Characteristic Analysis And Application Of Fractional Fourier Transform Aberration System

Fractional Fourier transform was put forward for the first time in1929, and fractional Fourier transform was introduced in optics in1993. It is the extension of Fourier optics. Compared with theconventional Fourier transform, fractional Fourier transform hasfractional order parameters, so Fractional Fourier transform has morepowerful functions and can be more widely used in many areas suchas optics and information processing.Lohman proposed that he took advantage of the free spacepropagation and the structure of lens combination by achievingfractional Fourier transform. The paper adopts dual-lens system. Atfirst the author analyzes the properties of the fractional Fouriertransform, and deduces any combination of the fractional Fouriertransform lens expression and the basic law of parameter selectionwhich is generated from optical fractional Fourier transform. He usesdouble lens which have same focal length, such as Ramsden ocular,Huygenian ocular, telescopes and other optical components, andverifies the expression and the law of parameter selection. Thus theresult is that the imaging processes of Ramsden ocular, Huygensocular and telescope are equivalent to fractional Fourier transform.Meanwhile monochromatic aberration theory is introduced infractional Fourier transform, getting the basic law of parameter selection,which generating from optical fractional Fourier transformwhich affected by the aberration. The author uses Ramsden ocularand Huygens ocular as an example to contrast the ocular light fielddistribution which is affected by the aberration with that which is notinfluenced by aberration, and gets that two kinds of ocular modeoptical field distribution,which is affected by aberration,areinfluenced by aberration coefficient, cluster parameters and thenumber of fractional order. But aberration coefficient is small anddual-lens model has the effect of coma makes elimination, so thedifference between double-lens model of optical field distributioninfluenced by aberration and the ideal imaging lens mode optical fielddistribution are smaller. When the aberration coefficient S is zero, twokinds of ocular lens mode optical field distribution which are notaffected by aberration degrades into ideal optical system of opticalfractional Fourier transform. When the number of fractional ordermeets different conditions, two kinds of ocular lens mode optical fielddistribution which are affected by aberration degrades intoconventional optical Fourier transformation. When the aberrationcoefficient is not zero and meets different conditions, two kinds ofocular lens mode optical field distribution which are affected byaberration can be simplified as the standard optical fractional Fouriertransform. This conclusion is proved that in theory parameterselection is correct whether any combination of the fractional Fouriertransform lens is affected by aberration or not. Computer simulationexperiments verify the reliability of the conclusion.