Modelling of Polishing Tools for High Spatial Frequency Defect Correction on Aspherical Surfaces

Abstract

Nowadays, precision Computer Controlled Optical Surfacing (CCOS) and processes like Ion Beam Finishing (IBF) or Magneto-Rheological Finishing (MRF) allow manufacturing of fused silica optics with nanometer precision. However, High spatial frequency defects remain on the optics and need to be previously smoothed. Full aperture semi-flexible polishing tools can be used, as they can guarantee uniform pressure on low frequency patterns to preserve the pre-formed aspherical shape while maintaining a high pressure differential on high frequency defects, thus smoothing them. That behavior can be obtained with tools that combine a continuous flexible layer for low frequency compliance and a fractionate viscoelastic polishing layer for high frequency defect polishing. The main goals of this study are predicting smoothing efficiency and form control of different tools, and then determining the best tool to achieve a good balance between them. To do this, a multiscale model is developed. First, at the whole tool scale, for a given aspherical shape, the largest misfit between tools and surfaces is mathematically determined, depending on machining parameters. Then a finite-element parametric study is performed and yields for the flexible layer the best mechanical properties and thickness as well as the optimal applied force to achieve pressure homogeneity at the global aspherical shape level. Second, at the viscoelastic polishing layer level, the Discrete Element Method (DEM) is used to investigate the tool – workpiece interface. A model based on the viscoelastic cohesive beam method is developed, thus allowing taking into account the polishing layer’s dynamic response depending on the excitation frequency. The optical surface is also modeled by interpenetrated discrete elements, paving the way for a full-DEM model of the polishing layer – workpiece interface. Smoothing simulations are separated in two steps : the first one is the initial pressure application, leading to an initial state of full tool – surface contact with an homogeneous pressure. Then the tool is moved over the surface and the dynamic pressure is calculated depending on defect and polishing layer properties as well as tool kinematics. By analyzing the pressure differential on defects it becomes possible to calculate the smoothing efficiency of a given polishing layer and therefore optimize its properties depending on the defects that need to be smoothed.