Abstract
BackgroundA new algorithm for precise characterisation of rotationally symmetric aspheric surfaces by the conic section and polynomial according to the ISO 10110 standard is described.MethodsThe 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.ResultsThe algorithm reaches sub-nanometre residuals even though the aspheric surface is translated and rotated in the space.Conclusionhe algorithm is computationally robust and an influence of local surface imperfections can be easily reduced by use of a criterion for residuals.
Highlights
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
The description of the aspheric surface by the conic section with a polynomial correction is common in ray tracing software and in producer specifications of aspheric lens
A simple and robust algorithm is still needed to evaluate the conic section from measurement data in the ISO 10110-12 form
Summary
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. Aspheric surfaces are recently widely used in industry. One of their applications is aspheric lens that often needs its precise characterisation of form. The description of the aspheric surface by the conic section with a polynomial correction is common in ray tracing software and in producer specifications of aspheric lens. The conic section surface fitting with a polynomial correction was addressed by several authors [1,2,3,4,5].
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