Related papers: Gabor-Type Holography Solved Analytically for Comp…
Coherent Diffractive Imaging is a lensless technique that allows imaging of matter at a spatial resolution not limited by lens aberrations. This technique exploits the measured diffraction pattern of a coherent beam scattered by periodic…
We present a method for imaging the polarization vector of an electric dipole distribution in a homogeneous medium from measurements of the electric field made at a passive array. We study an electromagnetic version of Kirchhoff imaging and…
An existing solvability result for relaxed one-sided Lipschitz algebraic inclusions is substantially improved. This enhanced solvability result allows the design of a very robust numerical method for the approximation of a solution of the…
In this paper, using the approximate particular solutions of Helmholtz equations, we solve the boundary value problems of Helmholtz equations by combining the methods of fundamental solutions (MFS) with the methods of particular solutions…
Phase retrieval in inline holography is a fundamental yet ill-posed inverse problem due to the nonlinear coupling between amplitude and phase in coherent imaging. We present a novel off-the-shelf solution that leverages a diffusion model…
We have developed a new on-axis digital holographic technique, heterodyne holography. The resolution of this technique is limited mainly by the amount of data recorded on two-dimensional photodetectors, i.e., the number of pixels and their…
Traditionally, the diffraction of a scalar wave satisfying Helmholtz equation through an aperture on an otherwise black screen can be solved approximately by Kirchhoff's integral over the aperture. Rubinowicz, on the other hand, was able to…
We present an alternative numerical reconstruction algorithm for direct tomographic reconstruction of a sample refractive indices from the measured intensities of its far-field coherent diffraction patterns. We formulate the well-known…
In a series of papers the present authors and their coworkers have developed a family of algebraic techniques to solve a number of problems in the theory of discrete or continuous dynamical systems and to analyze numerical integrators.…
This paper develops a fully discrete Fourier spectral Galerkin (FSG) method for the fractional Zakharov--Kuznetsov (fZK) equation posed on a two-dimensional periodic domain. The equation generalizes the classical ZK model by replacing the…
The object of this paper is the uniqueness for a $d$-dimensional Fokker-Planck type equation with non-homogeneous (possibly degenerated) measurable not necessarily bounded coefficients. We provide an application to the probabilistic…
Knowledge gained through X-ray crystallography fostered structural determination of materials and greatly facilitated the development of modern science and technology in the past century. Atomic details of sample structures is achievable by…
Fractional differential equations (FDEs) are an extension of the theory of fractional calculus. However, due to the difficulty in finding analytical solutions, there have not been extensive applications of FDEs until recent decades. With…
Phase field equations describe the novel approach to the Stefan problems. We calculate these equations numerically performed in two-dimensions. We take full advantage of the phase field parameter $\varphi$ to track the interface on which…
High-resolution imaging in the terahertz (THz) spectral range remains fundamentally constrained by the limited numerical apertures of currently existing state-of-the-art imagers, which restricts its applicability across many fields, such as…
Classical phasor analysis is fundamentally limited to sinusoidal single-frequency conditions, which poses challenges when working in the presence of harmonics. Furthermore, the conventional solution, which consists of decomposing signals…
In [1], we inaugurated a new area of optimal control (OC) theory that we called "periodic fractional OC theory," which was developed to find optimal ways to periodically control a fractional dynamic system. The typical mathematical…
The study of fractional order differential operators is receiving renewed attention in many scientific fields. In order to accommodate researchers doing work in these areas, there is a need for highly scalable numerical methods for solving…
It is well known that by modifying the wavefront in a certain manner, the light intensity can be turned into a certain shape. However, all known light modulation techniques allow for limited light modifications only: focusing within a…
In this article we present a theoretical study for Fraunhofer diffraction of a Laguerre-Gaussian laser beam with zeroth radial mode number and azimuthal mode number l by diffractive grating with embedded fork-shaped dislocations of integer…