Generalized M2 factor of hard-edged diffracted flattened Gaussian beams

On the basis of generalized truncated second-order moments, a closed-form expression for the generalized M2 factor of hard-edge diffracted flattened Gaussian beams is derived that is determined by the beam order and the truncation parameter. Special cases are discussed. Moreover, it is shown that the M2 factor of truncated plane waves is equal to 4sqaure root3/3, independent of the aperture width.