广义非球面透镜的设计、制作及应用研究
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摘要
随着光学技术的发展,光学系统中对光学元件的要求越来越高也越来越多样化,传统的球面透镜在一些场合已经不能很好的满足要求,比如对大发散角光束的准直,消除激光二极管的固有像散等,此时需要具有特殊面形的透镜形式,比如非球面透镜或者柱透镜等来实现,但传统制作透镜的方法如研磨法,较为适合球面透镜,对其它面形的透镜制作则比较繁琐,需要开发新的制作方式,如单点金刚石切削法,模压法等。这些方法各有优缺点,适合不同的需求。本文中我们主要研究使用电场调控液滴法来制作非球面透镜,具有成本低,表面质量高的特点,主要研究内容包括透镜的制作、检测及应用三个方面：
1.搭建了电场调控液滴制作非球面透镜的实验系统,系统能够施加电场改变液滴透镜面形,并通过检测模块测量透镜的质量,符合预期要求的时候使用紫外光固化透镜得到非球面透镜。对电场调控液滴面形的现象基于有限元软件COMSOL进行了数值模拟,分别使用水平集法及移动网格法对面形进行了求解,前者得到了面形的时变过程,后者可以得到稳态的面形,最终计算了不同电极形状下的电场力分布,讨论其可能的影响。对在椭圆基底上的液滴形状使用解析法和数值法进行了求解,前者能够获得长短轴曲率半径、液滴体积及基底尺寸之间的解析关系,后者基于Surface Evolver软件首先对解析法进行了验算,然后计算了重力对椭球面形的影响。对固化时光固胶收缩的问题进行了研究,使用神经网络的数值方法建立了固化前与固化后面形的映射关系,预测了固化后的面形,并与实验结果进行了对比。
2.对具有不同特点的非球面透镜进行了制作,首先为光纤准直透镜,将光纤放置在玻璃管内,在玻璃管端面放置液滴,调节面形后固化得到非球面透镜,从而获得一体化的光纤准直器,并通过实验进行了检测,光纤为单模时,发散角被压缩到2.5。,可以通过细致的调节进一步提高准直能力；然后制作得到了对数型锥透镜,在双凹透镜的基底上放置液滴,通过ZEMAX计算来检测是否符合锥透镜的要求,固化后得到对数型锥透镜,实验测量了锥透镜在平行光入射时的光斑分布特性,能够得到高分辨率的焦线,分别使用CCD及实验室自行研制的光斑测量仪基于相位复原技术测量了透镜出射的波前；最终基于非轴对称基底制作了非轴对称透镜,分别为机加工的方法制作了金属基底以及基于3D打印制作了椭圆基底,在两种基底上打孔以让光通过,使用此透镜开展了LD快轴方向准直的实验,测量了面形并与数值模拟结果进行了对比,验证了模拟的有效性,测量了平行光正入射及斜入射时的光强分布。
3.研究了对数型锥透镜的成像性质及其在复眼系统中的应用前景,表明在斜入射时光斑中心产生十字形状,便于实现光斑中心定位,在探测器倾斜时,探测到的光斑可视为在无衍射光束不同角度截面上的光斑,与非倾斜时相比光斑在一个方向上被拉伸,模拟了在对数型锥透镜中主动引入像散的情况,表明此时的相位形式能够在大视场入射时实现消像散,从而可以应用于平面复眼。研究了三次相位模板在复眼系统中的应用前景,表明在小视场入射时点扩散函数与正入射时几乎相同,适合成像的应用,大视场入射时单个透镜产生的像散会对成像质量有严重的影响,可以通过使用椭球透镜代替球透镜来克服,从而使其可应用于平面复眼中,实现大视场大景深,探测器倾斜时,三次相位模板能够改善一定视场内的成像质量,使其可以应用于球面复眼中。研究了单个椭球透镜应用于三维位置探测的特性,计算了光斑半径在不同视场入射时变化的解析解,并使用数值模拟得到了平行光入射时的光斑情况,进行了验证。研究了像散对双螺旋点扩散函数的影响,结果表明像散的影响与光斑的取向有关,在一个方向上影响与离焦类似,另一个方向上则几乎没有影响。
With the development of technology, more and more kinds of lenses have been adopted in modern optical systems. Traditional spherical lens will lead to relative poor performance in some applications, such as collimating beam with large divergence angle and correcting an astigmatic laser diode beam, where specific lenses are needed, such as aspherical lens and cylindrical lens. But traditional fabrication method for spherical lens, such as grinding, cannot be simply applied to fabricate these new types of lens, new technologies such as molding method and single point diamond turning have been developed to overcome this problem. In this thesis, we will study the fabrication, measurement and application of aspherical lens which is based on modulating the lens shape by electric field, listed as follows:
1. The experimental setup for the fabrication of aspherical lens is introduced, in which the liquid lens is modulated by applying electric field in the system, inspected by the measuring module and cured by UV light when its performance meets the requirements. Commercial software COMSOL based on finite element method (FEM) is employed to solve the deformation of droplet shape in an electric field. Level-set method and moving mesh method are used, respectively, the former can get the transition process of droplet deformation, while the latter can get the steady shape. Electrical force at the droplet interface under electrodes with different shapes is calculated to show the effects of electrode shape. Liquid lens shape on an elliptic substrate is solved both analytically and numerically. Analytical method reveals the relationship among the two curvatures, droplet volume, major axis length and minor axis length of the substrate. Numerical method based on Surface Evolver is then used to verify the analytical solution and study the effect of gravity. Phenomena of shrinkage of lens during UV curing are studied. Curve compensation is realized based on artificial neural network that maps the lens shape before UV curing to that after UV curing.
2. Different kinds of aspherical lens are fabricated. Firstly is fiber collimator lens. A fiber is put in a glass tube, on the end surface of which a droplet is injected. The collimator lens can then be obtained by curing the droplet after modulating the lens shape by electric field. Secondly is logarithmic axicon (LA). A droplet is put on a biconcave substrate which is used to extend the focal length. Commercial optical software is employed to evaluate the performance of the LA. Characteristic of the fabricated LA is measured by experiments, showing that a focal line with high resolution is obtained. Phase retrieval is then used to retrieve the wavefront exiting the LA based on multiple plane intensity distribution measured by a CCD with low resolution and a home-built scanning optical probe system with high resolution. Finally is anamorphic lens. Non-axisymmetric substrate fabricated by machinery and3D printing is used to form the anamorphic lens shape. Characteristic of the lens for laser diode beam collimation and3D position detection is studied by experiments.
4. Characteristic of LA is studied to show its application prospects in compound eye. Results show that the spot turns into cross bar under oblique illumination, which means that LA can be used to determine the positon of spot center. When the measuring plane is tilted, the spot on the plane is shown to be an elongation of the original spot in one dimension. Astigmatism is introduced in the simulation, showing that the phase can correct the astigmatism under large field of vie, which means it can be used in planar compound eye to get large field of view and large depth of field simultaneously. Application of cubic phase mask in compound eye is studied. Results show that the point spread function under small field of view is almost the same as that under normal illumination, meaning that it can be used in imaging, but under large field of view, the generated astigmatism will severely deteriorate the resolution. Ellipsoidal lens model is used to correct the astigmatism. Characteristic of single ellipsoidal lens for3D position detection is studied. Analytical solution and numerical solution of the spot shape under different fields of view are obtained. Effects of astigmatism on double helix point spread function are studied, results show that the effects are related to the orientation of the spot and it behalves like defocus in the orthogonal direction while it affects very little in the parallel direction.
1.搭建了电场调控液滴制作非球面透镜的实验系统,系统能够施加电场改变液滴透镜面形,并通过检测模块测量透镜的质量,符合预期要求的时候使用紫外光固化透镜得到非球面透镜。对电场调控液滴面形的现象基于有限元软件COMSOL进行了数值模拟,分别使用水平集法及移动网格法对面形进行了求解,前者得到了面形的时变过程,后者可以得到稳态的面形,最终计算了不同电极形状下的电场力分布,讨论其可能的影响。对在椭圆基底上的液滴形状使用解析法和数值法进行了求解,前者能够获得长短轴曲率半径、液滴体积及基底尺寸之间的解析关系,后者基于Surface Evolver软件首先对解析法进行了验算,然后计算了重力对椭球面形的影响。对固化时光固胶收缩的问题进行了研究,使用神经网络的数值方法建立了固化前与固化后面形的映射关系,预测了固化后的面形,并与实验结果进行了对比。
2.对具有不同特点的非球面透镜进行了制作,首先为光纤准直透镜,将光纤放置在玻璃管内,在玻璃管端面放置液滴,调节面形后固化得到非球面透镜,从而获得一体化的光纤准直器,并通过实验进行了检测,光纤为单模时,发散角被压缩到2.5。,可以通过细致的调节进一步提高准直能力；然后制作得到了对数型锥透镜,在双凹透镜的基底上放置液滴,通过ZEMAX计算来检测是否符合锥透镜的要求,固化后得到对数型锥透镜,实验测量了锥透镜在平行光入射时的光斑分布特性,能够得到高分辨率的焦线,分别使用CCD及实验室自行研制的光斑测量仪基于相位复原技术测量了透镜出射的波前；最终基于非轴对称基底制作了非轴对称透镜,分别为机加工的方法制作了金属基底以及基于3D打印制作了椭圆基底,在两种基底上打孔以让光通过,使用此透镜开展了LD快轴方向准直的实验,测量了面形并与数值模拟结果进行了对比,验证了模拟的有效性,测量了平行光正入射及斜入射时的光强分布。
3.研究了对数型锥透镜的成像性质及其在复眼系统中的应用前景,表明在斜入射时光斑中心产生十字形状,便于实现光斑中心定位,在探测器倾斜时,探测到的光斑可视为在无衍射光束不同角度截面上的光斑,与非倾斜时相比光斑在一个方向上被拉伸,模拟了在对数型锥透镜中主动引入像散的情况,表明此时的相位形式能够在大视场入射时实现消像散,从而可以应用于平面复眼。研究了三次相位模板在复眼系统中的应用前景,表明在小视场入射时点扩散函数与正入射时几乎相同,适合成像的应用,大视场入射时单个透镜产生的像散会对成像质量有严重的影响,可以通过使用椭球透镜代替球透镜来克服,从而使其可应用于平面复眼中,实现大视场大景深,探测器倾斜时,三次相位模板能够改善一定视场内的成像质量,使其可以应用于球面复眼中。研究了单个椭球透镜应用于三维位置探测的特性,计算了光斑半径在不同视场入射时变化的解析解,并使用数值模拟得到了平行光入射时的光斑情况,进行了验证。研究了像散对双螺旋点扩散函数的影响,结果表明像散的影响与光斑的取向有关,在一个方向上影响与离焦类似,另一个方向上则几乎没有影响。
With the development of technology, more and more kinds of lenses have been adopted in modern optical systems. Traditional spherical lens will lead to relative poor performance in some applications, such as collimating beam with large divergence angle and correcting an astigmatic laser diode beam, where specific lenses are needed, such as aspherical lens and cylindrical lens. But traditional fabrication method for spherical lens, such as grinding, cannot be simply applied to fabricate these new types of lens, new technologies such as molding method and single point diamond turning have been developed to overcome this problem. In this thesis, we will study the fabrication, measurement and application of aspherical lens which is based on modulating the lens shape by electric field, listed as follows:
1. The experimental setup for the fabrication of aspherical lens is introduced, in which the liquid lens is modulated by applying electric field in the system, inspected by the measuring module and cured by UV light when its performance meets the requirements. Commercial software COMSOL based on finite element method (FEM) is employed to solve the deformation of droplet shape in an electric field. Level-set method and moving mesh method are used, respectively, the former can get the transition process of droplet deformation, while the latter can get the steady shape. Electrical force at the droplet interface under electrodes with different shapes is calculated to show the effects of electrode shape. Liquid lens shape on an elliptic substrate is solved both analytically and numerically. Analytical method reveals the relationship among the two curvatures, droplet volume, major axis length and minor axis length of the substrate. Numerical method based on Surface Evolver is then used to verify the analytical solution and study the effect of gravity. Phenomena of shrinkage of lens during UV curing are studied. Curve compensation is realized based on artificial neural network that maps the lens shape before UV curing to that after UV curing.
2. Different kinds of aspherical lens are fabricated. Firstly is fiber collimator lens. A fiber is put in a glass tube, on the end surface of which a droplet is injected. The collimator lens can then be obtained by curing the droplet after modulating the lens shape by electric field. Secondly is logarithmic axicon (LA). A droplet is put on a biconcave substrate which is used to extend the focal length. Commercial optical software is employed to evaluate the performance of the LA. Characteristic of the fabricated LA is measured by experiments, showing that a focal line with high resolution is obtained. Phase retrieval is then used to retrieve the wavefront exiting the LA based on multiple plane intensity distribution measured by a CCD with low resolution and a home-built scanning optical probe system with high resolution. Finally is anamorphic lens. Non-axisymmetric substrate fabricated by machinery and3D printing is used to form the anamorphic lens shape. Characteristic of the lens for laser diode beam collimation and3D position detection is studied by experiments.
4. Characteristic of LA is studied to show its application prospects in compound eye. Results show that the spot turns into cross bar under oblique illumination, which means that LA can be used to determine the positon of spot center. When the measuring plane is tilted, the spot on the plane is shown to be an elongation of the original spot in one dimension. Astigmatism is introduced in the simulation, showing that the phase can correct the astigmatism under large field of vie, which means it can be used in planar compound eye to get large field of view and large depth of field simultaneously. Application of cubic phase mask in compound eye is studied. Results show that the point spread function under small field of view is almost the same as that under normal illumination, meaning that it can be used in imaging, but under large field of view, the generated astigmatism will severely deteriorate the resolution. Ellipsoidal lens model is used to correct the astigmatism. Characteristic of single ellipsoidal lens for3D position detection is studied. Analytical solution and numerical solution of the spot shape under different fields of view are obtained. Effects of astigmatism on double helix point spread function are studied, results show that the effects are related to the orientation of the spot and it behalves like defocus in the orthogonal direction while it affects very little in the parallel direction.
引文
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