Improving the accuracy of the caustic test

The caustic or Gaviola test, used for testing aspheric mirrors, has been studied with reference to the research of Schroader ["The caustic test," in Amateur Telescope Making III, A. G. Ingalls, ed. (Kingsport Press, Kingsport, Tenn., 1953), pp. 429-456]. It is shown that the two central formulas, which are used to determine the mirror quality, give significant errors for the large-diameter, short-focal-length mirrors commonly used in astronomical optics. We derive analytically two alternative equations, which are more exact, and show that they lead to significant improvement.