球面波照射下夫朗和费衍射公式和成立条件的修正

Modification of the Formulae and the Tenable Conditions of Fraunhofer Diffraction Under Spherical Wave Illumination

本文认为文献[1]～[7]对球面波照明下的夫朗和费衍射的若干近似处理方法不是十分妥当的。并从标量衍射理论的瑞利-索末菲公式出发,导出了描述通过照明波会聚或发散中心并与衍射屏平行的观察面所接受到的衍射花样的夫朗和费衍射公式,且详细讨论了其成立条件。指出当衍射距离满足远场条件时,公式在源点或场点或两者均非傍轴的情况下亦成立;当衍射距离zo较近时,公式仅在源点(可处于非傍轴位置)附近的小区域成立,但距离越远,成立的范围越大。在场点、源点均傍轴的特殊情况下,此公式可退化为文献[1][6][7]的结果。

It is pointed out that the methods of the approximate treatment of the Fraunhofer diffraction under spherical wave illumination in literatures [1-7] are not very proper. The Fraunhofer diffraction formulae, which describe the diffraction pattern received by an observing screen that is located at the convergence or divergence center of an illuminating spherical wave and is parallel with the diffracting screen, are deduced from the Rayleigh-Sommerfeld formula of the scalar diffraction theory. The scope of application of the formulae is discussed in detail. On the condition that the diffracting distance satisfies the far-field condition, it is pointed out that the formulae are tenable even if either the center of the lighting spherical wave or the observing point, or both, are located in the non-paraxial region. When the diffracting distance is nearer, the formulae are only tenable in the nearby region of the center of the illuminating spherical wave, but the center may be in the non-paraxial region. However, the further the diffracting distance is, the bigger the tenable region is. The formulae may be reduced to the results presented in literatures [1], [6] and [7] in the particular case that the illuminating source and the observing point are all close to the axes.