| 摘要 |
A method for designing a surface of an optical element includes the steps of prescribing initial wavefronts, selecting an initial parameterized representation of the surface, choosing a cost function in the parameters, and optimizing the cost function with respect to the parameters. The step of optimizing includes the steps of calculating a refracted wavefront for each of the initial wavefronts and analytically computing derivatives of the cost function. The method may also include the steps of precomputing eikonal functions between points in the vicinity of the initial wavefronts. Then the refracted wavefronts are calculated from the precomputed eikonal functions. A method for designing at least one surface of a multifocal optical element includes the step of concurrently considering in a design of the at least one surface any combination of an astigmatism distribution, a progressive power distribution and a prism distribution. When designing at least one surface of an optical element, a representation for each particular surface is created with a set of discrete points. Then for each discrete point in the set, nearest neighbor points from the set are selected, the particular surface is approximated in a vicinity of the discrete point by a polynomial of a predetermined order in two variables of the particular surface, and the coefficients of the polynomial are determined according to the selected nearest neighbor points without requiring continuity between polynomials for neighboring discrete points.
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