Open Access
Add to BibSonomy
Abstract
A straightforward technique for fabricating low-cost microlens arrays with controllable focal length is developed. By harnessing and manipulating the interfacial energy between the liquid-state acrylate resin and the solidified polydimethylsiloxane (PDMS), the surface of the acrylate resin in the PDMS microhole presents a spherical shape and the curvature can be flexibly controlled. With the change of the processing time for the surface modification of the PDMS microholes, the focal length of the concave microlenses varies from –296.3 μm to –67.4 μm. The numerical aperture of 0.45 is realized. The focal length and the aperture of the microlenses are also affected by the diameter of the microholes. The fabricated concave microlens array can be employed as a master to further duplicate convex microlens array. A good image quality can be achieved by using the convex microlens arrays.
© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Microlens arrays (MLAs) are fundamental optical diffractive elements which are widely used in the diverse applications such as three-dimensional imaging [1,2], protein detection [3], Bessel-like beam generation [4], micro-structure fabrication for generating surface plasmon resonance [5], light homogenization and wavefront sensing [6–8]. In the traditional manufacturing of optics, lenses are fabricated by using expensive high-precision milling machine, which requires sophisticated craftsmanship for lens design and machine operation. Due to the long production cycle and the high cost for designing and fabricating MLAs of various specifications, the productivity is low and the selection of MLAs on the market is limited. Hence, the traditional milling techniques are not very proper for the fabrication of MLAs.
Thanks to the excellent optical properties and low cost of the polymer, many conventional micro-machining techniques are applied to produce polymer MLAs including thermal reflow technique [9, 10], lithography technique and laser-induced structural modification technique [11, 12]. Thermal reflow technique provides a fast way to produce monolithic polymer MLAs by melting polymer cylinders into hemispherical shape. High numerical aperture and high fill-factor MLAs can be realized by using thermal reflow technique. When using lithography techniques, high-uniform MLAs could be directly produced by exposing photoresist in the ultra-violet (UV) light via a gray-scale mask or a programmable digital microlens array with the pattern corresponding to the three-dimensional profile of the MLA [13–16]. Besides directly producing MLAs, a 3D diffuser lithography technique was applied to fabricate a mold of an array of lens-shaped microholes. Then, high-fill-factor MLAs could be replicated from the mold [17]. Laser-induced structural modification technique can produce three-dimensional spherical structures on the polymer to form MLA by scanning and etching the material [18–22]. The design of MLA is flexible and the whole writing process is programmable. Complex profiles and structures of arbitrary surface curvature and various filling factor can be realized. Nevertheless, the fabrication process is slow and the surface roughness of the produced MLA is high [23].
The MLAs can be easily fabricated by transferring curable polymer micro-droplet onto a substrate by using laser-induced forward transfer (LIFT) technique [24, 25] and ink-jet printing technique [26, 27]. A femtosecond laser is required in the LIFT technique to transfer the prepolymer droplet from the donor film to a closely-placed substrate. High-quality MLAs of controllable size and focal length could be realized by tuning the laser pulse energy. In the ink-jet printing technique, a piezo-actuated ink-jet nozzle was used to transfer polymer droplet to a substrate. The controllable contact angle of the droplet was demonstrated by using different hydrophobic substrates, indicating that different focal length could be realized. To realize controllable curvature of the droplet on the substrate, the contact angle of the polymer droplet can be manipulated by gas plasma treatment and coating of the substrate surface [27, 28]. However, producing microlenses one by one is time-consuming and it requires high positioning accuracy.
Recently, several cost-effective techniques for the fabrication of MLAs are demonstrated by manipulating the surface curvature of liquid-state polymer and solidifying the curved structure afterwards. MLAs of controllable curvature could be fabricated by driving polymer to overcome the viscous resistance and flow through an air gap in between a hydrophilic substrate and a hydrophobic microhole array [23]. The surface curvature of the polymer beneath the microhole could be controlled by adjusting the gap between the substrate and the microhole array. Nevertheless, if the viscous resistance was larger than the driving force, i.e. surface tension force, a flat bottom was formed and the curvature was limited. Besides that, the surface curvature of the liquid polymer could be well manipulated by thermally changing the pressure difference across the interface of the air trapped in the microhole and the polymer. The MLAs of the numerical aperture of 0.49 and the focal length ranging from 51.4 μm to 71.9 μm were demonstrated [29]. In addition, electrowetting technique was applied to control the surface curvature of the polymer to form MLAs with different focal length [30–32]. To achieve a wide tuning range, a modulated high voltage signal with reversing polarity could retreat the movement of the contact angle and a small contact angle beyond the saturation could be obtained [33]. Microfluidic platform also provides an efficient way for MLA fabrication [34, 35]. MLAs with controllable focal length can be produced by injecting the liquid polymer into the microfluidic chip to deform elastic membrane through patterned microholes and solidifying the surface-curved polymer.
In this paper, we demonstrate a rapid way to fabricate large-area MLAs with controllable focal length. The surface of liquid acrylate resin in the microholes presents meniscus shape, forming concave microlenses. By modifying the surface wettability of the microholes, the curvature of interface between air and the liquid acrylate resin can be well manipulated. A wide tuning range of the focal length from –296.3 μm to –67.4 μm is achieved by controlling the processing time of the surface treatment. The influence of the microhole size over the focal length is investigated. The optical performance of the MLAs is evaluated in the optical imaging. Moreover, due to the high mechanical and thermal strength of the solidified acrylate resin, the fabricated concave MLAs can be used as a mold to further produce convex MLAs.
2. Fabrication of Microlens Arrays
The procedure for producing MLA is illustrated in Fig. 1(a). A master mold was firstly fabricated by using photolithography technique. A titanium (Ti) layer is plated onto a silicon wafer and then oxidized into titanium dioxide (TiO2). Photoresist is applied onto the wafer by spin coating at the rate of 1800 rpm for 1 min. After UV exposure under a mask which has a pattern of microholes, the photoresist in the unexposed regions is removed by developer. An array of 180 × 180 micro-pillars made of photoresist is formed on the wafer. The height of pillars was 45 μm. Then, liquid-state polydimethylsiloxane (PDMS), the silicone elastomer and a curing agent at a weight ratio of 10:1 (Sylgard 184, Dow Corning), was poured onto the silicon wafer for casting pillars. The casting process was conducted in the vacuum oven for removing bubbles. The PDMS was solidified after 4 h at 80 °C heating. The refractive index of solid-state PDMS is 1.403 [36]. The elastic solid PDMS was peeled off from the master mold and an array of microholes was formed on the one side of the PDMS. A pre-prepared PDMS sheet was used to cover the middle part of the PDMS on the flat side and the four edges were exposed in the air plasma for surface modification. After 2 min surface treatment, the PDMS sheet was removed and a piece of glass was bonded to the PDMS on the flat side.
Fig. 1 (a) Fabrication process of the concave MLA. (b) SEM image of the concave MLA fabricated with the condition of 40 s argon plasma treatment. (c) SEM image of the cross section of the concave microlens. (d) Photo of a fabricated MLA in an area of 1.6 cm × 1.6 cm.
Next, argon and oxygen (gas mixture ratio of argon to oxygen: 100:1) plasma was used to modify the PDMS surface on the microhole-array side in a plasma cleaner (Harrick Plasma) with the condition of 13 MHz radio frequency, 600 mTorr pressure, 11 W plasma power and 60 mL/min gas pump speed. After the surface treatment, the photosensitive resin (acrylate, viscosity: 500 mPa∙s at room temperature, density: ρ = 1.02 g/cm3, refractive index: n = 1.487, type 3492, Aroh Alona), which was previously heated at 80 °C for 10 min to reduce the viscosity (170 mPa∙s), was spun over the PDMS at the spin coating rate of 3000 rpm for 2 minutes and then placed in the vacuum machine (–750 Torr pressure) to ensure the acrylate resin fill in the microholes completely. The surface of the acrylate resin in the microholes became concave because the interfacial energy between the acrylate resin and the wall of the microholes enforced the surface curved. The acrylate resin was exposed to 365 nm ultraviolet (UV) light at the intensity of 1000 mJ/cm2. After 8 min UV exposure, the acrylate resin was completely solidified. Finally, the PDMS containing the acrylate resin with curved surface in the microholes was peeled off from the glass.
In the experiment, an XL30 ESEM-FEG scanning electron microscope (SEM, FEI), a Talysurf CCI-Lite non-contact 3D profiler (Taylor Hobson), a viscometer and an optical contact angle & interface tension meter (SL200B, KINO) were used to analyze the morphology of the microlenses and the properties of the material.
Figure 1(b) shows the SEM image of the fabricated concave microlens. The size of the microlens array is 16 mm × 16 mm × 3 mm (length × width × thickness). Each microhole in the PDMS has the diameter of 60 μm and the height of 45 μm. The separation of the microlenses is 30 μm. The separation of the microlenses or the fill factor of the MLA is mainly dominated by the resolution of the photolithography and the yield stress of the PDMS (2.59 MPa) [37].
In the fabrication, the surface of the PDMS was modified by exposing in the argon and oxygen plasma for 100 s. The cross-section SEM image is shown in Fig. 1(c). The acrylate resin in the microholes has a concave curvature. The sag height of the microlens is 18.1 μm. Figure 1(d) shows the fabricated concave MLA. According to the optical theory, the focal length and the numerical aperture (NA) are –69.6 μm and 0.43, respectively.
The fabricated concave MLA could be used as a mold to further produce convex MLAs, as shown in Fig. 2(a). Liquid PDMS of a mixture of the silicone elastomer and the curing agent at a weight ratio of 10:1 was poured onto the concave MLA. After that, the micro bubbles were evacuated from the liquid PDMS in a vacuum oven. The liquid PDMS was then heated for 4 hours at 80 °C. After solidification, the PDMS could be easily peeled off from the concave MLA. Due to the high thermal and mechanical strength of the acrylate resin (elongation at break: 40%, coefficient of thermal expansion: 3 × 10−6 /°C, operating temperature: –50 °C to 150 °C), the concave structure of the acrylate resin was replicated to the surface of the PDMS, forming a PDMS convex MLA.
The SEM image of the replicated PDMS convex MLA is shown in Fig. 2(b). The convex MLA has the same dimensions as the concave MLA. The convex microlenses are in good uniformity and have identical curvature as that of the concave microlenses with opposite sign. The focal length of the convex microlenses is 84.2 μm and the NA is 0.36.
3. Results and discussion
3.1 Influence of Surface Modification
The surface of the acrylate resin in the microhole is curved because of the interactions of interfacial tensions of the acrylate resin, the sidewalls of the microholes and air above the acrylate resin. Each microhole can be regarded as a capillary tube and the force can be described by the contact angle resulted from the thermodynamic equilibrium between three phases, i.e. liquid phase (the acrylate resin), solid phase (the solidified PDMS) and the gas phase (air in the microholes). Thus, the contact angle is a key factor to affect the surface curvature of the acrylate resin and the focal length of the microlenses. Furthermore, the contact angle can be precisely controlled by adjusting the interfacial energy between the acrylate resin and the PDMS with the surface treatment of the PDMS [38, 39]. Figure 3 shows the influence of the surface treatment over the contact angle. In the analysis, a 1μL acrylate resin droplet is pipetted onto a flat PDMS substrate whose surface is modified in the argon and oxygen plasma. The analysis is to imitate the situation in the microholes. The volume of the acrylate resin droplet is low enough for reducing the solid-liquid interfacial area so line tension should be taken into account [40]. The contact angle is about 71.5° without the surface treatment and becomes small with the increase of the processing time for exposing the PDMS in the plasma. The error bar stands for the standard deviation of different measurements. The maximum deviation is 3.2°. The surface treatment can efficiently change the surface tension between the PDMS and the acrylate resin. According to the Young equation, the contact angle as well as the curvature of the acrylate resin are affected with the change of the surface tension. Therefore, it is feasible to conduct the surface treatment of the PDMS for manipulating the curvature of the acrylate resin in the microholes. Furthermore, the size of the solidified acrylate resin droplet after the UV exposure slightly shrinks and the contact angle is reduced [41]. The influence of the solidification over the change of the contact angle becomes significant with the processing time of the surface treatment.
Fig. 3 (a) The contact angle measured after the UV exposure without the plasma treatment to the PDMS. (b) and (c) The contact angles measured after the UV exposure with the surface treatment to the PDMS for 40 s and 90 s. (d) The influence of the surface treatment to the PDMS over the contact angle.
The concave MLAs fabricated with the surface treatment for 20 s, 60 s and 120 s are shown in Figs. 4(a)-4(c). The profiles of the cross section are illustrated in Fig. 4(d). With the increasing of the time for the surface treatment of the PDMS, the sag height increases and the surface curvature of the acrylate resin in the PDMS microholes becomes large due to the reduction of the contact angle between the acrylate resin and the walls of the PDMS microholes. Figure 4(e) depicts the change of the sag height and the focal length of the MLAs with the time of the surface treatment. If the surface of the PDMS microholes is not modified, the sag height is 3.2 μm. When the PDMS is exposed in the plasma for different processing time, the sag height varies in an almost linear fashion from 3.2 μm to 19.6 μm. The deviation of the sag height is about 12%. Once the sag height is obtained, the focal length can be derived as follows.
where r is the radius of the microhole and n is the refractive index of the acrylate resin. The corresponding focal length of the MLAs changes from –296.3 μm to –67.4 μm and the NA varies from 0.1 to 0.45. Since the relation between the processing time of the surface treatment and the focal length exhibits as an inversely proportional function, the further surface treatment can hardly enforce the change of the focal length. The influence of the deviation of the sag height over the focal length is small especially when the sag height is large.Fig. 4 (a)-(c) SEM images of the concave MLAs fabricated with the surface treatment of 20 s, 60 s and 120 s. (d) The cross-sectional profiles of the fabricated concave MLAs. (e) The influence of the surface treatment over the sag height and the focal length of the fabricated concave MLAs.
In addition, the curvature of the acrylate resin is also determined by the radius of the microholes. Correspondingly, the focal length of the MLAs is affected by the size of the microholes. Figure 5 depicts the predicted and the measured focal length of the MLAs fabricated in the microholes of different sizes. The processing time of the surface treatment is fixed to 60 s. The red dashed curve is based on the theoretical analysis. In the analysis, the focal length is calculated according to the following equation by using the contact angle directly measured when the acrylate resin droplet is on the PDMS substrate.
where θ is the contact angle. The focal length increases with the size of the microholes due to the reduced curvature of the acrylate resin. The variation of the focal length is dominated by the change of the diameter of the microholes which is inversely proportional to the curvature of the acrylate resin-air interface. The blue solid curve presents the measured focal length which is obtained by measuring the sag height and then calculating the curvature of the acrylate resin surface based on Eq. (1). The focal length varies from –96.5 μm to –251.9 μm with the diameter change of the microhole from 60 μm to 200 μm. The deviation of the focal length is within 5%. The insets (α, β and γ) show the cross section of the microlenses formed in the microholes of different sizes. A smooth interface between the air and the acrylate resin can be clearly observed and presents in a spherical curve. The sag height of the microlens formed in the small microhole is slightly short and the surface has a large concave curvature. Thus, the microlens in the small microhole has short focal length. In contrast to the theoretical result, the deviation of the measured focal length becomes apparent especially when the size of the microhole is small. In the miniature microholes, the wetting radius is small and the effect of the line tension whose contribution pointing to the center cannot neglected. The contact angle in the microholes could be described as follows.where σs-g, σs-l and σl-g are the interfacial tension between the PDMS and air, the PDMS and the acrylate resin, and the acrylate resin and air, respectively. τ is the line tension. The contact angle which is affected by the line tension especially when the microhole is in the micro scale [42, 43]. As a result, the contact angle is larger in the microholes comparing to that of the droplet of the relatively larger size in the theoretical analysis. The actual focal length of the MLA is longer than the theoretical prediction. Moreover, to produce a spherical surface of the microlenses, the radius of the microholes should be smaller than , where g is gravity of earth [44]. The measured interfacial tension of the liquid acrylate resin is 31 × 10−3 N/m. Thus, the diameter of the microholes should be no more than 3.5 mm.Fig. 5 The influence of the size of the microholes over the focal length. Insets: α, β and γ are the cross profile of the microlens of different size.
3.2 Optical Feature
To verify the quality of the fabricated MLAs, an imaging experiment was conducted. The experimental setup for imaging is shown in Fig. 6. A white-light light emitting diode (LED) was used as light source for illumination and placed behind a mask. There is a cluster of transparent ‘USST’ letters on the mask. The concave MLA used in the imaging experiment was fabricated under the condition of 60 s surface treatment. The MLA has the focal length of –96.5 μm. The MLA was placed on a translation stage for adjusting the distance to the mask. A CCD mounted with an objective lens was located behind the MLA for capturing the image. An arrayed images of letters ‘USST’ was captured by the CCD on the false focal plane of the MLA, as shown in Fig. 6(b). The letters were uniform and could be clearly visualized, indicating the uniformity of the microlenses and the good imaging property of the MLA.
Fig. 6 (a) Imaging system for testing imaging performance of the fabricated concave MLA. (b) The image array of letter cluster 'USST' on the false focal plane of the concave MLA.
Furthermore, the focusing performance of the replicated convex MLA is verified. The experimental setup is shown in Fig. 7(a). In the experiment, the convex MLA has the focal length of 134 μm. Figures 7(b) and 7(c) show the image of the focused light spots and the intensity distribution of the light spots. The light spots are evenly distributed and have the same peak intensity, which indicates the uniformity of the MLA.
Fig. 7 (a) Imaging system for testing the focusing performance of the replicated convex MLA. (b) The image of the focused light spots. (c) The intensity distribution of the light spots.
4. Conclusion
A cost-effective technique for fabricating MLAs is demonstrated. Concave surface of liquid acrylate resin is formed in the microholes due to the surface tension on the interface of air and acrylate resin. The curvature of the curved surface can be flexibly manipulated by the surface treatment for adjusting the interfacial energy between the acrylate resin and the wall of the microholes. The fabrication process is straightforward and rapid. The size of the microholes affects not only the aperture of the microlenses but also the focal length. The line tension should be taken into account in the prediction of the focal length especially when the microhole is small. The MLAs have uniform structures and the clear images can be observed by using the MLAs in the imaging system. The convex MLAs of the opposite curvature can be obtained by replicating the concave MLAs. The technique for fabricating the MLAs could be applied to manufacture diverse micro devices efficiently.
Acknowledgments
The research work is supported by The National Key Research and Development Program of China (2016YFD0500603); National Natural Science Foundation of China (61601292, 61571287); Shanghai Science and Technology Committee (17JC1400601, 17060502500).
References and links
1. H. Arimoto and B. Javidi, “Integral three-dimensional imaging with digital reconstruction,” Opt. Lett. 26(3), 157–159 (2001). [CrossRef] [PubMed]
2. M. Cho and M. Danshpanah, “Three-dimensional optical sensing and visualization using integral imaging,” Proc. IEEE 99(4), 556–575 (2010).
3. F. Zhang, R. J. Gates, V. S. Smentkowski, S. Natarajan, B. K. Gale, R. K. Watt, M. C. Asplund, and M. R. Linford, “Direct adsorption and detection of proteins, including ferritin, onto microlens array patterned bioarrays,” J. Am. Chem. Soc. 129(30), 9252–9253 (2007). [CrossRef] [PubMed]
4. E. Stankevičius, M. Garliauskas, M. Gedvilas, and G. Račiukaitis, “Bessel-like beam array formation by periodical arrangement of the polymeric round-tip microstructures,” Opt. Express 23(22), 28557–28566 (2015). [CrossRef] [PubMed]
5. E. Stankevicius, M. Garliauskas, M. Gedvilas, N. Tarasenko, and G. Raciukaitis, “Structuring of surfaces with gold nanoparticles by using Bessel-Like beams,” Ann. Phys. (Berlin) 529(12), 170–174 (2017). [CrossRef]
6. F. Wippermann, U. D. Zeitner, P. Dannberg, A. Bräuer, and S. Sinzinger, “Beam homogenizers based on chirped microlens arrays,” Opt. Express 15(10), 6218–6231 (2007). [CrossRef] [PubMed]
7. L. Seifert, J. Liesener, and H. J. Tiziani, “The adaptive shack–hartmann sensor,” Opt. Commun. 216(4–6), 313–319 (2003). [CrossRef]
8. G. Y. Yoon, T. Jitsuno, M. Nakatsuka, and S. Nakai, “Shack Hartmann wave-front measurement with a large F-number plastic microlens array,” Appl. Opt. 35(1), 188–192 (1996). [CrossRef] [PubMed]
9. Z. D. Popovic, R. A. Sprague, and G. A. Connell, “Technique for monolithic fabrication of microlens arrays,” Appl. Opt. 27(7), 1281–1284 (1988). [CrossRef] [PubMed]
10. H. Jung and K. H. Jeong, “Monolithic polymer microlens arrays with high numerical aperture and high packing density,” ACS Appl. Mater. Interfaces 7(4), 2160–2165 (2015). [CrossRef] [PubMed]
11. E. Stankevicius, M. Gedvilas, and G. Raciukaitis, “Investigation of laser-induced polymerization using a smoothly varying intensity distribution,” Appl. Phys. B 119(3), 525–532 (2015). [CrossRef]
12. M. T. Gale, M. Rossi, J. Pedersen, and H. Schuetz, “Fabrication of continuous-relief micro-optical elements by direct laser writing in photoresists,” Opt. Eng. 33(11), 3556–3566 (1994). [CrossRef]
13. M. H. Wu, C. Park, and G. M. Whitesides, “Fabrication of arrays of microlenses with controlled profiles using gray-scale microlens projection photolithography,” Langmuir 18(24), 9312–9318 (2002). [CrossRef]
14. C. P. Lin, H. Yang, and C. K. Chao, “A new microlens array fabrication method using UV proximity printing,” J. Micromech. Microeng. 13(5), 748–757 (2003). [CrossRef]
15. Y. Lu and S. C. Chen, “Direct write of microlens array using digital projection photopolymerization,” Appl. Phys. Lett. 92(4), 041109 (2008). [CrossRef]
16. K. Totsu, K. Fujishiro, S. Tanaka, and M. Esashi, “Fabrication of three-dimensional microstructure using maskless gray-scale lithography,” Sens. Actuators A Phys. 130–131, 387–392 (2006). [CrossRef]
17. S. I. Chang and J. B. Yoon, “Shape-controlled, high fill-factor microlens arrays fabricated by a 3D diffuser lithography and plastic replication method,” Opt. Express 12(25), 6366–6371 (2004). [CrossRef] [PubMed]
18. B. Hao, H. Liu, F. Chen, Q. Yang, P. Qu, G. Du, J. Si, X. Wang, and X. Hou, “Versatile route to gapless microlens arrays using laser-tunable wet-etched curved surfaces,” Opt. Express 20(12), 12939–12948 (2012). [CrossRef] [PubMed]
19. Y. Ou, Q. Yang, F. Chen, Z. F. Deng, G. Q. Du, J. H. Wang, H. Bian, J. L. Yong, and X. Hou, “Direct fabrication of microlens arrays on PMMA with laser-induced structural modification,” IEEE Photonics Technol. Lett. 27(21), 2253–2256 (2015). [CrossRef]
20. C. H. Lin, L. Jiang, Y. H. Chai, H. Xiao, S. J. Chen, and H. L. Tsai, “Fabrication of microlens arrays in photosensitive glass by femtosecond laser direct writing,” Appl. Phys., A Mater. Sci. Process. 97(4), 751–757 (2009). [CrossRef]
21. J. Yong, F. Chen, Q. Yang, G. Du, H. Bian, D. Zhang, J. Si, F. Yun, and X. Hou, “Rapid fabrication of large-area concave microlens arrays on PDMS by a femtosecond laser,” ACS Appl. Mater. Interfaces 5(19), 9382–9385 (2013). [CrossRef] [PubMed]
22. S. Tong, H. Bian, Q. Yang, F. Chen, Z. Deng, J. Si, and X. Hou, “Large-scale high quality glass microlens arrays fabricated by laser enhanced wet etching,” Opt. Express 22(23), 29283–29291 (2014). [CrossRef] [PubMed]
23. C. Jiang, X. Li, H. Tian, C. Wang, J. Shao, Y. Ding, and L. Wang, “Lateral flow through a parallel gap driven by surface hydrophilicity and liquid edge pinning for creating microlens array,” ACS Appl. Mater. Interfaces 6(21), 18450–18456 (2014). [CrossRef] [PubMed]
24. S. Surdo, A. Diaspro, and M. Duocastella, “Microlens fabrication by replica molding of frozen laser-printed droplets,” Appl. Surf. Sci. 418, 554–558 (2016). [CrossRef]
25. C. Florian, S. Piazza, A. Diaspro, P. Serra, and M. Duocastella, “Direct laser printing of tailored polymeric microlenses,” ACS Appl. Mater. Interfaces 8(27), 17028–17032 (2016). [CrossRef] [PubMed]
26. J. Y. Kim, N. B. Brauer, V. Fakhfouri, D. L. Boiko, E. Charbon, G. Grutzner, and J. Brugger, “Hybrid polymer microlens arrays with high numerical apertures fabricated using simple ink-jet printing technique,” Opt. Mater. Express 2(1), 259–269 (2011). [CrossRef]
27. Y. Luo, L. Wang, Y. C. Ding, H. F. Wei, X. Q. Hao, D. D. Wang, Y. Dai, and J. F. Shic, “Direct fabrication of microlens arrays with high numerical aperture by ink-jetting on nanotextured surface,” Appl. Surf. Sci. 279, 36–40 (2013). [CrossRef]
28. W. L. Wader Jr, R. J. Mammone, and M. Binder, “Surface properties of commercial polymer films following various gas plasma treatments,” J. Appl. Polym. Sci. 43(9), 1589–1591 (1991). [CrossRef]
29. D. Zhang, Q. Xu, C. Fang, K. Wang, X. Wang, S. Zhuang, and B. Dai, “Fabrication of a microlens array with controlled curvature by thermally curving photosensitive gel film beneath microholes,” ACS Appl. Mater. Interfaces 9(19), 16604–16609 (2017). [CrossRef] [PubMed]
30. X. Li, Y. Ding, J. Shao, H. Liu, and H. Tian, “Fabrication of concave microlens arrays using controllable dielectrophoretic force in template holes,” Opt. Lett. 36(20), 4083–4085 (2011). [CrossRef] [PubMed]
31. X. Li, Y. Ding, J. Shao, H. Tian, and H. Liu, “Fabrication of microlens arrays with well-controlled curvature by liquid trapping and electrohydrodynamic deformation in microholes,” Adv. Mater. 24(23), OP165 (2012). [PubMed]
32. X. Li, H. Tian, Y. Ding, J. Shao, and Y. Wei, “Electrically templated dewetting of a UV-Curable prepolymer film for the fabrication of a concave microlens array with well-defined curvature,” ACS Appl. Mater. Interfaces 5(20), 9975–9982 (2013). [CrossRef] [PubMed]
33. X. M. Li, H. M. Tian, J. Y. Shao, Y. C. Ding, X. L. Chen, L. Wang, and B. G. Lu, “Decreasing the saturated contact angle in electrowettingon-dielectrics by controlling the charge trapping at liquid–solid interfaces,” Adv. Funct. Mater. 26(18), 2994–3002 (2016). [CrossRef]
34. A. Tripathi, T. V. Chokshi, and N. Chronis, “A high numerical aperture, polymer-based, planar microlens array,” Opt. Express 17(22), 19908–19918 (2009). [CrossRef] [PubMed]
35. P. C. Chen, Y. P. Chang, R. H. Zhang, C. C. Wu, and G. R. Tang, “Microfabricated microfluidic platforms for creating microlens array,” Opt. Express 25(14), 16101–16115 (2017). [CrossRef] [PubMed]
36. C. Fang, B. Dai, R. Zhuo, X. Yuan, X. Gao, J. Wen, B. Sheng, and D. Zhang, “Focal-length-tunable elastomer-based liquid-filled plano-convex mini lens,” Opt. Lett. 41(2), 404–407 (2016). [CrossRef] [PubMed]
37. B. C. Prorok, F. Barthelat, C. S. Korach, K. J. Grande-Allen, E. Lipke, G. Lykofatitits, and P. Zavattieri, Mechanics of Biological Systems and Materials, Vol. 5 (Mechanics, 2011).
38. H. T. Kim and O. C. Jeong, “PDMS surface modification using atmospheric pressure plasma,” Microelectron. Eng. 88(8), 2281–2285 (2011). [CrossRef]
39. V. Barbier, M. Tatoulian, H. Li, F. Arefi-Khonsari, A. Ajdari, and P. Tabeling, “Stable modification of PDMS surface properties by plasma polymerization: application to the formation of double emulsions in microfluidic systems,” Langmuir 22(12), 5230–5232 (2006). [CrossRef] [PubMed]
40. R. Tadmor, “Line energy, line tension and drop size,” Surf. Sci. 602(14), L108–L111 (2008). [CrossRef]
41. J. Fukai, H. Ishizuka, Y. Sakai, M. Kaneda, M. Morita, and A. Takahara, “Effects of droplet size and solute concentration on drying process of polymer solution droplets deposited on homogeneous surfaces,” Int. J. Heat Mass Transfer 49(19–20), 3561–3567 (2006). [CrossRef]
42. J. Drelich and J. D. Miller, “The effect of solid surface heterogeneity and roughness on the contact angle/drop (bubble) size relationship,” J. Colloid Interface Sci. 164(1), 252–259 (1994). [CrossRef]
43. A. Amirfazli, D. Y. Kwok, J. Gaydos, and A. W. Neumann, “Line tension measurements through drop size dependence of contact angle,” J. Colloid Interface Sci. 205(1), 1–11 (1998). [CrossRef] [PubMed]
44. P. G. de Gennes, and F. B. W. D. Quere, Capillarity and Wetting Phenomena (Classical Continuum Physics, 2004).
