A projection exposure apparatus includes a projection lens, a wavefront manipulator and a wavefront measuring device for measuring a wavefront in the projection lens. The wavefront measuring device includes a Moiré grating arrangement having an object grating and an image grating which are designed to be arranged in an object plane and an image plane, respectively, of the projection lens. The object grating and the image grating are coordinated with one another in a manner true to scale in such a way as to generate a Moiré superimposition pattern from an imaging of the object grating onto the image plane and the image grating. The Moiré grating arrangement is designed in such a way as to simultaneously generate the Moiré superimposition pattern for a plurality of field points of an object field in the object plane and/or of an image field in the image plane.