Method for correcting a lithography projection objective, and such a projection objective

A method for correcting at least one image defect of a projection objective of a lithography projection exposure machine, the projection objective comprising an optical arrangement composed of a plurality of lenses and at least one mirror, the at least one mirror having an optically operative surface that can be defective and is thus responsible for the at least one image defect, comprises the steps of: at least approximately determining a ratio VM of principal ray height hMH to marginal ray height hMR at the optically operative surface of the at least one mirror, at least approximately determining at least one optically operative lens surface among the lens surfaces of the lenses, at which the magnitude of a ratio VL of principal ray height hLH to marginal ray height hLR comes at least closest to the ratio VM, and selecting the at least one determined lens surface for the correction of the image defect.