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ComplexErrorFunctionRelatedVoigtHalfWidthHalfMaximumApproximation Method

An approximation formula for the half width at half maximum of the Voigt(Double, Double, Double) profile. The maximal relative error is 0.0216%. The error is vanishing in the limiting cases sigma>>gamma and gamma>>sigma.

Namespace: Altaxo.Calc
Assembly: AltaxoCore (in AltaxoCore.dll) Version: 4.8.3179.0 (4.8.3179.0)
Syntax
C#
Copy
public static double VoigtHalfWidthHalfMaximumApproximation(
	double sigma,
	double gamma
)

Parameters

sigma  Double
The parameter sigma (of the Gaussian).
gamma  Double
The parameter gamma (of the Lorentzian).

Return Value

Double
The half width at half maximum of the Voigt profile, see Voigt(Double, Double, Double).
Exceptions
ExceptionCondition
InvalidProgramException
Remarks

References:

[1] Olivero, Longbothum, Journal of Quantitative Spectroscopy and Radiative Transfer, 1977, 17:233

D. Lellinger: The constant C1 was calculated from C2 in order to ensure asymptotic correct behavior. C2 was chosen so that the maximum relative error is symmetrically around zero.

See Also