平面波圆环光阑衍射的边界衍射波理论

Boundary diffraction wave theory of plane waves diffracted at an annular aperture

根据M aggi-Rub inow ic边界衍射波理论和亥姆霍兹-基尔霍夫积分定理,给出了平面波圆环边界衍射波积分公式。圆孔、圆屏衍射以及轴上光场分布可作为其特例得到。分析了衍射场的轴上光强分布特点。数值计算比较表明,使用文中所给公式与直接用基尔霍夫衍射积分公式作数值计算的结果完全一致,而在近场使用瑞利衍射积分与文中结果有较大差异。

Starting from the Maggi-Rubinowic theory of the boundary diffraction wave and Helmhotz-Kirchhoff integral theorem,the diffraction integral formula of plane waves diffracted at an annular aperture is derived. The diffraction at a circular aperture and a circular screen,as well as the axial field distribution is treated as the special cases of our general result. The characteristics of axial intensity distribution of the diffracted field are analyzed. Numerical examples show that the results obtained by means of the formula given in this paper are in good agreement with the direct numerical integration of the Kirchhoff integral formula. In the near field there are noticeable discrepancies between our formula and the Rayleigh diffraction integral.