research papers
The theoretical framework and a joint quasi-Newton–Levenberg–Marquardt–simulated annealing (qNLMSA) algorithm are established to treat an inverse X-ray diffraction tomography (XRDT) problem for recovering the 3D displacement field function fCtpd(r − r0) = h · u(r − r0) due to a Coulomb-type point defect (Ctpd) located at a point r0 within a crystal [h is the diffraction vector and u(r − r0) is the displacement vector]. The joint qNLMSA algorithm operates in a special sequence to optimize the XRDT target function in a χ2 sense in order to recover the function fCtpd(r − r0) [ is the parameter vector that characterizes the 3D function fCtpd(r − r0) in the algorithm search]. A theoretical framework based on the analytical solution of the Takagi–Taupin equations in the semi-kinematical approach is elaborated. In the case of true 2D imaging patterns (2D-IPs) with low counting statistics (noise-free), the joint qNLMSA algorithm enforces the target function to tend towards the global minimum even if the vector in the search is initially chosen rather a long way from the true one.
Keywords: inverse X-ray diffraction tomography problem; semi-kinematical solution of the Takagi–Taupin equations; Coulomb-type point defects; quasi-Newton–Levenberg–Marquardt–simulated annealing algorithm.
Supporting information
Moving Picture Experts Group (MPG) video file https://doi.org/10.1107/S2053273320000145/lk5053sup1.mpg |