Abstract

A useful relationship between the fractional Fourier transform power spectra of a two-dimensional symmetric optical beam, on the one hand, and its Wigner distribution, on the other, is established. This relationship allows a significant simplification of the standard procedure for the reconstruction of the Wigner distribution from the field intensity distributions in the fractional Fourier domains. The Wigner distribution of a symmetric optical beam is analyzed, both in the coherent and in the partially coherent case.

© 2000 Optical Society of America

Wigner distribution moments in fractional Fourier transform systems

Martin J. Bastiaans and Tatiana Alieva
J. Opt. Soc. Am. A 19(9) 1763-1773 (2002)

Reconstruction of the Wigner transform of a rotationally symmetric two-dimensional beam from the Wigner transform of the beam’s one-dimensional sample

G. S. Agarwal and R. Simon
Opt. Lett. 25(18) 1379-1381 (2000)

Phase-space distributions in quasi-polar coordinates and the fractional Fourier transform

Tatiana Alieva and Martin J. Bastiaans
J. Opt. Soc. Am. A 17(12) 2324-2329 (2000)

Fractional Fourier transforms in two dimensions

R. Simon and Kurt Bernardo Wolf
J. Opt. Soc. Am. A 17(12) 2368-2381 (2000)

Can the Wigner transform of a two-dimensional rotationally symmetric beam be fully recovered from the Wigner transform of its one-dimensional approximation?

Daniela Dragoman
Opt. Lett. 25(5) 281-283 (2000)