An adaptive liquid lens with a reciprocating movement in a cylindrical hole Boya Jin,1 Miao Xu,1 Hongwen Ren,1,* and Qiong-Hua Wang2 1
BK Plus Haptic Polymer Composite Research Team, Department of polymer Nano-Science and Technology, Chonbuk National University, Jeonju, Jeonbuk, 561-756, South Korea 2 School of Electronics and Information Engineering, Sichuan University, Chengdu 610065, China * [email protected]
Abstract: We demonstrate a liquid droplet which can do a reciprocating movement in a cylindrical hole. The droplet in the hole exhibits a lens character. By applying a voltage, the border of the droplet is stretched to expand by the generated dielectric force. Due to the fixed volume, the dome of the droplet in the hole has to move toward the substrate without changing its surface profile. Therefore, the focal length of the droplet remains unchanged although the focal point is shifted. Once the voltage is removed, the droplet can return to its original state. The droplet with such a movement functions as an adaptive lens. Our lens can provide a high resolution (~114 lp/mm) whether or not it is actuated. The dynamic response time is reasonably fast. Integrating with a solid lens, the compound lens can provide a variable focal length. ©2014 Optical Society of America OCIS codes: (080.3630) Lenses; (110.1080) Active or adaptive optics; (230.3990) Microoptical devices; (250.0250) Optoelectronics.
References and links 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15.
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#224917 - $15.00 USD (C) 2014 OSA
Received 28 Oct 2014; revised 28 Nov 2014; accepted 28 Nov 2014; published 5 Dec 2014 15 Dec 2014 | Vol. 22, No. 25 | DOI:10.1364/OE.22.031041 | OPTICS EXPRESS 31041
16. H.-C. Cheng, S. Xu, Y. Liu, S. Levi, and S.-T. Wu, “Adaptive mechanical-wetting lens actuated by ferrofluids,” Opt. Commun. 284(8), 2118–2121 (2011). 17. 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). 18. L. Miccio, M. Paturzo, S. Grilli, V. Vespini, and P. Ferraro, “Hemicylindrical and toroidal liquid microlens formed by pyro-electro-wetting,” Opt. Lett. 34(7), 1075–1077 (2009). 19. B. Berge and J. Peseux, “Variable focus lens controlled by an external voltage: an application of electrowetting,” Eur. Phys. J. E 3(2), 159–163 (2000). 20. T. Krupenkin, S. Yang, and P. Mach, “Tunable liquid microlens,” Appl. Phys. Lett. 82(3), 316–318 (2003). 21. S. Kuiper and H. W. Hendriks, “Variable-focus liquid lens for miniature cameras,” Appl. Phys. Lett. 85(7), 1128–1130 (2004). 22. N. R. Smith, L. Hou, J. Zhang, and J. Heikenfeld, “Fabrication and demonstration of electrowetting liquid lens arrays,” J. Dis. Tech. 5(11), 411–413 (2009). 23. C. C. Cheng and J. A. Yeh, “Dielectrically actuated liquid lens,” Opt. Express 15(12), 7140–7145 (2007). 24. H. Ren, H. Xianyu, S. Xu, and S. T. Wu, “Adaptive dielectric liquid lens,” Opt. Express 16(19), 14954–14960 (2008). 25. K. Y. Hung, C. C. Fan, F. G. Tseng, and Y. K. Chen, “Design and fabrication of a copolymer aspheric bi-convex lens utilizing thermal energy and electrostatic force in a dynamic fluidic,” Opt. Express 18(6), 6014–6023 (2010). 26. S. Xu, H. Ren, and S. T. Wu, “Adaptive liquid lens actuated by liquid crystal pistons,” Opt. Express 20(27), 28518–28523 (2012). 27. Y.-S. Lu, H. Tu, Y. Xu, and H. Jiang, “Tunable dielectric liquid lens on flexible substrate,” Appl. Phys. Lett. 103(26), 261113 (2013). 28. H. Ren, Y.-H. Fan, Y.-H. Lin, and S.-T. Wu, “Tunable-focus microlens arrays using nanosized polymerdispersed liquid crystal droplets,” Opt. Commun. 247(1–3), 101–106 (2005). 29. Y. Li and S. T. Wu, “Polarization independent adaptive microlens with a blue-phase liquid crystal,” Opt. Express 19(9), 8045–8050 (2011). 30. K. H. Kang, “How electrostatic fields change contact angle in electrowetting,” Langmuir 18(26), 10318–10322 (2002). 31. M. Xu, H. Ren, L. Yoo, and Q. Wang, “An adaptive liquid lens with radial interdigitated electrode,” J. Opt. 16(10), 105601 (2014). 32. F. Mugele and J.-C. Baret, “Electrowetting: from basics to applications,” J. Phys. Condens. Matter 17(28), R705–R774 (2005). 33. E. Hecht, Optics, 4th ed., (Addison Wesley, Reading, MA, 2002). 34. L. Miccio, A. Finizio, S. Grilli, V. Vespini, M. Paturzo, S. De Nicola, and P. Ferraro, “Tunable liquid microlens arrays in electrode-less configuration and their accurate characterization by interference microscopy,” Opt. Express 17(4), 2487–2499 (2009).
1. Introduction An adaptive lens is an essential optical device which has been studied intensively in the past years. In contrast to a glass lens, an adaptive lens can obtain a tunable focus without moving parts. Therefore, it functions as a compound lens with the advantages of compact structure, easy operation, and high precision. Applications of an adaptive lens can widely find in imaging, information storage, target tracking, biometric identification, displays, and optical switches. Numerous adaptive lenses were demonstrated. Based on their operation mechanisms, they can be roughly classified into liquid crystal (LC) lens [1–8], elastic membrane lens [9–12], hydrogel lens [13], acoustic lens [14], ferrofluidic lens [15,16], electrowetting lens [17–22], and dielectric lens [23–27]. In a LC lens, a certain focal length can be obtained when the LC molecules produce a gradient refractive index profile across its aperture. By applying a voltage, the LC molecules in the lens cell are reoriented, leading to the change of the gradient of the refractive index profile. As a result, its focal length is tuned [1,2]. Most LC lenses need a polarizer because they are polarization-dependent, so the light efficiency is less than 50%. By employing polymer dispersed liquid crystals (PDLC) [28] or blue phase liquid crystals (PSBPLC) [29], the demonstrated lenses are polarization-insensitive. Because both PDLC and PSBPLC could not provide a distinct phase shift, the prepared lens presents a rather limited focus change. In comparison to a LC lens, a liquid lens focuses light based on the shape change. It can present good optical performances due to the optical isotropy. By controlling the surface profile of the liquid, it is possible to vary the focal length of the lens in a wide range. In the
#224917 - $15.00 USD (C) 2014 OSA
Received 28 Oct 2014; revised 28 Nov 2014; accepted 28 Nov 2014; published 5 Dec 2014 15 Dec 2014 | Vol. 22, No. 25 | DOI:10.1364/OE.22.031041 | OPTICS EXPRESS 31042
aforementioned liquid lenses, only electrowetting and dielectric lenses can be actuated electrically. The surface profile of the former lens is deformed by an electrostatic force [18– 21,30], while the surface profile of the latter is deformed by a dielectric force [23–25]. When the focal length of these lenses is tuned, their optical performance is changed accordingly. To largely reduce the focal length of the lens, a common method is to largely deform the shape of the liquid. By doing so not only the driving voltage is enhanced, but also the lens performance is degraded. It is highly desirable to develop an adaptive lens which can provide a high optical performance during dynamic imaging. In this work, we report a dielectric liquid lens using a radial-interdigitated electrode. Unlike conventional liquid lenses [23,24,31], our lens provides a focus change based on a reciprocating motion in a cylindrical hole. The lens with this movement functions as an adaptive lens. Since the surface profile of the lens in the hole is unchanged, its focal length is fixed although its focal point is shifted. As a result, the optical performance of the lens is not degraded whether or not it is actuated. Owing to the radial-interdigitated electrode, the generared fringing field can effectively actuate the lens with a relatively low driving voltage. In the voltage-on state, the droplet is stretched to expand in the transverse direction along the electrode. A little travel distance in radial direction can cause a distinct shift of the lens in longitudinal direction. Once the voltage is removed, the deformed droplet can quickly return to its original position. Therefore, our liquid lens possesses the advantages of high resolution (~114 lp/mm), a wide dynamic focus change, and reasonably fast response time. 2. Lens structure and theory 2.1 Device structure and characteristics Our device mainly consists of a top substrate, a bottom substrate, and a liquid droplet. The top substrate is relatively thick. Its center area has a through hole, as shown in Fig. 1(a). The surface of the cylindrical hole and its bottom surface are coated with a hydrophobic layer. The bottom substrate has an indium-tin-oxide (ITO) electrode, as depicted in Fig. 1(b). The electrode is etched with a radial-interdigitated pattern. Each ITO strip presents a fan shape and the adjacent strips are separated with a gap. The width of the ITO gap is uniform. The ITO stripes are circularly symmetric. The terminals marked “A” and “B” are used to apply a voltage. The surface of the ITO substrate is coated with a hydrophobic layer too. The top substrate and the bottom substrate are placed together to form a cell. The gap of the cell is controlled using glass spacers (not shown). The cross-sectional structure of the device is shown in Fig. 1(c). A small volume of a dielectric liquid is dripped in the hole to form a droplet. The top of the droplet is spherical and its bottom is flat. In the relaxing state, the droplet presents minimal surface-to-volume ratio with the lowest surface energy. Because the dome of the droplet is axially symmetrical, it exhibits a lens character. If an incident beam passes through it, the beam will be converged by its curved surface. When a voltage (V = V1) is applied to the ITO stripes (through terminals A and B), a fringing field is generated between adjacent ITO stripes. The region close to the edge of each ITO stripe experiences the largest gradient of electric field. If the dielectric constant of the droplet is larger than that of the surrounding media, then the molecules at the edge of the droplet suffer the highest dielectric force. This force pulls these molecules to move toward this region. Due to the cohesion between the adjacent molecules and the adhesion between the droplet and the substrates, the droplet is deformed. Along the ITO stripes the fringing field is continuous, so the droplet can expand in transverse direction. Since the volume of the droplet is fixed, the dome of the droplet has to move down in longitudinal direction, as shown in Fig. 1(d). Due to the spherical shape of the lens, it still focuses the light but with a shifted focal point.
#224917 - $15.00 USD (C) 2014 OSA
Received 28 Oct 2014; revised 28 Nov 2014; accepted 28 Nov 2014; published 5 Dec 2014 15 Dec 2014 | Vol. 22, No. 25 | DOI:10.1364/OE.22.031041 | OPTICS EXPRESS 31043
Hydrophobic layer Electrode
Hydrophobic layer Hole
A B
(a)
(b)
Electrode
Gap
Liquid Substrate
V1
0V
(d)
(c)
Fig. 1. Key parts of the liquid lens and the cross-sectional structure of the lens cell in the voltage-off and voltage-on states.
2.2 Contact angle To analyze the shape change of the droplet when it is actuated, let’s compare the surface of the droplet shown in Fig. 1(c) to that in Fig. 1(d). At V = 0, the curved surface of the droplet has a contact angle (θ0) on the surface of the hole. To define the contact angle, the crosssectional view of the droplet is partially redrawn as shown in in Fig. 2 (light pink). The angle between the surface of the liquid and the outline of the contact solid surface at the end point (M) is called the contact angle. According to Young’s equation, the contact angle is expressed by [32] cos θ 0 =
γSV − γSL γ LV
(1)
where γSL, γSV, and γLV are solid-liquid, solid-vapor, and liquid-vapor interfacial tensions, respectively. The shape of the dome is determined by the contact angle. If the radius of the curved surface is r, then the focal length (fL) of the droplet is fL =
r nL − nM
(2)
where nL and nM are the refractive indices of the liquid and the surrounding media, respectively. If air is the surrounding media, then nM≈1. When a voltage (V = V1) is applied to the electrode, the dome of the droplet moves down (dark pink), and the position of point M shifts to the position of point N. Since the interfacial tensions (γSL, γSV, and γLV) are unchanged, the contact angle keeps the same (θ0). Therefore, the focal length (fL) will not be affected except shifting its focusing point.
#224917 - $15.00 USD (C) 2014 OSA
Received 28 Oct 2014; revised 28 Nov 2014; accepted 28 Nov 2014; published 5 Dec 2014 15 Dec 2014 | Vol. 22, No. 25 | DOI:10.1364/OE.22.031041 | OPTICS EXPRESS 31044
γLV V=0
•M
γSL
V=V1
o
•
γSV Cell
•
Lens
•
•N •
(a)
(b)
fL d fS
o′
Fig. 2. (a) Surface profile of the droplet in the V = 0 and V = V1 states and (b) integrating with one lens for a variable focal length.
2.3 A compound lens To get a variable focal length, the liquid lens needs to combine with another lens to form a compound lens. If the bottom glass substrate of the lens cell shown in Fig. 1(c) is a plano convex lens, then the lens cell is called a compound lens, as shown in Fig. 2(b). The two lenses have a common axis (OO′) separated by a diatance d. Suppose the focal length of the bottom lens is fs, then the effective focal length for the lens system is given by [33] 1 1 1 d = + − f f L f S f L fS
(3)
From Eq. (3), if the separated distance d is mainly dependent on the travel distance of the droplet, then f can be changed effectively by an external voltage. As a result, this compound lens can provide a variable focal length. 3. Device fabrication To prepare a lens cell as sketched in Fig. 1(c), an aluminum substrate (1.5 × 1.5 cm with 6.3mm-thick) is chosen as the top substrate. A through hole is drilled in the center area. The diameter of the hole is 2.5 mm. The surface of the hole is coated with a Teflon layer (γT~19 mNm−1). Teflon is a good hydrophobic material which can provide a large contact angle for many liquids. An ITO glass is chosen as the bottom substrate. The ITO electrode is etched with a radial-interdigitated pattern. Part of the patterned electrode is shown in Fig. 3. The slightly dark area is covered with ITO electrode and the bright stripes are the region without electrode. The size of the substrate is 1.8 × 1.8 cm. The gap of adjacent ITO stripes is 20 μm, and each ITO strip has a fan shape. The radius of the center area without patterning is 1 mm. There are 44 ITO stripes around the circular aperture. The surface of the ITO glass substrate is then coated with a Teflon layer (1-μm-thick) too. The two substrates are placed together to form a cell. The gap of the cell is controlled using ~0.7-mm-thick glass spacers. The hole of the top substrate is positioned above the center area of the bottom substrate. A glycerol (εg ~47, ng = 1.47, γg ~63 mNm−1, from Aldrich) with high purity (> 99.5%) is chosen as the liquid. We choose glycerol as the lens material due to three reasons: large dielectric constant, large surface tension, and no evaporation. A small amount of the glycerol is dripped in the hole to form a droplet. Since the diameter of the hole is larger than the diameter of the circularly non-patterned ITO electrode, the border of the droplet covers the terminals of the ITO stripes. Due to the large surface tension, the droplet partially wets the bottom substrate and the bottom surface of the top substrate. The height of the droplet from its dome to the bottom substrate is measured to be ~3 mm.
#224917 - $15.00 USD (C) 2014 OSA
Received 28 Oct 2014; revised 28 Nov 2014; accepted 28 Nov 2014; published 5 Dec 2014 15 Dec 2014 | Vol. 22, No. 25 | DOI:10.1364/OE.22.031041 | OPTICS EXPRESS 31045
500 μm
Fig. 3. The ITO electrode is patterned with radial-interdigitated structure.
4. Results and discussion For a simple demo, the outside space of the droplet is filled with air. Since the refractive index of the droplet (ng~1.47) is larger than that of air (nM ~1), the liquid lens is a converging lens. To evaluate the focus change of the lens when it is actuated, a bird toy is chosen as the object. The object is placed under the lens cell at ~7.5 cm distance. A handheld digital microscope is placed above the cell to record the observed image. When V = 0, a clear image is observed in white light circumstance, as shown in Fig. 4(a). In contrast to the head direction of the object, the observed image is inverted. This result implies that the object is outside the focal length of the droplet. To actuate the liquid droplet, a voltage is applied to the cell. When the voltage is less than 30 Vrms, the size of the image does not change. This is because the generated dielectric force is still weak to stretch the droplet. When the voltage exceeds 35 Vrms, the image begins to grow. Figure 4(b) shows the image when V = 40 Vrms (500 Hz). The size of the image increases a little bit. This is because the droplet begins to shift, causing the clear image to defocus. The image keeps growing when the voltage is increased further. Figure 4(c) shows the magnified and blurry image when V = 60 Vrms.
Fig. 4. Images of the object observed through the liquid lens with different voltages. (a) V = 0 (Media 1), (b) V = 40 Vrms, (c) V = 60 Vrms, (d) V = 80 Vrms, (e) V = 100 Vrms, and (f) V = 120 Vrms.
When the voltage is sufficiently high, a large displacement of the droplet can cause a distinct defocus. Figures 4(d), 4(e), and 4(f) show the observed images when V = 80 Vrms, 100 Vrms, and 120 Vrms, respectively. When the voltage is higher than 120 Vrms, the object could
#224917 - $15.00 USD (C) 2014 OSA
Received 28 Oct 2014; revised 28 Nov 2014; accepted 28 Nov 2014; published 5 Dec 2014 15 Dec 2014 | Vol. 22, No. 25 | DOI:10.1364/OE.22.031041 | OPTICS EXPRESS 31046
not be recognized completely. For the patterned ITO stripes with 20-μm gap, the highest electric field is ~12 V/μm at V = 120 Vrms. This electric field is much lower than the breakdown field of the Teflon layer (~59 V/μm). Therefore, the liquid lens can be safely actuated with a high voltage. To visually observe the imaging of the droplet when it is impacted by a 120-Vrms voltage pulse, a dynamic movie (Media 1) is recorded as given in Fig. 4(a). Actuation with two cycles shows that the glycerol droplet can return to its original state quite well. To characterize the performance of the liquid lens, several methods can be adopted [9,16,18,34]. A simple method is to evaluate its resolution by observing a USAF resolution target. A resolution target is placed under the lens cell, and the image is observed using an optical microscope. To measure the focal length of the liquid droplet, the position of the lens cell is adjusted so that it focuses on the droplet surface. Then the cell position is adjusted vertically so that a clear image is observed. The distance that the cell traveled in vertical direction is the focal length of the droplet. Using this method, the focal length of the lens is measured to be ~8.6 mm. Figure 5(a) shows the observed image in the voltage-off state. The droplet could resolve group 6 and element 6, and the corresponding resolution is ~114 lp/mm. When V = 80 Vrms, the image becomes highly blurry, as shown in Fig. 5(b). We then readjust the position of the lens cell so that the dome of the droplet could return to its original place, and a clear image appears again. The distance of the cell moved from the positions of focus to refocus is the travel distance of the droplet. Figure 5(c) shows the refocused image which can clearly resolve the bars in group 7 and element 1. As a result, the corresponding resolution is ~128 lp/mm. In contrast to the size of the image shown in Fig. 5(a), the size of the image shown in Fig. 5(b) does not change obviously. This result implies that the power (1/fL) of the lens is not changed. When the droplet moves down, some abnormal rays are clipped by the cylindrical wall. This is perhaps the reason that the lens presents a slightly higher resolution after refocus.
Fig. 5. Images of a resolution target observed using an optical microscope. (a) focus at V = 0, (b) defocus at V = 80 Vrms, and (c) refocus at V = 80 Vrms.
Using the method of focus (V = 0), defocus (V = V1) and refocus (V = V1) as shown in Fig. 5, we can measure the displacement of the droplet in one direction at various voltages. The results are given in Fig. 6. A higher voltage leads to a larger displacement. The displacement of the droplet in the hole presents almost a linear change with the amplitude of the external voltage.
#224917 - $15.00 USD (C) 2014 OSA
Received 28 Oct 2014; revised 28 Nov 2014; accepted 28 Nov 2014; published 5 Dec 2014 15 Dec 2014 | Vol. 22, No. 25 | DOI:10.1364/OE.22.031041 | OPTICS EXPRESS 31047
Fig. 6. Droplet shift in the hole at various voltages.
When the droplet is actuated for dynamic imaging, the response time is an important parameter. To measure the response time, a photodiode detector is placed right above the lens cell. In the voltage-off state, a laser beam is focused at one point. When a voltage pulse is used to impact the droplet in order to shift its focusing point, the detector could detect the light intensity change. By connecting the photodiode with a digital oscilloscope, the light intensity change with time can be analyzed. Figure 7 shows the time dependent light intensity change when a square voltage burst at f = 500 Hz and 100 Vrms is applied to the electrode. The duration of the voltage pulse is 5 s. It takes ~20 ms for the droplet to move to the lowest position, and ~650 ms for the droplet to recover its original state. The cycle driving with two periods shows the droplet can present good reciprocal motion in the hole.
Fig. 7. Dynamic response of the liquid lens impacted by 100-Vrms voltage pulse.
Theoretically, it is still difficult to estimate the response time of a liquid lens because it depends on many parameters, such as the physical properties of the employed liquids, the interfacial tensions, the size of the droplet, and the driving voltage. Usually a larger droplet needs a longer time to restore its spherical state if its shape is severely deformed. For microscale lenses, their response time is in the range from several milliseconds to hundred milliseconds. For millimeter-scale lenses, their response time is in the range from hundred milliseconds to several seconds. In contrast to previous macro-scale liquid lenses [21,22,25,32], the response time of our lens is reasonably fast. This is mainly due to the large surface tension of the glycerol droplet when it is surrounded by air. Another reason is the expanding of the droplet in radial direction rather than in only one direction. In the voltage-on state, a little expanding of the droplet in radial direction can cause a large shift of the droplet in the hole. When the voltage is removed, the stretched part of the droplet along the electrode can quickly return to its original place due to the short displacement. Therefore, the dome of the droplet can rapidly recover to its initial position.
#224917 - $15.00 USD (C) 2014 OSA
Received 28 Oct 2014; revised 28 Nov 2014; accepted 28 Nov 2014; published 5 Dec 2014 15 Dec 2014 | Vol. 22, No. 25 | DOI:10.1364/OE.22.031041 | OPTICS EXPRESS 31048
Any liquid lens has its own merits and demerits. Except some unique advantages, our liquid lens has some disadvantages too. Our millimeter-scale lens works well in horizontal position because the gravity force is along the optical axis of the droplet. If the lens cell is tilted with a large angle or placed in vertical position, then the surface profile of the droplet will be distorted by the gravity force. To minimize the gravity effect for practical applications, an immiscible liquid whose density matches that of the glycerol can be adopted. Optical oil SL-5267 (no = 1.67, Santolight) could be the preferred liquid. The gap of adjacent ITO stripes used in this lens cell is still too large. To further reduce the driving voltage, a feasible method is to increase the ITO-strip number and decrease the gap of adjacent ITO stripes. In comparison with previous liquid lenses, our lens cell has the advantages of simple fabrication, compact package, high optical performance, and reasonably fast response time. Since the surface profile of the liquid lens does not change during dynamic actuation, it can present high performance whether or not it is actuated. Our lens can do a reciprocating movement with good repeat cycles in a cylindrical hole. As we mentioned above, this is a simple demo as a lens for adaptive focus. To enhance the optical performances, parameters of the lens cell, such as the size of the hole, the thickness of the top substrate, the gap of the cell, and the pattern of the electrode, need to be optimized. To achieve good mechanical stability, the outside space of the droplet should be filled with a suitable liquid rather than with air. 5. Conclusion We have reported an adaptive liquid lens whose dome could be shifted in a cylindrical hole without deforming its shape. The lens presents high optical performance (~114 lp/mm) in the voltage-off state. The optical performance is not degraded during dynamic actuation. Using radial-interdigitated ITO stripes for the lens, a symmetrical-inhomogeneous fringing field can be obtained. Such an electric field could effectively stretch the border of the droplet in radial direction. A little travel distance along the ITO stripes can cause a distinct shift of the droplet in the hole. At V = 80 Vrms, the droplet could travel ~1.6 mm. A higher voltage can lead to a larger displacement of the droplet. As a result, the liquid lens can provide a wide dynamic range with reasonably fast response time (τrise~20 ms, τdecay~650 ms). In contrast to previous liquid lenses, our lens cell remains the merits of simple fabrication, compact structure, and easy operation, and good optical performance. By optimizing the electrode structure, the driving voltage can be further reduced. Our liquid lens with a reciprocating movement in a cylindrical hole has promising applications in image processing, machine vision, microfluidic systems, biotechnology, and other lab-on-a-chip devices. Acknowledgments This work is financially supported by the National Research Foundation of Korea under Grant 2014001345 and partially supported by the Basic Science Research Program of NRF under Grant 2014064156.
#224917 - $15.00 USD (C) 2014 OSA
Received 28 Oct 2014; revised 28 Nov 2014; accepted 28 Nov 2014; published 5 Dec 2014 15 Dec 2014 | Vol. 22, No. 25 | DOI:10.1364/OE.22.031041 | OPTICS EXPRESS 31049
BK Plus Haptic Polymer Composite Research Team, Department of polymer Nano-Science and Technology, Chonbuk National University, Jeonju, Jeonbuk, 561-756, South Korea 2 School of Electronics and Information Engineering, Sichuan University, Chengdu 610065, China * [email protected]
Abstract: We demonstrate a liquid droplet which can do a reciprocating movement in a cylindrical hole. The droplet in the hole exhibits a lens character. By applying a voltage, the border of the droplet is stretched to expand by the generated dielectric force. Due to the fixed volume, the dome of the droplet in the hole has to move toward the substrate without changing its surface profile. Therefore, the focal length of the droplet remains unchanged although the focal point is shifted. Once the voltage is removed, the droplet can return to its original state. The droplet with such a movement functions as an adaptive lens. Our lens can provide a high resolution (~114 lp/mm) whether or not it is actuated. The dynamic response time is reasonably fast. Integrating with a solid lens, the compound lens can provide a variable focal length. ©2014 Optical Society of America OCIS codes: (080.3630) Lenses; (110.1080) Active or adaptive optics; (230.3990) Microoptical devices; (250.0250) Optoelectronics.
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Received 28 Oct 2014; revised 28 Nov 2014; accepted 28 Nov 2014; published 5 Dec 2014 15 Dec 2014 | Vol. 22, No. 25 | DOI:10.1364/OE.22.031041 | OPTICS EXPRESS 31041
16. H.-C. Cheng, S. Xu, Y. Liu, S. Levi, and S.-T. Wu, “Adaptive mechanical-wetting lens actuated by ferrofluids,” Opt. Commun. 284(8), 2118–2121 (2011). 17. 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). 18. L. Miccio, M. Paturzo, S. Grilli, V. Vespini, and P. Ferraro, “Hemicylindrical and toroidal liquid microlens formed by pyro-electro-wetting,” Opt. Lett. 34(7), 1075–1077 (2009). 19. B. Berge and J. Peseux, “Variable focus lens controlled by an external voltage: an application of electrowetting,” Eur. Phys. J. E 3(2), 159–163 (2000). 20. T. Krupenkin, S. Yang, and P. Mach, “Tunable liquid microlens,” Appl. Phys. Lett. 82(3), 316–318 (2003). 21. S. Kuiper and H. W. Hendriks, “Variable-focus liquid lens for miniature cameras,” Appl. Phys. Lett. 85(7), 1128–1130 (2004). 22. N. R. Smith, L. Hou, J. Zhang, and J. Heikenfeld, “Fabrication and demonstration of electrowetting liquid lens arrays,” J. Dis. Tech. 5(11), 411–413 (2009). 23. C. C. Cheng and J. A. Yeh, “Dielectrically actuated liquid lens,” Opt. Express 15(12), 7140–7145 (2007). 24. H. Ren, H. Xianyu, S. Xu, and S. T. Wu, “Adaptive dielectric liquid lens,” Opt. Express 16(19), 14954–14960 (2008). 25. K. Y. Hung, C. C. Fan, F. G. Tseng, and Y. K. Chen, “Design and fabrication of a copolymer aspheric bi-convex lens utilizing thermal energy and electrostatic force in a dynamic fluidic,” Opt. Express 18(6), 6014–6023 (2010). 26. S. Xu, H. Ren, and S. T. Wu, “Adaptive liquid lens actuated by liquid crystal pistons,” Opt. Express 20(27), 28518–28523 (2012). 27. Y.-S. Lu, H. Tu, Y. Xu, and H. Jiang, “Tunable dielectric liquid lens on flexible substrate,” Appl. Phys. Lett. 103(26), 261113 (2013). 28. H. Ren, Y.-H. Fan, Y.-H. Lin, and S.-T. Wu, “Tunable-focus microlens arrays using nanosized polymerdispersed liquid crystal droplets,” Opt. Commun. 247(1–3), 101–106 (2005). 29. Y. Li and S. T. Wu, “Polarization independent adaptive microlens with a blue-phase liquid crystal,” Opt. Express 19(9), 8045–8050 (2011). 30. K. H. Kang, “How electrostatic fields change contact angle in electrowetting,” Langmuir 18(26), 10318–10322 (2002). 31. M. Xu, H. Ren, L. Yoo, and Q. Wang, “An adaptive liquid lens with radial interdigitated electrode,” J. Opt. 16(10), 105601 (2014). 32. F. Mugele and J.-C. Baret, “Electrowetting: from basics to applications,” J. Phys. Condens. Matter 17(28), R705–R774 (2005). 33. E. Hecht, Optics, 4th ed., (Addison Wesley, Reading, MA, 2002). 34. L. Miccio, A. Finizio, S. Grilli, V. Vespini, M. Paturzo, S. De Nicola, and P. Ferraro, “Tunable liquid microlens arrays in electrode-less configuration and their accurate characterization by interference microscopy,” Opt. Express 17(4), 2487–2499 (2009).
1. Introduction An adaptive lens is an essential optical device which has been studied intensively in the past years. In contrast to a glass lens, an adaptive lens can obtain a tunable focus without moving parts. Therefore, it functions as a compound lens with the advantages of compact structure, easy operation, and high precision. Applications of an adaptive lens can widely find in imaging, information storage, target tracking, biometric identification, displays, and optical switches. Numerous adaptive lenses were demonstrated. Based on their operation mechanisms, they can be roughly classified into liquid crystal (LC) lens [1–8], elastic membrane lens [9–12], hydrogel lens [13], acoustic lens [14], ferrofluidic lens [15,16], electrowetting lens [17–22], and dielectric lens [23–27]. In a LC lens, a certain focal length can be obtained when the LC molecules produce a gradient refractive index profile across its aperture. By applying a voltage, the LC molecules in the lens cell are reoriented, leading to the change of the gradient of the refractive index profile. As a result, its focal length is tuned [1,2]. Most LC lenses need a polarizer because they are polarization-dependent, so the light efficiency is less than 50%. By employing polymer dispersed liquid crystals (PDLC) [28] or blue phase liquid crystals (PSBPLC) [29], the demonstrated lenses are polarization-insensitive. Because both PDLC and PSBPLC could not provide a distinct phase shift, the prepared lens presents a rather limited focus change. In comparison to a LC lens, a liquid lens focuses light based on the shape change. It can present good optical performances due to the optical isotropy. By controlling the surface profile of the liquid, it is possible to vary the focal length of the lens in a wide range. In the
#224917 - $15.00 USD (C) 2014 OSA
Received 28 Oct 2014; revised 28 Nov 2014; accepted 28 Nov 2014; published 5 Dec 2014 15 Dec 2014 | Vol. 22, No. 25 | DOI:10.1364/OE.22.031041 | OPTICS EXPRESS 31042
aforementioned liquid lenses, only electrowetting and dielectric lenses can be actuated electrically. The surface profile of the former lens is deformed by an electrostatic force [18– 21,30], while the surface profile of the latter is deformed by a dielectric force [23–25]. When the focal length of these lenses is tuned, their optical performance is changed accordingly. To largely reduce the focal length of the lens, a common method is to largely deform the shape of the liquid. By doing so not only the driving voltage is enhanced, but also the lens performance is degraded. It is highly desirable to develop an adaptive lens which can provide a high optical performance during dynamic imaging. In this work, we report a dielectric liquid lens using a radial-interdigitated electrode. Unlike conventional liquid lenses [23,24,31], our lens provides a focus change based on a reciprocating motion in a cylindrical hole. The lens with this movement functions as an adaptive lens. Since the surface profile of the lens in the hole is unchanged, its focal length is fixed although its focal point is shifted. As a result, the optical performance of the lens is not degraded whether or not it is actuated. Owing to the radial-interdigitated electrode, the generared fringing field can effectively actuate the lens with a relatively low driving voltage. In the voltage-on state, the droplet is stretched to expand in the transverse direction along the electrode. A little travel distance in radial direction can cause a distinct shift of the lens in longitudinal direction. Once the voltage is removed, the deformed droplet can quickly return to its original position. Therefore, our liquid lens possesses the advantages of high resolution (~114 lp/mm), a wide dynamic focus change, and reasonably fast response time. 2. Lens structure and theory 2.1 Device structure and characteristics Our device mainly consists of a top substrate, a bottom substrate, and a liquid droplet. The top substrate is relatively thick. Its center area has a through hole, as shown in Fig. 1(a). The surface of the cylindrical hole and its bottom surface are coated with a hydrophobic layer. The bottom substrate has an indium-tin-oxide (ITO) electrode, as depicted in Fig. 1(b). The electrode is etched with a radial-interdigitated pattern. Each ITO strip presents a fan shape and the adjacent strips are separated with a gap. The width of the ITO gap is uniform. The ITO stripes are circularly symmetric. The terminals marked “A” and “B” are used to apply a voltage. The surface of the ITO substrate is coated with a hydrophobic layer too. The top substrate and the bottom substrate are placed together to form a cell. The gap of the cell is controlled using glass spacers (not shown). The cross-sectional structure of the device is shown in Fig. 1(c). A small volume of a dielectric liquid is dripped in the hole to form a droplet. The top of the droplet is spherical and its bottom is flat. In the relaxing state, the droplet presents minimal surface-to-volume ratio with the lowest surface energy. Because the dome of the droplet is axially symmetrical, it exhibits a lens character. If an incident beam passes through it, the beam will be converged by its curved surface. When a voltage (V = V1) is applied to the ITO stripes (through terminals A and B), a fringing field is generated between adjacent ITO stripes. The region close to the edge of each ITO stripe experiences the largest gradient of electric field. If the dielectric constant of the droplet is larger than that of the surrounding media, then the molecules at the edge of the droplet suffer the highest dielectric force. This force pulls these molecules to move toward this region. Due to the cohesion between the adjacent molecules and the adhesion between the droplet and the substrates, the droplet is deformed. Along the ITO stripes the fringing field is continuous, so the droplet can expand in transverse direction. Since the volume of the droplet is fixed, the dome of the droplet has to move down in longitudinal direction, as shown in Fig. 1(d). Due to the spherical shape of the lens, it still focuses the light but with a shifted focal point.
#224917 - $15.00 USD (C) 2014 OSA
Received 28 Oct 2014; revised 28 Nov 2014; accepted 28 Nov 2014; published 5 Dec 2014 15 Dec 2014 | Vol. 22, No. 25 | DOI:10.1364/OE.22.031041 | OPTICS EXPRESS 31043
Hydrophobic layer Electrode
Hydrophobic layer Hole
A B
(a)
(b)
Electrode
Gap
Liquid Substrate
V1
0V
(d)
(c)
Fig. 1. Key parts of the liquid lens and the cross-sectional structure of the lens cell in the voltage-off and voltage-on states.
2.2 Contact angle To analyze the shape change of the droplet when it is actuated, let’s compare the surface of the droplet shown in Fig. 1(c) to that in Fig. 1(d). At V = 0, the curved surface of the droplet has a contact angle (θ0) on the surface of the hole. To define the contact angle, the crosssectional view of the droplet is partially redrawn as shown in in Fig. 2 (light pink). The angle between the surface of the liquid and the outline of the contact solid surface at the end point (M) is called the contact angle. According to Young’s equation, the contact angle is expressed by [32] cos θ 0 =
γSV − γSL γ LV
(1)
where γSL, γSV, and γLV are solid-liquid, solid-vapor, and liquid-vapor interfacial tensions, respectively. The shape of the dome is determined by the contact angle. If the radius of the curved surface is r, then the focal length (fL) of the droplet is fL =
r nL − nM
(2)
where nL and nM are the refractive indices of the liquid and the surrounding media, respectively. If air is the surrounding media, then nM≈1. When a voltage (V = V1) is applied to the electrode, the dome of the droplet moves down (dark pink), and the position of point M shifts to the position of point N. Since the interfacial tensions (γSL, γSV, and γLV) are unchanged, the contact angle keeps the same (θ0). Therefore, the focal length (fL) will not be affected except shifting its focusing point.
#224917 - $15.00 USD (C) 2014 OSA
Received 28 Oct 2014; revised 28 Nov 2014; accepted 28 Nov 2014; published 5 Dec 2014 15 Dec 2014 | Vol. 22, No. 25 | DOI:10.1364/OE.22.031041 | OPTICS EXPRESS 31044
γLV V=0
•M
γSL
V=V1
o
•
γSV Cell
•
Lens
•
•N •
(a)
(b)
fL d fS
o′
Fig. 2. (a) Surface profile of the droplet in the V = 0 and V = V1 states and (b) integrating with one lens for a variable focal length.
2.3 A compound lens To get a variable focal length, the liquid lens needs to combine with another lens to form a compound lens. If the bottom glass substrate of the lens cell shown in Fig. 1(c) is a plano convex lens, then the lens cell is called a compound lens, as shown in Fig. 2(b). The two lenses have a common axis (OO′) separated by a diatance d. Suppose the focal length of the bottom lens is fs, then the effective focal length for the lens system is given by [33] 1 1 1 d = + − f f L f S f L fS
(3)
From Eq. (3), if the separated distance d is mainly dependent on the travel distance of the droplet, then f can be changed effectively by an external voltage. As a result, this compound lens can provide a variable focal length. 3. Device fabrication To prepare a lens cell as sketched in Fig. 1(c), an aluminum substrate (1.5 × 1.5 cm with 6.3mm-thick) is chosen as the top substrate. A through hole is drilled in the center area. The diameter of the hole is 2.5 mm. The surface of the hole is coated with a Teflon layer (γT~19 mNm−1). Teflon is a good hydrophobic material which can provide a large contact angle for many liquids. An ITO glass is chosen as the bottom substrate. The ITO electrode is etched with a radial-interdigitated pattern. Part of the patterned electrode is shown in Fig. 3. The slightly dark area is covered with ITO electrode and the bright stripes are the region without electrode. The size of the substrate is 1.8 × 1.8 cm. The gap of adjacent ITO stripes is 20 μm, and each ITO strip has a fan shape. The radius of the center area without patterning is 1 mm. There are 44 ITO stripes around the circular aperture. The surface of the ITO glass substrate is then coated with a Teflon layer (1-μm-thick) too. The two substrates are placed together to form a cell. The gap of the cell is controlled using ~0.7-mm-thick glass spacers. The hole of the top substrate is positioned above the center area of the bottom substrate. A glycerol (εg ~47, ng = 1.47, γg ~63 mNm−1, from Aldrich) with high purity (> 99.5%) is chosen as the liquid. We choose glycerol as the lens material due to three reasons: large dielectric constant, large surface tension, and no evaporation. A small amount of the glycerol is dripped in the hole to form a droplet. Since the diameter of the hole is larger than the diameter of the circularly non-patterned ITO electrode, the border of the droplet covers the terminals of the ITO stripes. Due to the large surface tension, the droplet partially wets the bottom substrate and the bottom surface of the top substrate. The height of the droplet from its dome to the bottom substrate is measured to be ~3 mm.
#224917 - $15.00 USD (C) 2014 OSA
Received 28 Oct 2014; revised 28 Nov 2014; accepted 28 Nov 2014; published 5 Dec 2014 15 Dec 2014 | Vol. 22, No. 25 | DOI:10.1364/OE.22.031041 | OPTICS EXPRESS 31045
500 μm
Fig. 3. The ITO electrode is patterned with radial-interdigitated structure.
4. Results and discussion For a simple demo, the outside space of the droplet is filled with air. Since the refractive index of the droplet (ng~1.47) is larger than that of air (nM ~1), the liquid lens is a converging lens. To evaluate the focus change of the lens when it is actuated, a bird toy is chosen as the object. The object is placed under the lens cell at ~7.5 cm distance. A handheld digital microscope is placed above the cell to record the observed image. When V = 0, a clear image is observed in white light circumstance, as shown in Fig. 4(a). In contrast to the head direction of the object, the observed image is inverted. This result implies that the object is outside the focal length of the droplet. To actuate the liquid droplet, a voltage is applied to the cell. When the voltage is less than 30 Vrms, the size of the image does not change. This is because the generated dielectric force is still weak to stretch the droplet. When the voltage exceeds 35 Vrms, the image begins to grow. Figure 4(b) shows the image when V = 40 Vrms (500 Hz). The size of the image increases a little bit. This is because the droplet begins to shift, causing the clear image to defocus. The image keeps growing when the voltage is increased further. Figure 4(c) shows the magnified and blurry image when V = 60 Vrms.
Fig. 4. Images of the object observed through the liquid lens with different voltages. (a) V = 0 (Media 1), (b) V = 40 Vrms, (c) V = 60 Vrms, (d) V = 80 Vrms, (e) V = 100 Vrms, and (f) V = 120 Vrms.
When the voltage is sufficiently high, a large displacement of the droplet can cause a distinct defocus. Figures 4(d), 4(e), and 4(f) show the observed images when V = 80 Vrms, 100 Vrms, and 120 Vrms, respectively. When the voltage is higher than 120 Vrms, the object could
#224917 - $15.00 USD (C) 2014 OSA
Received 28 Oct 2014; revised 28 Nov 2014; accepted 28 Nov 2014; published 5 Dec 2014 15 Dec 2014 | Vol. 22, No. 25 | DOI:10.1364/OE.22.031041 | OPTICS EXPRESS 31046
not be recognized completely. For the patterned ITO stripes with 20-μm gap, the highest electric field is ~12 V/μm at V = 120 Vrms. This electric field is much lower than the breakdown field of the Teflon layer (~59 V/μm). Therefore, the liquid lens can be safely actuated with a high voltage. To visually observe the imaging of the droplet when it is impacted by a 120-Vrms voltage pulse, a dynamic movie (Media 1) is recorded as given in Fig. 4(a). Actuation with two cycles shows that the glycerol droplet can return to its original state quite well. To characterize the performance of the liquid lens, several methods can be adopted [9,16,18,34]. A simple method is to evaluate its resolution by observing a USAF resolution target. A resolution target is placed under the lens cell, and the image is observed using an optical microscope. To measure the focal length of the liquid droplet, the position of the lens cell is adjusted so that it focuses on the droplet surface. Then the cell position is adjusted vertically so that a clear image is observed. The distance that the cell traveled in vertical direction is the focal length of the droplet. Using this method, the focal length of the lens is measured to be ~8.6 mm. Figure 5(a) shows the observed image in the voltage-off state. The droplet could resolve group 6 and element 6, and the corresponding resolution is ~114 lp/mm. When V = 80 Vrms, the image becomes highly blurry, as shown in Fig. 5(b). We then readjust the position of the lens cell so that the dome of the droplet could return to its original place, and a clear image appears again. The distance of the cell moved from the positions of focus to refocus is the travel distance of the droplet. Figure 5(c) shows the refocused image which can clearly resolve the bars in group 7 and element 1. As a result, the corresponding resolution is ~128 lp/mm. In contrast to the size of the image shown in Fig. 5(a), the size of the image shown in Fig. 5(b) does not change obviously. This result implies that the power (1/fL) of the lens is not changed. When the droplet moves down, some abnormal rays are clipped by the cylindrical wall. This is perhaps the reason that the lens presents a slightly higher resolution after refocus.
Fig. 5. Images of a resolution target observed using an optical microscope. (a) focus at V = 0, (b) defocus at V = 80 Vrms, and (c) refocus at V = 80 Vrms.
Using the method of focus (V = 0), defocus (V = V1) and refocus (V = V1) as shown in Fig. 5, we can measure the displacement of the droplet in one direction at various voltages. The results are given in Fig. 6. A higher voltage leads to a larger displacement. The displacement of the droplet in the hole presents almost a linear change with the amplitude of the external voltage.
#224917 - $15.00 USD (C) 2014 OSA
Received 28 Oct 2014; revised 28 Nov 2014; accepted 28 Nov 2014; published 5 Dec 2014 15 Dec 2014 | Vol. 22, No. 25 | DOI:10.1364/OE.22.031041 | OPTICS EXPRESS 31047
Fig. 6. Droplet shift in the hole at various voltages.
When the droplet is actuated for dynamic imaging, the response time is an important parameter. To measure the response time, a photodiode detector is placed right above the lens cell. In the voltage-off state, a laser beam is focused at one point. When a voltage pulse is used to impact the droplet in order to shift its focusing point, the detector could detect the light intensity change. By connecting the photodiode with a digital oscilloscope, the light intensity change with time can be analyzed. Figure 7 shows the time dependent light intensity change when a square voltage burst at f = 500 Hz and 100 Vrms is applied to the electrode. The duration of the voltage pulse is 5 s. It takes ~20 ms for the droplet to move to the lowest position, and ~650 ms for the droplet to recover its original state. The cycle driving with two periods shows the droplet can present good reciprocal motion in the hole.
Fig. 7. Dynamic response of the liquid lens impacted by 100-Vrms voltage pulse.
Theoretically, it is still difficult to estimate the response time of a liquid lens because it depends on many parameters, such as the physical properties of the employed liquids, the interfacial tensions, the size of the droplet, and the driving voltage. Usually a larger droplet needs a longer time to restore its spherical state if its shape is severely deformed. For microscale lenses, their response time is in the range from several milliseconds to hundred milliseconds. For millimeter-scale lenses, their response time is in the range from hundred milliseconds to several seconds. In contrast to previous macro-scale liquid lenses [21,22,25,32], the response time of our lens is reasonably fast. This is mainly due to the large surface tension of the glycerol droplet when it is surrounded by air. Another reason is the expanding of the droplet in radial direction rather than in only one direction. In the voltage-on state, a little expanding of the droplet in radial direction can cause a large shift of the droplet in the hole. When the voltage is removed, the stretched part of the droplet along the electrode can quickly return to its original place due to the short displacement. Therefore, the dome of the droplet can rapidly recover to its initial position.
#224917 - $15.00 USD (C) 2014 OSA
Received 28 Oct 2014; revised 28 Nov 2014; accepted 28 Nov 2014; published 5 Dec 2014 15 Dec 2014 | Vol. 22, No. 25 | DOI:10.1364/OE.22.031041 | OPTICS EXPRESS 31048
Any liquid lens has its own merits and demerits. Except some unique advantages, our liquid lens has some disadvantages too. Our millimeter-scale lens works well in horizontal position because the gravity force is along the optical axis of the droplet. If the lens cell is tilted with a large angle or placed in vertical position, then the surface profile of the droplet will be distorted by the gravity force. To minimize the gravity effect for practical applications, an immiscible liquid whose density matches that of the glycerol can be adopted. Optical oil SL-5267 (no = 1.67, Santolight) could be the preferred liquid. The gap of adjacent ITO stripes used in this lens cell is still too large. To further reduce the driving voltage, a feasible method is to increase the ITO-strip number and decrease the gap of adjacent ITO stripes. In comparison with previous liquid lenses, our lens cell has the advantages of simple fabrication, compact package, high optical performance, and reasonably fast response time. Since the surface profile of the liquid lens does not change during dynamic actuation, it can present high performance whether or not it is actuated. Our lens can do a reciprocating movement with good repeat cycles in a cylindrical hole. As we mentioned above, this is a simple demo as a lens for adaptive focus. To enhance the optical performances, parameters of the lens cell, such as the size of the hole, the thickness of the top substrate, the gap of the cell, and the pattern of the electrode, need to be optimized. To achieve good mechanical stability, the outside space of the droplet should be filled with a suitable liquid rather than with air. 5. Conclusion We have reported an adaptive liquid lens whose dome could be shifted in a cylindrical hole without deforming its shape. The lens presents high optical performance (~114 lp/mm) in the voltage-off state. The optical performance is not degraded during dynamic actuation. Using radial-interdigitated ITO stripes for the lens, a symmetrical-inhomogeneous fringing field can be obtained. Such an electric field could effectively stretch the border of the droplet in radial direction. A little travel distance along the ITO stripes can cause a distinct shift of the droplet in the hole. At V = 80 Vrms, the droplet could travel ~1.6 mm. A higher voltage can lead to a larger displacement of the droplet. As a result, the liquid lens can provide a wide dynamic range with reasonably fast response time (τrise~20 ms, τdecay~650 ms). In contrast to previous liquid lenses, our lens cell remains the merits of simple fabrication, compact structure, and easy operation, and good optical performance. By optimizing the electrode structure, the driving voltage can be further reduced. Our liquid lens with a reciprocating movement in a cylindrical hole has promising applications in image processing, machine vision, microfluidic systems, biotechnology, and other lab-on-a-chip devices. Acknowledgments This work is financially supported by the National Research Foundation of Korea under Grant 2014001345 and partially supported by the Basic Science Research Program of NRF under Grant 2014064156.
#224917 - $15.00 USD (C) 2014 OSA
Received 28 Oct 2014; revised 28 Nov 2014; accepted 28 Nov 2014; published 5 Dec 2014 15 Dec 2014 | Vol. 22, No. 25 | DOI:10.1364/OE.22.031041 | OPTICS EXPRESS 31049
