中文摘要：

为了寻找一种适用于长程面形仪（Long Trace Profiler,LTP）测量数据的曲线拟合算法，提高同步辐射用光学反射镜表面几何参数拟合的准确性，并合理可靠地评价同步辐射用光学反射镜表面质量，本文对镜面曲率半径、测量环境噪声和镜面测量姿态这三个可能影响镜面几何参数拟合精度的因素进行了数值模拟，采用基于代数距离的最小二乘法、基于几何距离的最小二乘法和遗传算法对模拟面形进行了拟合对比。结果表明，基于几何距离的最小二乘法对以上三个因素均不敏感，最适合长程面形仪测量数据的拟合。该方法能够给上海同步辐射光源反射镜的面形检测提供一定的参考价值。

英文摘要：

Background： The Long Trace Profiler （LTP） has been widely used to measure the profile of optical mirrors used in synchrotron radiation applications. The Root Mean Square （RMS） of profile error from fitted profile is used to evaluate the quality of mirror. Purpose： This study aims to find a better fitting algorithm for measurement data of LTP and minimize system errors generated by fitting. Methods： Least square method （LSM） based on the algebraic distance, LSM based on geometric distance, and genetic algorithm have been compared for simulation profiles of the measured data of LTP with different radii, noise intensities and postures. Results： Simulation results showed that fitting algorithm of least-squares orthogonal geometric distances had a good noise robustness, and insensitiveness to the mirror＇s postures. Conclusion： Least-squares orthogonal distances is the most suitable curve fitting algorithm for LTP, it provides references for the profile testing of optical mirrors at SSRF.