Aberration Limited Optical Fractional Fourier Transform Systems

Since 1993 the introduction of optical fractional Fourier transform, scientists have given the definition in the optical system and optical realization of the basic unit. After 20 years of development, fractional Fourier transform has become a hot topic of information optics in recent years. So far, it has been throughout the optical measurement applications, information processing, information storage, security technology, neural network and other aspects. Although the system and disorders based on diffraction limited optical fractional Fourier transform systems theory have been reported, but limited system for the optical aberration fractional Fourier transform theory not yet see clearly the full report.This article is based on the Lohmann's two proposed optical implementation of fractional Fourier transform, the monochromatic aberration theory with fractional Fourier transform process, obtained the optical aberration scores limited system Fourier transform specific expression, and interprete its physical meaning. The concluded show that: Compared with the standard optical spectrum, two lens mode aberration limited optical spectra are modulated by astigmatism coefficient s3 standard focal length f0,fractional orderα。Because the aberration coefficient is small, and the dual-lens mode with the two lenses combinat are usaberrate.So the aberration limited optical system of dual-lens mode is closer to the standard spectrum of the optical points. When the astigmatism coefficient S3 is zero, aberration limited optical lens model system of two points are degenerate as a standard optical spectrum of fractional Fourier transform; Whenα=π/2, aberration limited optical lens model system of two points are degenerate as a standard optical spectrum of fractional Fourier transform; When the astigmatism coefficient S3 is not zero and for different conditions, aberration limited optical lens model system of two points are degenerate as a standard optical spectrum of fractional Fourier transform. Computer simulation proved the theory of reliability and feasibility.