Roughness and gradient parameters for characterising shape uniformity of laser beams

We define six parameters, the roughness parameter, the local gradient parameter, the directionless gradient parameter, the integral gradient parameter, the directionless integral gradient parameter and the absolute gradient parameter for characterising the uniformity of a laser beam in its transversal section. For shape-invariant beams the roughness parameter is propagation invariant. The absolute gradient parameter is propagation invariant for symmetric shape invariant beams. As an example, five of the defined parameters are calculated for a dummy irradiance. The values of the roughness parameter and the absolute parameter are calculated and tabulated for symmetric Hermite–Gaussian, Laguerre–Gaussian, spherical Gaussian, flattened Gaussian (at the waist plane) and super Gaussian beams (at the waist plane). The results are discussed.