【作者】 王超；

【导师】 肖木峥；

【作者基本信息】 北京理工大学 ， 机械工程， 2015， 硕士

【摘要】 非球面镜是十分重要的一种光学元件,被广泛应用在航天、航空、船舶、医学等各个领域。相比于球面镜,非球面镜的曲率半径不唯一、曲面形貌灵活,因而具有更多的应用优势。例如,非球面可以简化光学系统结构、减少系统重量、提高系统分辨率、改善成像质量等。然而,非球面检测,特别是大口径非球面检测,始终是光学测量领域的一大难题。对于小口径、非球面度较小的曲面,干涉式测量可以达到理想的检测精度;而对于大口径(或超大口径)非球面,干涉式测量将难以实现,接触式测量也会对镜片表面形成划伤。针对大口径非球面的测量难题,本论文提出了基于角度扫描法的大口径非球面高精度测量三维测量方法。角度扫描法的基本原理,是通过测量目标曲面各点的角度变化推导其曲率变化,再通过曲率值的数值积分计算出目标非球面的曲面形貌。具体开展了以下的研究内容:1.大口径非球面测量系统的总体方案设计。提出了面向200mm口径非球面的三维测量方案,完成了测量系统的结构设计;研究了系统中各部分结构的精度要求,并绘制了非球面测量系统的三维图纸;分析了非球面测量的主要流程,并制定了完成测量所需的操作步骤。2.大口径非球面测量的误差分析与补偿方法。分析了测量系统中不同来源的误差因素(包括随机误差与系统误差),计算了它们对于非球面测量的影响程度,确定了对测量精度影响最为严重的几种误差敏感因素;提出了针对上述敏感误差的一系列补偿方法,并计算了这些敏感因素在补偿后可以获得的测量不确定度;研究了敏感因素测量不确定度的传播,并在MATLAB中编写了用于计算系统不确定度传播的程序;最后通过蒙特卡洛仿真验证了该误差模型的正确性。3.大口径非球面的测量数据处理方法。应用了“同心扫描法”的方式来实现目标非球面的三维测量;提出了以空间柱坐标系来统一所有二维测量结果的数据处理方法,进而实现目标曲面由二维测量向三维测量的拓展;提出了通过LOESS非参数回归的算法来处理测量数据点云的数据处理方法;经多次蒙特卡洛仿真验证,本文所提出的测量数据处理方法稳定可靠,非球面面型RMS检测精度可达到λ/60(约10nm,λ=632.8nm),满足精度要求。更多还原

【Abstract】 An aspheric lens is a very important optical component, which is widely used in aerospace, aviation, shipbuilding, medical and other fields. Compared with the spherical lenses, an aspheric lens has various curvature radius, which means the aspheric surface is more flexible and has more application advantages. For example, the aspheric surface can simplify the structure of the optical system, reduce the weight of a system, and improve the resolution of a system as well as the image quality. However, the aspheric surface testing, particularly for the large surface, is always a big challenge in the field of optical measurement. For the small surface which has small asphericity, the interferometry measurement can help achieve the ideal measurement precision. However, the large or the super large aspheric surface cannot be measured by a general interferometer easily, and may be scratched by the contact measurement.Aiming to solve the measurement problem of a large aspheric surface, this paper has designed a kind of high-precision measurement system of large aspheric surface based on angle scanning. The basic principle of angle scanning measurement is to derive the variation of target surface curvature by measuring the variation of measurement position’s angle, and then to plot the target surface profile through numerical integration of the curvature values.The following research has been carried out in this paper.1. The structure design of large aspheric surface measurement system. The three-dimension measuring method for large aspheric surface whose aperture is below 200 mm is proposed and the structure design of large aspheric surface measurement system is completed. The types of hardware are determined after calculating the precision requirements of measurement system are obtained and then the 3-D CAD drawings of the aspheric surface measurement system are accomplished. The main process of aspheric surface measurement is analyzed and the measurement steps are formulated.2. Error analysis and compensation methods of large aspheric surface measurement. Different kinds of errors factors, including the random errors and system errors, in the measurement system are analyzed. The sensitive error factors which impact the accuracy of measurement seriously are analyzed through calculating their influence on aspheric surface measuring. A series of error compensation methods for sensitive errors are proposed, and then the measurement uncertainty of these factors after compensation is calculated. The propagation of measurement uncertainty of the sensitive factors is analyzed and the codes which are used to calculate the propagation of measurement uncertainty are written with MATLAB. Then the correctness of error model is verified by Monte Carlo Simulation.3. The method of measurement data processing for large aspheric surface. The 3-D measurement method which is achieved by the radial angle scanning for target surface is applied. A data processing method is proposed to unify all the 2-D measurement results by establishing a cylindrical coordinate, the 2-D measurement is expanded to 3-D measurement. Based on the “LOESS” algorithm, a type of non-parametric regression, a data processing method of analyzing the spatial points cloud is proposed. The reliability of the method for processing measurement results can be verified reliable after 50 times of the Monte Carlo Simulation and the RMS measurement precision of large aspheric surface achieves /60(about 10 nm, = 632.8nm), which meets the precision requirement perfectly.更多还原