Analysis Of Fractional Fourier Transform Based On Microscope Imaging

Fractional Fourier transform(FFT)is a generalization of the Fourier transform(FT)in generalized orders.The characteristics constructed by its unique local analysis,space frequency joint representation and cascade state are superior to the conventional FT for spectrum analysis of available data processing and non-stationary systems.Fractional Fourier optics has been involved in many fields,However,there is no clear and complete report on the work of the optical fractional Fourier transform analysis on the imaging process of the microscope.Based on the scalar diffraction theory and the near axis condition according to the Huygens Fresnel principle,the microscope imaging was analyzed from the point of view of the process of Fresnel diffraction;Based on the equivalance between Fresnel diffraction and Fractional Fourier transform,microscopy imaging course was outlined as the FFT process.With the help of the optical FFT realization patterns like the single lens mode and non lens model to set about the project,according to the Theory of Linear System and the cascade properties of FFT,microscopy imaging was interpreted for the cascade process of twice symmetric type single lens model of FFT and a non lens mode ofFFT,obtained the fractional Fourier spectrum mathematical expression of light field distribution of exit pupil plane of objects for a microscope system under monochromatic illumination,interpretation of the characteristics and the physical significance of optical field distribution.The results show that the microscopy imaging descriptions in Fresnel diffraction process is equivalent to the process of FFT;further verified the FT is used to describe Fraunhofer diffraction process of light band,while physical(optical)mechanism of FRFT is light Fresnel diffraction and corresponding the diffraction process of light from the Fresnel diffraction region to infinity area of Fraunhofer diffraction region;using optical FT to describe light band Fraunhofer diffraction is the special case of a common conclusion.At the same time analyzed objects of spatial structure with the phase dispersion,phase bending,deflection,displacement and zoom characteristics in the process of FFT.Based on the MATLAB software,the result of simulation and experiment verified the feasibility and reliability of the conclusion,this conclusion enriches the microscope imaging theory,and this is of reference value to the optical design and optical information processing.