广义B样条滤波器在表面形貌测量中的应用  

Application of generalized B spline filter to surface profile measurement

作　　者：张浩[1] 袁怡宝[1] 张峰[1] 许景波[2] 

机构地区：[1]哈尔滨工业大学电气与自动化学院,黑龙江哈尔滨150001 [2]哈尔滨理工大学测量与通信工程学院,黑龙江哈尔滨150040

出　　处：《光学精密工程》2008年第9期1722-1726,共5页Optics and Precision Engineering

基　　金：教育部留学回国人员科研基金资助项目(No.AEBQ24403704)

摘　　要：为了提取工件表面轮廓中线,给出了一种基于三阶广义B样条函数的数字光滑滤波器。由线性微分方程推导出广义B样条函数,并结合广义B样条函数和变分公式推导出由一IIR滤波器和间接广义B样条变换组成的数字平滑滤波器。给出了数字平滑滤波器的具体递归算法,并且证明了该滤波器的通用特性。最后,提取了实际工件表面中线。实验结果表明:该滤波器的截止特性比高斯滤波器的好,该算法利用普通计算机提取11 200点数据表面中线仅耗时0.002 s。提出的滤波器具有可调平滑性,零相移特性,克服了传统三阶样条插值的曲率低和振荡等缺陷,其递归滤波器的具体算法简洁,效率高。For acquiring the mean line of workpiece profile, a new kind of digital smoothing filter based on cubic generalized spline function was proposed. The generalized B spline functions were derived from the linear differential equation,and the digital smoothing filter consisting of a IIR filter and indirect generalized B spline transformation was deduced by combination with generalized B spline functions and variational principles. Then,the recursive algorithm of the filter was presented concretely, and the filter＇s universal property was testified. Finally, this filter process was applied to a workpiece to acquire mean line. The experimental results indicate that the filter has a better cut-off property than that of Gauss filter, and total calculation only requires 0.002 s for 11 200 data points by PC. The filter has advantages in adjustable smoothing property and zero phase transmission, which can overcome the drawbacks of low curvature and serious oscillations of traditional cubic spline interpolation. The recursive algorithm is efficient and simple.

关 键 词：广义B样条函数 光滑样条滤波器 形貌测量 

分 类 号：TN713.4[电子电信—电路与系统] TB92[一般工业技术—计量学]