Planar photonic crystals and other microstructured surfaces have important applications in a number of emerging technologies. However, these structures can be difficult to fabricate in a consistent manner. Rapid, precise measurements of critical parameters are needed to control the fabrication process, but current measurement techniques tend to be slow and often require that the sample be modified in order to make the measurement. Optical scattering can provide a rapid, non-destructive, and precise method for measuring these structures, and optical scatterometry is a good candidate technique for measuring micro-structured surfaces for process control. However, variations in the profile, such as those caused by edge roughness, can make significant contributions to the uncertainty in scatterometry measurements. Because of the multi- dimensional nature of the problem, modeling these variations can be computationally expensive. This dissertation examines the effects of edge roughness on optical scatterometry signals. Rigorous numerical simulations show that the effects of edge roughness are sensitive to the correlation length and the frequency content of the roughness as well as its amplitude. However, these rigorous calculations are computationally expensive. A less computationally expensive model based on a generalized Bruggeman effective medium approximation is developed and shown to be effective for modeling the effects of short correlation length edge roughness on optical scatterometry signals
