In this paper, first we clarify the differences between Contact Edge Roughness (CER) and Line Edge Roughness (LER) emanating from the circular form of the contact edge. Then, we investigate the effects of these differences on the characterization of the spatial and frequency aspects of CER: We define the height-height correlation function for a circular contact hole, use its shape to understand low-frequency deformations of contact holes from the ideal circle, generate model contact holes with predetermined CER and deformations, and finally study the relation between CER and Critical Dimension (CD) variation of the contact holes on a wafer.