The invention is directed to a method and an arrangement for cleaning optical surfaces of reflection optics which are arranged in a plasma-based radiation source or exposure device arranged downstream and contaminated by debris particles emitted by a hot plasma of the radiation source. It is the object of the invention to find a novel possibility for in-situ cleaning of the optical surfaces of reflection optics which are contaminated by debris in plasma-based radiation sources so as to allow an integrated generation of known gas radicals and the isotropic distribution thereof on the contaminated optical surfaces. According to the invention, this object is met in that the gas radicals are generated by dielectrically impeded discharge between two surface electrodes along the entire optical surface. The gas radicals are generated almost exclusively by electron transfer on at least one barrier layer which covers the entire surface of at least one of the surface electrodes, an AC voltage in the Hz to kHz range is applied to the surface electrodes for periodically eliminating the charge polarization at the barrier layer so that a cold plasma is generated continuously and the deposited debris particles are removed as gaseous reaction products by the gas flow guided over the optical surface.