Twyman effect mechanics in grinding and microgrinding

Assessment of sub-micron subsurface damage in glass

We present a new, to the best of our knowledge, experimental method for assessing sub-micron level subsurface damage (SSD) on optical glass. The method correlates surface characteristics such as the fracture toughness and Young's modulus via nanoindentation with the penetration depth into the tested surfaces at different overall penetration depths, as revealed by magnetorheological finishing spotting techniques. Our results on ground surfaces suggest that low surface roughness does not necessarily imply the absence of SSD. We also compared SSD on surfaces processed by deterministic microgrinding and femtosecond (fs) laser polishing. The fs-laser polished surfaces revealed no detectable SSD, thus establishing the feasibility of fs-laser polishing for precision optical manufacturing.

Grinding of silicon carbide for optical surface fabrication, Part 1: surface analysis

This paper presents a study of the grinding of three different grades of silicon carbide (SiC) under the same conditions. Surface topography is analyzed using coherent scanning interferometry and scanning electron microscopy. The study provides a baseline understanding of the process mechanics and targets effective selection of process parameters for grinding SiC optics with near optical level surface roughness, thus reducing the need for post-polishing. Samples are raster and spiral ground on conventional precision machines with metal and copper-resin bonded wheels under rough, medium, and finish grinding conditions. Material microstructure and grinding conditions affect attainable surface roughness. Local surface roughness of less than 3 nm RMS was attained in both chemical vapor deposition (CVD) and chemical vapor composite (CVC) SiC. The tool footprint is suitable for sub-aperture machining of a large freeform optics possibly without the need for surface finish correction by post-polishing. Subsurface damage will be assessed in Part 2 of this paper series.

Twyman effect in thin curved optics: effects of variable thickness and curvature

Grinding or finishing of thin curved optics introduces surface-localized stresses that may result in bending deformations, thus affecting optical performance (Twyman effect). The Twyman effect depends on local thickness of the optic as well as its curvature. We use numerical and analytical techniques to assess the effects of these variables for shallow and deeply curved axisymmetric optics. A useful metric of comparison, valid for shallow optics, is the deformation of a similar flat optic (window). This comparison is inadequate for more curved optics, which demonstrate a smaller deformation that is now localized in a boundary layer near the optic-free edge. The effects of thickness variation are also presented. Normal deflection and slope for a positive optic (thickness at the center greater than the tip) are well approximated by a constant thickness optic. This is not the case for a negative optic, where deformations near the apex are more pronounced, thus extending significant deformations through the full optic aperture.

Compressive strain formation in surface-damaged crystals

The mechanism of formation of residual strain in crystals with a damaged surface has been studied by transmission electron microscopy in GaAs wafers ground with sandpaper. The samples showed a dislocation network located near the sample surface penetrating to a depth of a few micrometres, comparable to the size of abrasive particles used for the treatment, and no other types of defects were observed. A simple model for the formation of a compressive strain induced by the dislocation network in the damaged layer is proposed, in satisfactory agreement with the measured strain. The strain is generated by the formation of dislocation half-loops at the crystal surface, having the same component of the Burgers vectors parallel to the surface of the crystal. This is equivalent to the insertion of extra half-planes from the crystal surface to the depth of the damaged zone. This model can be generalized for other crystal structures. An approximate calculation of the strain generated from the observed dislocation distribution in the sample agrees with the proposed model and permits the conclusion that this mechanism is in general sufficient to explain the observed compressive strain, without the need to consider other types of defects.

Surface stresses of mixed-mode grinding materials on borosilicate glass

Mixed-mode grinding occurs when a bound abrasive works in both brittle and ductile regimes simultaneously. Substrates ground in a mixed-mode behavior show reduced curvature induced by compressive surface forces than loose abrasives as demonstrated by observing the Twyman effect. This reduction in bending corresponds to reduced subsurface damage. This is verified by controlled acid etching, which shows the exponential decay of the compressive force per unit length. Loose abrasive particles, added to maintain pad wear due to low pressures, have no effect on the measured stresses. If loose abrasive wear ceases, the pads glaze. Glazing creates near-specular surfaces while reducing measurable stress. These effects for borosilicate glass and Trizact grinding pads are explored and quantified.

Subsurface damage in some single crystalline optical materials

We present a nondestructive method for estimating the depth of subsurface damage (SSD) in some single crystalline optical materials (silicon, lithium niobate, calcium fluoride, magnesium fluoride, and sapphire); the method is established by correlating surface microroughness measurements, specifically, the peak-to-valley (p-v) microroughness, to the depth of SSD found by a novel destructive method. Previous methods for directly determining the depth of SSD may be insufficient when applied to single crystals that are very soft or very hard. Our novel destructive technique uses magnetorheological finishing to polish spots onto a ground surface. We find that p-v surface microroughness, appropriately scaled, gives an upper bound to SSD. Our data suggest that SSD in the single crystalline optical materials included in our study (deterministically microground, lapped, and sawed) is always less than 1.4 times the p-v surface microroughness found by white-light interferometry. We also discuss another way of estimating SSD based on the abrasive size used.

Loose abrasive lapping hardness of optical glasses and its interpretation

We present an interpretation of the lapping hardness of commercially available optical glasses in terms of a micromechanics model of material removal by subsurface lateral cracking. We analyze data on loose abrasive microgrinding, or lapping at fixed nominal pressure, for many commercially available optical glasses in terms of this model. The Schott and Hoya data on lapping hardness are correlated with the results of such a model. Lapping hardness is a function of the mechanical properties of the glass: The volume removal rate increases approximately linearly with Young's modulus, and it decreases with fracture toughness and (approximately) the square of the Knoop hardness. The microroughness induced by lapping depends on the plastic and elastic properties of the glass, depending on abrasive shape. This is in contrast to deterministic microgrinding (fixed infeed rate), where it is determined from the plastic and fracture properties of the glass. We also show that Preston's coefficient has a similar dependence as lapping hardness on glass mechanical properties, as well as a linear dependence on abrasive size for the case of brittle material removal. These observations lead to the definition of an augmented Preston coefficient during brittle material removal. The augmented Preston coefficient does not depend on glass material properties or abrasive size and thus describes the interaction of the glass surface with the coolant-immersed abrasive grain and the backing plate. Numerical simulations of indentation are used to locate the origin of subsurface cracks and the distribution of residual surface and subsurface stresses, known to cause surface (radial) and subsurface (median, lateral) cracks.