Abstract: A damping device of an optical element of a projection exposure machine includes at least two mass dampers arranged spaced apart from one another, the vibration absorbers each having at least one damper mass and at least one damping element and the damper masses of the at least two mass dampers being interconnected by at least one connecting element. The optical element can be part of a projection exposure machine.

Abstract: A hexapod system for aligning an optical element in semiconductor clean rooms or in a vacuum, particularly in an illumination device for a microlithographic EUV projection exposure apparatus, comprises six hexapod supporting structures (42, 44, 46, 94; 42?, 44?, 46?, 94?, 106). Using a set of at least two replaceable spacer elements (94; 94?) having a different extent in at least one direction, at least one of the six supporting structures (42, 44, 46, 94; 42?, 44?, 46?, 94?, 106) can be adjusted. The latter is adapted so that a spacer element (94; 94?) can be removed or a spacer element (94; 94?) can be added while the coupling of the first coupling end (46; 46?) to the carrying structure (38; 38?) and the coupling of the second coupling end (54a; 54?) to the optical element (34; 34?) are maintained.