标量衍射理论的非傍轴近似及其有效性

当光束束腰（或衍射孔孔径）可与波长相比拟或光束具有较大的发散角时，傍轴近似不再成立.在标量瑞利.索末菲衍射积分的基础上，进一步研究了衍射场的非傍轴近似解，并详细分析了解的有效性.以平面波圆孔衍射为例，对衍射场的精确解、非傍轴近似解以及菲涅耳近似解进行了详细的数值计算和比较研究.结果表明，非傍轴近似对微小孔衍射非常精确、有效.

Non-paraxial Approximation of Scalar Diffraction Theory and Its Validity

It is well known that the paraxial approximation is no longer valid for the beams with large divergence angle and small spot size comparable with the wavelength.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.