The Voigt profile is a mathematical function which accurately represents the absorption cross section per atom,
α
ν
[cm
2
], for conditions under which the only significant operational linebroadening mechanisms are radiation damping (natural line width), collisional damping and thermal Doppler broadening. (With modification of the temperature parameter, T , it can also accommodate the broadening effects of microturbulence.) The Voigt profile is written,





0 a 

  a
2 e
 y
2

( u
 y )
2 dy .
In this expression

0

 e
2 mc f

1
 
D
 g n g n '
A nn '
 2
8

3
2
1
 
D
[ cm
2
] is called the "fictitious absorption coefficient." It corresponds to the central value of the absorption coefficient (
ν
=
ν
0
, u = 0) for the case of zero damping (
Γ
=
δ
= a = 0). Since such a case never occurs, the title is appropriate. The definitions and physical significances of each of the other parameters in the expression for α
ν
are as follows:
 
D

 c
0
2 kT is simply the
M
" Doppler wi dth" as has been previously defined.
 
'


0 v
 c

'
 ν
0 is the Doppler shift of the central frequency for radial velocity v .
δ  Γ /4π = δ r
+ δ c
 Γ r
/4π +  Γ c
/4π is the "damping" half width (a combination of radiation damping and collisional damping). y
 ν'/  ν
D is the ratio of the Doppler shift to the Doppler width, i.e
., the Doppler shift in units of the
Doppler width.
 ν = ν 
ν
0 is the displacement of the frequency under consideration from the line center, u

 
 

D
0 
 
 
D is the displacement of the frequency under consideration from the line center in units of the
Doppler width and

a


 
D is the ratio of the damping half width to the Doppler width, i.e
., the damping half width in units of the Doppler width. Note that a , u and y , all the variables in the explicit definition of the Voigt profile, except α
0
, are dimensionless.