Mirror, in particular for a microlithographic projection exposure apparatus

A method for producing a mirror for a microlithographic projection exposure apparatus, comprising:

• applying a layer system on a mirror substrate, said layer system having a reflection layer stack configured to reflect electromagnetic radiation impinging on the optical effective surface,
• applying a layer composed of a group III nitride before the reflection layer stack is applied to the mirror substrate, wherein the group III nitride comprises at least one of gallium nitride (GaN), aluminum nitride (AlN) or aluminum gallium nitride (AlGaN), and wherein the layer has a thickness of at least 0.1 μm and of at most 100 μm, and
• working a surface profile into the layer, wherein the surface profile at least partly compensates for mechanical strain formed between layers of the reflection layer stack.

The optical system as claimed in 9, wherein the microlithographic projection exposure apparatus is an illumination device or a projection lens.