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The atomic X-ray absorption spectrum (XAS) of a core-level in an absorbing atom is separated into states in the discrete part of the spectrum called "bounds final states" or "Rydberg states" below the ionization potential (IP) and "states in the continuum" part of the spectrum above the ionization potential due to excitations of the photoelectron in the vacuum.
Energy-dispersive X-ray spectroscopy (EDS, EDX, EDXS or XEDS), sometimes called energy dispersive X-ray analysis (EDXA or EDAX) or energy dispersive X-ray microanalysis (EDXMA), is an analytical technique used for the elemental analysis or chemical characterization of a sample. It relies on an interaction of some source of X-ray excitation and ...
Single-shot multi-contrast X-ray imaging; Sobolev space; Solid harmonics; Sparse Fourier transform; Spectral concentration problem; Spectral density; Spectral leakage; Spectrum continuation analysis; Spherical harmonics; Spin-weighted spherical harmonics; Stationary-wave integrated Fourier-transform spectrometry; Superoscillation
The three leading Slepian sequences for T=1000 and 2WT=6. Note that each higher order sequence has an extra zero crossing. The spectral concentration problem in Fourier analysis refers to finding a time sequence of a given length whose discrete Fourier transform is maximally localized on a given frequency interval, as measured by the spectral concentration.
There exist several efficient designs for analyzing an X-ray emission spectrum in the ultra soft X-ray region. The figure of merit for such instruments is the spectral throughput, i.e. the product of detected intensity and spectral resolving power. Usually, it is possible to change these parameters within a certain range while keeping their ...
The formulas provided at § Examples of window functions produce discrete sequences, as if a continuous window function has been "sampled". (See an example at Kaiser window.) Window sequences for spectral analysis are either symmetric or 1-sample short of symmetric (called periodic, [4] [5] DFT-even, or DFT-symmetric [2]: p.52 ).
Special examples are the Gaussian quadrature for polynomials and the Discrete Fourier Transform for plane waves. It should be stressed that the grid points and weights, x i , w i {\displaystyle x_{i},w_{i}} are a function of the basis and the number N {\displaystyle N} .
The analysis of the energy dependence of the emitted photons is the aim of the X-ray emission spectroscopy. [ 1 ] [ 2 ] [ 3 ] XES is also sometimes referred to as X-ray Fluorescence (XRF) spectroscopy, and while the terms can be used interchangeably, XES more often describes high energy resolution techniques [ 4 ] while XRF studies a wider ...