339
Airborne Water Vapor Differential Absorption Lidar
With a laser transmitter having a narrow spectral linewidth, the absorption coefficient can be given directly by the product of the absorption cross section and the
molecule number density. Thus, we have
∆
∆
α
α
α
ρ σ λ
σ λ
ρ σ
ab
ab on
ab off
n
on
off
n
=
−
= ⋅
−
=
,
,
( ( )
( ))
,
(14.5)
where ρ n is the molecule number density of the trace gas, and σ is the molecular
absorption cross section. In the idealized case, we find that
ρ
σ
n
on
off
R
d
dR
P R
P R
( )
ln
( )
( )
=
2∆
.
(14.6)
Equation 14.6 shows that DIAL is a self-calibrating measurement technique. All
instrument constants are removed by the sequential operations of forming a ratio
and taking the derivative with respect to range. However, it is based on the assumpwith respect to range. However, it is based on the assumpwith respect to range. However, it is based on the assumpit is based on the assumpis based on the assumpbased on the assumpd on the assumpon
assumption that there is no range-dependent difference in the DIAL responses at the two
different wavelengths. In fact, Fredriksson and Hertz (1984) provided an extensive
summary of experimental problems that could cause systematic differences at the
two wavelengths and consequent errors in the measured value of ρ n .
In practice, DIAL signals are not recorded or analyzed as continuous functions
but as values in discrete range bins. Expressing the derivative in Equation 14.6 in
terms of a range increment ΔR, we have
ρ
σ
n
off
on
off
on
R
R
P R P R
P R P R
( )
ln
( ) ( )
( ) ( )
=
1
2
2
1
1
2
∆ ∆
.
(14.7)
For a real DIAL system, the term in parentheses in Equation 14.7 is resolvable. For
a given Δσ, this term sets the detection limitation (ρ n,lim ) of a system. Equivalently,
Equation 14.7 can also be used to design a DIAL to fi nd the minimum range resolu7 can also be used to design a DIAL to fi nd the minimum range resolucan also be used to design a DIAL to fi nd the minimum range resolualso be used to design a DIAL to fi nd the minimum range resolube used to design a DIAL to fi nd the minimum range resoluto design a DIAL to fi nd the minimum range resoludesign a DIAL to fi nd the minimum range resoluDIAL to fi nd the minimum range resoluto find the minimum range resoluminimum range resoluminimum range resolution (ΔR min ) for a given value of Δσ.
14.2.3 dial MeaSuReMent eRRoRS
When Equation 14.7 is used to derive the water vapor density from measurements
of P on (R) and P off (R), it is necessary to know the parameters determining the
differential cross section (Δσ)/absorption cross section (σ on and σ off ). Moreover,
for high-resolution measurement the spectral distributions of the transmitted and
backscattered light have to be treated carefully, especially in the case that the
transmitted spectrum is not much narrower than the absorption line. Ismail and
Browell (1989) presented a thorough analysis of the sensitivity of DIAL measure(1989) presented a thorough analysis of the sensitivity of DIAL measurepresented a thorough analysis of the sensitivity of DIAL measurea thorough analysis of the sensitivity of DIAL measurea thorough analysis of the sensitivity of DIAL measurements to both differential absorption errors and random signal errors. The former
type of error arises from both atmospheric and system effects, including temperaincluding temperaincluding temperature and pressure sensitivities of the trace gas spectrum, Doppler broadening of
Airborne Water Vapor Differential Absorption Lidar
With a laser transmitter having a narrow spectral linewidth, the absorption coefficient can be given directly by the product of the absorption cross section and the
molecule number density. Thus, we have
∆
∆
α
α
α
ρ σ λ
σ λ
ρ σ
ab
ab on
ab off
n
on
off
n
=
−
= ⋅
−
=
,
,
( ( )
( ))
,
(14.5)
where ρ n is the molecule number density of the trace gas, and σ is the molecular
absorption cross section. In the idealized case, we find that
ρ
σ
n
on
off
R
d
dR
P R
P R
( )
ln
( )
( )
=
2∆
.
(14.6)
Equation 14.6 shows that DIAL is a self-calibrating measurement technique. All
instrument constants are removed by the sequential operations of forming a ratio
and taking the derivative with respect to range. However, it is based on the assumpwith respect to range. However, it is based on the assumpwith respect to range. However, it is based on the assumpit is based on the assumpis based on the assumpbased on the assumpd on the assumpon
assumption that there is no range-dependent difference in the DIAL responses at the two
different wavelengths. In fact, Fredriksson and Hertz (1984) provided an extensive
summary of experimental problems that could cause systematic differences at the
two wavelengths and consequent errors in the measured value of ρ n .
In practice, DIAL signals are not recorded or analyzed as continuous functions
but as values in discrete range bins. Expressing the derivative in Equation 14.6 in
terms of a range increment ΔR, we have
ρ
σ
n
off
on
off
on
R
R
P R P R
P R P R
( )
ln
( ) ( )
( ) ( )
=
1
2
2
1
1
2
∆ ∆
.
(14.7)
For a real DIAL system, the term in parentheses in Equation 14.7 is resolvable. For
a given Δσ, this term sets the detection limitation (ρ n,lim ) of a system. Equivalently,
Equation 14.7 can also be used to design a DIAL to fi nd the minimum range resolu7 can also be used to design a DIAL to fi nd the minimum range resolucan also be used to design a DIAL to fi nd the minimum range resolualso be used to design a DIAL to fi nd the minimum range resolube used to design a DIAL to fi nd the minimum range resoluto design a DIAL to fi nd the minimum range resoludesign a DIAL to fi nd the minimum range resoluDIAL to fi nd the minimum range resoluto find the minimum range resoluminimum range resoluminimum range resolution (ΔR min ) for a given value of Δσ.
14.2.3 dial MeaSuReMent eRRoRS
When Equation 14.7 is used to derive the water vapor density from measurements
of P on (R) and P off (R), it is necessary to know the parameters determining the
differential cross section (Δσ)/absorption cross section (σ on and σ off ). Moreover,
for high-resolution measurement the spectral distributions of the transmitted and
backscattered light have to be treated carefully, especially in the case that the
transmitted spectrum is not much narrower than the absorption line. Ismail and
Browell (1989) presented a thorough analysis of the sensitivity of DIAL measure(1989) presented a thorough analysis of the sensitivity of DIAL measurepresented a thorough analysis of the sensitivity of DIAL measurea thorough analysis of the sensitivity of DIAL measurea thorough analysis of the sensitivity of DIAL measurements to both differential absorption errors and random signal errors. The former
type of error arises from both atmospheric and system effects, including temperaincluding temperaincluding temperature and pressure sensitivities of the trace gas spectrum, Doppler broadening of