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Recent Advances in Ultraprecision Machining for Freeform Optics Xiaoqin Zhou, Ph.D. Prof. in Mechanical Engineering School of Mechanical Science and Engineering Jilin University, Changchun, China xqzhou@ Sino-German Symposium on Sustainable Manufacturing, 2014 2 Contents . Freeform optical surfaces o Definitions, Advantages, Mathematical Description, and Engineering Applications; . Diamond turning for freeform surfaces o Fast tool servo, Principle for generating freeform surface, Modeling freeform workpiece, Toolpath generation, topography of machined surface; . Polishing for freeform surfaces o Bonnet polishing (Zeeko), Magneto-rheological finishing (QED), Belt polishing (Optipro), etc. 3 How to define freeform optical surface? . Any non-rotationally symmetric (NRS) or non- axisymmetric optical surfaces (North Carolina State University, Prof. T. Dow, et al, 2005); . Optical surfaces without rotational symmetry, or that depart or deviate from rotational symmetry (Univ. of Rochester, Prof. J. Rolland, et al, 2012); . For the freeform surfaces described in S: z=f(ρ, θ ), the shape of S not only depends on the radial variable ρ, but also the azimuthal variable θ. 4 Geometrical features . Let S(ρ, θ, z) or S(x, y, z) be a freeform surface, then ofor the plane with z=z0, the generated contour is always a noncircular curve; ofor the cylindrical surface S2 (x=ρcosθ,y= ρsinθ,z), the space curve C can be formed by the intersection between the S2 and S, which could not be degenerated into a circle. An example of freeform optical surface, which is represented by