Abstract: The workpiece which is moved relative to the tool is processed by a tool configured in the form of a flexible membrane. On the rearward side of the membrane, loading units are arranged with the force of each unit being individually controlled. The pressure distribution exerted by the loading units on the workpiece is varied with time in dependence upon the position of the workpiece. With the method, large optical components such as telescope mirrors and grazing-incidence optical elements for x-ray telescopes can be polished more quickly than by the heretofore known methods. Also non-rotationally symmetrical defects of the surface can be eliminated. An apparatus for carrying out the method of the invention is disclosed.

Abstract: The workpiece which is moved relative to the tool is processed by a tool configured in the form of a strip-shaped flexible membrane. On the rearward side of the membrane, loading units are arranged with the force of each unit being individually controlled. The pressure distribution exerted by the loading units on the workpiece is varied with time in dependence upon the position of the workpiece. With the method, large optical components such as telescope mirrors and grazing-incidence optical elements for x-ray telescopes can be polished more quickly than by the heretofore known methods. Also non-rotationally symmetrical defects of the surface can be eliminated. An apparatus for carrying out the method of the invention is also disclosed.

Abstract: The invention is directed to a method and apparatus for lapping and polishing preferably larger aspheric mirrors such as for astronomical telescopes. The apparatus is in the form of a membrane covering the entire surface to be polished. On the rearward face of the membrane, a plurality of actuators are arranged close to one another and have pressure forces which are individually adjustable. The actuators are stationary relative to the workpiece or perform only small oscillatory movements when compared to the stroke of the lapping tool. With the aid of the actuators, a pressure distribution can be built up over the workpiece which permits different subareas of the workpiece to be removed in different intensities in a single working step.

Abstract: The invention relates to a three-dimensional length-measuring device which employs optical interferometry and in which the comparator principle is satisfied as excellently as possible with respect to all three axes. For this purpose, a workpiece holder which is displaceable in orthogonal horizontal directions carries a three-dimensional reflecting body which defines a measurement space and is in the form of three mutually perpendicular adjacent mirrors (triple mirrors). Extensions of measurement beams with which the three-dimensional reflecting body is measured intersect at a point only slightly offset from the workpiece holder, and to obtain high thermal stability, the measurement table and the housing of the measuring device are made of a material of low thermal expansion.