Speaker
Description
One of the major advantages of the xrt ray tracing and wave propagation package is its precise quantitative representation of the material properties of an optical element. xrt supports various kinds of X-ray optics including reflective (mirrors, capillaries), refractive (lenses), and dispersive (crystals, multilayers, zone plates and gratings). Complex amplitudes of reflectivity or transmittivity are calculated on the fly for a given set of direction, energy, and polarization, characteristic to an individual ray, thus eliminating the need for pre-calculated reflectivity maps and subsequent interpolation.
When it comes to the accurate calculation of the reflectivity of a bent crystal, either in Bragg or Laue geometry, there is no simple analytical solution. In the most general case, one would need to solve a system of ODEs called the Takagi-Taupin equations (TTE) numerically. A number of approximations have been developed over the years, including the Multi-Lamellar (for both Bragg and Laue cases) and the Penning-Polder (Laue only) models. Although not as precise as the TTE, they still pose a certain computational challenge.
In our work, we aimed to maintain the precision of the TTE method while increasing the performance to a level sufficient for real-time ray-tracing. We applied the adaptive Dormand-Prince method to calculate the amplitudes of forward-propagating and reflected waves inside a bent crystal and used the OpenCL framework to accelerate calculations. We rely on the pyTTE package to calculate a) elastic constants, required for integration, for a number of predefined crystals, such as Silicon, Germanium, Diamond, Alpha-Quartz, and some others, and b) the local orientation of the diffracting planes inside a crystal. The latter enables us to simulate phenomena such as monochromatic and polychromatic focusing, as well as sagittal focusing in asymmetrically cut Laue crystals. Performance-wise, we can process tens to hundreds of thousands of samples (rays) per second on a consumer-grade GPU.
The correctness of the calculations has been verified by a series of measurements performed at the BXDS beamline, Canadian Light Source, for a variety of asymmetrically cut Silicon crystals in Laue geometry.
Fig.1 Volumetric diffraction in asymmetrically cut Si[111] crystal with anticlastic bend, Laue geometry
| I plan to submit also conference proceedings | Yes |
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