Crystal diffraction prediction and partiality estimation using Gaussian basis functions

Brehm, W.; White, T.; Chapman, H.N.

doi:10.1107/S2053273323000682

Figure 1
The geometric construction visualizing the construction of the covariance matrices of the distributions of diffractive power in reciprocal space and the volume probed by an incident beam. The arrows indicate the components, akin to error bars, that the different distributions contribute to the covariance matrix in a 2D cut. The same contributions have a different effect on $[{\bf k}_{{\rm in}}]$ , $[\Delta{\bf k}]$ and $[{\bf k}_{{\rm out}}]$ , and where they have an effect they are indicated with the same colour as where they were introduced. The distribution of wavelengths in the incident beam leads to a distribution of lengths of $[{\bf k}_{\rm in}]$ ; the standard deviation is drawn with purple arrows. The distribution of incident-beam directions leads to different starting points of $[{\bf k}_{\rm in}]$ in the Ewald construction; its standard deviation is drawn in red. The scattering power of the crystal is smeared rotationally by mosaicity, drawn with brown arrows, and smeared radially by (a simplified) strain, drawn in cyan. The reciprocal peak shape as depicted in light green is a stylized shape transform, which too will be approximated as a Gaussian. To smooth the prediction over a range of output directions in order to simulate the detector point spread function and facilitate efficient sampling of the signal, a distribution of diffraction directions can be introduced, the standard deviation of which is drawn in dark blue.

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ISSN: 2053-2733

Volume 79| Part 2| March 2023| Pages 145-162

https://doi.org/10.1107/S2053273323000682

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