Characterization of micro-scale surface features using partial differential equations
Characterization of micro-scale surface features using partial differential equations
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使用偏微分方程表征微观表面特征
DOI：
10.1117/12.847757
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发表时间：
2010
期刊：
影响因子：
--
通讯作者：
González Castro G
中科院分区：
文献类型：
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作者：
González Castro G
具有微米和纳米尺度表面特征的组件的大规模生产被称为微成型，并且对许多变量非常敏感，这些变量可能导致组件表面几何形状的重要变化。表面本身被认为是决定产品功能的关键因素，因此必须经过全面的质量控制程序。为此，已经采用了许多表面测量技术，即，白色光干涉测量法（WLI）和原子力显微镜（AMF），其产生的数据以大的且相当难以管理的笛卡尔点云的形式给出。这项工作使用偏微分方程（PDE）作为手段，有效地表征与这些数据集相关的表面。这是通过求解受一组边界条件约束的双调和方程来实现的，该边界条件描述了从原始测量数据中提取的外表面轮廓。设计参数表示为与双调和方程的解析解相关的系数的函数，然后与描述理想表面轮廓的设计参数进行比较。因此，这里提出的技术提供了使用压缩数据集进行质量评估的手段。
Mass production of components with micro and nano scale surface features is known as micromoulding and is very sensitive to a number of variables that can cause important changes in the surface geometry of the components. The surface itself is regarded as a key element in determining the product's functionality and as such must be subject to thorough quality control procedures. To that end, a number of surface measurement techniques have been employed namely, White Light Interferometry (WLI) and Atomic Force Microscopy (AMF), whose resulting data is given in the form of large and rather unmanageable Cartesian point clouds. This work uses Partial Differential Equations (PDEs) as means for characterizing efficiently the surfaces associated with these data sets. This is carried out by solving the Biharmonic equation subject to a set of boundary conditions describing outer surface contours extracted from the raw measurement data. Design parameters are expressed as a function of the coefficients associated with the analytic solution of the Biharmonic equation and are then compared against the design parameters describing an ideal surface profile. Thus, the technique proposed here offers means for quality assessment using compressed data sets.