A projection exposure apparatus (10) for microlithography has a measuring system (50) for measuring an optical element of the projection exposure apparatus. The measuring system (50) includes an irradiation device (54), which is configured to radiate measuring radiation (62) in different directions (64) onto the optical element (20), such that the measuring radiation (62) covers respective optical path lengths (68) within the optical element (20) for the different directions (64) of incidence, a detection device (56), which is configured to measure, for the respective directions (64) of incidence, the respective optical path lengths covered by the measuring radiation (62) in the optical element (20), and an evaluation device, which is configured to determine a spatially resolved distribution of refractive indices in the optical element (20) by computed-tomographic back projection of the respective measured path lengths with respect to the respective directions of incidence.
