Abstract

We propose a new design for tuning the astigmatism of liquid micro-lenses using electric field and hydrostatic pressure as control parameters. We explore the feasibility and operating range of the lens with a self-consistent numerical calculation of the electric field distribution and the shape of the two-phase interface. Equilibrium shapes, including surface profiles parallel and perpendicular to a stripe electrode, are extracted to determine the astigmatism. The wavefronts are decomposed into Zernike polynomials under zero defocus conditions using a commercial ray-tracing software. We observe that the global curvature of the lens is primarily controlled by the hydrostatic pressure, while asphericity and astigmatism are controlled by the electric field. For optimized electrode geometries and simultaneous control of pressure and electric fields the astigmatism can be tuned from Z6 = 0…0.38 μm with minor changes in the focal length.

© 2016 Optical Society of America

Full Article  |  PDF Article
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References

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    [Crossref]
  34. I. Roghair, M. Musterd, D. van den Ende, C. Kleijn, M. Kreutzer, and F. Mugele, “A numerical tchnique to simulate display pixels based on electrowetting,” Microfluid. Nanofluidics 19(2), 465–482 (2015).
    [Crossref]
  35. N. C. Lima and M. A. d’Avila, “Numerical simulation of electrohydrodynamic flows of Newtonian and viscoelastic droplets,” J. Non-Newton. Fluid 213, 1–14 (2014).

2015 (2)

M. Xu, X. Wang, and H. Ren, “Tunable focus liquid lens with radial-patterned electrode,” Micromachines (Basel) 6(8), 1157–1165 (2015).
[Crossref]

I. Roghair, M. Musterd, D. van den Ende, C. Kleijn, M. Kreutzer, and F. Mugele, “A numerical tchnique to simulate display pixels based on electrowetting,” Microfluid. Nanofluidics 19(2), 465–482 (2015).
[Crossref]

2014 (5)

N. C. Lima and M. A. d’Avila, “Numerical simulation of electrohydrodynamic flows of Newtonian and viscoelastic droplets,” J. Non-Newton. Fluid 213, 1–14 (2014).

Y.-K. Fuh and C.-T. Huang, “Characterization of a tunable astigmatic fluidic lens with adaptive optics correction for compact phoropter application,” Opt. Commun. 323, 148–153 (2014).
[Crossref]

Z. Cao, C. Cheng, and K. Wang, “Numerical simulation on aspherical lens modulated by electrostatic force,” Proc. SPIE 9281, 92810H (2014).

K. Mishra, C. Murade, B. Carreel, I. Roghair, J. M. Oh, G. Manukyan, D. van den Ende, and F. Mugele, “Optofluidic lens with tunable focal length and asphericity,” Sci. Rep. 4, 6378 (2014).
[Crossref] [PubMed]

M. Xu, D. Xu, H. Ren, I.-S. Yoo, and Q.-H. Wang, “An adaptive liquid lens with radial interdigitated electrode,” J. Opt. 16(10), 105601 (2014).
[Crossref]

2013 (4)

Z. Cao, K. Wang, S. Wu, and Q. Wu, “Fabrication of refractive axicons utilizing electrostatic force,” Optik (Stuttg.) 124(18), 3761–3763 (2013).
[Crossref]

P. Liebetraut, S. Petsch, J. Liebeskind, and H. Zappe, “Elastomeric lenses with tunable astigmatism,” Light Sci. Appl. 2(9), e98 (2013).
[Crossref]

A. Santiago-Alvarado, J. Gonzalez-Garcia, F. Itubide-Jimenez, M. Campos-Garcia, V. M. Cruz-Martinez, and P. Rafferty, “Simulating the functioning of variable focus length liquid-filled lenses using the finite element method (FEM),” Optik (Stuttg.) 124(11), 1003–1010 (2013).
[Crossref]

Y.-K. Fuh, K.-C. Hsu, M.-X. Lin, and J.-R. Fan, “Characterization of adjustable fluidic lenses and capability for aberration correction of defocus and astigmatism,” Optik (Stuttg.) 124(8), 706–709 (2013).
[Crossref]

2012 (2)

C. U. Murade, D. van der Ende, and F. Mugele, “High speed adaptive liquid microlens array,” Opt. Express 20(16), 18180–18187 (2012).
[Crossref] [PubMed]

C. Li and H. Jiang, “Electrowetting-driven variable-focus microlens on flexible surfaces,” Appl. Phys. Lett. 100(23), 231105 (2012).
[Crossref] [PubMed]

2011 (4)

J. M. López-Herrera, S. Popinet, and M. A. Herrada, “A charge-conservative approach for simulating electrohydrodynamic two-phase flows using volume-of-fluid,” J. Comput. Phys. 230(5), 1939–1955 (2011).
[Crossref]

J. M. Oh, G. Manukyan, D. van den Ende, and F. Mugele, “Electric-field–driven instabilities on superhydrophobic surfaces,” Epl-Europhys. Lett. 93(5), 56001 (2011).
[Crossref]

G. Manukyan, J. M. Oh, D. van den Ende, R. G. H. Lammertink, and F. Mugele, “Electrical switching of wetting states on superhydrophobic surfaces: a route towards reversible Cassie-to-Wenzel transitions,” Phys. Rev. Lett. 106(1), 014501 (2011).
[Crossref] [PubMed]

C. U. Murade, J. M. Oh, D. van den Ende, and F. Mugele, “Electrowetting driven optical switch and tunable aperture,” Opt. Express 19(16), 15525–15531 (2011).
[Crossref] [PubMed]

2010 (2)

2009 (2)

2008 (2)

A. Jaworek and A. T. Sobczyk, “Electrospraying route to nanotechnology: an overview,” J. Electrost. 66(3–4), 197–219 (2008).
[Crossref]

U. Levy and R. Shamai, “Tunable optofluidic devices,” Microfluid. Nanofluidics 4(1–2), 97–105 (2008).
[Crossref]

2007 (5)

X. Mao, J. R. Waldeisen, B. K. Juluri, and T. J. Huang, “Hydrodynamically tunable optofluidic cylindrical microlens,” Lab Chip 7(10), 1303–1308 (2007).
[Crossref] [PubMed]

L. Dong, A. K. Agarwal, D. J. Beebe, and H. Jiang, “Variable-focus liquid microlenses and microlens arrays actuated by thermoresponsive hydrogels,” Adv. Mater. 19(3), 401–405 (2007).
[Crossref]

G. I. Kweon and C. H. Kim, “Aspherical lens design by using a numerical analysis,” J. Korean Phys. Soc. 51(1), 93–103 (2007).
[Crossref]

G. W. Forbes, “Shape specification for axially symmetric optical surfaces,” Opt. Express 15(8), 5218–5226 (2007).
[Crossref] [PubMed]

G. Tomar, D. Gerlach, G. Biswas, N. Alleborn, A. Sharma, F. Durst, S. W. J. Welch, and A. Delgado, “Two-phase electrohydrodynamic simulations using a volume-of-fluid approach,” J. Comput. Phys. 227(2), 1267–1285 (2007).
[Crossref]

2006 (1)

D. Psaltis, S. R. Quake, and C. Yang, “Developing optofluidic technology through the fusion of microfluidics and optics,” Nature 442(7101), 381–386 (2006).
[Crossref] [PubMed]

2000 (1)

B. Berge and J. Peseux, “Variable focal lens controlled by an external voltage: an application of electrowetting,” Eur. Phys. J. E 3(2), 159–163 (2000).
[Crossref]

1997 (1)

D. A. Saville, “Electrohydrodynamics:the Taylor-Melcher leaky dielectric model,” Annu. Rev. Fluid Mech. 29(1), 27–64 (1997).
[Crossref]

1981 (1)

C. W. Hirt and B. D. Nichols, “Volume of fluid (VOF) method for the dynamics of free boundaries,” J. Comput. Phys. 39(1), 201–225 (1981).
[Crossref]

1964 (1)

G. Taylor, “Disintegration of water drops in an electric field,” P. R. Soc. Lond. A-Conta. 280, 383 (1964).

Agarwal, A. K.

L. Dong, A. K. Agarwal, D. J. Beebe, and H. Jiang, “Variable-focus liquid microlenses and microlens arrays actuated by thermoresponsive hydrogels,” Adv. Mater. 19(3), 401–405 (2007).
[Crossref]

Alleborn, N.

G. Tomar, D. Gerlach, G. Biswas, N. Alleborn, A. Sharma, F. Durst, S. W. J. Welch, and A. Delgado, “Two-phase electrohydrodynamic simulations using a volume-of-fluid approach,” J. Comput. Phys. 227(2), 1267–1285 (2007).
[Crossref]

Beebe, D. J.

L. Dong, A. K. Agarwal, D. J. Beebe, and H. Jiang, “Variable-focus liquid microlenses and microlens arrays actuated by thermoresponsive hydrogels,” Adv. Mater. 19(3), 401–405 (2007).
[Crossref]

Berge, B.

B. Berge and J. Peseux, “Variable focal lens controlled by an external voltage: an application of electrowetting,” Eur. Phys. J. E 3(2), 159–163 (2000).
[Crossref]

Biswas, G.

G. Tomar, D. Gerlach, G. Biswas, N. Alleborn, A. Sharma, F. Durst, S. W. J. Welch, and A. Delgado, “Two-phase electrohydrodynamic simulations using a volume-of-fluid approach,” J. Comput. Phys. 227(2), 1267–1285 (2007).
[Crossref]

Campos-Garcia, M.

A. Santiago-Alvarado, J. Gonzalez-Garcia, F. Itubide-Jimenez, M. Campos-Garcia, V. M. Cruz-Martinez, and P. Rafferty, “Simulating the functioning of variable focus length liquid-filled lenses using the finite element method (FEM),” Optik (Stuttg.) 124(11), 1003–1010 (2013).
[Crossref]

Cao, Z.

Z. Cao, C. Cheng, and K. Wang, “Numerical simulation on aspherical lens modulated by electrostatic force,” Proc. SPIE 9281, 92810H (2014).

Z. Cao, K. Wang, S. Wu, and Q. Wu, “Fabrication of refractive axicons utilizing electrostatic force,” Optik (Stuttg.) 124(18), 3761–3763 (2013).
[Crossref]

Z. Zhan, K. Wang, H. Yao, and Z. Cao, “Fabrication and characterization of aspherical lens manipulated by electrostatic field,” Appl. Opt. 48(22), 4375–4380 (2009).
[Crossref] [PubMed]

Carreel, B.

K. Mishra, C. Murade, B. Carreel, I. Roghair, J. M. Oh, G. Manukyan, D. van den Ende, and F. Mugele, “Optofluidic lens with tunable focal length and asphericity,” Sci. Rep. 4, 6378 (2014).
[Crossref] [PubMed]

Chen, W.-C.

L. Sz-Yuan, H.-W. Tung, W.-C. Chen, and W. Fang, “Novel micro lens with tunable astigmatism,” in 2007 Solid-State Sensors, Actuators and Microsystems Conference (IEEE, 2007), pp. 2147–2150.

Cheng, C.

Z. Cao, C. Cheng, and K. Wang, “Numerical simulation on aspherical lens modulated by electrostatic force,” Proc. SPIE 9281, 92810H (2014).

Cruz-Martinez, V. M.

A. Santiago-Alvarado, J. Gonzalez-Garcia, F. Itubide-Jimenez, M. Campos-Garcia, V. M. Cruz-Martinez, and P. Rafferty, “Simulating the functioning of variable focus length liquid-filled lenses using the finite element method (FEM),” Optik (Stuttg.) 124(11), 1003–1010 (2013).
[Crossref]

d’Avila, M. A.

N. C. Lima and M. A. d’Avila, “Numerical simulation of electrohydrodynamic flows of Newtonian and viscoelastic droplets,” J. Non-Newton. Fluid 213, 1–14 (2014).

Delgado, A.

G. Tomar, D. Gerlach, G. Biswas, N. Alleborn, A. Sharma, F. Durst, S. W. J. Welch, and A. Delgado, “Two-phase electrohydrodynamic simulations using a volume-of-fluid approach,” J. Comput. Phys. 227(2), 1267–1285 (2007).
[Crossref]

Dong, L.

L. Dong, A. K. Agarwal, D. J. Beebe, and H. Jiang, “Variable-focus liquid microlenses and microlens arrays actuated by thermoresponsive hydrogels,” Adv. Mater. 19(3), 401–405 (2007).
[Crossref]

Durst, F.

G. Tomar, D. Gerlach, G. Biswas, N. Alleborn, A. Sharma, F. Durst, S. W. J. Welch, and A. Delgado, “Two-phase electrohydrodynamic simulations using a volume-of-fluid approach,” J. Comput. Phys. 227(2), 1267–1285 (2007).
[Crossref]

Fan, J.-R.

Y.-K. Fuh, K.-C. Hsu, M.-X. Lin, and J.-R. Fan, “Characterization of adjustable fluidic lenses and capability for aberration correction of defocus and astigmatism,” Optik (Stuttg.) 124(8), 706–709 (2013).
[Crossref]

Fang, W.

L. Sz-Yuan, H.-W. Tung, W.-C. Chen, and W. Fang, “Novel micro lens with tunable astigmatism,” in 2007 Solid-State Sensors, Actuators and Microsystems Conference (IEEE, 2007), pp. 2147–2150.

Forbes, G. W.

Fuh, Y.-K.

Y.-K. Fuh and C.-T. Huang, “Characterization of a tunable astigmatic fluidic lens with adaptive optics correction for compact phoropter application,” Opt. Commun. 323, 148–153 (2014).
[Crossref]

Y.-K. Fuh, K.-C. Hsu, M.-X. Lin, and J.-R. Fan, “Characterization of adjustable fluidic lenses and capability for aberration correction of defocus and astigmatism,” Optik (Stuttg.) 124(8), 706–709 (2013).
[Crossref]

Gerlach, D.

G. Tomar, D. Gerlach, G. Biswas, N. Alleborn, A. Sharma, F. Durst, S. W. J. Welch, and A. Delgado, “Two-phase electrohydrodynamic simulations using a volume-of-fluid approach,” J. Comput. Phys. 227(2), 1267–1285 (2007).
[Crossref]

Gonzalez-Garcia, J.

A. Santiago-Alvarado, J. Gonzalez-Garcia, F. Itubide-Jimenez, M. Campos-Garcia, V. M. Cruz-Martinez, and P. Rafferty, “Simulating the functioning of variable focus length liquid-filled lenses using the finite element method (FEM),” Optik (Stuttg.) 124(11), 1003–1010 (2013).
[Crossref]

Herrada, M. A.

J. M. López-Herrera, S. Popinet, and M. A. Herrada, “A charge-conservative approach for simulating electrohydrodynamic two-phase flows using volume-of-fluid,” J. Comput. Phys. 230(5), 1939–1955 (2011).
[Crossref]

Hirt, C. W.

C. W. Hirt and B. D. Nichols, “Volume of fluid (VOF) method for the dynamics of free boundaries,” J. Comput. Phys. 39(1), 201–225 (1981).
[Crossref]

Hsu, K.-C.

Y.-K. Fuh, K.-C. Hsu, M.-X. Lin, and J.-R. Fan, “Characterization of adjustable fluidic lenses and capability for aberration correction of defocus and astigmatism,” Optik (Stuttg.) 124(8), 706–709 (2013).
[Crossref]

Huang, C.-T.

Y.-K. Fuh and C.-T. Huang, “Characterization of a tunable astigmatic fluidic lens with adaptive optics correction for compact phoropter application,” Opt. Commun. 323, 148–153 (2014).
[Crossref]

Huang, T. J.

X. Mao, J. R. Waldeisen, B. K. Juluri, and T. J. Huang, “Hydrodynamically tunable optofluidic cylindrical microlens,” Lab Chip 7(10), 1303–1308 (2007).
[Crossref] [PubMed]

Itubide-Jimenez, F.

A. Santiago-Alvarado, J. Gonzalez-Garcia, F. Itubide-Jimenez, M. Campos-Garcia, V. M. Cruz-Martinez, and P. Rafferty, “Simulating the functioning of variable focus length liquid-filled lenses using the finite element method (FEM),” Optik (Stuttg.) 124(11), 1003–1010 (2013).
[Crossref]

Jaworek, A.

A. Jaworek and A. T. Sobczyk, “Electrospraying route to nanotechnology: an overview,” J. Electrost. 66(3–4), 197–219 (2008).
[Crossref]

Jiang, H.

C. Li and H. Jiang, “Electrowetting-driven variable-focus microlens on flexible surfaces,” Appl. Phys. Lett. 100(23), 231105 (2012).
[Crossref] [PubMed]

L. Dong, A. K. Agarwal, D. J. Beebe, and H. Jiang, “Variable-focus liquid microlenses and microlens arrays actuated by thermoresponsive hydrogels,” Adv. Mater. 19(3), 401–405 (2007).
[Crossref]

Juluri, B. K.

X. Mao, J. R. Waldeisen, B. K. Juluri, and T. J. Huang, “Hydrodynamically tunable optofluidic cylindrical microlens,” Lab Chip 7(10), 1303–1308 (2007).
[Crossref] [PubMed]

Kim, C. H.

G. I. Kweon and C. H. Kim, “Aspherical lens design by using a numerical analysis,” J. Korean Phys. Soc. 51(1), 93–103 (2007).
[Crossref]

Kleijn, C.

I. Roghair, M. Musterd, D. van den Ende, C. Kleijn, M. Kreutzer, and F. Mugele, “A numerical tchnique to simulate display pixels based on electrowetting,” Microfluid. Nanofluidics 19(2), 465–482 (2015).
[Crossref]

Kreutzer, M.

I. Roghair, M. Musterd, D. van den Ende, C. Kleijn, M. Kreutzer, and F. Mugele, “A numerical tchnique to simulate display pixels based on electrowetting,” Microfluid. Nanofluidics 19(2), 465–482 (2015).
[Crossref]

Kweon, G. I.

G. I. Kweon and C. H. Kim, “Aspherical lens design by using a numerical analysis,” J. Korean Phys. Soc. 51(1), 93–103 (2007).
[Crossref]

Lammertink, R. G. H.

G. Manukyan, J. M. Oh, D. van den Ende, R. G. H. Lammertink, and F. Mugele, “Electrical switching of wetting states on superhydrophobic surfaces: a route towards reversible Cassie-to-Wenzel transitions,” Phys. Rev. Lett. 106(1), 014501 (2011).
[Crossref] [PubMed]

Levy, U.

U. Levy and R. Shamai, “Tunable optofluidic devices,” Microfluid. Nanofluidics 4(1–2), 97–105 (2008).
[Crossref]

Li, C.

C. Li and H. Jiang, “Electrowetting-driven variable-focus microlens on flexible surfaces,” Appl. Phys. Lett. 100(23), 231105 (2012).
[Crossref] [PubMed]

Liebeskind, J.

P. Liebetraut, S. Petsch, J. Liebeskind, and H. Zappe, “Elastomeric lenses with tunable astigmatism,” Light Sci. Appl. 2(9), e98 (2013).
[Crossref]

Liebetraut, P.

P. Liebetraut, S. Petsch, J. Liebeskind, and H. Zappe, “Elastomeric lenses with tunable astigmatism,” Light Sci. Appl. 2(9), e98 (2013).
[Crossref]

Lima, N. C.

N. C. Lima and M. A. d’Avila, “Numerical simulation of electrohydrodynamic flows of Newtonian and viscoelastic droplets,” J. Non-Newton. Fluid 213, 1–14 (2014).

Lin, M.-X.

Y.-K. Fuh, K.-C. Hsu, M.-X. Lin, and J.-R. Fan, “Characterization of adjustable fluidic lenses and capability for aberration correction of defocus and astigmatism,” Optik (Stuttg.) 124(8), 706–709 (2013).
[Crossref]

López-Herrera, J. M.

J. M. López-Herrera, S. Popinet, and M. A. Herrada, “A charge-conservative approach for simulating electrohydrodynamic two-phase flows using volume-of-fluid,” J. Comput. Phys. 230(5), 1939–1955 (2011).
[Crossref]

Manukyan, G.

K. Mishra, C. Murade, B. Carreel, I. Roghair, J. M. Oh, G. Manukyan, D. van den Ende, and F. Mugele, “Optofluidic lens with tunable focal length and asphericity,” Sci. Rep. 4, 6378 (2014).
[Crossref] [PubMed]

G. Manukyan, J. M. Oh, D. van den Ende, R. G. H. Lammertink, and F. Mugele, “Electrical switching of wetting states on superhydrophobic surfaces: a route towards reversible Cassie-to-Wenzel transitions,” Phys. Rev. Lett. 106(1), 014501 (2011).
[Crossref] [PubMed]

J. M. Oh, G. Manukyan, D. van den Ende, and F. Mugele, “Electric-field–driven instabilities on superhydrophobic surfaces,” Epl-Europhys. Lett. 93(5), 56001 (2011).
[Crossref]

Mao, X.

X. Mao, J. R. Waldeisen, B. K. Juluri, and T. J. Huang, “Hydrodynamically tunable optofluidic cylindrical microlens,” Lab Chip 7(10), 1303–1308 (2007).
[Crossref] [PubMed]

Marks, R.

Mathine, D. L.

Mishra, K.

K. Mishra, C. Murade, B. Carreel, I. Roghair, J. M. Oh, G. Manukyan, D. van den Ende, and F. Mugele, “Optofluidic lens with tunable focal length and asphericity,” Sci. Rep. 4, 6378 (2014).
[Crossref] [PubMed]

Mugele, F.

I. Roghair, M. Musterd, D. van den Ende, C. Kleijn, M. Kreutzer, and F. Mugele, “A numerical tchnique to simulate display pixels based on electrowetting,” Microfluid. Nanofluidics 19(2), 465–482 (2015).
[Crossref]

K. Mishra, C. Murade, B. Carreel, I. Roghair, J. M. Oh, G. Manukyan, D. van den Ende, and F. Mugele, “Optofluidic lens with tunable focal length and asphericity,” Sci. Rep. 4, 6378 (2014).
[Crossref] [PubMed]

C. U. Murade, D. van der Ende, and F. Mugele, “High speed adaptive liquid microlens array,” Opt. Express 20(16), 18180–18187 (2012).
[Crossref] [PubMed]

C. U. Murade, J. M. Oh, D. van den Ende, and F. Mugele, “Electrowetting driven optical switch and tunable aperture,” Opt. Express 19(16), 15525–15531 (2011).
[Crossref] [PubMed]

G. Manukyan, J. M. Oh, D. van den Ende, R. G. H. Lammertink, and F. Mugele, “Electrical switching of wetting states on superhydrophobic surfaces: a route towards reversible Cassie-to-Wenzel transitions,” Phys. Rev. Lett. 106(1), 014501 (2011).
[Crossref] [PubMed]

J. M. Oh, G. Manukyan, D. van den Ende, and F. Mugele, “Electric-field–driven instabilities on superhydrophobic surfaces,” Epl-Europhys. Lett. 93(5), 56001 (2011).
[Crossref]

Murade, C.

K. Mishra, C. Murade, B. Carreel, I. Roghair, J. M. Oh, G. Manukyan, D. van den Ende, and F. Mugele, “Optofluidic lens with tunable focal length and asphericity,” Sci. Rep. 4, 6378 (2014).
[Crossref] [PubMed]

Murade, C. U.

Musterd, M.

I. Roghair, M. Musterd, D. van den Ende, C. Kleijn, M. Kreutzer, and F. Mugele, “A numerical tchnique to simulate display pixels based on electrowetting,” Microfluid. Nanofluidics 19(2), 465–482 (2015).
[Crossref]

Nguyen, N.-T.

N.-T. Nguyen, “Micro-optofluidic lenses: a review,” Biomicrofluidics 4(3), 031501 (2010).
[Crossref] [PubMed]

Nichols, B. D.

C. W. Hirt and B. D. Nichols, “Volume of fluid (VOF) method for the dynamics of free boundaries,” J. Comput. Phys. 39(1), 201–225 (1981).
[Crossref]

Oh, J. M.

K. Mishra, C. Murade, B. Carreel, I. Roghair, J. M. Oh, G. Manukyan, D. van den Ende, and F. Mugele, “Optofluidic lens with tunable focal length and asphericity,” Sci. Rep. 4, 6378 (2014).
[Crossref] [PubMed]

J. M. Oh, G. Manukyan, D. van den Ende, and F. Mugele, “Electric-field–driven instabilities on superhydrophobic surfaces,” Epl-Europhys. Lett. 93(5), 56001 (2011).
[Crossref]

G. Manukyan, J. M. Oh, D. van den Ende, R. G. H. Lammertink, and F. Mugele, “Electrical switching of wetting states on superhydrophobic surfaces: a route towards reversible Cassie-to-Wenzel transitions,” Phys. Rev. Lett. 106(1), 014501 (2011).
[Crossref] [PubMed]

C. U. Murade, J. M. Oh, D. van den Ende, and F. Mugele, “Electrowetting driven optical switch and tunable aperture,” Opt. Express 19(16), 15525–15531 (2011).
[Crossref] [PubMed]

Peseux, J.

B. Berge and J. Peseux, “Variable focal lens controlled by an external voltage: an application of electrowetting,” Eur. Phys. J. E 3(2), 159–163 (2000).
[Crossref]

Petsch, S.

P. Liebetraut, S. Petsch, J. Liebeskind, and H. Zappe, “Elastomeric lenses with tunable astigmatism,” Light Sci. Appl. 2(9), e98 (2013).
[Crossref]

Peyghambarian, N.

Peyman, G.

Popinet, S.

J. M. López-Herrera, S. Popinet, and M. A. Herrada, “A charge-conservative approach for simulating electrohydrodynamic two-phase flows using volume-of-fluid,” J. Comput. Phys. 230(5), 1939–1955 (2011).
[Crossref]

Psaltis, D.

D. Psaltis, S. R. Quake, and C. Yang, “Developing optofluidic technology through the fusion of microfluidics and optics,” Nature 442(7101), 381–386 (2006).
[Crossref] [PubMed]

Quake, S. R.

D. Psaltis, S. R. Quake, and C. Yang, “Developing optofluidic technology through the fusion of microfluidics and optics,” Nature 442(7101), 381–386 (2006).
[Crossref] [PubMed]

Rafferty, P.

A. Santiago-Alvarado, J. Gonzalez-Garcia, F. Itubide-Jimenez, M. Campos-Garcia, V. M. Cruz-Martinez, and P. Rafferty, “Simulating the functioning of variable focus length liquid-filled lenses using the finite element method (FEM),” Optik (Stuttg.) 124(11), 1003–1010 (2013).
[Crossref]

Ren, H.

M. Xu, X. Wang, and H. Ren, “Tunable focus liquid lens with radial-patterned electrode,” Micromachines (Basel) 6(8), 1157–1165 (2015).
[Crossref]

M. Xu, D. Xu, H. Ren, I.-S. Yoo, and Q.-H. Wang, “An adaptive liquid lens with radial interdigitated electrode,” J. Opt. 16(10), 105601 (2014).
[Crossref]

Roghair, I.

I. Roghair, M. Musterd, D. van den Ende, C. Kleijn, M. Kreutzer, and F. Mugele, “A numerical tchnique to simulate display pixels based on electrowetting,” Microfluid. Nanofluidics 19(2), 465–482 (2015).
[Crossref]

K. Mishra, C. Murade, B. Carreel, I. Roghair, J. M. Oh, G. Manukyan, D. van den Ende, and F. Mugele, “Optofluidic lens with tunable focal length and asphericity,” Sci. Rep. 4, 6378 (2014).
[Crossref] [PubMed]

Santiago-Alvarado, A.

A. Santiago-Alvarado, J. Gonzalez-Garcia, F. Itubide-Jimenez, M. Campos-Garcia, V. M. Cruz-Martinez, and P. Rafferty, “Simulating the functioning of variable focus length liquid-filled lenses using the finite element method (FEM),” Optik (Stuttg.) 124(11), 1003–1010 (2013).
[Crossref]

Saville, D. A.

D. A. Saville, “Electrohydrodynamics:the Taylor-Melcher leaky dielectric model,” Annu. Rev. Fluid Mech. 29(1), 27–64 (1997).
[Crossref]

Schwiegerling, J.

Shamai, R.

U. Levy and R. Shamai, “Tunable optofluidic devices,” Microfluid. Nanofluidics 4(1–2), 97–105 (2008).
[Crossref]

Sharma, A.

G. Tomar, D. Gerlach, G. Biswas, N. Alleborn, A. Sharma, F. Durst, S. W. J. Welch, and A. Delgado, “Two-phase electrohydrodynamic simulations using a volume-of-fluid approach,” J. Comput. Phys. 227(2), 1267–1285 (2007).
[Crossref]

Sobczyk, A. T.

A. Jaworek and A. T. Sobczyk, “Electrospraying route to nanotechnology: an overview,” J. Electrost. 66(3–4), 197–219 (2008).
[Crossref]

Sz-Yuan, L.

L. Sz-Yuan, H.-W. Tung, W.-C. Chen, and W. Fang, “Novel micro lens with tunable astigmatism,” in 2007 Solid-State Sensors, Actuators and Microsystems Conference (IEEE, 2007), pp. 2147–2150.

Taylor, G.

G. Taylor, “Disintegration of water drops in an electric field,” P. R. Soc. Lond. A-Conta. 280, 383 (1964).

Tomar, G.

G. Tomar, D. Gerlach, G. Biswas, N. Alleborn, A. Sharma, F. Durst, S. W. J. Welch, and A. Delgado, “Two-phase electrohydrodynamic simulations using a volume-of-fluid approach,” J. Comput. Phys. 227(2), 1267–1285 (2007).
[Crossref]

Tung, H.-W.

L. Sz-Yuan, H.-W. Tung, W.-C. Chen, and W. Fang, “Novel micro lens with tunable astigmatism,” in 2007 Solid-State Sensors, Actuators and Microsystems Conference (IEEE, 2007), pp. 2147–2150.

van den Ende, D.

I. Roghair, M. Musterd, D. van den Ende, C. Kleijn, M. Kreutzer, and F. Mugele, “A numerical tchnique to simulate display pixels based on electrowetting,” Microfluid. Nanofluidics 19(2), 465–482 (2015).
[Crossref]

K. Mishra, C. Murade, B. Carreel, I. Roghair, J. M. Oh, G. Manukyan, D. van den Ende, and F. Mugele, “Optofluidic lens with tunable focal length and asphericity,” Sci. Rep. 4, 6378 (2014).
[Crossref] [PubMed]

G. Manukyan, J. M. Oh, D. van den Ende, R. G. H. Lammertink, and F. Mugele, “Electrical switching of wetting states on superhydrophobic surfaces: a route towards reversible Cassie-to-Wenzel transitions,” Phys. Rev. Lett. 106(1), 014501 (2011).
[Crossref] [PubMed]

J. M. Oh, G. Manukyan, D. van den Ende, and F. Mugele, “Electric-field–driven instabilities on superhydrophobic surfaces,” Epl-Europhys. Lett. 93(5), 56001 (2011).
[Crossref]

C. U. Murade, J. M. Oh, D. van den Ende, and F. Mugele, “Electrowetting driven optical switch and tunable aperture,” Opt. Express 19(16), 15525–15531 (2011).
[Crossref] [PubMed]

van der Ende, D.

Waldeisen, J. R.

X. Mao, J. R. Waldeisen, B. K. Juluri, and T. J. Huang, “Hydrodynamically tunable optofluidic cylindrical microlens,” Lab Chip 7(10), 1303–1308 (2007).
[Crossref] [PubMed]

Wang, K.

Z. Cao, C. Cheng, and K. Wang, “Numerical simulation on aspherical lens modulated by electrostatic force,” Proc. SPIE 9281, 92810H (2014).

Z. Cao, K. Wang, S. Wu, and Q. Wu, “Fabrication of refractive axicons utilizing electrostatic force,” Optik (Stuttg.) 124(18), 3761–3763 (2013).
[Crossref]

Z. Zhan, K. Wang, H. Yao, and Z. Cao, “Fabrication and characterization of aspherical lens manipulated by electrostatic field,” Appl. Opt. 48(22), 4375–4380 (2009).
[Crossref] [PubMed]

Wang, Q.-H.

M. Xu, D. Xu, H. Ren, I.-S. Yoo, and Q.-H. Wang, “An adaptive liquid lens with radial interdigitated electrode,” J. Opt. 16(10), 105601 (2014).
[Crossref]

Wang, X.

M. Xu, X. Wang, and H. Ren, “Tunable focus liquid lens with radial-patterned electrode,” Micromachines (Basel) 6(8), 1157–1165 (2015).
[Crossref]

Welch, S. W. J.

G. Tomar, D. Gerlach, G. Biswas, N. Alleborn, A. Sharma, F. Durst, S. W. J. Welch, and A. Delgado, “Two-phase electrohydrodynamic simulations using a volume-of-fluid approach,” J. Comput. Phys. 227(2), 1267–1285 (2007).
[Crossref]

Wu, Q.

Z. Cao, K. Wang, S. Wu, and Q. Wu, “Fabrication of refractive axicons utilizing electrostatic force,” Optik (Stuttg.) 124(18), 3761–3763 (2013).
[Crossref]

Wu, S.

Z. Cao, K. Wang, S. Wu, and Q. Wu, “Fabrication of refractive axicons utilizing electrostatic force,” Optik (Stuttg.) 124(18), 3761–3763 (2013).
[Crossref]

Xu, D.

M. Xu, D. Xu, H. Ren, I.-S. Yoo, and Q.-H. Wang, “An adaptive liquid lens with radial interdigitated electrode,” J. Opt. 16(10), 105601 (2014).
[Crossref]

Xu, M.

M. Xu, X. Wang, and H. Ren, “Tunable focus liquid lens with radial-patterned electrode,” Micromachines (Basel) 6(8), 1157–1165 (2015).
[Crossref]

M. Xu, D. Xu, H. Ren, I.-S. Yoo, and Q.-H. Wang, “An adaptive liquid lens with radial interdigitated electrode,” J. Opt. 16(10), 105601 (2014).
[Crossref]

Yang, C.

D. Psaltis, S. R. Quake, and C. Yang, “Developing optofluidic technology through the fusion of microfluidics and optics,” Nature 442(7101), 381–386 (2006).
[Crossref] [PubMed]

Yao, H.

Yoo, I.-S.

M. Xu, D. Xu, H. Ren, I.-S. Yoo, and Q.-H. Wang, “An adaptive liquid lens with radial interdigitated electrode,” J. Opt. 16(10), 105601 (2014).
[Crossref]

Zappe, H.

P. Liebetraut, S. Petsch, J. Liebeskind, and H. Zappe, “Elastomeric lenses with tunable astigmatism,” Light Sci. Appl. 2(9), e98 (2013).
[Crossref]

Zhan, Z.

Adv. Mater. (1)

L. Dong, A. K. Agarwal, D. J. Beebe, and H. Jiang, “Variable-focus liquid microlenses and microlens arrays actuated by thermoresponsive hydrogels,” Adv. Mater. 19(3), 401–405 (2007).
[Crossref]

Annu. Rev. Fluid Mech. (1)

D. A. Saville, “Electrohydrodynamics:the Taylor-Melcher leaky dielectric model,” Annu. Rev. Fluid Mech. 29(1), 27–64 (1997).
[Crossref]

Appl. Opt. (2)

Appl. Phys. Lett. (1)

C. Li and H. Jiang, “Electrowetting-driven variable-focus microlens on flexible surfaces,” Appl. Phys. Lett. 100(23), 231105 (2012).
[Crossref] [PubMed]

Biomicrofluidics (1)

N.-T. Nguyen, “Micro-optofluidic lenses: a review,” Biomicrofluidics 4(3), 031501 (2010).
[Crossref] [PubMed]

Epl-Europhys. Lett. (1)

J. M. Oh, G. Manukyan, D. van den Ende, and F. Mugele, “Electric-field–driven instabilities on superhydrophobic surfaces,” Epl-Europhys. Lett. 93(5), 56001 (2011).
[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(2), 159–163 (2000).
[Crossref]

J. Comput. Phys. (3)

J. M. López-Herrera, S. Popinet, and M. A. Herrada, “A charge-conservative approach for simulating electrohydrodynamic two-phase flows using volume-of-fluid,” J. Comput. Phys. 230(5), 1939–1955 (2011).
[Crossref]

C. W. Hirt and B. D. Nichols, “Volume of fluid (VOF) method for the dynamics of free boundaries,” J. Comput. Phys. 39(1), 201–225 (1981).
[Crossref]

G. Tomar, D. Gerlach, G. Biswas, N. Alleborn, A. Sharma, F. Durst, S. W. J. Welch, and A. Delgado, “Two-phase electrohydrodynamic simulations using a volume-of-fluid approach,” J. Comput. Phys. 227(2), 1267–1285 (2007).
[Crossref]

J. Electrost. (1)

A. Jaworek and A. T. Sobczyk, “Electrospraying route to nanotechnology: an overview,” J. Electrost. 66(3–4), 197–219 (2008).
[Crossref]

J. Korean Phys. Soc. (1)

G. I. Kweon and C. H. Kim, “Aspherical lens design by using a numerical analysis,” J. Korean Phys. Soc. 51(1), 93–103 (2007).
[Crossref]

J. Non-Newton. Fluid (1)

N. C. Lima and M. A. d’Avila, “Numerical simulation of electrohydrodynamic flows of Newtonian and viscoelastic droplets,” J. Non-Newton. Fluid 213, 1–14 (2014).

J. Opt. (1)

M. Xu, D. Xu, H. Ren, I.-S. Yoo, and Q.-H. Wang, “An adaptive liquid lens with radial interdigitated electrode,” J. Opt. 16(10), 105601 (2014).
[Crossref]

Lab Chip (1)

X. Mao, J. R. Waldeisen, B. K. Juluri, and T. J. Huang, “Hydrodynamically tunable optofluidic cylindrical microlens,” Lab Chip 7(10), 1303–1308 (2007).
[Crossref] [PubMed]

Light Sci. Appl. (1)

P. Liebetraut, S. Petsch, J. Liebeskind, and H. Zappe, “Elastomeric lenses with tunable astigmatism,” Light Sci. Appl. 2(9), e98 (2013).
[Crossref]

Microfluid. Nanofluidics (2)

U. Levy and R. Shamai, “Tunable optofluidic devices,” Microfluid. Nanofluidics 4(1–2), 97–105 (2008).
[Crossref]

I. Roghair, M. Musterd, D. van den Ende, C. Kleijn, M. Kreutzer, and F. Mugele, “A numerical tchnique to simulate display pixels based on electrowetting,” Microfluid. Nanofluidics 19(2), 465–482 (2015).
[Crossref]

Micromachines (Basel) (1)

M. Xu, X. Wang, and H. Ren, “Tunable focus liquid lens with radial-patterned electrode,” Micromachines (Basel) 6(8), 1157–1165 (2015).
[Crossref]

Nature (1)

D. Psaltis, S. R. Quake, and C. Yang, “Developing optofluidic technology through the fusion of microfluidics and optics,” Nature 442(7101), 381–386 (2006).
[Crossref] [PubMed]

Opt. Commun. (1)

Y.-K. Fuh and C.-T. Huang, “Characterization of a tunable astigmatic fluidic lens with adaptive optics correction for compact phoropter application,” Opt. Commun. 323, 148–153 (2014).
[Crossref]

Opt. Express (3)

Opt. Lett. (1)

Optik (Stuttg.) (3)

Y.-K. Fuh, K.-C. Hsu, M.-X. Lin, and J.-R. Fan, “Characterization of adjustable fluidic lenses and capability for aberration correction of defocus and astigmatism,” Optik (Stuttg.) 124(8), 706–709 (2013).
[Crossref]

A. Santiago-Alvarado, J. Gonzalez-Garcia, F. Itubide-Jimenez, M. Campos-Garcia, V. M. Cruz-Martinez, and P. Rafferty, “Simulating the functioning of variable focus length liquid-filled lenses using the finite element method (FEM),” Optik (Stuttg.) 124(11), 1003–1010 (2013).
[Crossref]

Z. Cao, K. Wang, S. Wu, and Q. Wu, “Fabrication of refractive axicons utilizing electrostatic force,” Optik (Stuttg.) 124(18), 3761–3763 (2013).
[Crossref]

P. R. Soc. Lond. A-Conta. (1)

G. Taylor, “Disintegration of water drops in an electric field,” P. R. Soc. Lond. A-Conta. 280, 383 (1964).

Phys. Rev. Lett. (1)

G. Manukyan, J. M. Oh, D. van den Ende, R. G. H. Lammertink, and F. Mugele, “Electrical switching of wetting states on superhydrophobic surfaces: a route towards reversible Cassie-to-Wenzel transitions,” Phys. Rev. Lett. 106(1), 014501 (2011).
[Crossref] [PubMed]

Proc. SPIE (1)

Z. Cao, C. Cheng, and K. Wang, “Numerical simulation on aspherical lens modulated by electrostatic force,” Proc. SPIE 9281, 92810H (2014).

Sci. Rep. (1)

K. Mishra, C. Murade, B. Carreel, I. Roghair, J. M. Oh, G. Manukyan, D. van den Ende, and F. Mugele, “Optofluidic lens with tunable focal length and asphericity,” Sci. Rep. 4, 6378 (2014).
[Crossref] [PubMed]

Other (2)

L. Sz-Yuan, H.-W. Tung, W.-C. Chen, and W. Fang, “Novel micro lens with tunable astigmatism,” in 2007 Solid-State Sensors, Actuators and Microsystems Conference (IEEE, 2007), pp. 2147–2150.

J. E. Greivenkamp, “Field guide to geometrical optics,” Soc. Photo-Opt. Instrum. (2004).

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Figures (7)

Fig. 1
Fig. 1 (a) Sliced computational mesh. The image shows a local refinement for the stripe on the top boundary and a dynamic refinement on the lens (interface between both fluids). (b) View of the setup. A hydrostatic pressure ΔPh is applied between the lower plates (water phase) to induce global curvature changes on the lens with a circular aperture of radius a. The voltage U is applied between the upper plates (oil phase), separated by a distance h, using a stripe electrode (red stripe) of width d. When the voltage is applied, different profiles on the lens are achieved on the x and z planes (white and black cross lines, respectively). The optical axis of the system is represented by the dashed arrow.
Fig. 2
Fig. 2 (a) Normalized profiles of the lenses by applying different pressures at zero voltage. Simulation (dashed line) versus analytical results (solid line). (b) Normalized equilibrium deflection ζ0 as a function of the electrocapillary number Λ for two different electrode distances H = 1.0 and 2.0, where H = h / a and by considering a full electrode, i. e.d = 1.0 mm. Simulation (black lines) versus analytical results (colored lines) from the work of Oh et al. [26]. Open symbols denote the regions where instabilities were observed.
Fig. 3
Fig. 3 Lenses modulated by a pressure of 30 Pa and using a stripe electrode of 0.5 mm width for three different voltages 300 V, 500 V and 700 V. White and black lines correspond to the x and z sections, respectively. (Left) Front and side views of the lenses. (Right) Comparison of the x and z profiles normalized by the radius of the aperture.
Fig. 4
Fig. 4 (a) Normalized curvatures cx (open symbols) and cz (filled symbols) as a function of the voltage considering a stripe electrode of 0.5 mm width for three different pressures, 10 Pa, 30 Pa and 50 Pa. (b) Curvature for 30 Pa and the related variation of the paraxial back focal length as a function of the voltage. Open symbols correspond to the x plane and filled symbols correspond to the z plane.
Fig. 5
Fig. 5 (a) Influence of the stripe width d on the vertical astigmatism aberration Z6 considering two different voltages 500 V (black columns) and 700 V (grey columns) at zero hydrostatic pressure. (b) Corresponding x and z profiles, normalized by the radius of the aperture, considering three stripe widths 0.1, 0.5 and 0.9 mm for two voltages, 500 and 700 V.
Fig. 6
Fig. 6 (a) Transition of the image spot when increasing the voltage from 0 to 400V, considering a pressure of 30 Pa. The airy disk is represented by the black circle. Note the different scales as indicated on the left axes. (b) Plots showing the divergence between the tangential (blue curve) and the sagittal (red curve) MTF curves as the voltage increases. The black line represents the diffraction limited curve.
Fig. 7
Fig. 7 Color maps for both the front focal length (a) and the Zernike coefficient Z6 (b) for different combinations of voltages and pressures considering a stripe width of 0.5 mm. The small kinks in the lines result from the discretization of the data and the white space on the bottom left corner represents the regions where the surface remained almost flat.

Equations (8)

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

y ( x , z ) = c x x 2 + c z z 2 1 + 1 ( 1 + k x ) c x 2 x 2 ( 1 + k z ) c z 2 z 2 ,
u = 0 ,
  ρ ( u t + u u ) = p + [ μ ( u + u T ) ] + ρ g + F γ + F E ,
    ( ε E ) = ρ E ,
  ρ E t + ( σ E + ρ E u ) = 0 ,
  F E = [ ε ( E E | E | 2 2 I ) ] ,
  θ = α 1 θ p h a s e 1 + ( 1 α 1 ) θ p h a s e 2 ,
    α 1 t + ( α 1 u ) + [ α 1 ( 1 α 1 ) u r ] = 0 ,

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