Computationally efficient on X-ray-based measurement of overlays

Methods and systems for determination of overlay and edge placement errors of device structures on the basis of measurement data by means of X-ray diffraction are presented. The overlay errors between different layers of an object of measurement is estimated based on the change in intensity within each of X-ray diffraction order, which is measured under a plurality of different angles of incidence and azimuthal angles. Estimating the overlay comprises a parameterization of the intensity modulations of joint systems, so that a low-shape modulation is described by a set of basis functions and a high frequency overlay modulation is described by affine circular function containing a parameter indicative of an overlay. In addition to overlay a shape parameter of the measurement object is estimated on the basis of a fit analysis of a measurement model for the intensities of the measured diffraction orders. In some examples, the estimation of the overlay, and estimating one or more shape parameter values ​​are performed simultaneously.