圆形余弦光栅菲涅耳衍射场的研究

Study on Fresnel diffraction fields by a circular cosine-grating

基于波前相因子判断法并考虑到圆光栅孔径的影响,揭示了圆形余弦光栅的衍射场含有3种成分,它们是均受限于圆形孔径的平面衍射波、发散球面衍射波和会聚球面衍射波;分别给出了这3种衍射场的积分表达式,进而导出了沿轴的衍射场复振幅分布的3个公式,并显示了相应的沿轴衍射场实振幅分布曲线,得到了实焦斑的横向半值线宽和轴向半值线宽公式.本研究为圆形余弦光栅用于聚焦和成像技术进一步提供了一个理论基础.

Based on the method of wavefront phase- factors and considering of the influence of limited aperture of grating, we analyze the diffraction fields by a circular cosine-grating which contain three components, i. e. , the plane diffraction wave, the divergence spherical diffraction wave and the convergence spherical diffraction wave, they are all limited by the circular aperture. The corresponding three integral expressions of the diffraction fields are given. Three formulae of the amplitude distribution of diffraction fields along axis are obtained and corresponding a series of curves are shown. Finally the transverse line-width and the axial line-width of that real focal-spot are obtained. This study may further provide a theoretical foundation to analyze the technique of the diffraction focalization and image formation by a circular cosine-grating.