In certain aspects, catadioptric projection objectives for imaging a pattern from an object field arranged in an object surface of the projection objective onto an image field arranged in an image surface of the projection objective include a first objective part configured to image the pattern from the object surface into a first intermediate image, and having a first pupil surface, a second objective part configured to image the first intermediate image into a second intermediate image, and having a second pupil surface optically conjugate to the first pupil surface, and a third objective part configured to image the second intermediate image into the image surface, and having a third pupil surface optically conjugate to the first and second pupil surface. A pupil mirror having a reflective pupil mirror surface is positioned at or close to one of the first, second and third pupil surface. A pupil mirror manipulator operatively connected to the pupil mirror and configured to vary the shape of the reflective surface of the pupil mirror allows for dynamically correcting imaging aberrations originating from lens heating, compaction and other radiation induced imaging aberrations occurring during operation of the projection objective.