Beams Propagation In A Spherically Aberrated Fractional Fourier Transform System With An Aperture

As a generalized Fourier Transform,Fractional Fourier Transform enables us to study optical propagation,optical imaging,image processing,and information processing from a new point of view.Considering the existence of spherical aberration and aperture effect in lens,it is discussed that the influence of aperture and spherical aberration in Fractional Fourier Transform of beams can provide reference for the design of optical systems and beams control.Taking Lohmann I optical system as an example,the propagation characteristics of beams through a spherically aberrated Fractional Fourier Transform System with an aperture are studied by the Collins formula.The main work of this thesis are arranged as follows:1.The propagation characteristics of Bessel Beams through a spherically aberrated Fractional Fourier Transform System with an aperture are studied.Taking the transmission of Bessel beams in an ideal Fractional Fourier Transform system or a Fractional Fourier Transform system with an apertured as two special cases,the distribution of the output beams in different transform order and the intensity distribution of the traditional Fourier Transform surface in different apertures are discussed.It is shown that when the Fractional Fourier Transform system is an ideal system,the output beams are still Bessel beams.When the system contains an aperture,the high quality hollow beams can be obtained at Fourier Transform plane by choosing the appropriate aperture size.The influence of the lens aperture and spherical aberration on the transverse light intensity distribution and the axial light intensity distribution are studied in detail.It is shown that the effect of positive spherical aberration and negative spherical aberration on the output beams are no longer consistent under the other output plane in addition to the Fourier Transform plane.The higher quality output beam can be achieved with some positive spherical aberration than without spherical aberration.Themajor factor that influence the output beams is determined by aperture size,and the output beams mainly affected by the aperture when the size is small.But if the size exceeds a critical value,the intensity distribution on axis is mainly affected by spherical aberration.2.The propagation characteristics of Cosine-Gaussian Beams through a spherically aberrated Fractional Fourier Transform System with an aperture are studied.The variation of light intensity distribution with transform order in an ideal system and the change period of light intensity with transform order in a system containing only an aperture are discussed.The influence rule of positive spherical aberration and negative spherical aberration on the output beams are discussed when the system contains both an aperture and a spherical aberration.Furthermore the variation period of the output light intensity with transform order and the influence of the aperture,spherical aberration and modulation parameters on the axial light intensity distribution are studied.It is shown that Cosh-Gaussian beams can be obtained from the Fourier Transform plane in the ideal system.When the system contains only an aperture or both an aperture and a spherical aberration,the variation period of the output light intensity with transform order is 4.Moreover,the effect of positive and negative spherical aberration are inconsistent in a spherically aberrated Fractional Fourier Transform system with an aperture,and the better quality beams can be obtained under partial positive spherical aberration.The smaller the modulation parameter is,the greater the light intensity is affected by the spherical aberration.In this thesis,the propagation characteristics of beams in the Fractional Fourier Transform system with two non ideal factors of the aperture and spherical aberration is discussed for the first time.