Abstract

A variable-focus liquid-filled optical lens consists of a solid plate, a ring spacer, and an elastic film; a liquid fills this lens-shaped container. One varies the focus by changing the liquid volume in the lens. The lens shape calculated theoretically is a paraboloid. However, it is approximately a sphere near the central area. The deformation of the lens shape by gravity was also calculated with a simplified structure in which the lens was held vertically and found to be independent of the elastic properties of the film. The effect of gravity was found to be negligible when the pressure at the liquid pump was more than 30 times that induced in the liquid at the bottom of the lens by the gravity. The aberrations of the lens were calculated and observed to be negligibly small compared with the normal convex spherical single-glass lens. A liquid-filled lens was fabricated and experimentally evaluated.

© 1993 Optical Society of America

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References

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  1. D. Marcuse, S. E. Miller, “Analysis of a tubular gas lens,” Bell Syst. Technol. J. 43, 759–782 (1964).
  2. T. Suganuma, Y. Miyazaki, “LiNbO3 micro lens with non-uniformly diffused Ti controlled by electro-optical effect,” presented at the Joint Meeting of the Tokai Branch of the Japan Institute of Electrical Engineers, Tokyo, 1984.
  3. S. Yanase, T. Nose, S. Sato, “Molecular orientation and light collecting characteristics,” in Nematic Liquid Crystal Lens”, presented at the 35th Joint Meeting of the Japanese Institute of Applied Physics, Tokyo, 28–31 March 1988.
  4. B. M. Wright, “Improvements in or relating to valiable focus lenses,” English patent 1,209,234 (11March1968).
  5. Y. Kawai, S. Morita, S. Hattori, “Control of the polyelectrolyte gel lens by voltage application,” J. Eye 5, 1021–1023 (1988).
  6. G. C. Knollman, J. L. S. Bellin, J. L. Weaver, “Variable-focus liquid-filled hydroacoustic lens,” J. Acoust. Soc. Am. 49, 253–261 (1970).
    [CrossRef]
  7. S. D. Poisson, Memoirs of the Academy (Academy of Sciences, Paris, 1829), Vol. 8.
  8. L. Prandtl, Phys. Z 4, 190 (1903).
  9. A. A. Griffith, G. I. Taylor, Proc. Inst. Mech. Eng. (London, 1917), p. 755.

1988 (1)

Y. Kawai, S. Morita, S. Hattori, “Control of the polyelectrolyte gel lens by voltage application,” J. Eye 5, 1021–1023 (1988).

1970 (1)

G. C. Knollman, J. L. S. Bellin, J. L. Weaver, “Variable-focus liquid-filled hydroacoustic lens,” J. Acoust. Soc. Am. 49, 253–261 (1970).
[CrossRef]

1964 (1)

D. Marcuse, S. E. Miller, “Analysis of a tubular gas lens,” Bell Syst. Technol. J. 43, 759–782 (1964).

1903 (1)

L. Prandtl, Phys. Z 4, 190 (1903).

Bellin, J. L. S.

G. C. Knollman, J. L. S. Bellin, J. L. Weaver, “Variable-focus liquid-filled hydroacoustic lens,” J. Acoust. Soc. Am. 49, 253–261 (1970).
[CrossRef]

Griffith, A. A.

A. A. Griffith, G. I. Taylor, Proc. Inst. Mech. Eng. (London, 1917), p. 755.

Hattori, S.

Y. Kawai, S. Morita, S. Hattori, “Control of the polyelectrolyte gel lens by voltage application,” J. Eye 5, 1021–1023 (1988).

Kawai, Y.

Y. Kawai, S. Morita, S. Hattori, “Control of the polyelectrolyte gel lens by voltage application,” J. Eye 5, 1021–1023 (1988).

Knollman, G. C.

G. C. Knollman, J. L. S. Bellin, J. L. Weaver, “Variable-focus liquid-filled hydroacoustic lens,” J. Acoust. Soc. Am. 49, 253–261 (1970).
[CrossRef]

Marcuse, D.

D. Marcuse, S. E. Miller, “Analysis of a tubular gas lens,” Bell Syst. Technol. J. 43, 759–782 (1964).

Miller, S. E.

D. Marcuse, S. E. Miller, “Analysis of a tubular gas lens,” Bell Syst. Technol. J. 43, 759–782 (1964).

Miyazaki, Y.

T. Suganuma, Y. Miyazaki, “LiNbO3 micro lens with non-uniformly diffused Ti controlled by electro-optical effect,” presented at the Joint Meeting of the Tokai Branch of the Japan Institute of Electrical Engineers, Tokyo, 1984.

Morita, S.

Y. Kawai, S. Morita, S. Hattori, “Control of the polyelectrolyte gel lens by voltage application,” J. Eye 5, 1021–1023 (1988).

Nose, T.

S. Yanase, T. Nose, S. Sato, “Molecular orientation and light collecting characteristics,” in Nematic Liquid Crystal Lens”, presented at the 35th Joint Meeting of the Japanese Institute of Applied Physics, Tokyo, 28–31 March 1988.

Poisson, S. D.

S. D. Poisson, Memoirs of the Academy (Academy of Sciences, Paris, 1829), Vol. 8.

Prandtl, L.

L. Prandtl, Phys. Z 4, 190 (1903).

Sato, S.

S. Yanase, T. Nose, S. Sato, “Molecular orientation and light collecting characteristics,” in Nematic Liquid Crystal Lens”, presented at the 35th Joint Meeting of the Japanese Institute of Applied Physics, Tokyo, 28–31 March 1988.

Suganuma, T.

T. Suganuma, Y. Miyazaki, “LiNbO3 micro lens with non-uniformly diffused Ti controlled by electro-optical effect,” presented at the Joint Meeting of the Tokai Branch of the Japan Institute of Electrical Engineers, Tokyo, 1984.

Taylor, G. I.

A. A. Griffith, G. I. Taylor, Proc. Inst. Mech. Eng. (London, 1917), p. 755.

Weaver, J. L.

G. C. Knollman, J. L. S. Bellin, J. L. Weaver, “Variable-focus liquid-filled hydroacoustic lens,” J. Acoust. Soc. Am. 49, 253–261 (1970).
[CrossRef]

Wright, B. M.

B. M. Wright, “Improvements in or relating to valiable focus lenses,” English patent 1,209,234 (11March1968).

Yanase, S.

S. Yanase, T. Nose, S. Sato, “Molecular orientation and light collecting characteristics,” in Nematic Liquid Crystal Lens”, presented at the 35th Joint Meeting of the Japanese Institute of Applied Physics, Tokyo, 28–31 March 1988.

Bell Syst. Technol. J. (1)

D. Marcuse, S. E. Miller, “Analysis of a tubular gas lens,” Bell Syst. Technol. J. 43, 759–782 (1964).

J. Acoust. Soc. Am. (1)

G. C. Knollman, J. L. S. Bellin, J. L. Weaver, “Variable-focus liquid-filled hydroacoustic lens,” J. Acoust. Soc. Am. 49, 253–261 (1970).
[CrossRef]

J. Eye (1)

Y. Kawai, S. Morita, S. Hattori, “Control of the polyelectrolyte gel lens by voltage application,” J. Eye 5, 1021–1023 (1988).

Phys. Z (1)

L. Prandtl, Phys. Z 4, 190 (1903).

Other (5)

A. A. Griffith, G. I. Taylor, Proc. Inst. Mech. Eng. (London, 1917), p. 755.

S. D. Poisson, Memoirs of the Academy (Academy of Sciences, Paris, 1829), Vol. 8.

T. Suganuma, Y. Miyazaki, “LiNbO3 micro lens with non-uniformly diffused Ti controlled by electro-optical effect,” presented at the Joint Meeting of the Tokai Branch of the Japan Institute of Electrical Engineers, Tokyo, 1984.

S. Yanase, T. Nose, S. Sato, “Molecular orientation and light collecting characteristics,” in Nematic Liquid Crystal Lens”, presented at the 35th Joint Meeting of the Japanese Institute of Applied Physics, Tokyo, 28–31 March 1988.

B. M. Wright, “Improvements in or relating to valiable focus lenses,” English patent 1,209,234 (11March1968).

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Figures (11)

Fig. 1
Fig. 1

Sructure of liquid-filled lens.

Fig. 2
Fig. 2

Liquid-filled lens oriented horizontally for the calculation of lens shape.

Fig. 3
Fig. 3

Numerically calculated lens shape of liquid-filled lens oriented horizontally.

Fig. 4
Fig. 4

Liquid-filled lens oriented vertically for the calculation of gravity effect.

Fig. 5
Fig. 5

Vertical cross sections of liquid-filled lens under the effect of gravity for each k, where the lens diameter is 27 mm, the maximum deformation point is indicated by a small circle on the curve, and the ratios of the maximum distance that the center is shifted and the radius of original lens were indicated for each cross section.

Fig. 6
Fig. 6

Cross section of liquid-filled lens and the calculated optical path, (a) Whole figure, (b) enlarged area around the lens.

Fig. 7
Fig. 7

Aberrations of liquid-filled lens at a focus of 3 7 cm.

Fig. 8
Fig. 8

System used to measure the lens pressure.

Fig. 9
Fig. 9

Relation between the pressure and the input volume of silicon oil in the liquid-filled lens.

Fig. 10
Fig. 10

Relation between focal length and k value.

Fig. 11
Fig. 11

Pictures taken by the liquid-filled lens.

Equations (15)

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z r 2 z r 2 d r .
T r d θ ( + z r ) .
T ( r + d r ) d θ ( z r 2 z r 2 d r ) .
T d θ d r z r T d θ ( d r ) 2 2 z r 2 T r θ d r 2 z r 2 .
w r d θ d r + T d θ d r z r + T r d θ d r 2 z r 2 = 0 .
1 r r ( r z r ) = w T .
z = w 4 T r 2 + c 1 log r + c 2 .
z = [ w / ( 4 T ) ] ( a 2 r 2 ) ,
1 R ( r ) = d 2 z d r 2 = w 2 T ,
1 R ( θ ) = 1 r d z d r = w 2 T .
R ( r ) = R ( θ ) = ( 2 T ) / w .
z y at P , z y + 2 z y 2 d y at S .
T d x 2 z y 2 d y + d x d y [ w + ρ g ( 2 a y ) ] = 0 .
z = ρ g a T ( y 2 y 3 6 a 4 3 a y ) w 2 T ( y 2 2 a y ) .
z = ρ g a T [ ( y 2 y 3 6 a 4 3 a y ) + k ( y 2 2 a y ) ] .

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