The intensity profile of a radially symmetric beam is shown to be related to the inverse Abel transform of knife-edge-scan data. Two inversion algorithms, previously applied to problems in plasma diagnostics, are described and applied to knife-edge data from a confocal unstable resonator laser. The resulting profiles are shown to be in good agreement with each other but significantly different from the profile obtained by assuming the beam to be approximately Gaussian. As a beneficial consequence, the results are shown to imply a significantly higher laser damage threshold for polymethylmethacrylate than previously reported.