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Figure 8
Sensitivity of reconstruction method, evaluated using synthetic data. (a) The input synthetic GISAXS data (black curve), Id(qz) (example on left) can be iteratively fitted (purple curve), from which we reconstruct the undistorted scattering [IR(Qz), right]; the corresponding transmission channel (blue Id, Tc) and reflection channel (red Id, Rc) components are calculated using the known transmission ([|T|]) and reflectivity ([|R|]) curves (shown in center). Two different examples (right) are shown (reconstruction shown in purple, true scattering in black), demonstrating that the method works for sharp and diffuse features (with artifacts appearing towards the edges of the available qz range). (b) The method is relativity robust to errors in the assumed incident angle ([\theta _{\rm i}]) and film critical angle ([\theta _{\rm c}]). For a typical data set (left) with intentional errors introduced into [\theta _{\rm i}], the reconstruction becomes correspondingly shifted (right, numbers indicate intentional error in [\theta _{\rm i}]). The fit-error ([\chi _{\rm d}^{2}]) with respect to errors in the angles has a deep minimum at the true value, allowing this value to also be iteratively refined. (c) Errors in the assumed transmission and/or reflectivity curves necessarily corrupt the reconstruction. However, for modest errors in these curves, the reconstruction remains qualitatively correct. In the example presented here, incorrect transmission and reflectivity curves were used intentionally (center; true curves in black). The resulting reconstruction (right) exhibits artifacts yet nevertheless maintains the correct overall shape and intensity.

IUCrJ
Volume 5| Part 6| November 2018| Pages 737-752
ISSN: 2052-2525
https://doi.org/10.1107/S2052252518012058