Determination of the ten second order intensity moments

The general astigmatic beam can be characterized by its ten second order moments in first order approach. Most intensity moments, except the beam twist, can be determined by measuring the intensity in a reasonable number of positions around the waist of the beam. The beam twist is determined by applying a rotated cylindrical lens. The ten intensity moments of two kinds of astigmatic beam were determined: a simple astigmatic TEM_8,0 Hermite–Gaussian beam and a twisted beam generated from the TEM_8,0 mode. The experimental results were compared with the theoretical calculations and demonstrate that the ten second order moments of a beam can be determined in a rather simple way.