双级闪耀光栅位移精密测量的傅里叶分析

Fourier Analysis for Precision Displacement Measurement with a Doubly Blazed Reference Grating

采用傅里叶光学的理论对双级闪耀光栅位移测量原理进行了分析 ,导出了经光栅付衍射后光波的振幅和强度表达式 ,得出了位移测量公式 ,并指出形成的莫尔条纹为近乎理想的对比度极强的双光束干涉条纹 ,该结论与PostD的有关理论和实验结果完全一致。

In this paper, the fundamental principle of precision displacement measurement with a doubly blazed grating is analyzed in detail by means of Fourier Optics. The mathematical expressions about the amplitude and the intensity of diffracted light are derived, and the measurement formula is presented. At the same time it is indicated that moire fringes are nearly perfect two-beam interference fringes with superb contrast. These conclusions are consistent with the theoretical and experimental results given by Post D, and helpful to further development of the measurement principle.