Abstract

This paper proposes a tunable-focus liquid lens implemented with a simple cylindrical container structure and liquid as the lens material. The cylindrical container was constructed using a Pb [Zr0.52Ti0.48]O3 (PZT) ring transducer and a polydimethylsiloxane membrane that was attached to a flat side of the transducer. The free surface of the liquid in the cylindrical container can be driven as a static-like convex lens with different curvatures because the higher-order harmonic resonance of the PZT transducer was electrically controlled. Based on a capillary-force-dominant design, the activated liquid lens maintained surface curvature in an arbitrary orientation without a gravitational effect. Profiles of the liquid lenses were characterized with the driving voltages of the transducer ranging from 12 to 60 V peak-to-peak (Vpp) at a resonant frequency of 460 kHz. The temperature effects on the lenses caused by the continuous operation of the transducer were measured. Images showed the various curvatures of the lenses with a range of actuation voltages. A change in focal length of eight times (5.72 to 46.03 cm) was demonstrated within the 10 Vpp variation of the driving voltage. For the characterized liquid lenses, the distortion was less than 2%, and the modulation transfer function reached 63 line pairs per mm (lp/mm) using ZEMAX analysis.

© 2013 Optical Society of America

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  1. E. C. Tam, “Smart electro-optical zoom lens,” Opt. Lett. 17, 369–372 (1992).
    [CrossRef]
  2. M. Hatcher, “Liquid lenses eye commercial breakthrough,” Opt. Laser Eur. 111, 16 (2003).
  3. J. Kang, H. Yu, and H. Chen, “Liquid tunable lens integrated with a rotational symmetric surface for long depth of focus,” Appl. Opt. 49, 5493–5500 (2010).
    [CrossRef]
  4. K. Florian, M. Wolfgang, and Z. Hans, “Tunable liquid micro-lens system,” in Proceeding of the 13th Internal Conference on Solid-State Sensors, Actuators and Microsystems (IEEE, 2005, pp. 1014–1017.
  5. P. Liebetraut, S. Petsch, W. Mönch, and H. Zappe, “Tunable solid-body elastomer lenses with electromagnetic actuation,” Appl. Opt. 50, 3268–3274 (2011).
    [CrossRef]
  6. C. Li and H. Jiang, “Electrowetting-driven variable-focus microlens on flexible surfaces,” Appl. Phys. Lett. 100, 231105(2012).
    [CrossRef]
  7. J. K. Lee, J. C. Choi, W. I. Jang, H. R. Kim, and S. H. Kong, “Electrowetting lens employing hemispherical cavity formed by hydrofluoric acid, nitric acid, and acetic acid etching of silicon,” Jpn. J. Appl. Phys. 51, 06FL05 (2012).
    [CrossRef]
  8. A. M. Leshansky, A. Bransky, N. Korin, and U. Dinnar, “Tunable nonlinear viscoelastic ‘focusing’ in a microfluidic device,” Phys. Rev. Lett. 98, 234501 (2007).
    [CrossRef]
  9. H. Yu, G. Zhou, F. S. Chau, and S. K. Sinha, “Tunable electromagnetically actuated liquid-filled lens,” Sens. Actuat. A 167, 602–607 (2011).
    [CrossRef]
  10. D. Y. Zhang, N. Justis, and Y. H. Lo, “Fluidic adaptive zoom lens with high zoom ratio and widely tunable field of view,” Opt. Commun. 249, 175–182 (2005).
    [CrossRef]
  11. H. Ren, Y. H. Fan, and S. T. Wu, “Liquid-crystal microlens arrays using patterned polymer networks,” Opt. Lett. 29, 1608–1610 (2004).
    [CrossRef]
  12. Y. C. Lin and Y. H. Lin, “A fast response and large electrically tunable-focusing imaging system based on switching of two modes of a liquid crystal lens,” Appl. Phys. Lett. 97, 063505 (2010).
    [CrossRef]
  13. C.-C. Cheng and J. A. Yeh, “Dielectrically actuated liquid lens,” Opt. Express 15, 7140–7145 (2007).
    [CrossRef]
  14. C.-C. Yang, C.-W. G. Tsai, and J. A. Yeh, “Dynamic behavior of liquid microlenses actuated using dielectric force,” J. Microelectromech. Syst. 20, 1143–1149 (2011).
    [CrossRef]
  15. H. Ren and S. T. Wu, “Tunable-focus liquid microlens array using dielectrophoretic effect,” Opt. Express 16, 2646–2652 (2008).
    [CrossRef]
  16. D. Koyama, R. Isago, and K. Nakamura, “Liquid lens using acoustic radiation force: compact, high-speed variable-focus liquid lens using acoustic radiation force,” Opt. Express 18, 25158–25169 (2010).
    [CrossRef]
  17. D. Koyama, R. Isago, and K. Nakamura, “Ultrasonic variable-focus optical lens using viscoelastic material,” Appl. Phys. Lett. 100, 091102 (2012).
    [CrossRef]
  18. F. Zhu, “Rayleigh quotients for coupled free vibrations,” J. Sound Vib. 171, 641–649 (1994).
    [CrossRef]
  19. M. Amabili, “Ritz method and substructuring in the study of vibration with strong fluid-structure interaction,” J. Fluids Struct. 11, 507–523 (1997).
    [CrossRef]
  20. H. J.-P. Morand and E. Ohayon, Fluid Structure Interaction (Wiley, 1995).
  21. M. Amabili, M. P. Paidoussis, and A. A. Lakis, “Vibrations of partially filled cylindrical tanks with ring-stiffeners and flexible bottom,” J. Sound Vib. 213, 259–299 (1998).
    [CrossRef]
  22. S. Chantasiriwan, “Modal analysis of free vibration of liquid in rigid container by the method of fundamental solutions,” Eng. Anal. Bound. Elem. 33, 726–730 (2009).
    [CrossRef]
  23. G. H. Feng and Y. C. Chou, “Flexible meniscus/biconvex lens system with fluidic-controlled tunable-focus applications,” Appl. Opt. 48, 3284–3290 (2009).
    [CrossRef]

2012

C. Li and H. Jiang, “Electrowetting-driven variable-focus microlens on flexible surfaces,” Appl. Phys. Lett. 100, 231105(2012).
[CrossRef]

J. K. Lee, J. C. Choi, W. I. Jang, H. R. Kim, and S. H. Kong, “Electrowetting lens employing hemispherical cavity formed by hydrofluoric acid, nitric acid, and acetic acid etching of silicon,” Jpn. J. Appl. Phys. 51, 06FL05 (2012).
[CrossRef]

D. Koyama, R. Isago, and K. Nakamura, “Ultrasonic variable-focus optical lens using viscoelastic material,” Appl. Phys. Lett. 100, 091102 (2012).
[CrossRef]

2011

C.-C. Yang, C.-W. G. Tsai, and J. A. Yeh, “Dynamic behavior of liquid microlenses actuated using dielectric force,” J. Microelectromech. Syst. 20, 1143–1149 (2011).
[CrossRef]

H. Yu, G. Zhou, F. S. Chau, and S. K. Sinha, “Tunable electromagnetically actuated liquid-filled lens,” Sens. Actuat. A 167, 602–607 (2011).
[CrossRef]

P. Liebetraut, S. Petsch, W. Mönch, and H. Zappe, “Tunable solid-body elastomer lenses with electromagnetic actuation,” Appl. Opt. 50, 3268–3274 (2011).
[CrossRef]

2010

J. Kang, H. Yu, and H. Chen, “Liquid tunable lens integrated with a rotational symmetric surface for long depth of focus,” Appl. Opt. 49, 5493–5500 (2010).
[CrossRef]

Y. C. Lin and Y. H. Lin, “A fast response and large electrically tunable-focusing imaging system based on switching of two modes of a liquid crystal lens,” Appl. Phys. Lett. 97, 063505 (2010).
[CrossRef]

D. Koyama, R. Isago, and K. Nakamura, “Liquid lens using acoustic radiation force: compact, high-speed variable-focus liquid lens using acoustic radiation force,” Opt. Express 18, 25158–25169 (2010).
[CrossRef]

2009

S. Chantasiriwan, “Modal analysis of free vibration of liquid in rigid container by the method of fundamental solutions,” Eng. Anal. Bound. Elem. 33, 726–730 (2009).
[CrossRef]

G. H. Feng and Y. C. Chou, “Flexible meniscus/biconvex lens system with fluidic-controlled tunable-focus applications,” Appl. Opt. 48, 3284–3290 (2009).
[CrossRef]

2008

H. Ren and S. T. Wu, “Tunable-focus liquid microlens array using dielectrophoretic effect,” Opt. Express 16, 2646–2652 (2008).
[CrossRef]

2007

C.-C. Cheng and J. A. Yeh, “Dielectrically actuated liquid lens,” Opt. Express 15, 7140–7145 (2007).
[CrossRef]

A. M. Leshansky, A. Bransky, N. Korin, and U. Dinnar, “Tunable nonlinear viscoelastic ‘focusing’ in a microfluidic device,” Phys. Rev. Lett. 98, 234501 (2007).
[CrossRef]

2005

D. Y. Zhang, N. Justis, and Y. H. Lo, “Fluidic adaptive zoom lens with high zoom ratio and widely tunable field of view,” Opt. Commun. 249, 175–182 (2005).
[CrossRef]

2004

H. Ren, Y. H. Fan, and S. T. Wu, “Liquid-crystal microlens arrays using patterned polymer networks,” Opt. Lett. 29, 1608–1610 (2004).
[CrossRef]

2003

M. Hatcher, “Liquid lenses eye commercial breakthrough,” Opt. Laser Eur. 111, 16 (2003).

1998

M. Amabili, M. P. Paidoussis, and A. A. Lakis, “Vibrations of partially filled cylindrical tanks with ring-stiffeners and flexible bottom,” J. Sound Vib. 213, 259–299 (1998).
[CrossRef]

1997

M. Amabili, “Ritz method and substructuring in the study of vibration with strong fluid-structure interaction,” J. Fluids Struct. 11, 507–523 (1997).
[CrossRef]

1994

F. Zhu, “Rayleigh quotients for coupled free vibrations,” J. Sound Vib. 171, 641–649 (1994).
[CrossRef]

1992

E. C. Tam, “Smart electro-optical zoom lens,” Opt. Lett. 17, 369–372 (1992).
[CrossRef]

Amabili, M.

M. Amabili, M. P. Paidoussis, and A. A. Lakis, “Vibrations of partially filled cylindrical tanks with ring-stiffeners and flexible bottom,” J. Sound Vib. 213, 259–299 (1998).
[CrossRef]

M. Amabili, “Ritz method and substructuring in the study of vibration with strong fluid-structure interaction,” J. Fluids Struct. 11, 507–523 (1997).
[CrossRef]

Bransky, A.

A. M. Leshansky, A. Bransky, N. Korin, and U. Dinnar, “Tunable nonlinear viscoelastic ‘focusing’ in a microfluidic device,” Phys. Rev. Lett. 98, 234501 (2007).
[CrossRef]

Chantasiriwan, S.

S. Chantasiriwan, “Modal analysis of free vibration of liquid in rigid container by the method of fundamental solutions,” Eng. Anal. Bound. Elem. 33, 726–730 (2009).
[CrossRef]

Chau, F. S.

H. Yu, G. Zhou, F. S. Chau, and S. K. Sinha, “Tunable electromagnetically actuated liquid-filled lens,” Sens. Actuat. A 167, 602–607 (2011).
[CrossRef]

Chen, H.

J. Kang, H. Yu, and H. Chen, “Liquid tunable lens integrated with a rotational symmetric surface for long depth of focus,” Appl. Opt. 49, 5493–5500 (2010).
[CrossRef]

Cheng, C.-C.

C.-C. Cheng and J. A. Yeh, “Dielectrically actuated liquid lens,” Opt. Express 15, 7140–7145 (2007).
[CrossRef]

Choi, J. C.

J. K. Lee, J. C. Choi, W. I. Jang, H. R. Kim, and S. H. Kong, “Electrowetting lens employing hemispherical cavity formed by hydrofluoric acid, nitric acid, and acetic acid etching of silicon,” Jpn. J. Appl. Phys. 51, 06FL05 (2012).
[CrossRef]

Chou, Y. C.

G. H. Feng and Y. C. Chou, “Flexible meniscus/biconvex lens system with fluidic-controlled tunable-focus applications,” Appl. Opt. 48, 3284–3290 (2009).
[CrossRef]

Dinnar, U.

A. M. Leshansky, A. Bransky, N. Korin, and U. Dinnar, “Tunable nonlinear viscoelastic ‘focusing’ in a microfluidic device,” Phys. Rev. Lett. 98, 234501 (2007).
[CrossRef]

Fan, Y. H.

H. Ren, Y. H. Fan, and S. T. Wu, “Liquid-crystal microlens arrays using patterned polymer networks,” Opt. Lett. 29, 1608–1610 (2004).
[CrossRef]

Feng, G. H.

G. H. Feng and Y. C. Chou, “Flexible meniscus/biconvex lens system with fluidic-controlled tunable-focus applications,” Appl. Opt. 48, 3284–3290 (2009).
[CrossRef]

Florian, K.

K. Florian, M. Wolfgang, and Z. Hans, “Tunable liquid micro-lens system,” in Proceeding of the 13th Internal Conference on Solid-State Sensors, Actuators and Microsystems (IEEE, 2005, pp. 1014–1017.

Hans, Z.

K. Florian, M. Wolfgang, and Z. Hans, “Tunable liquid micro-lens system,” in Proceeding of the 13th Internal Conference on Solid-State Sensors, Actuators and Microsystems (IEEE, 2005, pp. 1014–1017.

Hatcher, M.

M. Hatcher, “Liquid lenses eye commercial breakthrough,” Opt. Laser Eur. 111, 16 (2003).

Isago, R.

D. Koyama, R. Isago, and K. Nakamura, “Ultrasonic variable-focus optical lens using viscoelastic material,” Appl. Phys. Lett. 100, 091102 (2012).
[CrossRef]

D. Koyama, R. Isago, and K. Nakamura, “Liquid lens using acoustic radiation force: compact, high-speed variable-focus liquid lens using acoustic radiation force,” Opt. Express 18, 25158–25169 (2010).
[CrossRef]

Jang, W. I.

J. K. Lee, J. C. Choi, W. I. Jang, H. R. Kim, and S. H. Kong, “Electrowetting lens employing hemispherical cavity formed by hydrofluoric acid, nitric acid, and acetic acid etching of silicon,” Jpn. J. Appl. Phys. 51, 06FL05 (2012).
[CrossRef]

Jiang, H.

C. Li and H. Jiang, “Electrowetting-driven variable-focus microlens on flexible surfaces,” Appl. Phys. Lett. 100, 231105(2012).
[CrossRef]

Justis, N.

D. Y. Zhang, N. Justis, and Y. H. Lo, “Fluidic adaptive zoom lens with high zoom ratio and widely tunable field of view,” Opt. Commun. 249, 175–182 (2005).
[CrossRef]

Kang, J.

J. Kang, H. Yu, and H. Chen, “Liquid tunable lens integrated with a rotational symmetric surface for long depth of focus,” Appl. Opt. 49, 5493–5500 (2010).
[CrossRef]

Kim, H. R.

J. K. Lee, J. C. Choi, W. I. Jang, H. R. Kim, and S. H. Kong, “Electrowetting lens employing hemispherical cavity formed by hydrofluoric acid, nitric acid, and acetic acid etching of silicon,” Jpn. J. Appl. Phys. 51, 06FL05 (2012).
[CrossRef]

Kong, S. H.

J. K. Lee, J. C. Choi, W. I. Jang, H. R. Kim, and S. H. Kong, “Electrowetting lens employing hemispherical cavity formed by hydrofluoric acid, nitric acid, and acetic acid etching of silicon,” Jpn. J. Appl. Phys. 51, 06FL05 (2012).
[CrossRef]

Korin, N.

A. M. Leshansky, A. Bransky, N. Korin, and U. Dinnar, “Tunable nonlinear viscoelastic ‘focusing’ in a microfluidic device,” Phys. Rev. Lett. 98, 234501 (2007).
[CrossRef]

Koyama, D.

D. Koyama, R. Isago, and K. Nakamura, “Ultrasonic variable-focus optical lens using viscoelastic material,” Appl. Phys. Lett. 100, 091102 (2012).
[CrossRef]

D. Koyama, R. Isago, and K. Nakamura, “Liquid lens using acoustic radiation force: compact, high-speed variable-focus liquid lens using acoustic radiation force,” Opt. Express 18, 25158–25169 (2010).
[CrossRef]

Lakis, A. A.

M. Amabili, M. P. Paidoussis, and A. A. Lakis, “Vibrations of partially filled cylindrical tanks with ring-stiffeners and flexible bottom,” J. Sound Vib. 213, 259–299 (1998).
[CrossRef]

Lee, J. K.

J. K. Lee, J. C. Choi, W. I. Jang, H. R. Kim, and S. H. Kong, “Electrowetting lens employing hemispherical cavity formed by hydrofluoric acid, nitric acid, and acetic acid etching of silicon,” Jpn. J. Appl. Phys. 51, 06FL05 (2012).
[CrossRef]

Leshansky, A. M.

A. M. Leshansky, A. Bransky, N. Korin, and U. Dinnar, “Tunable nonlinear viscoelastic ‘focusing’ in a microfluidic device,” Phys. Rev. Lett. 98, 234501 (2007).
[CrossRef]

Li, C.

C. Li and H. Jiang, “Electrowetting-driven variable-focus microlens on flexible surfaces,” Appl. Phys. Lett. 100, 231105(2012).
[CrossRef]

Liebetraut, P.

P. Liebetraut, S. Petsch, W. Mönch, and H. Zappe, “Tunable solid-body elastomer lenses with electromagnetic actuation,” Appl. Opt. 50, 3268–3274 (2011).
[CrossRef]

Lin, Y. C.

Y. C. Lin and Y. H. Lin, “A fast response and large electrically tunable-focusing imaging system based on switching of two modes of a liquid crystal lens,” Appl. Phys. Lett. 97, 063505 (2010).
[CrossRef]

Lin, Y. H.

Y. C. Lin and Y. H. Lin, “A fast response and large electrically tunable-focusing imaging system based on switching of two modes of a liquid crystal lens,” Appl. Phys. Lett. 97, 063505 (2010).
[CrossRef]

Lo, Y. H.

D. Y. Zhang, N. Justis, and Y. H. Lo, “Fluidic adaptive zoom lens with high zoom ratio and widely tunable field of view,” Opt. Commun. 249, 175–182 (2005).
[CrossRef]

Mönch, W.

P. Liebetraut, S. Petsch, W. Mönch, and H. Zappe, “Tunable solid-body elastomer lenses with electromagnetic actuation,” Appl. Opt. 50, 3268–3274 (2011).
[CrossRef]

Morand, H. J.-P.

H. J.-P. Morand and E. Ohayon, Fluid Structure Interaction (Wiley, 1995).

Nakamura, K.

D. Koyama, R. Isago, and K. Nakamura, “Ultrasonic variable-focus optical lens using viscoelastic material,” Appl. Phys. Lett. 100, 091102 (2012).
[CrossRef]

D. Koyama, R. Isago, and K. Nakamura, “Liquid lens using acoustic radiation force: compact, high-speed variable-focus liquid lens using acoustic radiation force,” Opt. Express 18, 25158–25169 (2010).
[CrossRef]

Ohayon, E.

H. J.-P. Morand and E. Ohayon, Fluid Structure Interaction (Wiley, 1995).

Paidoussis, M. P.

M. Amabili, M. P. Paidoussis, and A. A. Lakis, “Vibrations of partially filled cylindrical tanks with ring-stiffeners and flexible bottom,” J. Sound Vib. 213, 259–299 (1998).
[CrossRef]

Petsch, S.

P. Liebetraut, S. Petsch, W. Mönch, and H. Zappe, “Tunable solid-body elastomer lenses with electromagnetic actuation,” Appl. Opt. 50, 3268–3274 (2011).
[CrossRef]

Ren, H.

H. Ren and S. T. Wu, “Tunable-focus liquid microlens array using dielectrophoretic effect,” Opt. Express 16, 2646–2652 (2008).
[CrossRef]

H. Ren, Y. H. Fan, and S. T. Wu, “Liquid-crystal microlens arrays using patterned polymer networks,” Opt. Lett. 29, 1608–1610 (2004).
[CrossRef]

Sinha, S. K.

H. Yu, G. Zhou, F. S. Chau, and S. K. Sinha, “Tunable electromagnetically actuated liquid-filled lens,” Sens. Actuat. A 167, 602–607 (2011).
[CrossRef]

Tam, E. C.

E. C. Tam, “Smart electro-optical zoom lens,” Opt. Lett. 17, 369–372 (1992).
[CrossRef]

Tsai, C.-W. G.

C.-C. Yang, C.-W. G. Tsai, and J. A. Yeh, “Dynamic behavior of liquid microlenses actuated using dielectric force,” J. Microelectromech. Syst. 20, 1143–1149 (2011).
[CrossRef]

Wolfgang, M.

K. Florian, M. Wolfgang, and Z. Hans, “Tunable liquid micro-lens system,” in Proceeding of the 13th Internal Conference on Solid-State Sensors, Actuators and Microsystems (IEEE, 2005, pp. 1014–1017.

Wu, S. T.

H. Ren and S. T. Wu, “Tunable-focus liquid microlens array using dielectrophoretic effect,” Opt. Express 16, 2646–2652 (2008).
[CrossRef]

H. Ren, Y. H. Fan, and S. T. Wu, “Liquid-crystal microlens arrays using patterned polymer networks,” Opt. Lett. 29, 1608–1610 (2004).
[CrossRef]

Yang, C.-C.

C.-C. Yang, C.-W. G. Tsai, and J. A. Yeh, “Dynamic behavior of liquid microlenses actuated using dielectric force,” J. Microelectromech. Syst. 20, 1143–1149 (2011).
[CrossRef]

Yeh, J. A.

C.-C. Yang, C.-W. G. Tsai, and J. A. Yeh, “Dynamic behavior of liquid microlenses actuated using dielectric force,” J. Microelectromech. Syst. 20, 1143–1149 (2011).
[CrossRef]

C.-C. Cheng and J. A. Yeh, “Dielectrically actuated liquid lens,” Opt. Express 15, 7140–7145 (2007).
[CrossRef]

Yu, H.

H. Yu, G. Zhou, F. S. Chau, and S. K. Sinha, “Tunable electromagnetically actuated liquid-filled lens,” Sens. Actuat. A 167, 602–607 (2011).
[CrossRef]

J. Kang, H. Yu, and H. Chen, “Liquid tunable lens integrated with a rotational symmetric surface for long depth of focus,” Appl. Opt. 49, 5493–5500 (2010).
[CrossRef]

Zappe, H.

P. Liebetraut, S. Petsch, W. Mönch, and H. Zappe, “Tunable solid-body elastomer lenses with electromagnetic actuation,” Appl. Opt. 50, 3268–3274 (2011).
[CrossRef]

Zhang, D. Y.

D. Y. Zhang, N. Justis, and Y. H. Lo, “Fluidic adaptive zoom lens with high zoom ratio and widely tunable field of view,” Opt. Commun. 249, 175–182 (2005).
[CrossRef]

Zhou, G.

H. Yu, G. Zhou, F. S. Chau, and S. K. Sinha, “Tunable electromagnetically actuated liquid-filled lens,” Sens. Actuat. A 167, 602–607 (2011).
[CrossRef]

Zhu, F.

F. Zhu, “Rayleigh quotients for coupled free vibrations,” J. Sound Vib. 171, 641–649 (1994).
[CrossRef]

Appl. Opt.

J. Kang, H. Yu, and H. Chen, “Liquid tunable lens integrated with a rotational symmetric surface for long depth of focus,” Appl. Opt. 49, 5493–5500 (2010).
[CrossRef]

P. Liebetraut, S. Petsch, W. Mönch, and H. Zappe, “Tunable solid-body elastomer lenses with electromagnetic actuation,” Appl. Opt. 50, 3268–3274 (2011).
[CrossRef]

G. H. Feng and Y. C. Chou, “Flexible meniscus/biconvex lens system with fluidic-controlled tunable-focus applications,” Appl. Opt. 48, 3284–3290 (2009).
[CrossRef]

Appl. Phys. Lett.

C. Li and H. Jiang, “Electrowetting-driven variable-focus microlens on flexible surfaces,” Appl. Phys. Lett. 100, 231105(2012).
[CrossRef]

Y. C. Lin and Y. H. Lin, “A fast response and large electrically tunable-focusing imaging system based on switching of two modes of a liquid crystal lens,” Appl. Phys. Lett. 97, 063505 (2010).
[CrossRef]

D. Koyama, R. Isago, and K. Nakamura, “Ultrasonic variable-focus optical lens using viscoelastic material,” Appl. Phys. Lett. 100, 091102 (2012).
[CrossRef]

Eng. Anal. Bound. Elem.

S. Chantasiriwan, “Modal analysis of free vibration of liquid in rigid container by the method of fundamental solutions,” Eng. Anal. Bound. Elem. 33, 726–730 (2009).
[CrossRef]

J. Fluids Struct.

M. Amabili, “Ritz method and substructuring in the study of vibration with strong fluid-structure interaction,” J. Fluids Struct. 11, 507–523 (1997).
[CrossRef]

J. Microelectromech. Syst.

C.-C. Yang, C.-W. G. Tsai, and J. A. Yeh, “Dynamic behavior of liquid microlenses actuated using dielectric force,” J. Microelectromech. Syst. 20, 1143–1149 (2011).
[CrossRef]

J. Sound Vib.

F. Zhu, “Rayleigh quotients for coupled free vibrations,” J. Sound Vib. 171, 641–649 (1994).
[CrossRef]

M. Amabili, M. P. Paidoussis, and A. A. Lakis, “Vibrations of partially filled cylindrical tanks with ring-stiffeners and flexible bottom,” J. Sound Vib. 213, 259–299 (1998).
[CrossRef]

Jpn. J. Appl. Phys.

J. K. Lee, J. C. Choi, W. I. Jang, H. R. Kim, and S. H. Kong, “Electrowetting lens employing hemispherical cavity formed by hydrofluoric acid, nitric acid, and acetic acid etching of silicon,” Jpn. J. Appl. Phys. 51, 06FL05 (2012).
[CrossRef]

Opt. Commun.

D. Y. Zhang, N. Justis, and Y. H. Lo, “Fluidic adaptive zoom lens with high zoom ratio and widely tunable field of view,” Opt. Commun. 249, 175–182 (2005).
[CrossRef]

Opt. Express

C.-C. Cheng and J. A. Yeh, “Dielectrically actuated liquid lens,” Opt. Express 15, 7140–7145 (2007).
[CrossRef]

H. Ren and S. T. Wu, “Tunable-focus liquid microlens array using dielectrophoretic effect,” Opt. Express 16, 2646–2652 (2008).
[CrossRef]

D. Koyama, R. Isago, and K. Nakamura, “Liquid lens using acoustic radiation force: compact, high-speed variable-focus liquid lens using acoustic radiation force,” Opt. Express 18, 25158–25169 (2010).
[CrossRef]

Opt. Laser Eur.

M. Hatcher, “Liquid lenses eye commercial breakthrough,” Opt. Laser Eur. 111, 16 (2003).

Opt. Lett.

E. C. Tam, “Smart electro-optical zoom lens,” Opt. Lett. 17, 369–372 (1992).
[CrossRef]

H. Ren, Y. H. Fan, and S. T. Wu, “Liquid-crystal microlens arrays using patterned polymer networks,” Opt. Lett. 29, 1608–1610 (2004).
[CrossRef]

Phys. Rev. Lett.

A. M. Leshansky, A. Bransky, N. Korin, and U. Dinnar, “Tunable nonlinear viscoelastic ‘focusing’ in a microfluidic device,” Phys. Rev. Lett. 98, 234501 (2007).
[CrossRef]

Sens. Actuat. A

H. Yu, G. Zhou, F. S. Chau, and S. K. Sinha, “Tunable electromagnetically actuated liquid-filled lens,” Sens. Actuat. A 167, 602–607 (2011).
[CrossRef]

Other

K. Florian, M. Wolfgang, and Z. Hans, “Tunable liquid micro-lens system,” in Proceeding of the 13th Internal Conference on Solid-State Sensors, Actuators and Microsystems (IEEE, 2005, pp. 1014–1017.

H. J.-P. Morand and E. Ohayon, Fluid Structure Interaction (Wiley, 1995).

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Figures (11)

Fig. 1.
Fig. 1.

(a) Modeling of a certain amount of liquid in a cylindrical rigid container with a rigid ring and flexible bottom. (b) Profile of the free liquid surface is nearly the same as the main lobe of the Bessel function when the rigid ring is driven at a proper harmonic resonance.

Fig. 2.
Fig. 2.

Implementation of designed liquid lens constructed by PZT ring transducer, PDMS membrane, and DI water: (left) illustration and (right) photograph of fabrication result.

Fig. 3.
Fig. 3.

Images of various curvatures of the liquid surfaces obtained by the amplitudes of the driving signals from 12 to 60 Vpp at an operating frequency of 460 kHz.

Fig. 4.
Fig. 4.

Curve-fitting results of the six different lens profiles for the six amplitudes of the actuation voltages (unit: mm).

Fig. 5.
Fig. 5.

Results of finite element analysis (ANSYS software) elucidate the vibration mode of the PZT-ring/PDMS-membrane device at the resonant operation frequency of 460 kHz at different viewpoints: (a) top view, (b) side view, and (c) isometric view.

Fig. 6.
Fig. 6.

(a) Setup for acquiring images of the rotating lens from various angles at an identical electrical actuation. (b) through (f) Results of rotating the lenses at 180°, 135°, 90°, 45°, and 0°, respectively.

Fig. 7.
Fig. 7.

Results of the temperature measurement.

Fig. 8.
Fig. 8.

Images of the target at various distances adjusted for optimal focus at each distance, with the actuation voltages of the PZT transducer: (a) 30 Vpp, (b) 28 Vpp, (c) 26 Vpp, (d) 24 Vpp, (e) 22 Vpp, and (f) 20 Vpp.

Fig. 9.
Fig. 9.

Relationships among the driving voltage of the transducer (refer to Fig. 8), focal distance, and FOV value.

Fig. 10.
Fig. 10.

(a) ZEMAX model for simulation. Results of the field curvature/distortion by ZEMAX simulation for different actuation voltages of PZT transducer: (b) 60 Vpp, (c) 50 Vpp, and (d) 30 Vpp.

Fig. 11.
Fig. 11.

Results of the MTF by ZEMAX simulation for different actuation voltages of PZT transducer: (a) 60 Vpp, (b) 40 Vpp, (c) 30 Vpp, and (d) 12 Vpp.

Tables (1)

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Table 1. Coefficients of the Eighth-Order Polynomial Fitting Curves for the Liquid Lenses and Corresponding Fitting Errors

Equations (12)

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ϕr|r=a=w(x,θ),
ϕx|x=0=u(r,θ),
g·(ϕx|x=H)=ω2·(ϕ|x=H),
w(x,θ)=cos(nθ)s=1ps(2a/L)sin(sπx/L),
u(r,θ)=cos(nθ)i=0qi[AniJn(λnir/a)+CniIn(λnir/a)],
ϕ=ϕr+ϕb+ϕs,
g(ϕx|x=H)=ω2·ϕs|x=H.
ϕs=F00+m=1F0mJ0(ε0mra)cosh(ε0mxa),
δ(t)=ω2gϕs|x=H·ejωt=ϕx|x=H·ejωt.
ϕ˜t=pρ+gz+12ϕ˜·ϕ˜,
p=ρ(ϕ˜t)=ρω2·ϕ·ejωt.
F=Ap·dA,

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