Line width roughness (LWR) has been identified as a potential source of uncertainty in scatterometry measurements, and characterizing its effect is required to improve the method's accuracy and to make measurements traceable. In this work, we extend previous work by using rigorous coupled wave (RCW) analysis on two-dimensionally periodic structures to examine the effects of LWR. We compare the results with simpler models relying upon a number of effective medium approximations. We find that the effective medium approximations yield an approximate order of magnitude indicator of the effect, but that the quantitative agreement may not be good enough to include in scatterometry models.© (2009) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.