Based on the third-order aberration theory, the equation expressing the relationship between the conic constant and unaberration conjugate points is obtained. The corresponding graphs illuminating the relationship between e2 and β are given. According to the equation and graphs, the analyses of convex and concave surfaces are given in detail. We not only consider the unification of all kinds of reflective testing methods, such as Hindle test, concave elliptical mirror test and Ritchey-Common test etc, but also apply the unaberrational conjugate points test to refractive surface. The auto-collimating and interferometer diagnostic methods are powerful for the manufacture of lens. Kinds of convex and concave aspheric lenses have been manufactured with the detecting methods as mentioned above.