Abstract

By means of numerical simulations, using a computational fluid dynamics software together with an optical ray tracing analysis platform, we show that we can tune various optical aberrations by electrically manipulating the shape of liquid lenses using one hundred individually addressable electrodes. To demonstrate the flexibility of our design, we define electrode patterns based on specific Zernike modes and show that aspherical, cylindrical and decentered shapes of liquid lenses can be produced. Using different voltages, we evaluate the tuning range of spherical aberration (Z11), astigmatism (Z5 and Z6) and coma (Z7), while a hydrostatic pressure is applied to control the average curvature of a microlens with a diameter of 1mm. Upon activating all electrodes simultaneously spherical aberrations of 0.15 waves at a pressure of 30Pa can be suppressed almost completely for the highest voltages applied. For astigmatic and comatic patterns, the values of Z5, Z6 and Z7 increase monotonically with the voltage reaching values up to 0.06, 0.06 and 0.2 waves, respectively. Spot diagrams, wavefront maps and modulation transfer function are reported to quantify the optical performance of each lens. Crosstalk and independence of tunability are discussed in the context of possible applications of the approach for general wavefront shaping.

© 2017 Optical Society of America

Full Article  |  PDF Article
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References

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    [Crossref]
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    [Crossref]

2016 (4)

2015 (2)

P. Zhao, Ç. Ataman, and H. Zappe, “Spherical aberration free liquid-filled tunable lens with variable thickness membrane,” Opt. Express 23(16), 21264–21278 (2015).
[Crossref] [PubMed]

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 (3)

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]

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]

2013 (1)

Z. Cao, K. Wang, and Q. Wu, “Aspherical anamorphic lens for shaping laser diode beam,” Opt. Commun. 305, 53–56 (2013).
[Crossref]

2012 (1)

2011 (3)

V. Lakshminarayanan and A. Fleck, “Zernike polynomials: a guide,” J. Mod. Opt. 58(7), 545–561 (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]

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]

2010 (1)

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

2008 (1)

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

2007 (3)

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. 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]

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

2006 (2)

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]

1998 (1)

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]

1969 (1)

J. R. Melcher and G. I. Taylor, “Electrohydrodynamics: a review of the role of interfacial shear stresses,” Annu. Rev. Fluid Mech. 1(1), 111–146 (1969).
[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]

Artal, P.

Ataman, Ç.

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]

Cao, Z.

Z. Cao, K. Wang, and Q. Wu, “Aspherical anamorphic lens for shaping laser diode beam,” Opt. Commun. 305, 53–56 (2013).
[Crossref]

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]

Cavalli, A.

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]

Drexler, W.

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]

Fernández, E. J.

Fleck, A.

V. Lakshminarayanan and A. Fleck, “Zernike polynomials: a guide,” J. Mod. Opt. 58(7), 545–561 (2011).
[Crossref]

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]

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]

Hermann, B.

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]

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]

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]

Kopp, D.

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]

Lakshminarayanan, V.

V. Lakshminarayanan and A. Fleck, “Zernike polynomials: a guide,” J. Mod. Opt. 58(7), 545–561 (2011).
[Crossref]

Levy, U.

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

Lima, N. C.

N. C. Lima, A. Cavalli, K. Mishra, and F. Mugele, “Numerical simulation of astigmatic liquid lenses tuned by a stripe electrode,” Opt. Express 24(4), 4210–4220 (2016).
[Crossref] [PubMed]

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).

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]

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]

Melcher, J. R.

J. R. Melcher and G. I. Taylor, “Electrohydrodynamics: a review of the role of interfacial shear stresses,” Annu. Rev. Fluid Mech. 1(1), 111–146 (1969).
[Crossref]

Mishra, K.

N. C. Lima, A. Cavalli, K. Mishra, and F. Mugele, “Numerical simulation of astigmatic liquid lenses tuned by a stripe electrode,” Opt. Express 24(4), 4210–4220 (2016).
[Crossref] [PubMed]

K. Mishra, D. van den Ende, and F. Mugele, “Recent Developments in Optofluidic Lens Technology,” Micromachines (Basel) 7(102), 1–24 (2016).

K. Mishra and F. Mugele, “Numerical analysis of electrically tunable aspherical optofluidic lenses,” Opt. Express 24(13), 14672–14681 (2016).
[Crossref] [PubMed]

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.

K. Mishra and F. Mugele, “Numerical analysis of electrically tunable aspherical optofluidic lenses,” Opt. Express 24(13), 14672–14681 (2016).
[Crossref] [PubMed]

K. Mishra, D. van den Ende, and F. Mugele, “Recent Developments in Optofluidic Lens Technology,” Micromachines (Basel) 7(102), 1–24 (2016).

N. C. Lima, A. Cavalli, K. Mishra, and F. Mugele, “Numerical simulation of astigmatic liquid lenses tuned by a stripe electrode,” Opt. Express 24(4), 4210–4220 (2016).
[Crossref] [PubMed]

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]

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]

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]

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]

Povazay, B.

Prieto, P. M.

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]

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]

Saville, D. A.

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

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]

Taylor, G. I.

J. R. Melcher and G. I. Taylor, “Electrohydrodynamics: a review of the role of interfacial shear stresses,” Annu. Rev. Fluid Mech. 1(1), 111–146 (1969).
[Crossref]

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]

Unterhuber, A.

Vabre, L.

van den Ende, D.

K. Mishra, D. van den Ende, and F. Mugele, “Recent Developments in Optofluidic Lens Technology,” Micromachines (Basel) 7(102), 1–24 (2016).

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]

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]

van der Ende, D.

Vargas-Martín, F.

Wang, K.

Z. Cao, K. Wang, and Q. Wu, “Aspherical anamorphic lens for shaping laser diode beam,” Opt. Commun. 305, 53–56 (2013).
[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, and Q. Wu, “Aspherical anamorphic lens for shaping laser diode beam,” Opt. Commun. 305, 53–56 (2013).
[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]

Zappe, H.

Zhao, P.

Annu. Rev. Fluid Mech. (2)

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

J. R. Melcher and G. I. Taylor, “Electrohydrodynamics: a review of the role of interfacial shear stresses,” Annu. Rev. Fluid Mech. 1(1), 111–146 (1969).
[Crossref]

Biomicrofluidics (1)

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Figures (7)

Fig. 1
Fig. 1

(a) Image of the simulation domain with a sliced computational mesh. (b) Sketch of the top view showing the position of the aperture (dashed line) with respect to the top plate. (c) Sketch of the side view. The electric field distribution is represented by the red lines.

Fig. 2
Fig. 2

Left column: simulated actuation patterns aiming at (a) spherical aberration Z11, (b) astigmatism Z6, (c) 45° astigmatism Z5 and (d) coma Z7. Middle column: corresponding equilibrated surface profiles in perpendicular planes. The inset exhibit the details of the curves; Right column: corresponding spot diagrams. The black circle represents the airy disc.

Fig. 3
Fig. 3

Results of spherical aberration tuning: (a) MTF plots. The black line represents the diffraction-limited curve. (b) Wavefront map for 50 Pa and Umax = 200 V. (c) Zernike coefficients.

Fig. 4
Fig. 4

Results of 0° astigmatism tuning: (a) MTF plots. The black line represents the diffraction-limited curve. (b) Wavefront map for 30 Pa and Umax = 400 V. (c) Zernike coefficients.

Fig. 5
Fig. 5

Results of 45° astigmatism tuning: (a) MTF plots. The black line represents the diffraction-limited curve. (b) Wavefront map for 30 Pa and Umax = 400 V. (c) Zernike coefficients.

Fig. 6
Fig. 6

(a) Decentered configurations used to produce vertical positive coma. (b) Effect of each configuration on the Zernike coefficients considering Umax = 700 V and zero applied pressure. The inset shows a zoom on the Z6 astigmatism coefficient.

Fig. 7
Fig. 7

Results of vertical coma Z7 tuning using the excitation pattern 1 from Fig. 6(a): (a) MTF plots. The black line represents the diffraction-limited curve. (b) Wavefront map for 30 Pa and Umax = 400 V. (c) Zernike coefficients.

Tables (1)

Tables Icon

Table 1 Summary of the physical properties of both fluids: conductivity σ; permitivitty ε; density ρ; viscosity μ; and refractive index n.

Equations (8)

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

Δ P h =Δ P L + Π el ,
y( x,z )= c 1+ 1( 1+k ) c 2 + i=1 N A i E i ( x,z ) .
( εU )= ρ e
ρ e t +( σ E + ρ e u )=0
F e = Π el
ρ( u t + u u ) F μ =p+ρ g + F γ + F e
α 1 t +( α 1 u )+[ α 1 ( 1 α 1 ) u r ]=0
θ= α 1 θ phase1 +( 1 α 1 ) θ phase2

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