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Optics Express

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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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.

© 2012 OSA

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

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

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

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

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

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

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 θiand the angle of emergence isθo. As shown in the Fig. 1
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.
, refractive index n1and n2 (n2<n1) separately denote the conducting droplet and the external liquid. The paraxial image distance S0can be expressed as follow:
S0=-n2r(n2-n1).
(1)
The symbol r denotes the radius of curvature on vertex. Spherical aberration δScan be described as follow:

δS=S-S0.
(2)
tanθi=dzdx.
(3)
n1sinθi=n2sinθo.
(4)
S=xtan(θi-θo).
(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
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.
, 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.

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 μm. The volume of droplet is 134μL.The physical properties of the materials are presented as follows.

θ0=120,γlv=77.1354mJ/m2,ε=2.65,n1=1.333,n2=1.404.

Figures 4
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.
, 5
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.
, 6
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.
, and 7
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.
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.

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.
.

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

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

  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,” Langmuir25(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]

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