| Synchrotron x-ray optics, such as mirrors and monochromators, are used to reflect, focus, or spectrally filter x-ray beams. The effective delivery and utilization of x-ray beams rely on the quality and performance of these optics. One of the key issues affecting optimal performance is the deviation from ideal shape of the optical surfaces. Such deviation can be due to limitations in manufacturing, but, more often than not, they result from thermal and/or mechanical forces on the substrate. Thus, understanding the deformation and the methods used to minimize undesired deformation can ensure acceptable optical performance. This dissertation addresses rigorous analysis and design optimization of optical substrates subjected to thermal and/or mechanical loads.; An optical substrate may receive up to several kW of thermal load from an incident beam. Part of the heat is absorbed by the substrate, and the rest is reflected. To remove the absorbed heat, substrates are cooled either internally or externally. In either case, the resulting temperature profile in the substrate produces thermal deformation, which misdirects the reflected x-ray beam. This undesirable thermal deformation can be minimized by optimal design of the substrate and its cooling. A theoretical formulation of how optimal contact cooling can minimize thermal deformation is developed. Numerical computations are conducted to verify the analytical results. Design optimization is achieved by examining cooling and substrate geometry configurations.; An optical substrate may also be mechanically bent into a concave shape to focus a divergent incident x-ray beam. The desired shape could be cylindrical or elliptical. But, due to Poisson's effect, anticlastic bending occurs in the opposite direction. As a result, the substrate is bent into a saddle shape. Thus, when an incident x-ray beam is focused in one direction, it expands in the orthogonal direction. An optimal design to minimize anticlastic bending is important. Furthermore, in crystalline optical substrates, bending depends on crystal planes and cut orientation. Crystal anisotropy and its effects on the deformation of bendable optics are also described in this dissertation. Analytical, numerical and experimental results are provided. Crystal anisotropy can be advantageously exploited in the optimal optics design to minimize or maximize anticlastic bending. |
