Modelling of coherence scanning interferometry for complex surfaces based on a boundary element method
Modelling of coherence scanning interferometry for complex surfaces based on a boundary element method
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DOI：
10.1117/12.2526015
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发表时间：
2019-06
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影响因子：
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通讯作者：
Matthew Thomas;Rong Su;N. Nikolaev;J. Coupland;R. Leach
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文献类型：
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作者：
Matthew Thomas;Rong Su;N. Nikolaev;J. Coupland;R. Leach
相干扫描干涉测量(CSI)是一种基于干涉条纹的相干包络和相位测量表面形貌的成熟技术。最常用的表面重建方法，即频域分析、包络检测法和相关图相关法，通过假设两者成正比，获得每个像素的测量场的相位，并由此获得表面高度。对于与平面有微小偏差的表面，很容易证明散射场的相位是表面高度的线性函数。另一种称为“箔模型”的方法更一般地给出了散射场，这是对表面的“箔”表示进行线性过滤处理的结果。该模型假定表面在光学尺度上缓慢变化，并且不存在多次散射。然而，对于在光学尺度上粗糙或具有相干特征(如Ve型凹槽)的表面，多次散射的影响是不可忽略的，并且仍然是重建方法的一个问题。线性重建方法不能为复杂曲面提供精确的表面形貌，因为对于这类曲面，CSI的测量过程从根本上是非线性的。为了开发一种先进的CSI重建方法，需要一个准确的成像过程模型。本文采用边界元方法作为一种严格的散射模型来计算远处边界上的散射场。然后，将成像视为散射场的反向传播，结合反射参考场，计算出CSI信号。通过这种方法，几乎可以对任意表面几何形状的CSI系统的光学响应进行严格的预测。未来的工作将包括对该模型进行全面的实验验证，以及开发非线性曲面重建算法。
Coherence scanning interferometry (CSI) is a well-established technique for measuring surface topography based on the coherence envelope and phase of interference fringes. The most commonly used surface reconstruction methods, i.e. frequency domain analysis, the envelope detection method, and the correlogram correlation method, obtain the phase of the measured field for each pixel and, from this obtain the surface height, by assuming the two are directly proportional. For surfaces with minor deviations from a plane, it is straightforward to show that the scattered field’s phase is a linear function of surface height. An alternative approach known as the “foil model” gives more generally the scattered field as the result of a linear filtering process operating on a “foil” representation of the surface. This model assumes that the surface slowly varies on the optical scale and that there is no multiple scattering. However, for surfaces that are rough at the optical scale or have coherent features (e.g. vee-grooves), the effect of multiple scattering cannot be neglected and remains a problem for reconstruction methods. Linear reconstruction methods cannot provide accurate surface topographies for complex surfaces, since for such surfaces, the measurement process of CSI is fundamentally non-linear. To develop an advanced reconstruction method for CSI, an accurate model of the imaging process is required. In this paper, a boundary elements method is used as a rigorous scattering model to calculate the scattered field at a distant boundary. Then, the CSI signal is calculated by considering the image formation as back-propagation of the scattered field, combined with the reflected reference field. Through this approach, the optical response of a CSI system can be predicted rigorously for almost any arbitrary surface geometry. Future work will include a comprehensive experimental verification of this model, and development of the non-linear surface reconstruction algorithm.