Abstract

It is very difficult to fabricate tunable optical systems having an aperture below 1000 micrometers with the conventional means on macroscopic scale. Krogmann et al. (J. Opt. A 8, S330-S336, 2006) presented a MEMS-based tunable liquid micro-lens system with an aperture of 300 micrometers. The system exhibited a tuning range of back focal length between 2.3mm and infinity by using the electrowetting effect to change the contact angle of the meniscus shape on silicon with a voltage of 0–45V. However, spherical aberration was found in their lens system. In the present study, a numerical simulation is performed for this same physical configuration by solving the Young-Laplace equation on the interface of the lens liquid and the surrounding liquid. The resulting meniscus shape produces a back focal length that agrees with the experimental observation excellently. To eliminate the spherical aberration, an electric field is applied on the lens. The electric field alters the Young-Laplace equation and thus changes the meniscus shape and the lens quality. The numerical result shows that the spherical aberration of the lens can be essentially eliminated when a proper electric field is applied.

©2008 Optical Society of America

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References

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  1. B. Berge and J. Peseux, “Variable Focal Lens Controlled by an External Voltage: an Application of Electrowetting,” Eur. Phys. J. E 3, 159–163 (2000).
    [Crossref]
  2. C.-C. Cheng and J. A. Yeh, “Dielectrically Actuated Liquid Lens,” Opt. Express 15, 7140–7145 (2007).
    [Crossref] [PubMed]
  3. B. Berge, “Liquid Lens Technology: Principle of Electrowetting Based Lenses and Applications to Image,” Proceedings of the 18th IEEE Int. Conf. on Micro Electro Mechanical Systems (2005), pp. 227–230.
  4. S. Kuiper and B. H. W. Hendriks, “Variable-Focus Liquid Lens for Miniature Cameras,” Appl. Phys. Lett. 85, 1128–1130 (2004).
    [Crossref]
  5. B. H. W. Hendriks, S. Kuiper, M. A. J. van As, C. A. Renders, and T. W. Tukker, “Electrowetting-Based Variable-Focus Lens for Miniature Systems,” Opt. Rev. 12, 255–259 (2005).
    [Crossref]
  6. F. Krogmann, W. Monch, and H. Zappe, “A MEMS-Based Variable Micro-Lens System,” J. Opt. A 8, S330–S336 (2006).
    [Crossref]
  7. T. Sarpkaya, “Vorticity, free surface and surfactants,” Annu. Rev. Fluid Mech. 28, 83–128 (1996).
    [Crossref]
  8. S.-L. Lee and H.-D. Lee, “Evolution of Liquid Meniscus Shape in a Capillary Tube,” ASME J. Fluids Eng. 129, 957–965 (2007).
    [Crossref]
  9. S.-L. Lee and W.-B. Tien, “Growth and Detachment of Carbon Dioxide Bubbles on a Horizontal Porous Surface with a Uniform Mass Injection,” Int. J. Heat Mass Transfer (accepted for publication).
  10. B. Berge, “Electrocapillarite et Mouillage de Films Isolant par l’eau,” C. R. Acad. Sci. Paris III 317, 157–163 (1993).
  11. W. J. Smith, Modern Optical Engineering (McGraw-Hill, 2000), Chap. 10.
  12. A. Bateni, S. S. Susnar, A. Amirfazli, and A. W. Neumann, “Development of a New methodology to Study Drop Shape and Surface Tension in Electric Fields,” Langmuir 20, 7589–7597 (2004).
    [Crossref] [PubMed]
  13. A. Bateni, A. Ababneh, J. A. W. Elliott, A. W. Neumann, and A. Amirfazli, “Effect of Gravity and Electric Field on Shape and Surface Tension of Drops,” Adv. Space Res. 36, 64–69 (2005).
    [Crossref]
  14. C.-C. Cheng, C. A. Chang, C. G. Tsai, C.-L. Peng, and J. A. Yeh, “A Dielectrically Driven Liquid Lens with Optical Packaging,” IEEE/LEOS Int. Conf. on Optical MENS and Nanophotonics, pp. 65–66 (2007).
  15. S. L. Lee and C. R. Ou, “Integration Scheme for Elastic Deformation and Stresses,” ASME J. Appl. Mech. 66, 978–985 (1999).
    [Crossref]
  16. S. L. Lee and S. R. Sheu, “A New Formulation for Incompressible Viscous Free Surface Flow without Smearing the Free Surface,” Int. J. Heat Mass Transfer 44, 1837–1848 (2001).
    [Crossref]
  17. J. R. Sparrow, R. Ortiz, P. R. Macleish, and S. Chang, “Fibroblast Behavior at Aqueous Interfaces with Perfluorocarbon, Silicone, and Fluorosilicone Liquids,” Invest. Ophthalmol. Visual Sci. 31, 638–646 (1990).
  18. G. A. Peyman, J. A. Schulman, and B. Sullivan, “Perfluorocarbon Liquids in Ophthalmology,” Surv. Ophthalmol. 39, 375–395 (1995).
    [Crossref] [PubMed]
  19. H. Hoerauf, K. Kobuch, J. Dresp, and D.-H. Menz, “Combined use of Partially Fluorinated Alkanes, Perfluorocarbon Liquids and Silicon Oil: an Experimental Study,” Graefe’s Arch. Clin. Exp. Ophthalmol. 239, 373–381 (2001).
    [Crossref]
  20. K. Kobuch, D. H. Menz, H. Hoerauf, J. H. Dresp, and V.-P. Gabel, “New Substances for Intraocular Tamponades: Perfluorocarbon Liquids, Hydrofluorocarbon Liquids and Hydrofluorocarbon-Oligomers in Vitreoretinal Surgery,” Graefe’s Arch. Clin. Exp. Ophthalmol. 239, 635–642 (2001).
    [Crossref]
  21. M. Vallet, M. Vallade, and B. Berge, “Limiting Phenomena for the Spreading of Water on Polymer Films by Electrowetting,” Eur. Phys. J. B 11, 583–591 (1999).
    [Crossref]
  22. V. Peykov, A. Quinn, and J. Ralston, “Electrowetting: a Model for Contact-Angle Saturation,” Colloid Polym. Sci. 278, 789–793 (2000).
    [Crossref]

2007 (2)

S.-L. Lee and H.-D. Lee, “Evolution of Liquid Meniscus Shape in a Capillary Tube,” ASME J. Fluids Eng. 129, 957–965 (2007).
[Crossref]

C.-C. Cheng and J. A. Yeh, “Dielectrically Actuated Liquid Lens,” Opt. Express 15, 7140–7145 (2007).
[Crossref] [PubMed]

2006 (1)

F. Krogmann, W. Monch, and H. Zappe, “A MEMS-Based Variable Micro-Lens System,” J. Opt. A 8, S330–S336 (2006).
[Crossref]

2005 (2)

B. H. W. Hendriks, S. Kuiper, M. A. J. van As, C. A. Renders, and T. W. Tukker, “Electrowetting-Based Variable-Focus Lens for Miniature Systems,” Opt. Rev. 12, 255–259 (2005).
[Crossref]

A. Bateni, A. Ababneh, J. A. W. Elliott, A. W. Neumann, and A. Amirfazli, “Effect of Gravity and Electric Field on Shape and Surface Tension of Drops,” Adv. Space Res. 36, 64–69 (2005).
[Crossref]

2004 (2)

S. Kuiper and B. H. W. Hendriks, “Variable-Focus Liquid Lens for Miniature Cameras,” Appl. Phys. Lett. 85, 1128–1130 (2004).
[Crossref]

A. Bateni, S. S. Susnar, A. Amirfazli, and A. W. Neumann, “Development of a New methodology to Study Drop Shape and Surface Tension in Electric Fields,” Langmuir 20, 7589–7597 (2004).
[Crossref] [PubMed]

2001 (3)

S. L. Lee and S. R. Sheu, “A New Formulation for Incompressible Viscous Free Surface Flow without Smearing the Free Surface,” Int. J. Heat Mass Transfer 44, 1837–1848 (2001).
[Crossref]

H. Hoerauf, K. Kobuch, J. Dresp, and D.-H. Menz, “Combined use of Partially Fluorinated Alkanes, Perfluorocarbon Liquids and Silicon Oil: an Experimental Study,” Graefe’s Arch. Clin. Exp. Ophthalmol. 239, 373–381 (2001).
[Crossref]

K. Kobuch, D. H. Menz, H. Hoerauf, J. H. Dresp, and V.-P. Gabel, “New Substances for Intraocular Tamponades: Perfluorocarbon Liquids, Hydrofluorocarbon Liquids and Hydrofluorocarbon-Oligomers in Vitreoretinal Surgery,” Graefe’s Arch. Clin. Exp. Ophthalmol. 239, 635–642 (2001).
[Crossref]

2000 (2)

V. Peykov, A. Quinn, and J. Ralston, “Electrowetting: a Model for Contact-Angle Saturation,” Colloid Polym. Sci. 278, 789–793 (2000).
[Crossref]

B. Berge and J. Peseux, “Variable Focal Lens Controlled by an External Voltage: an Application of Electrowetting,” Eur. Phys. J. E 3, 159–163 (2000).
[Crossref]

1999 (2)

M. Vallet, M. Vallade, and B. Berge, “Limiting Phenomena for the Spreading of Water on Polymer Films by Electrowetting,” Eur. Phys. J. B 11, 583–591 (1999).
[Crossref]

S. L. Lee and C. R. Ou, “Integration Scheme for Elastic Deformation and Stresses,” ASME J. Appl. Mech. 66, 978–985 (1999).
[Crossref]

1996 (1)

T. Sarpkaya, “Vorticity, free surface and surfactants,” Annu. Rev. Fluid Mech. 28, 83–128 (1996).
[Crossref]

1995 (1)

G. A. Peyman, J. A. Schulman, and B. Sullivan, “Perfluorocarbon Liquids in Ophthalmology,” Surv. Ophthalmol. 39, 375–395 (1995).
[Crossref] [PubMed]

1993 (1)

B. Berge, “Electrocapillarite et Mouillage de Films Isolant par l’eau,” C. R. Acad. Sci. Paris III 317, 157–163 (1993).

1990 (1)

J. R. Sparrow, R. Ortiz, P. R. Macleish, and S. Chang, “Fibroblast Behavior at Aqueous Interfaces with Perfluorocarbon, Silicone, and Fluorosilicone Liquids,” Invest. Ophthalmol. Visual Sci. 31, 638–646 (1990).

Ababneh, A.

A. Bateni, A. Ababneh, J. A. W. Elliott, A. W. Neumann, and A. Amirfazli, “Effect of Gravity and Electric Field on Shape and Surface Tension of Drops,” Adv. Space Res. 36, 64–69 (2005).
[Crossref]

Amirfazli, A.

A. Bateni, A. Ababneh, J. A. W. Elliott, A. W. Neumann, and A. Amirfazli, “Effect of Gravity and Electric Field on Shape and Surface Tension of Drops,” Adv. Space Res. 36, 64–69 (2005).
[Crossref]

A. Bateni, S. S. Susnar, A. Amirfazli, and A. W. Neumann, “Development of a New methodology to Study Drop Shape and Surface Tension in Electric Fields,” Langmuir 20, 7589–7597 (2004).
[Crossref] [PubMed]

Bateni, A.

A. Bateni, A. Ababneh, J. A. W. Elliott, A. W. Neumann, and A. Amirfazli, “Effect of Gravity and Electric Field on Shape and Surface Tension of Drops,” Adv. Space Res. 36, 64–69 (2005).
[Crossref]

A. Bateni, S. S. Susnar, A. Amirfazli, and A. W. Neumann, “Development of a New methodology to Study Drop Shape and Surface Tension in Electric Fields,” Langmuir 20, 7589–7597 (2004).
[Crossref] [PubMed]

Berge, B.

B. Berge and J. Peseux, “Variable Focal Lens Controlled by an External Voltage: an Application of Electrowetting,” Eur. Phys. J. E 3, 159–163 (2000).
[Crossref]

M. Vallet, M. Vallade, and B. Berge, “Limiting Phenomena for the Spreading of Water on Polymer Films by Electrowetting,” Eur. Phys. J. B 11, 583–591 (1999).
[Crossref]

B. Berge, “Electrocapillarite et Mouillage de Films Isolant par l’eau,” C. R. Acad. Sci. Paris III 317, 157–163 (1993).

B. Berge, “Liquid Lens Technology: Principle of Electrowetting Based Lenses and Applications to Image,” Proceedings of the 18th IEEE Int. Conf. on Micro Electro Mechanical Systems (2005), pp. 227–230.

Chang, C. A.

C.-C. Cheng, C. A. Chang, C. G. Tsai, C.-L. Peng, and J. A. Yeh, “A Dielectrically Driven Liquid Lens with Optical Packaging,” IEEE/LEOS Int. Conf. on Optical MENS and Nanophotonics, pp. 65–66 (2007).

Chang, S.

J. R. Sparrow, R. Ortiz, P. R. Macleish, and S. Chang, “Fibroblast Behavior at Aqueous Interfaces with Perfluorocarbon, Silicone, and Fluorosilicone Liquids,” Invest. Ophthalmol. Visual Sci. 31, 638–646 (1990).

Cheng, C.-C.

C.-C. Cheng and J. A. Yeh, “Dielectrically Actuated Liquid Lens,” Opt. Express 15, 7140–7145 (2007).
[Crossref] [PubMed]

C.-C. Cheng, C. A. Chang, C. G. Tsai, C.-L. Peng, and J. A. Yeh, “A Dielectrically Driven Liquid Lens with Optical Packaging,” IEEE/LEOS Int. Conf. on Optical MENS and Nanophotonics, pp. 65–66 (2007).

Dresp, J.

H. Hoerauf, K. Kobuch, J. Dresp, and D.-H. Menz, “Combined use of Partially Fluorinated Alkanes, Perfluorocarbon Liquids and Silicon Oil: an Experimental Study,” Graefe’s Arch. Clin. Exp. Ophthalmol. 239, 373–381 (2001).
[Crossref]

Dresp, J. H.

K. Kobuch, D. H. Menz, H. Hoerauf, J. H. Dresp, and V.-P. Gabel, “New Substances for Intraocular Tamponades: Perfluorocarbon Liquids, Hydrofluorocarbon Liquids and Hydrofluorocarbon-Oligomers in Vitreoretinal Surgery,” Graefe’s Arch. Clin. Exp. Ophthalmol. 239, 635–642 (2001).
[Crossref]

Elliott, J. A. W.

A. Bateni, A. Ababneh, J. A. W. Elliott, A. W. Neumann, and A. Amirfazli, “Effect of Gravity and Electric Field on Shape and Surface Tension of Drops,” Adv. Space Res. 36, 64–69 (2005).
[Crossref]

Gabel, V.-P.

K. Kobuch, D. H. Menz, H. Hoerauf, J. H. Dresp, and V.-P. Gabel, “New Substances for Intraocular Tamponades: Perfluorocarbon Liquids, Hydrofluorocarbon Liquids and Hydrofluorocarbon-Oligomers in Vitreoretinal Surgery,” Graefe’s Arch. Clin. Exp. Ophthalmol. 239, 635–642 (2001).
[Crossref]

Hendriks, B. H. W.

B. H. W. Hendriks, S. Kuiper, M. A. J. van As, C. A. Renders, and T. W. Tukker, “Electrowetting-Based Variable-Focus Lens for Miniature Systems,” Opt. Rev. 12, 255–259 (2005).
[Crossref]

S. Kuiper and B. H. W. Hendriks, “Variable-Focus Liquid Lens for Miniature Cameras,” Appl. Phys. Lett. 85, 1128–1130 (2004).
[Crossref]

Hoerauf, H.

K. Kobuch, D. H. Menz, H. Hoerauf, J. H. Dresp, and V.-P. Gabel, “New Substances for Intraocular Tamponades: Perfluorocarbon Liquids, Hydrofluorocarbon Liquids and Hydrofluorocarbon-Oligomers in Vitreoretinal Surgery,” Graefe’s Arch. Clin. Exp. Ophthalmol. 239, 635–642 (2001).
[Crossref]

H. Hoerauf, K. Kobuch, J. Dresp, and D.-H. Menz, “Combined use of Partially Fluorinated Alkanes, Perfluorocarbon Liquids and Silicon Oil: an Experimental Study,” Graefe’s Arch. Clin. Exp. Ophthalmol. 239, 373–381 (2001).
[Crossref]

Kobuch, K.

H. Hoerauf, K. Kobuch, J. Dresp, and D.-H. Menz, “Combined use of Partially Fluorinated Alkanes, Perfluorocarbon Liquids and Silicon Oil: an Experimental Study,” Graefe’s Arch. Clin. Exp. Ophthalmol. 239, 373–381 (2001).
[Crossref]

K. Kobuch, D. H. Menz, H. Hoerauf, J. H. Dresp, and V.-P. Gabel, “New Substances for Intraocular Tamponades: Perfluorocarbon Liquids, Hydrofluorocarbon Liquids and Hydrofluorocarbon-Oligomers in Vitreoretinal Surgery,” Graefe’s Arch. Clin. Exp. Ophthalmol. 239, 635–642 (2001).
[Crossref]

Krogmann, F.

F. Krogmann, W. Monch, and H. Zappe, “A MEMS-Based Variable Micro-Lens System,” J. Opt. A 8, S330–S336 (2006).
[Crossref]

Kuiper, S.

B. H. W. Hendriks, S. Kuiper, M. A. J. van As, C. A. Renders, and T. W. Tukker, “Electrowetting-Based Variable-Focus Lens for Miniature Systems,” Opt. Rev. 12, 255–259 (2005).
[Crossref]

S. Kuiper and B. H. W. Hendriks, “Variable-Focus Liquid Lens for Miniature Cameras,” Appl. Phys. Lett. 85, 1128–1130 (2004).
[Crossref]

Lee, H.-D.

S.-L. Lee and H.-D. Lee, “Evolution of Liquid Meniscus Shape in a Capillary Tube,” ASME J. Fluids Eng. 129, 957–965 (2007).
[Crossref]

Lee, S. L.

S. L. Lee and S. R. Sheu, “A New Formulation for Incompressible Viscous Free Surface Flow without Smearing the Free Surface,” Int. J. Heat Mass Transfer 44, 1837–1848 (2001).
[Crossref]

S. L. Lee and C. R. Ou, “Integration Scheme for Elastic Deformation and Stresses,” ASME J. Appl. Mech. 66, 978–985 (1999).
[Crossref]

Lee, S.-L.

S.-L. Lee and H.-D. Lee, “Evolution of Liquid Meniscus Shape in a Capillary Tube,” ASME J. Fluids Eng. 129, 957–965 (2007).
[Crossref]

S.-L. Lee and W.-B. Tien, “Growth and Detachment of Carbon Dioxide Bubbles on a Horizontal Porous Surface with a Uniform Mass Injection,” Int. J. Heat Mass Transfer (accepted for publication).

Macleish, P. R.

J. R. Sparrow, R. Ortiz, P. R. Macleish, and S. Chang, “Fibroblast Behavior at Aqueous Interfaces with Perfluorocarbon, Silicone, and Fluorosilicone Liquids,” Invest. Ophthalmol. Visual Sci. 31, 638–646 (1990).

Menz, D. H.

K. Kobuch, D. H. Menz, H. Hoerauf, J. H. Dresp, and V.-P. Gabel, “New Substances for Intraocular Tamponades: Perfluorocarbon Liquids, Hydrofluorocarbon Liquids and Hydrofluorocarbon-Oligomers in Vitreoretinal Surgery,” Graefe’s Arch. Clin. Exp. Ophthalmol. 239, 635–642 (2001).
[Crossref]

Menz, D.-H.

H. Hoerauf, K. Kobuch, J. Dresp, and D.-H. Menz, “Combined use of Partially Fluorinated Alkanes, Perfluorocarbon Liquids and Silicon Oil: an Experimental Study,” Graefe’s Arch. Clin. Exp. Ophthalmol. 239, 373–381 (2001).
[Crossref]

Monch, W.

F. Krogmann, W. Monch, and H. Zappe, “A MEMS-Based Variable Micro-Lens System,” J. Opt. A 8, S330–S336 (2006).
[Crossref]

Neumann, A. W.

A. Bateni, A. Ababneh, J. A. W. Elliott, A. W. Neumann, and A. Amirfazli, “Effect of Gravity and Electric Field on Shape and Surface Tension of Drops,” Adv. Space Res. 36, 64–69 (2005).
[Crossref]

A. Bateni, S. S. Susnar, A. Amirfazli, and A. W. Neumann, “Development of a New methodology to Study Drop Shape and Surface Tension in Electric Fields,” Langmuir 20, 7589–7597 (2004).
[Crossref] [PubMed]

Ortiz, R.

J. R. Sparrow, R. Ortiz, P. R. Macleish, and S. Chang, “Fibroblast Behavior at Aqueous Interfaces with Perfluorocarbon, Silicone, and Fluorosilicone Liquids,” Invest. Ophthalmol. Visual Sci. 31, 638–646 (1990).

Ou, C. R.

S. L. Lee and C. R. Ou, “Integration Scheme for Elastic Deformation and Stresses,” ASME J. Appl. Mech. 66, 978–985 (1999).
[Crossref]

Peng, C.-L.

C.-C. Cheng, C. A. Chang, C. G. Tsai, C.-L. Peng, and J. A. Yeh, “A Dielectrically Driven Liquid Lens with Optical Packaging,” IEEE/LEOS Int. Conf. on Optical MENS and Nanophotonics, pp. 65–66 (2007).

Peseux, J.

B. Berge and J. Peseux, “Variable Focal Lens Controlled by an External Voltage: an Application of Electrowetting,” Eur. Phys. J. E 3, 159–163 (2000).
[Crossref]

Peykov, V.

V. Peykov, A. Quinn, and J. Ralston, “Electrowetting: a Model for Contact-Angle Saturation,” Colloid Polym. Sci. 278, 789–793 (2000).
[Crossref]

Peyman, G. A.

G. A. Peyman, J. A. Schulman, and B. Sullivan, “Perfluorocarbon Liquids in Ophthalmology,” Surv. Ophthalmol. 39, 375–395 (1995).
[Crossref] [PubMed]

Quinn, A.

V. Peykov, A. Quinn, and J. Ralston, “Electrowetting: a Model for Contact-Angle Saturation,” Colloid Polym. Sci. 278, 789–793 (2000).
[Crossref]

Ralston, J.

V. Peykov, A. Quinn, and J. Ralston, “Electrowetting: a Model for Contact-Angle Saturation,” Colloid Polym. Sci. 278, 789–793 (2000).
[Crossref]

Renders, C. A.

B. H. W. Hendriks, S. Kuiper, M. A. J. van As, C. A. Renders, and T. W. Tukker, “Electrowetting-Based Variable-Focus Lens for Miniature Systems,” Opt. Rev. 12, 255–259 (2005).
[Crossref]

Sarpkaya, T.

T. Sarpkaya, “Vorticity, free surface and surfactants,” Annu. Rev. Fluid Mech. 28, 83–128 (1996).
[Crossref]

Schulman, J. A.

G. A. Peyman, J. A. Schulman, and B. Sullivan, “Perfluorocarbon Liquids in Ophthalmology,” Surv. Ophthalmol. 39, 375–395 (1995).
[Crossref] [PubMed]

Sheu, S. R.

S. L. Lee and S. R. Sheu, “A New Formulation for Incompressible Viscous Free Surface Flow without Smearing the Free Surface,” Int. J. Heat Mass Transfer 44, 1837–1848 (2001).
[Crossref]

Smith, W. J.

W. J. Smith, Modern Optical Engineering (McGraw-Hill, 2000), Chap. 10.

Sparrow, J. R.

J. R. Sparrow, R. Ortiz, P. R. Macleish, and S. Chang, “Fibroblast Behavior at Aqueous Interfaces with Perfluorocarbon, Silicone, and Fluorosilicone Liquids,” Invest. Ophthalmol. Visual Sci. 31, 638–646 (1990).

Sullivan, B.

G. A. Peyman, J. A. Schulman, and B. Sullivan, “Perfluorocarbon Liquids in Ophthalmology,” Surv. Ophthalmol. 39, 375–395 (1995).
[Crossref] [PubMed]

Susnar, S. S.

A. Bateni, S. S. Susnar, A. Amirfazli, and A. W. Neumann, “Development of a New methodology to Study Drop Shape and Surface Tension in Electric Fields,” Langmuir 20, 7589–7597 (2004).
[Crossref] [PubMed]

Tien, W.-B.

S.-L. Lee and W.-B. Tien, “Growth and Detachment of Carbon Dioxide Bubbles on a Horizontal Porous Surface with a Uniform Mass Injection,” Int. J. Heat Mass Transfer (accepted for publication).

Tsai, C. G.

C.-C. Cheng, C. A. Chang, C. G. Tsai, C.-L. Peng, and J. A. Yeh, “A Dielectrically Driven Liquid Lens with Optical Packaging,” IEEE/LEOS Int. Conf. on Optical MENS and Nanophotonics, pp. 65–66 (2007).

Tukker, T. W.

B. H. W. Hendriks, S. Kuiper, M. A. J. van As, C. A. Renders, and T. W. Tukker, “Electrowetting-Based Variable-Focus Lens for Miniature Systems,” Opt. Rev. 12, 255–259 (2005).
[Crossref]

Vallade, M.

M. Vallet, M. Vallade, and B. Berge, “Limiting Phenomena for the Spreading of Water on Polymer Films by Electrowetting,” Eur. Phys. J. B 11, 583–591 (1999).
[Crossref]

Vallet, M.

M. Vallet, M. Vallade, and B. Berge, “Limiting Phenomena for the Spreading of Water on Polymer Films by Electrowetting,” Eur. Phys. J. B 11, 583–591 (1999).
[Crossref]

van As, M. A. J.

B. H. W. Hendriks, S. Kuiper, M. A. J. van As, C. A. Renders, and T. W. Tukker, “Electrowetting-Based Variable-Focus Lens for Miniature Systems,” Opt. Rev. 12, 255–259 (2005).
[Crossref]

Yeh, J. A.

C.-C. Cheng and J. A. Yeh, “Dielectrically Actuated Liquid Lens,” Opt. Express 15, 7140–7145 (2007).
[Crossref] [PubMed]

C.-C. Cheng, C. A. Chang, C. G. Tsai, C.-L. Peng, and J. A. Yeh, “A Dielectrically Driven Liquid Lens with Optical Packaging,” IEEE/LEOS Int. Conf. on Optical MENS and Nanophotonics, pp. 65–66 (2007).

Zappe, H.

F. Krogmann, W. Monch, and H. Zappe, “A MEMS-Based Variable Micro-Lens System,” J. Opt. A 8, S330–S336 (2006).
[Crossref]

Adv. Space Res. (1)

A. Bateni, A. Ababneh, J. A. W. Elliott, A. W. Neumann, and A. Amirfazli, “Effect of Gravity and Electric Field on Shape and Surface Tension of Drops,” Adv. Space Res. 36, 64–69 (2005).
[Crossref]

Annu. Rev. Fluid Mech. (1)

T. Sarpkaya, “Vorticity, free surface and surfactants,” Annu. Rev. Fluid Mech. 28, 83–128 (1996).
[Crossref]

Appl. Phys. Lett. (1)

S. Kuiper and B. H. W. Hendriks, “Variable-Focus Liquid Lens for Miniature Cameras,” Appl. Phys. Lett. 85, 1128–1130 (2004).
[Crossref]

ASME J. Appl. Mech. (1)

S. L. Lee and C. R. Ou, “Integration Scheme for Elastic Deformation and Stresses,” ASME J. Appl. Mech. 66, 978–985 (1999).
[Crossref]

ASME J. Fluids Eng. (1)

S.-L. Lee and H.-D. Lee, “Evolution of Liquid Meniscus Shape in a Capillary Tube,” ASME J. Fluids Eng. 129, 957–965 (2007).
[Crossref]

C. R. Acad. Sci. Paris III (1)

B. Berge, “Electrocapillarite et Mouillage de Films Isolant par l’eau,” C. R. Acad. Sci. Paris III 317, 157–163 (1993).

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V. Peykov, A. Quinn, and J. Ralston, “Electrowetting: a Model for Contact-Angle Saturation,” Colloid Polym. Sci. 278, 789–793 (2000).
[Crossref]

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M. Vallet, M. Vallade, and B. Berge, “Limiting Phenomena for the Spreading of Water on Polymer Films by Electrowetting,” Eur. Phys. J. B 11, 583–591 (1999).
[Crossref]

Eur. Phys. J. E (1)

B. Berge and J. Peseux, “Variable Focal Lens Controlled by an External Voltage: an Application of Electrowetting,” Eur. Phys. J. E 3, 159–163 (2000).
[Crossref]

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H. Hoerauf, K. Kobuch, J. Dresp, and D.-H. Menz, “Combined use of Partially Fluorinated Alkanes, Perfluorocarbon Liquids and Silicon Oil: an Experimental Study,” Graefe’s Arch. Clin. Exp. Ophthalmol. 239, 373–381 (2001).
[Crossref]

K. Kobuch, D. H. Menz, H. Hoerauf, J. H. Dresp, and V.-P. Gabel, “New Substances for Intraocular Tamponades: Perfluorocarbon Liquids, Hydrofluorocarbon Liquids and Hydrofluorocarbon-Oligomers in Vitreoretinal Surgery,” Graefe’s Arch. Clin. Exp. Ophthalmol. 239, 635–642 (2001).
[Crossref]

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S. L. Lee and S. R. Sheu, “A New Formulation for Incompressible Viscous Free Surface Flow without Smearing the Free Surface,” Int. J. Heat Mass Transfer 44, 1837–1848 (2001).
[Crossref]

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J. R. Sparrow, R. Ortiz, P. R. Macleish, and S. Chang, “Fibroblast Behavior at Aqueous Interfaces with Perfluorocarbon, Silicone, and Fluorosilicone Liquids,” Invest. Ophthalmol. Visual Sci. 31, 638–646 (1990).

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[Crossref]

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C.-C. Cheng, C. A. Chang, C. G. Tsai, C.-L. Peng, and J. A. Yeh, “A Dielectrically Driven Liquid Lens with Optical Packaging,” IEEE/LEOS Int. Conf. on Optical MENS and Nanophotonics, pp. 65–66 (2007).

B. Berge, “Liquid Lens Technology: Principle of Electrowetting Based Lenses and Applications to Image,” Proceedings of the 18th IEEE Int. Conf. on Micro Electro Mechanical Systems (2005), pp. 227–230.

W. J. Smith, Modern Optical Engineering (McGraw-Hill, 2000), Chap. 10.

S.-L. Lee and W.-B. Tien, “Growth and Detachment of Carbon Dioxide Bubbles on a Horizontal Porous Surface with a Uniform Mass Injection,” Int. J. Heat Mass Transfer (accepted for publication).

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Figures (15)

Fig. 1.
Fig. 1. Schematic View of the Tunable Liquid Micro-Lens System [6].

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Fig. 2.
Fig. 2. A Schematic Axial Ray Tracing through the Lens.

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Fig. 3.
Fig. 3. Interval between Points N and P where Meniscus Goes through.

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Fig. 4.
Fig. 4. Virtual Points E and S and Their Mirror-Reflections E′ and S′.

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Fig. 5.
Fig. 5. The Meniscus Shape for Various Contact Angles θ without the Body Force Effects.

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Fig. 6.
Fig. 6. The Back Focal Length for Various Contact Angles θ without the Body Force Effects.

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Fig. 7.
Fig. 7. Comparison of the Resulting Back Focal Length with the Experiment [6].

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Fig. 8.
Fig. 8. (a). Numerical Result of the Electrostatic Potential ϕ(r,z) for Boe =0.046 and θ=96°.

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Fig. 8.
Fig. 8. (b). The Normal and Tangent Components of the Electric Field on the Meniscus for 0.04Boe =6 and θ=96°.

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Fig. 8.
Fig. 8. (c). The Dielectric Force Function G(r) for Boe =0.046 and θ=96°.

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Fig. 9.
Fig. 9. Influence of the Electric Bond Number Boe on the Meniscus Shape.

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Fig. 10.
Fig. 10. (a). Influence of the electric Bond number Boe on the function β(b) for θ=96°.

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Fig. 10.
Fig. 10. (b). The Spherical Aberration (β(b)-β(0)) of the lens.

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Fig. 11.
Fig. 11. Axial Ray Tracing for (Boe ) opt =0.046 under the contact angle θ=96°.

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Fig. 12.
Fig. 12. The Optimal Electric Bond Number (Boe ) opt and the Corresponding Back Focal Length β(0).

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Equations (27)

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κ = Bo h − Ca ( p ̂ l − p ̂ s ) + constant
κ = κ 1 + κ 2 , κ 1 = h ″ ( 1 + h ′ 2 ) 1.5 , κ 2 = h ′ r ( 1 + h ′ 2 ) 0.5
Bo = ( ρ l − ρ s ) g L 2 γ , Ca = μ l U c γ
κ ( r ) = Bo ( h ( r ) − h ( 0 ) ) + κ ( 0 )
h ′ ( 0 ) = 0
h ′ ( r 0 ) = − tan ⁡ ( θ − α )
cos ⁡ θ = cos ⁡ θ 0 + C , C = ε d ε 0 2 γ d ( V d ) 2
BFL = Lim b → 0 β ( b )
n sinI = n ′ sinI ′
∂ ∂ r ( r σ ∂ ϕ ∂ r ) + ∂ ∂ z ( r σ ∂ ϕ ∂ z ) = 0
∂ ϕ ( 0 , z ) ⁄ ∂ r = 0 , ∂ ϕ ( r 0 , z ) ⁄ ∂ n = 0 , ϕ ( r , 0 ) = 0 , ϕ ( r , z 0 ) = 1
σ = { σ l ⁄ σ s in lens liquid 1 in surrounding liquid
λ = Δ z Δ r = tan ⁡ α = tan ⁡ 54.7 ° = 1.4124
a W ϕ W + a E ϕ E + a S ϕ S + a N ϕ N + a P ϕ P = 0
a W = ( r P − Δ r 2 ) σ eff λ , a E = ( r P + Δ r 2 ) σ eff λ , a S = r P σ eff λ , a N = r P σ eff λ
a P = − ( a W + a E + a S + a N )
σ eff = ( s σ l ⁄ σ s + 1 − s ) − 1
a W = ( r P − Δ r 2 ) ( σ l σ s ) λ , a E = ( r P + Δ r 2 ) ( σ l σ s ) λ , a S = r P λ ( σ l σ s ) , a N = r P σ eff λ
a W ϕ W + a N ϕ N + a P ϕ P = − a E ϕ E ′ − a S ϕ S ′
Δ P e = ε 0 2 ( ε s ( E n ) s 2 − ε l ( E n ) l 2 + ( ε l − ε s ) E t 2 )
E n = V 0 L ∂ ϕ ∂ n , E t = V 0 L ∂ ϕ ∂ t
κ ( r ) = Bo ( h ( r ) − h ( 0 ) ) − Bo e ( G ( r ) − G ( 0 ) ) + κ ( 0 )
G = ( e n ) s 2 − ε l ε s ( e n ) l 2 + ( ε l ε s − 1 ) e t 2 e n = ∂ φ ∂ n , e t = ∂ φ ∂ t , B o e = ε s ε 0 V 0 2 2 γ L
ρ s = 2100 kg ⁄ m 3 , γ = 0.02712 N ⁄ m , ε d = 1.93 , σ l ⁄ σ s = 20
n l = 1.510 , n s = 1.293 , ε s = 1.86 , ε l = 37.2
Bo = ρ s g L 2 γ ( ρ l ρ s − 1 ) = 0.006364 ( ρ l ρ s − 1 )
κ ( r ) = κ ( 0 ) = constant

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