短相干光显微干涉理论及摆臂式轮廓仪的非接触测量方法研究

In astronomical telescope manufacturing, it is always difficult to measure asphere, especially convex asphere profile, which has greatly limited their application and develoment. Swing arm profilometry is thought as an effective method to solve the problem. However, contact probe in traditional swing arm profilometer may possibly damage aspheric surface and introduce measurement error because of its tip size. Without losing any measuring abilities in traditional swing arm profilometry, non-contact probe based on low-coherence interferometry is proposed in this project. Contact probe is substituted with light point and measuring accurcy is hence increased because of the high positioning ability of optical interferometry. Aspheric surface form in each fabrication period including figuring, fine grinding and polishing can be measured. The interferometric model with low coherence microscopy will be established and different interferograms will be analyzed in temporal, spatial and spectral, in order to obtain profile of the asphere under test. Theoretical relationship among local slope of asphere, fringe carrier and zero optical path difference will be derived to build asphere profile retrieving algorithm for swing arm non-contact profilometer. The influence of vibration on non-contact profiling will be analyzed to recover the relationship between vibration frequency and profile retrieving error. Vibration compensating and suppressing algorithms will be studied to increase measuring accuracy. As a result, non-contact swing arm measurement of asphere profile will be realized.

在天文望远镜制造中，非球面尤其是凸非球面的面形检测成为限制其应用发展的技术瓶颈。摆臂轮廓仪是解决这一问题的有效手段，但其接触式测头可能造成非球面表面损伤，且测头直径会引入测量误差。本项目在保留传统摆臂轮廓仪测量通用性强的基础上，基于光干涉原理，研究非接触测量技术，用光点替代固体探头消除探头直径的影响，以短相干光精确定位提高探头的位移检测精度，实现非球面从粗磨、精磨到抛光各个加工阶段的面形测量。本项目建立短相干光显微干涉模型，研究短相干光时域、空域、频域干涉条纹处理方法，实现非球面轮廓的非接触定位；揭示非球面局部陡度变化、干涉条纹载频、条纹零位偏移之间的定量关系，建立基于短相干位移传感器的非球面轮廓恢复算法；分析振动对非接触摆臂轮廓仪的影响，建立振动误差与轮廓之间误差传递的定量关系，研究振动补偿及振动抑制算法，克服测量过程中环境振动的影响。构建非接触摆臂轮廓仪装置。

在天文望远镜制造中，大口径、高陡度的非球面尤其是凸非球面的面形检测成为限制其应用发展的技术瓶颈，摆臂轮廓仪是解决这一问题的有效手段。为避免传统摆臂轮廓仪接触式探头对非球面表面的损伤，采用非接触式光学探头进行测量。建立短相干光显微干涉模型，构建摆臂轮廓仪装置，分别研究了其非接触测量的时域、空域、谱域实现方案。.在摆臂轮廓仪非接触式测量的时域实现方案中，提出对移相误差及包络变化不敏感的宽带光八步移相算法。该算法通过定位宽带光干涉条纹的零相位差位置实现微观轮廓的测量。计算宽带光移相干涉信号中相邻采样点的相位差得到实际移相间隔，从而实现实际移相量的在线标定以及移相误差的校正。测量一SiC样品，计算结果的标准均方差为1.646 nm，与不存在移相误差时的计算结果吻合，表明宽带光八步移相算法能够抑制移相误差，对干涉包络的变化不敏感，是一种实用、高精度的表面轮廓测量方法；在摆臂轮廓仪非接触式测量的空域实现方案中，通过提取被测件截线上多个测量点处面形的曲率信息，结合测量点空间位置恢复面形。对于单个测量点，采用宽带光干涉显微镜测量出视场内面形信息，通过多项式拟合出中心点处的曲率值，在得到多个点的曲率值和空间位置信息情况下，采用二次积分法或者拟合法恢复被测件面形。实验测量一双曲面，测得的面形偏差PV=73.3nm，RMS=21.6nm，结果表明基于曲率测量恢复非球面面形的方法对环境振动引起的调整误差不敏感；在摆臂轮廓仪非接触式测量的谱域实现方案中，采用光谱仪作为探测器接收干涉条纹，将干涉条纹从空域转换至谱域进行分析。光谱仪记录相对光强随着波长变化情况，位移量的大小体现在谱域干涉条纹疏密的变化。采用傅里叶变换法处理单幅谱域干涉图，提取出初相位，对相位进行线性拟合即可提取位移量大小。测量一标称值为7.732μm的台阶，测量偏差为0.044μm。对于单点进行位移量测量，其传感精度优于0.02μm。相比于空域方案，谱域干涉法的测量范围大大提高，且无需轴向扫描，大大提高了测量效率。