基于区域定向上采样的白光干涉拟合算法  

White Light Interferometry Fitting Algorithm Based on Region⁃Directed Up⁃Sampling

作　　者：周辰 万新军[1] 韦晓孝 戴振秋 何晓冰 Zhou Chen;Wan Xinjun;Wei Xiaoxiao;Dai Zhenqiu;He Xiaobin(School of OpticalElectrical and Computer Engineering,University of Shanghai for Science and Technology,Shanghai 200093,China)

机构地区：[1]上海理工大学光电信息与计算机工程学院,上海200093

出　　处：《光学学报》2024年第20期94-102,共9页Acta Optica Sinica

基　　金：国家重点研发计划“基础科研条件与重大科学仪器设备研发”重点专项(2021YFF0700400)。

摘　　要：针对白光扫描干涉测量(SWLI)技术易受环境和扫描器件的非线性振动等影响,提出一种基于区域定向上采样的垂直扫描算法。首先,通过高精度光栅尺获得测量对象的实际扫描位置,然后对图像帧进行排序,利用重心法对相干峰进行粗略定位;然后,使用最小二乘法对干涉信号进行三角级数拟合,利用拟合函数的连续性特性,根据粗略定位确定定向采样范围并进行高密度上采样,计算上采样信号的峰值位置以获取精细的测量形貌。本研究通过数值仿真和实验对所提方法进行了验证,结果表明,所提方法有效降低了计算产生的波纹误差,具有较高的精度和较好的重复性。Objective White light scanning interferometry(SWLI),as a highprecision,noncontact measurement technique,is widely used in fiber optics,automotive industry,precision measurement,and manufacturing.SWLI can employ piezoelectric ceramics(PZT)or stepper motors for vertical scanning.Although PZT features extensive application due to its high precision,it requires expensive controllers to correct the hysteresis effects brought by the piezoelectric elements.Additionally,the range of PZT is typically limited to several tens of micrometers.In contrast,highprecision stepper motors used for axial scanning provide a broader range and reduce cost.However,the nonlinear stepping vibrations of stepper motors lead to greater displacement errors than PZT,resulting in significant random errors between the spacings of adjacent frames of interferometric images.This issue can cause obvious ripple errors or height jumps in morphology calculations,resulting in lower solution accuracy and challenges for SWLI in cost reduction and measurement in vibrating environments.The elimination of this problem will enhance the applicability and accuracy of SWLI technology,further advancing its development and application across various fields.Methods We improve and further investigate the fitting compensation techniques proposed by previous researchers.A stepper motor is used as the scanning component to support the objective lens in vertical displacement.A highprecision grating ruler is installed on the guide rail to directly read the displacements accurately and sort the signals.The sorted interference signals are then coarsely positioned at the center of the zeroorder fringe using the centroid method.Additionally,nonequidistantly sampled signals undergo trigonometric fitting using the Fourier series.By randomly sampling several coordinate points of the interference images,optimal angular frequency parameters are determined using a search algorithm,followed by matrix calculations and signal set fitting using the linear least squares method.Based on

关 键 词：测量 白光干涉 最小二乘估计 抗振测量 上采样 

分 类 号：O436[机械工程—光学工程]