Related papers: Paraxial Sharp-Edge Diffraction: A General Computa…
The classical $\overline \partial$-method has been generalized recently [lnv], [lnv2] to be used in the presence of exceptional points. We apply this generalization to solve Dirac inverse scattering problem with weak assumptions on…
Single-shot wide-angle diffraction imaging is a widely used method to investigate the structure of non-crystallizing objects such as nanoclusters, large proteins or even viruses. Its main advantage is that information about the…
A two-dimensional (2D) mathematical model of quadratically distorted (QD) grating is established with the principles of Fraunhofer diffraction and Fourier optics. Discrete sampling and bisection algorithm are applied for finding numerical…
We report on a matrix-based diffraction integral that evaluates the focal field of any diffraction-limited axisymmetric complex system. This diffraction formula is a generalization of the Debye integral applied to apertured focused beams,…
Numerous vector angular spectrum methods have been presented to model the vectorial nature of diffractive electromagnetic field, facilitating optical field engineering in polarization-related and high numerical aperture systems. However,…
Light diffraction at an aperture is a basic problem that has generated a tremendous amount of interest in optics. Some of the most significant diffraction results are the Fresnel-Kirchhoff and Rayleigh-Sommerfeld formulas. These theories…
In this paper we introduce an optical approximation into the theory of impedance calculation, one valid in the limit of high frequencies. This approximation neglects diffraction effects in the radiation process, and is conceptually…
We introduce a new class of fractional backward orthogonal functions designed for the spectral approximation of weakly singular adjoint Volterra integral equations. These basis functions generate an approximation space that naturally…
This study reexamines diffusive representations for fractional integrals with the goal of pioneering new variants of such representations. These variants aim to offer highly efficient numerical algorithms for the approximate computation of…
The chapter contains a detailed presentation of the surface integral theory for modelling light diffraction by surface-relief diffraction gratings having a one-dimensional periodicity. Several different approaches are presented, leading…
Plug-and-play approaches to solving inverse problems such as restoration and super-resolution have recently benefited from Diffusion-based generative priors for natural as well as medical images. However, solutions often use the standard…
Diffraction is a phenomenon, discussed for centuries from various points of view. The very simple principle, proposed by Huygens [1] and then modified by Fresnel[2], Stokes [3] and Kirchoff [4], allows us to make calculations, substituting…
Dispersion relation reflects the dependence of wave frequency on its wave vector when the wave passes through certain material. It demonstrates the properties of this material and thus it is critical. However, dispersion relation…
Several semianalytical approaches are now available for describing diffraction of a plane wave by the 2D (two dimensional) traction free isotropic elastic wedge. In this paper we follow Budaev and Bogy who reformulated the original…
Usually such area of mathematics as differential equations acts as a consumer of results given by functional analysis. This article will give an example of the reverse interaction of these two fields of knowledge. Namely, the derivation and…
The phasor field has been shown to be a valuable tool for non-line-of-sight imaging. We present a formal analysis of phasor-field imaging using paraxial wave optics. Then, we derive a set of propagation primitives---using the two-frequency,…
We extend a modal theory of diffraction by a set of parallel fibers to deal with the case of a hard boundary: that is a structure made for instance of air-holes inside a dielectric matrix. Numerical examples are given concerning some…
We present a simple 'shift-and-add' based improvement in the angular resolution of single electron backscatter diffraction (EBSD) patterns. Sub-pixel image registration is used to measure the (sub-pixel) difference in projection parameters…
One of the most prominent challenges in the field of diffractive imaging is the phase retrieval (PR) problem: In order to reconstruct an object from its diffraction pattern, the inverse Fourier transform must be computed. This is only…
While diffusion priors generate high-quality posterior samples across many inverse problems, they are often trained on limited training sets or purely simulated data, thus inheriting the errors and biases of these underlying sources.…