We obtain a Fourier transform scaling relation to find analytically, numerically, or experimentally the spectrum of an arbitrary scaled two-dimensional Dirac delta curve from the spectrum of the nonscaled curve. 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 the scaling relation we determine the spectrum of an elliptic curve by a circular geometry instead of an elliptical one. The generalization to N-dimensional Dirac delta curves is also included.
© 2004 Optical Society of America
(000.4430) General : Numerical approximation and analysis
(050.1960) Diffraction and gratings : Diffraction theory
(070.2590) Fourier optics and signal processing : ABCD transforms
(350.5500) Other areas of optics : Propagation
Manuel Guizar-Sicairos and Julio C. Gutiérrez-Vega, "Two-dimensional Fourier transform of scaled Dirac delta curves," J. Opt. Soc. Am. A 21, 1682-1688 (2004)