Achromatic N-prism beam expanders: optimal configurations.

In this paper, we calculate optimal prism configurations for achromatic N-prism beam expanders of a single material; we argue that for moderate to high magnifications, that is, M > [2 1(2N-1 -1)]N, the upup ... up-down configuration is generally optimal, in the sense that it maximizes the transmission for given magnification. We also derive exact expressions for the incidence and apex angles that optimize a nonachromatic N-prism beam expander of arbitrary materials. The use of simple three-prism (up-up-down) and four-prism (up-up-up-down) single-material achromatic beam expanders is suggested for applications requiring compactness, achromaticity, and temperature stability.