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Characteristics of wavefront correction using stacked liquid lens based on electrowetting-on-dielectric
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摘要:
设计了一种基于介电润湿效应的叠加式液体透镜，分析其对含有曲率误差、倾斜误差和活塞误差的畸变波前的校正能力。采用COMSOL软件构建叠加式液体透镜模型，仿真模拟了不同电压组合下液体界面面型的变化情况，获得该叠加式液体透镜内双液体界面的变化范围; 采用ZEMAX软件，借助点扩散函数变化，分析该透镜对波前任意点处曲率误差、倾斜误差和活塞误差的校正能力。结果表明：该叠加式液体透镜可以实现同时对不同类型畸变波前的校正，相应的峰谷值(PV)由校正前19.7853λ下降到校正后0.18λ，均方根值(RMS)由校正前5.6638λ减小到校正后0.0355λ，斯特列尔比(SR)由校正前的接近0值提高到0.962的较理想状态。
Abstract:A stacked liquid lens based on electrowetting-on-dielectric (EWOD) is designed to analyze the ability of correcting the distorted wavefront caused by curvature, tilt, and piston. The model of the stacked liquid lens is constructed by COMSOL software which is used to simulate the change of liquid interface with different voltage combinations, and the change range of the interface. The correction ability of the stacked liquid lens at a certain point in the wavefront is assessed from wavefront image and point spread function (PSF) is got by ZEMAX software. The results show that different types of distorted wavefront can be compensated via the stacked liquid lens. The peak-to-valley (PV) value decreases from 19.7853λ to 0.18λ, and the root mean square (RMS) value is down from 5.6638λ to 0.0355λ. Concurrently, the Strehl ratio (SR) increased from near 0 to 0.962. The related research results have broad prospects in the field of wavefront correction.
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Key words:
- liquid lens /
- electrowetting-on-dielectric /
- wavefront correction /
- Strehl ratio
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Overview: Adaptive optics is a technique used to correct the dynamic wavefront distortion caused by atmospheric turbulence and improve the performance of the optical system. As an important part of the adaptive optics system, wavefront corrector directly affects the imaging effect. At present, the most commonly used wavefront correctors are mainly divided into two types: deformable mirror and liquid crystal spatial light modulator. Deformable mirror has been studied for the longest time and has become the most mature technology. Its principle is to install a mirror on the surface of the actuator, changing the shape of the mirror by applying voltage, and then control the beam phase. Due to the high energy consumption, large volume, and high-cost problems caused by more actuators, the application of deformable mirror is greatly limited. The liquid crystal spatial light modulator adjusts the rotation direction of the rod-shaped liquid crystal molecules through the external loading voltage, which changes the refractive index and then increases or decreases the optical path to realize the modulation of the incident beam phase. Low power consumption, high precision, and small size are remarkable advantages of it. However, the polarization dependence, low correction frequency, and slow response speed of liquid crystal materials are the choke of development. The spatial modulator with small volume, high density, and fast response is the general trend.
In this paper, a kind of superimposed liquid lens based on the electrowetting on dielectric is proposed. The distortion wavefront can be corrected by controlling the liquid interface with the effect. It has the dominant position of small volume, easy array, no mechanical motion, no polarization dependence, and fast response speed comparing with the traditional deformable mirror and liquid crystal light modulator. Firstly, according to the theory of electrowetting on dielectric, the structure of the liquid lens system is designed, and the feasibility of the wavefront correction is deduced. Then, the changes of the liquid interface in the liquid lens units with different voltage combinations are simulated in COMSOL software. After that, aberration is introduced into the ideal wavefront of ZEMAX. On the basis of the voltage surface relationship obtained in COMSOL, the working voltage is adjusted to change the liquid interface surface shape, so as to realize the correction of the aberration. Finally, the phase distribution and point spread function distribution of the distorted wavefront correction process are given. The results show that the lens system has a good ability to correct the aberrations introduced at any point of the wavefront, the corresponding peak valley value decreases from 19.7853λ to 0.18λ, the root-mean-square value decreases from 5.6638λ to 0.0355λ, and Strehl ratio increases from near zero value to 0.962. The related research results will promote the development of wavefront correction technology and provide a theoretical basis for the realization of liquid lens for wavefront correction.
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图 1 叠加式液体透镜结构示意图。(a) 液体透镜结构；(b)~(d) 当只对底层棱镜单元施加电压(b)，对底层与中层结构施加电压(c)，对三层结构同时施加电压(d)时，液体界面变化情况
Figure 1. Structure of stacked liquid lens. (a) Structures of liquid lens; (b)~(d) When applying voltages to the bottom layer (b), applying voltages to both the bottom and the middle layer (c), and applying voltages to all three layers (d), the states of liquid interfaces is shown
图 2 叠加液体透镜畸变波前校正原理图。
Figure 2. Principle of distorted wavefront correction. (a) Process of correction; (b) Tilt error correction of the bottom layer; (c) Curvature error correction of the middle layer; (d) Piston error correction of the top layer
图 3 叠加式液体透镜界面面型图。(a) 自然状态下液体界面；(b) 施加电压使三层液体界面呈平面；(c) 改变底层电压；(d) 改变底层与中层电压；(e) 改变全部三层电压
Figure 3. Interface shape of the stacked liquid lens unit. (a) Liquid interface in natural state; (b) Flat liquid interface by applying voltages; (c) Voltages change in the bottom layer; (d) Voltages change in both the bottom and the middle layers; (e) Voltages change in all three layers
图 4 系统光路图。(a) 理想状态；(b) 携带三种误差；(c) 三种误差校正后
Figure 4. System optical path. (a) Perfect state; (b) Introducing distortions; (d) Complete correction
表 1 COMSOL参数设置
Table 1. Setting of COMSOL parameters
Parameter Value Remarks Theta1 & Theta2 135° Initial contact angle ([EMIm][NTf2] & Dodecane) Theta3 140° Initial contact angle (0.01%KCL/1wt%SDS & Dodecane) Gamma1 & Gamma2 0.011 N/m Surface tension([EMIm][NTf2] & Dodecane) Gamma3 0.069 N/m Surface tension(0.01%KCL/1wt%SDS & Dodecane) EPSR 2.65 Relative dielectric constant D_f 1 μm Dielectric thickness 
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表 2 液体参数设置
Table 2. Settings of liquid parameters
Liquid Density/(kg·m-3) Refractive index Dynamic viscosity/(cp) [EMIM][NTf2] 1380 1.4227 32 0.01%KCL/1wt%SDS 1000 1.33 2.7 Dodecane 753 1.4206 1.36
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表 3 系统结构参数
Table 3. Structural parameters of system
Surf. type Radius Thickness Glass Semi-diameter OBJ Standard Infinity Infinity 0 1 Zernike standard phase Infinity 0 1 2 Zernike standard phase Infinity 0 1 STO Standard Infinity 0 1 4 Non-sequential component Infinity - 1 5 Standard Infinity 0.566 1.33 1 6 Standard -3.864 0.434 1.4206 1 7 Standard Infinity 0.478 1.4206 1 8 Standard 28.654 0.522 1.4227 1 9 Standard Infinity 0 1 10 Standard -3.291E+011 0.2 BK7 1 11 Standard -7.752 15.001 1 IMA Standard Infinity - 1
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表 4 像差引入参数
Table 4. Introduction of distortions
Surf. type Norm radius Zernike 1 Zernike 2 Zernike 3 Zernike 4 1 Zernike standard phase 1 0 0 -15 -5.7 2 Zernike standard phase 0.5 -1E-003 0 0 0
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