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We implement an efficient method of computation of two dimensional Fourier-type integrals based on approximation of the integrand by Gaussian radial basis functions, which constitute a standard tool in approximation theory. As a result, we…
We use a scattering matrix approach to simulate the transmission through a hexagonal Photonic Crystal in the vicinity of the Dirac point. If the crystal is oriented so that the propagation direction perpendicular to the surface corresponds…
Conventional X-ray methods use incoming plane waves and result in discrete diffraction patterns when scattered at crystals. Here we find, by a systematic method, incoming waveforms which exhibit discrete diffraction patterns when scattered…
We study light scattering by a hedgehog-like and linear disclination topological defects in a nematic liquid crystal by a metric approach. Light propagating near such defects feels an effective metric equivalent to the spatial part of the…
Star test polarimetry is an imaging polarimetry technique in which an element with spatially-varying birefringence is placed in the pupil plane to encode polarization information into the point-spread function (PSF) of an imaging system. In…
In this article, we derive a theoretical formalism that unifies the rigorous coupled wave analysis and the dynamical diffraction theory. Based on this formalism, we design a computational approach for the diffraction calculation for the…
Radiation from a charged particle moving in a medium with Maxwell fish eye refraction index profile is considered. It is shown that the radiation spectrum has a discrete character. The main emitted wavelength is proportional to the…
Photon sieves are permeable diffractive optical elements generated by open apertures on a substrate. These elements are well suited for the monitoring of running fluids. Our analysis considers the fabrication constrains of the photon sieve…
Using the spectral theorem we compute the Quantum Fourier Transform (or Vacuum Characteristic Function) $\langle \Phi, e^{itH}\Phi\rangle$ of an observable $H$ defined as a self-adjoint sum of the generators of a finite-dimensional Lie…
Diffraction tomography is a widely used inverse scattering technique for quantitative imaging of weakly scattering media. In its conventional formulation, diffraction tomography assumes monochromatic plane wave illumination. This…
Development generating diffraction-related valuable expressions and formulas capable of initiating new era for diffraction and for scientific domains that use it provided. The main expression, among these, gives diffracted intensity as…
A shearing interferometer is presented which uses polarization control to shear the wavefront and to modulate the interference pattern. The shear is generated by spatial walk-off in a birefringent crystal. By adjusting the orientation of…
In the present article, the author uses Fourier theory of tempered distributions (generalized functions) in deriving a formula for Dirichlet-like integrals. The applied method is remarkably efficient and allows a solution in a few…
The image degradation produced by atmospheric turbulence and optical aberrations is usually alleviated using post-facto image reconstruction techniques, even when observing with adaptive optics systems. These techniques rely on the…
In this paper we give a concrete application of the spectral theory based on the notion of $S$-spectrum to fractional diffusion process. Precisely, we consider the Fourier law for the propagation of the heat in non homogeneous materials,…
Reconstruction of the point spread function (PSF) plays an important role in many areas of astronomy, including photometry, astrometry, galaxy morphology, and shear measurement. The atmospheric and instrumental effects are the two main…
The spectral gap is estimated for measure-valued diffusion processes induced by the intrinsic/extrinsic derivatives on the space of finite measures over a Riemannian manifold. This provides explicit exponential convergence rate for these…
A novel approach for measuring linear X-ray polarization over a broad-band using conventional imaging optics and cameras is described. A new type of high efficiency grating, called the critical angle transmission grating is used to disperse…
In this article, we report a lens design based on a concentric circular structure with continuous changing of thickness defined in a thin plate structure for focusing a plane wave into three spots (triple focusing) and for splitting elastic…
A spherical tensor expansion is carried out to express the resonant inelastic scattering cross-section as a sum of products of fundamental spectra with tensors involving wavevectors and polarization vectors of incident and scattered…