菲涅耳-基尔霍夫积分与半波带法分析衍射光谱

惠更斯菲 涅耳原理指出光的衍射本质是无穷多次波的相干叠加.在研究衍射光谱的强度时可使用菲涅耳-基尔霍夫衍射积分进行计算,但该积分的计算较为复杂.为了简化计算而引入菲涅耳半波带的概念,把积分运算简化为振幅矢量的叠加,从而在研究衍射时由菲涅耳-基尔霍夫衍射积分过渡到菲涅耳半波带法.在菲涅耳半波带法中波前上相邻两个半波带到达叠加点的光程差为半个波长,从而导致相位差π.因此相邻两个半波带引起的振动在叠加点发生相消,最终叠加点的光强由发出次波的半波带数目的奇偶性决定.奇数个半波带在叠加点的光强得到加强,偶数个半波带在叠加点的光强发生相消.

Analysis of Diffraction Spectrum by Fresnel-Kirchhoff Integral and Half-wave Zone Theorem

The essential of diffraction spectrum is superposition by infinite secondary waves based on Huggens-Fresnel principle. Fresnel-Kirchhoff integral was used to calculate the intensity of diffraction spectrum, but the integral was very complicated. In order to predigest the calculated process, Fresnel half-wave zone theorem was introduced. The calculate integral was translated into superposition by amplitude vector. So the Fresnel-Kirchhoff integral was transformed to Fresnel half- wave zone when analyzed the diffraction spectrum. The optical path difference is half wavelength at adjacent half-wave zone and the phase difference is zr, so the vibration of adjacent half-wave zone at field point is canceled each other. The intensity of light at field point is strengthened by odd half-wave zone ,whereas it is cancellation.