Simulation of the Intensity Distribution for Talbot Effect of Grating

Abstract

For simulating the laws of intensity distribution in image plane, the theory of Fresnel diffraction had been used based on Talbot effect of grating. Under the approximation condition of Fresnel diffraction, the space distribution of complex amplitude in the diffraction field in image plane had been expressed for transitivity function in object plane. The calculation results had shown three parts. The first one was that the width in the flat-top range of maximum intensity was increasing and the border was very clear when the scratch number was increasing. The Talbot effect was more and more obvious as the scratch number of the grating was larger and larger. The second one was that the central positions of the maximum intensity in image plane were in x=· kd on image plane, where k was integral number and d was grating constant. The Talbot effect will be loss with the distance between grating plane and image plane larger and larger. The third one was very important. When the distance between the grating plane and image plane was half-odd multiple of Talbot distance, the central positions of the maximum intensity in image plane were in x=· (2k+1)d on image plane. The positions were the centers of two neighbor-hood positions of maximum intensity in image plane when the distance between the grating plane and image plane was integral number times of Talbot distance. The important phenomenon was found. The phenomenon was the maximum light intensity appeared in the same time in x=· kd and x=· (2k+1)d on image plane.