Study of the influence of the slope interfaces upon the image quality of liquid optical lens

doi:10.1364/OE.20.024636

Optics Express

Editor: C. Martijn de Sterke
Vol. 20, Iss. 22 — Oct. 22, 2012
pp: 24636–24641

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Study of the influence of the slope interfaces upon the image quality of liquid optical lens

Dai Yu, Zhou Ying, Fang Liping, Liu Jun, Chen Shufen, Chen Jiabin, and Xin Jianguo »View Author Affiliations

Optics Express, Vol. 20, Issue 22, pp. 24636-24641 (2012)
http://dx.doi.org/10.1364/OE.20.024636

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▸ Article Outline
– Abstract
1. Introduction
2. Spherical aberration calculation method and analysis
3. Conclusion
– References and links

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Abstract

The solid interface of different slopes plays a significant role in influencing focus range and image quality of liquid controllable optical lens. In this paper, based on the theoretical model of liquid optical lens, the spherical aberration of the liquid optical lens is calculated. It is found that the spherical aberration is different from the two opposite sides of liquid optical lens, and at the same voltage range, the smaller the cone angle of the solid interface is, the larger the optical aperture of liquid optical lens changes. The spherical aberration of liquid lens can be minimized when a proper voltage is applied and a proper solid interface slope is selected.

1. Introduction

Compared with solid optical components and liquid crystal optical components, the liquid controllable optical technology has many advantages such as a wide focal range of optical system and a rapid deflection of the beam direction. The shape of liquid changes under the action of electric field, and only milliseconds are needed to realize a wide focal range which cannot be achieved by traditional solid optical devices [1

B. Berge and J. Peseux, “Variable Focal Lens Controlled by An External Voltage: An Application of Electrowetting,” J. Eur. Phys. J. E. 3(2), 159–163 (2000). [CrossRef]

,2

C. Quilliet and B. Berge, “Investigation of Effective Interface Potentials by Electrowetting,” Europhys. Lett. 60(1), 99–105 (2002). [CrossRef]

].

In 2004, a liquid lens developed by French Varioptic has reached a practical level [3

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

]. In the same year, S.Kuiper of Philips Company also launched a focus liquid lens based on EWOD (electro-wetting on dielectric) effect. Varioptic’s ARCTIC Series liquid lens only takes a maximum of 100ms for the focus that matches the distance to the photographic subject to go from 5cm to infinity. In order to keep the density and refractive index low, lithium chloride solution are selected as conducting fluid of variable-focus liquid lens by Philips [4

S. Kuiper and B. H. W. Hendriks, “Variable-focus Liquid Lens for Miniature Cameras,” Appl. Phys. Lett. 85(7), 1128–1131 (2004). [CrossRef]

]. As the insulating liquid a mixture of phenylmethylsiloxanes is used for its high refractive index and good electro-wetting properties. In 2010, Varioptic launched a four electrodes liquid lens which can achieve more complex optical functions such as astigmatism and tilt. The researches concern the selection of liquids and hydrophobic media, or the relationship between dynamic contact angle and voltage [5

B. Raj, M. Dhindsa, N. R. Smith, R. Laughlin, and J. Heikenfeld, “Ion and Liquid Dependent Dielectric Failure in Electrowetting Systems,” Langmuir 25(20), 12387–12392 (2009). [CrossRef] [PubMed]

–8

L. K. Koopal, “Wetting of Solid Surfaces: Fundamentals and Charge effects,” Adv. Colloid Interface Sci. 179-182, 29–42 (2012). [CrossRef] [PubMed]

].

As for a liquid optical lens, the spherical aberration depends on the meniscus shape of liquid lens which is affected by the slope interfaces. If the relationship among spherical aberration, voltage and the slope interfaces can be revealed, it will help design liquid lens with low spherical aberration.

2. Spherical aberration calculation method and analysis

As the parallel incident light is from the liquid of small refractive index to the liquid of large refractive index, the angle of incidence is

θ_{i}

and the angle of emergence is

θ_{o} .

As shown in the Fig. 1 , refractive index

n_{1}

and

n_{2}

{(n}_{2} {<n}_{1})

separately denote the conducting droplet and the external liquid. The paraxial image distance

S_{0}

can be expressed as follow:

S_{0} = - n_{2} r (n_{2} - n_{1}) .

(1)

The symbol

r

denotes the radius of curvature on vertex. Spherical aberration

δ S

can be described as follow:

Fig. 1 Calculation sketch of spherical aberration with the incident light from the liquid of small refractive index to the liquid of large refractive index.

δ S = S - S_{0} .

(2)

\tan θ_{i} = - \frac{d z}{d x} .

(3)

n_{1} \sin θ_{i} = n_{2} \sin θ o .

(4)

S = \frac{x}{\tan (θ i - θ o)} .

(5)

Therefore, in order to calculate the spherical aberration, the solution of Laplace equation is required to get the meniscus shape of liquid lens. Since the Laplace equation has no analytical solution, the fourth-order Runge-Kutta method is used for numerical integration and the Hermite interpolation is used to approximate the differential value.

As shown in the Fig. 2 , when the parallel incident light is from the opposite direction, the total internal reflection may appear, so that the incident lights cannot all pass through the liquid optical lens. In other words, under this condition there is an aperture.

Fig. 2 Calculation sketch of spherical aberration with the incident light from the liquid of large refractive index to the liquid of small refractive index.

The relationship between spherical aberration and voltage can be got by the Lippmann-Young equation.

\cos θ (V) = \cos θ_{0} + \frac{ε_{0} ε}{2 d γ_{l v}} V^{2} .

(6)

This equation reveals a relation between contact angle

θ

and the voltage V. The notation of

γ_{lv}

is the surface free energy between conducting liquid and insulating liquid. The symbol

ε

and

ε_{0}

denote the relative permittivity of insulating dielectric layer and vacuum permittivity. The thickness of insulating dielectric layer is represented by d.

θ_{0}

is the initial contact angle. As the solid phase is conical surface, the meniscus shape of liquid optical lens is related to the conical angle. The symbol α represents the half-apex angle of cone. The initial contact angle

θ_{0}^{'}

is described as

θ_{0}^{'} = θ_{0} - α .

The interface shape of solid phase is illustrated in Fig. 3 .

Fig. 3 The slope interface shape of solid phase.

A droplet of sodium chloride solution surrounded by methyl silicone oil is put on the film of Teflon. The material of insulating dielectric layer is Parylene N, and the thickness is 2

μ m .

The volume of droplet is 134

μ L .

The physical properties of the materials are presented as follows.

θ_{0} =120, γ_{lv} =77 {.1354mJ/m}^{2}, ε =2 .65, n_{1} =1 .333, n_{2} =1 .404 .

Figures 4 , 5 , 6 , and 7 respectively shows the relationship between spherical aberration and the slope interfaces. No matter the incident light is from the liquid of small refractive index or large refractive index, the slope interfaces have a great impact on spherical aberration, and the influence is particularly significant when voltage is off. The spherical aberration of the liquid optical lens becomes the smaller when an electric field is applied. However, it does not mean that the higher voltage is applied, the spherical aberration is smaller. Instead of becoming smaller, the spherical aberration is larger when the applied voltage exceeds a certain range.

Fig. 4 (a) The meniscus shape of liquid lens with cone angle α of 30 degrees. (b) Curves of spherical aberration with the incident light from the liquid of small refractive index. (c) Curves of spherical aberration with the incident light from the liquid of large refractive index.

Fig. 5 (a) The meniscus shape of liquid lens with cone angle α of 45 degrees. (b) Curves of spherical aberration with the incident light from the liquid of small refractive index. (c) Curves of spherical aberration with the incident light from the liquid of large refractive index.

Fig. 6 (a) The meniscus shape of liquid lens with cone angle α of 60 degrees. (b) Curves of spherical aberration with the incident light from the liquid of small refractive index. (c) Curves of spherical aberration with the incident light from the liquid of large refractive index.

Fig. 7 (a) The meniscus shape of liquid lens with cone angle α of 75 degrees. (b) Curves of spherical aberration with the incident light from the liquid of small refractive index. (c) Curves of spherical aberration with the incident light from the liquid of large refractive index.

When the parallel incident light is from the liquid of large refractive index to the liquid of small refractive index, the relation between aperture and the slope interfaces is shown in Fig. 8 .

Fig. 8 (a) Curves of the relation between voltage and the aperture of liquid lens with cone angle α of 30 degrees. (b) Curves of the relation between voltage and the aperture of liquid lens with cone angle α of 45 degrees. (c) Curves of the relation between voltage and the aperture of liquid lens with cone angle α of 60 degrees. (d) Curves of the relation between voltage and the aperture of liquid lens with cone angle α of 75 degrees.

The aperture is determined by the meniscus shape of liquid lens, and the meniscus shape of liquid lens depends on the voltage and the initial contact angle. As the solid phase is conical surface, the meniscus shape of liquid optical lens is related to the voltage and the conical angle

α .

The initial contact angle

θ_{0}^{'}

is described as

θ_{0}^{'} = θ_{0} - α .

As for the smaller the solid interface cone angle, the meniscus shape changes a wider range.

3. Conclusion

In this paper, the relationship among spherical aberration, voltage and the solid interfaces slope angle is studied. It is found that the spherical aberration with incident light from one side of liquid optical lens is different from the spherical aberration with incident light from the opposite direction, which is different from the traditional single solid lens; the spherical aberration of the liquid optical lens becomes the smaller when an electric field is applied than the voltage is off. At the same voltage range, the smaller the solid interface cone angle is, the larger the aperture changes. The image quality of liquid optical lens can be efficiently corrected by applying a proper electric field and selecting a proper solid slope interface.

References and links

1.	B. Berge and J. Peseux, “Variable Focal Lens Controlled by An External Voltage: An Application of Electrowetting,” J. Eur. Phys. J. E. 3(2), 159–163 (2000). [CrossRef]
2.	C. Quilliet and B. Berge, “Investigation of Effective Interface Potentials by Electrowetting,” Europhys. Lett. 60(1), 99–105 (2002). [CrossRef]
3.	B. Berge, “Liquid Lens Technology: Principle of Electrowetting Based Lenses and Applications to Image,” in Proceedings of IEEE Conference on Micro Electro Mechanical Systems (Miami, 2005), pp. 227–230.
4.	S. Kuiper and B. H. W. Hendriks, “Variable-focus Liquid Lens for Miniature Cameras,” Appl. Phys. Lett. 85(7), 1128–1131 (2004). [CrossRef]
5.	B. Raj, M. Dhindsa, N. R. Smith, R. Laughlin, and J. Heikenfeld, “Ion and Liquid Dependent Dielectric Failure in Electrowetting Systems,” Langmuir 25(20), 12387–12392 (2009). [CrossRef] [PubMed]
6.	H. Ren, S. Xu, Y. Liu, and S. T. Wu, “Liquid-based Infrared Optical Switch,” Appl. Phys. Lett. 101(4), 041104 (2012), http://apl.aip.org/resource/1/applab/v101/i4/p041104_s1. [CrossRef]
7.	H. Liu, S. Dharmatilleke, D. K. Maurya, and A. A. O. Tay, “Dielectric Materials for Electrowetting-on-dielectric Actuation,” Microsyst.Technol. 16(3), 449–460 (2010). [CrossRef]
8.	L. K. Koopal, “Wetting of Solid Surfaces: Fundamentals and Charge effects,” Adv. Colloid Interface Sci. 179-182, 29–42 (2012). [CrossRef] [PubMed]

OCIS Codes
(080.3630) Geometric optics : Lenses
(230.2090) Optical devices : Electro-optical devices

ToC Category:
Geometric Optics

History
Original Manuscript: July 27, 2012
Revised Manuscript: September 21, 2012
Manuscript Accepted: October 6, 2012
Published: October 12, 2012

Citation
Dai Yu, Zhou Ying, Fang Liping, Liu Jun, Chen Shufen, Chen Jiabin, and Xin Jianguo, "Study of the influence of the slope interfaces upon the image quality of liquid optical lens," Opt. Express 20, 24636-24641 (2012)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-20-22-24636

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References

B. Berge and J. Peseux, “Variable Focal Lens Controlled by An External Voltage: An Application of Electrowetting,” J. Eur. Phys. J. E.3(2), 159–163 (2000). [CrossRef]
C. Quilliet and B. Berge, “Investigation of Effective Interface Potentials by Electrowetting,” Europhys. Lett.60(1), 99–105 (2002). [CrossRef]
B. Berge, “Liquid Lens Technology: Principle of Electrowetting Based Lenses and Applications to Image,” in Proceedings of IEEE Conference on Micro Electro Mechanical Systems (Miami, 2005), pp. 227–230.
S. Kuiper and B. H. W. Hendriks, “Variable-focus Liquid Lens for Miniature Cameras,” Appl. Phys. Lett.85(7), 1128–1131 (2004). [CrossRef]
B. Raj, M. Dhindsa, N. R. Smith, R. Laughlin, and J. Heikenfeld, “Ion and Liquid Dependent Dielectric Failure in Electrowetting Systems,” Langmuir25(20), 12387–12392 (2009). [CrossRef] [PubMed]
H. Ren, S. Xu, Y. Liu, and S. T. Wu, “Liquid-based Infrared Optical Switch,” Appl. Phys. Lett.101(4), 041104 (2012), http://apl.aip.org/resource/1/applab/v101/i4/p041104_s1 . [CrossRef]
H. Liu, S. Dharmatilleke, D. K. Maurya, and A. A. O. Tay, “Dielectric Materials for Electrowetting-on-dielectric Actuation,” Microsyst.Technol.16(3), 449–460 (2010). [CrossRef]
L. K. Koopal, “Wetting of Solid Surfaces: Fundamentals and Charge effects,” Adv. Colloid Interface Sci.179-182, 29–42 (2012). [CrossRef] [PubMed]

Berge, B.
Dharmatilleke, S.
Dhindsa, M.
Heikenfeld, J.
Hendriks, B. H. W.
Koopal, L. K.
Kuiper, S.
Laughlin, R.
Liu, H.
Liu, Y.
Maurya, D. K.
Peseux, J.
Quilliet, C.
Raj, B.
Ren, H.
Smith, N. R.
Tay, A. A. O.
Wu, S. T.
Xu, S.

Adv. Colloid Interface Sci.

L. K. Koopal, “Wetting of Solid Surfaces: Fundamentals and Charge effects,” Adv. Colloid Interface Sci.179-182, 29–42 (2012). [CrossRef] [PubMed]

Appl. Phys. Lett.

H. Ren, S. Xu, Y. Liu, and S. T. Wu, “Liquid-based Infrared Optical Switch,” Appl. Phys. Lett.101(4), 041104 (2012), http://apl.aip.org/resource/1/applab/v101/i4/p041104_s1 . [CrossRef]
S. Kuiper and B. H. W. Hendriks, “Variable-focus Liquid Lens for Miniature Cameras,” Appl. Phys. Lett.85(7), 1128–1131 (2004). [CrossRef]

Europhys. Lett.

C. Quilliet and B. Berge, “Investigation of Effective Interface Potentials by Electrowetting,” Europhys. Lett.60(1), 99–105 (2002). [CrossRef]

J. Eur. Phys. J. E.

B. Berge and J. Peseux, “Variable Focal Lens Controlled by An External Voltage: An Application of Electrowetting,” J. Eur. Phys. J. E.3(2), 159–163 (2000). [CrossRef]

Langmuir

B. Raj, M. Dhindsa, N. R. Smith, R. Laughlin, and J. Heikenfeld, “Ion and Liquid Dependent Dielectric Failure in Electrowetting Systems,” Langmuir25(20), 12387–12392 (2009). [CrossRef] [PubMed]

Microsyst.Technol.

H. Liu, S. Dharmatilleke, D. K. Maurya, and A. A. O. Tay, “Dielectric Materials for Electrowetting-on-dielectric Actuation,” Microsyst.Technol.16(3), 449–460 (2010). [CrossRef]

Other

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

2012, Ren, Appl. Phys. Lett.
2012, Koopal, Adv. Colloid Interface Sci.
2010, Liu, Microsyst.Technol.
2009, Raj, Langmuir
2004, Kuiper, Appl. Phys. Lett.
2002, Quilliet, Europhys. Lett.
2000, Berge, J. Eur. Phys. J. E.

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