Keplerian and Galilean beam expanders

A Keplerian telescope consists of two plano-convex convergent lenses placed so that the distance between the lenses is equal to the sum of their focal length.  These simple beam expanders have high expansion ratios. Because the two lenses have positive focal lengths the input beam will focus at a point between the two lenses, enabling spatial filtering. However, that same property makes Keplerian beam expanders problematic for high power laser applications, as the resulting energy density and heat at the focal point can deflect light and lead to wavefront errors.

A Galilean telescope consists of one lens with a negative focal length (the objective) and another with a positive focal length (the image lens). These two lenses are also placed so the distance between them is equal to the sum of their focal lengths. As one of the lenses is negative, the objective and lens will be close together, and there will be no internal foci. This makes Galilean beam expanders a good choice of high-power laser applications, as there is no problem with high power density within the system. 

For both the Galilean and Keplerian configuration the output beam divergence can be calculated by the beam divergence of the input beam and the diameters of both output and input beams. In both cases, the ratio of input beam divergence to output beam divergence is equal to the ratio of output beam diameter to input beam diameter. This ratio is equal to the magnifying power of the beam expander system.