Charaterization of laser beams by using intensity moments

Any coherent and partially coherent laser beams can be characterized by their intensity moments. Generally a laser beam has maximal 4 first order moments and 10 second order moments. The centers of gravity of the beam in the near field and the far field are determined by the first order moments. The beam radii, far field divergences, radii of curvature, beam orientations and M2-factors can be obtained from the second order moments. Beam twist which is related to the orbital angular momentum can be also obtained from the second order moments. The intensity moments and related laser beam parameters obey parabolic propagation laws in the first order optical systems. They are measurable by the caustic method or the Hartmann-Shack wavefront sensor method. The principle and technical problems of these methods were analyzed. As examples the beams emitted from high power diode stack and the astigmatic beam with twist were experimentally investigated.