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.