METHOD FOR THE DESIGN OF MULTIFOCAL OPTICAL ELEMENTS

A method for designing a surface of a multifocal optical element, such as a progressive spectacle lens, includes the steps of partitioning a region into triangles, defining a set of functions, each representing a portion of the surface over one of the triangles, and optimizing the functions. A further embodiment includes the steps of partitioning a region into polygons, and defining a set of functions, each representing a portion of the surface over one of the polygons. Continuity constraints for values of the functions and values of the first derivatives of the functions at boundaries of the polygons are dictated. Continuity constraints for values of the second derivatives of the functions at boundaries of the polygons are not required. The functions are optimized subject to the dictated continuity constraints. Another embodiment includes the steps of partitioning a region into polygons, and defining a set of functions, each representing a portion of the surface over one of the polygons. A plurality of curves along a subset of boundaries of the polygons is determined. Values of at least one of the set including the functions, first derivatives of the functions and second derivatives of the functions, or any combination therefrom, are prescribed at selected vertices of polygons coincident with the plurality of curves. The functions are optimized subject to the prescribed values.