Measuring the profile of a simulated machined aspherical surface using a nonconventional optimization algorithm

We show an optimization method based on an evolutive algorithm to obtain the profile of a simulated machined aspherical surface starting from a set of noisy discrete Cartesian coordinates (x, y, z), where the experimental coordinates x and y are used to simulate the sagitta z of the analyzed surface. By minimizing an objective function, the proposed method fits the sagitta function to the set of noisy discrete coordinates; thus the geometrical parameters of the simulated surface under test, such as the paraxial radius of curvature, the conic constant, and the aspheric deformation constants, can be obtained. Numerical results show that our method can be successfully applied to retrieve the simulated machined surface profile. (C) 2008 Society of Photo-Optical Instrumentation Engineers.