基于Ronchi光栅的莫尔条纹函数建模

Modeling of Moiré Patterns Based on Ronchi Grating

莫尔条纹函数建模对于莫尔计量理论和应用研究都非常重要。分析了造成莫尔条纹函数建模复杂性的原因,运用傅立叶变换和图像旋转矩阵方法,给出了完整的Ronchi光栅干涉莫尔条纹透光函数,针对该函数为多值隐函数特性,通过二次拟合手段对原函数进行降次处理,得到了适合计算机模拟的莫尔条纹函数模型。用不同栅距和栅线交角的光栅对该模型做符合性检验,得到的拟合残差加权平方和小于1.8×10-5,表明并该函数模型与理论值吻合良好。

The function modeling of moire Patterns is very important to moire metrology. So, the reason for the complexity of this function modeling was analyzed. And through applying the Fourier Transform and Rotation matrix, the complete moire patterns function interfered by Ronchi grating was put forwards. To deal with this multi-value implicit function properly, the order reduction was adopted by two times fitting and the function modeling of moire patterns was got. Furthermore, a corresponding examination was made with the help of the main parameters of molte patterns, which shows the identity between the function modeling and the predicted value. The Sum of Squares Due to Error is smaller than 1.8×10^-5.