Disclosed are apparatus and methods for determining overlay error in a semiconductor target. For illumination x-rays having at least one angle of incidence (AOI), a correlation model is obtained, and the correlation model correlates overlay error of a target with a modulation intensity parameter for each of one or more diffraction orders (or a continuous diffraction intensity distribution) for x-rays scattered from the target in response to the illumination x-rays. A first target is illuminated with illumination x-rays having the at least one AOI and x-rays that are scattered from the first target in response to the illumination x-rays are collected. An overlay error of the first target is determined based on the modulation intensity parameter of the x-rays collected from the first target for each of the one or more diffraction orders (or the continuous diffraction intensity distribution) and the correlation model.