The Fourier Analysis Of Defocus System Illuminated By Coherent Light

The concept of Fourier transform was introduced in optics in 1946by Duffieux.x.P.M, and combined with physical optics ,formed animportant branch of information optics–Fourier optics ,FractionalFourier transform was introduced in optics in 1993 .So far, opticalFourier transform and Fractional Fourier transform both have beenwidely used in many fields .There are many descriptions about thestudy on non-ideal factors of their optical implementation system, butthe study on the position of the optimum focal plane of actual systeminfluenced by the aberration has not been explicitly reported.Based on the aberration theory, studied the location of diffractionfocal plane namely the best image plane of the system in thepresence of a certain amount of primary spherical aberration, and theoptimum defocusing amount. In order to study the effect of aberrationon Fourier spectrum of the object, the expression of Fourier spectrumof the object which is realized by the Fourier transform systemeffected by the spherical aberration was given, compared it with theideal condition spectrum expression, found the spherical aberrationmade the spectral energy distribution in the original geometrical focal plane scatter, and the clarity of the spectrum decline; Throughintroducing appropriate defocus aberration, got the expression ofspectrum realized by the Fourier system in the presence of sphericalaberration and defocus aberration, compared it with the expressionof the ideal condition and effecting by spherical aberration, found theintroduction of appropriate defocus could reduce the impact of thespherical aberration on the quality of Fourier spectral, got theposition of the quasi-ideal spectrum. Went into the effect of sphericalaberration on the symmetric single-lens fractional Fourier transformsystem, obtained the expression of fractional spectrum of sphericalaberration limited system and defocus spherical aberration system,compared them with the expression of fractional spectrum under theideal condition, found when the system with a certain amount ofprimary spherical aberration ,the spherical aberration, the standardfocal length of the system depends not only on the order of thefractional Fourier transform ,but also depends on the incident lightwavelength and the size of exit pupil i.e. the size of the lensaperture ,the fractional Fourier transform order of a certain sizevalues z corresponding to increases ;By introducing appropriatedefocus aberration ,the influence of spherical aberration on thefractional spectral energy distribution can be reduced ,obtained thebest position that can realize a certain order of fractional Fouriertransform. The computer simulation proved the reliability of theconclusion.