Ronchi光栅误差的数值仿真

为了解决光栅制造误差影响莫尔计量精度的问题,运用傅里叶光学理论和坐标变换方法给出了完整的莫尔条纹透光函数表达式,并用线性系统叠加理论对光栅误差函数进行模拟,再用得到的莫尔条纹模型对光栅误差进行仿真,获得了短周期误差和长周期误差的莫尔条纹波形,最后对误差仿真结果进行了分析和验证.结果表明,光栅短周期误差造成莫尔条纹信号波形出现高次谐波干扰,但数字滤波能有效消除其对计量精度的影响,而光栅长周期误差会严重影响光栅检测系统输出精度.

Error simulation of Ronchi gratings

In order to study the effect of grating manufacturing error on the accuracy of Moiré metrology, a transmittance function for Moiré fringes was built based on Fourier optical theory and coordinate conversion. The grating error function was simulated by means of linear superimposition. The grating errors were simulated based on previously received moiré fringe models. The Moiré fringe waveform caused by the short-period errors and long-period errors were obtained. Simulation results were analyzed and verified. Although short-period grating error induces high-order harmonics of Moiré fringe signal, its effect on measurement accuracy can be effectively removed after digital filtering. The long-period grating error can affect the accuracy of a grating test system.