针对两个物体或平面的相对位移和间隙的纳米级变化量,提出并研究了一种光栅测量方法。采用两组周期接近的微光栅重叠可以产生一组周期分布的条纹,条纹的周期相对于两光栅周期被大幅度放大,并将光栅间的位移反应在条纹的相位信息中。建立了关于双光栅产生叠栅条纹的复振幅分布的近似理论模型。基于该模型设计了一种能够测量两个平行平面相对位移和间隙的方法。针对光栅移动产生相应条纹的过程进行了数值计算。结果表明,两个平行平面的相对微位移将引起相应条纹的大位移,并且该方法最终能在纳米级以内分辨两平面(物体)的相对位移或者间隙变化量。

In order to measure the variation of displacement or gap of two parallel planes in nanometer level, a grating-based metrology was brought forward and researched. Two superposed micro-gratings with slightly different periods were adopted to generate a set of periodic moiré fringes, the period of which was hugely magnified with regard to that of two gratings. And the relative displacement of gratings was encoded in the phase of fringes. Firstly, an approximate theoretical model about distribution of complex amplitude of fringes of two gratings was built. Then, a method of measuring in-plane displacement and gap of two parallel planes was designed on the basis of this model. Finally, numerical computation about the process of movement of two gratings to generate corresponding fringes was performed. The results show that a small relative displacement of two gratings leads to a large displacement of corresponding fringes and this method can resolve the variation of displacement or gap of two parallel planes within nanometer.