Using cylindrical coordinates we examine some of the practical limits introduced by the use of an illuminating spherical lens of finite aperture in the implementation of the SOFT. By deriving simple rules of thumb, based on examining phase and intensity deviations from the ideal unapertured case, ...
A formalism and the corresponding numerical procedures that calculate the Fourier transform of a single-particle wave function defined on a grid of cylindrical ( \\\(ho\\\) , z ) coordinates is presented. Single-particle states in spherical and deformed nuclei have been chosen in view of futur...
Oscilloscopes - Fourier Series of a Square Wave (and Why Bandwidth Matters) It will be explained the occurrence of ringings in a signal from the perspective of the underlying theory (Fourier series as a method for solving partial differential equations), and then relate it back to using an os...
5.7). All electrode shapes were calculated so that a pure quadro-logarithmic potential exists inside the trapping cell, as expressed in the following equation: (5.7)Vrz=k2z2−r22+k2Rm2lnrRm+C, where r and z are cylindrical coordinates, Rm is termed as the characteristic radius, k the ...
The function F(ω)=F{f(x)} is called the Fourier transform of f(x). The function f(x) is the inverse Fourier transform of F(ω), that is, f(x)=F−1{F(ω)}. Example 3.2.1 Find the Fourier transform of the function in Fig. 3.6: f(x)={1if|x|a. Sign in to download...
High performance computational platform in Python for the spectral Galerkin method python hpc spectral fourier turbulence fenics mobius galerkin laguerre chebyshev legendre spectral-methods spherical-coordinates cylindrical-coordinates hermite curvilinear-coordinates polar-coordinates ultraspherical Updated Dec 3,...
The quasi-fast Hankel transform (FHT) algorithm is improved and tested for beam propagation calculations in cylindrical coordinates in order to develop an ... SC Sheng 被引量: 20发表: 1980年 Numerical analysis on the high frequency characteristics of six-cavity resonator with open boundary The nu...
Rotation-variant optical data processing using the 2-D nonsymmetric Fourier transform In this paper, we consider the properties of the nonsymmetrical Fourier transformation which is space-variant in both rectangular and polar coordinates. A coherent optical processor composed of two nonsymmetrical Fourier...
The concepts of adaptive coordinates and adaptive spatial resolution have proved to be a valuable tool to improve the convergence characteristics of the Fourier Modal Method (FMM), especially for metallo-dielectric systems. Yet, only two-dimensional adaptive coordinates were used so far. This paper ...
This article provides an introduction to Fourier transform-based mass spectrometry. The key performance characteristics of Fourier transform-based mass spectrometry, mass accuracy and resolution, are presented in the view of how they impact the interpretation of measurements in proteomic applications. The ...