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The Fourier transform in optics: from continuous to discrete or from analogous experiment to digital calculus

P. C. LOGOFATU1,* , D. APOSTOL1

Affiliation

  1. Lasers Dept., National Institute for Laser, Plasma and Radiation Physics, PO Box MG-36, 077125, Magurele, Romania

Abstract

Although extensively used in digital computation, the discrete Fourier transform (DFT) has a problematic relation with the physical or continuous Fourier transform (CFT), as we encounter it in practice, for instance in Fourier optics. This article first establishes the physical meaning of DFT by expressing it in terms of CFT using the Fourier series as an intermediary link between the two types of transforms. Then it studies some concrete examples of binary masks Fourier transformed using an optical plane wave and a lens and shows how one can make DFT a good approximation of CFT..

Keywords

Fourier optics, Discrete Fourier transform, Signal sampling.

Submitted at: June 29, 2007
Accepted at: Sept. 18, 2007

Citation

P. C. LOGOFATU, D. APOSTOL, The Fourier transform in optics: from continuous to discrete or from analogous experiment to digital calculus, Journal of Optoelectronics and Advanced Materials Vol. 9, Iss. 9, pp. 2838-2846 (2007)