Off-axis Fresnel numbers in laser systems

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.