The Open UniversitySkip to content

Homometric model sets and window covariograms

Baake, Michael and Grimm, Uwe (2007). Homometric model sets and window covariograms. Zeitschrift für Kristallographie, 222(2) pp. 54–58.

Full text available as:
PDF (Not Set) - Requires a PDF viewer such as GSview, Xpdf or Adobe Acrobat Reader
Download (1MB)
DOI (Digital Object Identifier) Link:
Google Scholar: Look up in Google Scholar


Two Delone sets are called homometric when they share the same autocorrelation or Patterson measure. A model set Lambda 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 Lambda is a pure point measure whose coefficients can be calculated via the so-called covariogram of W. Two windows with the same covariogram thus result in homometric model sets. On the other hand, the inverse problem of determining Lambda 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.

Item Type: Journal Item
ISSN: 0044-2968
Keywords: homometry; model sets; covariogram
Academic Unit/School: Faculty of Science, Technology, Engineering and Mathematics (STEM) > Mathematics and Statistics
Faculty of Science, Technology, Engineering and Mathematics (STEM)
Item ID: 6609
Depositing User: Uwe Grimm
Date Deposited: 06 Feb 2007
Last Modified: 10 Dec 2018 21:47
Share this page:


Altmetrics from Altmetric

Citations from Dimensions

Download history for this item

These details should be considered as only a guide to the number of downloads performed manually. Algorithmic methods have been applied in an attempt to remove automated downloads from the displayed statistics but no guarantee can be made as to the accuracy of the figures.

Actions (login may be required)

Policies | Disclaimer

© The Open University   contact the OU