sensors Article Dynamic Response of Elastomer-Based Liquid-Filled Variable Focus Lens Lihui Wang 1,2,* and Masatoshi Ishikawa 2,3 1 Guangdong Institute of Semiconductor Industrial Technology, Guangdong Academy of Sciences, No.363 Changxing Rd., Tianhe, Guangzhou 510-650, China 2 Department of Information Physics and Computing, University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-8656, Japan; [email protected] 3 Department of Creative Informatics, University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-8656, Japan * Correspondence: [email protected] or [email protected] Received: 20 September 2019; Accepted: 23 October 2019; Published: 24 October 2019 Abstract: Variable focus lenses are capable of dynamically varying their focal lengths. The focal length is varied by adjusting the curvature of the refractive surface and the media on both sides of the lens. The dynamic response is one of the most important criteria to determine the performance of variable focus lens. In this work, we investigated critical factors that affect the dynamic response of liquid-filled variable focus lens with a large aperture size. Based on a theoretical analysis of a circular disk representative of a deformable surface, we found that the dynamic response is significantly influenced by the diameter, thickness, and stiffness of the disk because these factors determine its first natural frequency. We also studied the dynamic response of elastomer-based liquid-filled variable focus lens prototype with different aperture sizes (20 and 30 mm) by using experiments and we found that the lens with the smaller aperture size had an excellent dynamic response. Keywords: liquid-filled variable focus lens; aperture sizes; dynamic response; natural frequency 1. Introduction In an optical system, the conventional method used to adjust the focal length of the system or zoom into an object is to employ a multitude of lenses and mechanically move these lenses over specific distances along the optical axis. Because the lenses are made of glass or plastic, the lenses have fixed optical properties after fabrication. Solid lenses can be processed to form a spherical or aspheric surface. Various materials are used to fabricate the lenses to fulfill the optical requirements of a specific application such as achromatic lenses made of crown and flint glass doublets. Specific materials such as silica glass and chalcogenide glass are also used to fabricate lenses for other spectrum imaging applications. Because of the fixed focal length of solid lenses, the response times of the focus and zoom functions are limited by the mechanical motion of the lenses in the optical system. The motors in the optical system move back and forth and the continuous forward and reverse rotations result in high power consumption. Hence, the functions of the optical system will be temporarily disabled by the built-in safety mechanism to prevent overheating caused by the frequent conversion of the positive and negative driving current. Such a mechanism is not suitable to achieve a high-speed dynamic response. A variable focus lens can dynamically change its focal length and therefore, only a single lens is needed in the optical system. Because a variable focus lens system does not require the back and forth motion of a multitude of lenses, variable focus lenses are favorable alternatives for optical design. Several compact optical systems with variable focus lenses have been reported [1–11]. Variable focus lenses can be used for visible, infrared, and terahertz (THz) imaging technologies based on the properties of the liquid candidates [12–14]. The focal length of a liquid-filled variable focus lens is Sensors 2019, 19, 4624; doi:10.3390/s19214624 www.mdpi.com/journal/sensors Sensors 2019, 19, 4624 2 of 13 varied by adjusting its bending curvature of the refractive surface, resulting in a rapid response time. Oku et al. [15] produced a silica glass-sealed tunable lens with a 1-kHz bandwidth frequency. Oku and Ishikawa [16] fabricated a lens prototype with a liquid-liquid interface. The prototype was driven by a piezo actuator and the maximum response time achieved was 2 ms. Maffli et al. [6] developed a dielectric elastomer-based tunable lens with a settling time of 0.175 ms. To achieve high optical performance for liquid-filled variable focus lens, it is crucial to ensure that the aperture size is small (i.e., diameter less than 10 mm) compared with the capillary length, while considering the physical constraints of the optical system [17]. If a liquid-filled variable focus lens has a large aperture size and the lens is positioned vertically, the lens profile may be asymmetrically deformed due to gravitational effects [18]. We [19] developed a variable focus lens with a liquid-membrane-liquid structure and large aperture size (a diameter of up to 30 mm). The lens was designed such that elastic force was the dominant force instead of surface tension force to significantly increase the capillary length. However, the dynamic response of this lens is not known. The dynamic response is one of the most important criteria for a variable focus lens and it is crucial to minimize the response time (settling time) of the lens. Hence, in this study, we investigated the critical factors that affect the dynamic response of an elastomer-based liquid-filled variable focus lens to minimize the response time. We studied the dynamic response of a circular disk model representative of a deformable surface (deformable plate and elastomer). We hypothesized that the diameter, thickness, and stiffness of the circular disk are the critical factors that influence the dynamic response of the liquid-filled variable focus lens. We fabricated the elastomer-based liquid-filled variable focus lens prototype with different aperture sizes (diameter: 20 and 30 mm) and we used a high-speed piezo stack actuator to measure the dynamic response of the lens with a change in the focal length. The piezo stack actuator was pushed into the deformable plate, whose diameter was larger than the aperture of the lens. The curvature of the variable focus lens formed by the transparent elastomer was passively controlled. Based on the experimental results, the lens prototype with an aperture size of 30 mm achieved a stable response at 30 Hz when we applied a sinusoidal wave as the active signal. The lens prototype with an aperture size of 20 mm achieved a stable response at 45 Hz. When we used a high-frequency sinusoidal wave, we observed that the amplitude of the feedback signal from the photodiode module significantly decreased, indicating that the vibrations of the elastomer surface were damped. When we applied a square wave as the active signal, we found that the settling times were 200 and 160 ms, respectively, when the lens prototype with an aperture size of 30 mm was switched from the relaxing phase to the contracting phase and vice versa. When the aperture size was reduced to 20 mm, the settling times of the lens prototype were significantly reduced to 60 and 40 ms, respectively, and the lens prototype was switched from the relaxing phase to the contracting phase and vice versa, indicating a marked improvement in the dynamic response of the lens prototype with a smaller aperture size. Our experimental results indeed indicate that the dynamic response of the liquid-filled variable focus lens is influenced by the diameter, thickness, and stiffness of the elastomer. Because our lens prototype can steadily vibrate to vary its focal length at a frequency of more than 30 Hz, the lens prototype can be potentially embedded in a high-speed projector to generate three-dimensional interactive scenes [20,21]. We believe that the lens prototype can also be used to realize a high-speed shape from focus and all-in-focus imaging [22,23]. Even though the elastomer used in our experiments can be easily fabricated, it lacks in terms of stiffness. If an elastomer with higher stiffness can be employed, this will considerably improve the dynamic response of the elastomer-based liquid-filled variable focus lens. Moreover, the dimensions of the lens can be tailored to fulfill the requirements of a particular application. We believe that the critical factors that affect the dynamic response of the liquid-filled variable focus lens identified in this work will be useful in the design of variable focus lens for optical systems. The manuscript is organized as follows. The design principle of the evaluation system is described in the Section2. In Section3, the building of the mathematical model of the system, the analysis of the dynamic performance of the deformable plate, and the building of the prototype is described. Sensors 2019,, 19,, x 4624 FOR PEER REVIEW 3 3of of 13 13 analysis of the dynamic performance of the deformable plate, and the building of the prototype is described.The experimental The experimental setups and setups procedures and procedures of the study of arethe illustratedstudy are illustrated in this section. in this The section. results The of resultsthe measurements of the measurements and the discussions and the discussions are presented are presented in Section 4in. TheSection conclusions 4. The conclusions of the study of arethe studypresented are presented in Section 5in. Section 5. 2.2. Design Design Principle Principle InIn this this work, work, we we focused focused on investigating on investigating the dy thenamic dynamic response response of an elastomer-based of an elastomer-based variable focusvariable lens focus with lensa large with aperture a large size aperture and therefore, size and we therefore, will not discuss we will variable not discuss focus variable lenses with focus a liquid-liquidlenses with astructure. liquid-liquid Our study structure.