Related papers: A short guide to pure point diffraction in cut-and…
We consider diffraction of waves on a product cone. We first show that diffractive waves enjoy a one-step polyhomogeneous asymptotic expansion, which is an improvement of Cheeger-Taylor's classical result of half-step polyhomogeneity of…
In this paper we explore the potential of stoichiometry determination for chalcogenide superlattices, promising candidates for next-generation phase-change memory, via X-ray diffraction. To this end, a set of epitaxial GeTe/Sb2Te3…
Crystals are the materials which can be described by uniform periodic lattices. Traditionally, only the 1-, 2-, 3-, 4- and 6-fold rotation symmetries are allowed in crystals because other n-fold rotation symmetries are forbidden by the…
The concept of the diffraction limit put forth by Ernst Abbe and others has been an important guiding principle limiting our ability to tightly focus classical waves, such as light and sound, in the far field. In the past decade, numerous…
Starting with Maxwell's equations, we derive the fundamental results of the Huygens-Fresnel-Kirchhoff and Rayleigh-Sommerfeld theories of scalar diffraction and scattering. These results are then extended to cover the case of vector…
In this article pattern statistics of typical cubical cut and project sets are studied. We give estimates for the rate of convergence of appearances of patches to their asymptotic frequencies. We also give bounds for repetitivity and…
The method of common lines is a well-established reconstruction technique in cryogenic electron microscopy (cryo-EM), which can be used to extract the relative orientations of an object given tomographic projection images from different…
We show that the Poincar\'e lemma we proved elsewhere in the context of crystalline cohomology of higher level behaves well with regard to the Hodge filtration. This allows us to prove the Poincar\'e lemma for transversal crystals of level…
The problem of diffraction by a Dirichlet quarter-plane (a flat cone) in a 3D space is studied. The Wiener-Hopf equation for this case is derived and involves two unknown (spectral) functions depending on two complex variables. The aim of…
We study three quasicontinuum approximations of a lattice model for crack propagation. The influence of the approximation on the bifurcation patterns is investigated. The estimate of the modeling error is applicable to near and beyond…
The discrepancy of a point set quantifies how well the points are distributed, with low-discrepancy point sets demonstrating exceptional uniform distribution properties. Such sets are integral to quasi-Monte Carlo methods, which approximate…
The cut and project method is a central construction in the theory of Aperiodic Order for generating quasicrystals with pure point diffraction. Linear repetitivity ({\bf LR}) is a form of ideal regularity of aperiodic patterns. Recently,…
An extension of the Gutzwiller trace formula is given that includes diffraction effects due to hard wall scatterers or other singularities. The new trace formula involves periodic orbits which have arcs on the surface of singularity and…
When a coherent quasi-monochromatic light is reflected from a step, a diffraction pattern is formed that can be described by Fresnel-Kirchhoff integral and visibility of the fringes depends on the height of the step. In this paper, it is…
We study the mechanisms responsible for quantum diffusion in the quasiperiodic kicked rotor. We report experimental measurements of the diffusion constant on the atomic version of the system and develop a theoretical approach (based on the…
We present a method to determine the static aberrations in a nearly diffraction-limited spectrograph introduced, for example, by alignment or manufacturing errors. We consider an instrument with two stages separated by a slit or image…
We develop embedding formulae for all possible diffraction problems with Dirichlet scatterers on square lattices using the Wiener--Hopf perspective. The embedding formula expresses solutions for arbitrary plane-wave incidence in terms of a…
We consider an optical diffraction grating in which the spatial distribution of open slits forms a fractal set. The Fraunhofer diffraction patterns through the fractal grating are obtained analytically for the simplest triad Cantor type and…
We consider a general method of deprojecting 2D images to reconstruct the 3D structure of the projected object, assuming axial symmetry. The method consists of the application of the Fourier Slice Theorem to the general case where the axis…
We establish a link between Fourier optics and a recent construction from the machine learning community termed the kernel mean map. Using the Fraunhofer approximation, it identifies the kernel with the squared Fourier transform of the…