计量光栅空间位姿参数光场输出模型与仿真

Output Model and Simulation for Optical Field with Metrological Grating Space Pose Parameters

光栅安装或应用过程中光栅传感器指示光栅、标尺光栅相互位置发生改变,导致莫尔条纹发生畸变,直接影响着测量精度和后续处理系统的复杂程度。本文采用傅里叶频谱分析方法,建立包含指示光栅、标尺光栅位置姿态参数的光场输出模型,给出了两栅不平行时输出光场的数学表达式,对主要影响因子进行了较详细的分析,并在Matlab中进行了仿真,给出了不同安装偏角下的莫尔条纹误差值及变化趋势,讨论了接收传感器的结构尺寸对测量结果的影响,得出了与莫尔条纹同尺度的接收系统有最小的测量误差,其结果对光栅副的精度设计和结构设计有较好的指导性。

Metrological gratings are now widely used in such fields as precision measurement,numerical control machine and so on.The mutual position change between instruction grating and scale grating of the sensor during grating installation or application procedure will result in the distortion of Moiré fringe,which directly influence the measurement accuracy and complexity degree for following process system.In this paper,Fourier spectrum analysis method was applied to build the optical field output model involving instruction grating and scale grating pose parameters,to introduce the mathematic formulas for output optical field with the two gratings unparallel mutually and to detailedly analyze the main influencing factors,all of which are simulated in Matlab.Moreover,this paper gave Moiré fringe error values and their variation trend for different assembling offset angles,discussed measuring results affected by configuration dimension of receiving sensor and obtained that the receiving system with its dimension the same as Moiré fringe had the minimum measuring error.The results are of great guiding for accuracy and configuration design of grating couples.