Beams Propagation In An Astigmatism Fractional Fourier Transform System With An Aperture

Fourier Transform has become one of the basic tools for solving problems in scientific research and engineering technology.Fourier Transform is also an important means to study linear systems and perform signal analysis.Due to the astigmatism and pupil effect in the lens,it can theoretically provide some references for the acquisition of the beam,the control of the beam and the design of the optical system by discussing the effect of the lens pupil and the lens astigmatism on optical fractional Fourier transform system.In this paper,the astigmatic Lohmann ? optical system and the Lohmann ? optical system are used to realize the Fractional Fourier Transform of the beams,which simulates the transmission of the Cosine-Gaussian Beams and the Bessel Beams in the Lohmann ? optical system.The Colins formula is used to study the transmission characteristics of the cosine Gaussian beam and Bessel beam when the two beams pass through the pupil astigmatic fractional Fourier transform system.The main tasks as follows:At first,the Lohmann ? optical system with astigmatism and the Lohmann ? optical system with astigmatism are studied.Studies have shown that in the astigmatic Lohmann ? optical system,tan(j/ 2)(28)0,astigmatism no longer affects the transmission of the beams through the lens system.In the Lohmann ? optical system,tanj(28)0,astigmatism does not affect the transmission of the beams through the lens system.Second,the propagation characteristics of the cosine-Gaussian beam are studied by an astigmatic fractional Fourier transform system with aperture.The variation of the intensity distribution with the transformation order in the ideal system and the period of change of the intensity of the transformation order in a system containing only astigmatism are discussed.The results show that the Cosh-Gaussian beam can beobtained from the Fourier transform plane in an ideal system.When the system contains only astigmatism or contains both aperture and astigmatism,the output light intensity varies with the order of transformation,and the period of variation is 4.And in the astigmatism-dispersion fractional Fourier Transform System,different astigmatism specific transformation orders can obtain a better quality output beams.The smaller the modulation parameter,the greater the light intensity is affected by the spherical aberration.At last,the aperture propagation characteristics of Bessel beams passing through an astigmatic fractional Fourier transform system are studied.The Bessel beam is transmitted to an ideal fractional Fourier transform system or a fractional Fourier transform system with astigmatism as two special cases.The results show that when the fractional Fourier transform system is an ideal system,the output beam is still a Bessel beam.And in the astigmatism-dispersion fractional Fourier Transform System,different astigmatism specific transformation orders can obtain a better quality output beams.