Loose abrasive grinding was performed on a wide range of optical workpiece materials [single crystals of Al 2 O 3 (sapphire), SiC, Y 3 Al 5 O 12 (YAG), CaF 2 , and LiB 3 O 5 (LBO); a SiO 2 -Al 2 O 3 -P 2 O 5 -Li 2 O glass-ceramic (Zerodur); and glasses of SiO 2 ∶TiO 2 (ULE), SiO 2 (fused silica), and P 2 O 5 -Al 2 O 3 -K 2 O-BaO (phosphate)]. Using the magneto rheological finishing (MRF) taper wedge technique (where a wedge was polished on each of the ground workpieces and the resulting samples were appropriately chemically etched), the subsurface mechanical damage (SSD) characteristics were measured. The SSD depth for most of the workpiece materials was found to scale as E 1 1∕2 ∕H 1 , where E 1 is the elastic modulus and H 1 is the hardness of the workpiece. This material scaling is the same as that for the growth of lateral cracks, suggesting that lateral cracks are a dominant source for SSD rather than radial/median cracks, as previously proposed. Utilizing the SSD depth data from both this study and others, semiempirical relationships have been formulated, which allows for estimating the SSD depth as a function of workpiece material and important grinding parameters (such as abrasive size and applied pressure).

During subaperture tool grinding and polishing, overlaps of the tool influence function can result in undesirable mid-spatial frequency (MSF) errors in the form of surface ripples, which are often corrected using a smoothing polishing step. In this study, flat multi-layer smoothing polishing tools are designed and tested to simultaneously (1) reduce or remove MSF errors, (2) minimize surface figure degradation, and (3) maximize the material removal rate. A time-dependent convergence model in which spatial material removal varies with a workpiece-tool height mismatch, combined with a finite element mechanical analysis to determine the interface contact pressure distribution, was developed to evaluate various smoothing tool designs as a function of tool material properties, thicknesses, pad textures, and displacements. An improvement in smoothing tool performance is achieved when the gap pressure constant, h¯ (which describes the inverse rate at which the pressure drops with a workpiece-tool height mismatch), is minimized for smaller spatial scale length surface features (namely, MSF errors) and maximized for large spatial scale length features (i.e., surface figure). Five specific smoothing tool designs were experimentally evaluated. A two-layer smoothing tool using a thin, grooved IC1000 polyurethane pad (with a high elastic modulus, Epad=360MPa), thicker blue foam (with an intermediate modulus, Efoam=5.3MPa) underlayer, and an optimized displacement (d t =1mm) provided the best overall performance (namely, high MSF error convergence, minimal surface figure degradation, and high material removal rate).

During sub-aperture tool polishing of glass optics, mid-spatial surface ripples are generated because of material removal non-uniformities during tool linear translation (resulting in feed ripples) and tool pathway step overlaps (resulting in pitch ripples). A variety of tool influence function (TIF) spots, trenches, and patches were created to understand and minimize such ripples on fused silica workpieces after polishing with cerium oxide slurry using a rotating hemispherical pad-foam tool. The feed ripple amplitude can be decreased by reducing the non-uniformities in the pad texture and/or by minimizing a derived feed ripple metric ( r f = V m a x 0.5 V f / R t ) via adjustments in processing parameters. Pitch ripples can be minimized by reducing relative step distance to spot radius ratio ( x s / a t ) and by achieving a flat bottom trench shape cross section or by reducing the material removal per pass. Using the combined methods, an overall ripple error of ∼ 1.2 n m rms has been achieved.

Sub-aperture tool polishing of precision optics requires a detailed understanding of the local material removal [tool influence function (TIF)] at the contact spot between the workpiece and tool to achieve high removal determinism and hence precision of the optic relative to the desired/design surface figure. In this study, the mechanisms influencing and the quantitative prediction of the removal rate and shape of TIF spots during polishing of fused silica glass with cerium oxide slurry using a rotating hemispherical pad-foam tool for a wide variety of process conditions (including tool properties, kinematics, and applied displacements) are investigated. The TIF volumetric removal rate can be estimated utilizing the average relative velocity and contact area using a simple analytical model. In addition, stability of the volumetric removal rate for fixed process conditions is shown to be greatly dependent on the pad preparation and amount of tool use (affecting both pad topography and slurry buildup), whose general behavior shows an increase in removal rate followed by stabilization with polishing time. The determination of the TIF removal shape is more complex. An extended version of the Preston removal model is developed to explain a comprehensive set of measured TIF removal shapes to within ∼ 22 % . This model incorporates a number of phenomena impacting the TIF removal shape including: (a) temporal and spatial dependent relative velocity between the workpiece and tool; (b) an elastic mechanics based, as well as hydrodynamic, pressure distribution; (c) a spatially dependent friction coefficient possibly caused by both reduced slurry replenishment in low velocity regions and pad slurry islands (100 µm scale) and porosity (millimeter scale); and (d) a shear-based removal mechanism on the periphery of the contact spot.

To fabricate high-precision and accurate optics relative to the optical design surface, a high level of deterministic control of material removal (i.e., the tool influence function, TIF) during subaperture tool polishing is required. In this study, a detailed analysis of the pressure distribution, which is a key component of the TIF, has been performed using finite element analysis to couple together solid mechanics and fluid dynamics. Modeling experimental parameters of recently published work reveals that, when considering tool deformation, which in turn influences the fluid film thickness between the tool and workpiece, the effective pressure profile has a flat-top distribution. This flat-top pressure profile differs from the parabolic pressure distributions predicted by Hertzian mechanics. Moreover, the shear contribution is shown here to be a key contributor to material removal, inducing the removal at the periphery of the contact edge and even outside the generally accepted contact area. Finally, the simulated fluid velocities provide evidence of mixed-mode contact polishing, supporting recent experimental findings that also suggest that onset of hydroplaning contributions lead to material removal drop-off.