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(2^N-1 - 1)]^N, the up-up … 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.

© 1985 Optical Society of America

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