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The design of an aplanatic optical system with two aspheric surfaces according to a method developed by Vaskas is treated in more detail. The shape of each aspheric surface is determined by a differential equation. It is shown that the ray trajectories through the optical surfaces, located between the two aspheres, are found by solving a system of N linear equations where N is the number of intermediate surfaces. An example of an aspherized aplanatic system is given.

A method of measuring the shape of high numerical aperture (NA <0.95), convex or concave, aspheric surfaces is described. The aspheric slope may be as large as 1200 waves/rad. The method is applied in two steps. First, a standard measurement is performed to obtain a reference surface. Second, the reproducibility of the fabrication of aspheric surfaces is tested by means of a holographic comparison method. The measuring error is smaller than 0.1 microm.