An optical system has a plurality of elements arranged to image radiation at a wavelength λ from an object surface to an image surface, the elements include mirror elements having a reflective surface positioned at a path of radiation. At least one of the mirror elements is a pupil mirror having a pupil mirror surface arranged at or near to a pupil surface of the optical system. At least one of the remaining mirror elements is a highly loaded mirror having a mirror surface arranged at a position where at least one of a largest value of a range of angles of incidence and a largest value of an average angle incidence of all remaining mirrors occurs, where the remaining mirrors include all mirrors except for the pupil mirror. The pupil mirror surface is formed by a reflective coating designed as a one-dimensionally graded coating including a multilayer stack of layers of different materials, the layers having a geometrical layer thickness which varies according to a first grading function in a first direction of the coating and which is substantially constant in a second direction perpendicular to the first direction. The mirror surface of the highly loaded mirror is coated with a reflective mirror coating designed as a graded coating according to a second grading function.