A projection objective, such as for EUV lithography, for imaging a pattern arranged in an object plane into an image plane with the aid of electromagnetic radiation from the extreme ultraviolet range is provided. The projection objective includes a plurality of mirrors provided with reflective coatings and arranged between the object plane and the image plane. At least one of the mirrors includes a graded reflective coating with a rotationally-asymmetric coating thickness profile in the mirror plane on a substrate with a rotationally-asymmetric or rotationally-symmetric surface profile. The projection objective can exhibit increased overall transmission.