Effects of multilayer roughness are explored based on rigorous electromagnetic simulation with TEMPEST and aerial image calculation with SPLAT. The TEMPEST simulation on small roughness features using an average material properties technique is validated by comparison with the simulation using finer gridding and approximate analytical methods. Simulations for rms roughness from 0 to 1.4 nm show a reflectivity reduction, a phase shift, and a polarization dependence. Midsize Gaussian defects are shown to be slightly less printable in the presence of roughness. For extreme ultraviolet lithography systems with roughness rms of 0.15 rim, the above effects are very second order.