Truncation error of the Laguerre-Gauss expansion of axially symmetric beams in terms of second-order intensity moments

From the expansion of a partially coherent axially symmetric beam in terms of Laguerre-Gauss functions, we investigate the degree of accuracy reached by approaching the exact field by means of the lower-order terms of the above series. The accuracy is evaluated analytically as a function of both the number of terms of the expansion and the (measurable) second-order intensity moments of the beam, namely, the beam width and the so-called beam quality factor .