Dynamic Response of Elastomer-Based Liquid-Filled Variable Focus Lens

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. is primarily Our study focused is primarily on liquid-membrane focused on and liquid-membrane liquid-membrane- and liquidliquid-membrane-liquid variable focus lenses. variable Figure focus 1 shows lenses. the Figureschematic1 shows of the the elastomer-based schematic of the variable elastomer-based focus lens system.variable In focus this lensdesign, system. two chambers In this design, are filled two chamberswith different are filled types with of liquid different and types these of liquid-filled liquid and chambersthese liquid-filled are separated chambers by a are piece separated of transparen by a piecet elastomer. of transparent Because elastomer. the liquids Because have the different liquids refractivehave different indices, refractive the curvature indices, the of curvature the elastome of ther at elastomer the liquid-membrane-liquid at the liquid-membrane-liquid interface interface can be consideredcan be considered as the lens as the surface. lens surface. The liqui Theds liquidsare assumed are assumed to be incompressible. to be incompressible. TheThe lower chamber (blue chamber) is is equipped with with a a deformable plate plate such such that the chamber volume is varied by the motion of the piezo stack actuator. When the piezo stack actuator is pushed downwardsdownwards on on the deformable plate, plate, the the volume volume of of the lower chamber decreases and the elastomer becomesbecomes deformed. The The elastomer elastomer is is prepared prepared by by applying applying a a homogeneous homogeneous in-plane in-plane pretension pretension force force andand its its circular circular boundary boundary is is fixed fixed such that that the the deformation deformation profile profile of the the elastomer elastomer is is reminiscent reminiscent of of aa paraboloid paraboloid profile. profile. Thus, Thus, the the focal focal length length changes due to changes in the bending curvature. ToTo monitor the high-speed variation of the elastome elastomerr surface, it is necessary to use a a high-speed high-speed piezo stack actuator instead of a syringe pump. Even Even though though the the piezo piezo stack stack actuator actuator can can realize displacementdisplacement variations withwith aa frequencyfrequency in in the the order order of of kilohertz kilohertz (kHz), (kHz), the the stroke stroke length length can can only only be beone-thousandth one-thousandth of itsof bodyits body length. length. However, However, the motion the motion of the of piezo the stackpiezo actuator stack actuator is still toois still short too to shortrealize to a realize considerable a considerable change in change the liquid in the volume. liquid For volume. this reason, For this a built-in reason, amplifying a built-in mechanismamplifying mechanismwas designed was [15 designed]. The designed [15]. The deformable designed deformable area of the area piezo of stack the piezo actuator stack consists actuator of consists two areas: of (1) active deformable area with size S and (2) passive deformable area of the elastomer (i.e., the variable two areas: (1) active deformable area with size S and (2) passive deformable area of the elastomer focus lens profile) with size s. Therefore, the lens surface will change by approximately S/s times (i.e., the variable focus lens profile) with size s . Therefore, the lens surface will change by relative to the deformable plate. With this design, we can realize a large elastomer deformation of the Ss/ approximatelyelastomer with only a times small relative stroke length to the ofdeformable the piezo stackplate.actuator. With this design, we can realize a large elastomer deformation of the elastomer with only a small stroke length of the piezo stack actuator. Collimated Beam

Deformable Piezo Plate Elastomer Liquid 1

Liquid 2

Focal Length A Focal Length B

Figure 1. Schematic of the variable focus lens system (cross-sectional view). The liquid chambers are Figure 1. Schematic of the variable focus lens system (cross-sectional view). The liquid chambers are filled with different types of liquid (Liquid 1 and Liquid 2) and a piece of transparent elastomer is filled with different types of liquid (Liquid 1 and Liquid 2) and a piece of transparent elastomer is inserted in between to separate the liquids. The lower chamber is equipped with a deformable plate, inserted in between to separate the liquids. The lower chamber is equipped with a deformable plate, which is passively deformed by a piezo stack actuator. The circular boundary of the elastomer is fixed which is passively deformed by a piezo stack actuator. The circular boundary of the elastomer is fixed such that the elastomer surface will change from a convex profile to a concave profile. such that the elastomer surface will change from a convex profile to a concave profile. In this lens design, the deformable plate and elastomer were actively and passively vibrated, In this lens design, the deformable plate and elastomer were actively and passively vibrated, respectively. The natural frequencies of these components determined the dynamic response of the respectively. The natural frequencies of these components determined the dynamic response of the liquid-filled variable focus lens. Hence, we developed a mathematical model of the deformable plate liquid-filled variable focus lens. Hence, we developed a mathematical model of the deformable plate

SensorsSensors 20192019, 19,, 19x FOR, 4624 PEER REVIEW 4 of 413 of 13 and elastomer. We performed numerical simulations to determine their natural frequencies and select theand optimal elastomer. candidates We performed for the deformable numerical plate simulations and elastomer. to determine their natural frequencies and select the optimal candidates for the deformable plate and elastomer. 3. Methodology 3. Methodology 3.1. Mathematical Model 3.1. Mathematical Model The elastomer-based liquid-filled variable focus lens consists of two parts that will vibrate: (1) a The elastomer-based liquid-filled variable focus lens consists of two parts that will vibrate: deformable plate and (2) an elastomer. Both the deformable plate and elastomer are circular disks (1) a deformable plate and (2) an elastomer. Both the deformable plate and elastomer are circular disks with a fixed boundary, and therefore, they can be represented by the same mathematical model. It is essentialwith a for fixed the boundary, deformable and plate therefore, and elastomer they can beto representedhave a high-speed by the samedynamic mathematical response and model. high It is naturalessential frequency. for the deformable plate and elastomer to have a high-speed dynamic response and high naturalThe deformable frequency. plate is deformed by the piezo stack actuator and the elastomer profile is passivelyThe controlled. deformable The plate elastomer is deformed profile by is the represen piezo stacktative actuator of a refractive and the lens elastomer surface profile and therefore, is passively it iscontrolled. imperative Theto maximize elastomer the profile optical is performance representative of ofthe a elastomer. refractive lens surface and therefore, it is imperativeThe conventional to maximize method the opticalused to performance increase the of natural the elastomer. frequency of a component is to build a tough structureThe conventional and select methoda stiff material. used to However, increase thethe naturalability to frequency deform is of an a essential component criterion is to for build a variablea tough focus structure lens. and Hence, select the a stibestff material.candidates However, for the deformable the ability toplate deform and iselastomer an essential are materials criterion for thata variablewill maintain focus a lens. high Hence, natural the frequency best candidates and elas forticity the for deformable deformation plate to andtake elastomer place. We are chose materials the materialsthat will that maintain would agive high the natural best trade-off frequency in andterms elasticity of the natural for deformation frequency to and take stiffness place. Wefor the chose deformablethe materials plate that and would elastomer. give the best trade-off in terms of the natural frequency and stiffness for the deformableWe developed plate the and mathematical elastomer. model to analyze the dynamic performance of the deformable plate andWe elastomer. developed Both the these mathematical components model have to analyzethe same the shape, dynamic and thus, performance they can ofbe the represented deformable by platethe same and elastomer. mathematical Both model. these components Figure 2 shows have thethe same schematic shape, of and the thus, circular they candisk be with represented a fixed by boundary,the same which mathematical is representative model. Figure of 2the shows deformab the schematicle plate ofor the elastomer. circular disk The with radius, a fixed thickness, boundary, which is representative of the deformable plate or elastomer. The radius, thickness, Young’s modulus,ρ Young’s modulus, density, and Poisson’s ratio of the circular disk are denoted by a, d , E , , density, and Poisson’s ratio of the circular disk are denoted by a, d, E, ρ, and v, respectively. and v, respectively.

FigureFigure 2. Schematic 2. Schematic of the of thecircular circular disk disk with with a fixed a ﬁxed boundary. boundary.

Based on the natural modes of vibration [24], the natural frequency w of the circular disk can be Based on the natural modes of vibration [24], the natural frequency w of the circular disk can written as be written as s 2 1 E ωm,n = k d , (m, n = 0, 1, 2, ...), (1) m,n 12(11 v2E) ρ ω ==kd2 ,,0,1,2,, ()mn mn,, mn −2  (1) 12() 1− v ρ where m and n denote the vibration modes. The parameter km,n is the solution of

m n k mn, where and denoteIm the(km ,vibrationna)Jm 1(k mmodes.,na) J mThe(km parameter,na)Im 1(km ,na) =is the0. solution of (2) − − − −= IkaJkammnm()()()(),1,−− mn JkaIka mmnm ,1, mn 0. (2) where Im is the mth modified Bessel function of the first kind and Jm is the mth Bessel function of the first kind. A vibration mode where m = 0 and n = 1 corresponds to the first natural vibration. I J Notewhere that k m isis proportionalthe mth modified to 1/a becauseBessel function it is the solutionof the first of Equation kind and (2). Hence,m is the it can mth be Bessel deduced m,n = = q function of the first kind. A vibration mode where m 0 and n 21 corresponds1 to Ethe first natural that the first natural frequency ω0,1 is positively correlated to 1/a , d, and 2 . k (1 v ) ρ vibration. Note that mn, is proportional to 1/a because it is the solution of Equation− (2). Hence, it

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ω 2 can be deduced that the first natural frequency 0,1 is positively correlated to 1/a , d , 1 E ()1− v2 ρ and . Sensors 2019, 19, 4624 5 of 13

3.2. Dynamic Performance of the Deformable Plate 3.2. Dynamic Performance of the Deformable Plate We performed finite element simulations to investigate the dynamic performance of the circular disk. We performedused COMSOL finite Multiphysics element simulations® modeling to investigate software (Version the dynamic 5.3 COMSOL performance Inc., of Stockholm, the circular Sweden)disk. We for used this COMSOL purpose, Multiphysicswhere the diameter® modeling 2a and software thickness (Version d of 5.3 the COMSOL rigid circular Inc., Stockholm,disk were setSweden) as 200 formm this and purpose, 2 mm, respectively. where the diameter The material2a and properties thickness ofd ofthe the deformable rigid circular plate disk were were set setas ρ follows:as 200mm (1) andYoung’s 2 mm, modulus, respectively. E : ~192.9 The materialMPa, (2) properties Poisson ratio, of the v deformable: ~0.3, and plate(3) density, were set as: 3 ~7930follows: kg/m3. (1) Young’s These properties modulus, E are: ~192.9 representative MPa, (2) Poisson of those ratio, for SUS304v: ~0.3, stainless and (3) density, steel. Figureρ: ~7930 3 shows kg/m . theThese simulation properties result are representativeand the first eigenfrequency of those for SUS304 of the stainless rigid circular steel.Figure disk was3 shows found the to simulation be 486.63 Hz.result Because and the the first deformable eigenfrequency plate corresponds of the rigid to circular the motion disk wasof the found high-speed to be 486.63 piezo Hz. stack Because actuator, the thedeformable feedback plateresponse corresponds of the deformable to the motion plate of shou theld high-speed be less than piezo 30% stack of its actuator, first eigenfrequency. the feedback Thus,response we assumed of the deformable that the most plate suitable should be dynamic less than vibrational 30% of its frequency first eigenfrequency. of the deformable Thus, we plate assumed was 146that Hz. the most suitable dynamic vibrational frequency of the deformable plate was 146 Hz.

Figure 3. First natural frequency (eigenfrequency) of the rigid circular disk obtained from finite Figureelement 3. simulations. First natural The frequency Young’s modulus,(eigenfrequency) Poisson’s of ratio, the rigid and densitycircular were disk set obtained as ~192.9 from MPa, finite ~0.3, elementand ~7930 simulations. kg/m3, respectively, The Young’s which modulus, are representative Poisson’s ratio, of and those densit for SUS304y were set stainless as ~192.9 steel. MPa, The ~0.3, first andeigenfrequency ~7930 kg/m3, was respectively, found to be which 486.63 are Hz. representative of those for SUS304 stainless steel. The first eigenfrequency was found to be 486.63 Hz. 3.3. Fabrication of the Elastomer-Based Liquid-Filled Variable Focus Lens Prototype 3.3. FabricationStiffness isof anthe importantElastomer-Based factor Liquid-Filled that will determine Variable Focus the first Lens natural Prototype frequency of a component. TheStiffness elastomer is an was important too soft factor compared that will with determ the SUS304ine the stainlessfirst natural steel frequency deformable of aplate. component. Hence, Thewe implantedelastomer anwas in-plane too soft pretension compared force with device the SUS3 in the04 elastomer stainless tosteel increase deformable its stiff nessplate. [17 Hence,]. Figure we4 implantedshows the an customized in-plane pretension forceforcedevice device fabricated in the elastomer in this work.to increase The pretension its stiffness force [17]. device Figure was 4 showsfixed on the top customized of a table andpretension a piece offorce elastomer device wasfabric fixedated atin the this center work. of The the device.pretension With force this device device, wasthe elastomerfixed on top can of be a table stretched, and a producing piece of elastomer a homogeneous was fixed in-plane at the center pretension of the force. device. The With in-plane this device,pretension the elastomer force improves can be the stretched, optical performance producing a of homogeneous the variable focus in-plane lens, pretension especially force. when The the lensin- planeis positioned pretension vertically force improves [17]. the optical performance of the variable focus lens, especially when the lens is positioned vertically [17].

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Direction of Rotation for Stretching

Direction of Rotation Figure 4. Photograph of thethe customizedcustomized in-planein-plane pretensionpretensionfor forceStretchingforce device. device.A A piece piece of of elastomer elastomer is is placed placedat the centerat the center of the of device the device and the and elastomer the elastomer is stretched is stretched over over a certain a certain period. period. Figure 4. Photograph of the customized in-plane pretension force device. A piece of elastomer is Figureplaced 55 showsatshows the center thethe experimentalexperimentalof the device and setup the elastomer fabricated is stretched in-house over to to ameasure measure certain period. the the dynamic dynamic response response of of the elastomer-basedthe elastomer-based liquid-filled liquid-filled variable variable focus focus lens prototypelens prototype with differentwith differe aperturent aperture sizes. Thesizes. deformable The platedeformable hadFigure a diameterplate 5 shows had and athe diameter thicknessexperimental and of thickness 200setup mm fabricated and of 200 2 mm, mmin-house respectively,and to2 mm, measure respectively, as shownthe dynamic on as the shownresponse left-hand on of the side of the elastomer-based liquid-filled variable focus lens prototype with different aperture sizes. The theleft-hand photograph. side of the A piezo photograph. stack actuator A piezo (Model: stack actuator P-841.60B, (Model: Physik P-841.60B, Instrumente Physik (PI) Instrumente GmbH & (PI) Co. KG, deformable plate had a diameter and thickness of 200 mm and 2 mm, respectively, as shown on the Germany)GmbH & Co. with KG, a Germany) stroke length with of a 90strokeµm waslength used of 90 in μ thism was work, used which in this was work, mounted which was on top mounted of a sturdy left-hand side of the photograph. A piezo stack actuator (Model: P-841.60B, Physik Instrumente (PI) platformon top of and a sturdy directed platform towards and the directed center of towards the deformable the center plate. of the The deform liquidable chambers plate. wereThe liquid filled with chambersGmbH &were Co. KG,filled Germany) with different with a typesstroke of length liquid of (each 90 μm with was useda different in this refractivework, which index). was mounted The liquid differenton top typesof a sturdy of liquid platform (each and with directed a different towards refractive the center index). of the The deform liquidable chambers plate. The were liquid connected chambers were connected to each other via a circular hole and a piece of elastomer was inserted in to eachchambers other were via afilled circular with different hole and types a piece of liquid of elastomer (each with was a different inserted refractive in between index). to separateThe liquid the two between to separate the two liquids. Polyacrylate (3MTM VHBTM Tape 4910, 3M, USA) was chosen as liquids.chambers Polyacrylate were connected (3MTM toVHB eachTM otherTape via 4910, a circul 3M,ar hole St. Paul, and a MN, piece USA) of elastomer was chosen was inserted as the elastomer in the elastomer in this study [8]. The polyacrylate was originally designed as a double-sided tape and in thisbetween study to separate [8]. The the polyacrylate two liquids. Polyacrylate was originally (3MTM designed VHBTM Tape as a 4910, double-sided 3M, USA) was tape chosen and therefore,as therefore, the polyacrylate elastomer was carefully taped to a doughnut-shaped plate. The elastomer the elastomer in this study [8]. The polyacrylate was originally designed as a double-sided tape and thewas polyacrylate stretched to elastomer1.5 times its was original carefully length taped to toincrease a doughnut-shaped its natural frequency plate. The and elastomer following was this, stretched the to 1.5therefore, times itstheoriginal polyacrylate length elastomer to increase was carefull its naturaly taped frequency to a doughnut-shaped and following plate. this, The the elastomer elastomer was elastomerwas stretched was affixed to 1.5 timesto the its plate. original The lengthplate was to in mountedcrease its andnatural fixed frequency to the circular and following hole between this, the the affixed to the plate. The plate was mounted and fixed to the circular hole between the two liquid twoelastomer liquid chambers. was affixed The to theinner plate. aperture The plate serves was asmounted the circular and fixed boundary to the circular condition hole of between the variable the chambers. The inner aperture serves as the circular boundary condition of the variable focus lens profile. focustwo lens liquid profile. chambers. We fabricated The inner two aperture plates serves with differentas the circular aperture boundary sizes (20 condition and 30 mm)of the to variable evaluate Wethefocus fabricateddynamic lens responseprofile. two plates We of fabricated the with elastomer-based different two plates aperture withliquid-f sizesdifferentilled (20 variable aperture and 30 mm)focus sizes to lens(20 evaluate and prototype 30 mm) the with dynamicto evaluate different response ofaperture thethe elastomer-baseddynamic sizes. response liquid-filledof the elastomer-based variable liquid-f focus lensilledprototype variable focus with lens different prototype aperture with different sizes. aperture sizes. Piezo Piezo

Lens Aperture Lens Aperture Deformable Plate Deformable Plate

Figure 5. Photograph of the in-house experimental setup used to measure the dynamic response of FigureFigure 5. 5.Photograph Photograph of of the thein-house in-house experimental se setuptup used used to to measure measure the the dynamic dynamic response response of of the the elastomer-based liquid-filled variable focus lens prototype with different aperture sizes. elastomer-basedthe elastomer-based liquid-ﬁlled liquid-filled variable variable focus focus lens lens prototype prototype withwith didifferentﬀerent aperture aperture sizes. sizes.

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3.4. 3.4.Experimental Experimental Setup Setup and andProcedure Procedure A glassA glass rod homogenizer rod homogenizer (Model: (Model: RHO-13S-E2, RHO-13S-E2, Sigma SigmaKoki, Co., Koki, Ltd., Co., Japan), Ltd., St.which Louis, serves MI, as USA), a lightwhich guide, serves was used as a to light illuminate guide, wasthe lens used prototype. to illuminate A photodiode the lens prototype. module (Model: A photodiode C10439-08, module Hamamatsu(Model: C10439-08,Photonics K.K., Hamamatsu Japan) was Photonics placed K.K., at the Japan) bottom was of placed the lower at the liquid bottom chamber of the to lower detect liquid variationschamber of the to detectlight luminance. variations When of the the light focal luminance. length of the When lens the prototype focal length changes, of the the lens density prototype of the lightchanges, that thestrikes density on the of photodiode the light that module strikes wi onll thechange, photodiode which can module be observed will change, from variations which can be of theobserved output fromvoltage. variations The variations of the output of the voltage. output Thevoltage variations of the ofphotodiode the output module voltage was of the observed photodiode frommodule Channel was 4 of observed the oscilloscope from Channel (Model: 4 of TDS the oscilloscope3034, Tektronix, (Model: Inc., TDSUSA). 3034, A function Tektronix, generator Inc., USA). (Model:A function AFG1022, generator Tektronix, (Model: Inc., AFG1022, Beaverton, Tektronix, Oregon, Inc.,OR, Beaverton,USA) was used Oregon, to generate OR, USA) the was active used to signal,generate which the directs active the signal, motion which of the directs piezo thestack motion actuator ofthe (Model: piezo P-841.60B, stack actuator Physik (Model: Instrumente P-841.60B, (PI) PhysikGmbH Instrumente& Co., Karlsruhe, (PI) GmbH Germany). & Co., The Karlsruhe, motion Germany).of the piezo The stack motion actuator of the was piezo monitored stack actuator on Channelwas monitored 1 of the oscilloscope. on Channel 1The of thereal-time oscilloscope. position The of real-time the piezo position stack actuator of the piezo was stack observed actuator on was Channelobserved 2 of the on Channeloscilloscope 2 of based the oscilloscope on the feedback based signal on the of feedback the posi signaltion sensor of the installed position in sensor the piezo installed stackin actuator. the piezo Figure stack actuator.6 shows the Figure schematic6 shows of the the schematic experimental of the setup experimental used to measure setup used the dynamic to measure frequenciesthe dynamic of the frequencies elastomer-based of the elastomer-basedliquid-filled variable liquid-ﬁlled focus lens variable prototype. focus lens prototype.

FigureFigure 6. Schematic 6. Schematic of the of experimental the experimental setup setup usedused to measure to measure the dynamic the dynamic frequencies frequencies of the of the elastomer-basedelastomer-based liquid-filled liquid-ﬁlled variable variable focus focus lens lensprototype. prototype.

3 TheThe lower lower chamber chamber (blue (blue chamber) chamber) was was filled filled with with pure pure water water (density: (density: ~0.997 ~0.997 g/cm g/3cm, refractive, refractive index:index: ~1.33), ~1.33), whereas whereas the upper the upper chamber chamber (green (green chamber) chamber) was wasfilled filled with with polydimethylsiloxane polydimethylsiloxane 3 (PDMS)(PDMS) (density: (density: ~0.975 ~0.975 g/cm g3,/ cmrefractive, refractive index: index: ~1.40). ~1.40). The elas Thetomer-taped elastomer-taped plate was plate fixed was on fixed the on connectionthe connection hole as holesoon as as soon the aspure the water pure water was infused. was infused. Following Following this, this,the upper the upper chamber chamber was was mountedmounted on top on topof the of theelastomer-tap elastomer-tapeded plate plate and and the thePDMS PDMS was was infused. infused. A sinusoidalA sinusoidal wave wave was wasused used as the as command the command signal signal to activate to activate the piezo the piezo stack stack actuator actuator and andthe the frequencyfrequency was was gradually gradually increased increased to confirm to confirm the thevibration vibration mode. mode. When When we used we used a low-frequency a low-frequency sinusoidalsinusoidal wave wave to togenerate generate the the vibrations, vibrations, wewe couldcould observe observe the the maximum maximum amplitude amplitude of the of feedback the feedbacksignal signal from from the photodiode the photodiode sensor. sensor. The amplitudeThe amplitude range range indicates indicates the variationsthe variations of the of the focal focal length lengthof theof lensthe lens prototype prototype from from minimum minimum to maximum. to maximum. As we As increased we increased the frequency the frequency of the sinusoidalof the sinusoidalwave, wewave, observed we observed that the that lens the prototype lens protot correspondsype corresponds to the to motion the motion of the of piezo the piezo stack stack actuator. actuator.However, However, when when we used we aused high-frequency a high-frequency sinusoidal sinusoidal wave wave as the as command the command signal, signal, we observed we observedthat the that amplitude the amplitude of the feedback of the signalfeedback from signal the photodiode from the sensorphotodiode significantly sensor decreasedsignificantly due to decreasedvibrational due to damping. vibrational damping.

4. Results and Discussion Figure 7 shows the measured waves displayed on the graphical user interface of the oscilloscope. Channel 1 (indicated by the yellow wave) refers to the sinusoidal wave with a frequency of 30 Hz

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4. Results and Discussion Sensors 2019, 19, x FOR PEER REVIEW 8 of 13 Figure7 shows the measured waves displayed on the graphical user interface of the oscilloscope. Channelgenerated 1 (indicatedfrom the function by the yellow generator wave) and refers transmitted to the sinusoidal to the piezo wave stack with aactuator. frequency Channel of 30 Hz 2 generated(indicated fromby the the green function wave) generator refers andto the transmitted real-time to position the piezo of stack the piezo actuator. stack Channel actuator 2 (indicated and it is byevident the green that the wave) deformation refers to theof the real-time deformable position plate of thecorresponds piezo stack to actuatorthe displacement and it is evidentof the piezo that thestack deformation actuator. Indeed, of the deformable the light power plate correspondschanges with to thea change displacement in the focal of the length piezo stackand it actuator. can be Indeed,observed the from light Channel power changes 4 (indicated with aby change the red in wa theve) focal that length the deformation and it can be of observed the elastomer from Channel surface 4corresponds (indicated by to thethe red applied wave) signal. that the The deformation threshold of frequency the elastomer of the surface vibration corresponds was 30 toHz the when applied the signal.aperture The size threshold of the lens frequency prototype of thewas vibration 30 mm. Wh wasen 30 a Hz high-frequency when the aperture sinusoidal size of wave the lens was prototype applied, wasthere 30 was mm. a Whenpronounced a high-frequency decrease sinusoidalin the amplitude wave was of applied,the feedback there wassignal a pronounced from the photodiode decrease in themodule amplitude (as shown of the feedbackon Channel signal 4), from indicating the photodiode that modulethe vibrations (as shown of onthe Channel elastomer 4), indicating surface thatwere the damped. vibrations of the elastomer surface were damped. In another experiment, we stretched a piece of elastomerelastomer to 1.5 times its original length and the elastomer was taped onto a plate with an aperture sizesize of 20 mm. Similarly, we applied a sinusoidal wave as the command signal of the piezo stack actuator and we gradually increased increased its its frequency. frequency. We foundfound that that the the vibrations vibrations of theof the elastomer elastomer surface surface were were damped damped when thewhen frequency the frequency of the applied of the signalapplied was signal more was than more 45 than Hz. 45 The Hz. results The results confirm conf thatirm the that aperture the aperture size ofsize the of lens the lens prototype prototype has ahas significant a significant effect effect on its on natural its natural frequency. frequency.

(a) (b)

Figure 7. (a) Measured waves obtained for the lens prototype with an aperture size of 30 mm and Figure 7. (a) Measured waves obtained for the lens prototype with an aperture size of 30 mm and the the elastomer was stretched to 1.5 times its original length. The piezo stack actuator was moving at elastomer was stretched to 1.5 times its original length. The piezo stack actuator was moving at a a frequency of 30 Hz with a full stroke of 90 µm. (b) Measured waves obtained for the lens prototype frequency of 30 Hz with a full stroke of 90 μm. (b) Measured waves obtained for the lens prototype with an aperture size of 20 mm. The piezo stack actuator was moving at a frequency of 45 Hz with with an aperture size of 20 mm. The piezo stack actuator was moving at a frequency of 45 Hz with a a full stroke of 90 µm. Similarly, the elastomer was stretched to 1.5 times its original length. full stroke of 90 μm. Similarly, the elastomer was stretched to 1.5 times its original length. Next, we performed experiments using a step signal (square wave) as the active signal. Next, we performed experiments using a step signal (square wave) as the active signal. The The response time for a square wave comprises the contractingτ time (τcontract) and relaxingτ time contract relax (responseτrelax). In time this experiment,for a square awave square comprises wave was the applied contracting to drive time the ( lens prototype,) and relaxing where time the ( active). signalIn this wasexperiment, switched a betweensquare wave 0 Vand was 5 applied V. Thus, toτ contractdrive theand lensτrelax prototype,are deﬁned where as the the time active taken signal for τ τ thewas lensswitched prototype between response 0 V and to 5 reach V. Thus, a steady-state contract and condition relax are whendefined the as applied the time signal taken isfor switched the lens fromprototype 0 V toresponse 5 V and to from reach 5 a V steady to 0 V,-state respectively. condition Figurewhen the8 shows applied the signal measured is switched responses from of 0 V the to lens5 V and prototype from 5 withV to 0 an V, aperture respectively. size ofFigure 20 and 8 shows 30 mm the displayed measured on responses the graphical of the user lens interface prototype of thewith oscilloscope. an aperture size Channel of 20 1and shows 30 mm the displayed square wave on the (indicated graphical by user the interface yellow wave) of the generated oscilloscope. by theChannel function 1 shows generator the square whereas wave Channel (indicated 4 shows by the theyellow variation wave) of generated the focal by length the function measured generator by the photodiodewhereas Channel module 4 (indicatedshows the byvariation the green of wave).the focal length measured by the photodiode module (indicatedIt can beby observedthe green from wave). the results that it takes a certain time for the response of the lens prototype to reachIt can a steady-state be observed condition. from the Whenresults the that active it ta signalkes a wascertain switched time for from the 0 response V to 5 V, theof the settling lens prototype to reach a steady-state condition. When the active signal was switched from 0 V to 5 V, the settling time required for the lens prototype with an aperture size of 20 mm to switch from the τ relaxing phase to the contracting phase ( contract ) was 60 ms. In contrast, when the active signal was switched from 5 V to 0 V, the settling time required of this lens prototype to switch from the

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Sensors 2019, 19, x FOR PEER REVIEW 9 of 13 time required for the lens prototype with an aperture size of 20 mm to switch from the relaxing phase to the contracting phase (τcontract) was 60 ms.τ In contrast, when the active signal was switched from contracting phase to the relaxing phase ( relax ) was reduced to 40 ms. We also used the same 5 V to 0 V, the settling time required of this lens prototype to switch from the contracting phase to measurement procedure for the lens prototype with a larger aperture size (diameter: 30 mm) and we the relaxing phase (τ ) was reduced to 40 ms. We also used the same measurement procedure for found that the settlingrelax time required for the lens prototype to switch from the relaxing phase to the the lens prototype withτ a larger aperture size (diameter: 30 mm) and we found that the settling time contracting phase ( contract ) was 200 ms. Similarly, the settling time required for this lens prototype to required for the lens prototype to switch from the relaxing phase to the contracting phase (τcontract) was τ 200switch ms. from Similarly, the contracting the settling phase time required to the relaxing for this lensphase prototype ( relax ) was to switch slightly from shorter, the contracting with a value phase of to160 the ms. relaxing The results phase are (τ relaxin a) good was slightly agreement shorter, with withour previous a value of discussion 160 ms. The where results the response are in a good time agreement(settling time) with of our the previous elastomer-based discussion liquid-filled where the responsevariable focus time (settling lens will time) increase of the when elastomer-based the aperture liquid-ﬁlledsize is increased. variable focus lens will increase when the aperture size is increased.

FigureFigure 8. MeasuredMeasured responses responses ofof the the elastomer-based elastomer-based liquid-filled liquid-ﬁlled variable variable focus focus lens lensprototype prototype with withan aperture an aperture size sizeof (a of, b ()a 20, b )mm 20 mmand and(c, d ()c ,30d )mm 30 mm displayed displayed on the on thegraphical graphical user user interface interface of the of theoscilloscope. oscilloscope. The Thesettling settling times times were were 60 and 60 and 40 ms, 40 ms, respectively, respectively, when when the the lens lens prototype prototype with with an anaperture aperture size size of of20 20mm mm switched switched from from the the relaxing relaxing phase phase to tocontracting contracting phase phase and and vice vice versa. versa. In Incontrast, contrast, the the settling settling times times were were significantly signiﬁcantly higher higher for the for lens the lensprototype prototype with with an aperture an aperture size of size 30 ofmm, 30 with mm, a with value a valueof 200 ofand 200 160 and ms, 160 respectively, ms, respectively, when the when lens the prototype lens prototype switched switched from the from relaxing the relaxingphase to phase the contracting to the contracting phase and phase vice and versa. vice versa.The active The activesignal signal(indicated (indicated by the by yellow the yellow wave) wave) was wasswitched switched (a, c ()a from, c) from 0 V 0to V 5 toV 5and V and(b, d (b) ,fromd) from 5 V 5to V 0 toV. 0 V.

FigureFigure9 9shows shows the the tunable tunable range range of theof the elastomer-based elastomer-based liquid-ﬁlled liquid-filled variable variable focus focus lens, lens, which which was measuredwas measured indirectly indirectly using using the experimentalthe experimental setup setup in Figure in Figure 10. The10. The displacement displacement at theat the center center of theof the elastomer elastomer was was measured measured by by a high-speeda high-speed laser laser displacement displacement sensor sensor (Model: (Model: LK-G400, LK-G400, KeyenceKeyence Corporation,Corporation, Osaka,Osaka, Japan). Japan). Because Because the the elastomer elastomer and and two two liquids liquids were were transparent, transparent, it wasit was diﬃ difficultcult to to measure the displacement of the elastomer membrane. Hence, we removed one of the liquid chambers and we affixed a small piece of paper at the center of the elastomer. With this modification, we were able to measure the displacement at the center of the elastomer when the laser beam struck

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SensorsmeasureSensors 2019, 192019, x the ,FOR 19 displacement, x PEER FOR PEERREVIEW REVIEWof the elastomer membrane. Hence, we removed one of the liquid10 chambersof 1013 of 13 and we affixed a small piece of paper at the center of the elastomer. With this modification, we were the pieceablethe piece toofmeasure paper. of paper. The the displacementlaserThe laserdisplacement displacement at the centersensor sensor of was the wasplaced elastomer placed on whentop on oftop the the of laser lensthe beam lensprototype. struckprototype. theThe piece The maximumofmaximum paper. displacement Thedisplacement laser displacementwas 2.2035was 2.2035 mm, sensor mm,indicating wasindicating placed that thethat on center topthe ofcenter of the the lensof elastomer the prototype. elastomer was The deflectedwas maximum deflected fromdisplacementfrom 0.0000 0.0000 mm tomm was 2.2035 to 2.2035 2.2035 mm. mm, mm. indicating that the center of the elastomer was deflected from 0.0000 mm toWe 2.2035 assumedWe assumed mm. that thethat deformed the deformed elastomer elastomer surface surface was symmetricwas symmetric and uniformand uniform and theand surface the surface profileprofile resembledWe resembled assumed a parabolic thata parabolic the shape deformed shape [14]. [14].When elastomer When the elastomer surfacethe elastomer was is not symmetric is considerably not considerably and uniform deformed deformed and relative the relative surface to itsprofileto aperture its aperture resembled size, size,the adeformation parabolicthe deformation shape can be [can14 approx]. be When approximated theimated elastomer by a sphericalby a is spherical not considerablyshape shape [7]. Thus, [7]. deformed Thus, the bending the relative bending to curvatureitscurvature aperture can becan size,calculated be thecalculated deformation based based on the can on displacement bethe approximated displacement of the byof elastomer. athe spherical elastomer. As shape shown As [shown7]. in Thus, Figure in theFigure 9, bending in 9, in R r − ABO,curvatureABO, the curvature the cancurvature be of calculated the of profile the basedprofile , on theR the ,aperture the displacement aperture radius radius of the, and elastomer.r , lengthand length of As OB shownof (i.e., OB in(i.e.,curvature Figure curvature9, in R ABO, R− displacementthe curvatureh ) ofcanh the be profile determinedR, the aperture from radiusthe right-anglr, and lengthed triangle. of OB (i.e., It curvatureshall be Rnoteddisplacement that displacement ) can be determined from the right-angled triangle. It shall −be2 noted that 222 2 2 =−h())22 can be + determined2 from the right-angled triangle. It shall be noted that R = (R h) + r . RRhrRRhr=−() + − . .

FigureFigure 9. Schematic 9. SchematicSchematic of the of lens the profile lens profile proﬁle when when the variable the variable focus focuslens has lens a hasconvex a convex profile. proﬁle.profile.

When the aperture radius was 10 mm and the displacement was 2.2035 mm, the bending curvature WhenWhen the aperturethe aperture radius radius was wa10 smm 10 mmand andthe displacementthe displacement was was2.2035 2.2035 mm, mm,the bendingthe bending was 23.793 mm. The power of the lens can be calculated from the following equation curvaturecurvature was 23.793was 23.793 mm. mm.The powerThe power of the of lens the canlens be can calculated be calculated from from the following the following equation equation − 1 1 NN12N1 −N2 P ==1 NN12. P =P === − .. (3) (3) fRf fRR

N standsN stands for the for refractive the refractiverefractive index indexindex of the ofof liquid. thethe liquid.liquid. When When the liquid the liquid pair pairconsisted consisted of pure of purewater water (refractive(refractive index: index:index: ~1.33) ~1.33) and siliconeand silicone oil (refractive oil (refractive index: index: ~1.40), ~1.40), the tunable the the tunable tunable focal focal focallength length length ranged ranged from from 339.9339.9 mm to mm infinity to inﬁnityinfinity and the and tunable the tunable power powerpower range rangerange was 0.00–2.94. waswas 0.00–2.94.0.00–2.94.

(a)(a) (b) (b)

FigureFigure 10. Schematic 10. Schematic of the of experimental thethe experimentalexperimental setup setup setup (a) used ( a(a)) used toused measure to to measure measure the displacement the the displacement displacement of the of of theelastomer the elastomer elastomer of b of thetheof elastomer-basedthe elastomer-based elastomer-based liquid-filled liquid-ﬁlled liquid-filled variablevariable variable focus focu lens.s foculens. Thes lens.The displacement displacementThe displacement at the at center the at center ofthe the center elastomerof the of the ( ) (i.e., displacement at the center of the lens aperture) was measured by a high-speed laser displacement elastomerelastomer (b) (i.e., (b) displacement (i.e., displacement at the at center the center of the of lens the aperture) lens aperture) was measur was measured byed a high-speed by a high-speed laser laser sensor (Model: LK-G400, Keyence Corporation, Osaka, Japan). displacementdisplacement sensor sensor (Model: (Model: LK-G400, LK-G400, Keyence Keyence Corporation, Corporation, Osaka, Osaka, Japan). Japan).

The USAFThe USAF 1951 1951resolution resolution test chart test chart was usedwas usedas the as target the target image image and it and was it placedwas placed 39 mm 39 awaymm away fromfrom the lensthe lensprototype. prototype. A camera A camera (Basler (Basler acA1300-200uc, acA1300-200uc, Basler Basler AG, AG,Ahrensburg, Ahrensburg, Germany) Germany) equippedequipped with witha microlens a microlens kit (Mod kit (Model: EO-39686el: EO-39686 and EO-55359, and EO-55359, Edmund Edmund Optics, Optics, Inc., Barrington,Inc., Barrington, NJ, NJ,

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The USAF 1951 resolution test chart was used as the target image and it was placed 39 mm away

Sensorsfrom the 2019 lens, 19, prototype.x FOR PEER REVIEW A camera (Basler acA1300-200uc, Basler AG, Ahrensburg, Germany) equipped11 of 13 with a microlens kit (Model: EO-39686 and EO-55359, Edmund Optics, Inc., Barrington, NJ, USA) USA)were usedwere to used capture to capture the image the ofimage the other of the size other of the size lens of prototype.the lens prototype. Figure 11 Figure shows 11 the shows recorded the recordedimage when image the when focal lengththe focal of thelength elastomer-based of the elastomer-based liquid-ﬁlled liquid-filled variable focus variable lens focus was 500.0 lens mm.was 500.0We achieved mm. We a resolutionachieved a of resolution 64.00 lp/mm of 64.00 (Group lp/mm 6, Element (Group 1) 6, and Element 50.80 lp1)/ mmand (Group50.80 lp/mm 5, Element (Group 5) in5, Elementthe vertical 5) in and the horizontal vertical and directions, horizontal respectively. directions, respectively.

Figure 11. ImageImage of of the the USAF USAF 1951 1951 resolution resolution test test char chartt captured captured when when the the focal focal length length of of the elastomer-based liquid-filled liquid-ﬁlled variable variable focus focus lens lens was was 500.0 mm. The resolutions achieved were 64.00 lp/mm lp/mm (Group 6, Element 1) an andd 50.80 lp/mm lp/mm (Group 5, Element 5) in the vertical vertical and and horizontal horizontal directions, respectively.

5. Conclusions 5. Conclusions In this work, we investigated the critical factors that affect the dynamic response of In this work, we investigated the critical factors that affect the dynamic response of an elastomer- an elastomer-based liquid-filled variable focus lens. Based on theoretical analysis of a deformable based liquid-filled variable focus lens. Based on theoretical analysis of a deformable circular disk circular disk (which is representative of a deformable surface), we found that the diameter, thickness, (which is representative of a deformable surface), we found that the diameter, thickness, and stiffness and stiffness of the circular disk are the critical factors that determine the first natural frequency of the of the circular disk are the critical factors that determine the first natural frequency of the variable variable focus lens. focus lens. We fabricated the elastomer-based liquid-filled variable focus lens prototype, which consisted of We fabricated the elastomer-based liquid-filled variable focus lens prototype, which consisted a deformable plate and elastomer-taped plate with different aperture sizes (diameter: 20 and 30 mm). of a deformable plate and elastomer-taped plate with different aperture sizes (diameter: 20 and We used a high-speed piezo stack actuator as the pumping unit and we devised a mechanism to 30 mm). We used a high-speed piezo stack actuator as the pumping unit and we devised a mechanism amplify the deformation of the deformable plate to the soft elastomer. The elastomer was stretched to to amplify the deformation of the deformable plate to the soft elastomer. The elastomer was stretched 1.5 times its original length prior to fabrication to implant the in-plane pretension force device and to 1.5 times its original length prior to fabrication to implant the in-plane pretension force device and increase the sti ness of the elastomer. increase the stiffnessff of the elastomer. When we applied a sinusoidal wave as the active signal on the deformable plate via the piezo stack When we applied a sinusoidal wave as the active signal on the deformable plate via the piezo stackactuator, actuator, we found we found that the that lens the prototype lens prototype with an with aperture an aperture size of 30 size mm of achieved 30 mm achieved a stableresponse a stable responseat 30 Hz. at In 30 contrast, Hz. In thecontrast, lens prototype the lens prototype with an aperture with an size aperture of 20 mm size achieved of 20 mm a stableachieved response a stable at response45 Hz. When at 45 weHz. applied When we a high-frequency applied a high-frequen sinusoidalcy sinusoidal wave on the wave deformable on the deformable plate, we observedplate, we observedthat the amplitude that the ofamplitude the feedback of the signal feedback from the signal photodiode from the module photodiode significantly module decreased significantly due to decreasedvibrational due damping to vibrational of the elastomer damping surface. of the elastomer surface. When we applied a square wave as the active signal, we found that the contracting time and relaxing time of the the lens lens prototype prototype with with an an aperture aperture size size of of 30 30 mm mm were were 200 200 and and 160 160 ms, ms, respectively. respectively. When we used a smaller aperture size (20 mm), the contracting time and relaxing time of the lens prototype were significantly reduced to 60 and 40 ms, respectively, indicating a marked improvement in the dynamic response of the elastomer-based liquid-filled variable focus lens. Because the elastomer-based liquid-filled variable focus lens can steadily vibrate to change its focal length at a frequency of more than 30 Hz, this lens can be potentially embedded in a high-speed

Sensors 2019, 19, 4624 12 of 13 prototype were significantly reduced to 60 and 40 ms, respectively, indicating a marked improvement in the dynamic response of the elastomer-based liquid-filled variable focus lens. Because the elastomer-based liquid-filled variable focus lens can steadily vibrate to change its focal length at a frequency of more than 30 Hz, this lens can be potentially embedded in a high-speed projector to generate three-dimensional interactive scenes [20,21]. This lens can also be used to realize a high-speed shape from focus and all-in-focus imaging [22,23]. Even though the elastomer employed in our experiments can be easily fabricated, it suffers from low stiffness. Hence, the dynamic response of the elastomer-based liquid-filled variable focus lens can be significantly improved by employing an elastomer with a higher stiffness. In addition, the dimensions of the elastomer-based liquid-filled variable focus lens can be custom-tailored to fulfill the optical requirements for a particular application and the critical factors that affect the dynamic response identified in this work will be useful in the design of variable focus lens for optical systems.

Author Contributions: Conceptualization, L.W. and M.I.; Methodology, L.W.; Software, L.W.; Validation, L.W.; Formal Analysis, L.W.; Investigation, L.W.; Resources, L.W.; Data Curation, L.W.; Writing-Original Draft Preparation, L.W.; Writing-Review & Editing, L.W.; Visualization, L.W.; Supervision, L.W. and M.I.; Project Administration, L.W. and M.I.; Funding Acquisition, L.W. and M.I. Funding: Accelerated Innovation Research Initiative Turning Top Science and Ideas into High-Impact Values Grant (JST) (JPMJAC15F1); KAKENHI Grant-in-Aid for Young Scientists by Japan Society for the Promotion of Science (JSPS) (15K16035). Acknowledgments: This work was partially supported from Konica Minolta Inc. Conﬂicts of Interest: The authors declare no conﬂict of interest.

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