Simulation, fabrication, and characterization of a tunable electrowetting-based lens with a wedge-shaped PDMS dielectric layer Mohammadreza Salehi Moghaddam,1 H. Latifi,1,2,* Hamidreza Shahraki,1 and Mohammad Sadegh Cheri1,2 1
Laser & Plasma Research Institute, Shahid Beheshti University, 1983963113 Evin, Tehran, Iran 2
Department of Physics, Shahid Beheshti University, 1983963113 Evin, Tehran, Iran *Corresponding author: [email protected]
Received 22 September 2014; revised 24 February 2015; accepted 25 February 2015; posted 25 February 2015 (Doc. ID 223580); published 31 March 2015
Microlenses with tunable focal length have wide applications in optofluidic devices. This work presents a numerical and experimental investigation on a tunable electrowetting-based concave lens. Optical properties such as focal length of the lens and visibility of images were investigated numerically and experimentally. A finite element analysis and a ZEMAX simulation were used for determination of surface profile and focal length of the lens. The results show that the theoretical surface profile and focal length of the lens are in good agreement with the experimental ones. The lens has a wide tuning focal length equal to 6.5 (cm). Because the polydimethylsiloxane (PDMS) layer is wedge shaped (as both the dielectric and hydrophobic layers), lower applied voltage is needed. A commercial program was used to find the focal length of the lens from maximum visibility value by tuning the applied voltage. © 2015 Optical Society of America OCIS codes: (080.3630) Lenses; (100.2960) Image analysis. http://dx.doi.org/10.1364/AO.54.003010
1. Introduction
In recent years, considerable effort has been devoted to the emerging multidisciplinary field of optofluidics. This field benefits from the advantages of microfluidics and optics and provides new opportunities and functionalities, such as optical reconfigurability and tunability for optofluidic devices. Optofluidic devices are therefore used for generating, manipulating, and controlling optical properties by fluid control [1–4]. Using an external field in optofluidic devices has resulted in the development of tunable optofluidic components such as optical switches [5,6], dye lasers [7], waveguides [8–10], gratings [11] prisms [12,13], and tunable microlenses [14–19].
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Optofluidic lenses are important components in optofluidic devices, which can be used in phone cameras [20–22], flow cytometry [23,24], single molecule detection [25], and refractive index measurement [26]. A tunable microlens (TML) can tune focal length [27], intensity [28], shape [29], direction, and polarization of incident light [30]. The tuning mechanism includes variation of refractive index and variation of surface curvature of the TML. The variation of refractive index is usually used in liquid-crystal lenses (LCLs). LCLs are based on spatial distribution variation of the refractive index in the nonuniform electric field. An LCL needs a liquid that is nonisotropic [31]. TMLs that are based on variation of surface curvature are divided into two categories. In the first category, a fluid volume (liquid or gas) is sealed in a cavity that includes a deformable membrane. The focal length of the lens changes
with the change in the surface curvature of the deformable membrane. By adjusting the internal pressure of the sealed liquid, the surface curvature of the deformable membrane is adjusted. Therefore, the deformable membrane acts like a TML. The deformation of the membrane can be actuated by hydropneumatic [32,33], thermopneumatic [34], electromagnetic [35], stimulus responsive hydrogels [36], photo-active polymers [37], and piezoelectric [38]. The second category is changing the interface curvature of two immiscible liquids sealed in a chamber using an electrowetting mechanism [21,39–42]. In an electrowetting-based lens, the focal length is adjusted by applying voltage to the chamber. Due to the applied voltage, the interface of the two immiscible liquids changes and results in a lens with a tunable focal length. This type of lens has attracted many researchers due to its interesting applications [21,22, 41,42]. Berge and Peseux [41] presented a variable focal lens that worked by controlling the shape of a drop resulting from change in the applied voltage. Kuiper and co-workers [21,22] presented a liquid lens consisting of two immiscible liquids for miniature cameras. Hsieh and Chen [42] indicated the ability of the electrowetting mechanism for controlling the lens profile during microlens fabrication using electrically conductive UV-curable polymer. In this paper, we present a tunable electrowettingbased lens with a wedge-shaped polydimethylsiloxane (PDMS) layer. The PDMS layer acts as both a dielectric and a hydrophobic layer. Operational principals are provided in Section 2. The fabrication process of the electrowetting lens is explained in Section 3. Finally, numerical and experimental results are discussed in Section 4. 2. Operational Principles A.
with the wall curve the interface of the two liquids, as shown in Fig. 1. This curvature of the interface acts like a lens. Figure 1(b) shows the optical rays that pass through the interface of the lens. The contact angle (θ) of the interface with the wall is determined by the balance of the forces at the contact point and is given by Young’s equation [43]. By applying a voltage to the wall, the surface energy of each liquid with the wall is modified and, therefore, the contact angle of the interface changes. Thus, the deformation of the interface changes the focal length of the lens and the direction of the optical rays. In fact, this lens set that includes two liquids and a cylindrical housing creates a capacitor with a given stored energy. When a potential difference is applied to the electrodes of the chamber, an electrostatic force attracts the upper liquid toward the lower liquid and alters the curvature of the interface. By using a minimum-energy approach, the new angle contact is determined by [41] cosθ cosθ0
(1)
where θ0 , εd , ε0 , d, γ, and V are the initial contact angle at zero voltage, permittivity of the insulating layer, permittivity of free space, wall thickness (PDMS), surface tension of the liquid–liquid interface, and the applied voltage, respectively. B. Optical Characterization
1. Focal Length As mentioned above, changing the voltage applied to the electrodes alters the interface of the two immiscible liquids and therefore creates a TML with variable focal length. The focal length of the lens can be obtained as follows [44]: 1 Δn ; f R
Electrowetting Principle
Two immiscible liquids including water (conductive sample) and oil (nonconductive sample) with different refractive indices and approximately the same densities are confined in a chamber. Figure 1 shows a cross section of the electrowetting-based lens at applied voltage of 0 V. Competition in surface energy between the two liquids and between each liquid
εd ε0 2 V ; 2dγ
(2)
where Δn and R are the refractive index difference and the curvature radius of the liquid interface, respectively. The surface profile a lens can be fitted by an aspherical profile as follows [45]: Z
Rr2 p ; 1 1 − R2 r2 1 K
(3)
where Z is the coordinate of the aspherical surface, r is the radial coordinate, K is the conic constant, and R is the curvature. The lens has a spherical profile if K 0 and a parabolic profile if K −1. The lens is a hyperboloid if K < −1, and an oblate ellipsoid if K > 0. Fig. 1. Interface of oil and water acts like a lens. (a) Electrowetting-based lens at applied voltage of 0 V. (b) Schematic view of the electrowetting-based lens and optical rays.
2. Visibility The visibility of gray images can be evaluated from image contrast as follows [44]: 1 April 2015 / Vol. 54, No. 10 / APPLIED OPTICS
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V
I max − I min ; I max I min
(4)
where I max and I min are the maximum and minimum intensities of the gray image, respectively. For a black and white image, I max 255 and I min 0. However, for a gray-scale image, these values are between 0 and 255 and, therefore, the visibility value is between 0 < V < 1. The values of 0 and 1 indicate blurred and sharp images, respectively [46]. 3. Fabrication Process
Two chambers were designed and were fabricated to obtain the profile and optical properties of the electrowetting lens. Figure 2 shows the schematic design of a glassy cuvette to obtain the lens profile. The cuvette consists of four glass lamellae. All the lamellae were cleaned by acetone and 2-propanol. Two lateral lamellae were coated by copper (Cu) with 70 nm thickness using the physical vapor deposition method. Then, all the lamellae were coated by a mixture of PDMS (weight ratio of 10∶1 (base: hardener, Dow Corning Corp., USA) using a deep coating method. The PDMS layer acts as a hydrophobic and dielectric layer. Figure 3 shows the chamber design used to obtain the optical properties of the lens. The chamber consists of a conductive cylinder with 10 mm height, and inside and outside diameters of 4 mm and 15 mm, respectively. The inside wall of the conductive cylinder was coated with the PDMS solution using the deep coating method. A lamella with 50 nm indium–tin oxide (ITO) coating was placed just below the conductive cylinder (copper). Finally, a 1 mm thick circuit board with a copper layer with a 4 mm diameter hole was placed between the conductive cylinder and the ITO plate. Both sides of the circuit board have a copper layer. The inside of the conductive cylinder was filled with the two immiscible liquids of oil and water with equal volume.
Fig. 2. Schematic design of the glassy cuvette: (a) 3D view and (b) lateral view. 3012
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Fig. 3. Chamber used to obtain the optical properties of the lens: (a) exploded view and (b) assembled view.
4. Results and Discussion A. Measurement of Interface Curvature
The variation of contact angle of the interface with the inside wall of the conductive cylinder was investigated experimentally by applying a voltage range of 0–300 V to the electrodes of the glassy cuvette. The cross-section images of the interface were captured by a digital minimicroscope (Smart-eye) and sent to the PC. A LabVIEW image-processing toolkit was used to record and analyze the captured images to obtain the contact angle. The image-processing program detected the edges of the interface and PDMS layer and fitted an imaginary line on the edges. A second-order polynomial as y A Bx2 was fitted on the detected edges of the interface by using Mathematica software, and the A and B values were extracted as A 0.935 and B 7.95 × 10−6 . According to Eq. (1), with the given values of γ, ε0 , and εd , the thickness of the PDMS layer was obtained as 53.3 μm. Finite element analysis was performed by COMSOL Multiphysics software to obtain the interface of the oil and water at applied voltages of 0–300 V. The parameters used for simulation of the interface of the lens at 20°C are shown in Table 1. Figure 4 shows the interface of the oil and water. The figure shows that, with the increase of the applied voltage, the curvature gradually reduces. By using the image processing program, the experimental and numerical values of the contact angle were obtained and compared. Figure 5 shows the comparison of the cosθ versus the applied voltage.
Table 1.
Parameters Required for Simulation of the Interface of the Lensa
Parameters Dynamic viscosity of oil Dynamic viscosity of water Oil density Water density Refractive index of oil Refractive index of water
Value (unit) 8 × 10−2 Pa:s 1.5 × 10−3 Pa:s 920 kg∕m3 1000 kg∕m3 1.46 1.33
a
Standard conditions of 20°C and 1 atm.
bottom of the inside wall of the conductive cylinder. The PDMS layer has a wedge shape with 42 and 61 μm thickness at the top and bottom of the inside wall of the conductive cylinder. By applying voltage to the electrodes, the interface is placed in a new PDMS thickness. The difference between simulation and experimental results in Fig. 5 is due to the vertical movement of the interface near the chamber wall. According to Fig. 5, the wedge-shaped PDMS layer has a maximum of 37% effect on the contact angle of the interface with the chamber wall at 300 V. According to Eq. (1), this is equal to a decrease of about 6% of the applied voltage. In other words, using a wedged-shape PDMS layer is useful in reduction of the applied voltage. B. Measurement of Focal Length
Fig. 4. Simulation of the interface curvature at applied voltages of 0 to 300 V.
As can be seen, the simulated and experimental graphs have good agreement and the values of θ decrease with the increase of applied voltage. Since the PDMS layer of the inside wall of the conductive cylinder was coated by using the deep-coating method, the PDMS layer has variable thickness from top to
Fig. 5. Comparison of experimental and numerical variation of cosθ versus the applied voltage.
The image of the interface of the oil and water was digitized using PlotDigitizer software. The digitized data were imported to Mathematica software. Figure 6 shows the digitized data obtained from the captured images at voltages of 0, 80, and 300 V. Equation (3) was fitted to the digitized data and values R and K were achieved for various applied voltages. Figure 7 shows a comparison of variation of the values R and K versus the applied voltage. Values R and K increase with the growth of the applied voltage. As mentioned, the difference between the simulated and experimental graphs is due to the wedge shape of the PDMS layer. Equation (3) with obtained values of R and K was imported into the ZEMAX ray-tracing program (ZEMAX Development Corp., Bellevue, Wash.) to obtain the profile and focal length of the lens. Figure 8 illustrates the profile of the lens versus the applied voltage using the ZEMAX ray-tracing program. As in the COMSOL simulations (Fig. 4), with the increase of voltage the curvature gradually reduces. Figure 9 shows the focal length versus applied voltage. As can be seen, with the increase of the applied voltage, the magnitude of the focal length is increased and the lens has a large dynamic focal length of 6.5 cm at applied voltage of 0 to 300 V. Figure 9 also shows that the theoretical focal length of the lens obtained from
Fig. 6. Digitized data of curvature profile for 0, 80, and 300 V. 1 April 2015 / Vol. 54, No. 10 / APPLIED OPTICS
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Fig. 9. Comparison of simulation and experimental variation of focal length versus applied voltage.
electrowetting lens. Also, the distance between the electrowetting lens and the digital minimicroscope is 2 cm. At first, the image of the person was focused on the digital minimicroscope at 0 V applied voltage. Then, by changing the applied voltage to 240 V, the sharp image of the needle was projected on the digital minimicroscope, and, finally, with reduction of applied voltage to 0 V, the sharp image of the person appeared on the digital minimicroscope again. Figure 10 shows the images of the needle and person on the digital minimicroscope at applied voltages of 0–240 V. C.
Fig. 7. Comparison of variation of values (a) R and (b) K versus the applied voltage.
the ZEMAX ray-tracing program has behavior similar to the experimental one. The ability of the lens to focus on two objects was demonstrated by projecting the images of two objects on the digital minimicroscope at applied voltages of 0 and 240 V. The objects are a needle and a person located at distances of 4.5 cm and 2.5 m from the
Fig. 8. Change of the interface curvature versus applied voltage obtained from the ZEMAX simulation. 3014
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Spot Size of Laser Beam
Another experiment was conducted to investigate the variation of the spot size of a laser beam versus the applied voltage. Figure 11 shows the schematic setup of the experiment for this purpose. After passing through a polarizer, mirror, and the fabricated electrowetting lens, an He–Ne laser beam (λ 633 nm) was focused on a CCD camera by an objective lens (10×). The polarizer is used to control the intensity of the laser to avoid saturation of the CCD camera. We adjusted the setup at 0 V to obtain the minimum value of the spot size of the laser beam.
Fig. 10. Images of the needle and the person projected on the digital minimicroscope at voltages of (a) 0, (b) 240, and (c) 0 V applied to the electrowetting lens.
Fig. 13. Evaluation of visibility by LabVIEW at the red dashed line.
Fig. 11. Schematic setup for the spot size measurement of the laser beam.
With the increase of the applied voltage, the spot size increases. The image of the spot size on the CCD camera was analyzed by LabVIEW, and variation of the spot size is illustrated in Fig. 12. D.
Visibility
For investigation of the visibility of the images captured by the digital minimicroscope, a photo including a square grid pattern is placed at a distance of 4.73 cm from the electrowetting lens, and the image of the pattern is focused on the digital minimicroscope at a distance of 2.76 cm. The pattern has maximum visibility at applied voltage of zero (the setup was set at 0 V to obtain the maximum value of visibility). Then by applying the voltage, the visibility of the image decreased and the image was blurred.
Fig. 12. Variation of spot size of the laser beam versus applied voltage.
Figure 13 shows the image of the pattern on the CCD camera. Using the LabVIEW program, the variation of visibility with applied voltage was calculated in direction of the red dashed line in Fig. 13. Figure 14 shows the variation of visibility versus increasing and decreasing the applied voltage. The increasing and decreasing graph has 7% hysteresis. Since the best focal length of the lens is equal to the maximum value of the image visibility, our LabVIEW program is able to find the sharp images of objects in real time by tuning the applied voltage. E. Distortion
As shown in Fig. 13, there is a barrel distortion in the square grid pattern that results from the lens design (the lens has various focal lengths and magnifications in different areas). Apart from the lens design, the degree of distortion is related to the focal length, and, usually, for lenses with short focal length, there is a larger degree of barrel distortion [47]. We employed the mathematical model used in the Ref. [47] for correction of the distortion in the square grid pattern, and a first-order distortion parameter (k1 ) was obtained about −8.2 × 10−6 pixels−2 . A MATLAB code was developed based on the mathematical model and applied to the distorted
Fig. 14. Variation of visibility versus increasing and decreasing the applied voltage. 1 April 2015 / Vol. 54, No. 10 / APPLIED OPTICS
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4. 5. 6. 7. Fig. 15. (a) Barrel-shaped distortion in the square grid pattern and (b) correction of the barrel-shaped distortion after using MATLAB code.
image in Fig. 13. Figure 15 shows the distorted and the corrected images. The barrel-shaped distortion in the square grid pattern seen in Fig. 15(a) is corrected in Fig. 15(b).
8. 9.
10. 11.
5. Conclusion
A numerical and experimental investigation was performed on a tunable electrowetting lens with a wedge-shaped PDMS dielectric layer. The optical properties of the lens, such as focal length and visibility of images, were investigated experimentally by changing the voltage applied to the lens. FEA along with ZEMAX simulations were used to obtain the curvature, R, and conic constant, K, as well as the focal length of the lens. The simulation and experimental results have similar behavior. The lens was fabricated using a simple method. A LabVIEW image-processing program was used to detect the surface profile of the lens. The experimental results show that the lens has a wide tuning range of focal length equal to 6.5 cm, and the focal length has a quadratic behavior versus the applied voltage. The wedge-shaped PDMS layer decreases the voltage applied to the lens. The experimental results also show that the visibility of images decreases, and the spot size of the laser beam and the magnitude of the focal length of the lens increase with increase of the applied voltage. A MATLAB code was developed for correction of barrel-shaped distortion of the images. The LabVIEW program can obtain the focal length from the maximum value of visibility in real time by tuning the applied voltage. The authors gratefully acknowledge Dr. Arash Moradi for his editorial comments and discussions to improve the quality of the paper. References 1. D. Psaltis, S. R. Quake, and C. Yang, “Developing optofluidic technology through the fusion of microfluidics and optics,” Nature 442, 381–386 (2006). 2. C. Monat, P. Domachuk, and B. J. Eggleton, “Integrated optofluidics: a new river of light,” Nat. Photonics 1, 106–114 (2007). 3. C. Monat, P. Domachuk, C. Grillet, M. Collins, B. J. Eggleton, M. Cronin-Golomb, S. Mutzenich, T. Mahmud, G. Rosengarten, and A. Mitchell, “Optofluidics: a novel generation of 3016
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Laser & Plasma Research Institute, Shahid Beheshti University, 1983963113 Evin, Tehran, Iran 2
Department of Physics, Shahid Beheshti University, 1983963113 Evin, Tehran, Iran *Corresponding author: [email protected]
Received 22 September 2014; revised 24 February 2015; accepted 25 February 2015; posted 25 February 2015 (Doc. ID 223580); published 31 March 2015
Microlenses with tunable focal length have wide applications in optofluidic devices. This work presents a numerical and experimental investigation on a tunable electrowetting-based concave lens. Optical properties such as focal length of the lens and visibility of images were investigated numerically and experimentally. A finite element analysis and a ZEMAX simulation were used for determination of surface profile and focal length of the lens. The results show that the theoretical surface profile and focal length of the lens are in good agreement with the experimental ones. The lens has a wide tuning focal length equal to 6.5 (cm). Because the polydimethylsiloxane (PDMS) layer is wedge shaped (as both the dielectric and hydrophobic layers), lower applied voltage is needed. A commercial program was used to find the focal length of the lens from maximum visibility value by tuning the applied voltage. © 2015 Optical Society of America OCIS codes: (080.3630) Lenses; (100.2960) Image analysis. http://dx.doi.org/10.1364/AO.54.003010
1. Introduction
In recent years, considerable effort has been devoted to the emerging multidisciplinary field of optofluidics. This field benefits from the advantages of microfluidics and optics and provides new opportunities and functionalities, such as optical reconfigurability and tunability for optofluidic devices. Optofluidic devices are therefore used for generating, manipulating, and controlling optical properties by fluid control [1–4]. Using an external field in optofluidic devices has resulted in the development of tunable optofluidic components such as optical switches [5,6], dye lasers [7], waveguides [8–10], gratings [11] prisms [12,13], and tunable microlenses [14–19].
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Optofluidic lenses are important components in optofluidic devices, which can be used in phone cameras [20–22], flow cytometry [23,24], single molecule detection [25], and refractive index measurement [26]. A tunable microlens (TML) can tune focal length [27], intensity [28], shape [29], direction, and polarization of incident light [30]. The tuning mechanism includes variation of refractive index and variation of surface curvature of the TML. The variation of refractive index is usually used in liquid-crystal lenses (LCLs). LCLs are based on spatial distribution variation of the refractive index in the nonuniform electric field. An LCL needs a liquid that is nonisotropic [31]. TMLs that are based on variation of surface curvature are divided into two categories. In the first category, a fluid volume (liquid or gas) is sealed in a cavity that includes a deformable membrane. The focal length of the lens changes
with the change in the surface curvature of the deformable membrane. By adjusting the internal pressure of the sealed liquid, the surface curvature of the deformable membrane is adjusted. Therefore, the deformable membrane acts like a TML. The deformation of the membrane can be actuated by hydropneumatic [32,33], thermopneumatic [34], electromagnetic [35], stimulus responsive hydrogels [36], photo-active polymers [37], and piezoelectric [38]. The second category is changing the interface curvature of two immiscible liquids sealed in a chamber using an electrowetting mechanism [21,39–42]. In an electrowetting-based lens, the focal length is adjusted by applying voltage to the chamber. Due to the applied voltage, the interface of the two immiscible liquids changes and results in a lens with a tunable focal length. This type of lens has attracted many researchers due to its interesting applications [21,22, 41,42]. Berge and Peseux [41] presented a variable focal lens that worked by controlling the shape of a drop resulting from change in the applied voltage. Kuiper and co-workers [21,22] presented a liquid lens consisting of two immiscible liquids for miniature cameras. Hsieh and Chen [42] indicated the ability of the electrowetting mechanism for controlling the lens profile during microlens fabrication using electrically conductive UV-curable polymer. In this paper, we present a tunable electrowettingbased lens with a wedge-shaped polydimethylsiloxane (PDMS) layer. The PDMS layer acts as both a dielectric and a hydrophobic layer. Operational principals are provided in Section 2. The fabrication process of the electrowetting lens is explained in Section 3. Finally, numerical and experimental results are discussed in Section 4. 2. Operational Principles A.
with the wall curve the interface of the two liquids, as shown in Fig. 1. This curvature of the interface acts like a lens. Figure 1(b) shows the optical rays that pass through the interface of the lens. The contact angle (θ) of the interface with the wall is determined by the balance of the forces at the contact point and is given by Young’s equation [43]. By applying a voltage to the wall, the surface energy of each liquid with the wall is modified and, therefore, the contact angle of the interface changes. Thus, the deformation of the interface changes the focal length of the lens and the direction of the optical rays. In fact, this lens set that includes two liquids and a cylindrical housing creates a capacitor with a given stored energy. When a potential difference is applied to the electrodes of the chamber, an electrostatic force attracts the upper liquid toward the lower liquid and alters the curvature of the interface. By using a minimum-energy approach, the new angle contact is determined by [41] cosθ cosθ0
(1)
where θ0 , εd , ε0 , d, γ, and V are the initial contact angle at zero voltage, permittivity of the insulating layer, permittivity of free space, wall thickness (PDMS), surface tension of the liquid–liquid interface, and the applied voltage, respectively. B. Optical Characterization
1. Focal Length As mentioned above, changing the voltage applied to the electrodes alters the interface of the two immiscible liquids and therefore creates a TML with variable focal length. The focal length of the lens can be obtained as follows [44]: 1 Δn ; f R
Electrowetting Principle
Two immiscible liquids including water (conductive sample) and oil (nonconductive sample) with different refractive indices and approximately the same densities are confined in a chamber. Figure 1 shows a cross section of the electrowetting-based lens at applied voltage of 0 V. Competition in surface energy between the two liquids and between each liquid
εd ε0 2 V ; 2dγ
(2)
where Δn and R are the refractive index difference and the curvature radius of the liquid interface, respectively. The surface profile a lens can be fitted by an aspherical profile as follows [45]: Z
Rr2 p ; 1 1 − R2 r2 1 K
(3)
where Z is the coordinate of the aspherical surface, r is the radial coordinate, K is the conic constant, and R is the curvature. The lens has a spherical profile if K 0 and a parabolic profile if K −1. The lens is a hyperboloid if K < −1, and an oblate ellipsoid if K > 0. Fig. 1. Interface of oil and water acts like a lens. (a) Electrowetting-based lens at applied voltage of 0 V. (b) Schematic view of the electrowetting-based lens and optical rays.
2. Visibility The visibility of gray images can be evaluated from image contrast as follows [44]: 1 April 2015 / Vol. 54, No. 10 / APPLIED OPTICS
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V
I max − I min ; I max I min
(4)
where I max and I min are the maximum and minimum intensities of the gray image, respectively. For a black and white image, I max 255 and I min 0. However, for a gray-scale image, these values are between 0 and 255 and, therefore, the visibility value is between 0 < V < 1. The values of 0 and 1 indicate blurred and sharp images, respectively [46]. 3. Fabrication Process
Two chambers were designed and were fabricated to obtain the profile and optical properties of the electrowetting lens. Figure 2 shows the schematic design of a glassy cuvette to obtain the lens profile. The cuvette consists of four glass lamellae. All the lamellae were cleaned by acetone and 2-propanol. Two lateral lamellae were coated by copper (Cu) with 70 nm thickness using the physical vapor deposition method. Then, all the lamellae were coated by a mixture of PDMS (weight ratio of 10∶1 (base: hardener, Dow Corning Corp., USA) using a deep coating method. The PDMS layer acts as a hydrophobic and dielectric layer. Figure 3 shows the chamber design used to obtain the optical properties of the lens. The chamber consists of a conductive cylinder with 10 mm height, and inside and outside diameters of 4 mm and 15 mm, respectively. The inside wall of the conductive cylinder was coated with the PDMS solution using the deep coating method. A lamella with 50 nm indium–tin oxide (ITO) coating was placed just below the conductive cylinder (copper). Finally, a 1 mm thick circuit board with a copper layer with a 4 mm diameter hole was placed between the conductive cylinder and the ITO plate. Both sides of the circuit board have a copper layer. The inside of the conductive cylinder was filled with the two immiscible liquids of oil and water with equal volume.
Fig. 2. Schematic design of the glassy cuvette: (a) 3D view and (b) lateral view. 3012
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Fig. 3. Chamber used to obtain the optical properties of the lens: (a) exploded view and (b) assembled view.
4. Results and Discussion A. Measurement of Interface Curvature
The variation of contact angle of the interface with the inside wall of the conductive cylinder was investigated experimentally by applying a voltage range of 0–300 V to the electrodes of the glassy cuvette. The cross-section images of the interface were captured by a digital minimicroscope (Smart-eye) and sent to the PC. A LabVIEW image-processing toolkit was used to record and analyze the captured images to obtain the contact angle. The image-processing program detected the edges of the interface and PDMS layer and fitted an imaginary line on the edges. A second-order polynomial as y A Bx2 was fitted on the detected edges of the interface by using Mathematica software, and the A and B values were extracted as A 0.935 and B 7.95 × 10−6 . According to Eq. (1), with the given values of γ, ε0 , and εd , the thickness of the PDMS layer was obtained as 53.3 μm. Finite element analysis was performed by COMSOL Multiphysics software to obtain the interface of the oil and water at applied voltages of 0–300 V. The parameters used for simulation of the interface of the lens at 20°C are shown in Table 1. Figure 4 shows the interface of the oil and water. The figure shows that, with the increase of the applied voltage, the curvature gradually reduces. By using the image processing program, the experimental and numerical values of the contact angle were obtained and compared. Figure 5 shows the comparison of the cosθ versus the applied voltage.
Table 1.
Parameters Required for Simulation of the Interface of the Lensa
Parameters Dynamic viscosity of oil Dynamic viscosity of water Oil density Water density Refractive index of oil Refractive index of water
Value (unit) 8 × 10−2 Pa:s 1.5 × 10−3 Pa:s 920 kg∕m3 1000 kg∕m3 1.46 1.33
a
Standard conditions of 20°C and 1 atm.
bottom of the inside wall of the conductive cylinder. The PDMS layer has a wedge shape with 42 and 61 μm thickness at the top and bottom of the inside wall of the conductive cylinder. By applying voltage to the electrodes, the interface is placed in a new PDMS thickness. The difference between simulation and experimental results in Fig. 5 is due to the vertical movement of the interface near the chamber wall. According to Fig. 5, the wedge-shaped PDMS layer has a maximum of 37% effect on the contact angle of the interface with the chamber wall at 300 V. According to Eq. (1), this is equal to a decrease of about 6% of the applied voltage. In other words, using a wedged-shape PDMS layer is useful in reduction of the applied voltage. B. Measurement of Focal Length
Fig. 4. Simulation of the interface curvature at applied voltages of 0 to 300 V.
As can be seen, the simulated and experimental graphs have good agreement and the values of θ decrease with the increase of applied voltage. Since the PDMS layer of the inside wall of the conductive cylinder was coated by using the deep-coating method, the PDMS layer has variable thickness from top to
Fig. 5. Comparison of experimental and numerical variation of cosθ versus the applied voltage.
The image of the interface of the oil and water was digitized using PlotDigitizer software. The digitized data were imported to Mathematica software. Figure 6 shows the digitized data obtained from the captured images at voltages of 0, 80, and 300 V. Equation (3) was fitted to the digitized data and values R and K were achieved for various applied voltages. Figure 7 shows a comparison of variation of the values R and K versus the applied voltage. Values R and K increase with the growth of the applied voltage. As mentioned, the difference between the simulated and experimental graphs is due to the wedge shape of the PDMS layer. Equation (3) with obtained values of R and K was imported into the ZEMAX ray-tracing program (ZEMAX Development Corp., Bellevue, Wash.) to obtain the profile and focal length of the lens. Figure 8 illustrates the profile of the lens versus the applied voltage using the ZEMAX ray-tracing program. As in the COMSOL simulations (Fig. 4), with the increase of voltage the curvature gradually reduces. Figure 9 shows the focal length versus applied voltage. As can be seen, with the increase of the applied voltage, the magnitude of the focal length is increased and the lens has a large dynamic focal length of 6.5 cm at applied voltage of 0 to 300 V. Figure 9 also shows that the theoretical focal length of the lens obtained from
Fig. 6. Digitized data of curvature profile for 0, 80, and 300 V. 1 April 2015 / Vol. 54, No. 10 / APPLIED OPTICS
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Fig. 9. Comparison of simulation and experimental variation of focal length versus applied voltage.
electrowetting lens. Also, the distance between the electrowetting lens and the digital minimicroscope is 2 cm. At first, the image of the person was focused on the digital minimicroscope at 0 V applied voltage. Then, by changing the applied voltage to 240 V, the sharp image of the needle was projected on the digital minimicroscope, and, finally, with reduction of applied voltage to 0 V, the sharp image of the person appeared on the digital minimicroscope again. Figure 10 shows the images of the needle and person on the digital minimicroscope at applied voltages of 0–240 V. C.
Fig. 7. Comparison of variation of values (a) R and (b) K versus the applied voltage.
the ZEMAX ray-tracing program has behavior similar to the experimental one. The ability of the lens to focus on two objects was demonstrated by projecting the images of two objects on the digital minimicroscope at applied voltages of 0 and 240 V. The objects are a needle and a person located at distances of 4.5 cm and 2.5 m from the
Fig. 8. Change of the interface curvature versus applied voltage obtained from the ZEMAX simulation. 3014
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Spot Size of Laser Beam
Another experiment was conducted to investigate the variation of the spot size of a laser beam versus the applied voltage. Figure 11 shows the schematic setup of the experiment for this purpose. After passing through a polarizer, mirror, and the fabricated electrowetting lens, an He–Ne laser beam (λ 633 nm) was focused on a CCD camera by an objective lens (10×). The polarizer is used to control the intensity of the laser to avoid saturation of the CCD camera. We adjusted the setup at 0 V to obtain the minimum value of the spot size of the laser beam.
Fig. 10. Images of the needle and the person projected on the digital minimicroscope at voltages of (a) 0, (b) 240, and (c) 0 V applied to the electrowetting lens.
Fig. 13. Evaluation of visibility by LabVIEW at the red dashed line.
Fig. 11. Schematic setup for the spot size measurement of the laser beam.
With the increase of the applied voltage, the spot size increases. The image of the spot size on the CCD camera was analyzed by LabVIEW, and variation of the spot size is illustrated in Fig. 12. D.
Visibility
For investigation of the visibility of the images captured by the digital minimicroscope, a photo including a square grid pattern is placed at a distance of 4.73 cm from the electrowetting lens, and the image of the pattern is focused on the digital minimicroscope at a distance of 2.76 cm. The pattern has maximum visibility at applied voltage of zero (the setup was set at 0 V to obtain the maximum value of visibility). Then by applying the voltage, the visibility of the image decreased and the image was blurred.
Fig. 12. Variation of spot size of the laser beam versus applied voltage.
Figure 13 shows the image of the pattern on the CCD camera. Using the LabVIEW program, the variation of visibility with applied voltage was calculated in direction of the red dashed line in Fig. 13. Figure 14 shows the variation of visibility versus increasing and decreasing the applied voltage. The increasing and decreasing graph has 7% hysteresis. Since the best focal length of the lens is equal to the maximum value of the image visibility, our LabVIEW program is able to find the sharp images of objects in real time by tuning the applied voltage. E. Distortion
As shown in Fig. 13, there is a barrel distortion in the square grid pattern that results from the lens design (the lens has various focal lengths and magnifications in different areas). Apart from the lens design, the degree of distortion is related to the focal length, and, usually, for lenses with short focal length, there is a larger degree of barrel distortion [47]. We employed the mathematical model used in the Ref. [47] for correction of the distortion in the square grid pattern, and a first-order distortion parameter (k1 ) was obtained about −8.2 × 10−6 pixels−2 . A MATLAB code was developed based on the mathematical model and applied to the distorted
Fig. 14. Variation of visibility versus increasing and decreasing the applied voltage. 1 April 2015 / Vol. 54, No. 10 / APPLIED OPTICS
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4. 5. 6. 7. Fig. 15. (a) Barrel-shaped distortion in the square grid pattern and (b) correction of the barrel-shaped distortion after using MATLAB code.
image in Fig. 13. Figure 15 shows the distorted and the corrected images. The barrel-shaped distortion in the square grid pattern seen in Fig. 15(a) is corrected in Fig. 15(b).
8. 9.
10. 11.
5. Conclusion
A numerical and experimental investigation was performed on a tunable electrowetting lens with a wedge-shaped PDMS dielectric layer. The optical properties of the lens, such as focal length and visibility of images, were investigated experimentally by changing the voltage applied to the lens. FEA along with ZEMAX simulations were used to obtain the curvature, R, and conic constant, K, as well as the focal length of the lens. The simulation and experimental results have similar behavior. The lens was fabricated using a simple method. A LabVIEW image-processing program was used to detect the surface profile of the lens. The experimental results show that the lens has a wide tuning range of focal length equal to 6.5 cm, and the focal length has a quadratic behavior versus the applied voltage. The wedge-shaped PDMS layer decreases the voltage applied to the lens. The experimental results also show that the visibility of images decreases, and the spot size of the laser beam and the magnitude of the focal length of the lens increase with increase of the applied voltage. A MATLAB code was developed for correction of barrel-shaped distortion of the images. The LabVIEW program can obtain the focal length from the maximum value of visibility in real time by tuning the applied voltage. The authors gratefully acknowledge Dr. Arash Moradi for his editorial comments and discussions to improve the quality of the paper. References 1. D. Psaltis, S. R. Quake, and C. Yang, “Developing optofluidic technology through the fusion of microfluidics and optics,” Nature 442, 381–386 (2006). 2. C. Monat, P. Domachuk, and B. J. Eggleton, “Integrated optofluidics: a new river of light,” Nat. Photonics 1, 106–114 (2007). 3. C. Monat, P. Domachuk, C. Grillet, M. Collins, B. J. Eggleton, M. Cronin-Golomb, S. Mutzenich, T. Mahmud, G. Rosengarten, and A. Mitchell, “Optofluidics: a novel generation of 3016
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