The distribution and characteristics of surface cracking (i.e. sub-surface damage or SSD) formed during standard grinding processes has been investigated on fused silica glass. The SSD distributions of the ground surfaces were determined by: 1) creating a shallow (18-108 μm) wedge/taper on the surface by magneto-rheological finishing; 2) exposing the SSD by HF acid etching; and 3) performing image analysis of the observed cracks from optical micrographs taken along the surface taper. The observed surface cracks are characterized as near-surface lateral and deeper trailing indent type fractures (i.e., chatter marks). The SSD depth distributions are typically described by a single exponential distribution followed by an asymptotic cutoff in depth (c max ). The length of the trailing indent is strongly correlated with a given process. Using established fracture indentation relationships, it is shown that only a small fraction of the abrasive particles are being mechanically loaded and causing fracture, and it is likely the larger particles in the abrasive particle size distribution that bear the higher loads. The SSD depth was observed to increase with load and with a small amount of larger contaminant particles. Using a simple brittle fracture model for grinding, the SSD depth distribution has been related to the SSD length distribution to gain insight into 'effective' size distribution of particles participating in the fracture. Both the average crack length and the surface roughness were found to scale linearly with the maximum SSD depth (c max ). These relationships can serve as useful rules-of-thumb for nondestructively estimating SSD depth and to identify the process that caused the SSD. In certain applications such as high intensity lasers, SSD on the glass optics can serve as a reservoir for minute amounts of impurities that absorb the high intensity laser light and lead to subsequent laser-induced surface damage. Hence a more scientific understanding of SSD formation can provide a means to establish recipes to fabricate SSD-free, laser damage resistant optical surfaces.

The effect of various HF‐based etching processes on the laser damage resistance of scratched fused silica surfaces has been investigated. Conventionally polished and subsequently scratched fused silica plates were treated by submerging in various HF‐based etchants (HF or NH4F:HF at various ratios and concentrations) under different process conditions (e.g., agitation frequencies, etch times, rinse conditions, and environmental cleanliness). Subsequently, the laser damage resistance (at 351 or 355 nm) of the treated surface was measured. The laser damage resistance was found to be strongly process dependent and scaled inversely with scratch width. The etching process was optimized to remove or prevent the presence of identified precursors (chemical impurities, fracture surfaces, and silica‐based redeposit) known to lead to laser damage initiation. The redeposit precursor was reduced (and hence the damage threshold was increased) by: (1) increasing the SiF62− solubility through reduction in the NH4F concentration and impurity cation impurities, and (2) improving the mass transport of reaction product (SiF62−) (using high‐frequency ultrasonic agitation and excessive spray rinsing) away from the etched surface. A 2D finite element crack‐etching and rinsing mass transport model (incorporating diffusion and advection) was used to predict reaction product concentration. The predictions are consistent with the experimentally observed process trends. The laser damage thresholds also increased with etched amount (up to ∼30 μm), which has been attributed to: (1) etching through lateral cracks where there is poor acid penetration, and (2) increasing the crack opening resulting in increased mass transport rates. With the optimized etch process, laser damage resistance increased dramatically; the average threshold fluence for damage initiation for 30 μm wide scratches increased from 7 to 41 J/cm2, and the statistical probability of damage initiation at 12 J/cm2 of an ensemble of scratches decreased from ∼100 mm−1 of scratch length to ∼0.001 mm−1.

Various ceria and colloidal silica polishing slurries were used to polish fused silica glass workpieces on a polyurethane pad. Characterization of the slurries' particle size distribution (PSD) (using both ensemble light scattering and single particle counting techniques) and of the polished workpiece surface (using atomic force microscopy) was performed. The results show the final workpiece surface roughness is quantitatively correlated with the logarithmic slope of the distribution function for the largest particles at the exponential tail end of the PSD. Using the measured PSD, fraction of pad area making contact, and mechanical properties of the workpiece, slurry, and pad as input parameters, an Ensemble Hertzian Gap (EHG) polishing model was formulated to estimate each particle's penetration, load, and contact zone. The model is based on multiple Hertzian contact of slurry particles at the workpiece-pad interface in which the effective interface gap is determined through an elastic load balance. Separately, ceria particle static contact and single pass sliding experiments were performed showing~1-nm depth removal per pass (i.e., a plastic type removal). Also, nanoindentation measurements on fused silica were made to estimate the critical load at which plastic type removal starts to occur (P crit~5 3 10 À5 N). Next the EHG model was extended to create simulated polished surfaces using the Monte Carlo method where each particle (with the calculated characteristics described above) slides and removes material from the silica surface in random directions. The polishing simulation utilized a constant depth removal mechanism (i.e., not scaling with particle size) of the elastic deformation zone cross section between the particle and silica surface, which was either 0.04 nm (for chemical removal) at low loads (

P crit ). The simulated surfaces quantitatively compare well with the measured rms roughness, power spectra, surface texture, absolute thickness material removal rate, and load dependence of removal rate.

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We demonstrate an additive manufacturing approach to produce gradient refractive index glass optics. Using direct ink writing with an active inline micromixer, we three-dimensionally print multimaterial green bodies with compositional gradients, consisting primarily of silica nanoparticles and varying concentrations of titania as the index-modifying dopant. The green bodies are then consolidated into glass and polished, resulting in optics with tailored spatial profiles of the refractive index. We show that this approach can be used to achieve a variety of conventional and unconventional optical functions in a flat glass component with no surface curvature.

a b s t r a c tThe effects of HF/NH 4 F, wet chemical etching on the morphology of individual surface fractures (indentations, scratches) and of an ensemble of surface fractures (ground surfaces) on fused silica glass has been characterized. For the individual surface fractures, a series of static or dynamic (sliding) Vickers and Brinnell indenters were used to create radial, lateral, Hertzian cone and trailing indentation fractures on a set of polished fused silica substrates which were subsequently etched. After short etch times, the visibility of both surface and subsurface cracks is significantly enhanced when observed by optical microscopy. This is attributed to the increased width of the cracks following etching, allowing for greater optical scatter at the fracture interface. The removal of material during etching was found to be isotropic except in areas where the etchant has difficulty penetrating or in areas that exhibit significant plastic deformation/ densification. Isolated fractures continue to etch, but will never be completely removed since the bottom and top of the crack both etch at the same rate. The etching behavior of ensembles of closely spaced cracks, such as those produced during grinding, has also been characterized. This was done using a second set of fused silica samples that were ground using either fixed or loose abrasives. The resulting samples were etched and both the etch rate and the morphology of the surfaces were monitored as a function of time. Etching results in the formation of a series of open cracks or cusps, each corresponding to the individual fractures originally on the surface of the substrate. During extended etching, the individual cusps coalesce with one another, providing a means of reducing the depth of subsurface damage and the peak-to-valley roughness. In addition, the material removal rate of the ground surfaces was found to scale with the surface area of the cracks as a function of etch time. The initial removal rate for the ground surface was typically 3.5Â the bulk etch rate. The evolving morphology of ground surfaces during etching was simulated using an isotropic finite difference model. This model illustrates the importance that the initial distributions of fracture sizes and spatial locations have on the evolution of roughness and the rate at which material is removed during the etching process. The etching of ground surfaces can be used during optical fabrication to convert subsurface damage into surface roughness thereby reducing the time required to produce polished surfaces that are free of subsurface damage.