Analysis of the optical transformation properties of 2-dimensional beam parameters and consequences for their measurability

Spatial moments, cumulants and scaled cumulants of the intensity distribution of a laser beam are argued to be relevant quantities for laser materials processing. Their propagation and optical transformation properties are analysed in an operator approach. A tensorial formulation of the ABCD transformation properties of the moments/cumulants is used to classify them in sets determinable and nondeterminable by beam divergence measurements.