Effective curvature matrices and mixed moments of general pulsed paraxial beams

On the basis of the space-time Wigner distribution function, we use the lea st-squares fitting method to derive the relationship between effective wave front curvature matrices and second-order mixed moments of quasi-monochroma tic and polychromatic pulsed paraxial beams. The expressions here are valid for both completely coherent and partially coherent light in the three-dim ensional space. Finally, the fitting method is extended to the higher-order situation; from this, a novel technique for characterizing the beam phase from the moments and their derivatives is presented.