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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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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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