From diffraction theory, an expression is derived for the radius of a gaussian beam, in an output plane of a single lens, on-axis optical system, as a function of input waist radius, lens focal length, input waist to lens spacing, and lens to output plane spacing. Several special cases are discussed and plots of the important cases are included. The choice of the plots, and their scaling, was made on the basis of providing useful information to those people involved with typical problems in laser scanning systems, such as the location and size of the focused spot. The derivation includes a discussion of truncation effects.
L. D. Dickson, "Characteristics of a Propagating Gaussian Beam," Appl. Opt. 9, 1854-1861 (1970)