傅氏级数和多项式结合的图像灰度建模及位移测量

利用图像传感器的成像灰度实现位移测量，需要在位移过程中用相机对靶标进行成像，进而建立位移值与成像灰度值之间的映射关系，即成像灰度模型，该方法的测量精度取决于成像灰度模型与灰度噪声水平。实际测量过程中，光照不均匀、靶标制造误差、相机成像系统畸变等外部误差源以及内部不同图像传感器单元之间成像特性的差异性均会使成像灰度模型偏离理想情况，从而影响测量结果。为了进一步提高测量精度，所提方法考虑了上述的非线性因素带来的建模误差，采用Fourier级数与高阶多项式结合构造成像灰度模型类，提高模型的泛化逼近能力进而提高建模精度，校正上述误差源导致的灰度畸变。在此基础上，采用基于位移连续性原理的顺序求解法解算位移，实验结果显示，使用该改进模型在10.46 mm行程下的位移测量误差标准差由校正前的56.4 μm降低至1.5 μm。

Image gray-scale modeling and displacement measurement based on the combination of Fourier series and polynomial

To achieve displacement measurement using the imaging grayscale of the image sensor, it is necessary to use the camera to image the target during the displacement process, and then establish the mapping relationship between the displacement value and the imaging grayscale value, i.e., the imaging grayscale model, and the measurement accuracy of this method depends on the imaging grayscale model and the grayscale noise level. In the actual measurement process, external error sources such as uneven illumination, target manufacturing errors, aberrations of the camera imaging system, and the variability of imaging characteristics between different internal image sensor units can cause the imaging grayscale model to deviate from the ideal situation, thus affecting the measurement results. To further improve the measurement accuracy, the modeling error caused by the aforementioned nonlinearities are taken into account, and a class of imaging grayscale models combining Fourier series and higher-order polynomials is proposed to improve the generalization approximation ability of the models and thus the modeling accuracy, correcting the grayscale distortion caused by the aforementioned error sources. On this basis, the displacement is solved by the sequential solution method based on the displacement continuity principle, and the experimental results show that the standard deviation of the displacement measurement error under the 10.46 mm stroke using this improved model is reduced from 56.4 μm before correction to 1.5 μm.