A new class of variable-radii diffraction optics for high-resolution x-ray spectroscopy at the National Ignition Facility (invited).

A new class of crystal shapes has been developed for x-ray spectroscopy of point-like or small (a few mm) emission sources. These optics allow for dramatic improvement in both achievable energy resolution and total throughput of the spectrometer as compared with traditional designs. This class of crystal shapes, collectively referred to as the Variable-Radii Spiral (VR-Spiral), utilize crystal shapes in which both the major and minor radii are variable. A crystal using this novel VR-Spiral shape has now been fabricated for high-resolution Extended X-ray Absorption Fine Structure (EXAFS) experiments targeting the Pb-L3 (13.0 keV) absorption edge at the National Ignition Facility. The performance of this crystal has been characterized in the laboratory using a microfocus x-ray source, showing that high-resolution high-throughput EXAFS spectra can be acquired using this geometry. Importantly, these successful tests show that the complex three-dimensional crystal shape is manufacturable with the required precision needed to realize the expected performance of better than 5 eV energy resolution while using a 30 mm high crystal. An improved generalized mathematical form for VR-Spiral shapes is also presented allowing improved optimization as compared to the first sinusoidal-spiral based design. This new formulation allows VR-Spiral spectrometers to be designed at any magnification with optimized energy resolution at all energies within the spectrometer bandwidth.

Effect of workpiece curvature on the tool influence function during hemispherical sub-aperture tool glass polishing.

The influence of workpiece curvature on the tool influence function spot during polishing of fused silica glass with cerium oxide slurry, while using a rotating hemispherical pad-foam tool for a wide variety of process conditions (tool displacement, inclination angle, and rotation rate), has been investigated. (Workpiece curvature ranged from 500 mm radius concave to 43 mm radius convex.) The TIF spot decreases in diameter and increases in the peak removal rate on more convex workpieces. In contrast, the TIF spot increases both in diameter and peak removal rate on more concave workpieces. For the range of workpiece curvatures investigated, both the spot size and the peak removal rate changed significantly, as much as 2 times. An elastic sphere-sphere contact mechanics model, which utilizes both a modified displacement (that leads to a change in the applied load) as well as a mismatch factor (that influences the pressure distribution shape), has been developed. The model was validated using both offline load-displacement measurements and finite-element analysis simulations. The model quantitatively describes the measured change in the relative contact diameter and relative pressure distribution, as well as semiquantitively describes the change in the relative volumetric removal rate on a large variety of TIF spots. The change in the volumetric removal rate for convex workpieces is a result of the balance between a decreasing spot size (reducing removal) and an increasing peak pressure (increasing removal), which usually results in relatively small changes in volumetric removal. In the case of concave workpieces, the volumetric removal rate change is also governed by a similar balance, but the spot size increase contribution dominates, resulting in a significant increase in volumetric removal rate. Understanding these trends can enable methods to add greater determinism during the fabrication of freeform optics by adjusting polishing parameters (such as dwell time) while the tool translates along a workpiece surface with different local curvatures.

Mechanisms influencing and prediction of tool influence function spots during hemispherical sub-aperture tool polishing on fused silica.

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.