相关论文: Discrete Tomography of F-Type Icosahedral Model Se…

The discrete tomography of B-type and F-type icosahedral model sets is investigated, with an emphasis on reconstruction and uniqueness problems. These are motivated by the request of materials science for the unique reconstruction of…

Various theoretical and algorithmic aspects of inverse problems in discrete tomography of planar Penrose model sets are discussed. These are motivated by the demand of materials science for the reconstruction of quasicrystalline structures…

Discrete tomography is a well-established method to investigate finite point sets, in particular finite subsets of periodic systems. Here, we start to develop an efficient approach for the treatment of finite subsets of mathematical…

It has been argued that in atomic-resolution transmission electron microscopy (TEM) of sparse weakly scattering structures, such as small biological molecules, multiple electron scattering usually has only a small effect, while the…

A modulated icosahedral shell with an inclusion is a concise description of many viruses, including recently-discovered large double-stranded DNA ones. Many X-ray scattering patterns of such viruses show major polygonal fringes, which can…

This paper studies the problem of reconstructing binary matrices that are only accessible through few evaluations of their discrete X-rays. Such question is prominently motivated by the demand in material science for developing a tool for…

Discrete tomography deals with the reconstruction of images from projections collected along a few given directions. Different approaches can be considered, according to different models. In this paper we adopt the grid model, where pixels…

Many important microscopy samples, such as liquid crystals, biological tissue, or starches, are birefringent in nature. They scatter light differently depending on the light polarization and molecular orientations. The complete…

We study inverse problems of reconstructing static and dynamic discrete structures from tomographic data (with a special focus on the `classical' task of reconstructing finite point sets in $\mathbb{R}^d$). The main emphasis is on recent…

There is a growing interest in reconstructing the density matrix of photoelectron wavepackets, in particular in complex systems where decoherence can be introduced either by a partial measurement of the system or through coupling with a…

This article is the second one of a series of three articles devoted to direct images of isocrystals: here we consider convergent isocrystals with Frobenius structure. Let V be a complete discrete valuation ring, with residue field k = V/m…

We consider a special type of self-similar sets, called fractal squares, and give a brief review on recent results and unsolved issues with an emphasis on their topological properties.

Dark-field images are formed by small-angle scattering of x-ray photons. The small-angle scattering signal is particularly sensitive to structural variations and density fluctuation on a length scale of several ten to hundred nanometers,…

Multiple-beam holography has been widely used for the realization of photonic quasicrystals with high rotational symmetries not achievable by the conventional periodic crystals. Accurate control of the properties of the interfering beams is…

Topological properties of crystals and quasicrystals is a subject of recent and growing interest. This Letter reports an experiment where, for certain quasicrystals, these properties can be directly retrieved from diffraction. We directly…

The paper presents mathematical models of quasicrystals with particular attention given to cut-and-project sets. We summarize the properties of higher-dimensional quasicrystal models and then focus on the one-dimensional ones. For the…

Model sets play a fundamental role in structure analysis of quasicrystals. The diffraction diagram of a quasicrystal admits as symmetry group a finite group G, and there is a G-cluster C (union of orbits of G) such that the quasicrystal can…

New type of tomographic probability distribution, which contains complete information on the density matrix (wave function) related to the Fresnel transform of the complex wave function, is introduced. Relation to symplectic tomographic…

The relative roles of multiple electron scattering and in-molecule free-space propagation in transmission electron microscopy of small molecules are discussed. It is argued that while multiple scattering tends to have only a moderate effect…

Quasicrystals, realized in metal alloys, are a class of lattices exhibiting symmetries that fall outside the usual classification for periodic crystals. They do not have translational symmetry and yet the lattice points are well ordered.…