Study on interferometry for high-precision optical surface flatness test

高精度平面光学元件是现代光学系统和高精密仪器中的重要组成部分，其面形质量的优劣直接关系到光学仪器的性能表现。干涉测量技术具有快速、非接触、可全场测量、高灵敏度和高精度等特点，在现代精密测量领域中获得了广泛应用。论文针对高精度光学平面面形干涉测量技术，围绕高精度单幅干涉图相位提取技术、平面绝对检验技术以及高反射率面形高精度检测开展研究。 全面分析了二维傅里叶变换(FFT)干涉图相位提取技术的边缘误差，窗函数与滤波器设计，干涉图延拓，载波条纹数等关键技术环节对相位提取精度的影响，完成了一套基于二维FFT的高精度相位提取算法程序，与Zygo相移法比对，实测干涉图相位提取误差可小于λ/300 RMS。二维FFT干涉图相位提取中，边缘0.05R环形区域的相位提取误差最大，且决定了全局误差的大小。窗函数能小幅减小边缘误差，优化滤波器设计对边缘误差有一定改善。干涉图延拓能有效减小边缘误差，对于光学平面检测而言是提高二维FFT法相位提取精度的最佳方法。干涉图载波频率为干涉图空间分辨率的1/13~1/3时均能得到较准确的测量结果，相位提取误差PV值可优于λ/20；载波频率越高，细节分辨能力越强。 开展了平面面形干涉绝对检验方法与实验研究。对现有典型平面面形绝对检验技术进行了总结，针对旋转偏心误差设计了一种旋转中心定位夹具，并完成了奇偶函数法绝对检验技术的实验验证。该旋转中心定位夹具采用可拆卸的十字叉丝，具有结构简单、操作方便、成本低的特点，能有效控制旋转偏心误差，提高测量精度。以奇偶函数法绝对检验6次测量步骤为例，给出了具体的旋转中心定位方法。利用奇偶函数法绝对检验技术对三块标称值为λ/20 PV的标准镜面形进行了实验测量，获得了三个平面的绝对面形，面形结果PV值与标称值相符。 提出了一种新的基于绝对检验的高反射率面形高精度检测方法，可实现12%反射率以上平面面形的高精度检测。对高反射面形测量过程中的干涉对比度、干涉条纹偏离正弦分布、相位提取误差进行了数值仿真分析。针对了现有Clapham-Dew镀膜法高反射率面形检测很难实现λ/20以上检测精度的问题，提出在标准参考镜和被测高反镜之间加入一块透过率为30%~36%的衰减片，并采用12%反射率被测镜对系统误差进行二维标定的方法，实现高反射率平面面形的绝对检验。实验结果表明该方法能改善干涉对比度和提高测量精度，是一种有效的高反射率面形的高精度检测解决方法。High-precision optical surface is the very important element of modern optical systems and high-precision instruments. The performance of optical instruments is decided by flatness of the surface. Optical interferometry, with the merits of fast, non-contact, whole-field measurement, high sensitivity and high accuracy, has a wide application in modern precision measurement area. Focusing on high-precision optical surface flatness test, high accurate phase retrieval technique based on single interferogram, absolute flatness test technique and high-reflectance surface flatness test with high accuracy are studied in this dissertation. The factors which impact phase retrieval accuracy of FFT method including edge errors, window function, filter design, interferogram extrapolation and the number of carrier fringes are analyzed comprehensively. A set of algorithm based on 2DFFT is completed. Compared with phase shift measurement results by Zygo interferometer, the phase retrieval error of actual interferogram using 2DFFT method is less than λ/300(RMS). It is found that for 2DFFT method, the edge 0.05R circular area of the interferogram has the biggest phase retrieval errors and decides the value of global errors. Window functions can make a small reduction for edge errors. Optimization of filter design can improve edge errors in some degree. Interferogram extrapolation can reduce edge errors effectively and is the best way to enhance phase retrieval accuracy for continuous optical surface test. Accurate measurement results can be achieved when the frequency is 1/13~1/3 of the space resolution of the interferogram with PV values of phase retrieval errors less than λ/20. The higher the carrier frequency is, the better the detail resolution is. The absolute flatness test method and experiment are studied. A brief review and comparison of several typical absolute flatness test methods are given first. A gripper used to fix rotation center is designed for the problem of rotation eccentricity and odd-even function absolute test method is verified by experiment. The gripper contain a crosshair can control rotation eccentricity effectively and enhance measurement accuracy with the merits of simply structure, easy operation and low cost. The detail method about how to fix rotation center is given out for the 6 measurement steps of odd-even function method. Also the surfaces of 3 standard flats with nominal λ/20(PV) are tested by odd-even function method. The PV values of test results are matched with the nominal. A new method with high accuracy based on absolute test for high-reflectance surface flatness test is proposed, especially for reflectance of test surface higher than 12%. The inference contrast, intensity distribution deviation from sinusoidal and phase retrieval error during high-reflectance surface flatness test are analyzed by numerical simulation. Since Clapham-Dew method is difficult to reach the accuracy higher than λ/20, the new method is proposed by insulting a filter between reference and test surface with the transmissivity from 0.30 to 0.36. Absolute flatness of high-reflectance surface can be acquired with system error calibration using a 12% reflectance flat. The experiments results show that the method can improve interference contrast and enhance measurement accuracy and is an effective solution for high-reflectance surface flatness test