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Proceedings Paper

Application of the two-dimensional Fourier transform scaling theorem to Dirac delta curves
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Paper Abstract

We propose a Fourier transform scaling relation to find analytically, numerically and experimentally the spatial frequency spectrum of a two-dimensional Dirac delta curve from the spectrum of the non-scaled curve, after an arbitrary coordinate scaling. An amplitude factor is derived and given explicitly in terms of the scaling factors and the angle of the forward tangent at each point of the curve about the positive x axis. With this formulation we experimentally obtain the spectrum of an elliptic contour in a circular geometry, thus acquiring non-diffracting beam characteristics. Additionally we include the generalization to N-dimensional Dirac delta curves.

Paper Details

Date Published: 30 August 2005
PDF: 11 pages
Proc. SPIE 5876, Laser Beam Shaping VI, 587610 (30 August 2005); doi: 10.1117/12.615514
Show Author Affiliations
Manuel Guizar-Sicairos, Instituto Tecnologico de Monterrey (Mexico)
Julio C. Gutierrez-Vega, Instituto Tecnologico de Monterrey (Mexico)

Published in SPIE Proceedings Vol. 5876:
Laser Beam Shaping VI
Fred M. Dickey; David L. Shealy, Editor(s)

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