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

Manuel Guizar-Sicairos; Julio C. Gutierrez-Vega

doi:10.1117/12.615514

30 August 2005 Application of the two-dimensional Fourier transform scaling theorem to Dirac delta curves

Manuel Guizar-Sicairos, Julio C. Gutierrez-Vega

Proceedings Volume 5876, Laser Beam Shaping VI; 587610 (2005) https://doi.org/10.1117/12.615514
Event: Optics and Photonics 2005, 2005, San Diego, California, United States

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.

Citation Download Citation

Manuel Guizar-Sicairos and Julio C. Gutierrez-Vega "Application of the two-dimensional Fourier transform scaling theorem to Dirac delta curves", Proc. SPIE 5876, Laser Beam Shaping VI, 587610 (30 August 2005); https://doi.org/10.1117/12.615514

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