Effective Curvature Matrices and Mixed Moments of General Pulsed Paraxial Beams

On the basis of the space-time Wigner distribution function, we use the least-squares fitting method to derive the relationship between effective wavefront curvature matrices and second-order mixed moments of quasi-monochromatic and polychromatic pulsed paraxial beams. The expressions here are valid for both completely coherent and partially coherent light in the three-dimensional 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.