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 halfwave zone when analyzed the diffraction spectrum.The optical path difference is half wavelength at adjacent half-wave zone and the phase difference is π,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.