Axially astigmatic surfaces have different curvatures in orthogonal di
ameters. Toroidal and spherocylindrical optical surfaces are two mathe
matically different special cases of axially astigmatic surfaces as no
ted by Menchaca and Malacara (1986), but they are almost identical in
the vicinity of the optical axis. The difference between these two sur
faces increases when the distance to the optical axis increases. We st
udy the general properties of astigmatic surfaces and some special int
eresting cases. (C) 1996 Society of Photo-Optical Instrumentation Engi
neers.