Discrete template to quantify goodness of fit between pole figures

Received 25 March 2023; Accepted 27 April 2023;
Citation: A.A. Zisman. Discrete template to quantify goodness of fit between pole figures. Lett. Mater., 2023, 13(3) 214-218
BibTex   https://doi.org/10.22226/2410-3535-2023-3-214-218


Trial points uniformly distributed over the upper hemisphere are stereographically projected on the plane of pole figures.To compare material textures, a discrete template of arranged trial points has been generated. It enables one-dimensional parameterization of respective pole figures and, therefore, use of the Kolmogorov-Smirnov criterion to assess their goodness of fit. The template is computationally simple and relevant to spherical symmetry of random orientation distribution that is a natural reference sample in the texture analysis. For a case study, virtual axial textures are compared with allowance for anticipated measurement errors. Based on the obtained results, ability of EBSD technique to determine representative textures is discussed.

References (12)

1. R. Bauer. J. Guid. Contr. Dyn. 23, 130 (2000). Crossref
2. C. G. Koay. J. Comput. Sci. 2, 88 (2011). Crossref
3. T. Lychagina, D. Nikolayev. J. Appl. Cryst. 49, 1290 (2016). Crossref
4. N. V. Smirnov. Bull. Moscow State Univ. 2 (2), 3 (1939). (in Russian) [Н.В. Смирнов. Бюллетень МГУ. 2 (2), 3 (1939).].
5. E. Demidenko. Kolmogorov-Smirnov test for image comparison. In: Computational Science and Its Applications - ICCSA 2004. Lecture Notes in Computer Science. Vol. 3046. (Ed. by A. Laganá, M. L. Gavrilova, V. Kumar, Y. Mun, C. J. K. Tan, O. Gervasi). Berlin, Springer (2004). Crossref
6. F. Baselice, G. Ferraioli, V. Pascazio, A. Sorriso. Magn. Reson. Imag. 57, 176 (2019). Crossref
7. A. Kolmogorov. G. Instit. Ital. Attuari. 4, 83 (1933).
8. J. C. Alonso, D. Estrada. J. Math. Stat. 15, 12 (2019). Crossref
9. A. Eres-Castellanos, L. Morales-Rivas, J. A. Jimenez, F. G. Caballero, C. Garsia-Mateo. Metall. Mater. Trans. A. 52, 4033 (2021). Crossref
10. Q. Zhou, T.-K. Lee, T. R. Bieler. Mater. Eng. A802, 140584 (2021). Crossref
11. A. Winkelmann, G. Nolze, G. Cios, T. Tokarski, P. Bala. Materials. 13, 2816 (2020). Crossref
12. R. Hielscher, T. Nyyssönen, F. Niessen, A. A. Gazder. Materialia. 22, 101399 (2022). Crossref


1. Russian Science Foundation - project No 22-19-00627