Curvature estimation for optical analysis

In the productive process of moulds for ophthalmic lenses, the availability of a specialized tool for the analysis of the optical property of 3D virtual models of ophthalmic lenses and relevant injection moulds, may reduce the tests on physical prototypes during the design phase. The optical properties of interest are usually power and astigmatism of the lens surface. Both of them are proportional to the geometric curvature of the lens surfaces. Therefore the identification of the optical properties of a surface can be brought back to the computation of the minimum and maximum curvature maps on lens surface. Some commercial software tools able to perform curvature analysis on both physical and virtual models exist, but they show some limitations: methods and algorithms used to compute the desired parameters are not declared, the size of the area used to compute the desired parameter cannot be set by the operator and no estimate on the accuracy of the computed results is given. These last two issues are crucial: the area considered in the analysis should be related to the area actually used; the accuracy of the adopted algorithm should be verified and compared with the eye sensitivity to geometric errors of the lens surface. Aim of the present work is to describe the functioning principles of a software tool for curvature analysis and optical properties computation of either virtual models expressed as high resolution meshes or physical prototypes of lenses sampled using a Coordinate Measuring Machines (CMMs), that overcomes the cited limitations. Such tool will be included into an integrated tool for design, analysis, manufacturing and verification of ophthalmic lenses. In particular, the algorithms used in the development of the software, based on the construction of a least squares regression quadric on the surrounding area of the curvature evaluation point, have been presented. Computing the errors introduced by the tool when evaluating virtual models of known curvature, it is possible to estimate the overall accuracy of the proposed tool, which usually shows a relative error of about 10-4. In order to optimize the tool performances, the error estimation has been performed varying the main influencing parameters: mesh density, size of mesh area considered to build the quadric, and nominal curvature radius of the virtual model.