Reconstruction of Single-Grain Orientation Distribution Functions for Crystalline Materials

    Research output: Contribution to journalJournal articleResearchpeer-review

    Abstract

    A fundamental imaging problem in microstructural analysis of metals is the reconstruction of local crystallographic orientations from X-ray diffraction measurements. This work develops a fast, accurate, and robust method for the computation of the three-dimensional orientation distribution function for individual grains of the material in consideration. We study two iterative large-scale reconstruction algorithms, the algebraic reconstruction technique (ART) and conjugate gradients for least squares (CGLS), and demonstrate that right preconditioning is necessary in both algorithms to provide satisfactory reconstructions. Our right preconditioner is not a traditional one that accelerates convergence; its purpose is to modify the smoothness properties of the reconstruction. We also show that a new stopping criterion, based on the information available in the residual vector, provides a robust choice of the number of iterations for these preconditioned methods.
    Original languageEnglish
    JournalSIAM Journal of Imaging Sciences
    Volume2
    Issue number2
    Pages (from-to)593-613
    ISSN1936-4954
    DOIs
    Publication statusPublished - 2009

    Keywords

    • materials science
    • Materials characterization and modelling
    • stopping criterion
    • preconditioning
    • regularizing iterations
    • orientation distribution function,
    • polycrystals

    Cite this

    @article{e9b22151552d4c1e8e07f374c5281471,
    title = "Reconstruction of Single-Grain Orientation Distribution Functions for Crystalline Materials",
    abstract = "A fundamental imaging problem in microstructural analysis of metals is the reconstruction of local crystallographic orientations from X-ray diffraction measurements. This work develops a fast, accurate, and robust method for the computation of the three-dimensional orientation distribution function for individual grains of the material in consideration. We study two iterative large-scale reconstruction algorithms, the algebraic reconstruction technique (ART) and conjugate gradients for least squares (CGLS), and demonstrate that right preconditioning is necessary in both algorithms to provide satisfactory reconstructions. Our right preconditioner is not a traditional one that accelerates convergence; its purpose is to modify the smoothness properties of the reconstruction. We also show that a new stopping criterion, based on the information available in the residual vector, provides a robust choice of the number of iterations for these preconditioned methods.",
    keywords = "materials science, Materials characterization and modelling, stopping criterion, preconditioning, regularizing iterations, orientation distribution function,, polycrystals, Materialekarakterisering og materialemodellering",
    author = "Hansen, {Per Christian} and S{\o}rensen, {Henning Osholm} and Zsuzsanna S{\"u}k{\"o}sd and Poulsen, {Henning Friis}",
    year = "2009",
    doi = "10.1137/080726021",
    language = "English",
    volume = "2",
    pages = "593--613",
    journal = "S I A M Journal on Imaging Sciences",
    issn = "1936-4954",
    publisher = "Society for Industrial and Applied Mathematics",
    number = "2",

    }

    Reconstruction of Single-Grain Orientation Distribution Functions for Crystalline Materials. / Hansen, Per Christian; Sørensen, Henning Osholm; Sükösd, Zsuzsanna; Poulsen, Henning Friis.

    In: SIAM Journal of Imaging Sciences, Vol. 2, No. 2, 2009, p. 593-613.

    Research output: Contribution to journalJournal articleResearchpeer-review

    TY - JOUR

    T1 - Reconstruction of Single-Grain Orientation Distribution Functions for Crystalline Materials

    AU - Hansen, Per Christian

    AU - Sørensen, Henning Osholm

    AU - Sükösd, Zsuzsanna

    AU - Poulsen, Henning Friis

    PY - 2009

    Y1 - 2009

    N2 - A fundamental imaging problem in microstructural analysis of metals is the reconstruction of local crystallographic orientations from X-ray diffraction measurements. This work develops a fast, accurate, and robust method for the computation of the three-dimensional orientation distribution function for individual grains of the material in consideration. We study two iterative large-scale reconstruction algorithms, the algebraic reconstruction technique (ART) and conjugate gradients for least squares (CGLS), and demonstrate that right preconditioning is necessary in both algorithms to provide satisfactory reconstructions. Our right preconditioner is not a traditional one that accelerates convergence; its purpose is to modify the smoothness properties of the reconstruction. We also show that a new stopping criterion, based on the information available in the residual vector, provides a robust choice of the number of iterations for these preconditioned methods.

    AB - A fundamental imaging problem in microstructural analysis of metals is the reconstruction of local crystallographic orientations from X-ray diffraction measurements. This work develops a fast, accurate, and robust method for the computation of the three-dimensional orientation distribution function for individual grains of the material in consideration. We study two iterative large-scale reconstruction algorithms, the algebraic reconstruction technique (ART) and conjugate gradients for least squares (CGLS), and demonstrate that right preconditioning is necessary in both algorithms to provide satisfactory reconstructions. Our right preconditioner is not a traditional one that accelerates convergence; its purpose is to modify the smoothness properties of the reconstruction. We also show that a new stopping criterion, based on the information available in the residual vector, provides a robust choice of the number of iterations for these preconditioned methods.

    KW - materials science

    KW - Materials characterization and modelling

    KW - stopping criterion

    KW - preconditioning

    KW - regularizing iterations

    KW - orientation distribution function,

    KW - polycrystals

    KW - Materialekarakterisering og materialemodellering

    U2 - 10.1137/080726021

    DO - 10.1137/080726021

    M3 - Journal article

    VL - 2

    SP - 593

    EP - 613

    JO - S I A M Journal on Imaging Sciences

    JF - S I A M Journal on Imaging Sciences

    SN - 1936-4954

    IS - 2

    ER -