Background: Line-edge roughness (LER) is often measured from top-down critical dimension scanning electron microscope (CD-SEM) images. The true three-dimensional roughness profile of the sidewall is typically ignored in such analyses. Aim: We study the response of a CD-SEM to sidewall roughness (SWR) by simulation. Approach: We generate random rough lines and spaces, where the SWR is modeled by a known power spectral density. We then obtain corresponding CD-SEM images using a Monte Carlo electron scattering simulator. We find the measured LER from these images and compare it to the known input roughness. Results: For isolated lines, the SEM measures the outermost extrusion of the rough sidewall. The result is that the measured LER is up to a factor of 2 less than the true on-wafer roughness. The effect can be modeled by making a top-down projection of the rough edge. Our model for isolated lines works fairly well for a dense grating of lines and spaces as long as the trench width exceeds the line height. Conclusions: In order to obtain and compare accurate LER values, the projection effect of SWR needs to be taken into account.