角谱公式与瑞利-索末菲公式的等价性

Equivalence of the Angular-spectrum Represention and Rayleigh-Sommerfeld Formulae

基于矢量平面波角谱公式和球面波的Weyl表示式,未采用任何近似处理,非常方便地推导出矢量形式的第一类和第二类瑞利-索末菲衍射积分公式。作为特例,当只考虑光场的一维横向分量时,类似地可得到标量形式的瑞利-索末菲衍射积分公式。结果表明:平面波角谱公式与瑞利-索末菲衍射公式是等价的。

Based on the vectorial angular-spectrum formula and the Weyl representation of a spherical wave, the vectorial Rayleigh- Sommerfeld （RS） diffraction formulae of the first and second kinds are readily derived. The scalar first and second RS diffraction formu- lae can be treated as special cases of the result and deduced by considering only one transversal component of the electric field. It is shown that the angular-spectrum formula and Rayleigh-Sommerfeld diffraction formulae are equivalence.