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

Abstract

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 7.78mm and a paraboloid with vertex radius 6.50mm are shown.