The key mechanisms & predictive models that determine the spatially dependent material removal rate (called the tool influence function (TIF) spots) during hemispherical sub-aperture tool polishing on flat & curved fused silica glass are presented.

A series of static and sliding indentation (ie, scratching) was performed and characterized on a wide range of optical workpiece materials [single crystals of Al2O3 (sapphire), SiC, Y3Al5O12 (YAG), CaF2, and LiB3O5 (LBO); a SiO2-Al2O3-P2O5-Li2O glass ceramic (Zerodur); and glasses of SiO2:TiO2 (ULE), SiO2 (fused silica), and P2O5-Al2O3-K2O-BaO (Phosphate)] at various applied loads using various indenters (Vickers, 10 mu m conical, and 200 mu m conical). Despite having different load dependencies, the lateral crack depth formed during sliding indentation quantitatively scales with that formed during static indentation, explaining why static indentation has been historically effective in describing various grinding parameters. Depending on the indenter geometry, the amount of residual trench damage (plastic deformation and local fracturing) during sliding indentation was often enhanced by more than an order of magnitude compared with static indentation. A simple ploughing scratch model, which considers both tangential and normal stresses (where the tangential stress is amplified by relatively small tangential contact area), explains this enhancement and other observed trends. Accounting for the high correlation between residual trench depth and volumetric fracturing, the model is extended to estimate the amount of fracture damage as a function of the material properties of the workpiece, indenter geometry, and applied load. Such a model has utility in the design of optimized grinding processes, particularly the abrasive geometry. Finally, at higher loads (>1 N), lateral cracks were often observed to preferentially propagate in the forward scratching direction, as opposed to perpendicular to the scratch as typically observed. High-speed imaging of the scratch process confirms that these cracks propagate ahead of the sliding indenter during the scratching event. Finite element stress analysis suggests the ploughing frictional forces increase the mode I tensile stresses at the leading edge of the sliding indenter explaining the direction of crack propagation of such cracks.

A series of controlled grinding experiments, utilizing loose or fixed abrasives of either alumina or diamond at various particle sizes, were performed on a wide range of optical workpiece materials [single crystals of Al2O3 (sapphire), SiC, Y3Al5O12 (YAG), CaF2, and LiB3O5 (LBO); a SiO2-Al2O3-P2O5-Li2O glass ceramic (Zerodur); and glasses of SiO2:TiO2 (ULE), SiO2 (fused silica), and P2O5-Al2O3-K2O-BaO (phosphate)]. The material removal rate, surface roughness, and morphology of surface fractures were measured. Separately, Vickers indentation was performed on the workpieces, and the depths of various crack types as a function of applied load was measured. Single pass grinding experiments showed distinct differences in the spatial pattern of surface fracturing between the loose alumina abrasive (isolated indent-type lateral cracking) and the loose or fixed diamond abrasive (scratch-type elongated lateral cracking). Each of the grinding methods had a removal rate and roughness that scaled with the lateral crack slope, sℓ (i.e., the rate of increase in lateral crack depth with the applied load) of the workpiece material. A grinding model (based on the volumetric removal of lateral cracks accounting for neighboring lateral crack removal efficiency and the fraction of abrasive particles leading to fracture initiation) and a roughness model (based on the depth of lateral cracks or the interface gap between the workpiece and lap) are shown to quantitatively describe the material removal rate and roughness as a function of workpiece material, abrasive size, applied pressure, and relative velocity. This broad, multiprocess variable grinding model can serve as a predictive tool for estimating grinding rates and surface roughness for various grinding processes on different workpiece materials.

The following study presents useful quantitative rules, based on fundamental mechanisms, for the determining the grinding & polishing rate and grinding roughness during optical fabrication for a variety of optical workpiece materials.

A partial charge-based chemical polishing model has been developed, which can serve as metric for describing the relative polishing material removal rate for different combinations of slurries and workpieces. A series of controlled polishing experiments utilizing a variety of colloidal polishing slurries (SiO2, CeO2, ZrO2, MgO, Sb2O5) and optical materials [single crystals of Al2O3 (sapphire), SiC, Y3Al5O12 (YAG), CaF2, and LiB3O5 (LBO); a SiO2-Al2O3-P2O5-Li2O glass ceramic (Zerodur); and glasses of SiO2:TiO2 (ULE), SiO2 (fused silica), and P2O5-Al2O3-K2O-BaO (Phosphate)] was performed and its material removal rate was measured. As previously proposed by Cook (J Non-Cryst Solids. 1990;120:152), for many polishing systems, the removal rate is governed by a series of chemical reactions which include the formation of a surface hydroxide, followed by condensation of that hydroxyl moiety with the polishing particle, and a subsequent hydrolysis reaction. The rate of condensation can often be the rate limiting step, thus it can determine the polishing material removal rate. By largely keeping the numerous other factors that influence material removal rate fixed (such as due to particle size distributions, interface interactions, pad topography, kinematics, and applied pressure), the material removal rate is shown to scale exponentially with the partial charge difference ((wp-s)) between the workpiece and polishing slurry particle for many of the slurry-workpiece combinations indicating that condensation rate is the rate limiting step. The partial charge () describes the equilibrium distribution of electron density between chemically bonded atoms and is related to the electronegativity of the atoms chemically bonded to one another. This partial charge model also explains the age-old experimental finding of why cerium oxide is the most effective polishing slurry for chemical removal of many workpieces. Some of the slurry-workpiece combinations that did not follow the partial charge dependence offer insight to other removal mechanisms or rate limiting reaction pathways.

Convergent Polishing is a novel polishing system and method for finishing flat and spherical glass optics in which a workpiece, independent of its initial shape (i.e., surface figure), will converge to final surface figure with excellent surface quality under a fixed, unchanging set of polishing parameters in a single polishing iteration. In contrast, conventional full aperture polishing methods require multiple, often long, iterative cycles involving polishing, metrology and process changes to achieve the desired surface figure. The Convergent Polishing process is based on the concept of workpiece-lap height mismatch resulting in pressure differential that decreases with removal and results in the workpiece converging to the shape of the lap. The successful implementation of the Convergent Polishing process is a result of the combination of a number of technologies to remove all sources of non-uniform spatial material removal (except for workpiece-lap mismatch) for surface figure convergence and to reduce the number of rogue particles in the system for low scratch densities and low roughness. The Convergent Polishing process has been demonstrated for the fabrication of both flats and spheres of various shapes, sizes, and aspect ratios on various glass materials. The practical impact is that high quality optical components can be fabricated more rapidly, more repeatedly, with less metrology, and with less labor, resulting in lower unit costs. In this study, the Convergent Polishing protocol is specifically described for fabricating 26.5 cm square fused silica flats from a fine ground surface to a polished ~λ/2 surface figure after polishing 4 hr per surface on a 81 cm diameter polisher.