Abstract

The liquid crystal adaptive lens (LCAL) is an electrooptic device that emulates a variable focal length lens. The LCAL focuses light by creating a parabolic refractive-index profile across the aperture of a liquid crystal cell. The focal length is electronically controlled by applying appropriate voltages to the array of independent electrodes, thus grading the refractive index of the liquid crystal material across the aperture. Beam translation perpendicular to the optical beam path is described theoretically and demonstrated. This capability coupled with the LCAL’s programmable focal length allows 3-D beam control. Meshing, the smoothing of the refractive index between adjacent electrodes, is a critical parameter in achieving near diffraction-limited optical performance. Using two planar electrodes and a ground plane immersed in an isotropic dielectric as a model, a steady-state dc theoretical computer simulation is compared with experiment. Improvements in the liquid crystal cell design demonstrate improved performance over previous LCALs. A larger number of electrodes creates an image without spatial aliasing within the aperture.

© 1988 Optical Society of America

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References

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  1. 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]
  2. S. T. Kowel, P. G. Kornreich, Akbar Nouhi, “Adaptive Spherical Lens,” Appl. Opt. 23, 2774 (1984).
    [Crossref] [PubMed]
  3. Modern Photography Staff, “Is There An All Electronic Lens In Your Future?,” Mod. Photogr.12 (Sept.1986).
  4. Nishimoto, U. S. Patent4,466,703 assigned to Cannon 21Aug.1984.
  5. S. Sato, A. Sugiyama, R. Sato, “Variable Focus Liquid-Crystal Fresnel Lens,” Jpn. J. Appl. Phys. 24, L626 (1985).
    [Crossref]
  6. J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968).
  7. C. Chu, “Meshing Properties in an Adaptive Liquid Crystal Lens,” Tech. Memo, Syracuse U. (10Oct.1984).
  8. E. Brabandt, “Liquid Crystal Lens Controller,” MS Thesis, U. California, Davis (Dec.1986).
  9. P. Brinkley, “Performance Characteristics of a High Resolution Liquid Crystal Lens,” MS Thesis, U. California, Davis, (Mar.1988).
  10. P. G. deGennes, The Physics of Liquid Crystals (Clarendon, Oxford, 1974).

1986 (1)

Modern Photography Staff, “Is There An All Electronic Lens In Your Future?,” Mod. Photogr.12 (Sept.1986).

1985 (1)

S. Sato, A. Sugiyama, R. Sato, “Variable Focus Liquid-Crystal Fresnel Lens,” Jpn. J. Appl. Phys. 24, L626 (1985).
[Crossref]

1984 (2)

Brabandt, E.

E. Brabandt, “Liquid Crystal Lens Controller,” MS Thesis, U. California, Davis (Dec.1986).

Brinkley, P.

P. Brinkley, “Performance Characteristics of a High Resolution Liquid Crystal Lens,” MS Thesis, U. California, Davis, (Mar.1988).

Chu, C.

C. Chu, “Meshing Properties in an Adaptive Liquid Crystal Lens,” Tech. Memo, Syracuse U. (10Oct.1984).

Cleverly, D. S.

deGennes, P. G.

P. G. deGennes, The Physics of Liquid Crystals (Clarendon, Oxford, 1974).

Goodman, J. W.

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

Kornreich, P. G.

Kowel, S. T.

Nishimoto,

Nishimoto, U. S. Patent4,466,703 assigned to Cannon 21Aug.1984.

Nouhi, Akbar

Sato, R.

S. Sato, A. Sugiyama, R. Sato, “Variable Focus Liquid-Crystal Fresnel Lens,” Jpn. J. Appl. Phys. 24, L626 (1985).
[Crossref]

Sato, S.

S. Sato, A. Sugiyama, R. Sato, “Variable Focus Liquid-Crystal Fresnel Lens,” Jpn. J. Appl. Phys. 24, L626 (1985).
[Crossref]

Sugiyama, A.

S. Sato, A. Sugiyama, R. Sato, “Variable Focus Liquid-Crystal Fresnel Lens,” Jpn. J. Appl. Phys. 24, L626 (1985).
[Crossref]

Appl. Opt. (2)

Jpn. J. Appl. Phys. (1)

S. Sato, A. Sugiyama, R. Sato, “Variable Focus Liquid-Crystal Fresnel Lens,” Jpn. J. Appl. Phys. 24, L626 (1985).
[Crossref]

Mod. Photogr. (1)

Modern Photography Staff, “Is There An All Electronic Lens In Your Future?,” Mod. Photogr.12 (Sept.1986).

Other (6)

Nishimoto, U. S. Patent4,466,703 assigned to Cannon 21Aug.1984.

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

C. Chu, “Meshing Properties in an Adaptive Liquid Crystal Lens,” Tech. Memo, Syracuse U. (10Oct.1984).

E. Brabandt, “Liquid Crystal Lens Controller,” MS Thesis, U. California, Davis (Dec.1986).

P. Brinkley, “Performance Characteristics of a High Resolution Liquid Crystal Lens,” MS Thesis, U. California, Davis, (Mar.1988).

P. G. deGennes, The Physics of Liquid Crystals (Clarendon, Oxford, 1974).

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Figures (19)

Fig. 1
Fig. 1

Beam translation experimental setup.

Fig. 2
Fig. 2

Contrast measurement of the focused line and the LCAL with 0.0 V applied to all electrodes.

Fig. 3
Fig. 3

Shifting voltage profiles used to obtain the beam translation.

Fig. 4
Fig. 4

Normalized intensity profiles for different voltage profile shifts.

Fig. 5
Fig. 5

All electrodes at 0.0 V.

Fig. 6
Fig. 6

All electrodes at 2.0 V.

Fig. 7
Fig. 7

Single liquid crystal cell with a 70-cm focal length.

Fig. 8
Fig. 8

Single liquid crystal cell with the beam translated by 10 electrodes (300 μm).

Fig. 9
Fig. 9

Two liquid crystal cells with a focal length of 70 cm.

Fig. 10
Fig. 10

Liquid crystal cell refractive-index profile without meshing.

Fig. 11
Fig. 11

Liquid crystal cell refractive-index profile with meshing.

Fig. 12
Fig. 12

Theoretical meshing calculation geometry.

Fig. 13
Fig. 13

Theoretical meshing voltage profile.

Fig. 14
Fig. 14

Theoretical center voltage as a function of the ratio of electrode width to the cell thickness.

Fig. 15
Fig. 15

Experimental electrode voltage profile as a function of distance. The ratio of electrode spacing to cell thickness is 0.42.

Fig. 16
Fig. 16

Experimental electrode voltage profile as a function of distance. The ratio of electrode spacing to cell thickness is 0.83.

Fig. 17
Fig. 17

Experimental electrode voltage profile as a function of distance. The ratio of electrode spacing to cell thickness is 1.7.

Fig. 18
Fig. 18

Experimental electrode voltage profile as a function of distance. The ratio of electrode spacing to cell thickness is 2.5.

Fig. 19
Fig. 19

Experimental electrode voltage profile as a function of distance. The ratio of electrode spacing to cell thickness is 3.3.

Equations (18)

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U ( x 0 , y 0 ) = exp ( j k z ) j λ z exp [ j k 2 z ( x 0 2 + y 0 2 ) ] × - + U a ( x 1 , y 1 ) exp [ j k 2 z ( x 1 2 + y 1 2 ) ] × exp [ - j 2 π λ z ( x 0 x 1 + y 0 y 1 ) ] d x 1 d y 1 ,
U a ( x 1 , y 1 ) = U ( x 1 , y 1 ) P ( x 1 , y 1 ) exp [ - j k 2 f ( x 1 2 + y 1 2 ) ] ,
P ( x 1 , y 1 ) = { 1 ( x 1 , y 1 ) within the aperture , 0 ( x 1 , y 1 ) outside the aperture ,
U ( x 0 , y 0 ) = A - + U ( x 1 , y 1 ) P ( x 1 , y 1 ) × exp [ - j 2 π λ f ( x 0 x 1 + y 0 y 1 ) ] d x 1 d y 1 .
U ( x 0 , y 0 ) = A T [ U ( x 1 , y 1 ) P ( x 1 , y 1 ) ] f X = x 0 λ f , f Y = y 0 λ f ,
U a ( x 1 , y 1 ) = U ( x 1 , y 1 ) P ( x 1 , y 1 ) exp { - j k 2 f [ ( x 1 - x s ) 2 + ( y 1 - y s 2 ) ] } .
U ( x 0 , y 0 ) = A - + U ( x 1 , y 1 ) P ( x 1 , y 1 ) × exp { - j k 2 f [ ( x 1 - x s ) 2 + ( y 1 - y s ) 2 ] } × exp [ j k 2 f ( x 1 2 + y 1 2 ) ] exp [ - j 2 π λ f ( x 0 x 1 + y 0 y 1 ) ] d x 1 d y 1 , x s , y s lens translation vector .
U ( x 0 , y 0 ) = A exp [ - j k 2 f ( x s 2 + y s 2 ) ] T { U ( x 1 , y 1 ) P ( x 1 , y 1 ) × exp [ j 2 π λ f ( x 0 , x s + y 0 y s ) ] } .
U ( x 0 , y 0 ) = A exp [ - j k 2 f ( x s 2 + y s 2 ) ] T { U ( x 1 , y 1 ) P ( x 1 , y 1 ) } f X = x 0 λ f - x s λ f f Y = y 0 λ f - y s λ f .
f X = x 0 - x s λ f = 0 x 0 = x s , f Y = y 0 - y s λ f = 0 y 0 = y s ,
f X = x 0 λ f = 0 x 0 = 0 , f Y = y 0 λ f = 0 y 0 = 0.
U a ( x 1 , y 1 ) = rect ( x 1 L ) rect ( y 1 L ) exp [ - j k 2 f ( x 1 2 + y 1 2 ) ] ,
rect ( x L ) { 1 if x L , 0 if x > L , L one - half the aperture width .
U ( x 0 , y 0 ) = A L 2 sinc ( L x 0 λ f ) sinc ( L y 0 λ f ) .
U a ( x 1 , y 1 ) = rect ( x 1 L ) rect ( y 1 L ) exp { - j k 2 f [ ( x 1 - x s ) 2 + ( y 1 - y s ) 2 ] } .
U ( x 0 , y 0 ) = A L 2 sinc ( L ( x 0 - x s ) λ f ) sinc ( L ( y 0 - y s ) λ f ) .
f = L 2 2 t ( n e - n o ) ,
Δ n ( r ) = r 2 2 t f L 2 ,

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