【作者】 李国旗；

【导师】 陈新度； 欧阳渺安；

【作者基本信息】 广东工业大学 ， 机械电子工程， 2007， 硕士

【摘要】 随着非球面光学元件的设计和加工技术的发展，对非球面光学元件的面形及其参数的检测提出了更高的要求。在己有高精度检测仪器的条件下，一方面要研究适合具体工件类型的新的检测方法，扩展仪器的检测范围以充分发挥检测仪器的功能；另一方面要尽可能分析并降低检测仪器的误差，以提高检测的精度。本文针对加工镜面模具形状误差小于100nm，表面粗糙度小于5nm的纳米级加工精度的检测开展研究。以非球面镜加工和检测为研究对象，在自行开发出的小型超精密加工机床SGT100硬件基础上，建立并实现了非球面光学元件在线检测系统。本文主要研究内容如下：1)对国内外超精密加工、检测方法的概况进行分析与研究，对常用的非球面检测方法进行了叙述，对“supperMM-n”型小型非球面轮廓测量仪的系统原理、硬件结构以及关键检测元器件的结构、性能参数及原理等进行了叙述。2)要实现高精度在线检测，检测误差模型的建立和误差参数的辨识是关键，本文分析研究了非球面轮廓仪在检测使用中的各种误差因素及校正方法，针对测量系统中存在的主要系统误差“定位误差与坐标系不重合误差”，建立了其包含测量误差的逆向求解数学模型。3)数据处理与误差分析技术的研究。运用数字滤波技术和数理统计方法对采集的数据进行预处理；根据轮廓仪检测结果中包含测量误差的数据，提出采用基于最小二乘法的Levenberg-marquardt和DFP变尺度优化迭代方法来对误差参数进行拟合求解。之后通过坐标变化得到真实测量数据值，并与理论数据进行代数运算，得到加工误差大小与PV(Peek-valley)值。该方法也可对未知的非球面方程的进行光学参数拟合，具有很好的通用性。4)在非球面加工、检测以及误差分析的理论基础上，开发了非球面镜超精密测量与误差分析系统。文中对系统的结构、功能、数据流进行了分析；对系统各模块的设计原理、算法原理、算法策略、算法实现都进行了深入的研究；对系统的使用和操作，做了简单的介绍。5)最后通过对一组实测数据的分析与计算来验证系统数据处理与误差分析算法的可靠性。结果证明该系统的算法有效、收敛速度快、精度高。为非球面的补偿工或进一步检测提供了参考，达到了预期的设计目标。更多还原

【Abstract】 With the greatly development of the design and fabrication , it is required more high-accuracy measurement about aspheric Lens with precising measurement instrument, on one hand, should research new testing method to extend the instrument testing range ; On the other hand , should analyze and decrease the measuring errors to enhance accuracyThe paper focuses on the measurement and analysi system of aspheric optics with nano manufacturing precision which the form error under 100 nm and the surface smoothness under 5nm The main researches are shown as follow:1. By analyzing the aspheric lens machining and measuring level at present, we established the machining measuring system of the aspheric lens on the small ultra-precision machining tools SGT100 hardware foundation. First, The paper made an elaboration to the hardware structure, the principle of minitype aspheric profilometer on machining measuring, made a study on the reason of cause error and the correction error method when measuring.2. In order to achieve ultra-precision testing, it is important to establish the measuring error mathematic model and distinguish of error parameter. Aim at the primary system error"Possition error and fringe Error" in the testing system, we established the inverse solution mathematic model. In order to obtain the optical parameter value and error parameter, the paper adopt the Lenverberg-marqurdt and the DFP Multi- dimensional variable scale method united the non-linear least squares method make the measured data curve fitting.3.Based on the theory above, we designed and achieved Ultra-precision Aspheric Lens’s measurement and Error analysis system and made a detailed expatiate on design ideology,the principle of algorithm,the strategy of algorithm, the realization of algorithm and also make an introduce to the use of system. At last, the paper developed the software on the VC++ platform.4. By introducing a calculation example to evaluate the reliablity of the system , obtain the surface shape’s error PV value and draw the figure error curve of aspheric lens,the paper made an brief introduction about the system working flow and the Algorithm flow of the measuring data processing . The finally result proved that the error analysis algorithm has a quickly convergence speed, stability and satisfy the request of precision of ultra-precision processing.1更多还原