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@ARTICLE{Vallinayagam:626083,
      author       = {Vallinayagam, Muthu and Nentwich, Melanie and Meyer, Dirk
                      C. and Zschornak, Matthias},
      title        = {{L}inearization routines for the parameter space concept to
                      determine crystal structures without {F}ourier inversion},
      journal      = {Journal of applied crystallography},
      volume       = {58},
      number       = {3},
      issn         = {0021-8898},
      address      = {Copenhagen},
      publisher    = {Munksgaard},
      reportid     = {PUBDB-2025-01288},
      pages        = {768 - 788},
      year         = {2025},
      abstract     = {We present the elaboration and first generally applicable
                      linearization routines of the parameter space concept (PSC)
                      for determining one-dimensionally projected structures of m
                      independent scatterers. This crystal determination approach
                      does not rely on Fourier inversion but rather considers all
                      structure parameter combinations consistent with available
                      diffraction data in a para- meter space of dimension m. The
                      method utilizes m structure-factor amplitudes or intensities
                      represented by piecewise analytic hyper-surfaces, to define
                      the acceptable parameter regions. By employing the
                      isosurfaces, the coordinates of the point scatterers are
                      obtained through the intersection of multiple isosur- faces.
                      This approach allows for the detection of all possible
                      solutions for the given structure-factor amplitudes in a
                      single derivation. Taking the resonant contrast into
                      account, the spatial resolution achieved by the presented
                      method may exceed that of traditional Fourier inversion, and
                      the algorithms can be significantly optimized by exploiting
                      the symmetry properties of the isosurfaces. The applied
                      one-dimensional projection demonstrates the efficiency of
                      the PSC linearization approach based on fewer reflections
                      than Fourier sums. The Monte Carlo simulations, using the
                      projections of various random two- and three-atom structure
                      examples, are presented to illustrate the universal
                      applicability of the proposed method. Furthermore, ongoing
                      efforts aim to enhance the efficiency of data handling and
                      to overcome current constraints, promising further
                      advancements in the capabilities and accuracy of the PSC
                      framework.},
      cin          = {IT},
      ddc          = {540},
      cid          = {I:(DE-H253)IT-20120731},
      pnm          = {611 - Fundamental Particles and Forces (POF4-611) / DFG
                      project G:(GEPRIS)442646446 - Parameter Space Concept als
                      Strukturlösungsmethodik für die Einkristalldiffraktometrie
                      (442646446)},
      pid          = {G:(DE-HGF)POF4-611 / G:(GEPRIS)442646446},
      experiment   = {EXP:(DE-MLZ)NOSPEC-20140101},
      typ          = {PUB:(DE-HGF)16},
      pubmed       = {pmid:40475935},
      doi          = {10.1107/S1600576725001955},
      url          = {https://bib-pubdb1.desy.de/record/626083},
}