The Point Spreed Function Of Imaging System By Polychromatic Light Illumination

The mathematic definition of fractional fourier transform was first given by Namias in 1980 for solving Schrodinger equation. Fractional Fourier transform was introduced into optics in 1993,and rapidly became a hot topic of information optics.Now the research about the main nature and basic unit,and the applied of optical FRFT has been much reported. Now fractional Fourier transform has been used in the optical measurement, neural network, encryption, , information preserving information processing and so on.But combined to system theory and based on Rayleigh - Sommerfeld diffraction theory, the resear on polychromatic light illumination ,the conventional imaging system point spread function and the fractional point spread function ,as well as polychromatic light illuminatio,the overall transmission performance of imaging systems and related research work had not been given.Based on the equivalence of TRFT and fresnel diffraction ,and systemtheory . analysis the basic properties ,coordinates and time transmission characteristics of imaging system by polychromatic light illumination,construction of the time transfer function , inverse Fourier transform with it, get the time piont spread function . starting from the optical definition of Fractional Fourier Transform(FFT) the paper obtains simulation of imaging system's transmission expressed in optical FFT,decomposed the fractional fourier into two Ruili Suo Sommerfeld and lens combination of phase transformation.Conventional,induction and generalization the Fourier and Fractional fourier contional point spread function ,and transfer function,specification of the two types of function scope and terms of use,interpretation of its physical meaning. In general,it may be assumed that when the wavelength of the light takes a single-value,the conventional and fractional temporal point spread functions degenerate into the imaging system's point spread functions in the monochromatic light.When fractional numerical series is 1, the fractional and conventional point spread functions give the same results,which are drawed by the later if object distance and image distance take the focal length.At the same time,the temporal point spread function degenerates into the fourier transform's kernel which described in polychromatic light.Through computer's verify and experiment's analysis,the author makes a comparative analysis between the conventional and fractional temporal point spread functions and at last arrives at a conclusion that the result is reliable and feasible.