Fractional Fourier transform in optics - a new perspective

摘要

This paper presents the optical implementation of fractional Fourier transform using bulk optics in a new light. We used a two-lens Fourier transforming setup. The field distribution at the half order fractional Fourier transform plane is obtained using Fresnel transform as the analysing tool. It is shown that the half-order fractional Fourier transform of any function is a product of Fresnel function and the Fourier transform of the product of the given function in a reduced coordinate with another Fresnel function. Then analytical expressions are also deduced for the nature of the half order Fourier transform of a, plane wave; delta function, sinusoidal grating; rectangular:, aperture as ell as Gaussian input function. We verified our theoretical prediction experimentally with a square-top grating as the object. The effect of spatial filtering at the half transform plane is also explored.