关于菲涅耳衍射图样相似性的分析与讨论

Analysis and discussion on the similarity of Fresnel diffraction patterns

与夫琅禾费衍射不同,菲涅耳衍射图样对于给定波长,当衍射距离变化或输入图像几何缩放时一般都不具有相似性.但我们的分析表明,若波长、衍射距离和输入图像几何线度诸参数满足一定关系,或对于某些特殊类型孔径,菲涅耳衍射图样有可能彼此相似.本文导出了在上述诸参数发生变化时菲涅耳衍射图样保持相似性的普适条件,以及此时衍射图样大小与诸参数的定量关系,并对包括圆孔衍射和直边衍射等情况都得到了一系列有价值的推论.

Different from Fraunhofer diffraction, Fresnel diffraction has been considered to have no the property of similarity. However, our study shown that Fresnel diffraction patterns also have similarity property under certain conditions. In this paper the general requirement for this property is given, and the relation between the scale of the Fresnel diffraction pattern and the parameters of the diffraction system is quantitatively derived. As an inferences, some special cases such as the circular aperture diffraction and straight-edge diffraction are discussed and a series of important conclusions are obtained.