Abstract

Following a general procedure developed previously [Ann. Henri Poincaré 1, 685 (2000)], here we construct Wigner functions on a phase space related to the similitude group in two dimensions. Since the group space in this case is topologically homeomorphic to the phase space in question, the Wigner functions so constructed may also be considered as being functions on the group space itself. Previously the similitude group was used to construct wavelets for two-dimensional image analysis; we discuss here the connection between the wavelet transform and the Wigner function.

© 2000 Optical Society of America

Canonical-covariant Wigner function in polar form

T. Hakioğlu
J. Opt. Soc. Am. A 17(12) 2411-2421 (2000)

Quasi-probability distributions for the simplest dynamical groups

A. B. Klimov and S. M. Chumakov
J. Opt. Soc. Am. A 17(12) 2315-2318 (2000)

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)

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)