This paper discusses the automatic shaping technology for the convex hyperbolic surfaces of the secondary mirrors of telescopes with asphericity to 400 ?m, 1 m or more in diameter. It describes a method of testing a convex mirror with an auxiliary Hindle sphere and of optimizing this method by using two Hindle spheres of smaller diameter for one item instead of one sphere of greater diameter. A method is proposed of joining the topographical maps obtained from the results of testing the surface of a hyperboloid with two spheres. The features of fabricated auxiliary equipment (load-bearing fixtures, containers, devices for cementing interface elements) are presented.
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