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Basic tasks of signal processing in spectroscopy
Published in Dževad Belkić, Karen Belkić, Signal Processing in Magnetic Resonance Spectroscopy with Biomedical Applications, 2010
As such, the Voigt function can be perceived as a broadened Lorentzian, or equivalently, a narrowed Gaussian depending upon which of the two constituents (Gaussian or Lorentzian) is taken to be the primary profile. Originally, the Voigt profile was introduced in optics with the purpose of accounting for the Doppler broadening (via Gaussians) of the primary line-shapes given by dispersion functions (Lorentzians) to describe absorption spectra [95]–[97]. After this initial appearance, many applications of the Voigt profile emerged in diverse fields, including MRS [98, 99]. Being a symmetric function, the Voigt frequency profile is intermediate to a Gaussian and a Lorentzian. More specifically, the Voigt profile is reduced to a Gaussian or a Lorentzian function in the pertinent limiting cases of the two widths. For instance, not too far from the center ω ≈ ω1, the Lorentz and Gauss distributions look very much alike. Nevertheless, the discrepancy between these two distributions becomes appreciable away from the center where a Lorentzian decreases more slowly than a Gaussian when the value of the frequency variable ω is augmented.
Electrostatics, Electrodynamics and Fluid Mechanics of Plasma
Published in Alexander Fridman, Lawrence A. Kennedy, Plasma Physics and Engineering, 2021
Alexander Fridman, Lawrence A. Kennedy
The Voigt profile is a result of the convolution of the Gaussian and Lorentzian profiles. Prove that the integral Voigt profile Eq. (6.278) becomes either Gaussian or Lorentzian in the cases of significant prevailing of the Doppler or Stark (or pressure) broadening effects.
Selected properties of surface modified GaxFe3-xO4 with 0≤x≤1.5
Published in Phase Transitions, 2023
M. Orzechowska, K. Rećko, D. Soloviov, U. Klekotka, M. Biernacka, D. Satuła, W. Olszewski, B. Kalska-Szostko, A. Beskrovnyy, K. Szymański
Figure 4b illustrates the crystallite size dependence on Ga content obtained for different series. Pseudo-Voigt profile function appeared to be most adequate for diffraction data refinements. Due to Lorentz and Gaussian broadening caused by the crystalline and lattice strain, respectively, the Langford method [23] was used to obtain results presented in Figure 4b. The Langford approach is based on the convolution of the Lorentz and Gauss distributions (see Equations 1 and 2) where the widening of the peaks derived from the size of the crystallites is characterized by the Lorentz distribution, while the widening associated with the distortion of the lattice, i.e. strain, is subject to the Gaussian distribution. As a result of this transformation, the following formulas are obtained: where K – Scherrer constant, λ – incident radiation wavelength, dhkl – crystallite size, θ – scattering angle, ϵ – crystal lattice stress, Bs – Williamson-Hall equation.
A Novel Method of Curve Fitting Based on Optimized Extreme Learning Machine
Published in Applied Artificial Intelligence, 2020
The second category of the test dataset is taken from synthetized spectroscopic data. Spectroscopy is an important technique to detect the underlying structure of matter by analyzing measured spectral curves. Curve fitting is an essential procedure in spectral data analysis in order to extract quantitative structure information. As the result of electromagnetic radiation and atom interactions, the measured spectroscopic data in Raman, Infrared spectroscopy, and other spectroscopy usually appear in form of three basic line shapes, which are Gaussian, Lorentzian and Voigt profile with noises, respectively. The Voigt line shape is a convolution of Gaussian and Lorentzian line shape, without a simple analytical expression. We consider three spectral datasets for the test purpose – one for each line shape. These datasets are synthetized from the true spectral line shape functions with adding zero-mean normal noise. The first one is taken from the Gaussian2 dataset of NIST statistics and nonlinear regression library (http://www.itl.nist.gov/div898/strd/nls/data/gauss2.shtml), which is comprised of a double-peak Gaussian with an exponential baseline (250 data points). The true functions of the second and third dataset (200 data points) are the distorted Lorentzian and pseudo-Voigt, respectively, which is an approximate combination of Gaussian and Lorentzian. Expressed in mathematical equations, they are
Matterwave interferometric velocimetry of cold Rb atoms
Published in Journal of Modern Optics, 2018
Max Carey, Mohammad Belal, Matthew Himsworth, James Bateman, Tim Freegarde
In both c.w. and Ramsey spectroscopy, the signal observed is the convolution of the Doppler-shifted resonance with the cross-correlation of the atom-laser coherence. In conventional spectroscopy, the atom-laser interaction is dominated by the atomic and laser linewidths, collisions, and inhomogeneities in intensity, magnetic field and Zeeman sub-state, most of which contribute to a Voigt profile. Here, it is instead dominated by the double pulse of the Ramsey interaction, whose Fourier transform results in the sinusoidal fringes. In principle, there should be no Doppler sensitivity within the -pulses - although power constraints mean that in our case there are, as addressed in the Appendix 1.