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A coherent rotationally symmetric two-dimensional beam is essentially one-dimensional in content: It is fully determined by the one-dimensional sample along a diagonal of the circularly symmetric field distribution in a transverse plane. The linear transform that reconstructs the four-dimensional Wigner distribution of the full two-dimensional beam from the two-dimensional Wigner distribution of the one-dimensional sample is presented.doi:10.1364/ol.25.001379 pmid:18066223 fatcat:52uzer22ybcdzl42urd23nymx4