Abstract

A novel design of a zoom lens system without motorized movements is proposed. The lens system consists of a fixed lens and two double-liquid variable-focus lenses. The liquid lenses, made out of two immiscible liquids, are based on the principle of electrowetting: an effect controlling the wetting properties of a liquid on a solid by modifying the applied voltage at the solid-liquid interface. The structure and principle of the lens system are introduced in this paper. Detailed calculations and simulation examples are presented to show that this zoom lens system appears viable as the next-generation zoom lens.

© 2007 Optical Society of America

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References

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  1. L. Saurei, G. Mathieu, and B. Berge, "Design of an autofocus lens for VGA ¼-in. CCD and CMOS sensors," Proc. SPIE 5249, 288-296 (2004).
    [CrossRef]
  2. G. I. Swanson and W. B. Veldkamp, "Infrared applications of diffractive optical elements," Proc. SPIE 883, 155-158 (1988).
  3. M. Ignacio, L. Claudio, M. Andres, C. Juan, and J. Y. Maria, "Modulation light efficiency of diffractive lenses displayed in a restricted phase-mostly modulation display," Appl. Opt. 43, 6278-6284 (2004).
  4. A. H. Robert and B. J. Feenstra, "Video-speed electronic paper based on electrowetting," Nature 25, 383-385 (2003).
  5. B. H. W. Hendriks, S. Kuiper, M. A. J. van As, C. A. Renders, and T. W. Tukker, "Variable liquid lenses for electronic products," Proc. SPIE 6034, 603402-1-603402-9 (2006).
    [CrossRef]
  6. B. Berge and J. Peseux, "Variable focal lens controlled by an external voltage," Eur. Phys. J. E. 3, 159-163 (2000).
    [CrossRef]
  7. S. Kuiper and B. H. W. Hendriks, "Variable-focus liquid lens for miniature cameras," Appl. Phys. Lett. 85, 1128-1130 (2004).
    [CrossRef]

2004

L. Saurei, G. Mathieu, and B. Berge, "Design of an autofocus lens for VGA ¼-in. CCD and CMOS sensors," Proc. SPIE 5249, 288-296 (2004).
[CrossRef]

S. Kuiper and B. H. W. Hendriks, "Variable-focus liquid lens for miniature cameras," Appl. Phys. Lett. 85, 1128-1130 (2004).
[CrossRef]

M. Ignacio, L. Claudio, M. Andres, C. Juan, and J. Y. Maria, "Modulation light efficiency of diffractive lenses displayed in a restricted phase-mostly modulation display," Appl. Opt. 43, 6278-6284 (2004).

2003

A. H. Robert and B. J. Feenstra, "Video-speed electronic paper based on electrowetting," Nature 25, 383-385 (2003).

2000

B. Berge and J. Peseux, "Variable focal lens controlled by an external voltage," Eur. Phys. J. E. 3, 159-163 (2000).
[CrossRef]

1988

G. I. Swanson and W. B. Veldkamp, "Infrared applications of diffractive optical elements," Proc. SPIE 883, 155-158 (1988).

Andres, M.

Berge, B.

L. Saurei, G. Mathieu, and B. Berge, "Design of an autofocus lens for VGA ¼-in. CCD and CMOS sensors," Proc. SPIE 5249, 288-296 (2004).
[CrossRef]

B. Berge and J. Peseux, "Variable focal lens controlled by an external voltage," Eur. Phys. J. E. 3, 159-163 (2000).
[CrossRef]

Claudio, L.

Feenstra, B. J.

A. H. Robert and B. J. Feenstra, "Video-speed electronic paper based on electrowetting," Nature 25, 383-385 (2003).

Hendriks, B. H. W.

S. Kuiper and B. H. W. Hendriks, "Variable-focus liquid lens for miniature cameras," Appl. Phys. Lett. 85, 1128-1130 (2004).
[CrossRef]

Ignacio, M.

Juan, C.

Kuiper, S.

S. Kuiper and B. H. W. Hendriks, "Variable-focus liquid lens for miniature cameras," Appl. Phys. Lett. 85, 1128-1130 (2004).
[CrossRef]

Maria, J. Y.

Mathieu, G.

L. Saurei, G. Mathieu, and B. Berge, "Design of an autofocus lens for VGA ¼-in. CCD and CMOS sensors," Proc. SPIE 5249, 288-296 (2004).
[CrossRef]

Peseux, J.

B. Berge and J. Peseux, "Variable focal lens controlled by an external voltage," Eur. Phys. J. E. 3, 159-163 (2000).
[CrossRef]

Robert, A. H.

A. H. Robert and B. J. Feenstra, "Video-speed electronic paper based on electrowetting," Nature 25, 383-385 (2003).

Saurei, L.

L. Saurei, G. Mathieu, and B. Berge, "Design of an autofocus lens for VGA ¼-in. CCD and CMOS sensors," Proc. SPIE 5249, 288-296 (2004).
[CrossRef]

Swanson, G. I.

G. I. Swanson and W. B. Veldkamp, "Infrared applications of diffractive optical elements," Proc. SPIE 883, 155-158 (1988).

Veldkamp, W. B.

G. I. Swanson and W. B. Veldkamp, "Infrared applications of diffractive optical elements," Proc. SPIE 883, 155-158 (1988).

Appl. Opt.

Appl. Phys. Lett.

S. Kuiper and B. H. W. Hendriks, "Variable-focus liquid lens for miniature cameras," Appl. Phys. Lett. 85, 1128-1130 (2004).
[CrossRef]

Eur. Phys. J. E.

B. Berge and J. Peseux, "Variable focal lens controlled by an external voltage," Eur. Phys. J. E. 3, 159-163 (2000).
[CrossRef]

Nature

A. H. Robert and B. J. Feenstra, "Video-speed electronic paper based on electrowetting," Nature 25, 383-385 (2003).

Proc. SPIE

L. Saurei, G. Mathieu, and B. Berge, "Design of an autofocus lens for VGA ¼-in. CCD and CMOS sensors," Proc. SPIE 5249, 288-296 (2004).
[CrossRef]

G. I. Swanson and W. B. Veldkamp, "Infrared applications of diffractive optical elements," Proc. SPIE 883, 155-158 (1988).

Other

B. H. W. Hendriks, S. Kuiper, M. A. J. van As, C. A. Renders, and T. W. Tukker, "Variable liquid lenses for electronic products," Proc. SPIE 6034, 603402-1-603402-9 (2006).
[CrossRef]

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Figures (6)

Fig. 1.
Fig. 1.

Cross section view of the double-liquid variable focus lens. The resulting interface shape is indicated by the dashed line.

Fig. 2.
Fig. 2.

Schematic of the proposed zoom lens. 1: fixed lens; 2: exit pupil of the fixed lens; 3, 4: double-liquid lens.

Fig. 3.
Fig. 3.

Schematic of a zoom lens with zero focal power for both liquid lenses. f 0 is the focal length of the fixed lens and P is the convergent point of rays from infinity.

Fig. 4.
Fig. 4.

Schematic of a zoom lens with non-zero focal power for both liquid lenses. is the convergent point of rays from infinity

Fig. 5.
Fig. 5.

Interface radius of the second liquid lens as a function of the interface radius of the first liquid lens.

Fig. 6.
Fig. 6.

(a). Voltage U 2 as a function of U 1 and (b) f , the focal length of the whole system as a function of U 1 for a dielectric layer with thicknesses of 1μm (circle) and 0.5μm (cross)

Equations (12)

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r = a [ cos θ 0 + ε 0 ε r U 2 ( 2 γ 12 d ) ] ,
l = ( f 0 d 1 ) n 0 d 2 n 1 n 0 d 3 n 2 d 4 n 0 d 5 n 1 n 0 d 6 n 2 ,
l = ( f 0 d 1 d 4 ) n 0 ( k 1 d 01 + k 2 d 02 ) ( n 2 n 1 ) ( n 1 n 2 ) n 0 ( d 01 + d 02 ) n 2 ,
l ′′ = n 0 n 2 [ n 2 ( n 1 α n 0 d 5 ) r 5 n 1 r 5 + ( n 1 α n 0 d 5 ) ( n 2 n 1 ) ( d 02 d 5 ) ] ,
α = n 0 n 2 { n 2 r 2 [ n 1 ( f 0 d 1 ) n 0 d 2 ] n 1 r 2 + [ n 1 ( f 0 d 1 ) n 0 d 2 ] ( n 2 n 1 ) ( d 01 d 2 ) } d 4 .
d 2 = k 1 d 01 + [ 2 r 2 3 + 2 r 2 2 ( r 2 2 a 1 2 ) 1 / 2 3 a 1 2 r 2 2 a 1 2 ( r 2 2 a 1 2 ) 1 / 2 ] ( 3 a 1 2 ) , r 2 < 0
d 5 = = k 2 d 02 + [ 2 r 5 3 2 r 5 2 ( r 5 2 a 2 2 ) 1 / 2 3 a 2 2 r 5 + 2 a 2 2 ( r 5 2 a 2 2 ) 1 / 2 ] ( 3 a 2 2 ) , r 5 > 0
l ′′ = l .
r 5 = ( n 2 l + d 02 d 5 = ) ( n 1 α d 5 ) ( n 2 n 1 ) n 2 ( n 1 α d 5 ) n 1 ( n 2 l + d 02 d 5 ) ,
r 2 = a 1 [ cos θ 0 + ε 0 ε r U 1 2 ( 2 γ 12 d ) ] .
r 5 = a 2 [ cos θ 0 + ε 0 ε r U 2 2 ( 2 γ 12 d ) ] .
f = n 1 2 r 2 r 5 f 0 { n 1 r 2 + [ n 1 ( f 0 d 1 ) n 0 d 2 ] ( n 2 n 1 ) } [ ( n 2 n 1 ) ( n 1 α n 0 d 5 ) + n 1 r 5 ] .

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