We address the problem of eliminating measurement errors by filtering in such a way as to minimize the smoothing of real data while attempting to remove effects introduced by hardware functions. A critical analysis was performed of a range of existing filters for X-ray mirrors with subnanometer precision, including not only classical smoothing filters but also specialized filters designed for filtering X-ray mirror problems. Because the standard filters under consideration did not allow us to remove diffraction rings and peaks for our X-ray mirrors, we developed a novel technique for such image filtering. The proposed Fourier filtering of the interferometer data allows us to eliminate some of the measurement errors, thereby increasing the accuracy of the measured X-ray mirrors in the subnanometer range.