Related papers: Fourier Transform of Annular Beams
We define a nonlinear Fourier transform which maps sequences of contractive $n \times n$ matrices to $SU(2n)$-valued functions on the circle $\mathbb{T}$. We characterize the image of finitely supported sequences and square-summable…
The Fourier-based diffraction approach is an established method to extract order and symmetry propertiesfrom a given point set. We want to investigate a different method for planar sets which works in direct spaceand relies on reduction of…
We numerically investigate the implementation of Haar-random unitarity transformations and Fourier transformations in photonic devices consisting of beam splitters and phase shifters, which are used for integrated photonics implementations…
The usage of optical transition radiation for profile monitoring of relativistic electron beams is well known. This report presents the case for beam diagnostic application of optical transition radiation for non-relativistic ion beams. The…
When measuring diameters of partially resolved sources often a technique called gaussian deconvolution is used. This technique yields a gaussian diameter which subsequently has to be multiplied with a conversion factor to obtain the true…
Diffraction tomography is an inverse scattering technique used to reconstruct the spatial distribution of the material properties of a weakly scattering object. The object is exposed to radiation, typically light or ultrasound, and the…
Conceptual studies and numerical simulations are performed for imaging devices that transform a near-field pattern into magnified far-zone images and are based on high-order spatial transformation in cylindrical domains. A lens translating…
In this paper we couple Synchrotron Radiation (SR) theory with a branch of physical optics, namely laser beam optics. We show that the theory of laser beams is successful in characterizing radiation fields associated with any SR source.…
This paper proposes a technique for designing flat lenses using Field Transformation (FT), as opposed to Ray Optics (RO) or Transformation Optics (TO). The lens design consists of 10 layers of graded index dielectric in the radial direction…
We study theoretically the accuracy of the method based on the Fourier property of lenses that is commonly used for the far field measurement. We consider a simple optical setup in which the far-field intensity pattern of a light beam…
The Quaternion Fourier transform (QFT) is one of the key tools in studying color image processing. Indeed, a deep understanding of the QFT has created the color images to be transformed as whole, rather than as color separated component. In…
Accurate and fast modeling of electric fields in layered structures have a great scientific and practical value. Prevalent method for that is transfer-matrix method. However, transfer matrix method is limited to infinite plane wave…
Surface plasmons are usually described as surface waves with either a complex wavevector or a complex frequency. When discussing their merits in terms of field confinment or enhancement of the local density of states, controversies…
Many interesting and fundamentally practical optimization problems, ranging from optics, to signal processing, to radar and acoustics, involve constraints on the Fourier transform of a function. It is well-known that the {\em fast Fourier…
In this paper, we investigate the behavior of the Fourier transform on finite dimensional 2-step Lie groups and develop a general theory akin to that of the whole space or the torus. We provide a familiar framework in which computations are…
A novel method for computation of the discrete Fourier transform over a finite field with reduced multiplicative complexity is described. If the number of multiplications is to be minimized, then the novel method for the finite field of…
Many media are divided into elementary units with irregular shape and size, as exemplified by domains in magnetic materials, bubbles in foams, or cells in biological tissues. Such media are essentially characterized by geometrical disorder…
Optical spectrum analysis is the cornerstone of spectroscopic sensing, optical network performance monitoring, and hyperspectral imaging. While conventional high-performance spectrometers used to perform such analysis are often large…
The two-dimensional (2D) orientation field transform has been proved to be effective at enhancing 2D contours and curves in images by means of top-down processing. It, however, has no counterpart in three-dimensional (3D) images due to the…
We demonstrate experimentally and theoretically a controllable way of shifting the frequency of an optical pulse by using a combination of spectral hole burning, slow light effect, and linear Stark effect in a rare-earth-ion doped crystal.…