The Voigt Profile as a Sum of a Gaussian and a Lorentzian Functions, when the Weight Coefficient Depends Only on the Widths Ratio

Rocco, H. O. Di; Cruzado, A.

doi:10.12693/aphyspola.122.666

Cited by 26 publications

(18 citation statements)

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“…1 shows the comparison in the logarithmic scale. This approximation has been studied in detail in [22] and we have also verified with our experiment a good match between the two curves. The closeness of the match depends on the σ 2 =γ.…”

Section: Simulation Resultssupporting

confidence: 80%

“…This motivates us to rewrite the Voigt profile as the sum of two new Cauchy and Gaussian functions, which is called pseudo-Voigt function [20][21][22][23]:…”

Section: M-estimator With Pseudo-voigt Functionmentioning

confidence: 99%

“…For the sake of computational simplicity, previous works [20][21][22] focus on μ a ðγ; σ 2 Þ instead of μ a ðe n ; γ; σ 2 Þ. The most accurate method among them is calculating μ a ðγ; σ 2 Þ by normalizing (25) …”

Section: M-estimator With Pseudo-voigt Functionmentioning

confidence: 99%

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Optimum linear regression in additive Cauchy–Gaussian noise

Chen

Kuruoğlu

2015

Signal Processing

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Section: Simulation Resultssupporting

confidence: 80%

“…This motivates us to rewrite the Voigt profile as the sum of two new Cauchy and Gaussian functions, which is called pseudo-Voigt function [20][21][22][23]:…”

Section: M-estimator With Pseudo-voigt Functionmentioning

confidence: 99%

See 1 more Smart Citation

Optimum linear regression in additive Cauchy–Gaussian noise

Chen

Kuruoğlu

2015

Signal Processing

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“…3. µ(a, x) as a function on x for two dierent a values. µ (1, x) and µ (2, x) are displayed as functions on x for wG = 1. µ (1) and µ (2), as obtained in PI, are also shown for comparison.…”

Section: Resultsmentioning

confidence: 99%

“…(1) in a previous paper [1] (PI hereafter), we analytically found µ as a function only on a, using the property of the normalized area.…”

Section: Introductionmentioning

confidence: 99%

The Voigt Profile as a Sum of a Gaussian and a Lorentzian Functions, when the Weight Coefficient Depends on the Widths Ratio and the Independent Variable

Rocco

Cruzado

2012

Acta Phys. Pol. A

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Assuming that V (x) ≈ (1 − µ) G1(x) + µL1(x) is a very good approximation of the Voigt function, in this work we analytically nd µ from mathematical properties of V (x). G1(x) and L1(x) represent a Gaussian and a Lorentzian function, respectively, with the same height and HWHM as V (x), the Voigt function, x being the distance from the function center. In this paper we extend the analysis that we have done in a previous paper, where µ is only a function of a; a being the ratio of the Lorentz width to the Gaussian width. Using one of the dierential equation that V (x) satises, in the present paper we obtain µ as a function, not only of a, but also of x. Kielkopf rst proposed µ(a, x) based on numerical arguments. We nd that the Voigt function calculated with the expression µ(a, x) we have obtained in this paper, deviates from the exact value less than µ(a) does, specially for high |x| values.

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X‐Ray Photoelectron Spectroscopy

Scopelliti

2021

Spectroscopy for Materials Characterization

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The Voigt Profile as a Sum of a Gaussian and a Lorentzian Functions, when the Weight Coefficient Depends Only on the Widths Ratio

Cited by 26 publications

References 3 publications

Optimum linear regression in additive Cauchy–Gaussian noise

Optimum linear regression in additive Cauchy–Gaussian noise

The Voigt Profile as a Sum of a Gaussian and a Lorentzian Functions, when the Weight Coefficient Depends on the Widths Ratio and the Independent Variable

X‐Ray Photoelectron Spectroscopy

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