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

It is shown that the full four-dimensional Wigner transform of a coherent, rotationally symmetric light beam can be completely recovered by measuremen t, in one step, of the Wigner transform of an equivalent one-dimensional li ght beam. The method of generating this equivalent light beam from a two-di mensional circular (C) 2000 Optical Society of America light beam is presen ted. OCIS codes: 070.0070, 070.4560, 110.0110, 110.2990.