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Control optimization of spherical modal liquid crystal lenses

A. F. Naumov, G. D. Love, M. Yu. Loktev, and F. L. Vladimirov

Open Access Open Access

Abstract

Liquid crystal modal lenses are switchable lenses with a continuous phase variation across the lens. A critical issue for such lenses is the minimization of phase aberrations. In this paper we present results of a simulation of control signals that have a range of harmonics. Experimental results using optimal sinusoidal and rectangular voltages are presented. A lack of uniqueness in the specification of the control voltage parameters is explained. The influence of a variable duty cycle of the control voltage on an adaptive lens is investigated. Finally we present experimental results showing a liquid crystal lens varying its focal length.

©1999 Optical Society of America

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References

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  • Year
  • Author
  • Publication
  1. V. Laude, “Twisted-nematic liquid-crystal pixelated active lens,” Opt. Comm. 153, 134–152 (1998).
    [Crossref]
  2. W. W. Chan and S. T. Kowel, ”Imaging performance of the liquid-crystal-adaptive lens with conductive ladder meshing,” Appl. Opt. 36, 8958–8969 (1997).
    [Crossref]
  3. J. S. Patel and K. Rastani, “Electrically controlled polarization-independent liquid-crystal Fresnel lens arrays,” Opt. Lett. 16, 532–534 (1991).
    [Crossref] [PubMed]
  4. C. W. Fowler and E. S. Pateras, “Liquid crystal lens review,” Ophthal. Physiol. Opt. 10, 186–194 (1990).
    [Crossref]
  5. S. Masuda, S. Takahashi, T. Nose, S. Sato, and H. Ito, “Liquid-crystal microlens with a beam-steering function,” Appl. Opt. 36, 4772–4778 (1997).
    [Crossref] [PubMed]
  6. A. F. Naumov, “Modal wavefront correctors,” Proc. of P. N. Lebedev Phys. Inst. 217, 177–182 (1993).
  7. A. F. Naumov and G. V. Vdovin, “Multichannel LC-based wavefront corrector with modal influence functions,” Opt. Lett. 23, 1550–1552 (1998).
    [Crossref]
  8. E. G. Abramochkin, A. A. Vasiliev, P. V. Vashurin, L. I. Zhmurova, V. A. Ignatov, and A. F. Naumov, “Controlled liquid crystal lens,” preprint of P. N. Lebedev Phys. Inst. 194, 18p. (1988).
  9. A. F. Naumov, M. Yu. Loktev, I. R. Guralnik, and G. V. Vdovin, “Liquid crystal adaptive lenses with modal control,” Opt. Lett. 23, 992–994 (1998).
    [Crossref]
  10. G. D. Love, J. V. Major, and A. Purvis, “Liquid-crystal prisms for tip-tilt adaptive optics,” Opt. Lett. 19, 1170–1172 (1994).
    [Crossref] [PubMed]
  11. F. L. Vladimirov, I. E. Morichev, L. I. Petrova, and N. I. Pletneva, “Analog indicator based on liquid crystals,” Opto-Mekhanicheskaja Promishlennost 3, 27–28 (1987).
  12. G. D. Love, “Liquid-crystal phase modulator for unpolarized light,” Appl. Opt. 32, 2222–2223 (1993).
    [Crossref] [PubMed]
  13. J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill Book Company, New York, 1968).
  14. A. F. Naumov, M. Yu. Loktev, and I. R. Guralnik, “Cylindrical and spherical adaptive liquid crystal lenses,” SPIE 3684, pp.18–27 (1998).
    [Crossref]
  15. L. M. Blinov, Electro-Optical and Magneto-Optical Properties of Liquid Crystals (Wiley, New York, 1983).
  16. A. F. Naumov, M. Yu. Loktev, I. R. Guralnik, S. V. Sheyenkov, and G. V. Vdovin, ”Modal liquid crystal adaptive lenses,” preprint of P. N. Lebedev Phys. Inst. 13, 28p. (1998).
  17. B. R. Frieden (ed.), The Computer in Optical Research. Methods and Applications (Springer-Verlag, Berlin, Heidelberg, New York, 1980).
    [Crossref]

1998 (5)

V. Laude, “Twisted-nematic liquid-crystal pixelated active lens,” Opt. Comm. 153, 134–152 (1998).
[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, M. Yu. Loktev, I. R. Guralnik, and G. V. Vdovin, “Liquid crystal adaptive lenses with modal control,” Opt. Lett. 23, 992–994 (1998).
[Crossref]

A. F. Naumov, M. Yu. Loktev, and I. R. Guralnik, “Cylindrical and spherical adaptive liquid crystal lenses,” SPIE 3684, pp.18–27 (1998).
[Crossref]

A. F. Naumov, M. Yu. Loktev, I. R. Guralnik, S. V. Sheyenkov, and G. V. Vdovin, ”Modal liquid crystal adaptive lenses,” preprint of P. N. Lebedev Phys. Inst. 13, 28p. (1998).

1997 (2)

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. of P. N. Lebedev Phys. Inst. 217, 177–182 (1993).

1991 (1)

1990 (1)

C. W. Fowler and E. S. Pateras, “Liquid crystal lens review,” Ophthal. Physiol. Opt. 10, 186–194 (1990).
[Crossref]

1988 (1)

E. G. Abramochkin, A. A. Vasiliev, P. V. Vashurin, L. I. Zhmurova, V. A. Ignatov, and A. F. Naumov, “Controlled liquid crystal lens,” preprint of P. N. Lebedev Phys. Inst. 194, 18p. (1988).

1987 (1)

F. L. Vladimirov, I. E. Morichev, L. I. Petrova, and N. I. Pletneva, “Analog indicator based on liquid crystals,” Opto-Mekhanicheskaja Promishlennost 3, 27–28 (1987).

Abramochkin, E. G.

E. G. Abramochkin, A. A. Vasiliev, P. V. Vashurin, L. I. Zhmurova, V. A. Ignatov, and A. F. Naumov, “Controlled liquid crystal lens,” preprint of P. N. Lebedev Phys. Inst. 194, 18p. (1988).

Blinov, L. M.

L. M. Blinov, Electro-Optical and Magneto-Optical Properties of Liquid Crystals (Wiley, New York, 1983).

Chan, W. W.

Fowler, C. W.

C. W. Fowler and E. S. Pateras, “Liquid crystal lens review,” Ophthal. Physiol. Opt. 10, 186–194 (1990).
[Crossref]

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill Book Company, New York, 1968).

Guralnik, I. R.

A. F. Naumov, M. Yu. Loktev, and I. R. Guralnik, “Cylindrical and spherical adaptive liquid crystal lenses,” SPIE 3684, pp.18–27 (1998).
[Crossref]

A. F. Naumov, M. Yu. Loktev, I. R. Guralnik, S. V. Sheyenkov, and G. V. Vdovin, ”Modal liquid crystal adaptive lenses,” preprint of P. N. Lebedev Phys. Inst. 13, 28p. (1998).

A. F. Naumov, M. Yu. Loktev, I. R. Guralnik, and G. V. Vdovin, “Liquid crystal adaptive lenses with modal control,” Opt. Lett. 23, 992–994 (1998).
[Crossref]

Ignatov, V. A.

E. G. Abramochkin, A. A. Vasiliev, P. V. Vashurin, L. I. Zhmurova, V. A. Ignatov, and A. F. Naumov, “Controlled liquid crystal lens,” preprint of P. N. Lebedev Phys. Inst. 194, 18p. (1988).

Ito, H.

Kowel, S. T.

Laude, V.

V. Laude, “Twisted-nematic liquid-crystal pixelated active lens,” Opt. Comm. 153, 134–152 (1998).
[Crossref]

Loktev, M. Yu.

A. F. Naumov, M. Yu. Loktev, and I. R. Guralnik, “Cylindrical and spherical adaptive liquid crystal lenses,” SPIE 3684, pp.18–27 (1998).
[Crossref]

Love, G. D.

Major, J. V.

Masuda, S.

Morichev, I. E.

F. L. Vladimirov, I. E. Morichev, L. I. Petrova, and N. I. Pletneva, “Analog indicator based on liquid crystals,” Opto-Mekhanicheskaja Promishlennost 3, 27–28 (1987).

Naumov, A. F.

A. F. Naumov, M. Yu. Loktev, I. R. Guralnik, and G. V. Vdovin, “Liquid crystal adaptive lenses with modal control,” Opt. Lett. 23, 992–994 (1998).
[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, M. Yu. Loktev, and I. R. Guralnik, “Cylindrical and spherical adaptive liquid crystal lenses,” SPIE 3684, pp.18–27 (1998).
[Crossref]

A. F. Naumov, M. Yu. Loktev, I. R. Guralnik, S. V. Sheyenkov, and G. V. Vdovin, ”Modal liquid crystal adaptive lenses,” preprint of P. N. Lebedev Phys. Inst. 13, 28p. (1998).

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

E. G. Abramochkin, A. A. Vasiliev, P. V. Vashurin, L. I. Zhmurova, V. A. Ignatov, and A. F. Naumov, “Controlled liquid crystal lens,” preprint of P. N. Lebedev Phys. Inst. 194, 18p. (1988).

Nose, T.

Patel, J. S.

Pateras, E. S.

C. W. Fowler and E. S. Pateras, “Liquid crystal lens review,” Ophthal. Physiol. Opt. 10, 186–194 (1990).
[Crossref]

Petrova, L. I.

F. L. Vladimirov, I. E. Morichev, L. I. Petrova, and N. I. Pletneva, “Analog indicator based on liquid crystals,” Opto-Mekhanicheskaja Promishlennost 3, 27–28 (1987).

Pletneva, N. I.

F. L. Vladimirov, I. E. Morichev, L. I. Petrova, and N. I. Pletneva, “Analog indicator based on liquid crystals,” Opto-Mekhanicheskaja Promishlennost 3, 27–28 (1987).

Purvis, A.

Rastani, K.

Sato, S.

Sheyenkov, S. V.

A. F. Naumov, M. Yu. Loktev, I. R. Guralnik, S. V. Sheyenkov, and G. V. Vdovin, ”Modal liquid crystal adaptive lenses,” preprint of P. N. Lebedev Phys. Inst. 13, 28p. (1998).

Takahashi, S.

Vashurin, P. V.

E. G. Abramochkin, A. A. Vasiliev, P. V. Vashurin, L. I. Zhmurova, V. A. Ignatov, and A. F. Naumov, “Controlled liquid crystal lens,” preprint of P. N. Lebedev Phys. Inst. 194, 18p. (1988).

Vasiliev, A. A.

E. G. Abramochkin, A. A. Vasiliev, P. V. Vashurin, L. I. Zhmurova, V. A. Ignatov, and A. F. Naumov, “Controlled liquid crystal lens,” preprint of P. N. Lebedev Phys. Inst. 194, 18p. (1988).

Vdovin, G. V.

Vladimirov, F. L.

F. L. Vladimirov, I. E. Morichev, L. I. Petrova, and N. I. Pletneva, “Analog indicator based on liquid crystals,” Opto-Mekhanicheskaja Promishlennost 3, 27–28 (1987).

Yu. Loktev, M.

A. F. Naumov, M. Yu. Loktev, I. R. Guralnik, and G. V. Vdovin, “Liquid crystal adaptive lenses with modal control,” Opt. Lett. 23, 992–994 (1998).
[Crossref]

A. F. Naumov, M. Yu. Loktev, I. R. Guralnik, S. V. Sheyenkov, and G. V. Vdovin, ”Modal liquid crystal adaptive lenses,” preprint of P. N. Lebedev Phys. Inst. 13, 28p. (1998).

Zhmurova, L. I.

E. G. Abramochkin, A. A. Vasiliev, P. V. Vashurin, L. I. Zhmurova, V. A. Ignatov, and A. F. Naumov, “Controlled liquid crystal lens,” preprint of P. N. Lebedev Phys. Inst. 194, 18p. (1988).

Appl. Opt. (3)

Ophthal. Physiol. Opt. (1)

C. W. Fowler and E. S. Pateras, “Liquid crystal lens review,” Ophthal. Physiol. Opt. 10, 186–194 (1990).
[Crossref]

Opt. Comm. (1)

V. Laude, “Twisted-nematic liquid-crystal pixelated active lens,” Opt. Comm. 153, 134–152 (1998).
[Crossref]

Opt. Lett. (4)

Opto-Mekhanicheskaja Promishlennost (1)

F. L. Vladimirov, I. E. Morichev, L. I. Petrova, and N. I. Pletneva, “Analog indicator based on liquid crystals,” Opto-Mekhanicheskaja Promishlennost 3, 27–28 (1987).

preprint of P. N. Lebedev Phys. Inst. (2)

A. F. Naumov, M. Yu. Loktev, I. R. Guralnik, S. V. Sheyenkov, and G. V. Vdovin, ”Modal liquid crystal adaptive lenses,” preprint of P. N. Lebedev Phys. Inst. 13, 28p. (1998).

E. G. Abramochkin, A. A. Vasiliev, P. V. Vashurin, L. I. Zhmurova, V. A. Ignatov, and A. F. Naumov, “Controlled liquid crystal lens,” preprint of P. N. Lebedev Phys. Inst. 194, 18p. (1988).

Proc. of P. N. Lebedev Phys. Inst. (1)

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

SPIE (1)

A. F. Naumov, M. Yu. Loktev, and I. R. Guralnik, “Cylindrical and spherical adaptive liquid crystal lenses,” SPIE 3684, pp.18–27 (1998).
[Crossref]

Other (3)

L. M. Blinov, Electro-Optical and Magneto-Optical Properties of Liquid Crystals (Wiley, New York, 1983).

B. R. Frieden (ed.), The Computer in Optical Research. Methods and Applications (Springer-Verlag, Berlin, Heidelberg, New York, 1980).
[Crossref]

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill Book Company, New York, 1968).

Supplementary Material (1)

Media 1: MOV (508 KB)     

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Figures (10)
Fig. 1.
Fig. 1. A spherical modal liquid crystal lens.

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Fig. 2.
Fig. 2. (a) Theoretical dependence of the optimal control voltages and frequencies versus focal length for a modal liquid crystal lens. (b) Dependence of the rms phase deviation from an ideal parabola versus focal length.

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Fig. 3.
Fig. 3. Dependence of the rms phase deviation from an ideal parabola versus number of harmonic components m in the control signal U 0 ∑k=1m αk sin(ωkt) for F = 0.6 m.

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Fig. 4.
Fig. 4. Optical set-up for calibration of MLCL using (a) single pass and (b) double pass of collimated laser beam through LC layer: E⃗ is direction of laser beam polarization, n⃗ is initial alignment of LC molecules, p⃗ is direction of polarizer orientation.

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Fig. 5.
Fig. 5. Calibration by sinusoidal and bipolar rectangular voltage. Optimal voltage (a), frequency (b) and rms dependencies on focal length.

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Fig. 6.
Fig. 6. Optimal control voltage parameters for different experimental samples of MLCL. 1,2,3,4 are for four different lenses.

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Fig. 7.
Fig. 7. Demonstration of lack of uniqueness in the definition of the optimal control voltage parameters.

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Fig. 8.
Fig. 8. The alternation of control voltage parameters for different focal lengths.

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Fig. 9.
Fig. 9. Interferograms obtained using different duty cycles for bipolar rectangular control voltages with 9 V amplitude and 4 kHz frequency: q is indicated in the top-left corner of each interferogram. The resultant focal length and the rms phase deviation from an ideal parabola are shown on each lower insert.

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Fig. 10.
Fig. 10. (507 KB) Correction of defocus by a MLCL (left) and the corresponding interferogram variation (right).

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Tables (1)

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Table 1. MLCL parameters used in compute simulation.

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Equations (3)

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F = π l 2 ( Δ Φ c − Δ Φ e ) λ ,
i 0 = ∑ i ∑ j A ij · i ∑ i ∑ j A ij , j 0 = ∑ i ∑ j A ij · j ∑ i ∑ j A ij ,
B ˜ j = B j * e − j 2 ρ 2 .

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