导出了复杂光学系统中任一观察面对入射面光阑的菲涅耳数表达式N=(a2/λ)[(A/B) + (1/R)].它是用光学系统的光线矩阵元表示的,具有较大的普遍性.引入了有效传输距离的概念:L(eff)=B/A,它反映了光学系统对衍射场的影响.对一些常见的典型光学系统给出了菲涅耳数的具体表达式.对高功率激光系统中真空空间滤波器的像传递作用给出了理论证明,并导出完善像传递的必要条件.最后,把菲涅耳数推广到复数域,并用于研究截断高斯光束的衍射问题.

The number of Fresnel half-period zones for complex optical systems is derived. It s formula is N=(a2/λ) [(A/B) + (1/R)] . Since it is expressed by the ray matrix elements, there is a universal significance. We have introduced a concept of "effective propagation path" Leff=B/A, which reflects the influence of optical system on the diffraction field. For several typical systems the concrete expressions of the Fresnel number are given. The imaging properties of the vacumm spatial filter are indicated using the ray matrix theory. The perfect image-relaying conditions are determined. Finally we extend the Fresnel number to the region of complex number, and use it to investigate the diffraction problem of a truncated Gaussian beam.