A significant aspect of the propagation of coherent light beams is that the shape of the transverse field distribution changes. In this paper, the concepts of shape-invariance error and shape-invariance range are used to characterize such effects in a quantitative way. Applications of the theoretical analysis to some simple but significant cases are presented.
Vicalvi S, Borghi R, Santarsiero M, & Gori F (1998). Shape-invariance error for axially symmetric light beams. IEEE JOURNAL OF QUANTUM ELECTRONICS, 34(11), 2109-2116.