Phase measuring deflectometry is a highly precise and full field metrology technique for specular surfaces based on the distortion of known reference patterns observed as a reflection at the surface under test. Typically, liquid crystal displays are employed to provide the required patterns. Due to a lack of research, these displays are used without sufficient calibration. In this work, we present an enhanced calibration for phase measuring deflectometry, taking flatness deviations of the display surface into account. The display shape is modelled as a polynomial surface whose coefficients are determined by minimizing the retrace error in a global optimization procedure during calibration. This approach does not require any additional measurements or hardware. Improvements due to the enhanced calibration model are qualified experimentally using a flat and a spherical concave mirror. The model-based parameterization of the display surface yields significant improvement on both samples. The peak to valley (PV) of measured deviations on the plane mirror are reduced by 67% to 0.55 μm. Measuring the spherical sample without the display parameterization leads to a rather large shape deviation of 33.40 μm PV which is reduced by 94% to 1.98 μm. The viability of our approach confirms the dominant role of flatness deviations of the display surface as an error source in absolute shape measurement using phase measuring deflectometry.

中文翻译：

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通过显示形状的多项式表示来改善相位测量偏折法的校准

相位测量折光法是一种用于镜面的高精度和全场计量技术，它基于在测试表面反射的已知参考图案的畸变。通常，采用液晶显示器来提供所需的图案。由于缺乏研究，这些显示器在没有充分校准的情况下使用。在这项工作中，我们考虑到显示表面的平面度偏差，提出了一种改进的相位测量偏折法校准。显示形状被建模为多项式表面，其系数是通过在校准期间通过全局优化过程中的回扫误差最小化来确定的。这种方法不需要任何其他测量或硬件。由于使用了改进的校准模型，因此可以使用平面和球面凹面镜对改进进行实验验证。显示器表面的基于模型的参数化在两个样本上均产生了显着改善。在平面镜上测得的偏差的峰谷（PV）降低了67％，为0.55μm。在没有显示参数化的情况下测量球形样品会导致33.40μmPV的较大形状偏差，PV偏差降低了94％至1.98μm。我们方法的可行性证实了在使用相位测量偏折法进行绝对形状测量时，显示表面的平面度偏差是误差源的主要作用。在平面镜上测得的偏差的峰谷（PV）降低了67％，为0.55μm。在没有显示参数化的情况下测量球形样品会导致33.40μmPV的较大形状偏差，该偏差会降低94％至1.98μm。我们方法的可行性证实了在使用相位测量偏折法进行绝对形状测量时，显示表面的平面度偏差是误差源的主要作用。在平面镜上测得的偏差的峰谷（PV）降低了67％，为0.55μm。在没有显示参数化的情况下测量球形样品会导致33.40μmPV的较大形状偏差，PV偏差降低了94％至1.98μm。我们方法的可行性证实了在使用相位测量偏转法进行绝对形状测量时，显示表面的平面度偏差是误差源的主要作用。