We present a method to extract aberrations from through-focus aerial images of mask roughness on an Extreme Ultraviolet (EUV) lithography mask. The algorithm uses a phase recovery algorithm based on the Weak Object Transfer Function to recover the phase and amplitude of the roughness, while considering aberrations and partially coherent illumination. Using the self-consistency of the recovered object, aberrations, and measured images as a metric, we optimize over the space of aberrations to estimate aberrations. Partially coherent illumination is needed to allow the effects of the object field and aberrations to be separated. We apply the algorithm to the EUV aerial image microscope, SHARP, using a parameterized ray tracing model to calculate the aberrations from a lower dimensional parameter space.