本文以余弦光栅为模型，运用波前相因子分析方法，得到了有一定距离的双余弦光栅衍射斑的强度公式. 推导出了双光栅之一作纵向或横向微谐振动时，远场衍射光斑强度的变化公式. 这些公式呈现出复合余弦函数的变化规律，并且分析出了光强随时间的变化与光栅振幅之间的关系. 为微小振动的测量提供了一种新的方法. 最后，文章给出了衍射斑强度变化信号的数值计算结果.

Based on cosine-style grating，the interference of diffraction by a double grating is studied theoretically with a wavefront phase-factors method. The patterns of Fraunhofer diffraction are shown by some formulas. Intensities’changing of each order diffraction is deduced as one grating translates along another horizontally and vertically. The intensities’changing figures are also shown by numerical simulation. These formulas form a foundation for experimental applications. One of these obvious applications is to measure the amplitude and the frequency of a harmonic micro-vibrating.