光学自由曲面加工误差对光学性能的影响

发布时间：2018-01-31 05:32

本文关键词： 光学自由曲面加工误差光线追迹波像差散射传递函数　出处：《吉林大学》2011年硕士论文　论文类型：学位论文

【摘要】：光学自由曲面是指没有任何回转对称性的光学曲面。与现有的回转对称非球面相比,自由曲面光学元件具有改善光学系统成像质量、减少光学系统的元件数量和大小、增加光学设计的柔性等优点。正是由于这些优点,自由曲面光学元件在许多光电产品和光通信产品中有极为广泛的应用需求。然而由于光学自由曲面的几何特征复杂,且面形精度和表面质量要求较高,使得加工和检测过程变得极为困难。无论是哪一种加工方法,在自由曲面光学元件加工中都不可避免地会在已加工表面产生面形误差和表面粗糙度等。这些面形误差和表面粗糙度的存在,导致光学系统的光学性能降低。因此,研究面形误差和表面粗糙度对光学性能的影响就显得很重要。本文利用高斯滤波方法,从所获取的自由表面形貌数据,分离出面形误差和表面粗糙度,以分别研究面形误差和表面粗糙度对光学性能的影响。对于仅有面形误差的光学自由曲面,利用波像差分析面形误差的影响。对于仅有粗糙度的光学自由曲面,在比较现有的表面散射理论的基础上,将利用Harvey-Shack散射理论推导的散射表面传递函数分析表面粗糙度的影响。波像差的求解主要包括：光线追迹、实际波阵面和理想波阵面的拟合以及波像差计算等步骤。在现有的针对非球面光线追迹方法中,主要是利用迭代算法计算入射光线与光学曲面的交点,再利用矢量形式的折反射定律进行光路计算。然而在这个过程中,由于迭代起点选择问题,会存在“伪交点”和“光线溢出”的情况,导致整个追迹过程失败。为了避免这个问题,本文提出将光学自由曲面离散化的做法,将平行光直接入射到离散点上,采用矢量形式的折反射定律进行光线追迹。通过球面验证了所提出的光线追迹方法的可行性。这种算法既能避免上述存在的问题,算法也比较简单。光线追迹完成后,建立理想波阵面与实际波阵面的Zernike多项式的拟合方法；求解理想波阵面与实际波阵面偏差,即可研究面形误差对光学性能的影响。表面粗糙度对光学散射有着直接的影响。在现有的表面散射理论中,Harvey-Shack散射理论是从线性系统理论出发的,适用于研究任何入射角度的散射。然而,Harvey-Shack散射理论推导出的表面散射传递函数是以平面作为基准面进行研究的。对于光学自由曲面,其基准面不再是平面,而是自由曲面。本文将表面粗糙的光学自由曲面看作是一个随机场,利用统计学方法对表面粗糙的光学自由曲面进行了数学推导,得到的结论是：Harvey-Shack推导出的散射表面传递函数不依赖于基准面。因此,本文对光学自由曲面的光散射分析,是通过对散射表面传递函数进行傅里叶逆变换得到点扩散函数后,通过点扩散函数来研究表面粗糙度对光学性能的影响。
[Abstract]:Optical free surface is an optical surface without any rotational symmetry. Compared with the existing rotational symmetric aspherical surface, the free-form surface optical element can improve the imaging quality of optical system. It is precisely because of these advantages that the number and size of optical components are reduced and the flexibility of optical design is increased. Free-form optical elements are widely used in many optoelectronic products and optical communication products. However, due to the complexity of geometric characteristics of optical free-form surfaces, the surface accuracy and surface quality requirements are high. Making the processing and testing process extremely difficult, regardless of the processing method. In the machining of free-form surface optical elements, it is inevitable to produce surface shape error and surface roughness on the machined surface. Therefore, it is very important to study the effect of surface shape error and surface roughness on optical performance. In this paper, Gao Si filtering method is used to separate the profile error and surface roughness from the free surface topography data. The influence of surface shape error and surface roughness on optical performance is studied respectively. For optical free surface with only plane shape error, the influence of plane shape error is analyzed by wave aberration, and for optical free surface with only roughness, the effect of surface shape error is analyzed by using wave aberration. On the basis of comparing the existing surface scattering theory, the influence of surface roughness is analyzed by using the scattering surface transfer function derived from Harvey-Shack scattering theory. The solution of wave aberration mainly includes the steps of ray tracing, fitting of actual and ideal wavefront planes and calculation of wavefront aberration. The iterative algorithm is mainly used to calculate the intersection of incident light and optical surface, and then to calculate the optical path by using the law of refraction in vector form. However, in this process, due to the problem of iterative starting point selection. There will be "pseudo-intersection" and "ray overflow", which will lead to the failure of the whole tracing process. In order to avoid this problem, the method of discretization of optical free surface is proposed. The parallel light is directly incident to the discrete point. The method of ray tracing in vector form is used to trace the ray. The feasibility of the proposed method is verified by spherical surface. This algorithm can avoid the above problems. The algorithm is also relatively simple. After ray tracing is completed, the fitting method of Zernike polynomials between ideal wavefront and real wavefront is established. The influence of the shape error on the optical performance can be studied by solving the deviation between the ideal and the actual wavefront. Surface roughness has direct influence on optical scattering. Harvey-Shack scattering theory is based on linear system theory. However, the surface scattering transfer function derived from Harvey-Shack scattering theory is based on the plane as the datum. In this paper, the rough surface of the optical free surface is regarded as a random field, and the mathematical derivation of the rough surface of optical free surface is carried out by using the statistical method. The conclusion obtained is that the scattering surface transfer function derived by: Harvey-Shack does not depend on the datum. Therefore, the light scattering analysis of the optical free surface is presented in this paper. The point diffusion function is obtained by inverse Fourier transform of scattering surface transfer function, and the influence of surface roughness on optical properties is studied by point diffusion function.
【学位授予单位】：吉林大学
【学位级别】：硕士
【学位授予年份】：2011
【分类号】：TH161

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