Abstract

Research has been conducted on a variable-focus liquid-filled optical lens built from a polymer elastic-film window and a rigid plastic window with a transparent refractive liquid between these windows. The pressure inside the lens deforms the elastic film, which takes the form of a paraboloid. The absolute value of the tension in the film was calculated, allowing theoretical evaluation of the focal length of the lens and its aberrations. The developed mathematical model of the liquid-filled flexible lens agrees well with experimental results.

© 1996 Optical Society of America

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References

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  1. N. Sugiura, S. Morita, “Variable-focus liquid-filled optical lens,” Appl. Opt. 32, 4181–4186 (1993).
    [CrossRef] [PubMed]
  2. 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]
  3. J. Prescott, Applied Elasticity (Longmans, Green, London, 1924), Chap. 12, p. 327.
  4. MATLAB User's Guide (The MathWorks, Inc., Natick, Mass., 1992).
  5. W. G. Driscoll, ed., Handbook of Optics (McGraw-Hill, New York, 1978), Sec. 2, pp. 11–13.
  6. R. C. Weast, ed., Handbook of Chemistry and Physics (CRC Press, Cleveland, Ohio, 1969), Sec. C, pp. 766, 768–769.
  7. J. Brandrup, E. H. Immergut, eds., Polymer Handbook (Interscience, New York, 1966), Chap. 6, pp. 58–59, 76.
  8. H. Reismann, P. S. Pawlik, Elasticity (Wiley, New York, 1980), Chap. 4, p. 135.
  9. S. Timoshenko, D. H. Young, Elements of Strength of Materials (Van Nostrand, Princeton, N.J., 1962), Chap. 1, p. 11.
  10. C.-H. Wu, “Variable lens assembly,” U.S. patent5,233,470 (3August1993).
  11. S. Kurtin, “Variable focal length lens,” U.S. patent5,138,494, (11August1992).

1993

1970

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]

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]

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]

Kurtin, S.

S. Kurtin, “Variable focal length lens,” U.S. patent5,138,494, (11August1992).

Morita, S.

Pawlik, P. S.

H. Reismann, P. S. Pawlik, Elasticity (Wiley, New York, 1980), Chap. 4, p. 135.

Prescott, J.

J. Prescott, Applied Elasticity (Longmans, Green, London, 1924), Chap. 12, p. 327.

Reismann, H.

H. Reismann, P. S. Pawlik, Elasticity (Wiley, New York, 1980), Chap. 4, p. 135.

Sugiura, N.

Timoshenko, S.

S. Timoshenko, D. H. Young, Elements of Strength of Materials (Van Nostrand, Princeton, N.J., 1962), Chap. 1, p. 11.

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]

Wu, C.-H.

C.-H. Wu, “Variable lens assembly,” U.S. patent5,233,470 (3August1993).

Young, D. H.

S. Timoshenko, D. H. Young, Elements of Strength of Materials (Van Nostrand, Princeton, N.J., 1962), Chap. 1, p. 11.

Appl. Opt.

J. Acoust. Soc. Am.

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]

Other

J. Prescott, Applied Elasticity (Longmans, Green, London, 1924), Chap. 12, p. 327.

MATLAB User's Guide (The MathWorks, Inc., Natick, Mass., 1992).

W. G. Driscoll, ed., Handbook of Optics (McGraw-Hill, New York, 1978), Sec. 2, pp. 11–13.

R. C. Weast, ed., Handbook of Chemistry and Physics (CRC Press, Cleveland, Ohio, 1969), Sec. C, pp. 766, 768–769.

J. Brandrup, E. H. Immergut, eds., Polymer Handbook (Interscience, New York, 1966), Chap. 6, pp. 58–59, 76.

H. Reismann, P. S. Pawlik, Elasticity (Wiley, New York, 1980), Chap. 4, p. 135.

S. Timoshenko, D. H. Young, Elements of Strength of Materials (Van Nostrand, Princeton, N.J., 1962), Chap. 1, p. 11.

C.-H. Wu, “Variable lens assembly,” U.S. patent5,233,470 (3August1993).

S. Kurtin, “Variable focal length lens,” U.S. patent5,138,494, (11August1992).

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Figures (4)

Fig. 1.
Fig. 1.

Optical media of the variable-focus liquid-filled optical lens.

Fig. 2.
Fig. 2.

Focal length F l of the variable-focus liquid-filled optical lens versus the pressure w inside the lens.

Fig. 3.
Fig. 3.

Longitudinal spherical aberration ds of the variable-focus liquid-filled optical lens versus the height x at which a ray strikes the anterior surface of the thin elastic film.

Fig. 4.
Fig. 4.

Design of the variable-focus liquid-filled optical lens.

Tables (1)

Tables Icon

Table 1. Experimental and Theoretical Evaluations of the Focal Length of the Variable-Focus Liquid-Filled Optical Lens

Equations (5)

Equations on this page are rendered with MathJax. Learn more.

y = ( w / 4 T ) ( a 2 x 2 ) ,
E b = ( T / h ) m [ w + ( T / h ) ] ,
b = ( s 2 a ) / 2 a ,
s = 2 0 a { cos [ arctan ( w x / 2 T ) ] } 1 d x .
T 3 [ ( m / h ) ( 1 / h ) ] + T 2 m w + 0.04167 w 2 a 2 = 0.

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