where m is the molecule mass; k is Boltzmann’s constant; T is the absolute
temperature. Doppler’s halfwidth of the absorption line is a
ðiÞ
D
ffiffiffiffiffiffiffi
ln 2
p
.
The comparison of Lorenz and Doppler’s contours is shown in the Fig. 3.2.
Voigt’s contour. The mutual accounting for both Lorenz and Doppler’s broadening in calculating the function f i ðn; n
ðiÞ
0 Þ leads to Lorenz-Doppler’s contour that is
called the Voigt’s contour. The absorption coefficient in the Eq. 8.1 is assumed as
k
ðiÞ
n ¼ k
ðiÞ
0n f i n; n
ðiÞ
0
;
(3.11)
where
k
ðiÞ
0n ¼
ffiffiffiffiffiffiffiffi
ln 2
p
r
S i ðTÞ
a D
:
(3.12)
The expression for the contour of i-th spectral line is following:
f i n; n
ðiÞ
0
¼
a
p
ð
1
À1
e
Àx
2
a 2 þ w À x
ð
Þ
2
dx;
(3.13)
where
a ¼
ffiffiffiffiffiffiffi
ln 2
p
a
ðiÞ
L
a
ðiÞ
D
;
(3.14)
w ¼
ffiffiffiffiffiffiffi
ln 2
p
n À n
ðiÞ
0
a
ðiÞ
D
:
(3.15)
Doppler
Lorenz
-3
-2
-1
0
1
2
3
Fig. 3.2 Comparison of
Lorenz’s and Doppler’s
contours 1 – Lorenz’s contour,
2 – Doppler’s contour
32
3 The Direct Calculation of the Absorption Coefficient of Atmosphere Gases