Robust and precise algorithm for aspheric surfaces characterization by the conic section

Abstract

Background: A new algorithm for precise characterisation of rotationally symmetric aspheric surfaces by the conic section and polynomial according to the ISO 10110 standard is described. Methods: The algorithm uses only the iterative linear least squares. It uses fitting the surface form in a combination with terms containing its spatial derivatives that represent infinitesimal transformations of form. Results: The algorithm reaches sub-nanometre residuals even though the aspheric surface is translated and rotated in the space. Conclusion: he algorithm is computationally robust and an influence of local surface imperfections can be easily reduced by use of a criterion for residuals.