Abstract

Nonlinear large deformation of a transparent elastomer membrane under hydraulic pressure was analyzed to investigate its optical performance for a variable-focus liquid-filled membrane microlens. In most membrane microlenses, actuators control the hydraulic pressure of optical fluid so that the elastomer membrane together with the internal optical fluid changes its shape, which alters the light path of the microlens to adapt its optical power. A fluid-structure interaction simulation was performed to estimate the transient behavior of the microlens under the operation of electroactive polymer actuators, demonstrating that the viscosity of the optical fluid successfully stabilizes the fluctuations within a fairly short period of time during dynamic operations. Axisymmetric nonlinear plate theory was used to calculate the deformation profile of the membrane under hydrostatic pressure, with which optical characteristics of the membrane microlens were estimated. The effects of gravitation and viscoelastic behavior of the elastomer membrane on the optical performance of the membrane microlens were also evaluated with finite element analysis.

© 2014 Optical Society of America

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References

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  1. N. Chronis, G. Liu, K. H. Jeong, L. Lee, “Tunable liquid-filled microlens array integrated with microfluidic network,” Opt. Express 11(19), 2370–2378 (2003).
    [CrossRef] [PubMed]
  2. S. W. Lee, S. S. Lee, “Focal tunable liquid lens integrated with an electromagnetic actuator,” Appl. Phys. Lett. 90(12), 121129 (2007).
    [CrossRef]
  3. F. Schneider, C. Müller, U. Wallrabe, “A low cost adaptive silicone membrane lens,” J. Opt. A, Pure Appl. Opt. 10(4), 044002 (2008).
    [CrossRef]
  4. F. Schneider, J. Draheim, C. Müller, U. Wallrabe, “Optimization of an adaptive PDMS-membrane lens with an integrated actuator,” Sens. Actuator A Phys. 154(2), 316–321 (2009).
    [CrossRef]
  5. J. Draheim, F. Schneider, R. Kamberger, C. Mueller, U. Wallrabe, “Fabrication of a fluidic membrane lens system,” J. Micromech. Microeng. 19(9), 095013 (2009).
    [CrossRef]
  6. F. Schneider, J. Draheim, R. Kamberger, P. Waibel, U. Wallrabe, “Optical characterization of adaptive fluidic silicone-membrane lenses,” Opt. Express 17(14), 11813–11821 (2009).
    [CrossRef] [PubMed]
  7. S. T. Choi, J. Y. Lee, J. O. Kwon, S. Lee, W. Kim, “Varifocal liquid-filled microlens operated by an electroactive polymer actuator,” Opt. Lett. 36(10), 1920–1922 (2011).
    [CrossRef] [PubMed]
  8. W. Zhang, K. Aljasem, H. Zappe, A. Seifert, “Completely integrated, thermo-pneumatically tunable microlens,” Opt. Express 19(3), 2347–2362 (2011).
    [CrossRef] [PubMed]
  9. A. Pouydebasque, C. Bridoux, F. Jacquet, S. Moreau, E. Sage, D. Saint-Patrice, C. Bouvier, C. Kopp, G. Marchand, S. Bolis, N. Sillon, E. Vigier-Blanc, “Varifocal liquid lenses with integrated actuator, high focusing power and low operating voltage fabricated on 200 mm wafers,” Sens. Actuator A Phys. 172(1), 280–286 (2011).
    [CrossRef]
  10. H. Choi, D. S. Han, Y. H. Won, “Adaptive double-sided fluidic lens of polydimethylsiloxane membranes of matching thickness,” Opt. Lett. 36(23), 4701–4703 (2011).
    [CrossRef] [PubMed]
  11. H. Choi, D. S. Han, Y. H. Won, “Fluidic lens of PDMS membrane driven by voice-coil and magnet,” IEEE Photonics Technol. Lett. 24(19), 1683–1685 (2012).
    [CrossRef]
  12. J. K. Lee, K. Park, J. C. Choi, H. Kim, S. H. Kong, “Design and fabrication of PMMA-micromachined fluid lens based on electromagnetic actuation on PMMA-PDMS bonded membrane,” J. Micromech. Microeng. 22(11), 115028 (2012).
    [CrossRef]
  13. S. Shian, R. M. Diebold, D. R. Clarke, “Tunable lenses using transparent dielectric elastomer actuators,” Opt. Express 21(7), 8669–8676 (2013).
    [CrossRef] [PubMed]
  14. S. T. Choi, J. O. Kwon, F. Bauer, “Multilayered relaxor ferroelectric polymer actuators for low-voltage operation fabricated with an adhesion-mediated film transfer technique,” Sens. Actuators A Phys. 203, 282–290 (2013).
    [CrossRef]
  15. COMSOL, “COMSOL Multiphysics, Version 3.3” (2006).
  16. S. T. Choi, S. J. Jeong, Y. Y. Earmme, “Modified-creep experiment of an elastomer film on a rigid substrate using nanoindentation with a flat-ended cylindrical tip,” Scr. Mater. 58(3), 199–202 (2008).
    [CrossRef]
  17. S. Timoshenko, S. Woinowsky-Krieger, and S. Woinowsky, Theory of Plates and Shells (McGraw-Hill, 1959).
  18. D. Malacara and Z. Malacara, Handbook of Optical Design (Marcel Dekker, 2004).
  19. Dassault Systèmes Simulia Corp., “ABAQUS Version 6.12” (2013).
  20. R. Christensen, Theory of Viscoelasticity: An Introduction (Elsevier, 1982).

2013 (2)

S. T. Choi, J. O. Kwon, F. Bauer, “Multilayered relaxor ferroelectric polymer actuators for low-voltage operation fabricated with an adhesion-mediated film transfer technique,” Sens. Actuators A Phys. 203, 282–290 (2013).
[CrossRef]

S. Shian, R. M. Diebold, D. R. Clarke, “Tunable lenses using transparent dielectric elastomer actuators,” Opt. Express 21(7), 8669–8676 (2013).
[CrossRef] [PubMed]

2012 (2)

H. Choi, D. S. Han, Y. H. Won, “Fluidic lens of PDMS membrane driven by voice-coil and magnet,” IEEE Photonics Technol. Lett. 24(19), 1683–1685 (2012).
[CrossRef]

J. K. Lee, K. Park, J. C. Choi, H. Kim, S. H. Kong, “Design and fabrication of PMMA-micromachined fluid lens based on electromagnetic actuation on PMMA-PDMS bonded membrane,” J. Micromech. Microeng. 22(11), 115028 (2012).
[CrossRef]

2011 (4)

2009 (3)

F. Schneider, J. Draheim, R. Kamberger, P. Waibel, U. Wallrabe, “Optical characterization of adaptive fluidic silicone-membrane lenses,” Opt. Express 17(14), 11813–11821 (2009).
[CrossRef] [PubMed]

F. Schneider, J. Draheim, C. Müller, U. Wallrabe, “Optimization of an adaptive PDMS-membrane lens with an integrated actuator,” Sens. Actuator A Phys. 154(2), 316–321 (2009).
[CrossRef]

J. Draheim, F. Schneider, R. Kamberger, C. Mueller, U. Wallrabe, “Fabrication of a fluidic membrane lens system,” J. Micromech. Microeng. 19(9), 095013 (2009).
[CrossRef]

2008 (2)

F. Schneider, C. Müller, U. Wallrabe, “A low cost adaptive silicone membrane lens,” J. Opt. A, Pure Appl. Opt. 10(4), 044002 (2008).
[CrossRef]

S. T. Choi, S. J. Jeong, Y. Y. Earmme, “Modified-creep experiment of an elastomer film on a rigid substrate using nanoindentation with a flat-ended cylindrical tip,” Scr. Mater. 58(3), 199–202 (2008).
[CrossRef]

2007 (1)

S. W. Lee, S. S. Lee, “Focal tunable liquid lens integrated with an electromagnetic actuator,” Appl. Phys. Lett. 90(12), 121129 (2007).
[CrossRef]

2003 (1)

Aljasem, K.

Bauer, F.

S. T. Choi, J. O. Kwon, F. Bauer, “Multilayered relaxor ferroelectric polymer actuators for low-voltage operation fabricated with an adhesion-mediated film transfer technique,” Sens. Actuators A Phys. 203, 282–290 (2013).
[CrossRef]

Bolis, S.

A. Pouydebasque, C. Bridoux, F. Jacquet, S. Moreau, E. Sage, D. Saint-Patrice, C. Bouvier, C. Kopp, G. Marchand, S. Bolis, N. Sillon, E. Vigier-Blanc, “Varifocal liquid lenses with integrated actuator, high focusing power and low operating voltage fabricated on 200 mm wafers,” Sens. Actuator A Phys. 172(1), 280–286 (2011).
[CrossRef]

Bouvier, C.

A. Pouydebasque, C. Bridoux, F. Jacquet, S. Moreau, E. Sage, D. Saint-Patrice, C. Bouvier, C. Kopp, G. Marchand, S. Bolis, N. Sillon, E. Vigier-Blanc, “Varifocal liquid lenses with integrated actuator, high focusing power and low operating voltage fabricated on 200 mm wafers,” Sens. Actuator A Phys. 172(1), 280–286 (2011).
[CrossRef]

Bridoux, C.

A. Pouydebasque, C. Bridoux, F. Jacquet, S. Moreau, E. Sage, D. Saint-Patrice, C. Bouvier, C. Kopp, G. Marchand, S. Bolis, N. Sillon, E. Vigier-Blanc, “Varifocal liquid lenses with integrated actuator, high focusing power and low operating voltage fabricated on 200 mm wafers,” Sens. Actuator A Phys. 172(1), 280–286 (2011).
[CrossRef]

Choi, H.

H. Choi, D. S. Han, Y. H. Won, “Fluidic lens of PDMS membrane driven by voice-coil and magnet,” IEEE Photonics Technol. Lett. 24(19), 1683–1685 (2012).
[CrossRef]

H. Choi, D. S. Han, Y. H. Won, “Adaptive double-sided fluidic lens of polydimethylsiloxane membranes of matching thickness,” Opt. Lett. 36(23), 4701–4703 (2011).
[CrossRef] [PubMed]

Choi, J. C.

J. K. Lee, K. Park, J. C. Choi, H. Kim, S. H. Kong, “Design and fabrication of PMMA-micromachined fluid lens based on electromagnetic actuation on PMMA-PDMS bonded membrane,” J. Micromech. Microeng. 22(11), 115028 (2012).
[CrossRef]

Choi, S. T.

S. T. Choi, J. O. Kwon, F. Bauer, “Multilayered relaxor ferroelectric polymer actuators for low-voltage operation fabricated with an adhesion-mediated film transfer technique,” Sens. Actuators A Phys. 203, 282–290 (2013).
[CrossRef]

S. T. Choi, J. Y. Lee, J. O. Kwon, S. Lee, W. Kim, “Varifocal liquid-filled microlens operated by an electroactive polymer actuator,” Opt. Lett. 36(10), 1920–1922 (2011).
[CrossRef] [PubMed]

S. T. Choi, S. J. Jeong, Y. Y. Earmme, “Modified-creep experiment of an elastomer film on a rigid substrate using nanoindentation with a flat-ended cylindrical tip,” Scr. Mater. 58(3), 199–202 (2008).
[CrossRef]

Chronis, N.

Clarke, D. R.

Diebold, R. M.

Draheim, J.

J. Draheim, F. Schneider, R. Kamberger, C. Mueller, U. Wallrabe, “Fabrication of a fluidic membrane lens system,” J. Micromech. Microeng. 19(9), 095013 (2009).
[CrossRef]

F. Schneider, J. Draheim, R. Kamberger, P. Waibel, U. Wallrabe, “Optical characterization of adaptive fluidic silicone-membrane lenses,” Opt. Express 17(14), 11813–11821 (2009).
[CrossRef] [PubMed]

F. Schneider, J. Draheim, C. Müller, U. Wallrabe, “Optimization of an adaptive PDMS-membrane lens with an integrated actuator,” Sens. Actuator A Phys. 154(2), 316–321 (2009).
[CrossRef]

Earmme, Y. Y.

S. T. Choi, S. J. Jeong, Y. Y. Earmme, “Modified-creep experiment of an elastomer film on a rigid substrate using nanoindentation with a flat-ended cylindrical tip,” Scr. Mater. 58(3), 199–202 (2008).
[CrossRef]

Han, D. S.

H. Choi, D. S. Han, Y. H. Won, “Fluidic lens of PDMS membrane driven by voice-coil and magnet,” IEEE Photonics Technol. Lett. 24(19), 1683–1685 (2012).
[CrossRef]

H. Choi, D. S. Han, Y. H. Won, “Adaptive double-sided fluidic lens of polydimethylsiloxane membranes of matching thickness,” Opt. Lett. 36(23), 4701–4703 (2011).
[CrossRef] [PubMed]

Jacquet, F.

A. Pouydebasque, C. Bridoux, F. Jacquet, S. Moreau, E. Sage, D. Saint-Patrice, C. Bouvier, C. Kopp, G. Marchand, S. Bolis, N. Sillon, E. Vigier-Blanc, “Varifocal liquid lenses with integrated actuator, high focusing power and low operating voltage fabricated on 200 mm wafers,” Sens. Actuator A Phys. 172(1), 280–286 (2011).
[CrossRef]

Jeong, K. H.

Jeong, S. J.

S. T. Choi, S. J. Jeong, Y. Y. Earmme, “Modified-creep experiment of an elastomer film on a rigid substrate using nanoindentation with a flat-ended cylindrical tip,” Scr. Mater. 58(3), 199–202 (2008).
[CrossRef]

Kamberger, R.

J. Draheim, F. Schneider, R. Kamberger, C. Mueller, U. Wallrabe, “Fabrication of a fluidic membrane lens system,” J. Micromech. Microeng. 19(9), 095013 (2009).
[CrossRef]

F. Schneider, J. Draheim, R. Kamberger, P. Waibel, U. Wallrabe, “Optical characterization of adaptive fluidic silicone-membrane lenses,” Opt. Express 17(14), 11813–11821 (2009).
[CrossRef] [PubMed]

Kim, H.

J. K. Lee, K. Park, J. C. Choi, H. Kim, S. H. Kong, “Design and fabrication of PMMA-micromachined fluid lens based on electromagnetic actuation on PMMA-PDMS bonded membrane,” J. Micromech. Microeng. 22(11), 115028 (2012).
[CrossRef]

Kim, W.

Kong, S. H.

J. K. Lee, K. Park, J. C. Choi, H. Kim, S. H. Kong, “Design and fabrication of PMMA-micromachined fluid lens based on electromagnetic actuation on PMMA-PDMS bonded membrane,” J. Micromech. Microeng. 22(11), 115028 (2012).
[CrossRef]

Kopp, C.

A. Pouydebasque, C. Bridoux, F. Jacquet, S. Moreau, E. Sage, D. Saint-Patrice, C. Bouvier, C. Kopp, G. Marchand, S. Bolis, N. Sillon, E. Vigier-Blanc, “Varifocal liquid lenses with integrated actuator, high focusing power and low operating voltage fabricated on 200 mm wafers,” Sens. Actuator A Phys. 172(1), 280–286 (2011).
[CrossRef]

Kwon, J. O.

S. T. Choi, J. O. Kwon, F. Bauer, “Multilayered relaxor ferroelectric polymer actuators for low-voltage operation fabricated with an adhesion-mediated film transfer technique,” Sens. Actuators A Phys. 203, 282–290 (2013).
[CrossRef]

S. T. Choi, J. Y. Lee, J. O. Kwon, S. Lee, W. Kim, “Varifocal liquid-filled microlens operated by an electroactive polymer actuator,” Opt. Lett. 36(10), 1920–1922 (2011).
[CrossRef] [PubMed]

Lee, J. K.

J. K. Lee, K. Park, J. C. Choi, H. Kim, S. H. Kong, “Design and fabrication of PMMA-micromachined fluid lens based on electromagnetic actuation on PMMA-PDMS bonded membrane,” J. Micromech. Microeng. 22(11), 115028 (2012).
[CrossRef]

Lee, J. Y.

Lee, L.

Lee, S.

Lee, S. S.

S. W. Lee, S. S. Lee, “Focal tunable liquid lens integrated with an electromagnetic actuator,” Appl. Phys. Lett. 90(12), 121129 (2007).
[CrossRef]

Lee, S. W.

S. W. Lee, S. S. Lee, “Focal tunable liquid lens integrated with an electromagnetic actuator,” Appl. Phys. Lett. 90(12), 121129 (2007).
[CrossRef]

Liu, G.

Marchand, G.

A. Pouydebasque, C. Bridoux, F. Jacquet, S. Moreau, E. Sage, D. Saint-Patrice, C. Bouvier, C. Kopp, G. Marchand, S. Bolis, N. Sillon, E. Vigier-Blanc, “Varifocal liquid lenses with integrated actuator, high focusing power and low operating voltage fabricated on 200 mm wafers,” Sens. Actuator A Phys. 172(1), 280–286 (2011).
[CrossRef]

Moreau, S.

A. Pouydebasque, C. Bridoux, F. Jacquet, S. Moreau, E. Sage, D. Saint-Patrice, C. Bouvier, C. Kopp, G. Marchand, S. Bolis, N. Sillon, E. Vigier-Blanc, “Varifocal liquid lenses with integrated actuator, high focusing power and low operating voltage fabricated on 200 mm wafers,” Sens. Actuator A Phys. 172(1), 280–286 (2011).
[CrossRef]

Mueller, C.

J. Draheim, F. Schneider, R. Kamberger, C. Mueller, U. Wallrabe, “Fabrication of a fluidic membrane lens system,” J. Micromech. Microeng. 19(9), 095013 (2009).
[CrossRef]

Müller, C.

F. Schneider, J. Draheim, C. Müller, U. Wallrabe, “Optimization of an adaptive PDMS-membrane lens with an integrated actuator,” Sens. Actuator A Phys. 154(2), 316–321 (2009).
[CrossRef]

F. Schneider, C. Müller, U. Wallrabe, “A low cost adaptive silicone membrane lens,” J. Opt. A, Pure Appl. Opt. 10(4), 044002 (2008).
[CrossRef]

Park, K.

J. K. Lee, K. Park, J. C. Choi, H. Kim, S. H. Kong, “Design and fabrication of PMMA-micromachined fluid lens based on electromagnetic actuation on PMMA-PDMS bonded membrane,” J. Micromech. Microeng. 22(11), 115028 (2012).
[CrossRef]

Pouydebasque, A.

A. Pouydebasque, C. Bridoux, F. Jacquet, S. Moreau, E. Sage, D. Saint-Patrice, C. Bouvier, C. Kopp, G. Marchand, S. Bolis, N. Sillon, E. Vigier-Blanc, “Varifocal liquid lenses with integrated actuator, high focusing power and low operating voltage fabricated on 200 mm wafers,” Sens. Actuator A Phys. 172(1), 280–286 (2011).
[CrossRef]

Sage, E.

A. Pouydebasque, C. Bridoux, F. Jacquet, S. Moreau, E. Sage, D. Saint-Patrice, C. Bouvier, C. Kopp, G. Marchand, S. Bolis, N. Sillon, E. Vigier-Blanc, “Varifocal liquid lenses with integrated actuator, high focusing power and low operating voltage fabricated on 200 mm wafers,” Sens. Actuator A Phys. 172(1), 280–286 (2011).
[CrossRef]

Saint-Patrice, D.

A. Pouydebasque, C. Bridoux, F. Jacquet, S. Moreau, E. Sage, D. Saint-Patrice, C. Bouvier, C. Kopp, G. Marchand, S. Bolis, N. Sillon, E. Vigier-Blanc, “Varifocal liquid lenses with integrated actuator, high focusing power and low operating voltage fabricated on 200 mm wafers,” Sens. Actuator A Phys. 172(1), 280–286 (2011).
[CrossRef]

Schneider, F.

J. Draheim, F. Schneider, R. Kamberger, C. Mueller, U. Wallrabe, “Fabrication of a fluidic membrane lens system,” J. Micromech. Microeng. 19(9), 095013 (2009).
[CrossRef]

F. Schneider, J. Draheim, C. Müller, U. Wallrabe, “Optimization of an adaptive PDMS-membrane lens with an integrated actuator,” Sens. Actuator A Phys. 154(2), 316–321 (2009).
[CrossRef]

F. Schneider, J. Draheim, R. Kamberger, P. Waibel, U. Wallrabe, “Optical characterization of adaptive fluidic silicone-membrane lenses,” Opt. Express 17(14), 11813–11821 (2009).
[CrossRef] [PubMed]

F. Schneider, C. Müller, U. Wallrabe, “A low cost adaptive silicone membrane lens,” J. Opt. A, Pure Appl. Opt. 10(4), 044002 (2008).
[CrossRef]

Seifert, A.

Shian, S.

Sillon, N.

A. Pouydebasque, C. Bridoux, F. Jacquet, S. Moreau, E. Sage, D. Saint-Patrice, C. Bouvier, C. Kopp, G. Marchand, S. Bolis, N. Sillon, E. Vigier-Blanc, “Varifocal liquid lenses with integrated actuator, high focusing power and low operating voltage fabricated on 200 mm wafers,” Sens. Actuator A Phys. 172(1), 280–286 (2011).
[CrossRef]

Vigier-Blanc, E.

A. Pouydebasque, C. Bridoux, F. Jacquet, S. Moreau, E. Sage, D. Saint-Patrice, C. Bouvier, C. Kopp, G. Marchand, S. Bolis, N. Sillon, E. Vigier-Blanc, “Varifocal liquid lenses with integrated actuator, high focusing power and low operating voltage fabricated on 200 mm wafers,” Sens. Actuator A Phys. 172(1), 280–286 (2011).
[CrossRef]

Waibel, P.

Wallrabe, U.

F. Schneider, J. Draheim, R. Kamberger, P. Waibel, U. Wallrabe, “Optical characterization of adaptive fluidic silicone-membrane lenses,” Opt. Express 17(14), 11813–11821 (2009).
[CrossRef] [PubMed]

F. Schneider, J. Draheim, C. Müller, U. Wallrabe, “Optimization of an adaptive PDMS-membrane lens with an integrated actuator,” Sens. Actuator A Phys. 154(2), 316–321 (2009).
[CrossRef]

J. Draheim, F. Schneider, R. Kamberger, C. Mueller, U. Wallrabe, “Fabrication of a fluidic membrane lens system,” J. Micromech. Microeng. 19(9), 095013 (2009).
[CrossRef]

F. Schneider, C. Müller, U. Wallrabe, “A low cost adaptive silicone membrane lens,” J. Opt. A, Pure Appl. Opt. 10(4), 044002 (2008).
[CrossRef]

Won, Y. H.

H. Choi, D. S. Han, Y. H. Won, “Fluidic lens of PDMS membrane driven by voice-coil and magnet,” IEEE Photonics Technol. Lett. 24(19), 1683–1685 (2012).
[CrossRef]

H. Choi, D. S. Han, Y. H. Won, “Adaptive double-sided fluidic lens of polydimethylsiloxane membranes of matching thickness,” Opt. Lett. 36(23), 4701–4703 (2011).
[CrossRef] [PubMed]

Zappe, H.

Zhang, W.

Appl. Phys. Lett. (1)

S. W. Lee, S. S. Lee, “Focal tunable liquid lens integrated with an electromagnetic actuator,” Appl. Phys. Lett. 90(12), 121129 (2007).
[CrossRef]

IEEE Photonics Technol. Lett. (1)

H. Choi, D. S. Han, Y. H. Won, “Fluidic lens of PDMS membrane driven by voice-coil and magnet,” IEEE Photonics Technol. Lett. 24(19), 1683–1685 (2012).
[CrossRef]

J. Micromech. Microeng. (2)

J. K. Lee, K. Park, J. C. Choi, H. Kim, S. H. Kong, “Design and fabrication of PMMA-micromachined fluid lens based on electromagnetic actuation on PMMA-PDMS bonded membrane,” J. Micromech. Microeng. 22(11), 115028 (2012).
[CrossRef]

J. Draheim, F. Schneider, R. Kamberger, C. Mueller, U. Wallrabe, “Fabrication of a fluidic membrane lens system,” J. Micromech. Microeng. 19(9), 095013 (2009).
[CrossRef]

J. Opt. A, Pure Appl. Opt. (1)

F. Schneider, C. Müller, U. Wallrabe, “A low cost adaptive silicone membrane lens,” J. Opt. A, Pure Appl. Opt. 10(4), 044002 (2008).
[CrossRef]

Opt. Express (4)

Opt. Lett. (2)

Scr. Mater. (1)

S. T. Choi, S. J. Jeong, Y. Y. Earmme, “Modified-creep experiment of an elastomer film on a rigid substrate using nanoindentation with a flat-ended cylindrical tip,” Scr. Mater. 58(3), 199–202 (2008).
[CrossRef]

Sens. Actuator A Phys. (2)

A. Pouydebasque, C. Bridoux, F. Jacquet, S. Moreau, E. Sage, D. Saint-Patrice, C. Bouvier, C. Kopp, G. Marchand, S. Bolis, N. Sillon, E. Vigier-Blanc, “Varifocal liquid lenses with integrated actuator, high focusing power and low operating voltage fabricated on 200 mm wafers,” Sens. Actuator A Phys. 172(1), 280–286 (2011).
[CrossRef]

F. Schneider, J. Draheim, C. Müller, U. Wallrabe, “Optimization of an adaptive PDMS-membrane lens with an integrated actuator,” Sens. Actuator A Phys. 154(2), 316–321 (2009).
[CrossRef]

Sens. Actuators A Phys. (1)

S. T. Choi, J. O. Kwon, F. Bauer, “Multilayered relaxor ferroelectric polymer actuators for low-voltage operation fabricated with an adhesion-mediated film transfer technique,” Sens. Actuators A Phys. 203, 282–290 (2013).
[CrossRef]

Other (5)

COMSOL, “COMSOL Multiphysics, Version 3.3” (2006).

S. Timoshenko, S. Woinowsky-Krieger, and S. Woinowsky, Theory of Plates and Shells (McGraw-Hill, 1959).

D. Malacara and Z. Malacara, Handbook of Optical Design (Marcel Dekker, 2004).

Dassault Systèmes Simulia Corp., “ABAQUS Version 6.12” (2013).

R. Christensen, Theory of Viscoelasticity: An Introduction (Elsevier, 1982).

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Figures (9)

Fig. 1
Fig. 1

The varifocal microlens developed by Choi et al. [7] as a typical example of variable-focus liquid-filled membrane microlenses, whose focal length varies with the deformation of a transparent elastomer membrane under hydraulic pressure tailored by four P(VDF-TrFE-CTFE) polymer actuators [14].

Fig. 2
Fig. 2

Fluid-structure interaction analysis of a varifocal liquid-filled membrane microlens with commercial software COMSOL 3.3. (a) Simulation model, (b) transient response of deflection at the center of the varifocal microlens membrane, and (c) response time as a function of the viscosity of optical fluid.

Fig. 3
Fig. 3

(a) Model geometry of an axisymmetric elastomer membrane with clamped edge loaded by uniform hydrostatic pressure. (b) Deformation profile of the elastomer membrane (Young’s modulus = 1.12 MPa, Poisson’s ratio = 0.48, thickness = 50 μm). (c) Maximum deflection at the center of the elastomer membrane as a function of the normalized pressure.

Fig. 4
Fig. 4

Vertex curvature of the deformation profile of an elastomer membrane under hydrostatic pressure.

Fig. 5
Fig. 5

Wave front error of the varifocal liquid-filled microlens obtained by ray tracing simulation with commercial software, Code V.

Fig. 6
Fig. 6

Finite element analysis of gravity effects on membrane deformation: (a) Contour plot of the deformed shape of the elastomer membrane under hydraulic pressure in the vertical position, and (b) the deformation profile along the vertical center line of the elastomer membrane.

Fig. 7
Fig. 7

Wave front error of the varifocal liquid-filled microlens due to gravity obtained by ray tracing simulation with Code V.

Fig. 8
Fig. 8

(a) Spontaneous deformation profiles and creep behavior of a viscoelastic PDMS membrane obtained by FEA, and (b) normalized relative maximum deflection at the center of the viscoelastic PDMS membrane as a function of time.

Fig. 9
Fig. 9

Percent change of the focal length of the liquid-filled membrane microlens for 10 seconds due to the viscoelastic behavior of the PDMS membrane.

Equations (16)

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

p a = 5 π [ tan 1 ( 2 t 6 ) + 2 ] ( kPa ) ,
d 2 u d r 2 + 1 r d u d r u r 2 = 1 ν 2 r ( d w d r ) 2 d w d r d 2 w d r 2 ,
d 3 w d r 3 + 1 r d 2 w d r 2 1 r 2 d w d r = 12 t 2 d w d r [ d u d r + ν u r + 1 2 ( d w d r ) 2 ] + p r 2 D ,
u = d w d r = 0 , at r = 0 ,
u = w = d w d r = 0 , at r = r a .
w ( r ) = 8 t [ C 1 2 ( r t ) 2 + C 3 4 ( r t ) 4 + C 5 6 ( r t ) 6 + ] ,
N r ( r ) = t E [ B 0 + B 2 ( r t ) 2 + B 4 ( r t ) 4 + ] ,
B k = 4 k ( k + 2 ) m = 1 , 3 , 5 , k 1 C m C k m , k = 2 , 4 , 6 ,
C k = 12 ( 1 ν 2 ) k 2 1 m = 0 , 2 , 4 , k 3 B m C k 2 m , k = 5 , 7 , 9 ,
C 3 = 3 2 ( 1 ν 2 ) ( p 4 2 E + B 0 C 1 ) .
w ( r ) = c r 2 1 + 1 ( 1 + K ) c 2 r 2 + k = 2 A 2 k r 2 k ,
c = 8 t C 1 , A 2 k = 2 C 2 k 1 k t 2 k 1 , ( k = 2 , 3 , )
p ( x , y ) = ρ g y + p 0 ,
δ max = 3 ( 1 ν 2 ) p g d 4 16 E t 3 = 3 ( 1 ν 2 ) ρ g d 5 16 E t 3 .
δ gravity = A P ( 1 ν 2 ) ρ d 5 E t 3 ,
μ PDMS ( t ) = 188.59 + 19.78 e t 3.58 + 37.10 e t 44.55 + 32.47 e t 311.23 + 99.97 e t 4908.22 (kPa) .

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