Abstract

This paper reports the creation of a tandem liquid crystal cell arrangement capable of simulating the performance of a spherical lens. Electrical modulation of the index of refraction creates focusing behavior. The modulation is induced by a set of electrodes whose individual voltages are arranged to provide a cylindrical exit wave front for a uniform plane-wave input. Two such cells with orthogonal electrodes arranged in cascade create spherical lens performance. Experimental evidence using a lens with a relatively small number of electrodes is presented. Applications for such structures, once improved, would include real-time focus adjustment for optical disk readers and hand-held photographic equipment as well as aberration compensation for long path-length optical systems.

© 1984 Optical Society of America

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References

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  1. S. T. Kowel, D. S. Cleverly, “A Liquid Crystal Adaptive Lens,” in Proceedings, NASA Conference on Optical Information Processing for Aerospace Applications, Hampton, Va. (1981).
  2. D. S. Cleverly, “Creation of a Lens by Field-Controlled Variation of the Index of Refraction in a Liquid Crystal,” Ph.D. Dissertation, Syracuse U., Syracuse, N.Y. (1982).
  3. S. T. Kowel, D. S. Cleverly, P. G. Kornreich, “Focusing by Electrical Modulation of Refraction in a Liquid Crystal Cell,” Appl. Opt. 23, 278 (1984).
    [CrossRef] [PubMed]
  4. J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968).

1984 (1)

Cleverly, D. S.

S. T. Kowel, D. S. Cleverly, P. G. Kornreich, “Focusing by Electrical Modulation of Refraction in a Liquid Crystal Cell,” Appl. Opt. 23, 278 (1984).
[CrossRef] [PubMed]

S. T. Kowel, D. S. Cleverly, “A Liquid Crystal Adaptive Lens,” in Proceedings, NASA Conference on Optical Information Processing for Aerospace Applications, Hampton, Va. (1981).

D. S. Cleverly, “Creation of a Lens by Field-Controlled Variation of the Index of Refraction in a Liquid Crystal,” Ph.D. Dissertation, Syracuse U., Syracuse, N.Y. (1982).

Goodman, J. W.

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

Kornreich, P. G.

Kowel, S. T.

S. T. Kowel, D. S. Cleverly, P. G. Kornreich, “Focusing by Electrical Modulation of Refraction in a Liquid Crystal Cell,” Appl. Opt. 23, 278 (1984).
[CrossRef] [PubMed]

S. T. Kowel, D. S. Cleverly, “A Liquid Crystal Adaptive Lens,” in Proceedings, NASA Conference on Optical Information Processing for Aerospace Applications, Hampton, Va. (1981).

Appl. Opt. (1)

Other (3)

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

S. T. Kowel, D. S. Cleverly, “A Liquid Crystal Adaptive Lens,” in Proceedings, NASA Conference on Optical Information Processing for Aerospace Applications, Hampton, Va. (1981).

D. S. Cleverly, “Creation of a Lens by Field-Controlled Variation of the Index of Refraction in a Liquid Crystal,” Ph.D. Dissertation, Syracuse U., Syracuse, N.Y. (1982).

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Figures (10)

Fig. 1
Fig. 1

A four-cell arrangement needed to create a spherical lens for light with arbitrary polarization in the xy plane.

Fig. 2
Fig. 2

Effective variation of refractive index with applied voltage for linearly polarized light at 515 nm. These data are derived from birefringence measurements.

Fig. 3
Fig. 3

Pattern of light just after emerging from liquid crystal lenses. The top portion of one cell no longer responds to applied voltage properly.

Fig. 4
Fig. 4

Pattern of light 3 m from the lenses. Note the focusing and diffraction replication caused by discrete sampling of the index of refraction.

Fig. 5
Fig. 5

Pattern of light at the focal plane 9 m from the lens.

Fig. 6
Fig. 6

Light pattern ~12 m from the lens.

Fig. 7
Fig. 7

Light pattern at the focal plane when the cell with vertical electrodes is turned off.

Fig. 8
Fig. 8

Light pattern when all electrodes are below threshold. Rings are due to lack of spatial filtering of the input light in this case.

Fig. 9
Fig. 9

Intensity profile across a collimated beam after passing through the liquid crystal lens measured at a point 9 m from the lens. Figure 9(a) shows the lens in the off state, while Fig. 9(b) shows the lens in the on state with appropriate voltages. The length of the horizontal axis corresponds to a range of 10 mm centered on the axis of the beam scanned by the photodiode. The vertical axis indicates the relative light intensity at the corresponding position.

Fig. 10
Fig. 10

Addressing scheme. Each electrode is selected to receive the appropriate analog voltage by a microprocessor-derived digital signal used to adjust the output of the source (pulse-train) wave generator.

Tables (1)

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Table I Calculated Voltages and Change in Refractive Index for a Spherical Liquid Crystal Cell for a Light of λ = 514.5 nm

Equations (4)

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t p ( x , y = exp - ( j k r 2 ) / 2 f = [ exp - ( j k x 2 ) / 2 f ] [ exp - ( j k y 2 ) / 2 f ] ,
n ( r ) = n e + ( n i - n e r o 2 ) ,
0 < 1 f 2 Δ ( n e - n i ) r o 2 ,
f = r o 2 2 Δ ( n o - n e ) = [ ( 0.75 ) × 10 - 2 ] 2 2 × 18 × 10 - 6 ( 0.22 ) = 7.1 m .

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