Abstract

Results are presented of the properties of a liquid crystal wavefront corrector for adaptive optics. The device is controlled using modal addressing in which case the device behaves more like a continuous facesheet deformable mirror than a segmented one. Furthermore, the width and shape of the influence functions are electrically controllable. We describe the construction of the device, the optical properties, and we show experimental results of low order aberration generation.

© 2002 Optical Society of America

Full Article  |  PDF Article
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References

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  1. R. H. Freeman and J. E. Pearson, “Deformable mirrors for all seasons and reasons,” Appl. Opt. 21, 580–588 (1982).
    [Crossref] [PubMed]
  2. G. Vdovin, S. Middlehoek, and P.M. Sarro, “Technology and application of micromachined silicon adaptive mirrors,” Opt. Eng. 35, 1382–1390 (1997).
    [Crossref]
  3. C. Paterson, I. Munro, and J.C. Dainty, “A low cost adaptive optics system using a membrane mirror,” Opt. Express 6, 175–185 (2000) http://www.opticsexpress.org/abstract.cfm?URI=OPEX-6-9-175
    [Crossref] [PubMed]
  4. D. Dayton, S.R. Restaino, J. Gonglewski, J. Gallegos, S. McDermott, S. Browne, S. Rogers, M. Vaidyanathan, and M. Shilko. “Laboratory and field demonstration of a low cost membrane mirror adaptive optics system,” Opt. Commun. 176, 339–345 (2000)
    [Crossref]
  5. Gordon D. Love. “Liquid crystal adaptive optics.” In Adaptive Optics Engineering Handbook, Robert K. Tyson, Ed. (Marcel Dekker Inc, 1999) and references therein.
    [Crossref]
  6. S.R. Restaino, D. Dayton, S. Browne, J. Gonglewski, J. Baker, S. Rogers, S. McDermott, J. Gallegos, and M. Shilko, “On the use of dual-frequency nematic material for adaptive optics systems: first results of a closed-loop experiment,” Opt. Express 6, 2–6 (2000). http://www.opticsexpress.org/abstract.cfm?URI=OPEX-4-9-344
    [Crossref] [PubMed]
  7. D. Dayton, S. Browne, J. Gonglewski, and S.R. Restaino. “Characterization and control of a multielement dual-frequency liquid-crystal device for high-speed adaptive optical wave-front correction,” Appl. Opt. 40, 2345–2355(2001)
    [Crossref]
  8. G.D. Love, “Liquid-crystal phase modulator for unpolarized light,“ Appl. Opt. 32, 2222–2223 (1993).
    [Crossref] [PubMed]
  9. Thu-Lan Kelly and Gordon D. Love. “White-light performance of a polarization-independent liquid crystal phase modulator,” Appl. Opt. 38,1986–1989 (1999).
    [Crossref]
  10. Gordon D. Love, “Wavefront correction and production of Zernike modes with a liquid crystal SLM,” Appl. Opt. 36, 1517–1524(1997).
    [Crossref] [PubMed]
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    [Crossref] [PubMed]
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    [Crossref]
  14. G. V. Vdovin, I. R. Guralnik, S. P. Kotova, M. Yu. Loktev, and A. F. Naumov, “Liquid crystal lenses with programmable focal distance. Part I: Theory, Part II: Experiment,” Quantum Electron. 29, 256–264 (1999).
    [Crossref]
  15. A. F. Naumov, “Modal wavefront correctors,” Proc. P. N. Lebedev Physical Institute 217, 177–182 (1993).
  16. A. F. Naumov and G. V. Vdovin, “Multichannel LC-based wavefront corrector with modal influence functions,” Opt. Lett. 23, 1550–1552 (1998).
    [Crossref]
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  18. I. Guralnik, M. Loktev, and A. Naumov, “Modal control principle: a new way to the design of liquid-crystal adaptive optics devices,” in Propagation in the Atmosphere and Adaptive Optics.Proc. SPIE 4338, 171–181, 2000.
    [Crossref]
  19. I. R. Guralnik, V. N. Belopukhov, G. D. Love, and A. F. Naumov, “Interdependence of the electrical and optical properties of liquid crystals for phase modulation applications,” J. Appl. Phys. 87, 4069–4074 (2000).
    [Crossref]
  20. A. Korn and M. KornMathematical Handbook (McGraw-Hill, 1968).
  21. M.B. Allen and E.I. Isaacson, Numerical analysis for applied science (Wiley, New York, 1998).
  22. http://www.cyanogen.com/products/quickfringe
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    [Crossref]
  24. Xilinx Inc., San Jose, Ca. http://www.xilinx.com/
  25. X Engineering Software Systems Corp., Apex, NC. http://www.xess.com
  26. M. Loktev, G. Vdovin, and P. Sarro. “Development of a silicon based modal liquid crystal wavefront corrector,” To be published in SPIE (2002)

2001 (1)

2000 (5)

C. Paterson, I. Munro, and J.C. Dainty, “A low cost adaptive optics system using a membrane mirror,” Opt. Express 6, 175–185 (2000) http://www.opticsexpress.org/abstract.cfm?URI=OPEX-6-9-175
[Crossref] [PubMed]

D. Dayton, S.R. Restaino, J. Gonglewski, J. Gallegos, S. McDermott, S. Browne, S. Rogers, M. Vaidyanathan, and M. Shilko. “Laboratory and field demonstration of a low cost membrane mirror adaptive optics system,” Opt. Commun. 176, 339–345 (2000)
[Crossref]

S.R. Restaino, D. Dayton, S. Browne, J. Gonglewski, J. Baker, S. Rogers, S. McDermott, J. Gallegos, and M. Shilko, “On the use of dual-frequency nematic material for adaptive optics systems: first results of a closed-loop experiment,” Opt. Express 6, 2–6 (2000). http://www.opticsexpress.org/abstract.cfm?URI=OPEX-4-9-344
[Crossref] [PubMed]

I. Guralnik, M. Loktev, and A. Naumov, “Modal control principle: a new way to the design of liquid-crystal adaptive optics devices,” in Propagation in the Atmosphere and Adaptive Optics.Proc. SPIE 4338, 171–181, 2000.
[Crossref]

I. R. Guralnik, V. N. Belopukhov, G. D. Love, and A. F. Naumov, “Interdependence of the electrical and optical properties of liquid crystals for phase modulation applications,” J. Appl. Phys. 87, 4069–4074 (2000).
[Crossref]

1999 (3)

O. A. Zayakin, M. Yu. Loktev, G. D. Love, and A. F. Naumov, “Cylindrical adaptive lenses,” in 6th International Symposium on Atmospheric and Ocean Optics, Proc. SPIE 3983, 112–117 (1999).
[Crossref]

G. V. Vdovin, I. R. Guralnik, S. P. Kotova, M. Yu. Loktev, and A. F. Naumov, “Liquid crystal lenses with programmable focal distance. Part I: Theory, Part II: Experiment,” Quantum Electron. 29, 256–264 (1999).
[Crossref]

Thu-Lan Kelly and Gordon D. Love. “White-light performance of a polarization-independent liquid crystal phase modulator,” Appl. Opt. 38,1986–1989 (1999).
[Crossref]

1998 (1)

1997 (2)

Gordon D. Love, “Wavefront correction and production of Zernike modes with a liquid crystal SLM,” Appl. Opt. 36, 1517–1524(1997).
[Crossref] [PubMed]

G. Vdovin, S. Middlehoek, and P.M. Sarro, “Technology and application of micromachined silicon adaptive mirrors,” Opt. Eng. 35, 1382–1390 (1997).
[Crossref]

1994 (1)

1993 (2)

G.D. Love, “Liquid-crystal phase modulator for unpolarized light,“ Appl. Opt. 32, 2222–2223 (1993).
[Crossref] [PubMed]

A. F. Naumov, “Modal wavefront correctors,” Proc. P. N. Lebedev Physical Institute 217, 177–182 (1993).

1986 (1)

1982 (1)

Allen, M.B.

M.B. Allen and E.I. Isaacson, Numerical analysis for applied science (Wiley, New York, 1998).

Baker, J.

Bates, T. D.

Belopukhov, V. N.

I. R. Guralnik, V. N. Belopukhov, G. D. Love, and A. F. Naumov, “Interdependence of the electrical and optical properties of liquid crystals for phase modulation applications,” J. Appl. Phys. 87, 4069–4074 (2000).
[Crossref]

Browne, S.

Dainty, J.C.

Dayton, D.

Efron, U.

Freeman, R. H.

Gallegos, J.

S.R. Restaino, D. Dayton, S. Browne, J. Gonglewski, J. Baker, S. Rogers, S. McDermott, J. Gallegos, and M. Shilko, “On the use of dual-frequency nematic material for adaptive optics systems: first results of a closed-loop experiment,” Opt. Express 6, 2–6 (2000). http://www.opticsexpress.org/abstract.cfm?URI=OPEX-4-9-344
[Crossref] [PubMed]

D. Dayton, S.R. Restaino, J. Gonglewski, J. Gallegos, S. McDermott, S. Browne, S. Rogers, M. Vaidyanathan, and M. Shilko. “Laboratory and field demonstration of a low cost membrane mirror adaptive optics system,” Opt. Commun. 176, 339–345 (2000)
[Crossref]

Gonglewski, J.

Guralnik, I.

I. Guralnik, M. Loktev, and A. Naumov, “Modal control principle: a new way to the design of liquid-crystal adaptive optics devices,” in Propagation in the Atmosphere and Adaptive Optics.Proc. SPIE 4338, 171–181, 2000.
[Crossref]

Guralnik, I. R.

I. R. Guralnik, V. N. Belopukhov, G. D. Love, and A. F. Naumov, “Interdependence of the electrical and optical properties of liquid crystals for phase modulation applications,” J. Appl. Phys. 87, 4069–4074 (2000).
[Crossref]

G. V. Vdovin, I. R. Guralnik, S. P. Kotova, M. Yu. Loktev, and A. F. Naumov, “Liquid crystal lenses with programmable focal distance. Part I: Theory, Part II: Experiment,” Quantum Electron. 29, 256–264 (1999).
[Crossref]

S. P. Kotova, I. R. Guralnik, M. Yu. Loktev, and A. F. Naumov, “Adaptive optics modal LC devices,” in Proceedings of First Asia-Pacific Conference APCOM’2000 (Vladivostok, Russia),“Fundamental problems of opto- and microelectronics” 183–189 (2000).

Isaacson, E.I.

M.B. Allen and E.I. Isaacson, Numerical analysis for applied science (Wiley, New York, 1998).

Kelly, Thu-Lan

Korn, A.

A. Korn and M. KornMathematical Handbook (McGraw-Hill, 1968).

Korn, M.

A. Korn and M. KornMathematical Handbook (McGraw-Hill, 1968).

Kotova, S. P.

G. V. Vdovin, I. R. Guralnik, S. P. Kotova, M. Yu. Loktev, and A. F. Naumov, “Liquid crystal lenses with programmable focal distance. Part I: Theory, Part II: Experiment,” Quantum Electron. 29, 256–264 (1999).
[Crossref]

S. P. Kotova, I. R. Guralnik, M. Yu. Loktev, and A. F. Naumov, “Adaptive optics modal LC devices,” in Proceedings of First Asia-Pacific Conference APCOM’2000 (Vladivostok, Russia),“Fundamental problems of opto- and microelectronics” 183–189 (2000).

Loktev, M.

I. Guralnik, M. Loktev, and A. Naumov, “Modal control principle: a new way to the design of liquid-crystal adaptive optics devices,” in Propagation in the Atmosphere and Adaptive Optics.Proc. SPIE 4338, 171–181, 2000.
[Crossref]

M. Loktev, G. Vdovin, and P. Sarro. “Development of a silicon based modal liquid crystal wavefront corrector,” To be published in SPIE (2002)

Loktev, M. Yu.

G. V. Vdovin, I. R. Guralnik, S. P. Kotova, M. Yu. Loktev, and A. F. Naumov, “Liquid crystal lenses with programmable focal distance. Part I: Theory, Part II: Experiment,” Quantum Electron. 29, 256–264 (1999).
[Crossref]

O. A. Zayakin, M. Yu. Loktev, G. D. Love, and A. F. Naumov, “Cylindrical adaptive lenses,” in 6th International Symposium on Atmospheric and Ocean Optics, Proc. SPIE 3983, 112–117 (1999).
[Crossref]

S. P. Kotova, I. R. Guralnik, M. Yu. Loktev, and A. F. Naumov, “Adaptive optics modal LC devices,” in Proceedings of First Asia-Pacific Conference APCOM’2000 (Vladivostok, Russia),“Fundamental problems of opto- and microelectronics” 183–189 (2000).

Love, G.

Love, G. D.

I. R. Guralnik, V. N. Belopukhov, G. D. Love, and A. F. Naumov, “Interdependence of the electrical and optical properties of liquid crystals for phase modulation applications,” J. Appl. Phys. 87, 4069–4074 (2000).
[Crossref]

O. A. Zayakin, M. Yu. Loktev, G. D. Love, and A. F. Naumov, “Cylindrical adaptive lenses,” in 6th International Symposium on Atmospheric and Ocean Optics, Proc. SPIE 3983, 112–117 (1999).
[Crossref]

Love, G.D.

Love, Gordon D.

Major, J.

McDermott, S.

S.R. Restaino, D. Dayton, S. Browne, J. Gonglewski, J. Baker, S. Rogers, S. McDermott, J. Gallegos, and M. Shilko, “On the use of dual-frequency nematic material for adaptive optics systems: first results of a closed-loop experiment,” Opt. Express 6, 2–6 (2000). http://www.opticsexpress.org/abstract.cfm?URI=OPEX-4-9-344
[Crossref] [PubMed]

D. Dayton, S.R. Restaino, J. Gonglewski, J. Gallegos, S. McDermott, S. Browne, S. Rogers, M. Vaidyanathan, and M. Shilko. “Laboratory and field demonstration of a low cost membrane mirror adaptive optics system,” Opt. Commun. 176, 339–345 (2000)
[Crossref]

Middlehoek, S.

G. Vdovin, S. Middlehoek, and P.M. Sarro, “Technology and application of micromachined silicon adaptive mirrors,” Opt. Eng. 35, 1382–1390 (1997).
[Crossref]

Munro, I.

Naumov, A.

I. Guralnik, M. Loktev, and A. Naumov, “Modal control principle: a new way to the design of liquid-crystal adaptive optics devices,” in Propagation in the Atmosphere and Adaptive Optics.Proc. SPIE 4338, 171–181, 2000.
[Crossref]

Naumov, A. F.

I. R. Guralnik, V. N. Belopukhov, G. D. Love, and A. F. Naumov, “Interdependence of the electrical and optical properties of liquid crystals for phase modulation applications,” J. Appl. Phys. 87, 4069–4074 (2000).
[Crossref]

G. V. Vdovin, I. R. Guralnik, S. P. Kotova, M. Yu. Loktev, and A. F. Naumov, “Liquid crystal lenses with programmable focal distance. Part I: Theory, Part II: Experiment,” Quantum Electron. 29, 256–264 (1999).
[Crossref]

O. A. Zayakin, M. Yu. Loktev, G. D. Love, and A. F. Naumov, “Cylindrical adaptive lenses,” in 6th International Symposium on Atmospheric and Ocean Optics, Proc. SPIE 3983, 112–117 (1999).
[Crossref]

A. F. Naumov and G. V. Vdovin, “Multichannel LC-based wavefront corrector with modal influence functions,” Opt. Lett. 23, 1550–1552 (1998).
[Crossref]

A. F. Naumov, “Modal wavefront correctors,” Proc. P. N. Lebedev Physical Institute 217, 177–182 (1993).

S. P. Kotova, I. R. Guralnik, M. Yu. Loktev, and A. F. Naumov, “Adaptive optics modal LC devices,” in Proceedings of First Asia-Pacific Conference APCOM’2000 (Vladivostok, Russia),“Fundamental problems of opto- and microelectronics” 183–189 (2000).

A. F. Naumov “Wavefront correctors based on liquid crystal modulators,” in XVI All-Union Tutorial: Physical Principles of Holography, “Holography methods in science and technique,” Leningrad216–221 (1985).

Paterson, C.

Pearson, J. E.

Purvis, A.

Restaino, S.R.

Rogers, S.

D. Dayton, S.R. Restaino, J. Gonglewski, J. Gallegos, S. McDermott, S. Browne, S. Rogers, M. Vaidyanathan, and M. Shilko. “Laboratory and field demonstration of a low cost membrane mirror adaptive optics system,” Opt. Commun. 176, 339–345 (2000)
[Crossref]

S.R. Restaino, D. Dayton, S. Browne, J. Gonglewski, J. Baker, S. Rogers, S. McDermott, J. Gallegos, and M. Shilko, “On the use of dual-frequency nematic material for adaptive optics systems: first results of a closed-loop experiment,” Opt. Express 6, 2–6 (2000). http://www.opticsexpress.org/abstract.cfm?URI=OPEX-4-9-344
[Crossref] [PubMed]

Sarro, P.

M. Loktev, G. Vdovin, and P. Sarro. “Development of a silicon based modal liquid crystal wavefront corrector,” To be published in SPIE (2002)

Sarro, P.M.

G. Vdovin, S. Middlehoek, and P.M. Sarro, “Technology and application of micromachined silicon adaptive mirrors,” Opt. Eng. 35, 1382–1390 (1997).
[Crossref]

Shilko, M.

D. Dayton, S.R. Restaino, J. Gonglewski, J. Gallegos, S. McDermott, S. Browne, S. Rogers, M. Vaidyanathan, and M. Shilko. “Laboratory and field demonstration of a low cost membrane mirror adaptive optics system,” Opt. Commun. 176, 339–345 (2000)
[Crossref]

S.R. Restaino, D. Dayton, S. Browne, J. Gonglewski, J. Baker, S. Rogers, S. McDermott, J. Gallegos, and M. Shilko, “On the use of dual-frequency nematic material for adaptive optics systems: first results of a closed-loop experiment,” Opt. Express 6, 2–6 (2000). http://www.opticsexpress.org/abstract.cfm?URI=OPEX-4-9-344
[Crossref] [PubMed]

Vaidyanathan, M.

D. Dayton, S.R. Restaino, J. Gonglewski, J. Gallegos, S. McDermott, S. Browne, S. Rogers, M. Vaidyanathan, and M. Shilko. “Laboratory and field demonstration of a low cost membrane mirror adaptive optics system,” Opt. Commun. 176, 339–345 (2000)
[Crossref]

Vdovin, G.

G. Vdovin, S. Middlehoek, and P.M. Sarro, “Technology and application of micromachined silicon adaptive mirrors,” Opt. Eng. 35, 1382–1390 (1997).
[Crossref]

M. Loktev, G. Vdovin, and P. Sarro. “Development of a silicon based modal liquid crystal wavefront corrector,” To be published in SPIE (2002)

Vdovin, G. V.

G. V. Vdovin, I. R. Guralnik, S. P. Kotova, M. Yu. Loktev, and A. F. Naumov, “Liquid crystal lenses with programmable focal distance. Part I: Theory, Part II: Experiment,” Quantum Electron. 29, 256–264 (1999).
[Crossref]

A. F. Naumov and G. V. Vdovin, “Multichannel LC-based wavefront corrector with modal influence functions,” Opt. Lett. 23, 1550–1552 (1998).
[Crossref]

Wu, S. T.

Zayakin, O. A.

O. A. Zayakin, M. Yu. Loktev, G. D. Love, and A. F. Naumov, “Cylindrical adaptive lenses,” in 6th International Symposium on Atmospheric and Ocean Optics, Proc. SPIE 3983, 112–117 (1999).
[Crossref]

Appl. Opt. (5)

J. Appl. Phys. (1)

I. R. Guralnik, V. N. Belopukhov, G. D. Love, and A. F. Naumov, “Interdependence of the electrical and optical properties of liquid crystals for phase modulation applications,” J. Appl. Phys. 87, 4069–4074 (2000).
[Crossref]

J. Opt. Soc. Am. B (1)

Opt. Commun. (1)

D. Dayton, S.R. Restaino, J. Gonglewski, J. Gallegos, S. McDermott, S. Browne, S. Rogers, M. Vaidyanathan, and M. Shilko. “Laboratory and field demonstration of a low cost membrane mirror adaptive optics system,” Opt. Commun. 176, 339–345 (2000)
[Crossref]

Opt. Eng. (1)

G. Vdovin, S. Middlehoek, and P.M. Sarro, “Technology and application of micromachined silicon adaptive mirrors,” Opt. Eng. 35, 1382–1390 (1997).
[Crossref]

Opt. Express (2)

Opt. Lett. (2)

Proc. P. N. Lebedev Physical Institute (1)

A. F. Naumov, “Modal wavefront correctors,” Proc. P. N. Lebedev Physical Institute 217, 177–182 (1993).

Proc. SPIE (2)

O. A. Zayakin, M. Yu. Loktev, G. D. Love, and A. F. Naumov, “Cylindrical adaptive lenses,” in 6th International Symposium on Atmospheric and Ocean Optics, Proc. SPIE 3983, 112–117 (1999).
[Crossref]

I. Guralnik, M. Loktev, and A. Naumov, “Modal control principle: a new way to the design of liquid-crystal adaptive optics devices,” in Propagation in the Atmosphere and Adaptive Optics.Proc. SPIE 4338, 171–181, 2000.
[Crossref]

Quantum Electron. (1)

G. V. Vdovin, I. R. Guralnik, S. P. Kotova, M. Yu. Loktev, and A. F. Naumov, “Liquid crystal lenses with programmable focal distance. Part I: Theory, Part II: Experiment,” Quantum Electron. 29, 256–264 (1999).
[Crossref]

Other (9)

A. Korn and M. KornMathematical Handbook (McGraw-Hill, 1968).

M.B. Allen and E.I. Isaacson, Numerical analysis for applied science (Wiley, New York, 1998).

http://www.cyanogen.com/products/quickfringe

Gordon D. Love. “Liquid crystal adaptive optics.” In Adaptive Optics Engineering Handbook, Robert K. Tyson, Ed. (Marcel Dekker Inc, 1999) and references therein.
[Crossref]

A. F. Naumov “Wavefront correctors based on liquid crystal modulators,” in XVI All-Union Tutorial: Physical Principles of Holography, “Holography methods in science and technique,” Leningrad216–221 (1985).

S. P. Kotova, I. R. Guralnik, M. Yu. Loktev, and A. F. Naumov, “Adaptive optics modal LC devices,” in Proceedings of First Asia-Pacific Conference APCOM’2000 (Vladivostok, Russia),“Fundamental problems of opto- and microelectronics” 183–189 (2000).

Xilinx Inc., San Jose, Ca. http://www.xilinx.com/

X Engineering Software Systems Corp., Apex, NC. http://www.xess.com

M. Loktev, G. Vdovin, and P. Sarro. “Development of a silicon based modal liquid crystal wavefront corrector,” To be published in SPIE (2002)

Supplementary Material (4)

» Media 1: MPG (548 KB)     
» Media 2: MPG (548 KB)     
» Media 3: MPG (412 KB)     
» Media 4: MPG (448 KB)     

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Figures (15)

Fig. 1.
Fig. 1.

a) Schematic diagram of a multichannel LC wavefront corrector; b) contact arrangement; c) simplified equivalent circuit: ρ is the sheet resistance of the high resistance electrode, c and g denote the capacitance and conductance of the LC layer per unit area. Ø denotes an external electrical connection.

Fig 2.
Fig 2.

Experimental and theoretical curves for the dependence of the rms voltage across the cell versus the distance from the contact, for an applied voltage of 5V. The lines show the theoretical results (continuous = 100 Hz, and dashed = 1KHz) and the points show the experimental points for 100 Hz (squares) and 1Khz (diamonds).

Fig 3.
Fig 3.

Experimental apparatus for measuring the optical characteristics of the LC-MWC. In the setup shown, the apparatus can be used to measure the global properties (such as voltage-phase response, and switching times). Lens 2, the diaphragm, and the photodiode are replaced with the inset apparatus (lens 3, CCD and monitor) to image the device.

Fig. 4.
Fig. 4.

The central part of the LC-MWC showing how the influence function varies with both the amplitude and frequency of the voltage. a) V= 4V, f =100 Hz; b) V= 10V, f =100 Hz; c) V= 10V, f =10241Hz. The other contacts are not earthed. N.B. The field of view of each photo is slightly different, but the spacing between the contacts can be used as a measure of scale.

Fig. 5.
Fig. 5.

Half-widths of the influence function versus (a) frequency and (b) voltage. Curve 1 corresponds to the case when the adjacent contacts are not connected, and curve 2 - when they are grounded. The horizontal dotted line shows the spacing between contacts.

Fig. 6.
Fig. 6.

Polarization interferograms for the central part of the LC-MWC for different applied control signals. fcen = frequency on central electrode. fadj = frequency on the electrodes adjacent to the central electrode.

Fig. 7.
Fig. 7.

Movies showing how the voltage applied to the contacts affects the influence functions. In 7a. (547 KB) the voltage is increased from 0 to 20V on the central electrode at a frequency of 20Hz. The other contacts are not earthed. 7b (547 KB) is identical except that the surrounding electrodes are earthed. In 7c. (412 KB) the voltage is fixed at 20V and the frequency varies from 50 Hz to 90KHz (the other connections are earthed). A 20V 50Hz voltage is applied to two adjacent contacts in 7d (447 KB) and the relative phase is varied from 0 to π. The dark band across the whole field is due to a non-uniform LC layer. Some further blemishes in the cell can be seen as dark marks. The fringes are not distinct because of losses due to file compression.

Fig. 8.
Fig. 8.

Total intensity modulation of reflected laser beam from LC-MWC, obtained by means of polarizer.

Fig. 9.
Fig. 9.

The LC-MWC with a constant voltage and frequency being applied to all the contacts: top -10V, bottom - 2V. The voltage varies by a small amount in between the control contacts, but because the voltage-phase response is non-linear (with the highest sensitivity at low voltages) then the phase varies across the device for low voltages, as shown.

Fig. 10.
Fig. 10.

Voltage-phase shift dependencies for LC-MWC (1) and for LC material (2).

Fig. 11.
Fig. 11.

Theoretical voltage response functions of the LC-MWC for a single-frequency control voltage: (a) f=40 Hz; (b) 10 kHz; (c) 100 kHz; the results are obtained by numerical simulation.

Fig. 12.
Fig. 12.

Comparison of calculated and experimental phase distributions for 37-contact MCC prototype with hexagonal arrangement of contacts: (a) parabola with positive sign, numerical simulation; b) parabola with positive sign, experiment; (c) parabola with negative sign, numerical simulation; d) parabola with negative sign, experiment.

Fig. 13.
Fig. 13.

(a) A photo front a rear connectors of a 33mm aperture device. (b)-(f) Qualitative generation of low order Zernike modes: (b) tilt, (c) defocus, (d) astigmatism, (e) coma and (f) spherical aberration. The contour lines are drawn at half-wave intervals (λ=0.633μm).

Fig. 14.
Fig. 14.

Block diagram of the FPGA control unit.

Fig. 15.
Fig. 15.

A larger aperture (70mm) liquid crystal modal wavefront corrector (the battery is shown for scale).

Equations (10)

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χ 2 = ρ ( g + iωc ) ,
x , y 2 V = χ 2 V .
V ( r ) = V N 1 ( iχl ) J 0 ( iχr ) J 1 ( iχl ) N 0 ( iχr ) N 1 ( iχl ) J 0 ( iχa ) J 1 ( iχl ) N 0 ( iχa ) ,
c = ε 0 ε d , g = ε 0 ε ′′ ω d ,
V ( x x k ) 2 + ( y y k ) 2 a 2 = V k , k = 1 . . 37 ,
y V x + y V y = 0 .
{ u i 1 , j 2 u ij + u i + 1 , j h x 2 + u i , j 1 2 u ij + u i , j + 1 h y 2 = ρ ( gu ij + ωcv ij ) v i 1 , j 2 v ij + v i + 1 , j h x 2 + v i , j 1 2 v ij + v i , j + 1 h y 2 = ρ ( gv ij ωcu ij ) .
Δ = δ 1 2 δ 0 δ 1 ,
V x y = k = 1 37 V k φ k x y ,
φ k ( x i , y i ) = { 1 , i = k , 0 , i k ,

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