The physical meaning and essence of Fresnel numbers are discussed,and two definitions of these numbers for offaxis optical systems are proposed.The universal Fresnel number is found to be N =(a2/λz) * C1+ C2.The Rayleigh–Sommerfeld nonparaxial diffraction formula states that a simple analytical formula for the nonparaxial intensity distribution after a circular aperture can be obtained.Theoretical derivations and numerical calculations reveal that the first correction factor C1 is equal to cos θ and the second factor C2 is a function of the incident wavefront and the shape of the diffractive aperture.Finally,some diffraction phenomena in off-axis optical systems are explained by the off-axis Fresnel number.
