Open Access
Add to BibSonomy
Abstract
Varifocal lenses (especially large-aperture lenses), which are formed by two immiscible liquids based on electrowetting and dielectrophoretic effects, are usually modulated by an external high-voltage power source, with respect to the volume of the liquid. Hence, a Maxwell force-driven liquid lens with large aperture and low threshold voltage is proposed. With the polarization effect, the accumulated negative charges on the surface of the polyvinyl chloride/dibutyl adipate gel near the anode results in the generation of Maxwell force and deformation with cosine wave. The effect of surface roughness on wettability is linear with the cosine of the contact angle, leading to a sharp reduction in the threshold voltage when the volume of liquid is increased. When the volume of the droplet increases to 80 μl, the threshold voltage is about 10 V. Hence, the aperture of polarization effect-driven liquid lenses can potentially reach the centimeter level. Moreover, when Maxwell force increases, the lens ranges from concave to convex lens, which holds great promise in rich application such as those in light-sheet microscopes and virtual reality systems.
© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Liquid lenses formed by two immiscible liquids of equal densities allow the optical axis to remain stable [1]. Such lenses have attracted considerable attention because of their advantages, such as simple structure, focal length tunability, and low gravitational effect, and thus have been widely applied in optical imaging systems [2–7].
In accordance with the tunable principle, these lenses can be classified into two categories; one corresponds to electrowetting-based liquid lens whose focal length is modulated to change the contact angle [8,9], and the other corresponds to liquid lens actuated by the dielectrophoretic effect [10]. Usually, the lens’ aperture takes the liquid volume into account, which affects the focal length.
As shown in Eq. (1), the focal length depends on the volume of liquid, so large-aperture liquid lenses are modulated by a high voltage.
High threshold voltages remain a challenge because they consume a substantial amount of energy, thus making it impossible to achieve large-aperture liquid lenses with low driving voltage and large focal length tunable range.
For electrowetting liquid lenses formed in cylindrical chambers, as the aperture increases to 10 mm, the threshold voltage reaches to 50 V when the conducting liquid volume is ∼50 μl [11]; for dielectrophoretic liquid lenses formed in cylindrical chambers, the threshold voltage is 50 V when the aperture is 3 mm [12].
To fabricate a liquid lens with large aperture and low threshold voltage, we propose a Maxwell force-driven liquid lens, which consists of polyvinyl chloride/dibutyl adipate (PVC/DBA) gel, deionized water, and white oil. When a direct current (DC) electric field is applied, the polarization effect causes the surface roughness of the PVC/DBA gel to change, leading to changes in wettability. According to the Wenzel equation, the cosine of the apparent contact angle is linear with the surface roughness; hence, the threshold voltage of Maxwell force-driven liquid lens with large aperture is small. To characterize the property, we fabricate a gel plate membrane and an aspheric gel tube and study the surface wettability caused by droplets with different volume deformation. In addition, the lens system can work as either convex or concave lens, whose focal length can be tuned precisely.
2. Wettability under the application of electric field
2.1 Wetting ability changes with the PVC/DBA gel with a plate
Fig. 1. (a) Cross-section structure of the diamond-like electrode, (b) wettability analysis under the application of voltage, (c) schematic of the PVC/DBA gel based on electro-mechanism, (d) deformation of gel resulting in the focused light.
The contact angle of saline droplets on a hydrophobic layer changes because of the changing of wettability; thus, it has attracted wide attention in adaptive optics (e.g., adaptive liquid lenses). However, as aperture increases, the threshold voltage increases sharply, thus limiting the application in studies on the morphology and function of biological samples. To decrease the threshold voltage, we propose a method in which wettability is driven on the basis of Maxwell force, resulting in changes in the gel membrane surface; wettability is given by the Wenzel equation [13].
Fig. 2. . Wettability of the deionized water under the electric field. (a)–(d) volume of deionized water: 5, 30, 50, and 60 μl, respectively; (e) threshold and sliding voltages of droplets in different volumes; ([a]–[c] scale bar: 500 μm, [d] scale bar: 600 μm).
where ${R_w}$ is the roughness factor with related to the deformation of gel, $\theta ^{\prime}$ and $\theta$ are the apparent and real contact angle, respectively.
To characterize gel deformation, a gel membrane was obtained by the spin-coating method using a spin processor at 1000 r/s; the membrane was coated on the glass substrate with a diamond-like electrode. Figure 1(a) shows the diamond-like indium tin oxide (ITO) electrode. Then, deionized water was dripped on the PVC/DBA gel membrane; under equilibrium state, hydrostatic pressure and surface tension achieved a balance, the real contact angle was $\theta$. However, the apparent contact angle was $\theta ^{\prime}$ due to the deformation of gel resulting from Maxwell force [shown in Fig. 1(b)].
Figure 1(c) shows a schematic of the PVC/DBA on the basis of Maxwell force mechanism. The expanded and collimated beam ($\lambda = 532$ nm) through the substrate was detected by beam analyzer, as shown in Fig. 1(d). Under the absence of electric field, a uniform intensity distribution was obtained; however, at U = 280 V, the deformation of gel with cosine wave resulted in the gel membrane having a lens characteristic, and the light was focused.
Figure 2 shows the initial edge profile of the droplet with 5 μl of deionized water dripped on the PVC/DBA gel membrane. According to research on PVC/DBA gel [14–16], the generated Maxwell force increases with the increase in extra electric field, and the edge profile becomes large [as shown in Fig. 2(a)]. However, the droplet of the deionized water slides after the driving voltage becomes greater than 220 V.
Usually, the aperture of the liquid lens is proportional to the volume of the liquids; thus, the wettability of the larger volume of deionized water under different Maxwell forces was investigated. As shown in Figs. 2(b)–2(d), the volume of the deionized water is 30, 50, and 60 μl, respectively. The threshold voltage and sliding voltage of the droplet of different deionized water are shown in Fig. 2(e).
As shown in Fig. 2, the surface wettability changed because of the polarization response of charges and the accumulated electric charges near the anode; thus, Maxwell force was generated, and PVC/DBA gel was deformed asymmetrically. The contact angle increased due to the increase in wettability, leading to the growth of the edge profile of the droplet. The edge profile of the droplet changed with different volumes because the change of the surface wettability of the gel varied. The threshold voltage decreased as the volume of the deionized water increasing to 50 μl, but it increased as the volume of the deionized water increased continuously. Given the non-uniform electric field effect, the droplet slid at a certain voltage. Moreover, the sliding voltage decreased as the volume of the deionized water increasing to 60 μl, but increased as the volume increased continuously. The above results reveal that the Maxwell force wetting-driven method offers a new idea for liquid lens.
2.2. Wetting ability changes with the PVC/DBA gel as the surrounding liquid
To avoid the sliding of the droplet, a PVC/DBA gel with aspheric wave was proposed, as shown in Fig. 3. The volume of the surrounding liquid (i.e., PVC/DBA gel) was 1 ml, but the volume of deionized water gradually increased (i.e., 30, 50, and 80 μl).
Under the application of electric field, the meniscus (deionized water–air interface) was also reconstructed because of the accumulated electric charges on the surface of the PVC/DBA gel. To evaluate wettability, the droplet was placed under microscope, and the parallel light through the droplet of deionized water was detected using a charge-coupled device (CCD). The spot increased with the Maxwell force generated under the application of electric field, as shown in Fig. 4.
Fig. 4. Spot through the meniscus increased because of the changes of the surface wettability of the PVC/DBA gel with aspheric wave. (a) Experiment setup for wettability evaluation, (b)–(d) volume of deionized water: 30, 50, and 80 μl (scale bar: 200 μm).
As shown in Fig. 4, the surface wettability also changed under the condition of the PVC/DBA gel reconstructed to an aspheric wave; when the volume of the droplet increased to 80 μl, the threshold voltage was also less than 10 V.
3. Liquid lens based on polarization effect modulation
3.1 Structure and operation mechanism of the liquid lens
In this study, we propose an aspheric lens with double liquid based on the polarization effect. Figure 5 shows the structure of the proposed liquid system, which consists of PVC/DBA gel, deionized water, white oil, and an ITO-deposited glass substrate. A cylindrical chamber with 2 cm diameter was assembled on the ITO glass substrate. Next, a 60 μl droplet of deionized water was added on the glass substrate. Afterward, 1 ml of PVC/DBA gel as surrounding solution was added in the chamber. Lastly, 20 μl of deionized water was added. Therefore, the chamber with spherical wave was fabricated, and then the white oil filled the entire chamber as the surrounding solution, as shown in Fig. 5(a); the aperture is approximately 11 mm.
Fig. 5. Structure and operation mechanism of the aspherical lens. (a), (d) The lens has concave characteristics, and the light is diverged. (b), (e) The lens has planar characteristics, and the light is neither focused nor diverged, (c), (d) The lens has convex characteristics, and the light through it is focused.
In the absence of electric field, the radius of the liquid–liquid (deionized water–white oil) surface was negative. Given the small refractive index of deionized water, the lens system had the characteristics of concave lens, as shown in Fig. 5(a). As the applied voltage increased, the force generated in the PVC gel was expected, and the wettability increased. Hence, the radius of the liquid–liquid surface increased, and the lens could make the light to neither focus nor diverge, as shown in Fig. 5(b). As the applied voltage increased continuously, the force also increased because more negative charges moved toward anode; as a result, the radius of the liquid–liquid surface became positive, and the lens system had the characteristics of a convex lens, as shown in Fig. 5(c).
To test the characteristics of the lens, the laser beam was expanded by a spatial filter/beam expander, then, focused through the aspheric liquid lens. The value of applied voltage was U = 0 V, and the light was diverging through the proposed lens, as shown in Fig. 5(d); therefore, the proposed aspherical liquid lens had the characteristics of a concave lens. At U = 30 V, the light was not deflected [as shown in Fig. 5(e)], thus proving that the lens can be considered planar. As the applied voltage increased, the lens became convex, and the light through the proposed lens converged, as shown in Fig. 5(f).
Given the bubbles generated by encapsulation, the image quality of the lens deteriorated; therefore, we propose the stitching encapsulation method. First, a $3\textrm{cm} \times 3\textrm{cm}$ glass substrate marked “1” was assembled on the metal chamber, which was not completely covered. Then, for the bubble to reduce and move to the area outside the encapsulated glass substrate, white oil was added into the metal chamber. Second, a small glass substrate marked “2” was assembled on the other area of the metal chamber, and a small bubble was spitted and located on the edge of the unencapsulated area. Lastly, a trace amount of PVC/DBA gel in liquid state (marked “3”) was added; it solidified after 0.5 hours. Given the fluidity of the gel in liquid state, the above bubble disappeared, as shown in Fig. 6.
3.2. Experiment results and optical characteristics
To test the light-focusing property of the proposed aspheric lens, an experiment setup was built, as shown in Fig. 7. A spatial filter/beam expander was used to expand the laser beam, and it was focused through the aspheric liquid lens, which was detected by the CCD.
The focal lengths of the proposed lens system as a function of applied voltage were experimentally measured. The measurement implementation is described as follows: An expanded laser with a wavelength of 532 nm was incident normally through the object of a thin glass plate with two black horizontal bars and the proposed lens system. The object was placed 2 mm away from the proposed lens.
Clear images were captured using a CCD camera under the application of different electric fields, and the focal length was calculated. The results of the single-object focusing test are shown in Fig. 8. The focal length can be tuned in (−∞, −6.7 mm), ∪(15.3 mm, +∞) as the applied voltage increase from 0 V to 70 V.
To evaluate the response time of the proposed lens, A Si-amplified detector (Thorlabs PDA10A–EC) was used to record the light intensity changing process through the proposed lens system to evaluate the response time of the lens. When the applied voltage was switched to 25 and 55 V, the response time of the acquired lens was within 150 and 400 ms, respectively, as shown in Fig. 9. As the applied voltage decreased to 0 V, the response time remained the same.
Fig. 9. Response time of the proposed aspheric liquid lens, (a) The applied voltage increased from 0 V to 25 V. (b) The applied voltage dropped back from 25 V to 0 V. (c) The applied voltage increased from 0 V to 55 V. (d) The applied voltage dropped back from 55 V to 0 V.
To characterize the imaging property, USAF 1951 resolution target as the object, we adjusted the objective lens to bring the object in the focused state, and clear images were obtained by CCD camera at U = 0 V, and U = 30 V, as shown in Figs. 10(a) and 10(b), respectively.
Fig. 10. Image of the resolution target observed through the proposed liquid lens. (a)–(b) Voltage: 0 V, 30 V, respectively.
At U = 0 V, the lens has concave characteristic, the system has larger numerical aperture, the resolution is about 102.0 lp/mm, as the voltage increases to 30 V, the lens can be seen as a parallel plate, the resolution dropped slowly to 90.5 lp/mm.
4. Discussion
Here, the wettability of the DBA solution under electric field was evaluated, and it was reconstructed as an aspheric wave because of the different densities of the DBA and deionized water solutions. Although the applied voltage increased, the light through the meniscus remained stable, as shown in Fig. 11.
Fig. 11. Wettability remains stable under the application of electric field. (a)–(c) Voltage: 0, 80, and 300 V, respectively (scale bar: 300 μm).
The results further confirmed that wettability changes with respect to polarization charges and accumulates on the surface. In this study, the diamond-like ITO electrode was chosen, and the nonuniform electric field led to liquid-liquid surface therefore, the edge profile of the droplet of deionized water must be symmetrical about the center of the electrode.
In addition, the original contact angle became smaller than the lens only with deionized water and white oil because of the large difference in the surface tension between gel and water; thus, the lens had a large focal length tuning range.
Here, we also study the wettability changing of conductive solution under the application of electric field, as shown in Fig. 12. The volume of saline water is about 20 μl.
Fig. 12. Wettability of the saline water under the electric field. (a)–(c) Voltage: 0 V, 80 V, and 300 V, respectively. (scale bar: 500 μm).
As shown in Fig. 12, the edge profile just a little increased at U = 300 V, it implied the wettability of conduction solution remained unchanged. Therefore, the other non-conductive liquid can be also as candidate, such as glycerol, silicone oil, but the conductive liquid is not appropriate.
5. Conclusion
In summary, we reported an aspheric liquid lens with large aperture and low threshold voltage. In this lens, the focal length could be modulated by the Maxwell force generated by the polarization response of the charges of the PVC/DBA gel. The force was used to continuously change the shape of the meniscus (liquid–liquid surface) from convex to concave wave. The performance of the wettability of the PVC/DBA gel was investigated using reconstruction as plat and aspherical wave. With the PVC/DBA gel with plat wave, the threshold voltage decreased as the volume of the droplet of deionized water increased to less than 50 μl, and the threshold voltage decreased; with the PVC/DBA gel with aspherical wave, the threshold voltage was less than 10 V until the volume of the droplet increased to 80 μl. Hence, the proposed lens consisted of a large volume of liquid (80 μl), and the focal length can tune in (−∞, −6.7 mm), ∪(15.3 mm, +∞), and the threshold voltage decreased to 10 V.
Funding
National Natural Science Foundation of China (61675153, 61811530334).
Disclosures
The authors declare that there are no conflicts of interest related to this article.
References
1. B. Berge, “Liquid lens technology: Principle of electrowetting based lenses and applications to imaging, Micro Electro Mechanical System,” 18th IEEE International Conference, 227–230(2005).
2. P. Pozzi, M. Quintavalla, A. B. Wong, J. G. G. Borst, S. Bonora, and M. Verhaegen, “Plug–and–play adaptive optics for commercial laser scanning fluorescence microscopes based on an adaptive lens,” Opt. Lett. 45(13), 3585–3588 (2020). [CrossRef]
3. F. O. Fahrbach, F. F. Voigt, B. Schmid, F. Helmchen, and J. Huisken, “Rapid 3d light-sheet microscopy with a tunable lens,” Opt. Express 21(18), 21010–21026 (2013). [CrossRef]
4. N. Koukourakis, M. Finkeldey, M. Stiirmer, C. Leithold, N. C. Gerhardt, M. R. Hofmann, U. Wallrabe, J. W. Czarske, and A. Fischer, “Axial scanning in confocal microscopy employing adaptive lenses(CAL),” Opt. Express 22(5), 6025–6039 (2014). [CrossRef]
5. D. Shin, C. Kim, G. Koo, and Y. H. Won, “Depth plane adaptive integral imaging system using a varifocal liquid lens array for realizing augmented reality,” Opt. Express 28(4), 5602–5616 (2020). [CrossRef]
6. D. W. Lei Li, C. Liu, and Q. Wang, “Zoom microscope objective using electrowetting lenses,” Opt. Express 24(3), 2931–2940 (2016). [CrossRef]
7. N. Hasan, A. a. Banerjee, H. Kim, and C. H. Mastrangelo, “Tunable–focus lens for adaptive eyeglasses,” Opt. Express 25(2), 1221–1233 (2017). [CrossRef]
8. L. Li, C. Liu, H. Ren, H. Deng, and Q. Wang, “Annular folded electrowetting liquid lens,” Opt. Lett. 40(9), 1968–1971 (2015). [CrossRef]
9. S. Grilli, L. Miccio, V. Vespini, A. Finizio, S. De Nicola, and P. Ferraro, “Liquid micro-lens array activated by selective electrowetting on lithium niobate substrates,” Opt. Express 16(11), 8084–8093 (2008). [CrossRef]
10. H. Zhang, H. Ren, S. Xu, and S. Wu, “Temperature effects on dielectric liquid lenses,” Opt. Express 22(2), 1930–1939 (2014). [CrossRef]
11. X. Song, H. Zhang, D. Li, D. Jia, and T. Liu, “Electrowetting lens with large and focal length tunability,” Sci. Rep. 10(1), 16318 (2020). [CrossRef]
12. C. C. Cheng and J. Andrew Yeh, “Dielectrically actuated liquid lens,” Opt. Express 15(12), 7140–7145 (2007). [CrossRef]
13. M. Yedji and G. G. Ross, “Effect of electric charge accumulation on the surface properties of PS samples irradiated with low energy ions,” Nucl. Instrum. Methods Phys. Res., Sect. B 256(1), 396–401 (2007). [CrossRef]
14. Y. Li, Y. Li, and M. Hashimoto, “Low-voltage planar PVC gel actuator with high performances,” Sens. Actuators, B 282, 482–489 (2019). [CrossRef]
15. M. T. Hongxia and T. Hirai, “Actuation mechanism of plasticized PVC by electric field,” Sens. Actuators, A 157(2), 307–312 (2010). [CrossRef]
16. M. Xu, B. Jin, R. He, and H. Ren, “Adaptive lenticular microlens array based on voltage–induced waves at the surface of polyvinyl chloride/dibutyl phthalate gels,” Opt. Express 24(8), 8142–8148 (2016). [CrossRef]
