Optical Fractional Fourier Transform Of Sphere-end Selfoc Lens

D.Mendlovic and H.M.Ozaktas first explained the optical realization structure and definition of fractional Fourier transform through the optical theory related to gradient refractive index medium in 1993.At the same time,fractional Fourier theory was also introduced into optics.As a new mathematical method in science and technology,Fractional Fourier transform has many practical applications in information storage,spatial filtering,image encryption and neural network.Therefore,it also plays a wide and effective role in optical and signal processing.Different from the medium with constant refractive index and uniform distribution,the refractive index of gradient refractive index medium is not constant and non-uniform,and its refractive index varies continuously with the observation point in the process of light propagation.Also often named as variable refractive index medium or gradient refractive index medium.According to the distribution of refractive index,the variable refractive index medium is usually divided into three types: axial variable refractive index medium,radial variable refractive index medium and spherically variable refractive index medium.In recent years,the study of self-focusing lens has been more and more in-depth in our country,which has formed a relatively complete theory of geometric optics,wave optics,matrix optics and so on.On the system.The self-focusing lens has the same ability to modulate the optical wave phase as the lens,so the self-focusing lens can be used as the basic optical element to realize Fourier transform.In view of the fact that the spherical end face has the effect of convergence on the beam,in order to reduce the aberration and the diameter of the outgoing spot and increase the numerical aperture in the actual fabrication process of the self-focusing lens,the object is usually used to reduce the aberration and increase the diameter of the output spot.It is generally necessary to make the end plane of the self-focusing lens into a spherical or aspheric sphere with a certain radius of curvature.By deducing the phase transformation factor of the spherical self-focusing lens and using the Fresnel diffraction formula,the complex amplitude distribution of the light field in the rear of the spherical self-focusing lens with plane wave,spherical wave and Gaussianbeam is obtained,respectively.The parameter selection rule of optical fractional Fourier transform using spherical self-focusing lens is also discussed.The results show that the optical path structure of Fourier transform and fractional Fourier transform using spherical self-focusing lens is independent of the properties of incident light.The distribution of light intensity on the observation surface was simulated by computer experiments with rectangular light holes,and the feasibility and accuracy of the conclusions were verified.