波面PSD的干涉测试与计算软件研究

【作者】 宋德臣；

【导师】 高志山；

【作者基本信息】 南京理工大学 ， 光学工程， 2010， 硕士

【摘要】 传统的面形误差评价指标有峰谷值,均方根值,波面凹凸等,它们有着各自的特点和内在联系。大功率激光器件的出现,使中频面形误差评价受到广泛重视,而传统的评价指标应用在评价中频面形误差上都存在不足。本文研究了可用于中频面形误差评价的功率谱密度的定义和物理内涵、功率谱密度的数值计算方法、功率谱密度在评价中频面形误差时的应用、PSD有效频宽和干涉仪的标定。由傅立叶变换导出了一维和二维功率谱密度计算的公式,对积分式进行离散化,建立功率谱密度计算的离散数学模型。详细分析了PSD有效频宽与采样长度和采样宽度的关系。通过测量干涉仪的频率响应函数得到测量波面的绝对“真”值。编写了"PSD计算软件”：软件具有一定的通用性,可对任何采样数据序列进行PSD计算。软件采用了模块化设计,快速傅立叶算法和直观的人机界面,强大的Visual C++程序开发软件使程序具有良好的可移植性和功能拓展性。通过对两种不同样品的实验测量,测量结果与Zygo Metropro软件的计算结果进行对比,其计算结果表明PSD计算模型正确,窗口函数选择合适,可以接收工程化测量的考核。更多还原

【Abstract】 The traditional surface error evaluation methods includes peak to valley value method, root mean square method and wave surface bump method etc. They have their own characteristics and the intrinsic link between each other. Intermediate frequency surface error evaluation is more and more widely concerned due to the application of high-power lasers. Compared to the shortage in the traditional intermediate frequency surface error evaluation, power spectral density method is applied to the new evaluation.The definition and physical significance of power spectral density are mainly discussed in this paper, which can be applied to evaluate the intermediate frequency surface error. The corresponding numerical method is proposed to calculate the power spectral density. Besides, we have talked about the applications in the intermediate frequency evaluation, PSD effective bandwidth and the calibration of interferometer. The calculation of one-dimensional PSD and two-dimensional PSD can be derived from the classical Fourier transform. According to the discretization of integral, we can build the discrete PSD mathematical model. Then, the relation between the PSD effective bandwidth and the sampling width has been discussed in detail. At last, the absolute "true" value of the measured wavefront can be obtained by means of the measurement of interferometer’s frequency response.The software of power spectral density calculation is programmed in this paper, and this software has some commonality, with the function of any sampling sequence PSD calculation. It has modular design, fast Fourier transform algorithm and intuitive user interface. With the help of Visual C++ program, the software has good portability and functional development. At last, according to the contrast of two measurements and calculation results with the calculation result in Zygo Metropro software, we have verified the correctness of PSD calculation model and the appropriate selection of window function.更多还原