Fractal Roughness Structure of Diamond-Turned Copper Mirrors

Single-point diamond turning of suitable materials (copper, aluminum, and electroless-plated nickel, etc.) can generate high precision mirrors and aspherical optics rapidly and repeatedly. We have examined the diamond-turned copper mirrors that exhibit a high-frequency periodic feature with an atomic force microscope on various scales. Like other super-smooth surfaces, such as super-ground surfaces, single-point-diamond-turned surfaces may also be identified as a self-affine fractal in the stochastic sense with its correlation length. The exponent for root-mean-square roughness was obtained to be 0.28 for a feed rate of 1.4 μm/rev. With this value, we can predict the roughness value of the single-point-diamond-turned copper mirrors at any scale length, if the scale is within the correlation length, and provided that one such value of a scale is known. The roughness exponent is a very useful parameter, knowledge of which helps to improve the quality of the mirror surface and evaluate its performance in optical instruments.