Voigt Class Reference

A Voigt profile is the convolution of a Lorentzian and a Gaussian profile. More...

#include <LineBroadener.h>

Inheritance diagram for Voigt:

Collaboration diagram for Voigt:

Public Member Functions
	Voigt (doublereal sigma, doublereal gamma)
	Constructor.
virtual doublereal	profile (doublereal deltaFreq)
	Voigt profile.
void	testv ()
doublereal	operator() (doublereal deltaFreq)
virtual doublereal	cumulative (doublereal deltaFreq)
	The cumulative profile, defined as \[ C(\Delta \nu) = \int_{-\infty}^{\Delta \nu} P(x) dx \] .
virtual doublereal	width ()

Protected Member Functions
doublereal	F (doublereal x)
	This method evaluates the function \[ F(x, y) = \frac{y}{\pi}\int_{-\infty}^{+\infty} \frac{e^{-z^2}} {(x - z)^2 + y^2} dz \] The algorithm used to cmpute this function is described in the reference below.

Protected Attributes
doublereal	m_sigma
doublereal	m_gamma_lor
doublereal	m_sigma2
doublereal	m_width
doublereal	m_gamma
doublereal	m_sigsqrt2
doublereal	m_a
doublereal	m_eps

Detailed Description

A Voigt profile is the convolution of a Lorentzian and a Gaussian profile.

This profile results when Doppler broadening and collisional broadening both are important.

Definition at line 119 of file LineBroadener.h.

Constructor & Destructor Documentation

Voigt	(	doublereal	sigma,
		doublereal	gamma
	)

Constructor.

Parameters

sigma	The standard deviation of the Gaussian
gamma	The half-width of the Lorentzian.

Definition at line 84 of file LineBroadener.cpp.

References Cantera::SqrtTwo.

Member Function Documentation

doublereal profile ( doublereal  deltaFreq )

virtual

Voigt profile.

Not sure that constant is right.

Reimplemented from LineBroadener.

Definition at line 170 of file LineBroadener.cpp.

References Cantera::SqrtPi.

doublereal F ( doublereal  x )

protected

This method evaluates the function

\[ F(x, y) = \frac{y}{\pi}\int_{-\infty}^{+\infty} \frac{e^{-z^2}} {(x - z)^2 + y^2} dz \]

The algorithm used to cmpute this function is described in the reference below.

See Also

F. G. Lether and P. R. Wenston, "The numerical computation of the Voigt function by a corrected midpoint quadrature rule for \( (-\infty, \infty) \). Journal of Computational and Applied Mathematics}, 34 (1):75–92, 1991.

Definition at line 115 of file LineBroadener.cpp.

References Cantera::Pi, Cantera::SqrtPi, and Cantera::SqrtTwo.

virtual doublereal cumulative ( doublereal  deltaFreq )

inlinevirtualinherited

The cumulative profile, defined as

\[ C(\Delta \nu) = \int_{-\infty}^{\Delta \nu} P(x) dx \]

.

Reimplemented in GaussianProfile, and LorentzianProfile.

Definition at line 56 of file LineBroadener.h.

---

The documentation for this class was generated from the following files:

• LineBroadener.h
• LineBroadener.cpp