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Tunable liquid lens integrated with aspheric surface
Optics Communications 445 (2019) 56–63
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Optics Communications journal homepage: www.elsevier.com/locate/optcom
Tunable liquid lens integrated with aspheric surface Jin-Hui Wang a , Xin Zhou a , Lin Luo a , Rong-Ying Yuan a , Qiong-Hua Wang b ,∗ a b
School of Electronics and Information Engineering, Sichuan University, Chengdu 610065, China School of Instrumentation and Optoelectronic Engineering, Beihang University, Beijing 100191, China
ARTICLE Keywords: Liquid Lens Aspheric Surface Spherical aberration Distortion
INFO
ABSTRACT In this paper, we propose and experimentally demonstrate a tunable liquid lens integrated with an aspherical surface for spherical aberration and distortion compensation. Through optimizing the aspherical surface’s morphology, the spherical aberration and distortion can be significantly reduced. The root mean square spot size at focus is distinctly reduced from 55.7 μm to 2.095 μm after performing optimum optimization. The tunable liquid lens is integrated with the aspheric surface with 6 mm clear aperture and 19.2 mm minimum focal length and demonstrate the improvement in optical performance over the conventional lens without an aspheric surface over a focal length range. Its applications in microscope system and tunable-focus eyeglasses are foreseeable.
1. Introduction Tunable liquid lenses have excited widespread attention courtesy of their optical tuning capability without mechanical moving parts [1– 5]. Their applications for optical imaging systems are foreseeable [6]. Various liquid tunable lenses have been demonstrated for imaging systems over the past decades, such as fluidic pressure lenses [7,8], thermal effect lenses [9], electromagnetic wave lenses [10], adaptive hydrogel lenses [11], dielectrophoresis lenses [12,13] and electrowetting lenses [1,2,14,15]. However, because of the saturation of contact angle, most of these lenses only allow for tuning the focal length while retaining a spherical shape. The optical performance might degrade further if the lens profile deviates from sphericity [16,17]. A hybrid tunable lens for eliminating optical aberration was proposed [18]. With the doublet lens, the lens can eliminate optical aberration. And both images with good quality and focal length tunability can be simultaneously achieved in the same liquid lens. However, the complex doublet lens leads to a relative bulky and expensive structure. Fortunately, aspherical lenses (ALs) comprise curved surfaces, the curvature of which varies spatially to generate a sharp image of an object that is devoid of common optical aberrations [19–22]. Nevertheless, the manufacturing of the APLs has been extremely difficult and time-consuming to date. They require experienced technicians to manually perform grinding and polishing. Recent developments, therefore, have shown the potential of some optofluidic approaches to obtain non-spherical lens shapes that allow to correct the corresponding aberrations. A gradient electrostatic force modulated microaspheric lens has been proposed [23]. However, the aberration is corrected at the cost of high driving voltage. A more straightforward but less versatile solution has been proposed to ∗
develop a tunable liquid-filled lens integrated with a fixed aspherical surface for spherical aberration compensation [24]. With the design, the spherical aberration associated with the conventional designs can be compensated. As a result, the corresponding optical performance of the lens can be significantly improved within particular operation regions. However, fabrication and integration of the device is cumbersome and expensive, because the method requires sophisticated facilities. This greatly limits the rapid and low-cost production of lenses. A liquid-tunable lens with a plano-convex membrane has been designed [25]. The optical performance of the aspherical liquid lens has been improved over a focal length range. However, the liquid-filled lens always encounters a disadvantage that cannot be ignored by the effect of gravity effects. The method of external voltage is used to realize liquid driving, so that the device can be seamlessly connected with electronic products and equipment. Therefore, it is still urging to study tunable liquid lens with good imaging quality, compact, low cost, and large zoom range. In this paper, we propose and experimentally demonstrate a tunable liquid lens integrated with an aspherical surface for spherical aberration and distortion compensation. Through optimizing the aspherical surface contour, the aforementioned aberration normally associated with tunable liquid lens operation can be significantly reduced within a particular range. The paper first describes the design principle of the proposed lens. Then, the fabrication process of the aspherical lens is discussed. Finally, we simulation our lens to optimize the optical performance using ZEMAX-EE, and then the proposed lens is experimentally demonstrated in an imaging system.
Corresponding author. E-mail address: [email protected] (Q.-H. Wang).
https://doi.org/10.1016/j.optcom.2019.03.066 Received 29 October 2018; Received in revised form 18 March 2019; Accepted 25 March 2019 Available online 4 April 2019 0030-4018/© 2019 Elsevier B.V. All rights reserved.
J.-H. Wang, X. Zhou, L. Luo et al.
Optics Communications 445 (2019) 56–63
Fig. 1. Schematic 3D and cross-sectional structure of the proposed lens. (a) Structure of the proposed lens. (b) Non-drive state. (c) Drive state.
2. Device structure and principle Our variable-focus liquid lens utilizes the refractive index difference between two immiscible liquids and its focal point can be translated along the optical axis by deforming the interface between the two liquids. The tunable liquid lens in this work is shown in Fig. 1(a). The lens consists of ALs, two pieces of window glasses and a lens cavity. As shown in Figs. 1(b) and (c), we can easily understand the principle of the proposed lens. The light firstly passes through the window glass before the salt solution–oil interface, then through the aspherical lens, and finally through the window glass below. By applying different driving voltages to the aluminum electrode on the side, the curvature of the liquid surface changes, thereby changing the focal length of the lens. At the same time, when the light passes through the aspherical lens, it bends along a transparent curved surface due to the differences of the refractive index along the interface. The radius of the curvature of a thin lens can have different degree of parabolicity. The light can be precisely gathered to eliminate spherical aberration and distortion.
Fig. 2. Fabricated prototype of the tunable liquid lens integrated with aspherical surface. (a) Whole device. (b) All the elements of the device.
3. Fabrication
Application of a voltage between the electrodes results in an electric field across the insulator, which effectively lowers the interfacial tension between the conductive liquid and the insulator. The resulting change in contact angle 𝜃 of the conducting liquid with the wall can be described by: cos 𝜃1 = cos 𝜃0 +
𝜀𝑈 2 , 2𝑑𝛾12
The effective aperture of the fabricated liquid lens is ∼6 mm. The fabricated device is shown in Fig. 2(a). All the fabricated elements are shown in Fig. 2(b). The AL is made of polydimethylsiloxane (PDMS). The material of two pieces of window glass is K9. For the whole device, the inner diameter is 6.5 mm, the outer diameter is 12 mm, the height is 8 mm. The lens cavity using aluminum is filled with two immiscible liquids. The two kinds of liquids have same density but different refractive indices. One of the liquids is conductive, the other is insulating. The parameters of the salt solution and silicone oil are shown in Table 1. The aspherical lens is embedded in the lower window glass. The window glass is placed on the platform in cylindrical cavity and bonded together by UV glue. The grounding electrode is the upper half of an aluminum column, while the counter electrode is the lower half of an aluminum column and in direct contact with the conducting liquid. There is a layer of insulation board to prevent the two electrodes from being joined. To guarantee perfect pinning of the water–oil interface to the edge of the aperture, a hydrophobic and dielectric coating is applied to the inner wall of the aluminum cylindrical cavity by Spraying Teflon.
(1)
where 𝜀 is the dielectric constant of the hydrophobic and dielectric film, d is its thickness, U is the applied voltage, 𝛾12 is the liquid/liquid interfacial tension, 𝜃0 is the initial contact angle between the conductive liquid and inner wall, and 𝜃1 is the contact angle between the conductive liquid and inner wall under driving state. Eq. (1) can be used to derive an expression for the dioptric power D of the meniscus radius R and the refractive indices 𝑛o and 𝑛w for the insulating and conductive liquid, respectively, 𝐷 = 𝐷0 + 𝐷1 +
(𝑛o − 𝑛w ) , 𝑅
(2)
where 𝐷0 is the dioptric power in the initial state of no AL, and 𝐷1 is the dioptric power of the aspheric lens. For a 6.5 mm diameter lens we can control the dioptric power between −50 and +67 diopters. 57
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Optics Communications 445 (2019) 56–63
Table 1 Properties of the materials we used. Material
Density (g/cm3 )
Refractive index
Abbe number
Transparent
Aqueous solution Oil
1.09 1.09
1.34 1.48
58.13 34.59
Yes Yes
Fig. 5. Height of the fabricated ALs to the volume of the PDMS solution.
Fig. 3. Inverted additive fabrication processing route of ALs.
Fig. 6. Comparison of surface profiles of ALs.
That is to say, the PDMS monomer and hardener (Sylgard 184, Dow Corning) are mixed by a weight ratio of 10:1, and then placed in a vacuum desiccator until all bubbles are removed. A 1 ml hypodermic needle is dipped vertically into the mixture to extract a small drop. The extracted PDMS droplet is allowed to slide slowly onto the window glass. In order to keep the aperture of aspherical lenses consistent, a ruled surface structure is designed to fix its caliber, as shown Fig. 3. After that, the window glass is inverted and PDMS is cured at 60 ◦ C and at 90 ◦ C for 10 min and 20 min, respectively. In order to increase the asphericity of the aspheric lens, one can control the amount of the PDMS used for each lens to increase gradually. As shown in Fig. 4, we have shown six types of the ALs (a–e). At each APL, the contact angle is measured: (a) 20.3◦ , (b) 26.8◦ , (c) 28.8◦ , (d) 40.4◦ , and (e) 48.5◦ . On increasing the volume of the PDMS solutions, the contact angles become larger.
Fig. 4. Six types of the APLs based on the various volume of additive PDMS solution.
4. Generation of aspheric lens The AL is prepared by cross-linking a hanging polymeric drop. The drop is affected by gravity acting to pull it down, meanwhile, the drop is subjected to the surface tension trying to hold the droplet up against the flat surface. Therefore, the surface of the polymer droplet is aspherical. The AL is formed of PDMS, which has been prepared using the typical soft lithography PDMS procedure, as shown in Fig. 3.
Table 2 Relation between surface profile and curing time (Ti.), and curing temperature (Te.). Droplet volume (0.5 ml)
First Te.
Second Te.
First Te.
Second Ti.
50 55 60 65 60
5 10 15 20 10
90
H
C
𝜅
2nd Order
4nd Order
6nd Order
Same Ti. (10/20 min)
3.00 2.80 2.70 2.50 2.71 2.70 2.69 2.70
1.47 1.31 1.18 1.02 1.19 1.18 1.17 1.18
−1 −1 −1 −1 −1 −1 −1 −1
4.82E−4 4.82E−4 4.81E−4 4.71E−4 4.81E−4 4.81E−4 4.81E−4 4.81E−4
4.11E−4 1.10E−2 −1.04E−3 1.91E−3 −3.02E−4 3.28E−2 −3.03E−4 1.10E−2
5.92E−7 −6.96E−13 −8.13E−13 −4.19E−8 2.37E−9 3.28E−7 6.39E−12 −6.96E−10
Same Te. (60/90 ◦ C)
2.79 2.76 2.73 2.73 2.70 2.70 2.71 2.70
1.38 1.26 1.23 1.23 1.18 1.18 1.19 1.18
−1 −1 −1 −1 −1 −1 −1 −1
4.82E−4 4.82E−4 4.81E−4 4.81E−4 4.81E−4 4.81E−4 4.81E−4 4.81E−4
2.34E−3 5.85E−4 1.93E−3 −5.16E−3 −2.79E−4 −1.02E−4 5.30E−4 5.91E−4
1.51E−11 2.39E−11 3.2E−8 1.17E−11 1.23E−11 −6.47E−12 1.04E−8 −1.84E−6
70 80 90 100 20
10 20 30 40
58
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Optics Communications 445 (2019) 56–63
Fig. 7. RMS of the conventional lens and proposed lens at different fields of view. (a) (c) (e) the conventional lens; (b) (d) (f) the proposed lens. Scale bar: (a) (c) (e) 80 μm, (b) (d) (f) 20 μm.
The relationship between the volume of PDMS solutions and the height(H) of the lenses is shown in Fig. 5. The dependence of the lens height and the volume of the PDMS solutions are evident from the experiment, which shows that the lens height increases with increase in volume of the PDMS solutions. The variation of the lens curvature as a function of volume of additive PDMS solution is measured using a profilometer; the profiles are plotted in Fig. 6. In addition, the effect of temperature and time of two curing cycles on the lens profile is also studied, as shown in Table 2. Note should be made that time and temperature in the first curing are much more important than time and temperature in the second solidification, because the PDMS has high fluidity at the first solidification. Due to the gravity, it is easy to produce the tendency of sagging. At the second solidification, the PDMS hardly sags with little fluidity. A function is used to fit the surface profile based on the measured data using the aspheric curve
formula [26]: ∑ ℎ2 + 𝐴2𝑛 ℎ2𝑛 , √ ℎ 2 𝑅𝑠 [1 + 1 − (1 + 𝜅)( 𝑅𝑠 ) ] 𝑛=2 𝑚
𝑧(ℎ) =
(3)
where h is the radial coordinate, 𝑅𝑠 the vertex radius, 𝜅 is the conic constant and 𝐴2𝑛 the coefficients of a correction polynomial. Different types of conic sections can be identified as follows: 𝜅>0 oblate ellipse, 𝜅=0 sphere, −1<𝜅<0 prolate ellipse, 𝜅=−1 parabola, 𝜅<−1 hyperbola. 5. Simulation results According to the surface profiles of ALs in Fig. 6, an effective focal length of 30 mm is chosen as the optimized target and only 92.3% lens aperture (namely 6 mm aperture size) is used during the simulation by considering the characteristic of the tunable liquid lens. As shown in Fig. 7, from the ZEMAX simulation, the mean square radius of the lens 59
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Optics Communications 445 (2019) 56–63
Fig. 8. ZEMAX simulation results. (a) conventional design; (b) optimized design.
distortion of the conventional design is 0.7%. However, the minimum distortion of our lens is 0.00186%. As for astigmatism and coma, there is no distinct performance improvement.
we mentioned is far less than the size of Airy spot. We can conclude that the imaging quality of our lens is very well. It can be seen that the RMS at focus (f = 50 mm) is distinctly reduced from 55.7 μm (no AL) to 2.095 μm after performing optimum optimization (type d AL), which indicates that our lens has reduced spherical aberration. When the focal length is 30 mm, the RMS radius of the conventional lens is 61.308 μm. However, the RMS radius of the proposed lens decreases to 15.986 μm. When the focal length is 90 mm, the RMS radius of the conventional lens is 68.769 μm. In this case, the RMS radius of the proposed lens decreases to 17.514 μm. At the same time, the minimum spherical aberration of the lens working over different focal lengths are studied. It is seen that with respect to the without AL electrowetting lens, its spherical aberration will always be positive. It is seen that with respect to the proposed lens, its spherical aberration increases with increasing focal length from 30 mm to nearly 50 mm, whilst that, the spherical aberration gradually decreases from 50 mm to nearly 90 mm. The appearance of larger spherical aberration at f = 30 mm is caused by the over-compensation effect introduced by the aspherical surface. The results of ray tracing and the corresponding wavefront maps at the focus are also shown in Fig. 8. Since the root mean square (RMS) of the wavefront error with respect to reference spherical at focus is mainly caused by spherical aberration, and the resultant decreases in their original values of 1.4478 waves to optimized 0.0034 waves (λ = 486 nm). We can come to conclusion that the spherical aberration can be reduced when our lens works in some regions. The AL design is currently focused on spherical aberration, it also effects on other lens performance criteria, such as distortion. The distortion is caused by variation in magnification of the image across the field of view or object height. When the magnification of a lens differs at the edge of the lens and at the center, the image of a square object will be curved abnormally. The optical compensation surface of the aspheric surface is designed to compensate the wave phase difference produced by the large aperture distortion. So, the adaptive lens still has good optical characteristics in the case of large aperture. The aperture of our lens is 6.5 mm. With respect to the distortion, our lens demonstrates distinct performance improvement compared to the lens without AL, as shown in Fig. 9. When the field of view is 2 degrees, the minimum
6. Experimental results Like most tunable liquid lenses, the key parameter is their capability for focal length variation. The characteristic of our lens is investigated. We designed an experiment set-up to evaluate the focal length. As shown in Fig. 10(a), the experiment set-up consists of a collimator (FPG-7, Hua Zhong Precision Instruments Co., Ltd., China), a beam splitter, the proposed lens, a CMOS camera and a computer. We used the CMOS digital camera as an image plane to collect light spot. For the positive lens, the spot is obtained by the COMS camera. The CMOS acquisition plane is just the focal plane of the lens, and the spot is the smallest. When the spot diameter is less than 1 mm, the focal length of the lens is obtained. The distance between the lens and CMOS is the focal length. The resolution and the pixel size of the CMOS are 2592 × 1944 and 2.2 μm × 2.2 μm, respectively. The variation of the focal length as a function of the applied voltage is obtained, as shown in Fig. 10(b) (using type e AL). From Fig. 10(b), we can see that the focal length of our lens decreases from 265 mm to 20.5 mm when the operating voltage increases from 30 V to 75 V. And we can conclude that the focal length of the proposed lens is smaller than the focal length of the lens without AL at different voltages. That is because the aspheric lens bears part of focal power. To evaluate the proposed lens performance during focus change, we recorded the image of an object using high speed camera through the liquid lens under natural light environment. A test target was placed vertically above our lens. In our experiment, the distance between the target and the lens is always 56 mm. The recorded images of without AL lens are seen in Figs. 11(a)–(d). The recorded images of our lens are seen in Figs. 11(e)–(h). When comparing these pictures carefully, we can find that the images obtained by our lens is clearer than that of the lens without AL. Obviously, our lens reduces the aberrations under different degrees of zoom mainly because of the AL. In addition, the edge of the lines of our lens is more distinct than 60
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Optics Communications 445 (2019) 56–63
Fig. 9. ZEMAX simulation results of distortion and field curvature. (a) conventional design; (b) optimized design.
Fig. 10. Measurement of focal length. (a) Experiment set-up; (b) Tunable focal length as a function of applied voltage.
Fig. 11. Captured images of different magnification degree by the (a)–(d) with ALs and (e)–(h) without ALs at the object distance of 56 mm. Scale bar (a)–(h) 1.5 mm.
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Optics Communications 445 (2019) 56–63
Fig. 12. Quantification of the imaging resolution of1 the lenses. (a) Imaging of the lens without AL. (b) Imaging of the proposed lens. (linewidth: 0.0125 mm).
Fig. 13. Captured images by the (a) conventional lens and (b) proposed lens at the focal length of 30 mm.
the one without AL. From a theoretical analysis, when negligible even no spherical aberration and distortion is present, thus demonstrating the effectiveness of the correction provided by the aspherical surface design. The optical resolution of a lens is typically defined by smallest resolvable structure. Light emitted by an LED is collimated by a collector lens that is diffused to provide an even illumination over the FBLB-101 resolution card. We used resolution target for quantitatively characterizing the improved optical performance. For convenience, we chose the highest power lens (highest driving voltage, U = 75 V). When the resolution of the lens without AL and our lens is all 10 line pairs per mm, as shown in Fig. 12. The image obtained by our lens is clearer. The improvement in the optical performance has been demonstrated directly. In order to further verify that imaging quality of our lens is better than that of the conventional lens, the optical quality of the lenses is measured with quantitative parameters. We measured the optical resolution of the lens using the experimental device to measure the focal length in Fig. 10(a). However, the difference is that a resolution target is added behind the light source of the collimator. Actually, we need to slightly adjust the voltage to obtain the clearest image. The used wavelength is ∼595 nm. The captured images by the conventional lens and proposed lens are shown in Figs. 13(a) and (b), respectively. Compared the images with f = 50 mm, we can see that the images of the proposed lens are clearer than the conventional lens. The corresponding resolution target is element 13 of target 1. So the minimum resolution of the proposed lens is 32.9′′ . Comparing Figs. 14(a) with (b), we can get the similar conclusion. The corresponding resolution target is element 9 of target 1. So the minimum resolution of the proposed lens is 40′′ at present. Our lens reduces the aberrations in some focal length range mainly because of the polymer aspheric lens.
Fig. 14. Captured images by the (a) conventional lens and (b) proposed lens at the focal length of 50 mm.
Acknowledgments The work is supported by the National Natural Science Foundation of China under Grant No. 61535007 and the Equipment Research Program in Advance of China under Grant No. JZX2017-1570/Y464. References
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In summary, the proposed lens is composed of an electrowetting lens and an aspherical lens. But the overall size of the device does not change, which meets the requirements of the lightweight system. In addition, it has for many years been an ambition of researchers in imaging to create a flexible low-cost system. Therefore, the aspheric lens is made by PDMS, which has low cost and is easy to be treated as we expect. More importantly, spherical aberration and distortion can be basically eliminated. Thereby, one can get better optical imaging quality using the proposed lens than electrowetting lens alone. Its applications for zoom microscope system and tunable-focus eyeglasses are foreseeable. 62
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Contents lists available at ScienceDirect
Optics Communications journal homepage: www.elsevier.com/locate/optcom
Tunable liquid lens integrated with aspheric surface Jin-Hui Wang a , Xin Zhou a , Lin Luo a , Rong-Ying Yuan a , Qiong-Hua Wang b ,∗ a b
School of Electronics and Information Engineering, Sichuan University, Chengdu 610065, China School of Instrumentation and Optoelectronic Engineering, Beihang University, Beijing 100191, China
ARTICLE Keywords: Liquid Lens Aspheric Surface Spherical aberration Distortion
INFO
ABSTRACT In this paper, we propose and experimentally demonstrate a tunable liquid lens integrated with an aspherical surface for spherical aberration and distortion compensation. Through optimizing the aspherical surface’s morphology, the spherical aberration and distortion can be significantly reduced. The root mean square spot size at focus is distinctly reduced from 55.7 μm to 2.095 μm after performing optimum optimization. The tunable liquid lens is integrated with the aspheric surface with 6 mm clear aperture and 19.2 mm minimum focal length and demonstrate the improvement in optical performance over the conventional lens without an aspheric surface over a focal length range. Its applications in microscope system and tunable-focus eyeglasses are foreseeable.
1. Introduction Tunable liquid lenses have excited widespread attention courtesy of their optical tuning capability without mechanical moving parts [1– 5]. Their applications for optical imaging systems are foreseeable [6]. Various liquid tunable lenses have been demonstrated for imaging systems over the past decades, such as fluidic pressure lenses [7,8], thermal effect lenses [9], electromagnetic wave lenses [10], adaptive hydrogel lenses [11], dielectrophoresis lenses [12,13] and electrowetting lenses [1,2,14,15]. However, because of the saturation of contact angle, most of these lenses only allow for tuning the focal length while retaining a spherical shape. The optical performance might degrade further if the lens profile deviates from sphericity [16,17]. A hybrid tunable lens for eliminating optical aberration was proposed [18]. With the doublet lens, the lens can eliminate optical aberration. And both images with good quality and focal length tunability can be simultaneously achieved in the same liquid lens. However, the complex doublet lens leads to a relative bulky and expensive structure. Fortunately, aspherical lenses (ALs) comprise curved surfaces, the curvature of which varies spatially to generate a sharp image of an object that is devoid of common optical aberrations [19–22]. Nevertheless, the manufacturing of the APLs has been extremely difficult and time-consuming to date. They require experienced technicians to manually perform grinding and polishing. Recent developments, therefore, have shown the potential of some optofluidic approaches to obtain non-spherical lens shapes that allow to correct the corresponding aberrations. A gradient electrostatic force modulated microaspheric lens has been proposed [23]. However, the aberration is corrected at the cost of high driving voltage. A more straightforward but less versatile solution has been proposed to ∗
develop a tunable liquid-filled lens integrated with a fixed aspherical surface for spherical aberration compensation [24]. With the design, the spherical aberration associated with the conventional designs can be compensated. As a result, the corresponding optical performance of the lens can be significantly improved within particular operation regions. However, fabrication and integration of the device is cumbersome and expensive, because the method requires sophisticated facilities. This greatly limits the rapid and low-cost production of lenses. A liquid-tunable lens with a plano-convex membrane has been designed [25]. The optical performance of the aspherical liquid lens has been improved over a focal length range. However, the liquid-filled lens always encounters a disadvantage that cannot be ignored by the effect of gravity effects. The method of external voltage is used to realize liquid driving, so that the device can be seamlessly connected with electronic products and equipment. Therefore, it is still urging to study tunable liquid lens with good imaging quality, compact, low cost, and large zoom range. In this paper, we propose and experimentally demonstrate a tunable liquid lens integrated with an aspherical surface for spherical aberration and distortion compensation. Through optimizing the aspherical surface contour, the aforementioned aberration normally associated with tunable liquid lens operation can be significantly reduced within a particular range. The paper first describes the design principle of the proposed lens. Then, the fabrication process of the aspherical lens is discussed. Finally, we simulation our lens to optimize the optical performance using ZEMAX-EE, and then the proposed lens is experimentally demonstrated in an imaging system.
Corresponding author. E-mail address: [email protected] (Q.-H. Wang).
https://doi.org/10.1016/j.optcom.2019.03.066 Received 29 October 2018; Received in revised form 18 March 2019; Accepted 25 March 2019 Available online 4 April 2019 0030-4018/© 2019 Elsevier B.V. All rights reserved.
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Fig. 1. Schematic 3D and cross-sectional structure of the proposed lens. (a) Structure of the proposed lens. (b) Non-drive state. (c) Drive state.
2. Device structure and principle Our variable-focus liquid lens utilizes the refractive index difference between two immiscible liquids and its focal point can be translated along the optical axis by deforming the interface between the two liquids. The tunable liquid lens in this work is shown in Fig. 1(a). The lens consists of ALs, two pieces of window glasses and a lens cavity. As shown in Figs. 1(b) and (c), we can easily understand the principle of the proposed lens. The light firstly passes through the window glass before the salt solution–oil interface, then through the aspherical lens, and finally through the window glass below. By applying different driving voltages to the aluminum electrode on the side, the curvature of the liquid surface changes, thereby changing the focal length of the lens. At the same time, when the light passes through the aspherical lens, it bends along a transparent curved surface due to the differences of the refractive index along the interface. The radius of the curvature of a thin lens can have different degree of parabolicity. The light can be precisely gathered to eliminate spherical aberration and distortion.
Fig. 2. Fabricated prototype of the tunable liquid lens integrated with aspherical surface. (a) Whole device. (b) All the elements of the device.
3. Fabrication
Application of a voltage between the electrodes results in an electric field across the insulator, which effectively lowers the interfacial tension between the conductive liquid and the insulator. The resulting change in contact angle 𝜃 of the conducting liquid with the wall can be described by: cos 𝜃1 = cos 𝜃0 +
𝜀𝑈 2 , 2𝑑𝛾12
The effective aperture of the fabricated liquid lens is ∼6 mm. The fabricated device is shown in Fig. 2(a). All the fabricated elements are shown in Fig. 2(b). The AL is made of polydimethylsiloxane (PDMS). The material of two pieces of window glass is K9. For the whole device, the inner diameter is 6.5 mm, the outer diameter is 12 mm, the height is 8 mm. The lens cavity using aluminum is filled with two immiscible liquids. The two kinds of liquids have same density but different refractive indices. One of the liquids is conductive, the other is insulating. The parameters of the salt solution and silicone oil are shown in Table 1. The aspherical lens is embedded in the lower window glass. The window glass is placed on the platform in cylindrical cavity and bonded together by UV glue. The grounding electrode is the upper half of an aluminum column, while the counter electrode is the lower half of an aluminum column and in direct contact with the conducting liquid. There is a layer of insulation board to prevent the two electrodes from being joined. To guarantee perfect pinning of the water–oil interface to the edge of the aperture, a hydrophobic and dielectric coating is applied to the inner wall of the aluminum cylindrical cavity by Spraying Teflon.
(1)
where 𝜀 is the dielectric constant of the hydrophobic and dielectric film, d is its thickness, U is the applied voltage, 𝛾12 is the liquid/liquid interfacial tension, 𝜃0 is the initial contact angle between the conductive liquid and inner wall, and 𝜃1 is the contact angle between the conductive liquid and inner wall under driving state. Eq. (1) can be used to derive an expression for the dioptric power D of the meniscus radius R and the refractive indices 𝑛o and 𝑛w for the insulating and conductive liquid, respectively, 𝐷 = 𝐷0 + 𝐷1 +
(𝑛o − 𝑛w ) , 𝑅
(2)
where 𝐷0 is the dioptric power in the initial state of no AL, and 𝐷1 is the dioptric power of the aspheric lens. For a 6.5 mm diameter lens we can control the dioptric power between −50 and +67 diopters. 57
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Table 1 Properties of the materials we used. Material
Density (g/cm3 )
Refractive index
Abbe number
Transparent
Aqueous solution Oil
1.09 1.09
1.34 1.48
58.13 34.59
Yes Yes
Fig. 5. Height of the fabricated ALs to the volume of the PDMS solution.
Fig. 3. Inverted additive fabrication processing route of ALs.
Fig. 6. Comparison of surface profiles of ALs.
That is to say, the PDMS monomer and hardener (Sylgard 184, Dow Corning) are mixed by a weight ratio of 10:1, and then placed in a vacuum desiccator until all bubbles are removed. A 1 ml hypodermic needle is dipped vertically into the mixture to extract a small drop. The extracted PDMS droplet is allowed to slide slowly onto the window glass. In order to keep the aperture of aspherical lenses consistent, a ruled surface structure is designed to fix its caliber, as shown Fig. 3. After that, the window glass is inverted and PDMS is cured at 60 ◦ C and at 90 ◦ C for 10 min and 20 min, respectively. In order to increase the asphericity of the aspheric lens, one can control the amount of the PDMS used for each lens to increase gradually. As shown in Fig. 4, we have shown six types of the ALs (a–e). At each APL, the contact angle is measured: (a) 20.3◦ , (b) 26.8◦ , (c) 28.8◦ , (d) 40.4◦ , and (e) 48.5◦ . On increasing the volume of the PDMS solutions, the contact angles become larger.
Fig. 4. Six types of the APLs based on the various volume of additive PDMS solution.
4. Generation of aspheric lens The AL is prepared by cross-linking a hanging polymeric drop. The drop is affected by gravity acting to pull it down, meanwhile, the drop is subjected to the surface tension trying to hold the droplet up against the flat surface. Therefore, the surface of the polymer droplet is aspherical. The AL is formed of PDMS, which has been prepared using the typical soft lithography PDMS procedure, as shown in Fig. 3.
Table 2 Relation between surface profile and curing time (Ti.), and curing temperature (Te.). Droplet volume (0.5 ml)
First Te.
Second Te.
First Te.
Second Ti.
50 55 60 65 60
5 10 15 20 10
90
H
C
𝜅
2nd Order
4nd Order
6nd Order
Same Ti. (10/20 min)
3.00 2.80 2.70 2.50 2.71 2.70 2.69 2.70
1.47 1.31 1.18 1.02 1.19 1.18 1.17 1.18
−1 −1 −1 −1 −1 −1 −1 −1
4.82E−4 4.82E−4 4.81E−4 4.71E−4 4.81E−4 4.81E−4 4.81E−4 4.81E−4
4.11E−4 1.10E−2 −1.04E−3 1.91E−3 −3.02E−4 3.28E−2 −3.03E−4 1.10E−2
5.92E−7 −6.96E−13 −8.13E−13 −4.19E−8 2.37E−9 3.28E−7 6.39E−12 −6.96E−10
Same Te. (60/90 ◦ C)
2.79 2.76 2.73 2.73 2.70 2.70 2.71 2.70
1.38 1.26 1.23 1.23 1.18 1.18 1.19 1.18
−1 −1 −1 −1 −1 −1 −1 −1
4.82E−4 4.82E−4 4.81E−4 4.81E−4 4.81E−4 4.81E−4 4.81E−4 4.81E−4
2.34E−3 5.85E−4 1.93E−3 −5.16E−3 −2.79E−4 −1.02E−4 5.30E−4 5.91E−4
1.51E−11 2.39E−11 3.2E−8 1.17E−11 1.23E−11 −6.47E−12 1.04E−8 −1.84E−6
70 80 90 100 20
10 20 30 40
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Fig. 7. RMS of the conventional lens and proposed lens at different fields of view. (a) (c) (e) the conventional lens; (b) (d) (f) the proposed lens. Scale bar: (a) (c) (e) 80 μm, (b) (d) (f) 20 μm.
The relationship between the volume of PDMS solutions and the height(H) of the lenses is shown in Fig. 5. The dependence of the lens height and the volume of the PDMS solutions are evident from the experiment, which shows that the lens height increases with increase in volume of the PDMS solutions. The variation of the lens curvature as a function of volume of additive PDMS solution is measured using a profilometer; the profiles are plotted in Fig. 6. In addition, the effect of temperature and time of two curing cycles on the lens profile is also studied, as shown in Table 2. Note should be made that time and temperature in the first curing are much more important than time and temperature in the second solidification, because the PDMS has high fluidity at the first solidification. Due to the gravity, it is easy to produce the tendency of sagging. At the second solidification, the PDMS hardly sags with little fluidity. A function is used to fit the surface profile based on the measured data using the aspheric curve
formula [26]: ∑ ℎ2 + 𝐴2𝑛 ℎ2𝑛 , √ ℎ 2 𝑅𝑠 [1 + 1 − (1 + 𝜅)( 𝑅𝑠 ) ] 𝑛=2 𝑚
𝑧(ℎ) =
(3)
where h is the radial coordinate, 𝑅𝑠 the vertex radius, 𝜅 is the conic constant and 𝐴2𝑛 the coefficients of a correction polynomial. Different types of conic sections can be identified as follows: 𝜅>0 oblate ellipse, 𝜅=0 sphere, −1<𝜅<0 prolate ellipse, 𝜅=−1 parabola, 𝜅<−1 hyperbola. 5. Simulation results According to the surface profiles of ALs in Fig. 6, an effective focal length of 30 mm is chosen as the optimized target and only 92.3% lens aperture (namely 6 mm aperture size) is used during the simulation by considering the characteristic of the tunable liquid lens. As shown in Fig. 7, from the ZEMAX simulation, the mean square radius of the lens 59
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Fig. 8. ZEMAX simulation results. (a) conventional design; (b) optimized design.
distortion of the conventional design is 0.7%. However, the minimum distortion of our lens is 0.00186%. As for astigmatism and coma, there is no distinct performance improvement.
we mentioned is far less than the size of Airy spot. We can conclude that the imaging quality of our lens is very well. It can be seen that the RMS at focus (f = 50 mm) is distinctly reduced from 55.7 μm (no AL) to 2.095 μm after performing optimum optimization (type d AL), which indicates that our lens has reduced spherical aberration. When the focal length is 30 mm, the RMS radius of the conventional lens is 61.308 μm. However, the RMS radius of the proposed lens decreases to 15.986 μm. When the focal length is 90 mm, the RMS radius of the conventional lens is 68.769 μm. In this case, the RMS radius of the proposed lens decreases to 17.514 μm. At the same time, the minimum spherical aberration of the lens working over different focal lengths are studied. It is seen that with respect to the without AL electrowetting lens, its spherical aberration will always be positive. It is seen that with respect to the proposed lens, its spherical aberration increases with increasing focal length from 30 mm to nearly 50 mm, whilst that, the spherical aberration gradually decreases from 50 mm to nearly 90 mm. The appearance of larger spherical aberration at f = 30 mm is caused by the over-compensation effect introduced by the aspherical surface. The results of ray tracing and the corresponding wavefront maps at the focus are also shown in Fig. 8. Since the root mean square (RMS) of the wavefront error with respect to reference spherical at focus is mainly caused by spherical aberration, and the resultant decreases in their original values of 1.4478 waves to optimized 0.0034 waves (λ = 486 nm). We can come to conclusion that the spherical aberration can be reduced when our lens works in some regions. The AL design is currently focused on spherical aberration, it also effects on other lens performance criteria, such as distortion. The distortion is caused by variation in magnification of the image across the field of view or object height. When the magnification of a lens differs at the edge of the lens and at the center, the image of a square object will be curved abnormally. The optical compensation surface of the aspheric surface is designed to compensate the wave phase difference produced by the large aperture distortion. So, the adaptive lens still has good optical characteristics in the case of large aperture. The aperture of our lens is 6.5 mm. With respect to the distortion, our lens demonstrates distinct performance improvement compared to the lens without AL, as shown in Fig. 9. When the field of view is 2 degrees, the minimum
6. Experimental results Like most tunable liquid lenses, the key parameter is their capability for focal length variation. The characteristic of our lens is investigated. We designed an experiment set-up to evaluate the focal length. As shown in Fig. 10(a), the experiment set-up consists of a collimator (FPG-7, Hua Zhong Precision Instruments Co., Ltd., China), a beam splitter, the proposed lens, a CMOS camera and a computer. We used the CMOS digital camera as an image plane to collect light spot. For the positive lens, the spot is obtained by the COMS camera. The CMOS acquisition plane is just the focal plane of the lens, and the spot is the smallest. When the spot diameter is less than 1 mm, the focal length of the lens is obtained. The distance between the lens and CMOS is the focal length. The resolution and the pixel size of the CMOS are 2592 × 1944 and 2.2 μm × 2.2 μm, respectively. The variation of the focal length as a function of the applied voltage is obtained, as shown in Fig. 10(b) (using type e AL). From Fig. 10(b), we can see that the focal length of our lens decreases from 265 mm to 20.5 mm when the operating voltage increases from 30 V to 75 V. And we can conclude that the focal length of the proposed lens is smaller than the focal length of the lens without AL at different voltages. That is because the aspheric lens bears part of focal power. To evaluate the proposed lens performance during focus change, we recorded the image of an object using high speed camera through the liquid lens under natural light environment. A test target was placed vertically above our lens. In our experiment, the distance between the target and the lens is always 56 mm. The recorded images of without AL lens are seen in Figs. 11(a)–(d). The recorded images of our lens are seen in Figs. 11(e)–(h). When comparing these pictures carefully, we can find that the images obtained by our lens is clearer than that of the lens without AL. Obviously, our lens reduces the aberrations under different degrees of zoom mainly because of the AL. In addition, the edge of the lines of our lens is more distinct than 60
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Fig. 9. ZEMAX simulation results of distortion and field curvature. (a) conventional design; (b) optimized design.
Fig. 10. Measurement of focal length. (a) Experiment set-up; (b) Tunable focal length as a function of applied voltage.
Fig. 11. Captured images of different magnification degree by the (a)–(d) with ALs and (e)–(h) without ALs at the object distance of 56 mm. Scale bar (a)–(h) 1.5 mm.
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Fig. 12. Quantification of the imaging resolution of1 the lenses. (a) Imaging of the lens without AL. (b) Imaging of the proposed lens. (linewidth: 0.0125 mm).
Fig. 13. Captured images by the (a) conventional lens and (b) proposed lens at the focal length of 30 mm.
the one without AL. From a theoretical analysis, when negligible even no spherical aberration and distortion is present, thus demonstrating the effectiveness of the correction provided by the aspherical surface design. The optical resolution of a lens is typically defined by smallest resolvable structure. Light emitted by an LED is collimated by a collector lens that is diffused to provide an even illumination over the FBLB-101 resolution card. We used resolution target for quantitatively characterizing the improved optical performance. For convenience, we chose the highest power lens (highest driving voltage, U = 75 V). When the resolution of the lens without AL and our lens is all 10 line pairs per mm, as shown in Fig. 12. The image obtained by our lens is clearer. The improvement in the optical performance has been demonstrated directly. In order to further verify that imaging quality of our lens is better than that of the conventional lens, the optical quality of the lenses is measured with quantitative parameters. We measured the optical resolution of the lens using the experimental device to measure the focal length in Fig. 10(a). However, the difference is that a resolution target is added behind the light source of the collimator. Actually, we need to slightly adjust the voltage to obtain the clearest image. The used wavelength is ∼595 nm. The captured images by the conventional lens and proposed lens are shown in Figs. 13(a) and (b), respectively. Compared the images with f = 50 mm, we can see that the images of the proposed lens are clearer than the conventional lens. The corresponding resolution target is element 13 of target 1. So the minimum resolution of the proposed lens is 32.9′′ . Comparing Figs. 14(a) with (b), we can get the similar conclusion. The corresponding resolution target is element 9 of target 1. So the minimum resolution of the proposed lens is 40′′ at present. Our lens reduces the aberrations in some focal length range mainly because of the polymer aspheric lens.
Fig. 14. Captured images by the (a) conventional lens and (b) proposed lens at the focal length of 50 mm.
Acknowledgments The work is supported by the National Natural Science Foundation of China under Grant No. 61535007 and the Equipment Research Program in Advance of China under Grant No. JZX2017-1570/Y464. References
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In summary, the proposed lens is composed of an electrowetting lens and an aspherical lens. But the overall size of the device does not change, which meets the requirements of the lightweight system. In addition, it has for many years been an ambition of researchers in imaging to create a flexible low-cost system. Therefore, the aspheric lens is made by PDMS, which has low cost and is easy to be treated as we expect. More importantly, spherical aberration and distortion can be basically eliminated. Thereby, one can get better optical imaging quality using the proposed lens than electrowetting lens alone. Its applications for zoom microscope system and tunable-focus eyeglasses are foreseeable. 62
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