Measuring conic constant and vertex radius of fast convex conic surfaces from a set of Hartmann patterns

•We use an ellipsoidal null screen to apply a Hartmann test in convex conic surfaces.•From several Hartmann patterns we obtain the conic constant and vertex radius.•We simulate Hartmann patterns when the optical system has symmetry of revolution.•We obtain experimental results for small conic surfaces like contact lenses.

A method for measuring conic constant and vertex radius of fast conic surfaces from Hartmann patterns obtained for different axial positions of the surface is proposed. For each pattern the evaluation of the surface is carried out through an exact ray tracing algorithm, including the vector form of the Law of Reflection. Every reconstructed surface is fitted to an even radial polynomial; analyzing the behavior of the coefficients for the second, fourth, and sixth order terms of the polynomial in terms of the axial position, the right values of the conic constant and the vertex radius are found. Experimental results for a sphere with radius 7.78 mm and a paraboloid with vertex radius 6.50 mm are shown.