Defining the effective radius of curvature for a nonideal optical beam

A simple expression is given for evaluating the effective or average radius of curvature R(z) of an arbitrarily wrinkled, distorted, or nondiffraction-limited optical beam. This real-beam radius of curvature obeys the same free-space propagation equation as does the wavefront curvature of an ideal Gaussian beam. Extracting this correctable curvature from the beam at any plane simultaneously collimates the beam, makes that location a waist for the real beam, and minimizes the far-field beam divergence starting from that position