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We show that, for any rotationally symmetric projection with a single virtual viewpoint, it is possible to design a two-mirror rotationally symmetric system that realizes the projection exactly. These mirror pairs are derived from two coupled differential equations. We give examples in which the projections from the sphere at infinity are stereographic, perspective, and equiresolution.doi:10.1364/ao.45.007205 pmid:16983405 fatcat:azayatrtwjf7fk2qdhbhi2t4fa