The invention relates to a mirror, in particular for a microlithographic projection exposure system, and to a method for operating a deformable mirror. According to one aspect of the invention, a mirror has an optical active surface (11), a mirror substrate (12), a reflection layer stack (21) for reflecting electromagnetic radiation impinging on the optical active surface (11), and at least one piezoelectric layer (16), which is arranged between the mirror substrate (12) and the reflection layer stack (21) and via a first electrode arrangement located on the side of the piezoelectric layer (16) facing the reflection layer stack (21) and a second side of the piezoelectric layer facing the mirror substrate (12) (16) located electrode arrangement with an electric field to generate a locally variable deformation, said piezoelectric layer (16) having a plurality of columns spatially separated from one another by column boundaries, with an average column diameter of these columns being in the range from 0.1 μm to 50 μm ,
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