An Electrically Tunable Zoom System Using Liquid

Article

An Electrically Tunable Zoom System Using Liquid Lenses Heng Li 1,† , Xuemin Cheng 2,† and Qun Hao 1, * Received: 4 November 2015; Accepted: 28 December 2015; Published: 31 December 2015 Academic Editor: Manuela Vieira 1 2

* †

School of Optoelectronics, Beijing Institute of Technology, Beijing 100081, China; [email protected] Graduate School at Shenzhen, Department of Precision Instrument, Tsinghua University, Shenzhen 518055, China; [email protected] Correspondence: [email protected]; Tel./Fax: +86-10-6891-4738 These authors contributed equally to this work.

Abstract: A four-group stabilized zoom system using two liquid lenses and two fixed lens groups is proposed. We describe the design principle, realization, and the testing of a 5.06:1 zoom system. The realized effective focal length (EFL) range is 6.93 mm to 35.06 mm, and the field of view (FOV) range is 8˝ to 40˝ . The system can zoom fast when liquid lens 1’s (L1 ’s) optical power take the value from 0.0087 mm´1 to 0.0192 mm´1 and liquid lens 2’s (L2 ’s) optical power take the value from 0.0185 mm´1 to ´0.01 mm´1 . Response time of the realized zoom system was less than 2.5 ms, and the settling time was less than 15 ms.The analysis of elements’ parameters and the measurement of lens performance not only verify the design principle further, but also show the zooming process by the use of two liquid lenses. The system is useful for motion carriers e.g., robot, ground vehicle, and unmanned aerial vehicles considering that it is fast, reliable, and miniature. Keywords: optical imaging; liquid lens; stabilized zoom system; Gaussian bracket

1. Introduction The optical zoom system used for imaging or projection is widely applied to many fields, such as surveillance, medicine, aviation, and aerospace [1–5]. Optical zoom systems used in imaging must satisfy two basic conditions: adjustable focal length and a fixed image plane. Traditional zoom systems usually comprise several lens groups and the separation between adjacent groups is allowed to vary. Focal length of the zoom system is varied continuously by the displacements of lens groups, the individual lens group must move along the precise track, and the action of multiple lens groups must ensure synchronization [6]. As a result, a complex mechanical camera system is required in the process of zooming. As the conventional zoom system is applied to high-speed moving vehicles, the reliability of the conventional zoom systems will be reduced due to vibration, and the response time is hard to meet the requirement of high-speed as well. A novel optical zoom system based on focal length variable optical components has been presented. Focal length of such optical components can be adjusted by varying its surface shape or refractive index [7,8]. Different from traditional optical zoom systems, this new type of optical zoom system can operate by adjusting the focal length variable optical components without involving any motorized movements. This novel optical zoom system is more attractive because of the low complexity, high reliability, and the ability to be easily miniaturized, which make it suitable for being utilized in robots or other moving carriers. Many researchers designed zoom systems based on such focal length variable optical components, which reduced the dependence on motorized components, therefore effectively decreasing the complexity of the system [9–17]. However, there still remain

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difficulties in the realization of stabilized zoom systems using optical power as a zoom variable. For variable. For example, it would be ideal if the focal length variable elements would compensate for example, it would be ideal if the focal length variable elements would compensate for the image shift the image shift while taking over the variations of the focal length of the zoom system. This is one while taking over the variations of the focal length of the zoom system. This is one reason why most of reason why most of the existing designs still have a small amount of motorized components. the existing designs still have a small amount of motorized components. Requirements in large zoom Requirements in large zoom ratio, high zoom precision, high imaging quality, and excellent ratio, high zoom precision, high imaging quality, and excellent electrical performance are also giving electrical performance are also giving lens design greater challenges. lens design greater challenges. In this paper, we propose to realize a four-group stabilized zoom system based on two liquid In this paper, we propose to realize a four-group stabilized zoom system based on two liquid lenses. Firstly, we analyze the solution of image displacement compensation, and discuss the design lenses. Firstly, we analyze the solution of image displacement compensation, and discuss the design method based on the theory of Gaussian brackets. Stable image plane provides help for improving method based on the theory of Gaussian brackets. Stable image plane provides help for improving the imaging quality. The method has been presented in our previous work [18]. It solved the the imaging quality. The method has been presented in our previous work [18]. It solved the problem problem of increasing zoom ratio with a mathematical method. Optimization of parameters was of increasing zoom ratio with a mathematical method. Optimization of parameters was realized realized by mathematically solving extreme value and maximum gradient of the function. by mathematically solving extreme value and maximum gradient of the function. Application of Application of the method has been extended in this paper. In view of the specific application, we the method has been extended in this paper. In view of the specific application, we designed and designed and optimized a realizable zoom system, and the zoom ratio is designed to be 5:1. optimized a realizable zoom system, and the zoom ratio is designed to be 5:1. Secondly, we realized Secondly, we realized the zoom device and set up an experiment platform to test the performance of the zoom device and set up an experiment platform to test the performance of the zoom system. We the zoom system. We test zoom ratio, zoom precision, and imaging quality. The results show that the test zoom ratio, zoom precision, and imaging quality. The results show that the realized system has realized system has good electrical performance and high imaging quality. Zoom ratio and precision good electrical performance and high imaging quality. Zoom ratio and precision of the system have of the system have reached the design target. reached the design target.

Theory Analysis Analysis and and Design Design 2.2. Theory 2.1.Imaging ImagingSystem SystemDesign Design 2.1. Wepresented presenteda adesign designmethod methodthat thatisisapplicable applicabletotofour-group four-groupstabilized stabilizedzoom zoomsystem systemininthe the We previouswork work[18]. [18].The Theoptical opticallayout layoutofofthe thefour-group four-groupstabilized stabilizedzoom zoomsystem systemisisshown shownininFigure Figure1,1, previous whereΦΦ andΦΦ3 3 are arethe theoptical opticalpower powerofofthe thefixed fixedgroups, groups,ΦΦ andΦΦ4 4are areoptical opticalpower powerofofthe the where 1 1and 2 2and stabilizedfocal-length-variable focal-length-variable groups. The terms e2the , e3separations are the separations the stabilized groups. The terms e1 , e2 , ee31,are between the between consecutive consecutive principle group, e4 is the separation between last the image principle planes in eachplanes group,ine4each is the separation between the last groupthe and thegroup imageand plane, mi is plane, mi is magnification of each group. magnification of each group.

Figure1.1.Structure Structureofofthe thezoom zoomsystem. system. Figure

In previous work, we analyzed this four-group stabilized zoom systems using the optical In previous work, we analyzed this four-group stabilized zoom systems using the optical power power of the optical element as the independent variables in the zoom equation. Simplified of the optical element as the independent variables in the zoom equation. Simplified differential differential function is used to describe the relationship between the focal length variation of function is used to describe the relationship between the focal length variation of varifocal elements varifocal elements and the focal length variation of zoom system. The differentiable condition and the focal length variation of zoom system. The differentiable condition optimization can be used optimization can be used to get the analytic solution. In the zooming process, the function of the to get the analytic solution. In the zooming process, the function of the optical power of the focal optical power of the focal length variable groups is monotonic, and the function of magnification has length variable groups is monotonic, and the function of magnification has a breakpoint. The optical a breakpoint. The optical layout can be miniaturized as magnification has a larger derivative near layout can be miniaturized as magnification has a larger derivative near the breakpoint. If the sign of the breakpoint. If the sign of m3 is changeable during zooming, a larger derivative of m3 can be m3 is changeable during zooming, a larger derivative of m3 can be found near the breakpoint. Then found near the breakpoint. Then we optimize the Gaussian parameters of the fixed lens groups,

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e4 1  e11 e4 1 ´ e1 φ1 2 make and parameters ( of Bthe  e 2 ,  3lens ,  e 3 groups,   3  e 2  e 3 is Gaussian we optimize the Gaussian and brackets   e 2  e 3 make 4  fixed 2 2 2 p1 ´ e1 φ1 q ¨ B4 e4 ¨ 2 B 4 (1  e11 )  B4 e4  B4 2 B4 “ r´e2 ,converge φ3 , ´e3 s “toea2 ¨minimum e3 ¨ φ3 ´ e2to´reach e3 is Gaussian (parameter) bracketsofparameter) converge to a minimum to the requirement zoom ratio. reachInthe requirement of zoom ratio. this paper, the optical design of a 5:1 stabilized zoom system is investigated. The zoom range In this paper, optical of a 5:1parameters stabilized zoom system is investigated. zoom range is designed to be 7the mm to 35 design mm. Design are determined based on theThe requirement of is a designed to be 7 mm to 35 mm. Design parameters are determined based on the requirement of a kind kind of ground vehicle being deployed on a bumpy road. The values of the Gaussian parameters are of ground vehicle being deployed on a bumpy The values of the Gaussian parameters are listed ˇ 1 road. ˇ e1ˇˇ1 e4 ˇˇ ˇ ˇ 1 ´ e φ e 1 1 ˇ  0.001 .  0.12and ˇ ˇ “ 0.12, ˇ 1, 4 listed in 1, Table , and in Table 2 ˇ “ 0.001. ˇ e ¨e 2 B ˇ p1 ´ e φ(1 2 )  2ˇ B 1 1 q ¨e11B 4 4 4 4  4B4 The relationship between m , m and m is shown in Figure 2, a larger derivative of m can be The relationship between m22, m33 and m44 is shown in Figure 2, a larger derivative of m33 can be found near the breakpoint since the sign of m is changeable. found near the breakpoint since the sign of m33 is changeable. Table 1. Gaussian parameters of the zoom system. Table 1. Gaussian parameters of the zoom system. ´1 ) −1 1/Φ (mm) Φ2 (mm ) −1)Φ4 (mm 1/Φ (mm) Φ2´1 (mm Φ4 (mm )

Wide Wide 7.27 7.27 Middle Middle26.14 26.14 Tele Tele 36.34 36.34

0.0080.008 0.0190.019 0.02 0.02

0.019 0.019 0 0 ´0.01 −0.01

mm 22

1.28 1.28 2.31 2.31 2.53 2.53

mm 3 3 −0.28 ´0.28 0.11 0.11 0.19 0.19

m4 m4 0.56 0.56 1.03 1.03 1.24 1.24

Figure 2. Relationship Figure 2. Relationship between between m m22,, m m33, , and and m m44. . AAlarger largerderivative derivative of of m m33 can can be be found found near near the the breakpoint since the sign of m 3 is changeable. breakpoint since the sign of m3 is changeable.

We use two liquid lenses (L1 and L2) as the focal length variable groups (Φ2, Φ4), the variation of We use two liquid lenses (L1 and L2 ) as the focal length variable groups (Φ2 , Φ4 ), the variation of Φ2 and Φ4 can be obtained as follows: Φ2 and Φ4 can be obtained as follows: e   [ , ( e  e ), 3 ,  e3 ]  2 e4 Φ4 ´ rφ1 ,1 ´pe11 ` 2e22 q, φ , ´e3 s (1) (1  e  )  B 3 (1) Φ2 “ p1 ´ e11φ11 q ¨ 2 4B4 2 B  e [  e2 ,  3 ] 1 e   4 1 ´ e φ12 1  2 B4 ´ 4e 2 r´e (2) 1 1 4 e  4 B 2 , φ3 s Φ4 “ e4 2 B4` (2) 4 4 2 e4 Φ ¨ B 4 e4 ¨ B 4 ee44   ∆Φ ∆Φ 2 (3) 2 “2 ( 1  e  p1 ´ e11φ11)q ¨ B24B4 ˆ ˙ 1 1´ee11φ11  11  ∆Φ “ ∆ (4) 4 4    (4) Φ  e4e ¨ 22BB4   4 4 ˆ ˙ 1 1 1 where ∆Φ “ Φs ´ Φl is the variation of the system optical power, ∆  1 “ 1 ´ 1 , Φs and Φl where    s   l is the variation of the system optical power,  Φ    Φs  Φl , Φs and Φl s l  end  respectively, represent the system optical power at the wide-angle end and the telephoto ∆Φ2 and 1 the 1telephoto end respectively, ∆Φ2 represent the system optical power at the wide-angle end and ∆Φ4 are the variation needed to achieve a given zoom range to . Φs 1Φl 1 and ∆Φ4 are the variation needed to achieve a given zoom range to . s

l

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The general parameters of the zoom system are shown in Table 2. The initial lens structure of The general parameters ofGaussian the zoomparameters system areisshown in Table 2. The initial lens of the optical system using these simulated and optimized with thestructure commercial the optical system using these Gaussian parameters is simulated and optimized with the commercial optical design software named CODE V (Optical Research Associates, Tucson, AZ, USA), the result optical design software CODE V (Optical Research AZ, USA), result is is shown in Figure 3, named as the wide-angle end, the middleAssociates, phase, andTucson, the telephoto endthe are shown shown in Figure 3, as the wide-angle end, the middle phase, and the telephoto end are shown in (a), in (a), (b), and (c), respectively. (b), and (c), respectively.

Figure 3. Initial lens structure of the optical system.

Figure 3. Initial lens structure of the optical system. Table 2. General parameters of the zoom system. Table 2. General parameters of the zoom system. # Curvature Radius Thickness

Surface

Surface Object Object

#

Glass

Curvature Radius Thickness Glass Infinity Infinity Infinity Infinity 1 Infinity ´9.7160 1 Infinity −9.7160 2 ´27.4979 3.7885 HLAF4_CDGM 3 7.5970 1.4003 2 −27.4979 3.7885 HLAF4_CDGM Fixed Lens1 4 ´9.0978 7.8405 ZK9_CHINA 3 7.5970 1.4003 Fixed 5 ´8.1539 1.5000 Lens1 4 −9.0978 7.8405 ZK9_CHINA 6 Infinity 0.1000 5 −8.1539 1.5000 7 Infinity 0.5000 BK7_SCHOTT 8 Infinity zoom 6 Infinity 0.1000 Liquid Lens1 9 zoom zoom “OL1024” 7 Infinity 0.5000 BK7_SCHOTT 10 Infinity 0.5000 BK7_SCHOTT 8 Infinity zoom 11 Infinity 1.1000 Liquid 12 25.9971 9 zoomInfinity zoom “OL1024” Lens1 Infinity 81.4883 10 13 Infinity 0.5000 BK7_SCHOTT 14 77.7631 8.2500 ZK9_CHINA 11 Infinity 1.1000 15 ´18.8293 0.1000 Fixed Lens2 12 Infinity 25.9971 16 ´18.5589 1.5000 ZF50_CDGM ´41.6000 7.0723 13 17 Infinity 81.4883 Infinity 0.0500 14 18 77.7631 8.2500 ZK9_CHINA 19 Infinity 0.5000 BK7_SCHOTT 15 −18.8293 0.1000 Fixed 20 Infinity zoom Lens2 16 −18.5589 1.5000 ZF50_CDGM Liquid Lens2 21 zoom zoom “OL1024” Infinity 0.5000 BK7_SCHOTT 17 22 −41.6000 7.0723 Infinity 3.4500 18 23 Infinity 0.0500 24 Infinity 0.8943 19 Infinity 0.5000 BK7_SCHOTT 25 Infinity 17.9482 20 Infinity zoom Image Infinity 0.0000 Liquid 21 zoom zoom “OL1024” Lens2 22 Infinity 0.5000 BK7_SCHOTT 2.2. Operating Range and Precision 23 Infinity 3.4500 The zoom system operates by changing of two liquid lenses (L1 ’s optical power 24 Infinity the optical power 0.8943 Φ2 , and L2 ’s optical power Φ ). Two focus tunable lenses (Optotune, Swizerland) are used in the 4 25 Infinity 17.9482 experiments, a 10 mm aperture commercial lens EL-10-30 for L1 , and a 20 mm aperture custom-design Image Infinity 0.0000

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2.2. Operating Range and Precision 2.2. Operating Range and Precision SensorsThe 2016,zoom 16, 45 system operates by changing the optical power of two liquid lenses (L1’s optical 5 of 13 The operates by changing the optical power of two liquid lenses (L1’s optical power Φ2,zoom and Lsystem 2’s optical power Φ4). Two focus tunable lenses (Optotune, Swizerland) are used in power Φ2, and L2’saoptical power Φ4). Two focus tunable lenses (Optotune, Swizerland) areaperture used in the experiments, 10 mm aperture commercial lens EL-10-30 for L1, and a 20 mm the experiments, 10 Lmm aperture lens lenses, EL-10-30 L1, and arefractive 20ofmm aperture lens for L2 . Both La1 for and are liquid-filled the for refractive index the lenses is custom-design lens 2L . 2Both L1 and commercial L2 aremembrane liquid-filled membrane lenses, the index of custom-design lens for L 2100. . Both L 1 and L 2 are liquid-filled membrane lenses, the refractive index of 1.30, and Abbe number is Φ and Φ are controlled by adjusting L ’s control current (I ) and L 1 current 2 ’s 2 4 the lenses is 1.30, and Abbe number is 100. Φ2 and Φ4 are controlled by1 adjusting L1’s control ´ 1 ´ 1 the lenses is 1.30, and Abbe number is 100. Φ 2 and Φ 4 are controlled by adjusting L 1 ’s control current control (I2 ), respectively. of Φ2 is 0.008ofmm 0.022mm mm control precision is −1 to, 0.022 −1, control (I1) andcurrent L2’s control current (I2), Range respectively. Range Φ2 is to 0.008 mm 5 control ´1 . current ´of 1 to ´1 , −1the −1, control (I 1) and L 2´ ’s (I 2), Φ respectively. Range Φ 2 is 0.008 mm to 0.022 mm 4.67 ˆ 10 mm Range of is ´0.0142 mm 0.02 mm control precision −5 −1 −1 −1 −4 precision is 4.67 × 10 mm . Range of4 Φ4 is −0.0142 mm to 0.02 mm , the control precision is 3 × 10is ´4 mm ´1 , ×zero −5 mm−1. Range of Φ4 is −0.0142 mm−1 to 0.02 mm−1, the control precision is 3 × 10−4 is 4.67 10 3precision ˆ 10 optical power is attainable. The relationships between optical power and control mm−1, zero optical power is attainable. The relationships between optical power and control currents −1, zero optical power is attainable. The relationships between optical power and control currents mm currents areinshown 4. Asinshown figure, precision of L1 higher is much higher thanwe L2 ,use thusL2we are shown Figurein4.Figure As shown figure,inprecision of L1 is much than L2, thus as are shown in Figure 4. As shown in figure, precision of L 1 is much higher than L 2 , thus we use L2 as use L as active element, and use L as servo element to compensate the image displacement. active2 element, and use L1 as servo1element to compensate the image displacement. active element, and use L1 as servo element to compensate the image displacement.

Figure 4. Optical power of the liquid lenses as functions of control currents. Figure 4. Optical power of the liquid lenses as functions of control currents. Figure 4. Optical power of the liquid lenses as functions of control currents.

Our purpose is to design a zoom system with effective focal length (EFL) of 7 mm to 35 mm. In Our purpose is to design a zoom system with effective focal length (EFL) of 7 mm to 35 In 35 mm. mm. Section 2.1, we calculated the Gaussian parameters of the system, and optimizedmm the to system with Section 2.1, we calculated the Gaussian parameters of the system, and optimized system with Gaussian system, optimized the system CODE V. From calculated Equation (2), we can calculate EFL of the zoom system theoretically. The calculated CODE V. From Equation (2), we can calculate EFL of the zoom system theoretically. The calculated V. From Equation (2), we can calculate EFL of the zoom system theoretically. The calculated range of EFL is 7.27 mm to 36.34 mm, the zoom ratio is 5:1. Then we simulate the designed system, range of EFL is 7.27 mm 36.34 mm, zoom ratio is 5:1. simulate the designed system, mm to toset 36.34 mm,5the the 5:1. Then weRelationships select 20 sampling points, I2 from mAzoom to 100ratio mA, respectively. between EFL and select 20 points, set I2I2from respectively. Relationships between EFL and I2 select 20 sampling sampling points, setsimulated from55mA mAto to100 100mA, Relationships between and I2 are shown in Figure 5. The EFL range ismA, 6.46respectively. mm to 33.97 mm, and the zoom ratio EFL is 5.26:1. are shown inin Figure 5. 5.The 5.26:1. I2 are shown Figure Thesimulated simulatedEFL EFLrange rangeisis6.46 6.46mm mmto to33.97 33.97mm, mm, and and the the zoom ratio is 5.26:1.

Figure 5. Calculated and simulated EFL as functions of I2. The “simulated dots” mark the EFL of Figure 5. Calculated and simulated EFL as functions of I2. The “simulated dots” mark the EFL of sampling that be obtained by CODE The “simulated line” is the fitting curve of the Figure 5. points Calculated and simulated EFL asV. functions of I2 . The “simulated dots” mark the dots. EFL of sampling points that be obtained by CODE V. The “simulated line” is the fitting curve of the dots. sampling points that be obtained by CODE V. The “simulated line” is the fitting curve of the dots.

In this paper, zoom precision is defined as the minimum variation of EFL that can be adjusted In this paper,ofzoom precision is defined as the minimum variation of EFL cantheoretically be adjusted i.e., the variation EFL when I2 increase or decrease 1 mA. From Equation (4), that we can In this paper,ofzoom precision is defined as the minimum variation of EFL cantheoretically be adjusted i.e., the variation EFL when I2 increase or decrease 1 mA. From Equation (4),that we can i.e., the variation of EFL when I2 increase or decrease 1 mA. From Equation (4), we can theoretically calculate the zoom precision to be 0.3 mm. Then we simulate the zoom precision with CODE V. We

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precision to be 0.3 mm. Then we simulate the zoom precision with CODE 6V.of We 13 firstly select 20 sampling points when I2 takes different values listed in Table 3, then make I2 increase 1 mA, corresponding values of Φ4 can be obtained from Figure 4. The simulated results are firstly 20 sampling points when I2 takes different values listed in Table 3, then make I2 increase shownselect in Table 3. 1 mA, corresponding values of Φ4 can be obtained from Figure 4. The simulated results are shown in Table 3. Table 3. Simulated zoom precision of the zoom system. 3. Simulated zoom precision of the Zoom zoom system. I2 (mA) Table Zoom Precision (mm) I2 (mA) Precision (mm) 5 0.2911 55 0.2945 I2 (mA)10 Zoom Precision Zoom Precision (mm) 0.2731 (mm) 60I2 (mA) 0.2924 5 15 0.2911 0.2612 65 55 0.2898 0.2945 10 20 0.2731 0.2762 70 60 0.2867 0.2924 15 0.2612 65 0.2898 25 0.2862 75 0.2832 20 0.2762 70 0.2867 0.292 80 75 0.2792 0.2832 25 30 0.2862 0.295 85 80 0.2749 0.2792 30 35 0.292 35 40 0.295 85 0.2964 90 0.2703 0.2749 40 0.2964 90 45 0.2966 95 0.2652 0.2703 45 0.2966 95 0.2652 0.2959 100 100 0.2601 0.2601 50 50 0.2959 Average 0.2830 RMSRMS 0.0122 0.0122 Average 0.2830

Therefore, we designed and simulated a zoom system with 5:1 zoom ratio. The calculated EFL Therefore, we designed and simulated a zoom system with 5:1 zoom ratio. The calculated EFL range is 7.27 mm to 36.34 mm while the simulated range is 6.46 mm to 33.97 mm. The calculated range is 7.27 mm to 36.34 mm while the simulated range is 6.46 mm to 33.97 mm. The calculated zoom zoom precision is 0.3 mm while the average simulated value is 0.2830, and root-mean-square (RMS) precision is 0.3 mm while the average simulated value is 0.2830, and root-mean-square (RMS) of the of the simulated zoom precision is 0.0122 mm. simulated zoom precision is 0.0122 mm. 3.3. Experimental Experimental and and Analysis Analysis

3.1.Experimental ExperimentalSetup Setup 3.1. Inorder ordertototest testthe theperformance performanceofofthe the zoom system, experimental platform shown In zoom system, wewe setset upup anan experimental platform shown in in Figure 6. Test targets were backlit with white light and two forms of targets were used in Figure 6. Test targets were backlit with white light and two forms of targets were used in measurement. measurement. The size of240 themm target wasmm. 240 mm 170 mm. Thewas zoom system was placed between The size of the target was ˆ 170 The ×zoom system placed between the test target the test target and the CCD camera, and the object distance was set to be 265 mm. The CCD was 1/4 and the CCD camera, and the object distance was set to be 265 mm. The CCD was 1/4 inch, pixel size inch, pixel which was μm.system In fact,and thethe zoom system and thefixed CCDconnected camera were fixed of which wassize 7.4 of µm. In fact, the7.4 zoom CCD camera were through a standard lens mount. CCDthe camera captured thesent images and sent them aconnected standard through C lens mount. CCDCcamera captured images and then them to then the computer. to the computer. We obtainedonthe information onand imaging quality and magnification through image We obtained the information imaging quality magnification through image processing, and processing, and then sent new control to the zoom system. A dc power was used then sent new control parameters to theparameters zoom system. A dc power supply was usedsupply to complete the to complete the D/A conversion. D/A conversion.

Figure6.6.Structure Structureof ofthe theexperimental experimentalplatform. platform. Figure

There were two major parameters we needed to measure: EFL and modulation transfer There were two major parameters we needed to measure: EFL and modulation transfer function function (MTF). EFL was used to evaluate the zoom ratio and zoom precision, and MTF was used to (MTF). EFL was used to evaluate the zoom ratio and zoom precision, and MTF was used to evaluate the

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imaging quality. During measurement, we selected 20 sampling points as we had done in simulation evaluate the imaging quality. During measurement, we selected 20 sampling points as we had done when adjusted I2 from 5 mA to 100 mA. The forms of targets and the methods of measuring EFL and in simulation when adjusted I2 from 5 mA to 100 mA. The forms of targets and the methods of MTF would be discussed in the following sections. measuring EFL and MTF would be discussed in the following sections. 3.2. Initial Structure 3.2. Initial Structure In their initial state, I1 and I2 both took 0 mA. MTF was used to evaluate the quality of imaging. In their initial state, I1 and I2 both took 0 mA. MTF was used to evaluate the quality of imaging. The method of calculating MTF of the system would be provided in Section 3.6, we currently used The method of calculating MTF of the system would be provided in Section 3.6, we currently used the calculation result. Initial parameters of the zoom system are shown in Table 4. MTF value when the calculation result. Initial parameters of the zoom system are shown in Table 4. MTF value when spatial frequency took 20 lp/mm was used to evaluate the image quality. spatial frequency took 20 lp/mm was used to evaluate the image quality. Table 4. Initial parameters of the zoom system. Table 4. Initial parameters of the zoom system I2 (mA)I2 (mA) 0 0 5 5

EFL(mm) (mm) FOV (Degree) FOV (Degree) MTF at 20l p/mm EFL MTF Value atValue 20l p/mm 6.56 0.01 6.56 41.7 41.7 0.01 6.93 39.7 0.28 6.93 39.7 0.28

Image quality was poor because 1 had not compensated 2 and the optical aberration Image quality was poor because L1Lhad not compensated forfor L2Land the optical aberration of of L2L2 was high when 4 took values near the limit position. was high when Φ4Φtook values near the limit position. order achieve high image quality whole zoom process, I2 5= mA 5 mA and adjusted InIn order to to achieve high image quality in in thethe whole zoom process, wewe setset I2 = and adjusted 1 to compensate . MTFdiagram diagramis isshown shown Figure Parameters the zoom system when L1Lto compensate forfor L2L. 2MTF inin Figure 7. 7. Parameters ofof the zoom system when I2 I2 takes 5 mA shown Table takes 5 mA areare shown in in Table 4. 4.

Figure 7. MTF curve of the zoom system when I2 took 0 mA and 5 mA, respectively. Figure 7. MTF curve of the zoom system when I2 took 0 mA and 5 mA, respectively.

In the following discussion, we take the state when I2 = 5 mA as the initial state. In the following discussion, we take the state when I2 = 5 mA as the initial state. 3.3. Electrical Performance Testing 3.3. Electrical Performance Testing In the process of measuring, L2 was adjusted actively to change EFL of the zoom system when In the process of measuring, L2 was adjusted actively to change EFL of the zoom system when L1 L1 supplied compensation to get clear images. The relationship between I1 and I2 can be calculated supplied compensation to get clear images. The relationship between I1 and I2 can be calculated from from Equations (1) and (2). Equations (1) and (2). We set I2 to a value, coarsely adjusted I1 till we got clear image on computer, and then tightly We set I2 to a value, coarsely adjusted I1 till we got clear image on computer, and then tightly adjusted I1. Range of tight adjustment was usually less than ±4 mA in actual measurement. We adjusted I1 . Range of tight adjustment was usually less than ˘4 mA in actual measurement. We could could obtain the real-time MTF of the zoom system with the software written by ourselves on obtain the real-time MTF of the zoom system with the software written by ourselves on computer. In computer. In fact, the MTF curve had no obvious change when we adjusted I1 in ±2 mA range. For I1, fact, the MTF curve had no obvious change when we adjusted I1 in ˘2 mA range. For I1 , this was this was an acceptable error range. Then we chose the value of MTF when spatial frequency was 20l an acceptable error range. Then we chose the value of MTF when spatial frequency was 20l p/mm p/mm as the image quality factor (Q). We considered the zoom system to achieve highest imaging as the image quality factor (Q). We considered the zoom system to achieve highest imaging quality quality when Q got maximum, and I1 would be recorded. The results of simulation and when Q got maximum, and I1 would be recorded. The results of simulation and measurement are measurement are shown in Figure 8. Although there were differences between simulated curve and shown in Figure 8. Although there were differences between simulated curve and measured curve, measured curve, we could easily obtain I1 as function of I2 by curve fitting. This enabled the zoom system to realize precise electric control. Both the simulated and the measured curves could be fitted

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we could easily Sensors 2016, 16, 45obtain I1 as function of I2 by curve fitting. This enabled the zoom system to realize 8 of 13 precise electric control. Both the simulated and the measured curves could be fitted well by three-order polynomials, and the correlation coefficients were largercoefficients than 0.999. This onlyThis needed a well by three-order polynomials, and the correlation weremeant largerthat thanwe 0.999. meant small addition and multiplication operations to obtain I1 byoperations I2 . that amount we only of needed a small amount of addition and multiplication to obtain I1 by I2.

Figure 8. L1’s control current (I1) as function of L2’s control current (I2). Figure 8. L1 ’s control current (I1 ) as function of L2 ’s control current (I2 ).

Optical power of the liquid lens was the only variant in the zoom system. Although in actual Optical power of thevehicle, liquid lens was the only variant inI1the in actual application on ground it needed time to calculate andzoom I2 forsystem. specificAlthough EFL, the calculation application on ground vehicle, it needed time to calculate I and I for specific EFL, the calculation 1 2 time was usually at a microsecond level for most of the processors since there were only multiply time was usually at a microsecond level for most of the processors since there were only multiply and and add operations in the fitting function. Therefore, the zoom speed depended only on the add operations in the fitting function. Therefore, the zoom speed depended only on the performance performance of the liquid lens. The response time of the system was less than 2.5 ms, and the settling oftime the liquid lens. The15response time of the system was less than 2.5 ms, and the settling time was less was less than ms due to fluid viscosity. than 15 ms due to fluid viscosity. 3.4. Zoom Ratio Testing 3.4. Zoom Ratio Testing Relationships between EFL, field of view (FOV), object height (OH), paraxial image height Relationships between EFL, field of view (FOV), object height (OH), paraxial image height (PIH), (PIH), and object distance (OD) could be obtained refer to Equations (5) and (6). and object distance (OD) could be obtained refer to Equations (5) and (6).

1 PIH  EFL  tan(1 FOV ) PI H “ EFL ¨ tanp 2FOVq 2 11 OHOH “ OD ¨ tanp  OD tan(2 FOVq FOV )

2

(5) (5) (6) (6)

We obtained the magnification (m) of the zoom system by imaging a fixed length (lo ) target. The We obtained magnification of the zoom by the imaging fixed length (lo) target. magnification could the be calculated refer(m) to Equation (7) bysystem counting pixelsa(n) when the pixel size The magnification could be calculated refer to Equation (7) by counting the pixels (n) when the pixel (µ) of the CCD camera was known. size (μ) of the CCD camera was known. m “mn¨ µ{l H{OH n  o “ lo PIPIH OH

(7)(7)

Thus Equations (5)´(7), Thusfrom from Equations (5)−(7),we wecan canobtain obtainEFL EFLrefer refertotoEquation Equation(8). (8).

 ¨mOD  OD EFLEFL “m

(8)(8)

Themeasured measuredand andsimulated simulatedresults resultsofofEFLs EFLsare areshown shownininTable Table5,5,and andthe theEFL EFLcomparison comparison The diagramofofcalculated calculatedvalue, value,simulated simulatedvalue valueand andmeasured measuredvalue valueis isshown shown Figure An diagram in in Figure 9. 9.An approximatelinear linearrelationship relationshipexists existsbetween betweenEFL EFLand and Thus,we wecan caneasily easilydetermine determineI2 Ito 2 to approximate I2 .I2.Thus, achieve specific EFL actual application. presented in Section I1 could be calculated achieve specific EFL in in actual application. AsAs presented in Section 3.3,3.3, I1 could be calculated out out by I2by I2 through the fitting function. far, issues of determining control parameters to achieve specific through the fitting function. ThusThus far, issues of determining control parameters to achieve specific EFL EFL are completely are completely solved.solved.

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Table 5. Comparisons between simulated EFL and measured EFL.

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I2 (mA) Simulated EFL (mm) Measured EFL (mm) Difference (mm) 5 Table 5. Comparisons 6.46 6.93EFL and measured EFL. 0.47 between simulated 10 8.14 7.81 −0.33 15 9.78 EFL (mm) 8.58 EFL (mm) −1.20 (mm) I2 (mA) Simulated Measured Difference 20 11.12 9.77 −1.35 5 6.46 6.93 0.47 25 12.52 10.85 −1.67 10 8.14 7.81 ´0.33 15 9.78 8.58 ´1.20 30 13.97 12.15 −1.82 20 11.12 9.77 ´1.35 35 15.43 13.38 −2.05 25 12.52 10.85 ´1.67 40 16.91 14.80 −2.11 30 13.97 12.15 ´1.82 45 18.39 16.28 −2.11 35 15.43 13.38 ´2.05 50 19.88 17.95 −1.93 40 16.91 14.80 ´2.11 45 18.39 16.28 ´2.11 55 21.35 19.67 −1.68 50 19.88 17.95 ´1.93 60 22.82 21.40 −1.42 55 21.35 19.67 ´1.68 65 24.28 23.19 −1.09 60 22.82 21.40 ´1.42 70 25.72 24.91 −0.81 65 24.28 23.19 ´1.09 70 25.72 24.91 ´0.81 75 27.15 26.7 −0.45 75 27.15 26.7 ´0.45 80 28.56 28.55 0.01 80 28.56 28.55 0.01 85 29.94 30.77 0.830.83 85 29.94 30.77 90 31.31 32.31 1.001.00 90 31.31 32.31 95 32.65 33.46 95 32.65 33.46 0.810.81 100 33.97 35.06 100 33.97 35.06 1.091.09

Figure 9. EFL comparison among calculated value, simulated value, and measured value. Figure 9. EFL comparison among calculated value, simulated value, and measured value.

Therefore, the measured EFL range of the zoom system is 6.93 mm to 35.06 mm, the zoom ratio Therefore, range of the zoom is 6.93 to 35.06 the zoom ratio is is 5.06:1. When the I2 = measured 5 mA, EFLEFL takes minimum, at thissystem moment Φ2 =mm 0.0087 mm−1mm, and Φ 4 = 0.0185 mm−1, ´1 and Φ = 0.0185 mm´1 , 5.06:1. When I = 5 mA, EFL takes minimum, at this moment Φ = 0.0087 mm −1 2 4 the FOV is 40°.2 When I2 = 100 mA, EFL takes maximum, Φ2 = 0.0192 mm and Φ4 = −0.0100 mm−1 at this ˝ . When I = 100 mA, EFL takes maximum, Φ = 0.0192 mm´1 and Φ = ´0.0100 mm´1 the FOV is 40 2 4 moment, the FOV is 8°.2 ˝. at thisImages moment, the FOV is 8 captured in different EFL are shown in Figure 10a–c show the wide end, the middle Images captured in respectively. different EFL In arewide shown in Figure showthe thezoom wide system end, thehas middle phase, phase, and the tele end end, EFL is 10a–c 6.93 mm, the widest and tele endare respectively. In wide two end,red EFLlines is 6.93 mm,in the zoom10a. system hasend, the EFL widest FOV,mm, and FOV,the and there 18 pixels between shown Figure In tele is 35.06 there are 18 pixels between two red lines shown in Figure 10a. In tele end, EFL is 35.06 mm, the zoom the zoom system is most detailed, and the number of pixels between two red lines shown in Figure 10c system is most of pixelsofbetween redratio. lines shown in Figure increases increases to 91.detailed, We can and alsothe getnumber the conclusion a 5.06:1two zoom A middle phase 10c is presented to 91.inWe canto also get readers the conclusion a 5.06:1 ratio. A middle phase is presented too, in order too, order make observeofthe zoomzoom process from wide end to tele end visually. to make readers observe the zoom process from wide end to tele end visually.

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Figure 10. Images captured in different EFL. (a) wide end, when I2 = 5 mA, 18 pixels between two red Figure 10. Images captured (a) when =I 5=mA, 18 pixels between twomA, red =different 60 mA, EFL. 59 pixels between two redI2lines; tele end, when I2 = 100 lines; (b)10. middle phase, wheninin I2 different Figure Images captured EFL. (a)wide wideend, end, when 5(c)mA, 18 pixels between two 2 2 = 60 mA, 59 pixels between two red lines; (c) tele end, when I2 = 100 mA, lines; (b) middle phase, when I 91 twophase, red lines. redpixels lines;between (b) middle when I2 = 60 mA, 59 pixels between two red lines; (c) tele end, when pixels between two red lines. I91 2 = 100 mA, 91 pixels between two red lines.

3.5. Zoom Precision Testing 3.5. Zoom Precision Testing 3.5. Zoom Precision Testing In order to measure the zoom precision of the system, we set I2 to a value firstly, measured EFL In order to measure the zoomprecision precision the1system, system, weset setI Ito 2 to a value firstly, measured EFL at this moment. Then we adjusted I2 to increase mA, and measured the variation of EFL. EFL In the In order to measure the zoom ofofthe we a value firstly, measured at 2 at this moment. Then we adjusted I 2 to increase 1 mA, and measured the variation of EFL. In the above, we had simulated the test process. simulated results the hadvariation been shown in Table The this moment. Then we adjusted I2 to increaseThe 1 mA, and measured of EFL. In the 3. above, above, had simulated theintest process. simulated results been Table 3. The measured results are Table andThe diagram of had comparison among calculated, simulated, we had we simulated the shown test process. The6,simulated results beenhad shown in shown Table 3.inThe measured measured results areTable shown in in Table 6, 11. and diagram ofamong comparison among calculated, and measured results is shown Figure results are shown in 6, and diagram of comparison calculated, simulated, andsimulated, measured and measured results is shown in Figure 11. results is shown in Figure 11. I2 (mA) I2 (mA) 5 I2 (mA) 5 10 5 10 15 10 15 1520 20 2025 25 2530 30 30 35 35 35 4040 40 4545 45 5050 Average 50 Average Average

Table 6. Measured zoom precision. Table 6. Measured Measured zoom zoom precision. precision. Table 6.

Zoom Precision (mm) Zoom Precision 0.2975 (mm) Zoom Precision (mm) 0.2975 0.2725 0.2975 0.2725 0.3000 0.2725 0.3000 0.2750 0.3000 0.2750 0.2700 0.2750 0.2700 0.2700 0.2675 0.2675 0.2675 0.3150 0.3150 0.3150 0.2750 0.2750 0.2750 0.3150 0.3150 0.3150 0.3075 0.3075 0.2885 0.3075 0.2885 0.2885

I2 (mA) Zoom Precision (mm) I2 (mA) Zoom Precision 55 0.3125 (mm) I2 (mA) Zoom Precision (mm) 55 0.3125 60 0.2900 55 60 0.29000.3125 65 0.2750 60 65 0.27500.2900 70 0.2650 65 0.2750 70 70 0.26500.2650 75 0.3000 75 75 0.30000.3000 80 0.2625 80 80 0.26250.2625 85 0.2825 85 85 0.28250.2825 90 0.3050 90 0.3050 90 95 0.30500.3050 95 0.3050 95 100 0.30500.2775 100 0.2775 RMS 100 0.27750.0181 RMS 0.0181 RMS 0.0181

Figure 11. Zoom precision comparison among calculated, simulated, and measured values. Figure 11. Zoom precision comparison among calculated, simulated, and measured values. Figure 11. Zoom precision comparison among calculated, simulated, and measured values.

Zoom precision of the realized zoom system is approximately uniform in the whole zoom Zoom precision realized zoom system is is approximately uniform the whole zoom process. precision ofthe the realized zoom system is approximately in thevalue whole zoom process. The averageof of measured zoom precision 0.2885 mm, near touniform theincalculated 0.3 mm, The average of measured zoom precision is 0.2885 mm, near to the calculated value 0.3 mm, and all of process. The average of measured zoom precision is 0.2885 mm, near to the calculated value 0.3 and all of measured values are in the range of ±0.0265 mm to average zoom precision, RMS ofmm, the and all of measured values are in the range of ±0.0265 mm to average zoom precision, RMS of the

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measured values are in the range of ˘0.0265 mm to average zoom precision, RMS of the measured Sensors 2016, 16, 45 11 of 13 zoom precision 0.0181 mm. Parameters the realized are consistent with the calculated measured zoomisprecision is 0.0181 mm. of Parameters of lens the realized lens are consistent with and the simulated values. measured zoom precision is 0.0181 mm. Parameters of the realized lens are consistent with the calculated and simulated values. Therefore, there are states in the entire zoom range, spaces between adjacent states calculated and simulated values. EFL Therefore, there are96 96discrete discrete EFL states in the entire zoom range, spaces between adjacent Therefore, there are 96 discrete EFL states in the entire zoom range, spaces between adjacent are approximately uniform to be 0.2885 mm. Because the EFL states are so compact, we can consider states are approximately uniform to be 0.2885 mm. Because the EFL states are so compact, we can states approximately uniform to be 0.2885 mm. Because the EFL states are so compact, we can the realized system assystem a continuous zoom system. consider theare realized as a continuous zoom system. consider the realized system as a continuous zoom system.

3.6. Imaging ImagingQuality QualityTesting Testing 3.6.

3.6. Imaging Quality Testing

We used MTF totoevaluate thethe imaging quality of the zoomzoom system. The test target used in imaging We used MTFMTF evaluate imaging system. The target We used to evaluate the imagingquality quality of of the the zoom system. The testtest target usedused in in quality testing is shown in Figure 12, similar to a black and white chessboard. The tilt of edge was imaging quality testing is shown in in Figure blackand andwhite white chessboard. tilt set of imaging quality testing is shown Figure12, 12,similar similar to to aa black chessboard. TheThe tilt of ˝ according to 5 to ISO12233. edge was 5°toaccording to ISO12233. edgeset wastoset 5° according to ISO12233.

Figure 12. Structure of the target used to test the imaging quality.

Figure 12. Structure of the target used to test the imaging quality. Figure 12. Structure of the target used to test the imaging quality. In the test process, we selected a region-of-interest (ROI) that contains a slanted-edge in the beginning, obtained the Edge Spread Function (ESF) (ROI) by the that use ofcontains knife-edge slanted-edge method and got In the the test test then process, we selected selected region-of-interest in the the In process, we aa region-of-interest (ROI) that contains aa slanted-edge in the Line Spread Function (LSF) through the differential of ESF. The MTF could be computed by a got beginning, then obtained the Edge Spread Function (ESF) by the use of knife-edge method and beginning, then obtained the Edge Spread Function (ESF) by the use of knife-edge method and got FastSpread Fourier Transform(LSF) (FFT) of LSF. MTFs were measured when I2 took different values. The results the Line Line ofof ESF. The MTF could be computed by aby Fast the SpreadinFunction Function (LSF)through throughthe thedifferential differential ESF. The MTF could be computed a are shown Figure 13a.

Fourier Transform (FFT) of LSF. MTFs werewere measured when I2 took different values. TheThe results are Fast Fourier Transform (FFT) of LSF. MTFs measured when I2 took different values. results shown in Figure 13a. are shown in Figure 13a.

Figure 13. MTF of the zoom system. (a) MTFs were measured when I2 took different values; (b) relationship between MTF and I2 at 20 lp/mm.

At 20 lp/mm, the relationship between MTF and I2 is shown in Figure 13b. The zoom system got the highest imaging quality when I2 = 30(a) mA, MTFwere reached 0.40 at 20 lp/mm. Whendifferent I2 > 90 mA, MTF Figure Figure 13. 13. MTF MTF of of the the zoom zoom system. system. (a)MTFs MTFs weremeasured measured when when I2I2 took took different values; values; reduced to 0.17 at 20 lp/mm. (b) (b) relationship relationship between between MTF MTF and and II22 at at20 20lp/mm. lp/mm.

At 20 lp/mm, the relationship between MTF and I2 is shown in Figure 13b. The zoom system got the highest imaging quality when I2 = 30 mA, MTF reached 0.40 at 20 lp/mm. When I2 > 90 mA, MTF reduced to 0.17 at 20 lp/mm.

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At 20 lp/mm, the relationship between MTF and I2 is shown in Figure 13b. The zoom system got the highest imaging quality when I2 = 30 mA, MTF reached 0.40 at 20 lp/mm. When I2 > 90 mA, MTF reduced to 0.17 at 20 lp/mm. 4. Conclusions In this paper, we designed and realized an electrically tunable four-group stabilized zoom system by using two liquid lenses. The zoom equations were established by using Gaussian bracket method. L1 and L2 were used as the second and the fourth lens group that were focal length variable. The calculated EFL range was 7.27 mm to 36.34 mm while the zoom precision was calculated to be 0.3 mm. We simulated the zoom system, got the simulated EFL range was 6.46 mm to 33.97 mm and the zoom precision was 0.283 mm. Then we made a series of experiments to verify the performance of the realized system. Response time of the realized zoom system was less than 2.5 ms, and the settling time was less than 15 ms. The measured EFL range was 6.93 mm to 35.06 mm, the zoom ratio was 5.06:1. When Φ2 = 0.0087 mm´1 and Φ4 = 0.0185 mm´1 , EFL got the minimum value, the FOV was 40˝ . When Φ2 = 0.0192 mm´1 and Φ4 = ´0.01 mm´1 , EFL got the maximum value, the FOV was 8˝ . The measured EFL adjust precision was 0.2885 mm, the RMS of precision was 0.0181 mm. MTF was used to evaluate the imaging quality of the zoom system. The range of MTF was 0.17 to 0.40 at 20 lp/mm. The lens realized in this paper had only four groups of elements, and none of them was motorized, thus it had good anti-shake performance. It was applicable to many fields e.g., ground vehicles used in a field-environment, and was also suitable for applications in high speed vehicles and fast moving target tracking as a result of the good electrical performance. However, the gravity influence of liquid lens was not considered in this paper. Although in the experiments, no apparent gravity effect had been observed, it would exist in theory. In fact, gravity effect in the stationary state had been contained in the parameter “wavefront error” in the datasheet of the liquid lens, the wavefront error was less than 0.5λ. In practice, we need to consider the system working in doubling even tripling gravitational acceleration environments. We will do more research on this issue in future works. Acknowledgments: The work was supported by the National Natural Science Foundation of China (NSFC) (61275003, 51327005, 91420203). Author Contributions: Qun Hao and Xuemin Cheng conceived and designed the experiments; Heng Li performed the experiments and analyzed the data; Heng Li and Xuemin Cheng wrote the paper. Conflicts of Interest: The authors declare no conflict of interest.

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