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Abstract
Inspired by the arrangement of iris and crystalline lens in human eyes, we propose a three-phase electrowetting liquid lens with a deformable liquid iris (TELL-DLI). The proposed electrowetting liquid lens has three-phase fluid: air, conductive liquid, and dyed insulating liquid. The insulating liquid is distributed on the inner wall of the chamber in a ring shape. By applying voltage, the contact angle is changed, so that the dyed insulating liquid contracts towards the center, which is similar to the contraction of iris and the function of crystalline lens muscle in human eyes. The variation range of focal length is from -451.9 mm to -107.9 mm. The variation range of the aperture is from 4.89 mm to 0.6 mm. Under the step voltage of 200 V, the TELL-DLI can be switched between the maximum aperture state and the zero aperture state, and the switching time is ∼150/200 ms. Because of the discrete electrodes, TELL-DLI can regionally control the shape and position of the iris, and switch between circle, ellipse, sector, and strip. The TELL-DLI has a wide application prospect in imaging systems, such as microscopic imaging system, and has the potential to be applied in the field of complex beam navigation.
© 2023 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Liquid lens has a wide range of applications, such as microscopes, telescopes, cameras, laparoscopes, and so on [1–10]. In fact, there are already liquid lenses in nature, such as the crystalline lens in the human eye [11]. Among all kinds of liquid lenses, electrowetting liquid lens has the characteristics of continuous zoom without mechanical movement, fast response time, and uncomplicated process [12–20]. Thus, the electrowetting liquid lens has been widely studied and realized commercialization since 2002 by Varioptic. The electrowetting liquid lens works on the electrowetting on dielectric (EWOD) effect and the electrowetting liquid lens zooms by changing the curvature of the interface. The structure of the electrowetting liquid lens changes from flat plate to cylinder to cone to sphere under the rapid development of the requirements about the range of dioptric power [12–17].
At the same time, with the change of structure, the quantity and distribution of filling liquid components of electrowetting liquid lens have been changing, which directly affects the distribution of interfaces between fluids, and finally makes the driving mechanism of electrowetting liquid lens different.
In the early years, the liquid distribution method of electrowetting liquid lens was a single layer of conductive liquid or a single droplet [12,13]. The conductive liquid and air form a gas-liquid interface. The advantage of this method is that the refractive index difference between gas and liquid is large, but the interface deformation is limited. At present, the liquid layer distribution of mature electrowetting liquid lens is mainly a conductive liquid layer and an insulating liquid layer, which form a liquid-liquid (L-L) interface [14–25]. The density of the conductive liquid and the insulating liquid is the same, and they have a certain refractive index difference. This method has the advantages of increasing the variation range of contact angle, resisting the gravity effect and enhancing the robustness of the lens.
In recent years, the liquid distribution method of electrowetting liquid lens is that there are at least two liquid-liquid interfaces between the liquid layers of multi-layer conductive liquid and insulating liquid. The advantage of this method is that multiple liquid-liquid interfaces increase the variation range of optical power. Many researchers have carried out related research. In 2017, an all-liquid optical zoom system based on two independently controllable liquid-liquid interfaces was proposed, which were integrated into a single cylindrical housing [26]. Multiple liquid-liquid interfaces are more flexible and can be applied to the bionic field. In 2019, an optical model of a human eye’s crystalline lens based on a triple-layer electrowetting liquid lens was proposed [27]. In this model, the insulating liquid is used to represent the crystalline lens in human eyes, and the conductive liquid is used to represent the ocular media such as water media and glass media before and after the crystalline lens. In 2023, our group proposed a three-layer liquid electrowetting liquid lens based on spherical chamber, which realizes a large zoom ratio under the joint action of chamber structure and multi-layer liquid [28].
It can be seen from the above that if the components of the electrowetting liquid lens are two phases, the deformation interface is a gas-liquid interface or a liquid-liquid interface. If the components of the electrowetting liquid lens are three phases or more, the deformation interfaces are liquid-liquid interfaces.
In this paper, inspired by the arrangement of iris and crystalline lens in human eyes, we propose a three-phase electrowetting liquid lens with deformable iris (TELL-DLI). The proposed TELL-DLI has three-phase fluid: air, conductive liquid, and insulating liquid. And three kinds interfaces are formed between the three-phase fluids. The insulating liquid is distributed on the inner wall of the chamber in a ring shape. The conductive liquid forms a downward concave interface in the central area under the joint action of insulating liquid and air. By applying voltage, the contact angle is changed, so that the insulating liquid contracts towards the center, and the aperture and interface curvature are changed to realize zooming, which is similar to the contraction of iris and the function of crystalline lens muscle in human eyes. The insulating liquid can completely cover the conductive liquid and completely block the light. Because of the discrete electrodes, TELL-DLI can regionally control the shape and position of the iris, and switch between circle, ellipse, sector, and strip. The experimental results prove that TELL-DLI has a wide application prospect in imaging systems and beam navigation.
2. Principle
The working principle and structure diagram of the TELL-DLI are shown in Fig. 1. The chamber structure is composed of a polymethyl methacrylate (PMMA) tube, a discrete flexible ITO film, an ITO glass, a hydrophobic layer, and a dielectric layer. The fluid component is composed of conductive liquid in the lower layer, dyed insulating liquid attached to the inner wall of the chamber and the edge of the conductive liquid, and the air. The dyed insulating liquid looks like an iris ring, and is similar to the contraction of iris and the crystalline lens muscle in human eyes. The interface between air and insulating liquid is responsible for imaging and zooming, which is equivalent to the crystalline lens in human eyes. When a certain voltage is applied, the iris ring will be squeezed in the axial direction under the effect of electrowetting, resulting in the inward contraction of the iris. At the same time, the deformation of the iris will lead to the deformation of the imaging area in the middle of the lens and change the radius of curvature. Finally, the adjustment of aperture and focal length is realized.
Fig. 1. Working princeple and structure diagram of the TELL-DLI. (a) Initial state. (b) Zoom state. (c) The structure of the proposed liquid lens.
In order to discuss the driving mechanism of this brand-new electrowetting liquid lens, we analyzed the force between the layers of fluids. The force distribution between the TELL-DLI interfaces is shown in Fig. 2. There are three fluid phases and one solid phase. The blue part in the fluid phase is air, which is phase A. The green part is conductive liquid, which is phase B. The red part is insulating liquid, which is phase C. The inn wall of the chamber is solid phase composed of hydrophobic layer, dielectric layer, and electrodes, which is phase D, as shown in Figs. 2(a) and (b).
Fig. 2. Force distribution between the TELL-DLI interfaces. (a) Initial state. (b) Zoom state. Distortion simulation of phase B and phase C in (c) initial state and (d) zoom state. (Phase A is air, phase B is conductive liquid and phase C is insulating liquid)
There are three kinds of interfaces between fluids and two kinds of solid-liquid interfaces. γAC (green arrow) is the interface tension between the air and the dyed insulating liquid. γBC (yellow arrow) is the interface tension between the conductive liquid and the dyed insulating liquid. γAB (red arrow) is the interface tension between the conductive liquid and the air. γAD (gray arrow) is interface tension between the air and the chamber. γBD (purple arrow) is the interface tension between the conductive liquid and the chamber. γCD (blue arrow) is the interface tension between the dyed insulating liquid and the chamber. In this way, three kinds of three-phase contact lines can be abstracted. Phases A, B, and C form the three-phase contact line A. Phases A, C, and D form the three-phase contact line B. Phases B, C, and D form the three-phase contact line C as shown in Fig. 2(b). Distortion simulation of phase B and phase C in initial state and zoom state are shown in Figs. 2(c) and (d).
In the initial state, at three-phase contact line B, according to Young's equation, the force distribution is:
where θa is the air-solid contact angle between γAD and γAC. At three-phase contact line C, according to Young's equation, the force distribution is: where θe is the electrowetting contact angle. According to the young lippmann equation, the electrowetting contact angle θe and the applied voltage U can be described as follows: where ε is the dielectric constant of the insulating layer, d is the thickness of the dielectric layer, γAB is the interface tension of conductive liquid/insulating liquid, and θ0 is the initial contact angle. At three-phase contact line A, the force distribution is:In the zoom state, at three-phase contact line B, the force distribution still satisfies Eq. (1). At three-phase contact line C, due to the introduction of electrowetting force under EWOD effect, the electrowetting contact angle changes. The electrowetting force drives the three-phase contact line to move upwards. And after balancing, the force distribution changes as follows:
At three-phase contact line A, the relationship among θA, θB, and θC is:
Combined with Eq. (4), it can be concluded that θA, θB, and θC are constant values. Therefore, the magnitude of the interface tension at the three-phase contact line A remains unchanged, and the included angle between the interface tensions remains unchanged, but the direction of the interface tension changes, which still satisfies Eq. (4). Distortion simulation of phase B and phase C in initial state and zoom state can show the shape of each phase interface changes under the combined force of three-phase contact lines at different positions, as shown in Figs. 2(c) and (d). The focal length of the TELL-DLI can be expressed by the following:
where R is the curvature radius of imaging interface, r is radius of iris, nB is the refractive index of conductive liquid.We use the physical field of ternary phase field to simulate the multiphase flow-laminar flow in TELL-DLI. The interface tension between the air and the dyed insulating liquid γAC is 0.0298N/m, the interface tension between the conductive liquid and the dyed insulating liquid γBC is 0.021N/m and the interface tension between the conductive liquid and the air γAB is 0.0152 N/m. The densities of air, conductive liquid and insulating liquid are 1.29 Kg/m3, 1048 Kg/m3 and 1048 Kg/m3, respectively. θa is 140° and θ0 is 130°. The simulation results running on COMSOL of TELL-DLI are shown in Fig. 3. We simulate the interfaces deformation of the TELL-DLI under the electrowetting contact angles with 130° - 90°. It can be seen that with the gradual decrease of the electrowetting contact angle, the three-phase contact line C moves upward. And under the action of electrowetting force, the iris ring is squeezed vertically, which makes the inner side of the iris ring contract to the center, as shown in Fig. 3(a). At the same time, according to Eq. (4), this contraction makes the three-phase contact line A rotate inward while contracting inward, which changes the radius of curvature of the imaging area and achieves the zoom effect, as shown in Fig. 3(b). Moreover, the axial position of the three-phase contact line is almost unchanged, as shown by the yellow dotted line in Figs. 3(a) and (b). This is very different from the traditional electrowetting liquid lens which drives the L-L interface to zoom through the axial displacement of the three-phase contact line. The three-dimensional diagram of the deformation simulation of each interface shows the principle of iris diameter change and zoom more clearly, as shown in Figs. 3(c) and (d).
Fig. 3. Simulation of interfaces deformation of the TELL-DLI under different electrowetting contact angles. (a) Three-phase side view. (b) Side view of deformation of each interface. Three-dimensional diagram of deformation simulation of each interface under (c) θe = 130° and (d) θe = 90°.
We also simulate the interfaces deformation of the TELL-DLI under different volumes of the insulating liquid, as shown in Fig. 4. It can be seen that in the initial state, with the increase of the dyeing insulating liquid, the radius of curvature of the imaging area gradually increases, and the diameter of the iris becomes smaller, and the three-phase contact line A moves upward and rotate outward while contracting inward, as shown in Fig. 4(a). It can also be seen that in the zoom state, with the increase of dyeing insulating liquid, the radius of curvature of the imaging area gradually increases, the diameter of the iris becomes smaller, and the three-phase contact line A moves upward and rotates outward while contracting inward, as shown in Fig. 4(b).
Fig. 4. Simulation of interfaces deformation of the TELL-DLI under different volume of the insulating liquid. (a) Initial state. (b) Zoom state.
3. Fabrication
The fabrication process of the TELL-DLI is shown in Fig. 5. Firstly, the flexible ITO film is discretized into four independent electrodes, as shown in Fig. 5(a). Insert the flexible ITO electrodes into a PMMA tube, and then plate dielectric layer and hydrophobic layer on the flexible ITO electrodes in turn, which forms the chamber of the TELL-DLI, as shown in Fig. 5(b). Then, bond the chamber and the ITO glass through UV glue in ultraviolet environment, and inject the conductive liquid, as shown in Fig. 5(c). Next, inject the dyed insulating liquid in a way of rotating around the inner wall of the chamber while injecting the liquid, so as to ensure that the dyed insulating liquid can form a uniform iris ring, as shown in Fig. 5(d). Finally, connect four electrode chucks to four independent flexible ITO electrodes, and connect the grounding electrode chuck to the ITO glass, as shown in Fig. 5(e).
Fig. 5. Fabrication process of the propose liquid lens. (a) and (b) Discrete sidewall dielectric layer electrode. (c) Inject the conductive liquids. (d) Inject the dyed insulating liquid. (e) Connect electrodes.
4. Experimental, results and discussion
We carry out imaging experiments to characterize the zoom ability of the TELL-DLI under different volumes of the dyed insulating liquid, as shown in Fig. 6. Figure 6(a) shows the contrast of the imaging effect of the TELL-DLI in the initial state when the volume of dyed insulating liquid is 50 µL,100 µL, and150 εL. We can see that with the increase of the volume of dyed insulating liquid, the aperture of the lens decreases and the magnification increases, which indicates that the curvature radius of the imaging area is gradually increasing. This is consistent with the simulation results in Figs. 3 and 4 shows the contrast of the imaging effect of the TELL-DLI in the zoom state when the volume of dyed insulating liquid is 50 µL,100 µL, and150 µL under an applied voltage with 160 V. We can also see that with the increase of the volume of dyed insulating liquid, the aperture of the lens decreases and the magnification increases, which also indicates that the curvature radius of the imaging area is gradually increasing. It also shows that the magnification decreases with the increase of the voltage, which proves that the radius of curvature of the imaging interface decreases with the increase of the voltage, and the electrically adjustable zoom is realized. This is consistent with the simulation results in Figs. 3 and 4.
Fig. 6. Experimental results of imaging under different volumes of the dyed insulating liquid. (a) Initial state. (b) Zoom state.
We carry out focal length measurement experiments under different applied voltages and different volumes of the dyed insulating liquid, as shown in Fig. 7. At the initial state, the focal lengths of the TELL-DLI are -237.5 mm, -284.3 mm, -329.4 mm, -387.2 mm, and -451.9 mm, under the volume of the dyed insulating liquid of 50 µL, 75 µL, 100 µL, 125 µL, and 150 µL, respectively. Gradually increasing the voltage, the TELL-DLI has no obvious change until 60 V. The threshold voltage is ∼60 V. Continue to increase the voltage, and the focal length decreases. Finally, when the applied voltage is 200 V, the focal lengths of the TELL-DLI are -107.9 mm, -126.5 mm, -142.9 mm, -168.1 mm, and -190.8 mm, under the volume of the dyed insulating liquid of 50 µL, 75 µL, 100 µL, 125 µL, and 150 µL, respectively.
Fig. 7. Experimental results of focal length under different applied voltages and different volumes of the dyed insulating liquid.
We carry out aperture measurement experiments under different applied voltages and different volumes of the dyed insulating liquid, as shown in Fig. 8. At the initial state, the aperture of the TELL-DLI is 4.89 mm, 4.34 mm, 3.68 mm, 2.98 mm, and 2.68 mm, 2.23 mm, 1.90 mm, and 1.77 mm under the volume of the dyed insulating liquid of 50 µL, 75 µL, 100 µL, 125 µL, 150 µL, 175 µL, 200 µL, and 225 µL, respectively. When the applied voltage is 200 V, the aperture of the TELL-DLI is 4.39 mm, 3.62 mm, 3.14 mm, 2.15 mm, 1.87 mm, 1.33 mm, 0.93 mm, and 0.6 mm under the volume of the dyed insulating liquid of 50 µL, 75 µL, 100 µL, 125 µL, and 150 µL, 175 µL, 200 µL, and 225 µL, respectively.
Fig. 8. Experimental results of aperture under different applied voltages and different volumes of the dyed insulating liquid.
From the above aperture experiments, it can be found that the aperture is close to 0 mm, and it is inferred that the dyed insulating liquid can completely cover the surface of the conductive liquid and can completely block the passage of light. In the simulation, we simulated the topological changes between the three-phase liquid interfaces. The simulation results show that the surface insulating liquid can be changed from iris ring to layered structure, and finally completely covered on the conductive liquid, as shown in Fig. 9(a). In practical experiments, the volume of insulating liquid is 150 µL, and the applied voltage changes from 0 V to 200 V in a step way. We found that the insulating liquid flows quickly to the center and finally covered the conductive liquid completely. After the voltage is removed, the insulating liquid flows around, and the conductive liquid emerges and returns to its original state, as shown in Fig. 9(b). We use a photoelectric detector to detect the change of light intensity (the detected light intensity is converted into voltage) passing through TELL-DLI with time to reflect the response time, as shown in Fig. 9(c). It can be found that the response time from maximum aperture state to the zero aperture state is about 150 ms, and the response time from the zero aperture state to maximum the state is about 200 ms after the voltage is removed.
Fig. 9. Experimental results of response time between the maximum aperture state and zero aperture state. (a) Simulation of topological structure change of liquid layers of the TELL-DLI. (b) Top view of real object when realizing optical switch function. (c) Response time curve.
The TELL-DLI dielectric layer electrodes we proposed are four discrete independent electrodes, so the shape and position of the iris can be controlled by controlling each electrode independently, and the function of the sub-zone optical switch can be realized. As shown in Fig. 10(a), the voltages applied by the four flexible ITO electrodes are V1, V2, V3, and V4, respectively. When V1, V2, V3 and V4 are 100 V, it can be seen that the shape of the iris has changed, from round to oval, and it moves in the direction where the electrified electrode is located, and the insulating liquid gradually flows in other directions, as shown in Fig. 10(b); When V1, V2, V3, and V4 are 120 V, it can be seen that the shape of the iris has changed further, the ellipse has become more slender, and the boundary of the elliptical light-transmitting area has gradually moved to the direction where the electrified electrode is located, as shown in Fig. 10(c). When V1, V2, V3 and V4 are 140 V, the boundary of the elliptical light-transmitting area continues to move towards the electrified electrode, and finally it has completely contacted with the inner wall of the chamber, as shown in Fig. 10(d).
Fig. 10. Experimental results of deformable liquid iris by different single electrode. (a) Schematic diagram of electrode distribution. Apply (b) 100 V, (c) 120 V and (d) 140 V voltage on V1, V2, V3 and V4, separately and sequentially.
In order to further study the working mechanism, we observed the movement of the L-L interface between the insulating liquid and the conductive liquid when the sub-zone voltage is applied, as shown in Fig. 11. It can be clearly seen that with the application of sub-zone voltage, the L-L interface on the electrified electrode moves up under the EWOD effect, while the L-L interface on the opposite position of the side electrode moves down. In this process, the conductive liquid on the electrified electrode displaces the upper dyeing insulating liquid, and with the increase of voltage, the L-L interface on this side moves up higher. When the voltage reaches 140 V, the L-L interface moves to the limit of the interface position between insulating liquid and air. From the top view, the iris touches the inner wall of the chamber.
Fig. 11. Side view and top view of liquid-liquid interface under different single electrode. (a) V1 = 140 V. (b) Initial state. (c) V3 = 140 V.
In addition, by energizing the two electrodes at the same time, the light passing area and the shape of the sub-zone optical switch can be extended, as shown in Fig. 12. When a voltage of 140 V is applied to two adjacent electrodes, the L-L interface on the two electrode areas has risen to the limit position, and the iris has been increased, as shown in Fig. 12(a). When a voltage of 140 V is applied to two opposite electrodes, the iris extends from a circle to two electrode positions to form a long strip similar to the iris of a cat eye, as shown in Fig. 12(b).
Fig. 12. Experimental results of deformable liquid iris by two electrodes. (a) Two electrodes are adjacent. (b) The two electrodes are opposite.
5. Conclusion
In this paper, we propose a three-phase bionic electrowetting liquid lens with iris and optical switch function via a gas-liquid-liquid interface. The TELL-DLI we propose has three-phase fluid: air, conductive liquid, and dyed insulating liquid. And three kinds of interfaces are formed between the three-phase liquids. The dyed insulating liquid has a ring shape. By applying voltage, the electrowetting contact angle is changed, causing the insulating liquid ring to contract. The variation range of the aperture is from 4.89 mm to 0.6 mm, the variation range of the focal length is from -451.9 mm to -107.9 mm, and the variation range of magnification is from 0.520 × to 0.714 × . Under the step voltage of 200 V and the volume of dyed insulating liquid of 150 µL, the TELL-DLI can be switched between the maximum aperture state and the zero aperture state, and the switching time is ∼150/200 ms. Because of the discrete electrodes, the TELL-DLI can regionally control the shape and position of the iris, and switch between circle, ellipse, sector, and strip. The TELL-DLI has a wide application prospect in imaging systems, such as microscopic imaging systems. And its high degree of freedom optical switch function can be applied to the field of complex beam navigation.
Funding
National Key Research and Development Program of China (2021YFB3600601); National Natural Science Foundation of China (62175006); Beijing Municipal Natural Science Foundation (4222069); Science, Technology and Innovation Commission of Shenzhen Municipality (JCYJ20220818100413030).
Disclosures
The authors declare that there are no conflicts of interest related to this article.
Data availability
No data were generated or analyzed in the presented research.
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