Top: Sum over the power spectra of all polished particle images in micrograph EMD-2984_0000 of EMPIAR-10061 (left) and the averages and standard deviations of that sum over Fourier rings between 10 Å and 2.5 Å (right). The dashed grey curves are located one std. deviation of each ring above and below the average. The overall rise in spectral power as a function of frequency is a consequence of particle polishing. Bottom: The corresponding plot for the sum over the real components of , instead of the power spectra. Note that the latter term is not only centered around zero, obviating the need to estimate the background intensity, but it also offers a higher signal-to-noise ratio.