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Abstract
A dielectric liquid lens driven using a chevron-patterned electrode is prepared. The bending angle of the electrode is 90°. This newly designed electrode can effectively and symmetrically deform the shape of the liquid lens, which in turn leads to a variable focus. For a 3-mm-diameter lens, a driving voltage changed from 0 to 52 V can vary its focal length from ~19.3 to ~4.9 mm. Using a 40-Vrms pulse voltage to impact the lens, the dynamic response time is ~6.7 s. Using a step voltage to impact the liquid lens, the response time can be largely reduced. Multiple lenses or a microlens array can be driven at the same time. Due to in-plane actuation, the driving voltage is insensitive to the size of the liquid lens.
© 2017 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Adaptive lenses have been investigated intensively in recent years. These lenses can be simply classified into elastic membrane lenses [1–3], polymeric lenses [4–6], liquid crystal (LC) lenses [7–11], electro-wetting lenses [12–17], and dielectrophoretic (or dielectric) lenses [18–23]. Each type of lenses has its own strengths and limitations. Among them, dielectric lenses can present more merits, such as simple fabrication, compact structure, voltage actuation, optical isotropy, and easy operation. Unlike electro-wetting lenses, dielectric lenses do not employ salt water as the critical liquid, so their optical performances can be improved by choosing suitable dielectric liquids.
In a dielectric lens, the driving voltage can be affected by the pattern of its electrode. In previously demonstrated dielectric lenses, their electrodes have three different patterns. In the first pattern, the electrode is flat or curved without etching [19,20]. Because the diameter of the lens is dependent on the cell gap, a larger diameter needs a thicker cell gap. As a result, a higher driving voltage is required. In the second pattern, the electrode is etched with concentric zones [18,21]. A dielectric lens with zone-patterned electrode belongs to in-plane actuation. Therefore, the driving voltage is independent on the cell gap, and the size of the lens is scalable. Since the zone-patterned electrode provides a discontinuous fringing field in radial direction, the shape of the liquid could not be deformed effectively. Moreover, the lens center must coincide with the zone center of the electrode. Any deviation of the two centers may distort the liquid surface during actuation. In the third pattern, the electrode is etched with radial stripes [23]. The radial electrode can provide a continuous fringing field in radial direction, so the liquid lens can be effectively deformed. Similarly, the lens and the radial electrode must be coaxial in order to avoid shape distortion during actuation. Because the gap and width of the electrode stripes are constrained by the center of the radial electrode, it is rather limited to increase the density of the electrode stripes. Therefore, the driving voltage cannot be reduced largely by optimizing the electrode structure.
To overcome these obstacles, here we report a dielectric liquid lens integrated with a chevron-patterned electrode. The bending angle of the chevron electrode is 90°. By applying an external voltage, this electrode can deform the shape of the liquid lens symmetrically. As a result, the focal length of the liquid lens can be changed. Compared to previous dielectric liquid lenses using zoned- and radial-patterned electrodes, the chevron electrode has no symmetrical center. Any position deviation of the liquid droplet on the electrode will not cause shape distortion during actuation. Since the density of the electrode stripes can be increased, it is feasible to enhance the dynamic range of the liquid lens with a low driving voltage. The dielectric lens with a chevron-patterned electrode has promising applications in imaging biometrics, sensing, and other lab-on-chip devices.
2. Device structure and simulation
The side-view structure of the proposed lens cell is depicted in Fig. 1(a). From bottom to top, it consists of a glass substrate, an indium-tin-oxide (ITO) electrode, a dielectric layer, liquid-1 (L-1), liquid-2 (L-2), and a glass substrate. L-1 forms a droplet on bottom substrate. L-2 is used to fill the surrounding of L-1. L-2 is used to balance the gravity effect of L-1 and lubricate the surface of the bottom surface. The two liquids should be immiscible. The electrode on the bottom substrate has chevron pattern, as shown in Fig. 1(b). The bending angle of the electrode stripes is 90°
In the voltage-off state (V = 0), the droplet (L-1) has minimum surface energy. When a voltage is applied to the electrode (V = V1), a fringing field is generated across adjacent ITO stripes. According to Kelvin’s theory, the border of the droplet experiences a dielectric force. The dielectric force is expressed by [24]
where ε0 represents the permittivity of free space, ε1 and ε2 represent the relative dielectric constants of L-1 and L-2, respectively, and ∇E is the gradient of the electric field. If ε1<ε2, then the border of the droplet experiences the largest dielectric force along the ITO strips. The molecules of the droplet at the edge are pushed to shift toward the region with lower electric field. As a result, the droplet shrinks by yielding a space for L-2.To reshape the droplet symmetrically without distortion, the generated dielectric force should be circularly symmetrical. To analyze the fringing field generated by the chevron ITO stripes [Fig. 1(b)], a x, y, z coordinate system is established. To simplify the calculation, the x-axis (y-axis) is set to parallel (perpendicular) to the ITO stripes at the origin of the coordinate, and the z-axis is perpendicular to the substrate. The simulation area is set to be 569.1 × 848.54 μm, and the gap along Z direction is 12 μm. The width and gap of ITO stripes are both 20 μm. The bending angle of the ITO stripes is 90°. The electrode length between the two bending points is 200 μm. The simulation is carried out by commercial simulation software (3D TechWiz Korea). We compute the potential distribution by solving the Poisson equation and then the distribution of electric field in the media. If the voltage applied to the electrode is 40 Vrms, then the simulated electric field distribution in the yoz plane is given in Fig. 2(a). The fringing field can be decomposed into two parts: i) perpendicular to the ITO stripe and ii) along the z-direction. Near the edges of ITO stripes the electric field is the strongest. There is no electric field vector along the ITO stripes. The distribution of electric field strength in the xy plane is given in Fig. 2(b). Along the ITO stripes the fringing field is continuous, while in the direction perpendicular to the ITO stripes, the electric field is discontinuous. Using such a chevron electrode, the droplet [Fig. 1(a)] can be largely actuated in the direction along the ITO stripes. Since the bending angle of the ITO stripes is 90°, the border of the droplet experiences an equivalent dielectric force along x-axis and y-axis if the droplet is much larger than the width of an ITO stripe. Therefore, the droplet can be actuated symmetrically in the xoy plane.
Fig. 2 Simulation of electric field distribution with chevron ITO stripes (a) yoz plane (b) xoy plane.
3. Experiment
To demonstrate a liquid lens as depicted in Fig. 1(a), an ITO glass substrate was chosen. The ITO electrode was etched according to the above simulated parameters: the width and gap of the ITO stripes are both 20 μm. The bending angle is 90° and the electrode length between the two bending points is 200 μm. Teflon (400S1-100-1, DuPont, γ~19 dyne/cm at room temperature) was spin-coated on the ITO substrate to form a thin layer. After baking at 240 °C for 30 minutes, a solidified dielectric layer was formed. Optical oil SL5267 (SantoLight Optical Fluid, no~1.67, εo~5, ρ~1.25 g/cm) was dripped on the Teflon surface to form some small droplets. Glycerol (Sigma-Aldrich, purity> 99.9%, ng~1.47, εg~47, ρ~1.26 g/cm) was used to fill the surrounding of these droplets. The two liquids were covered with a glass plate to form a cell. The periphery of the cell was tightly sealed using adhesive glue.
4. Results and discussion
In the voltage-off state, each droplet can partially wet the Teflon surface with a contact angle. The contact angle (θ) is defined geometrically as the angle formed by the droplet at the three-phase boundary where the droplet, the glycerol, and the Teflon layer intersect. Here we chose a medium droplet for characterizing. The other droplets should obey the same working principle. To observe the aperture change of the droplet, we first examined the top-view of droplet driven at different voltages using a digital microscope (Model B0ll, 500 × ). The results are given in Fig. 3. At V = 0 (left), the aperture of the droplet is circular. The diameter of this droplet on the glass substrate is ~3 mm. When a voltage is applied to the ITO stripes, the droplet is contracted because its dielectric constant is smaller than that of the glycerol. At V = 20 Vrms (middle), the diameter is ~2.4 mm. At V = 40 Vrms (right), the diameter reduces to ~1.78 mm. The droplet shrinks a lot, but the aperture presents a circular shape. The droplet does not move randomly. This result implies that the border of the droplet experiences an equivalent dielectric force. Therefore, the center of the droplet is the center of the lens.
Fig. 3 The aperture change of the droplet driven at different voltages (300 Hz). The surrounding of the droplet is covered by glycerol.
To study the shape change of the droplet at various voltages, one method is to observe its side-view profile using the digital microscope. The voltage-dependent shape change of the droplet is shown in Fig. 4. At V = 0 (top-left), the radius of the curvature is maximal, so the contact angle of the droplet is minimum. When a voltage applied to the electrode exceeds ~10 Vrms, the droplet can be reshaped. At V = 12 Vrms (top-middle), the droplet shrinks slightly. At V = 20 Vrms (top-right), the droplet shrinks a lot. As compared to the shapes of the droplet at V = 24 Vrms (bottom-left), 32 Vrms (bottom-middle), and 40 Vrms (bottom-right), the droplet can be contracted continuously. The droplet keeps its symmetrical shape during actuation. To visually observe the shape change, a voltage changed from 0 to 40 Vrms was applied to the electrode. A movie (see Visualization 1) was recorded as given in Fig. 4. A smaller droplet (left) was recorded as well. At V = 0, the diameter of the smaller droplet (left) is ~1.6 mm. The two droplets can response to the voltage at the same time.
Fig. 4 Voltage-induced shape change of the droplets covered with glycerol. A video can be found in Visualization 1.
The ITO stripes with 90° bending angle are circularly asymmetrical, but the droplet can be reshaped symmetrically. To explain this consequence, we observe the border of the droplet using an optical microscope (Nikon LV100POL) during actuation. The results are shown in Fig. 5.
At V = 15 Vrms, the droplet is squeezed by the generated dielectric force. The edge on the gap of adjacent ITO stripes shrinks largely. Therefore, only its edge has a sawtooth shape, as shown in Fig. 5(a). The sawtooth coincides with the chevron ITO stripe. Due to the interfacial tension, the surface of the droplet away from its edge is very smooth. When the droplet shrinks at V = 30 Vrms, the smooth surface is unchanged except its sawtooth border, as shown in Fig. 5(b).
The droplet exhibits a lens character because it possesses a rotational symmetry around its principal axis. Theoretically, the relationship between the focus length (f) of the droplet and its contact angle (θ) on the substrate is expressed by [25]
where V is the volume of the droplet. The contact angle (θ) of the droplet at various voltages was measured. By increasing the voltage from 0 to 52 Vrms and decreasing the voltage from 52 to 0 Vrms, the advancing contact angle (filled circles) and the receding contact angle (empty circles) were measured, respectively. The results are given in Fig. 6. There is a little hysteresis between the advancing contact angle and the receding contact angle. The largest hysteresis is ~9° at V = 28 Vrms. This hysteresis is related to the viscosity and the interfacial tension of the liquids.If we treat the droplet as a spherical shape, then the radius of the curvature can be calculated. The result is shown in Fig. 6. Corresponding to the advancing contact angle changed from 20.9 to 62.3°, the radius of the curvature changes from ~5.2 to ~0.9 mm.
In the voltage-off state, the volume (V) of the droplet was measured to be ~0.78 mm3. The focal length of the droplet was calculated according to the measured advancing contact angles θ and Eq. (2). The result is given in Fig. 7. When the voltage is changed from 0 to 52 Vrms, the focal length is tuned from ~19.3 to ~4.9 mm. When the focal length is reduced, the diameter of the droplet on the substrate decreases too. Such characteristics can be described using f-number. f-number is the ratio of the lens's focal length to the diameter of the lens (f/D). According to the measured focal length and the diameter of the droplet, the f-number at various voltages is given in Fig. 7. When the voltage increases, its f-number decreases. At V > 40 Vrms, the f-number tends to be saturated.
As a lens, its optical performance can be evaluated by observing the image of an object. A tiny lion toy was placed at a distance of ~12 cm under the lens cell as the object. The image observed through the lens was recorded using the digital microscope. A clear image was observed at V = 0, as shown in Fig. 8(a). Because the object is outside the focal length, the image is inverted and real. By applying a 20-Vrms voltage (300 Hz) to the electrode, image becomes blurry due to defocus. By adjusting the lens cell in vertical position, a clear image with diminished size is observed, as shown in Fig. 8(b). The smaller image implies that the focal length is reduced. Figure 8(c) shows a clear image observed at V = 40 Vrms. Continuously increasing the voltage can further reduce the image size. The resolution of the lens at V = 40 Vrms can be estimated by observing a USAF resolution target using the optical microscope. The distance of the resolution chart to the lens was adjusted to ~62 mm. The diameter of the lens aperture was ~1.78 mm. The observed resolution chart is real and inverted. It can resolve group 4 and element 5, as shown in Fig. 8(d). The corresponding resolution is ~25 lp/mm.
Fig. 8 Images observed through the lens at various voltages. (a) V = 0, (b) 20 Vrms, (c) 40 Vrms, and (d) resolution chart observed using the optical microscope at V = 40 Vrms.
If the lens has no aberration, and the distance of the object to the lens (s) is much larger than the diameter of the lens aperture (d) (<<s), then the resolution of the lens is limited by diffraction [26,27]. In this condition, the limiting resolution (or cutoff frequency) R(c) is simply expressed by
where λ is the wavelength of light. For s~62 mm, d~1.78 mm, and λ~0.55 μm, the diffraction-limited resolution is calculated to be ~52 lp/mm. The observed resolution is much smaller than the diffraction-limited resolution. The main reason is due to the lens aberration degrading its optical performance.Response time is an important factor for an adaptive lens. The response time of our lens can be measured when it is used to control a laser beam. Suppose the light intensity is changed from Io (V = V1) to I1 (at V = 0) and is detected using a photodiode, by connecting a digital oscilloscope to the photodiode, the change of light intensity with time can be analyzed. The response time includes rise time (τrise) and decay time (τdecay). τrise is defined as the time required to change the light intensity from Io to I1 (90% to 10%) and τdecay is the time taken to change the light intensity from I1 to Io (10% to 90%). Figure 9 shows the response time of the lens driven with various pulse voltages (300 Hz). τrise and τdecay are dependent on the amplitude of the voltage. A higher voltage provides a stronger dielectric force, leading to a faster shape deformation. To recover to its original shape, a larger deformed droplet needs a longer distance to travel, leading to a slower response time. At V = 40 Vrms, τrise and τdecay were measured to be ~0.7 s and ~6 s, respectively. For a large dynamic range, the response time is fairly slow.
Sometimes it is not necessary to obtain a large dynamic range for imaging. If a limited focal length change is acceptable, then the response time will not be a concern. To get a limited focal length change, one method is to use a step voltage to actuate the liquid lens. Figure 10 shows the light intensity change when a step voltage from 30 to 40 Vrms is applied to the device. For the dynamic range Δf ~2.1 mm, τrise and τdecay were measured to be ~0.6 and ~1.7 s, respectively. The total response time is ~2.3 s. The response time is largely reduced.
Similar to the dielectric lenses with zone- and radial-patterned electrodes, the liquid lens driven using the newly designed ITO pattern belongs to in-plane actuation too. Therefore, the droplet is insensitive to the driving voltage, and the size of the liquid lens is scalable. Because the diameter of the lens is much larger than the width of the ITO stripe, the liquid droplet can be deformed symmetrically. To actuate a micro-sized liquid lens symmetrically, the width and gap of ITO stripes should be reduced further. However, extremely increasing the number of ITO stripes will enhance light diffraction. To improve the optical performance of the liquid lens, the structure of the chevron electrode should be optimized, and the surface of the droplet could not be severely deformed. The response time is dependent on the amplitude of the driving voltage and the dynamic range. A large dynamic range can lead to a slow response time, while a limited dynamic range driven by a step voltage can enhance the dynamic response. The response time can also be reduced if a suitable dielectric liquid is used to replace the viscous glycerol. Since the densities of the two liquids match well, the gravitational effect on distorting the shape of the liquid lens is negligible. Moreover, the lens will not shift randomly if it is used in an optical system. In contrast to previous liquid lenses using zone- and radial-patterned electrodes, the chevron electrode can actuate multiple liquid lenses or a microlens array at the same time. When the droplet is pinned down by the substrate, there is no decenter issue with such an electrode. The liquid lens is insensitive to vibrating, shocking and shaking, so it is mechanically stable.
5. Conclusion
A dielectric liquid lens driven using a chevron ITO electrode has been demonstrated. The bending angle of the ITO stripes is 90°. By applying a voltage to the ITO electrode, the generated dielectric forces along x-axis and y-axis of the ITO stripes are equivalent. Therefore, the liquid lens can be deformed symmetrically. Due to in-plane actuation, the lens is insensitive to the driving voltage, and the diameter of the lens is scalable. For the liquid lens with 3-mm-diameter, its focal length can be tuned from ~19.3 to ~4.9 mm when the applied voltage is changed from 0 to 40 Vrms. Using a 40-Vrms pulse voltage to impact the liquid lens, the total response time is ~6.7 s. Using a step voltage from 30 to 40 Vrms to impact the liquid lens, the total response time can be reduced to ~2.3 s. The observed resolution of the liquid lens is ~25 lp/mm at V = 40 Vrms. To symmetrically actuate micro-sized liquid lenses, a feasible method is to increase the number of the ITO stripes. The trade-off is that light diffraction will be enhanced. In contrast to the liquid lenses with zone- or radial-patterned electrode, the chevron electrode can actuate multiple liquid lenses or a microlens array. There is no decenter issue with such an electrode, so the liquid lens is mechanically stable. The liquid lens driven using a chevron electrode has potential applications in imaging, sensing, biometrics, and portable electronic devices.
Funding
National research foundation (NRF) of Korea (2016R1D1A1B04934256).
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