Prisms have been needlessly neglected as components used in modern optical design. In optical throughput, stray light, flexibility, and in their ability to be used in direct-view geometry, they excel over gratings. Here we show that even their well-known weak dispersion relative to gratings has been overrated by designing doublet and double Amici direct-vision compound prisms that have $14°$ and $23°$ of dispersion across the visible spectrum, equivalent to 800 and $1300\mathrm{lines}/\mathrm{mm}$ gratings. By taking advantage of the multiple degrees of freedom available in a compound prism design, we also show prisms whose angular dispersion shows improved linearity in wavelength. In order to achieve these designs, we exploit the well-behaved nature of prism design space to write customized algorithms that optimize directly in the nonlinear design space. Using these algorithms, we showcase a number of prism designs that illustrate a performance and flexibility that goes beyond what has often been considered possible with prisms.

© 2011 Optical Society of America

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