light by use of FLC SLM without inducing further phase aberrations. Furthermore, we show that system errors have only a small effect on the phase of the transmitted beam.

© 1996 Optical Society of America

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References

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  1. Also known as amplitude-only modulation. We use the word “intensity” to avoid confusion with the complex amplitude (or amplitude and phase).
  2. J. R. P. Angel, Nature (London) 368, 203 (1994).
    [CrossRef]
  3. S. S. Stahl, D. G. Sandler, Astrophys. J. Lett. 454, L153 (1995).
    [CrossRef]
  4. G. Moddel, “Ferroelectric liquid crystal spatial light modulators,” in Spatial Light Modulator Technology, U. Efron, ed. (Dekker, London, 1995).
  5. G. D. Love, J. S. Fender, S. R. Restaino, Opt. Photon. News 6(10), 16 (1995).
    [CrossRef]
  6. K. Lu, B. E. A. Saleh, Appl. Opt. 30, 2354 (1991).
    [CrossRef] [PubMed]
  7. D. A. Gregory, J. C. Kirsch, E. C. Tam, Appl. Opt. 31, 163 (1992).
    [CrossRef] [PubMed]
  8. S. Garoff, R. B. Meyer, Phys. Rev. Lett. 38, 848 (1977).
    [CrossRef]
  9. R. Bhandari, Phys. Lett. A 157, 221 (1991).
    [CrossRef]
  10. R. Bhandari, Phys. Lett. A 138, 469 (1989).
    [CrossRef]
  11. For example, 10x10b FLC-SLM, 2200 Displaytech, Boulder, Colo.

1995 (2)

S. S. Stahl, D. G. Sandler, Astrophys. J. Lett. 454, L153 (1995).
[CrossRef]

G. D. Love, J. S. Fender, S. R. Restaino, Opt. Photon. News 6(10), 16 (1995).
[CrossRef]

1994 (1)

J. R. P. Angel, Nature (London) 368, 203 (1994).
[CrossRef]

1992 (1)

1991 (2)

1989 (1)

R. Bhandari, Phys. Lett. A 138, 469 (1989).
[CrossRef]

1977 (1)

S. Garoff, R. B. Meyer, Phys. Rev. Lett. 38, 848 (1977).
[CrossRef]

Angel, J. R. P.

J. R. P. Angel, Nature (London) 368, 203 (1994).
[CrossRef]

Bhandari, R.

R. Bhandari, Phys. Lett. A 157, 221 (1991).
[CrossRef]

R. Bhandari, Phys. Lett. A 138, 469 (1989).
[CrossRef]

Fender, J. S.

G. D. Love, J. S. Fender, S. R. Restaino, Opt. Photon. News 6(10), 16 (1995).
[CrossRef]

Garoff, S.

S. Garoff, R. B. Meyer, Phys. Rev. Lett. 38, 848 (1977).
[CrossRef]

Gregory, D. A.

Kirsch, J. C.

Love, G. D.

G. D. Love, J. S. Fender, S. R. Restaino, Opt. Photon. News 6(10), 16 (1995).
[CrossRef]

Lu, K.

Meyer, R. B.

S. Garoff, R. B. Meyer, Phys. Rev. Lett. 38, 848 (1977).
[CrossRef]

Moddel, G.

G. Moddel, “Ferroelectric liquid crystal spatial light modulators,” in Spatial Light Modulator Technology, U. Efron, ed. (Dekker, London, 1995).

Restaino, S. R.

G. D. Love, J. S. Fender, S. R. Restaino, Opt. Photon. News 6(10), 16 (1995).
[CrossRef]

Saleh, B. E. A.

Sandler, D. G.

S. S. Stahl, D. G. Sandler, Astrophys. J. Lett. 454, L153 (1995).
[CrossRef]

Stahl, S. S.

S. S. Stahl, D. G. Sandler, Astrophys. J. Lett. 454, L153 (1995).
[CrossRef]

Tam, E. C.

Appl. Opt. (2)

Astrophys. J. Lett. (1)

S. S. Stahl, D. G. Sandler, Astrophys. J. Lett. 454, L153 (1995).
[CrossRef]

Nature (London (1)

J. R. P. Angel, Nature (London) 368, 203 (1994).
[CrossRef]

Opt. Photon. News (1)

G. D. Love, J. S. Fender, S. R. Restaino, Opt. Photon. News 6(10), 16 (1995).
[CrossRef]

Phys. Lett. A (2)

R. Bhandari, Phys. Lett. A 157, 221 (1991).
[CrossRef]

R. Bhandari, Phys. Lett. A 138, 469 (1989).
[CrossRef]

Phys. Rev. Lett. (1)

S. Garoff, R. B. Meyer, Phys. Rev. Lett. 38, 848 (1977).
[CrossRef]

Other (3)

For example, 10x10b FLC-SLM, 2200 Displaytech, Boulder, Colo.

Also known as amplitude-only modulation. We use the word “intensity” to avoid confusion with the complex amplitude (or amplitude and phase).

G. Moddel, “Ferroelectric liquid crystal spatial light modulators,” in Spatial Light Modulator Technology, U. Efron, ed. (Dekker, London, 1995).

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Figures (3)

Fig. 1
Fig. 1

Poincaré sphere showing the effect of a FLC SLM placed between parallel polarizers. The incident light after the first polarizer is given by point A. The FLC SLM rotates point A through 180° about C to B. The second polarizer returns the light to state A along the equator. HLP, horizontal linear polarization; LP@45°, linear polarization at 45°; RHCP, right-handed circular polarization.

Fig. 2
Fig. 2

(a) Normalized FLC SLM transmission versus FLC orientation. (b) Phase shift induced by rotating the FLC SLM optical axis. The solid curve is for an ideal FLC retardance of π, and the dashed curve is for a retardance of 1.1π.

Fig. 3
Fig. 3

Contour plot showing the phase shift induced by a FLC SLM versus wavelength and normalized transmission. The contour units are in thousandths of a wavelength at the optimum wavelength of 1 μm.

Equations (9)

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ψ r = [ 1 0 0 0 ] × [ cos 2 θ + e i δ sin 2 θ ( 1 e i δ ) sin θ cos θ ( 1 e i δ ) sin θ cos θ sin 2 θ + e i δ cos 2 θ ] [ 1 0 ] ,
ψ r = [ cos 2 θ 0 ] .
ϕ g = ( π / 2 ) ( 1 cos α ) .
n eff = cos 2 θ n e + sin 2 θ n o .
ϕ d = ½ δ cos 2 θ ½ δ + ( 2 π / λ ) n o d .
ψ r = [ cos 2 θ + e i δ sin 2 θ 0 ] .
ϕ r = tan 1 [ Im ( ψ r ) Re ( ψ r ) ] ,
ϕ r = tan 1 ( sin δ sin 2 θ cos 2 θ + cos δ sin 2 θ ) .
ψ r = α [ ( 1 e i δ ) cos θ sin θ 0 ] ,

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