Second-order moments matrix and M2 factor of optical beams

Based on the 4×4 second-order moments matrix,the M2 factor and intrinsic astigmatism a of general optical beams a restudied.The analytical expressions for the M2 factor and intrin sic astigmatism a of some typical types of beam,such as the general astigmatic beam,rotationally simple astigmatic beam,aligned simple astigmatic beam and stigmatic beam,are given and analyzed.It is shown that the twist result is an increase of the intrinsic astigmatism,but doesn't affect the M2 factor in general.