Abstract

To allow angular separation of the beam reflected off a liquid crystal wavefront corrector from the incident beam, it is convenient to introduce a small incident angle. This avoids using a beam splitter and the associated energy losses. The effect of the tilt incidence on the liquid crystal wavefront corrector was investigated in this paper. For a parallel aligned liquid crystal wavefront corrector, a simplified model was established and used to analyze the change of the phase modulation under the tilt incidence. The simulated results showed that the effect of the tilt incidence on the phase modulation can be ignored when the angle of tilt incidence is less than 6°. The phase modulation related to the incident angle was measured and the changing trend was similar to the calculated results. The effect of the tilt incidence on the diffraction efficiency of the liquid crystal wavefront corrector was also discussed. The simulated results indicated that the reduction of the diffraction efficiency is less than 1% for incidence angles under 3°. Last, a closed loop correction experiment was done with an incident angle of 1°. After correction, the averaged peak to valley (PV) and root mean square (RMS) of the wavefront were down to 0.15λ and 0.03λ, respectively, and a resolvable image was acquired.

© 2008 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. L. Hu, L. Xuan, Y. Liu, Z. Cao, D. Li, and Q. Mu, “Phase-only liquid crystal spatial light modulator for wavefront correction with high precision,” Opt. Express 12, 6403-6409 (2004).
    [CrossRef] [PubMed]
  2. G. D. Love, “Wave-front correction and production of Zernike modes with a liquid-crystal spatial light modulator,” Appl. Opt. 36, 1517-1524 (1997).
    [CrossRef] [PubMed]
  3. F. Vargas-Martín and P. Artal, “Phasor averaging for wavefront correction with liquid crystal spatial light modulators,” Opt. Commun. 152, 233-238 (1998).
    [CrossRef]
  4. S. Serati and J. Stockley, “Advances in liquid crystal based devices for wavefront control and beam steering,” Proc. SPIE 5894, 58940K-1-58940K-13 (2005).
  5. D. Dayton, J. Gonglewski, S. Restaino, and S. Browne, “MEMS adaptive optics for high resolution imaging of low Earth orbit satellites,” Proc. SPIE 5490, 1514-1525 (2004).
    [CrossRef]
  6. Q. Mu, Z. Cao, L. Hu, D. Li, and L. Xuan, “Adaptive optics imaging system based on a high-resolution liquid crystal on silicon device,” Opt. Express 14, 8013-8018 (2006).
    [CrossRef] [PubMed]
  7. Q. Mu, Z. Cao, D. Li, L. Hu, and L. Xuan, “Liquid crystal based adaptive optics system to compensate both low and high order aberrations in model eye,” Opt. Express 15, 1946-1953 (2007).
    [CrossRef] [PubMed]
  8. U. Efron, J. Grinberg, P. O. Braatz, M. J. Little, P. G. Reif, and R. N. Schwartz, “The silicon liquid-crystal light valve”, J. Appl. Phys. 57, 1356-1368 (1985).
    [CrossRef]
  9. U. Efron, S. T. Wu, J. Grinberg, and L. D. Hess, “Liquid-crystal-based visible-to-infrared dynamic image converter,” Opt. Eng. 24, 111-118 (1985).
  10. N. Konforti, E. Marom, and S. T. Wu, “Phase-only modulation with twisted nematic liquid-crystal spatial light modulators,” Opt. Lett. 13, 251-253 (1988).
    [CrossRef] [PubMed]
  11. D. Dayton, J. Gonglewski, and S. Restaino et al., “Demonstration of new technology MEMS and liquid crystal adaptive optics on bright astronomical objects and satellites,” Opt. Express 10, 1508-1519 (2002).
    [PubMed]
  12. Z. Cao, L. Xuan, L. Hu, Y. Liu, Q. Mu, and D. Li, “Investigation of optical testing with a phase-only liquid crystal spatial light modulator,” Opt. Express 13, 1059-1065 (2005).
    [CrossRef] [PubMed]
  13. J. A. Jordan, P. M. Hirsch, L. B. Lesem, and D. L. Van Rooy, “Kinoform lenses,” Appl. Opt. 9, 1883-1887 (1970).
    [PubMed]
  14. Z. Cao, L. Xuan, L. Hu, Y. Liu, and Q. Mu, “Effects of the space-bandwidth product on the liquid-crystal kinoform,” Opt. Express 13, 5186-5191 (2005).
    [CrossRef] [PubMed]
  15. Z. Cao, Q. Mu, L. Hu, Y. Liu, Z. Peng, and L. Xuan, “Diffractive characteristics of the liquid crystal spatial light modulator,” Chin. Phys. 16, 1665-1671 (2007).
    [CrossRef]
  16. M. Ferstl, B. Kuhlow, and E. Pawlowski, “Effect of fabrication errors on multilevel Fresnel zone lens,” Opt. Eng. 33, 1229-1235 (1994).
    [CrossRef]
  17. P.-Y. Madec, “Control techniques,” in Adaptive Optics in Astronomy, F. Roddier, ed. (Cambridge University Press, 1999), pp. 131-154.
    [CrossRef]

2007 (2)

Z. Cao, Q. Mu, L. Hu, Y. Liu, Z. Peng, and L. Xuan, “Diffractive characteristics of the liquid crystal spatial light modulator,” Chin. Phys. 16, 1665-1671 (2007).
[CrossRef]

Q. Mu, Z. Cao, D. Li, L. Hu, and L. Xuan, “Liquid crystal based adaptive optics system to compensate both low and high order aberrations in model eye,” Opt. Express 15, 1946-1953 (2007).
[CrossRef] [PubMed]

2006 (1)

2005 (3)

2004 (2)

D. Dayton, J. Gonglewski, S. Restaino, and S. Browne, “MEMS adaptive optics for high resolution imaging of low Earth orbit satellites,” Proc. SPIE 5490, 1514-1525 (2004).
[CrossRef]

L. Hu, L. Xuan, Y. Liu, Z. Cao, D. Li, and Q. Mu, “Phase-only liquid crystal spatial light modulator for wavefront correction with high precision,” Opt. Express 12, 6403-6409 (2004).
[CrossRef] [PubMed]

2002 (1)

1998 (1)

F. Vargas-Martín and P. Artal, “Phasor averaging for wavefront correction with liquid crystal spatial light modulators,” Opt. Commun. 152, 233-238 (1998).
[CrossRef]

1997 (1)

1994 (1)

M. Ferstl, B. Kuhlow, and E. Pawlowski, “Effect of fabrication errors on multilevel Fresnel zone lens,” Opt. Eng. 33, 1229-1235 (1994).
[CrossRef]

1988 (1)

1985 (2)

U. Efron, J. Grinberg, P. O. Braatz, M. J. Little, P. G. Reif, and R. N. Schwartz, “The silicon liquid-crystal light valve”, J. Appl. Phys. 57, 1356-1368 (1985).
[CrossRef]

U. Efron, S. T. Wu, J. Grinberg, and L. D. Hess, “Liquid-crystal-based visible-to-infrared dynamic image converter,” Opt. Eng. 24, 111-118 (1985).

1970 (1)

Artal, P.

F. Vargas-Martín and P. Artal, “Phasor averaging for wavefront correction with liquid crystal spatial light modulators,” Opt. Commun. 152, 233-238 (1998).
[CrossRef]

Braatz, P. O.

U. Efron, J. Grinberg, P. O. Braatz, M. J. Little, P. G. Reif, and R. N. Schwartz, “The silicon liquid-crystal light valve”, J. Appl. Phys. 57, 1356-1368 (1985).
[CrossRef]

Browne, S.

D. Dayton, J. Gonglewski, S. Restaino, and S. Browne, “MEMS adaptive optics for high resolution imaging of low Earth orbit satellites,” Proc. SPIE 5490, 1514-1525 (2004).
[CrossRef]

Cao, Z.

Dayton, D.

D. Dayton, J. Gonglewski, S. Restaino, and S. Browne, “MEMS adaptive optics for high resolution imaging of low Earth orbit satellites,” Proc. SPIE 5490, 1514-1525 (2004).
[CrossRef]

D. Dayton, J. Gonglewski, and S. Restaino et al., “Demonstration of new technology MEMS and liquid crystal adaptive optics on bright astronomical objects and satellites,” Opt. Express 10, 1508-1519 (2002).
[PubMed]

Efron, U.

U. Efron, J. Grinberg, P. O. Braatz, M. J. Little, P. G. Reif, and R. N. Schwartz, “The silicon liquid-crystal light valve”, J. Appl. Phys. 57, 1356-1368 (1985).
[CrossRef]

U. Efron, S. T. Wu, J. Grinberg, and L. D. Hess, “Liquid-crystal-based visible-to-infrared dynamic image converter,” Opt. Eng. 24, 111-118 (1985).

Ferstl, M.

M. Ferstl, B. Kuhlow, and E. Pawlowski, “Effect of fabrication errors on multilevel Fresnel zone lens,” Opt. Eng. 33, 1229-1235 (1994).
[CrossRef]

Gonglewski, J.

D. Dayton, J. Gonglewski, S. Restaino, and S. Browne, “MEMS adaptive optics for high resolution imaging of low Earth orbit satellites,” Proc. SPIE 5490, 1514-1525 (2004).
[CrossRef]

D. Dayton, J. Gonglewski, and S. Restaino et al., “Demonstration of new technology MEMS and liquid crystal adaptive optics on bright astronomical objects and satellites,” Opt. Express 10, 1508-1519 (2002).
[PubMed]

Grinberg, J.

U. Efron, J. Grinberg, P. O. Braatz, M. J. Little, P. G. Reif, and R. N. Schwartz, “The silicon liquid-crystal light valve”, J. Appl. Phys. 57, 1356-1368 (1985).
[CrossRef]

U. Efron, S. T. Wu, J. Grinberg, and L. D. Hess, “Liquid-crystal-based visible-to-infrared dynamic image converter,” Opt. Eng. 24, 111-118 (1985).

Hess, L. D.

U. Efron, S. T. Wu, J. Grinberg, and L. D. Hess, “Liquid-crystal-based visible-to-infrared dynamic image converter,” Opt. Eng. 24, 111-118 (1985).

Hirsch, P. M.

Hu, L.

Jordan, J. A.

Konforti, N.

Kuhlow, B.

M. Ferstl, B. Kuhlow, and E. Pawlowski, “Effect of fabrication errors on multilevel Fresnel zone lens,” Opt. Eng. 33, 1229-1235 (1994).
[CrossRef]

Lesem, L. B.

Li, D.

Little, M. J.

U. Efron, J. Grinberg, P. O. Braatz, M. J. Little, P. G. Reif, and R. N. Schwartz, “The silicon liquid-crystal light valve”, J. Appl. Phys. 57, 1356-1368 (1985).
[CrossRef]

Liu, Y.

Love, G. D.

Madec, P.-Y.

P.-Y. Madec, “Control techniques,” in Adaptive Optics in Astronomy, F. Roddier, ed. (Cambridge University Press, 1999), pp. 131-154.
[CrossRef]

Marom, E.

Mu, Q.

Pawlowski, E.

M. Ferstl, B. Kuhlow, and E. Pawlowski, “Effect of fabrication errors on multilevel Fresnel zone lens,” Opt. Eng. 33, 1229-1235 (1994).
[CrossRef]

Peng, Z.

Z. Cao, Q. Mu, L. Hu, Y. Liu, Z. Peng, and L. Xuan, “Diffractive characteristics of the liquid crystal spatial light modulator,” Chin. Phys. 16, 1665-1671 (2007).
[CrossRef]

Reif, P. G.

U. Efron, J. Grinberg, P. O. Braatz, M. J. Little, P. G. Reif, and R. N. Schwartz, “The silicon liquid-crystal light valve”, J. Appl. Phys. 57, 1356-1368 (1985).
[CrossRef]

Restaino, S.

D. Dayton, J. Gonglewski, S. Restaino, and S. Browne, “MEMS adaptive optics for high resolution imaging of low Earth orbit satellites,” Proc. SPIE 5490, 1514-1525 (2004).
[CrossRef]

D. Dayton, J. Gonglewski, and S. Restaino et al., “Demonstration of new technology MEMS and liquid crystal adaptive optics on bright astronomical objects and satellites,” Opt. Express 10, 1508-1519 (2002).
[PubMed]

Schwartz, R. N.

U. Efron, J. Grinberg, P. O. Braatz, M. J. Little, P. G. Reif, and R. N. Schwartz, “The silicon liquid-crystal light valve”, J. Appl. Phys. 57, 1356-1368 (1985).
[CrossRef]

Serati, S.

S. Serati and J. Stockley, “Advances in liquid crystal based devices for wavefront control and beam steering,” Proc. SPIE 5894, 58940K-1-58940K-13 (2005).

Stockley, J.

S. Serati and J. Stockley, “Advances in liquid crystal based devices for wavefront control and beam steering,” Proc. SPIE 5894, 58940K-1-58940K-13 (2005).

Van Rooy, D. L.

Vargas-Martín, F.

F. Vargas-Martín and P. Artal, “Phasor averaging for wavefront correction with liquid crystal spatial light modulators,” Opt. Commun. 152, 233-238 (1998).
[CrossRef]

Wu, S. T.

N. Konforti, E. Marom, and S. T. Wu, “Phase-only modulation with twisted nematic liquid-crystal spatial light modulators,” Opt. Lett. 13, 251-253 (1988).
[CrossRef] [PubMed]

U. Efron, S. T. Wu, J. Grinberg, and L. D. Hess, “Liquid-crystal-based visible-to-infrared dynamic image converter,” Opt. Eng. 24, 111-118 (1985).

Xuan, L.

Appl. Opt. (2)

Chin. Phys. (1)

Z. Cao, Q. Mu, L. Hu, Y. Liu, Z. Peng, and L. Xuan, “Diffractive characteristics of the liquid crystal spatial light modulator,” Chin. Phys. 16, 1665-1671 (2007).
[CrossRef]

J. Appl. Phys. (1)

U. Efron, J. Grinberg, P. O. Braatz, M. J. Little, P. G. Reif, and R. N. Schwartz, “The silicon liquid-crystal light valve”, J. Appl. Phys. 57, 1356-1368 (1985).
[CrossRef]

Opt. Commun. (1)

F. Vargas-Martín and P. Artal, “Phasor averaging for wavefront correction with liquid crystal spatial light modulators,” Opt. Commun. 152, 233-238 (1998).
[CrossRef]

Opt. Eng. (2)

U. Efron, S. T. Wu, J. Grinberg, and L. D. Hess, “Liquid-crystal-based visible-to-infrared dynamic image converter,” Opt. Eng. 24, 111-118 (1985).

M. Ferstl, B. Kuhlow, and E. Pawlowski, “Effect of fabrication errors on multilevel Fresnel zone lens,” Opt. Eng. 33, 1229-1235 (1994).
[CrossRef]

Opt. Express (6)

Opt. Lett. (1)

Proc. SPIE (2)

S. Serati and J. Stockley, “Advances in liquid crystal based devices for wavefront control and beam steering,” Proc. SPIE 5894, 58940K-1-58940K-13 (2005).

D. Dayton, J. Gonglewski, S. Restaino, and S. Browne, “MEMS adaptive optics for high resolution imaging of low Earth orbit satellites,” Proc. SPIE 5490, 1514-1525 (2004).
[CrossRef]

Other (1)

P.-Y. Madec, “Control techniques,” in Adaptive Optics in Astronomy, F. Roddier, ed. (Cambridge University Press, 1999), pp. 131-154.
[CrossRef]

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (9)

Fig. 1
Fig. 1

Simplified model of the RLC WFC with tilt incidence.

Fig. 2
Fig. 2

Phase shift as a function of the incident angle; • is the measured curve; ⋆ represents the simulated data.

Fig. 3
Fig. 3

Illustration of the pixel crossover; P1, P2, and P3 are pixels, d is the thickness of the cell

Fig. 4
Fig. 4

Pixel crossover W as a function of incident angle.

Fig. 5
Fig. 5

Principle of the kinoform technique with quantification.

Fig. 6
Fig. 6

Diffraction efficiency as a function of the incident angle.

Fig. 7
Fig. 7

Optical layout for the closed loop correction experiment; L1, L2, L3, L4, and L5 are the achromatic lens, M is the mirror, WFS is the wavefront sensor.

Fig. 8
Fig. 8

Phase distribution of the wavefront: (a) the distorted wavefront and (b) the corrected wavefront.

Fig. 9
Fig. 9

Image of the fiber bundle achieved with the CCD camera: (a) without correction and (b) the corrected image.

Equations (3)

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

n e ( θ ) = n o n e ( n o 2 cos 2 θ + n e 2 sin 2 θ ) 1 / 2 ,
P tilt = 2 π ( n e ( θ ) n o ) d λ cos θ .
P tilt = 2 π ( n e ( θ + θ 0 ) n o ) d λ cos θ ,

Metrics