Spherical Wave Illumination Single Lens Realize Fractional Fourier Transform

Fractional Fourier Transform is a generalization of Fourier Transform,a new parameter order involved.More characteristics appear with this parameter compared with Fourier Transform,which means a wider application at the same time.With the development and improvement of the theory,Fractional Fourier Transform has become an effective means to analyze and solve problems.How to implement the fractional Fourier transform becomes a problem in practical application.Now there has been a lot of implementation methods of fractional Fourier transform,for example computer simulation,propagation through the gradient refractive index medium.The classic optical implementation apparatus of fractional Fourier transform are Lohmann I and Lohmann II model.One optical implement of fractional Fourier transform by a single lens has been set forth.The optical apparatus consists of a single lens and the space in front of and behind the lens and is illuminated by a point light source.The analysis base on scalar diffraction theory,the relationship between fractional Fourier transform and Fresnel diffraction theory and the phase transformation of lens.The analytic expression of the transformation is obtained by theoretical analysis,and the parameter selection rule of the transformation model is deduced.The same analysis has been taken over other two modes,object near lens mode and object behind lens mode.The optical field distribution on observed plane and the parameter selection rule has been also given.By simulation,the intensity distribution and phase distribution on the observed plane of all three transform mode has been given.A comparison between all three transform mode and the fractional Fourier transform has been carried.The simulation results show that the method is reliable and feasible.