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Figure 3
Schematics indicate the 6D tomography reconstruction process. (a) Transformation between the spherical coordinate system and the Cartesian coordinate system (CSYS). (b) A schematic representation of the 2D matrices in the X-ray path and the sum of those matrices at the same position (r, c). (c) A matrix-transformation process is performed on [I_{i,\varphi \left({r,c} \right)}^{{{\rm L}_f}}] to get [I_{i,\varphi \left({r,c} \right)}^{\rm s}] to fulfill rotational invariance. (d) The 2D intensity map [[I_{i,\varphi \left({r,c} \right)}^{\rm s}]] is then reshaped into a list of nodes with intensity indicated as [I_{i,\varphi \left({r,c} \right)}^{{{\rm s}_v}}], with each node assigned a 2D index of (r, c). (e) A projection with M raster scanning points will generate intensity maps for M columns. (f) Sinograms of each specific node (r0, c0) on the retrieved and transformed [{\rm QS}\left({110} \right)_{i,\varphi \left({r,c} \right)}^{\rm s}] maps are extracted for the next paralleled reconstruction step. (g) The nodes on the reconstructed 2D intensity maps [[I_{j\left({r = {r_0},c = {c_0}} \right)}^{\rm s'}]] are used to assemble the final 3D [{\rm QS}\left({110} \right)_j^{\rm s'}] spheres [[I_j^{\rm s'}({q_x},{q_y},{q_z})]] for each voxel.

IUCrJ
Volume 11| Part 4| July 2024| Pages 502-509
ISSN: 2052-2525
https://doi.org/10.1107/S2052252524003750