利用泽尼克系数求取衍射光栅的分辨本领

Solving Resolution of Diffraction Gratings Using Coefficients of Zernike Polynomials

光栅分辨本领检测设备的焦距通常达几米甚至十几米,采用直接测量法难度大、成本高,利用衍射波前间接求取光栅分辨本领是解决该问题的有效途径之一。在光栅光谱成像傅里叶变换理论基础上,建立了利用泽尼克多项式拟合系数求解衍射光栅分辨本领的归一化模型,揭示了光栅衍射波前与分辨本领的求取关系,提出了依据泽尼克多项式拟合系数求取衍射光栅分辨本领的新方法。根据该方法实测了一块衍射光栅的分辨本领,并与直接测量法进行对比测试。结果表明该方法误差小于4.42%,降低了分辨本领的测试难度,是衍射光栅分辨本领求取的有效手段,应用于ZYGO干涉仪等仪器中,通过简单的波前测试即可得到定量的衍射光栅分辨本领指标。

It is hard and costly to test resolution directl y,because the focal length of testing equipment could be nearly ten meters.Sol ving resolution by diffraction wavefront aberration indirectly is an effective s olution to this problem.A normalization model of solving resolution using fitti ng coefficients of Zernike polynomials was established based on the spectral ima ging theory of Fourier optics.The relationship between resolution and wavefront aberration of diffraction gratings was illustrated by this model.Finally,a ne w method of testing resolution using fitting coefficients of Zernike polynomials was proposed.According to this method,the resolution of a grating is tested b y ZYGO interferometer indirectly.Compared with direct method,results indicate that the error of indirect method is less than 4.22%,and this method could be a n effective way to avoid the difficulty of direct method to solve resolution.Me anwhile,this method can be used in ZYGO interferometer to solve resolution by w avefront testing easily.