Homometric model sets and window covariograms

Baake M, Grimm U (2007)
Zeitschrift für Kristallographie 222(2): 54-58.

Zeitschriftenaufsatz | Veröffentlicht | Englisch
 
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Autor*in
Baake, MichaelUniBi; Grimm, Uwe
Abstract / Bemerkung
Two Delone sets are called homometric when they share the same autocorrelation or Patterson measure. A model set A within a given cut and project scheme is a Delone set that is defined through a window W in internal space. The autocorrelation measure of A is a pure point measure whose coefficients can be calculated via the socalled covariogram of W. Two windows with the same covariogram thus result in homometric model sets. On the other hand, the inverse problem of determining A from its diffraction image ultimately amounts to reconstructing W from its covariogram. This is also known as Matheron's covariogram problem. It is well studied in convex geometry, where certain uniqueness results have been obtained in recent years. However, for non-convex windows, uniqueness fails in a relevant way, so that interesting applications to the homometry problem emerge. We discuss this in a simple setting and show a planar example of distinct homometric model sets.
Stichworte
homometry; covariogram; model sets
Erscheinungsjahr
2007
Zeitschriftentitel
Zeitschrift für Kristallographie
Band
222
Ausgabe
2
Seite(n)
54-58
ISSN
0044-2968
Page URI
https://pub.uni-bielefeld.de/record/1595704

Zitieren

Baake M, Grimm U. Homometric model sets and window covariograms. Zeitschrift für Kristallographie. 2007;222(2):54-58.
Baake, M., & Grimm, U. (2007). Homometric model sets and window covariograms. Zeitschrift für Kristallographie, 222(2), 54-58. https://doi.org/10.1524/zkri.2007.222.2.54
Baake, M., and Grimm, U. (2007). Homometric model sets and window covariograms. Zeitschrift für Kristallographie 222, 54-58.
Baake, M., & Grimm, U., 2007. Homometric model sets and window covariograms. Zeitschrift für Kristallographie, 222(2), p 54-58.
M. Baake and U. Grimm, “Homometric model sets and window covariograms”, Zeitschrift für Kristallographie, vol. 222, 2007, pp. 54-58.
Baake, M., Grimm, U.: Homometric model sets and window covariograms. Zeitschrift für Kristallographie. 222, 54-58 (2007).
Baake, Michael, and Grimm, Uwe. “Homometric model sets and window covariograms”. Zeitschrift für Kristallographie 222.2 (2007): 54-58.

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