A method for producing a reflecting optical element for a projection exposure apparatus (1). The element has a substrate (30) with a substrate surface (31), a protection layer (38) and a layer partial system (39) suitable for the EUV wavelength range. The method includes: (a) measuring the substrate surface (31), (b) irradiating the substrate (30) with electrons (36), and (c) tempering the substrate (30). Furthermore, an associated reflective optical element for the EUV wavelength range, a projection lens with a mirror (18, 19, 20) as reflective optical element, and a projection exposure apparatus (1) including such a projection lens.