A packaged liquid lens driven by the dielectric force was demonstrated. The liquid lens consisted of a low dielectric constant droplet and a high dielectric constant sealing liquid. The two non-conductive liquids were sealed in a chamber under the condition of iso-density. Focal length of a liquid lens with an aperture of 3mm changed from 34mm to 12mm in the range of 0-200V. Hysteresis was observed in the liquid lens, with a maximum value measured of 12.5° at 120 volts in terms of droplet’s contact angle. The focal spot size measured approximately 80μm. Rise and fall times were 650ms and 300ms, respectively. The lens consumed 1mW of power when applying a 200 volt, 1 kHz signal. The longitudinal and transverse spherical aberrations were estimated to be nearly invariant when the focal length exceeded 20mm.
©2007 Optical Society of America
Focal length tuning in imaging systems is typically accomplished using electromechanical motors to change the spacing between solid lenses. Portable optical devices with low electric power consumption are currently in strong demand. Electromechanical motors, however, consume high electric power and occupy large space, so they may be inappropriate for many portable applications. For focal length tuning, other alternatives to varying lens spacing include spatial redistribution of the refractive index within a lens and surface profile deformation of a lens. The spatial distribution of liquid crystal′s refractive index in a graded-index lens can be adjusted by non-uniform electric fields. [1-5] Liquid crystal molecules are forced to align parallel to the spatially distributed electric fields by electrostatic forces, inducing a lensing effect. The graded-index lens has low spectral transmission due to its requirement for polarized-light, limiting its applications in imaging systems.
Surface profile deformation of a liquid lens has also been investigated for focal length tuning. Such an approach has been demonstrated using fluidic pressure, [6-8] the electrowetting effect [9-13] and dielectric force . Fluidic pressure provided by an external pump deformed the polymer film cover of a liquid-filled lens, resulting in focal length change. However, the additional volume requirement for an external pump is also disadvantageous for portability. An electrowetting-based liquid lens adjusted its surface profile by changing the interfacial energy between salt water and oil. When a voltage was applied, the salt water coerced free electric charges to the boundary between the solutions. The interfacial energy increased due to the electric double layer effect, redefining the contact angle of the salt water. Such a contact angle change initiated focal length alternation of the liquid lens. However, the transportation of the free electric charges may produce electrolysis in the salt water and the alternating electric fields may generate microbubbles due to the heating of the solution.
A droplet of isotropic liquid crystal performed focal length tuning using the dielectric force in 2006.  The non-conductive liquid crystal did not introduce electrolysis, Joule heating or microbubbles that often appear in electrowetting-based liquid lenses. Nevertheless, a blurred image due to the birefringence effect was observed in  when the ambient temperature was below the transition temperature of the liquid crystal. To overcome such a problem, we introduced new liquids to a packaged liquid lens that are actuated by a dielectric force.
2. Lens configuration and driving mechanism
Figure 1(a) depicts the configuration of a liquid lens actuated by the dielectric force. The liquid lens consists of a 15μL (liquid) droplet with a low dielectric constant and a sealing liquid with a high dielectric constant. The bottom diameter of the droplet was 7mm when no voltage was applied. The two liquids were injected inside a 3mm thick PMMA (polymethyl methacrylate) chamber that was sealed between two ITO glass substrates. The concentric ITO electrodes on the bottom glass substrate were coated with 1μm thick Teflon® to reduce friction between the droplet and the glass substrate. The width and spacing of the ITO electrodes was 50μm. The mass density of the sealing liquid was adjusted to match that of the droplet to minimize the gravitational effect, since the gravitational effect may induce nonuniform deformation of the droplet profile, causing optical aberrations. As the voltage was applied, a dielectric force arose on the droplet due to the difference in the dielectric constant between the two liquids. The dielectric force shrunk the droplet, increasing the droplet′s contact angle and shortening the focal length of the liquid lens. The dielectric force induced is described by Eq. (1).
where ε0 is the permittivity of free space, ε1 and ε2 are dielectric constants of the sealing liquid and the droplet, respectively. E denotes the electric field intensity across the interface of the two liquids.
In the liquid lens demonstrated, the refractive indices were 1.4 and 1.6 for the sealing liquid and the droplet (optical fluids SL-5267, SantoLightTM), respectively. The two liquids had a difference in dielectric constant of about 35 and possessed a wide temperature range of isotropic liquid phase over 150°C. The liquid lens demonstrated was convex and had an electrically tunable focal length. Figure 1(b) shows the images of the word “Green” captured using the liquid lens at the rest state and at 75 volts. The images were captured at a distance of 15mm from the actuated liquid lens. At the rest state, the liquid lens had a long focal length due to the low intrinsic contact angle of the droplet. At 75 volts, the shortened focal length magnified the virtual image so only a few of the letters were captured. Figure 1(c) shows the video of the focal tuning using the liquid lens. The object was placed at a distance of 50cm away from the lens.
3. Lens characterizations
The optical characteristic of the liquid lens that were measured experimentally included the droplet′s contact angle and its hysteresis, the conic constant of the droplet, focal length tuning, and focal spot size. Further, focal length tuning, focal spot size and spherical aberration were verified using simulation tools and theory. The contact angle of the droplet in the packaged liquid lens was measured at various voltages as shown in Figure 2(a). The intrinsic contact angle of the droplet was measured to be 25°. The contact angle began to significantly increase at voltages over 50 volts and reached 58° at 200 volts. Hysteresis of the droplet′s contact angle was observed and its maximum was found to be 12.5° at 120 volts. Figure 2(b) shows that the conic constants of the droplet were close to zero at various voltages, implying that the droplet maintained a spherical profile at all focal lengths. Hence, the surface profile of the droplet could be assumed to be spherical during actuation. The actuation of the droplet in the liquid lens was captured by a high-speed CCD camera. The rise time was measured to be about 650ms when the liquid lens was actuated from the rest state to 200 volts. When the applied voltage was switched off, the measured fall time was 300ms.
Focal length measurement of the liquid lens was conducted using a laser with a wavelength of 532nm and a beam scanner (0180-XY/LL/SW/1μm/5Hz, Photon Inc.) . The focal length was determined for advancing actuation based on the minimum spot size resolved along the optic axis. Further, the measured advancing focal lengths were compared with the paraxial approximation based on the advancing contact angles in Fig. 2. The measurement results and the paraxial approximation were in good agreement (see Fig. 3). When the voltage increased from zero to 200 volts, the liquid lens shortened its focal length from 34mm to 12mm. The electric power consumed was determined to be less than 1mW.
Figure 4 shows the focal spot sizes of the liquid lens at various actuated focal lengths. The focal spot size was measured an average of approximately 80μm at different focal lengths. The measurement results were verified by the optical simulation software ASAP (Breault Research Organization Inc.) with internal reflection taken into account. The internal reflection was found to broaden the focal spot size. The focal spot sizes are almost constant on the variety of the actuated focal planes, implying a nearly invariant focal spot size of the liquid lens. Given the constant volume of the droplet, the bottom diameter of the droplet shrunk as the focal length shortened. Hence, the focal spot size, the ratio of focal length to collimated beam diameter entering the lens, remains nearly the same for all the actuated focal lengths.
Spherical aberration corresponds to the dimension of aperture stop and the curvature of a lens. Given negligible change of the conic constants, the longitudinal spherical aberration (LA) and the transverse spherical aberration (HR) were calculated based on the surface profile of a liquid lens. The calculated results in Fig. 5 show that the spherical aberrations were nearly invariant for focal lengths greater than 20mm. The optical property of the constant aberration facilitates a lens set design for aberration correction in an imaging system.
A liquid lens actuated using the dielectric force was demonstrated. The liquid lens consists of two nonconductive liquids that were sealed between two ITO glasses. The liquid lens was capable of tuning its focal length from 34mm to 12mm in the range of 0-200V. Almost all the focal spot sizes at the various focal lengths measured 80μm in average. The rise and fall times of the liquid lens were 650ms and 300ms, respectively. The spherical aberrations remained nearly constant when the focal length was greater than 20mm.
We are grateful to Shiang-Ruei Ouyang for the help in the optical measurement. We would also like to thank Tzu-Chun, Liao for the ITO patterning.
References and links
1. T. Nose, S. Masuda, and S. Sato, “A liquid crystal microlens with hole-patterned electrodes on both substrates,” Jpn. J. Appl. Phys. 31, 1643–1646 (1992). [CrossRef]
3. A. Y. Gvozdarev, G. E. Nevskaya, and I. B. Yudin, “Adjustable liquid-crystal microlenses with homeotropic orientation,” J. Opt. Technol. 68, 682–686 (2001). [CrossRef]
4. H. S. Ji, J. H. Kim, and S. Kumar, “Electrically controllable microlens array fabricated by anisotropic phase separation from liquid-crystal and polymer composite materials,” Opt. Lett. 28, 1147–1149 (2003). [CrossRef] [PubMed]
5. C-C Cheng, C. A. Chang, C-H Liu, and J. A. Yeh, “A tunable liquid-crystal microlens with hybrid alignment,” J. Opt. A: Pure Appl. Opt. 8, S365–S369 (2006). [CrossRef]
8. W. Wang, J. Fang, and K. Varahramyan, “Compact variable-focusing microlens with integrated thermal actuator and sensor,” IEEE Photon. Technol. Lett. 17, 2643–2645 (2005). [CrossRef]
9. B. Berge and J. Peseux, “Variable focal lens controlled by an external voltage - An application of electrowetting,” Eur. Phys. J. E 3, 159–163 (2000). [CrossRef]
10. S. Kuiper and B. H. W. Hendriks, “Variable-focus liquid lens for miniature cameras,” Appl. Phys. Lett. 85, 1128–1130 (2004). [CrossRef]
11. T. Krupenkin, S. Yang, and P. Mach, “Tunable liquid microlens,” Appl. Phys. Lett. 82, 316–318 (2003). [CrossRef]
12. A. Quinn, R. Sedev, and J. Ralston, “Influence of the electrical double layer in electrowetting,” J. Phys. Chem. B 107, 1163–1169 (2003). [CrossRef]
13. F. Mugele and J-C Baret, “Electrowetting: from basics to applications,” J. Phys.: Condens. Matter 17, R705–R774 (2005). [CrossRef]