Fractional Fourier transform in optics – a new perspective
Source: Optik International Journal for Light and Electron Optics, Volume 115, Number 2, May 2004 , pp. 77-85(9)
Publisher: Urban & Fischer
Abstract: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 well 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.
Document Type: Research Article
Affiliations: 1: Optical Science Lab, Department of Mechanical Engineering, Shizuoka University, 3-5-1 Johoku, Hamamatsu City, Shizuoka Prefecture, 432-8011, Japan 2: Department of Applied Physics, Calcutta University, 92 Acharya Prafulla Chandra Road, Kolkata-700009, India 3: Department of Computer Science & Engineering, Calcutta University, 92 Acharya Prafulla Chandra Road, Kolkata-700009, India
Publication date: May 1, 2004