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Courses in WS 2023/24:

  • Mathematics for Engineers 1, see OPAL
  • Functional Theory, see OPAL
  • Analysis 3, see OPAL
  • Current Topics in Analysis
  • Mathematical Seminar


  • Interplay between habit plane and orientation relationship using the example of η'-Al8Fe3 in η-Al5Fe2: an electron backscatter analysis
    Hanka Becker, Ralf Hielscher, Andreas Leineweber: Crystals 12(6), 2022.
  • Approximating the Derivative of Manifold-valued Functions
    R. Hielscher, L. Lippert: arXiv:2102.12562, 2021.

Publications in Journals (Google Scholar)

  • An Optical Flow Model in Electron Backscatter Diffraction
    M. Gräf, S. Neumayer, R. Hielscher, G. Steidl, M. Liesegang, T. Beck: SIAM J. Imaging Sci. 15, 2022.
  • Optimality of Cross-validation in Scattered Data Approximation
    F. Bartel, R. Hielscher: J. Approx. Theory 277, 2022
  • The variant graph approach to improved parent grain reconstruction
    R. Hielscher, T. Nyyssönen, F. Niessen, A. A. Gazder: Materialia 2022.
  • Parent grain reconstruction from partially or fully transformed microstructures in MTEX
    F. Niessen, T. Nyyssönen, A. A. Gazder, R. Hielscher: J. Appl. Cryst. 55, 2022
  • Isometric Embeddings of Quotients of the Rotation Group Modulo Finite Symmetries
    R. Hielscher, L. Lippert: J. Multivariate Anal. 185, 104764, 2021.
  • Fast Cross-validation in Harmonic Analysis
    F. Bartel, R. Hielscher and D. Potts: Appl. Numer. Harmon. Anal. 49(2), 2020.
  • Approximant-based orientation determination of quasicrystals using electron backscatter diffraction
    C. Grzegorz, G. Nolze, A. Winkelmann, T. Tokarski, R. Hielscher, R. Strzałka, I. Bugański, J. Wolny and P. Bała: Ultramicroscopy 218, 2020.
  • EBSD orientation analysis based on experimental Kikuchi reference patterns
    A. Winkelmann, G. Cios, T. Tokarski Show, G. Nolze, R. Hielscher and T. Kozieł: Acta Materialia 188, 2020.
  • Optimised reconstruction of the crystallographic orientation density function based on a reduced set of orientations
    A. Biswas, N. Vajragupta, R. Hielscher and A. Hartmaier: Journal of Applied Crystallography 53(1), 2020.
  • Visualisation of texture components using MTEX
    G. Rafailov, E. N. Caspi, R. Hielscher, E. Tiferet, R. Schneck and C. Vogel: J. Appl. Cryst. 53, 2020
  • Gazing at crystal balls - Electron backscatter diffraction indexing and cross correlation on a sphere
    R. Hielscher, B. Britton and F. Bartel: Ultramicroscopy, 2019.
  • Denoising of Crystal Orientation Maps
    R. Hielscher, C. Silbermann, E. Schmidl, J. Ihlemann: Journal of Applied Crystallography 52, 2019.
  • An analytical finite-strain parametrisation for texture evolution in deforming olivine polycrystals
    N. M. Ribe, R. Hielscher and O. Castelnau: Geophysical Journal International 216, 486-514, 2019.
  • The cone-beam transform and spherical convolution operators
    M. Quellmalz, R. Hielscher and A. K. Louis: Inverse Problems 34 (2018) 105006, 2018.
  • An SVD in Spherical Surface Wave Tomography
    R. Hielscher, D. Potts and M. Quellmalz: In: Bernd Hofmann, Antonio Leitao and Jorge P. Zubelli (Eds.). New Trends in Parameter Identification for Mathematical Models, Birkhäuser Basel, 2018.
  • On three-dimensional misorientation spaces
    R. Krakow, R. J. Bennett, D. N. Johnstone, Z. Vukmanovic, W. Solano-Alvarez, S. J. Laine, J. F. Einsle, P. A. Midgley, C. M. F. Rae, R. Hielscher: Proceedings of the Royal Society A, 473, 2017.
  • Electron Backscatter Diffraction beyond the mainstream
    G. Nolze, R. Hielscher, A. Winkelmann: Crystal Research & Technolog, 25(1), 2017.
  • Orientations - perfectly coloured
    G. Nolze, R. Hielscher: Journal of Applied Crystallography, 49, 1786-1802, 2016.
  • Reconstructing a Function on the Sphere from Its Means Along Vertical Slices
    R. Hielscher, M. Quellmalz: Inverse Problems and Imaging, 10 (3), 711-739, 2016.
  • Restoration of Manifold-Valued Images by Half-Quadratic Minimisation
    R. Bergmann, R. H. Chan, R. Hielscher, J. Persch, G. Steidl, Inverse Problems and Imaging, 10 (2), 281-304, 2016.
  • Optimal mollifiers for spherical deconvolution
    R. Hielscher, M. Quellmalz: Inverse Problems, 31, art. no. 085001, 2015.
  • Global optimisation on the torus, the sphere and the rotation group
    M. Gräf, R. Hielscher: SIAM J. Optim, 25, 540 - 564, 2015.
  • Calculating anisotropic piezoelectric properties from texture data using the MTEX open source package
    D. Mainprice, F. Bachmann, R. Hielscher, H. Schaeben: Geological Society, London, Special Publications, 409, 2014.
  • Descriptive tools for the analysis of texture projects with large datasets using MTEX: strength, symmetry and components
    D. Mainprice, F. Bachmann, R. Hielscher, H. Schaeben: Geological Society, London, Special Publications, 409, 2014.
  • Numerical Inversion of the Funk transform on the Rotation Group
    R. Hielscher: Inverse Problems, 29, art. no. 125014, 2013.
  • Kernel Density Estimation on the Rotation Group and its Application to Crystallographic Texture Analysis
    R. Hielscher: J. Multivariate Anal., 119, 119 - 143, 2013.
  • Efficient and accurate computation of spherical mean values at scattered centre points
    T. Görner, R. Hielscher, S. Kunis: Inverse Prob. Imaging, 6, 645 - 661, 2012.
  • Optimising the experimental design of texture goniometry
    F. Bachmann, R. Hielscher, H. Schaeben: J. Appl. Cryst., 45, 1173-1181, 2012.
  • Grain detection from 2d and 3d EBSD data - Specification of the MTEX algorithm
    F. Bachmann, R. Hielscher, H. Schaeben: Ultramicroscopy, 111, 1720-1733, 2011.
  • Calculating anisotropic physical properties from texture data using the MTEX open source package
    D. Mainprice, R. Hielscher, H. Schaeben: Prior, D.J., Rutter, E.H., Tatham, D. J. (eds) Deformation Mechanisms, Rheology and Tectonics: Microstructures, Mechanics and Anisotropy. Geological Society, London, Special Publications, 360, 175-192, 2011.
  • Inferential statistics of electron backscatter diffraction data from within individual crystalline grains
    F. Bachmann, R. Hielscher, P. E. Jupp, W. Pantleon, H. Schaeben, E. Wegert: J. Appl. Cryst. 43, 1338-1355, 2010.
  • Fast summation of functions on the rotation group
    R. Hielscher, J. Prestin, A. Vollrath, Math. Geosci., 42, 773-794, 2010.
  • Texture analysis with MTEX- Free and open source software toolbox
    F. Bachmann, R. Hielscher, H. Schaeben: Solid State Phenomena, 160, 63-68, 2010.
  • Orientation Distribution Within a Single Hematite Crystal
    R. Hielscher, H. Schaeben, H. Siemes: Math. Geosci., 42, 395-375, 2010.
  • Reconstruction from circular and spherical mean data
    F. Filbir, R. Hielscher, W.R. Madych: Appl. Comput. Harmon. Anal., 29, 111 - 120, 2010.
  • The generalised totally geodesic Radon transform and its application to texture analysis
    S. Bernstein, R. Hielscher, H. Schaeben: Math. Methods Appl. Sci., 32, 379 - 394, 2009.
  • A novel pole figure inversion method: specification of the MTEX algorithm
    R. Hielscher, H. Schaeben: J. Appl. Cryst. 41, 1024-1037, 2008
  • The radon transform on SO(3): a Fourier slice theorem and numerical inversion
    R. Hielscher, D. Potts, J. Prestin, H. Schaeben, M. Schmalz: Inverse Problems 24, 025011 - 025032, 2008
  • Multi-scale texture modelling
    R. Hielscher, H. Schaeben: Math. Geosci., 40, 63 - 82, 2008
  • On the calibration of fission-track annealing models
    S. Guedes, R. Jonckheere, P.A.F.P. Moreira, R. Hielscher: Chem. Geol., 248, 1-13, 2007
  • Orientation density function-controlled pole probability density function measurements: automated adaptive control of texture goniometers.
    H. Schaeben, R. Hielscher, J. J. Fundenberger, D. Potts and J. Prestin: J. Appl. Cryst., 40, 570-579, 2007.
  • On the entropy to texture index relationship in quantitative texture analysis
    R. Hielscher, H. Schaeben, D. Chateigner: J. Appl. Cryst., 40, 371-375, 2007.
  • Kernel-based methods for inversion of the Radon transform on SO(3) and their applications to texture analysis
    K. van den Boogaart, R. Hielscher, J. Prestin, H. Schaeben: J. Comp. Appl. Math., 199, 122-140, 2006.

MTEX is the leading open-source platform for the analysis of crystallographic textures, texture modelling, calculations of crystallographic orientations and related objects such as vectors, tensors or crystal symmetries as well as a vendor-independent workbench for the analysis of EBSD and pole figure data.

All relevant information such as

  • download
  • documentation
  • workshops
  • publications

can be found on the MTEX homepage.