The purpose of this paper is to use thermal energy and electrostatic force as an alternative to high-cost precision cutting or traditional injection molding in the fabrication of COC (cyclo-olefin copolymer) plastic aspheric bi-convex lenses with high Blu-Ray transmittance (92% at 405 nm). A glass substrate was used, and ultrasonic drilling defined the clear aperture of the aspheric bi-convex lens. The copolymer lens material was measured, filled and melted into the hole. A gradient electrical potential was applied between the top and bottom electrodes of the COC liquid droplet to control the profile of the lens. The thermal energy melted the COC into a dynamic fluid, and the electrostatic force controlled the aspheric morphology of the designed profile. The resulting lenses have a clear aperture of approximately 1.14 mm and a front focal length of 4.97 mm, and the spot size of the fabricated aspheric bi-convex lenses can be controlled to approximately 0.588 µm. This technology is capable of fabricating lenses for application in micro-optical systems.
©2010 Optical Society of America
The fabrication of microlenses generally involves the use of hydraulic control , electro-wetting [2–7], stamping [7,8], molding  or two-phase liquid methods . Many studies in recent years on regulating the liquid surface shape involved the application of electro-wetting to fabricate varifocal lenses [2–6]. The principle is that with the interface deformation between these two immiscible dielectric liquids, the focal length becomes tunable. S. Xu et al.  used a glass based plano-convex microlens array stamper to form a well-shaped polymer concave base. After coating a conductive layer onto the base, a well-shaped electrode was created to fix the position of the microlens and reduce the driving voltage. The electrodes were with a top planar electrode and a bottom well-shaped electrode. Using different plano-convex microlens array stampers, microlens arrays with various apertures and densities can be easily fabricated. In addition, the application of dielectric force to the nanomechanical resonator was presented by Q. P. Unterreithmeier et al. . They demonstrated the design of a set of on-chip electrodes to create an electric field gradient and to control the inhomogeneous electric field. Electrolysis, Joule heating and microbubble formation often occur in electro-wetting lenses due to the transportation of the free electric charges and the alternating electric fields. Although dielectric lenses do not have these problems, they require a patterned-electrode to generate an inhomogeneous electric field, which adds complexity to the fabrication process . The biggest advantage of electrostatic control is that electrode does not require actual contact with the surface of the liquid, so the lens surface remains very smooth, and it can be used in an array process. Now this method is mostly applied to the fabrication of zoom-type lenses. C. C. Cheng  used electro-wetting and changed the contact angle of the oil and water in the cavity to change the curvature of the medium, but its penetration was only about 70%.
K. Y. Hung (2008)  also mentioned the problem of a low transmittance limit for the liquid material SU-8 for 405nm light. For a high transmittance plastic material, most plastics such as PMMA, PC, COC and PBS are solid at room temperature and cannot be shaped by any of the methods mentioned above. Therefore, in order to meet the requirements of high transmittance and optical performance while effectively controlling the shape of the aspheric lens, this paper introduces a novel technology to fabricate aspheric bi-convex lenses from high-transmittance COC plastic with thermal energy and electrostatic force. In addition, in order to achieve the modulation of the liquid to an aspherical morphology, the electrostatic force was applied to the dynamic fluid. The optimum was found from the plastic melting temperature curves, and the material was evenly distributed at the molecular level, enabling electrostatic attraction to effectively control the lens shape.
2. Design Principle
The fabrication concept of the bi-aspheric lens is shown in Fig. 1 . The system includes copper as the thermal conductivity cradle, an overhead dielectric glass substrate, alumina as the thermal insulation cradle and spacer to place between bottom and top aluminum electrode. Ultrasonic drilling of the bottom glass substrate was used to define the clear aperture of the bi-aspheric lens. The copolymer lens material was melted into the hole. A gradient electrical potential was applied between the top and bottom substrates of the COC liquid droplet to control the profile of the lens. The relations of electric field E, applied voltage V, liquid lens height t, electrode spacing d, gravity of the COC and permittivity of the liquid lens ( is the dielectric constant of the air) can be expressed as the following, Eq. (1) [Fig. 2(a) ]:
The net electrostatic force F on COC is related to the gradient of the electric field, the difference in permittivity between the two media and the gravity of COC suffered FCOC.
Thus, when the applied voltage and spacing between the electrodes are fixed, the attraction of liquid lens has a different distribution in accordance with the surface shape of liquid lens. Based on these principles, we can re-shape the morphology of the spherical droplets by the balance of the gradient of the electric field and gravity.
The attractive electrostatic force in the center is greater than on the sides; therefore, the entire droplet is pulled upwards with a shape that is tunable according to the aspheric shape. The CFDRC theory model for electrostatic force simulation with different voltages is showed in Fig. 2(b). The concept of aspherical morphology control is described above. In the following we describe the design concept for the optical simulation.
In this paper, the use of the sequential ray-tracing simulation software OSLO aided the optical design of the lens, the optimization function to optimize parameters was used to obtain the smallest spot, curvature and thickness of the lens. Then the parameter values were input to Mathematica software and re-calculated to find the true height, to ensure the accuracy of thickness and curvature in this experiment. The lens material was set to COC, the refractive index was 1.53, and the transmittance for 405 nm light source was about 92%. The following are the parameters for the design and performance of the lens: 1.14 mm clear aperture of the lens; to adopt the structure of a finite conjugate, set forward focal length is 4.97 mm. The conic constant k is −1, and the order of the aspheric coefficient is 10. Then we obtained a spot size under the diffraction limit of 0.3861 μm, and the working distance is 0.3539 mm according to OSLO. According to the simulation results, we could obtain the actual amount of required plastic by integrating the aspheric profile curve.
Z is the sag of the aspheric surface, r is the curvature radius of the lens, c is the inverse of the radius of curvature, c1, c2, c3, and c4 are the higher-order coefficients of the aspheric equation for S1, and k is the conic constant. All the simulation results of the lens by OSLO were summary in Table 1 .
3. Fabrication Process
In this paper, we verified the effect of the aspheric shape and different voltage by experiments and CFD simulation. The COC lens was shaped in the melt state by electrostatic force. Copper was used as a good thermal conductivity medium between the glass substrate and the hot-plate in order to transfer heat and melt the COC plastic. An aluminum block with low resistance was used as the top electrode, and an aluminum thin film on the glass substrate was used as the bottom electrode for the applied voltage.
The detailed fabrication process of the glass bottom substrate is shown in Fig. 4(a) . First, we spin photoresist to avoid pollution of the glass substrate after ultrasonic drilling. For ultrasonic drilling, the drilled out holes are observation under 4X microscope and found to have a front and back aperture size difference of about 5 μm compared to UV laser drilling that produces a front and back aperture difference of about 200μm. Thus, ultrasonic drilling produces better roundness and smoother aperture walls, which are helpful to the stability of the experimental parameters and manufacturing process yield. Then using E-GUN deposition, 3000Å of aluminum is deposited as the electrode layer. A teflon (AF 1601S-6, DuPont Inc.) pattern was employed by lift-off process as a dielectric layer and a hydrophobic barrier to assist in shaping the COC lens. The optimum temperature curves of the COC melt for resolving a yellow air bubble and cooling are shown in Fig. 4(b). Finally, an electrostatic field is applied during the high temperature, resulting in electrostatic attraction that stretches the lens into the required aspheric morphology. The aspheric lens is cooled to room temperature after forming.
In this paper, the analysis results mainly include the lens profile analysis and the optical properties.
4.1. Lens profile analysis
In this study, in order to optimum the process parameters, the profile curve of the experimental and OSLO design lens were compared. First, a sample of the side-view  of each lens was analyzed using image processing software Image-Pro. Laplace filters were applied to reduce the noise impact on the edge detection. There was typically a high-frequency noise, so a low-pass filter was used. Then we use images of the smooth edge detection and locations to obtain the lens edge profile expressed in binary. At last, using the binary 0 and 1 graph we find the coordinate, enter the coordinate into the numerical analysis software Origin Pro and obtain the aspherical expression for curve fitting for the sample topography and high-order aspherical curvature coefficient. We then enter the final fitting parameters to Mathematica to rebuild the profile and compare with design values.
4.2. Lens optical properties
In this paper, the optical system shown in Fig. 5 was set up to carry out spot size measurements. A 405 nm laser diode (power = 8.5 mW) was used as the light source. In this system, a NA = 0.1 (4X) microscope objective lens was used as a spatial filter and to ensure that the measurement would not introduce unwanted aberrations. Then we used a pinhole (40 μm) to filter out redundant high-frequency noise. The light was incident on the aspherical lens. Then, a ND filter was used in order to avoid CCD (Watec WAT-221S, pixel size 8.4 µm(H)*9.8 µm(V)) saturation. In addition, in order to improve the optical system resolution, we used a 100X magnification long-working distance lens before the CCD. Image processing software was used to calculate the pixels of the optical energy distribution and to analyze the full width at half maximum (FWHM) of the spot size.
Figure 6(a) –6(d) show four bi-aspheric lenses made of COC shaped in a dynamic fluid under different electrostatic forces between the top and bottom electrodes. These experimental results give a COC plastic material error of 0.122% with a fixed electrode spacing and melting the same COC repeatedly but different applied voltages. Figure 6(e) shows the curve fitting profile of the COC lens in Fig. 6(a)–6(d)and the designed profile. It shows that the optimum voltage is 2600V for our design.
From Fig. 6 we see that the higher the applied voltage, the greater the electrostatic force on the first surface S1 to attract the upper parts of the lens, resulting in greater curvature; while the second surface S2 of the lens is also pulled. When the applied voltage is too large, although the curvature of the upper surface is larger, the lens shape begins to show spherical aberration and lower optical quality. When the voltage was 2600 V, the morphology of the fabricated lens was closest to the design profile. In the central part of the upper surface, the shape error of the lens was almost 0.
Figure 7 shows the shape error of the lenses [Fig. 7(a), 7(b)] shown in Fig. 6(b)–6(d) (in comparison to the design specifications) produced by the gradient electrostatic force and thermal energy in the z direction, and the intensity distribution [Fig. 7(c)], spot size of the lens [Fig. 7(d)] illustrated in Fig. 6(c) (in comparison to a commercial lens). Finally, the focus light spot size of the aspherical lens shown in Fig. 6(c) is 0.588 µm, similar to that of a commercial DVD double convex objective lens with a spot size of 0.42 µm [Fig. 7(e)–7(g)]. The error on the lens edge of S1 was about maximum 8 μm, and the error on the surface S2 was almost 0. The morphology of errors led to the generation of aberration, so that the spot size 0.588 µm of our lens was larger to commercial lens 0.42 µm, which we can see in Fig. 7.
In this paper, we demonstrate aspheric lens fabrication technology in a dynamic fluidic by balancing the electrostatic force and the thermal energy. The results successfully demonstrated the capability of dynamic manipulation in the fabrication of microlenses by employing a gradient electrostatic potential and thermal energy. Finally, the focus light spot size of the aspherical lens is 0.588 µm, similar to that of a commercial DVD double convex objective lens with a spot size of 0.42 µm. In most other studies, the main application of electrostatics is the production of zoom lenses. However, this study confirms that it could also be useful for image lenses or pickup head lenses.
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