Quality descriptors of optical beams based on centred reduced moments I: spot analysis

A method for analyzing beam spots is discussed. It is based on the central reduced moments of the spot and its associated density functions. These functions allow us to separately analyze specific spot fractions, in such a way that specific combinations of higher order moments can be interpreted as coordinates of their centre of mass and the length and orientations of their principal axis. So, the descriptors of the associated density functions deal with the quantitative estimation of spot features, such as coma-like and astigmatism-like distortions. To assure high accuracy, background noise suppression and an optimal match of the spot support onto the region [-1,1]x[- 1,1] are performed prior to the calculation of the moments. Simulations were performed for illustrating the method.