Abstract
Recently the author described a method that gave the complete solution set for four-mirror anastigmats in which all the mirrors were spherical. Even though a large variety of such systems were shown to exist, most of these were not practical due to large central obstructions. The author has now modified his previous approach by setting up partial systems with good first order characteristics and adding the minimum number of aspheres necessary to give anastigmatic correction. In this way, surveys of useful four-mirror anastigmats with one, two or three-mirrors kept strictly spherical can be carried out.
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