Non-paraxial Approximation of Scalar Diffraction Theory and Its Validity
标量衍射理论的非傍轴近似及其有效性

It is well known that the paraxial approximation is no longer valid for the beams with large divergence angle and small spot size comparable with the wavelength. Thus, a rigorous non-paraxial treatment becomes necessary. In this paper, based on the scalar Rayleigh-Sommerfeld diffraction formula, the non-paraxial approximation solution and its validity are studied. Detailed numerical calculations for the exact solution, non-paraxial approximation solution and Fresnel approximation solution of circular aperture diffraction are performed and compared; It is shown that the non-paraxial approximation solution is rigorous and valid for the diffraction of a small aperture.