An astigmatic optical surface has two different orthogonal curvatures. There are a great number of them, but only a few are in common use in optical instruments. These are similar in shape but have some important differences to be considered. These differences must be taken into account during the design, fabrication, and testing of optical systems that includes such surfaces. A comparative description of some surfaces is made with some of its characteristics reviewed. Finally, an analysis of their properties and testing possibilities is made. An important conclusion of this analysis is that the two main surfaces, the toroidal and the spherocylindrical surfaces, may differ in their shape by an ashtray component (an x~(2)y~(2) term) as large as several wavelengths.
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