Abstract: For optimization and for image analysis of optical systems it is necessary to calculate derivatives of aberrations. The main task is to calculate a derivative matrix. This has to be done repeatedly during optimization. The conventional finite difference method suffers form two major drawbacks, i.e. inefficiency and inaccuracy. Since some years a new elegant differential technique for analytical calculation of the derivative matrices was developed here first by the senior author and later competed by co-workers. We represent the central parts of the differential technique in this paper, and the concrete application possibilities will not be given in details. A comparison of differential derivative and the conventional finite different method is made at last. The analytical formulas have been derived for the following types of variables: surface radius, axial distance, refractive indices and aspherical coefficients. With the help of an optimally organized program structure we realized an efficient tool for optimization and system analysis. !6
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