In this paper, a new methodology is presented to derive the aberration state of a lithographic projection system from wafer metrology data. For this purpose, new types of phase-shift gratings (PSGs) are introduced, with special features that give rise to a simple linear relation between the PSG image displacement and the phase aberration function of the imaging system. By using the PSGs as the top grating in a diffraction-based overlay stack, their displacement can be measured as an overlay error using a standard wafer metrology tool. In this way, the overlay error can be used as a measurand based on which the phase aberration function in the exit pupil of the lithographic system can be reconstructed. In practice, the overlay error is measured for a set of different PSG targets, after which this information serves as input to a least-squares optimization problem that, upon solving, provides estimates for the Zernike coefficients describing the aberration state of the lithographic system. In addition to a detailed method description, this paper also deals with the additional complications that arise when the method is implemented experimentally and this leads to a number of model refinements and a required calibration step. Finally, the overall performance of the method is assessed through a number of experiments in which the aberration state of the lithographic system is intentionally detuned and subsequently estimated by the new method. These experiments show a remarkably good agreement, with an error smaller than 5 mλ, among the requested aberrations, the aberrations measured by the on-tool aberration sensor, and the results of the new wafer-based method.