By means of third-order optical theory as well as ray-tracing simulations we have investigated the feasibility of wide-field imaging atmospheric Cherenkov telescopes with a reflective prime-focus design. For a range of desired optical resolutions, we have determined the largest available field-of-view of single-piece spherical, single-piece parabolic, tessellated spherical, tessellated parabolic and Davies-Cotton designs, always considering a wide range of design parameters. The Davies-Cotton design exhibits a surprising similarity to the tessellated parabolic design in its qualitative behaviour. Also, elliptic telescope designs with better off-axis imaging properties than Davies-Cotton are presented. We show that by using f/2 optics it is possible to build prime-focus telescopes with a full field-of-view of 10 degree at 0.1 degree resolution.
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