基于平板电极的非球面组合液体透镜的仿真与实验分析【增强内容出版】
As an important branch of microfluidic optics, microfluidic optics has become a key technology to promote the development of highly miniaturized and functional optics. Liquid lenses are a common form of microfluidic optical lenses, and as an important part of optical systems, they have obvious advantages over solid lenses, such as a reconfigurable geometry and tunable refractive index. At present, researchers have explored various techniques and tuning mechanisms to make liquid lenses, including fluid pressure lenses, electromagnetic wave lenses, electrowetting lenses and dielectrophoresis lenses. Unlike electrowetting driven liquid lenses, dielectrophoresis driven liquid lenses do not require conducting liquid and do not produce problems such as evaporation or microbubbles. To correct aberrations in practical applications, it is necessary to design a liquid lens with an aspherical surface, which has the advantages of a simple structure and easy realization because of the use of continuous electrodes compared with patterned electrodes.
Based on the dielectrophoresis effect, we design an aspherical combined liquid lens based on flat electrode. A certain dielectric constant difference exists between the two liquid materials filled with miscible pairs in the cavity. When the external voltage is applied, the droplet with high dielectric constant will move along the electric field direction and squeeze the droplet with low dielectric constant, and the curvature radius of the liquid-liquid interface will change. By adjusting the voltage applied to the two indium tin oxide (ITO) conductive glass flats in the middle, the curvature radius of the liquid-liquid interface can be changed to adjust the focal length. First, a model of an aspherical combined liquid lens based on a parallel flat electrode under different voltages is built by COMSOL, and the surface profile data of the aspherical interface are obtained. Then, the aspherical surface profile data and aspherical formula are fitted by MATLAB to obtain the corresponding aspherical coefficient. Finally, on this basis, the optical model of the aspherical combined liquid lens based on flat electrode is built by Zemax, and the focal length of the aspherical combined liquid lens under different voltages is obtained.
First, we compare the aspherical combined liquid lens based on the flat electrode with the aspherical single liquid lens, which has the same liquid material and droplet volume as the aspherical composite liquid lens. The results show that the aspherical combined liquid lens has a smaller focal length and stronger focusing ability than the aspherical single liquid lens and is more suitable for camera lenses requiring a large depth of field (Fig. 5). In order to further study the characteristics of aspherical combined liquid lens based on flat electrode, COMSOL software is used to simulate the change of the interface profile of aspherical combined liquid lens based on flat electrode under different parallelism. In the simulation process of the model, the lower flat is set to be placed horizontally. When the upper and lower flat are not parallel, that is, the upper flat and the horizontal direction have a certain tilt angle, the electric field distribution in the liquid lens model is analyzed (Fig. 6). The interface profile data obtained in COMSOL is derived, then MATLAB is applied to fit the profile, and the comparison and analysis of aspherical combined liquid lenses with different parallelism is carried out by using Zemax. It is found that the focal length of the aspherical combined liquid lens is little affected when the flat electrode has a small inclination (1° to 4°) (Fig. 7).
Based on the dielectrophoresis effect, an aspherical combined liquid lens based on flat electrode is designed in this study. The liquid lens consists of four ITO conductive flat glass plates, cavities, dielectric layers and hydrophobic layers parallel up and down. The focal length of the aspherical combined liquid lens under different voltages is calculated by using the relevant optical model, and the results show that the focal length of the aspherical combined liquid lens is smaller than that of the aspherical single liquid lens, and the imaging quality is better. The influence of the parallelism of the flat electrode on the focal length of the aspherical combined liquid lens is also discussed. The aspherical combined liquid lens is prepared experimentally, and its focal length and imaging resolution are measured. When the operating voltage increases from 0 to 280 V, the focal length varies from 28.7135 mm to 20.1943 mm, which is basically consistent with the simulation. The feasibility of the lens structure is verified by experiments. The imaging resolution is up to 49.8244 lp/mm. The designed aspherical combined liquid lens based on a flat electrode can provide a new scheme for the high-quality imaging of liquid lenses and their applications and can expand the application.
1 引言
与传统的固体透镜相比,液体透镜具有体积小、无需外部机械装置、反应速度快、寿命长、成本低等特点[1],在手机摄像头、内窥镜、全息成像等方面得到了广泛的应用[2]。目前科研工作者已经探索了各种技术和调谐机制来制作液体透镜,包括流体压力透镜[3-4]、热效应透镜[5]、电磁波透镜[6]、自适应水凝胶透镜[7]、介电泳透镜[8]和电润湿透镜[9]等。其中,流体压力透镜需要由外部泵提供流体压力,这增加了器件的体积;基于电润湿效应的液体透镜通过改变盐水和油之间的界面来调整其表面轮廓,然而自由电荷的传输可能会在盐水中产生电解,且交变电场可能会使溶液受热,从而产生微气泡;而介电泳透镜无需导电液体,且不会产生蒸发和微气泡等问题[10]。
在光学系统中,球差往往是研究人员特别关注的像差,所以对于液体透镜首先需要考虑其球差的校正。对于传统的可调焦液体透镜,其形变后表面轮廓的形状近似于球面,所以会引入显著的球差,而设置液体透镜的表面为非球面则可以提高透镜校正像差的能力。2009年,Zhan等[11]提出了一种利用静电力调控的非球面聚合物液体透镜。光固化聚合物的绝缘液滴放置在两个透明氧化铟锡(ITO)玻璃电极之间的介质基板上,在强静电场作用下,液体透镜可以从初始的球形变形为抛物线形,甚至近圆锥形,但是固化之后的液滴便失去了可调节性。2017年,Mishra团队提出了一种利用流体静压力和静电力结合的非球面液体透镜[12]。通过在10×10电极阵列上施加不同的电压以产生复杂的电场分布,从而动态调节透镜的形状,进而调节球差、彗差、像散等像差。由于透镜的电极数量较多,单元电极的控制比较困难。2019年,Wang等[13]提出了一种集成非球面的液体透镜系统,利用聚二甲基硅氧烷(PDMS)液滴的重力以及液体界面张力,可以固化得到相应的非球面面型,并与电润湿透镜组合,在不改变透镜尺寸的前提下,实现球差的调节。然而该器件制备工艺较复杂,不利于透镜的快速、低成本生产。本课题组基于液体的密度差,在液体透镜中引入了非球面面型,分别进行了非球面双液体透镜的光学特性分析、非球面三层液体透镜在人眼晶状体光学模型中的应用研究,以及方腔结构的非球面液体透镜的实验分析[14-16]。
本文在已有的研究基础之上,通过仿真与实验分析,研究了一种基于平板电极的非球面组合液体透镜。通过理论仿真,结合基于平行平板电极的单个非球面双液体透镜,对比分析了不同电压下的双液体透镜的焦距变化,讨论了平板电极的平行度对非球面液体透镜组合结构焦距的影响,并对其焦距和成像质量进行了实验分析,实验结果与仿真基本一致。与图案化电极相比,该非球面组合液体透镜结构使用连续电极,加工更简单,成本更低,更易于实现,更具有实用性。
2 基本原理与结构设计
介电泳(DEP)力是在非均匀电场影响下施加在不带电的介电粒子或导电粒子的电偶极矩上的力。电场使粒子极化,两极沿着电场线受力,根据偶极子的方向,力可以相互吸引或相互排斥。由于电场是不均匀的,所以电场较大的一极将会支配另一极,粒子产生移动,并且偶极子的方向取决于粒子和介质的相对极化率。当施加电压时,由于两种液体材料之间介电常数存在差异,因此在液滴上产生介电泳力。介电泳力使液滴收缩,从而增加液滴的接触角,介电泳力[17]可表示为
表 1. 液体材料的关键参数
Table 1. Key parameters of liquid materials
|
式中:
图 1. 基于平行平板电极的非球面组合液体透镜系统的结构示意图
Fig. 1. Structural diagram of aspherical combined liquid lens system based on parallel flat electrodes
3 仿真分析
利用COMSOL、MATLAB和Zemax软件对基于平行平板电极的非球面组合液体透镜系统进行建模与仿真分析,其主要的流程示意图如
图 2. 非球面组合液体透镜的仿真分析流程图
Fig. 2. Flow chart of simulation analysis of aspherical combined liquid lens
采用COMSOL软件对所提的非球面组合液体透镜进行建模与仿真分析,该组合系统的几何结构模型如
图 3. 非球面组合液体透镜模型的建模示意图。(a)初始状态下的立体图;(b)电场线分布图(40 V)
Fig. 3. Modeling diagram of aspherical combined liquid lens model. (a) Stereogram in initial state; (b) electric field line distribution diagram (40 V)
在MATLAB软件中导入由COMSOL得到的非球面面型数据,可拟合获得不同电压下的非球面系数,计算公式为
式中:(x, y, z)为非球面上某一点的坐标;a为双液体界面的位置;b、c、d、e、f为多项式系数。将得到的系数代入到Zemax中,建立相应的非球面组合液体透镜的光学模型。为了进一步研究非球面组合液体透镜的特性,将其与非球面单个液体透镜进行对比,两种液体透镜的液体材料、腔体结构和液滴体积的设置保持一致。
图 4. 在280 V电压下的非球面液体透镜光路图。(a)非球面组合液体透镜;(b)非球面单个液体透镜
Fig. 4. Optical path diagram of aspherical liquid lens at 280 V voltage. (a) Aspherical combined liquid lens; (b) aspherical single liquid lens
当外加电压由0逐渐增加到280 V时,介电液滴的曲率会发生变化,因此可以实现透镜焦距的调节。利用Zemax软件搭建不同外加电压下非球面组合和单个液体透镜的光学模型,可以得到其变焦范围,将二者的变焦范围进行对比分析,结果如
图 5. 不同电压下非球面组合和单个液体透镜的焦距对比
Fig. 5. Comparison of focal lengths between aspherical combined and single liquid lens at different voltages
此外,考虑到平板电极的平行度可能对非球面组合液体透镜存在影响,利用COMSOL软件模拟了不同平行度下的基于平板电极的非球面组合液体透镜界面面型变化情况。在模型的仿真过程中,将下平板设置为水平放置,当上平板与下平板不平行时,即上平板与水平方向存在一定的倾斜角度时,分析液体透镜模型中的电场分布情况。设置上平板倾斜4°并施加40 V电压,非球面组合液体透镜中的电势分布如
图 6. 上平板倾斜4°时40 V电压下非球面组合液体透镜电势分布
Fig. 6. Potential distribution of aspherical combined liquid lens with 40 V voltage when upper flat is tilted 4°
图 7. 不同平行度下非球面组合液体透镜的焦距对比
Fig. 7. Focal length comparison of aspherical combined liquid lens with different parallelism
4 实验分析
4.1 实验制备
本实验所用的ITO导电平面玻璃板的尺寸为30 mm×30 mm,厚度为0.4 mm,首先用无水乙醇对ITO导电平面玻璃板正反两面进行完全清洗,接着用无尘纸擦去表面可见的乙醇;然后将玻璃板放入超声波清洗仪中,利用去离子水清洗电极3 min左右,清洗完毕之后关闭清洗仪,取出玻璃片并再次用无尘纸擦拭干净。在ITO导电平面玻璃板上先涂覆SU8,利用匀胶机涂覆均匀(厚度约为6 μm),放入烤箱中烘烤。在烘烤完毕的ITO导电平面玻璃板上涂覆Parylene溶液,以获得更大的初始接触角,选择圆柱形透明亚克力管作为腔体材料,该透明亚克力管的具体参数:外径为17 mm,内径为13 mm,壁厚为2 mm,高为5 mm。在处理好的ITO电极导电平面玻璃板上用紫外线固化胶(UV胶)固定好腔体,先注入体积约为圆柱形腔体体积的5/6的去离子水,然后利用针管注入甲基硅油充当介电液滴,确保甲基硅油滴在疏水层的中心,注入的甲基硅油液滴在松弛状态下覆盖底面的半径约为2.7 mm,再次注入去离子水至液面高于腔体呈微凸起状态。最后,将所得到的液体透镜结构封装,顶部采用涂覆6
图 8. 封装后的基于平行平板电极的非球面组合液体透镜
Fig. 8. Packaged aspherical combined liquid lens based on parallel flat electrode
4.2 焦距与成像分析
本实验使用实验室自制的焦距仪[19],通过记录目镜中不同线对的位置读数,来测试并计算出所制备的液体组合透镜的聚焦能力。如
图 9. 不同电压下仿真与实验测得的焦距对比
Fig. 9. Comparison of focal length measured by simulation and experiment at different voltages
利用该非球面组合液体透镜对USAF 1951分辨率板进行成像实验分析,得到不同电压下的成像结果,如
图 10. 不同电压下基于平板电极的非球面组合液体透镜的分辨率。(a) 0;(b) 160 V;(c) 280 V
Fig. 10. Resolution of aspherical combined liquid lens based on flat electrode at different voltages. (a) 0; (b) 160 V; (c) 280 V
5 结论
基于介电泳原理提出了一种基于平行平板电极的非球面组合液体透镜,该液体透镜由两个密封有两种非导电液体的非球面单个液体透镜组合而成。利用软件搭建了相关的光学模型,计算得到不同电压下的非球面组合液体透镜的焦距,并与非球面单个液体透镜进行对比分析,结果表明非球面组合液体透镜的焦距段要比非球面单个液体透镜要小,成像质量也更好;此外还讨论平板电极的平行度对非球面组合液体透镜的焦距的影响。对所设计的非球面组合液体透镜进行了实验制备,测量了其焦距和成像分辨率,当工作电压由0增加至280 V时,焦距由28.7135 mm变化为20.1943 mm,与仿真基本一致,实验验证了该透镜结构的可行性,其成像分辨率最大可达到49.8244 lp/mm。
本实验所设计的非球面组合液体透镜与之前所提出基于平行平板电极的单个非球面双液体透镜[20]相比,两者结构都比较简单,尺寸也都在毫米数量级,但后者的成像分辨率约为45.2550 lp/mm,而前者的成像分辨率最大可达到49.8244 lp/mm,像质优于之前所提出的非球面双液体透镜。
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Article Outline
孔梅梅, 董媛, 徐春生, 刘悦, 薛银燕, 李明洋, 张舒涵. 基于平板电极的非球面组合液体透镜的仿真与实验分析[J]. 光学学报, 2024, 44(8): 0823002. Meimei Kong, Yuan Dong, Chunsheng Xu, Yue Liu, Yinyan Xue, Mingyang Li, Shuhan Zhang. Simulation and Experimental Analysis of Aspherical Combined Liquid Lens Based on Flat Electrode[J]. Acta Optica Sinica, 2024, 44(8): 0823002.