Recent advances have made it viable to fabricate optical surfaces that are not rotationally symmetric using a new generation of diamond-turning machines. These surfaces can greatly extend the field of view of optical systems and provide compact solutions. Through the use of optimization and analysis methods that track aberration content throughout the field of view, two non-rotationally symmetric designs that provide a compact mirror based geometry with a 10 degree full field of view are presented and compared. It is shown that a φ-polynomial surface provides superior optical performance to an anamorphic asphere because the surface can be made comatic.© (2010) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.