Single crystal calcium fluoride (CaF2) shows significant variation in material properties as a function of crystallographic orientation. The surfaces generated by material removal processes such as diamond turning are influenced by this anisotropy and consequently show periodic undulations aligned with the crystal structure. This article explores the relationship between surface figure and cutting forces measured during the diamond turning of single crystal calcium fluoride. The cutting forces, when mapped to the physical geometry of CaF2 piano (flat) optics, show good correlation with surface figure measured by interferometry. A model is presented to predict the surface figure error from the experimentally measured normal component of the cutting force. The model also shows how the surface figure obtained under various machining parameters may be extrapolated from force measurements made during a single diamond turning operation. (C) 2005 American Vacuum Society.