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.