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
Tatiana Alieva and Martin J. Bastiaans, "Wigner distribution and fractional Fourier transform for two-dimensional symmetric optical beams," J. Opt. Soc. Am. A 17, 2319-2323 (2000)