The present invention relates to an arrangement of an optical imaging device for microlithography, in particular for the use of light in the extreme UV range (EUV), with a support structure (111), an optical element (109) and a cooling device (112), the support structure (111) is designed to support the optical element (109), the optical element (109) being connected to the support structure (111) for support via at least one support unit (111.1). The cooling device (112) is designed to cool the optical element (109), the cooling device (112) making contact with the optical element (109) for heat transfer. The cooling device (112) is connected to the optical element (109) in such a way that the cooling device (112) is supported by the at least one support unit (111.1).
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