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A. Maity et al.
Now, let us put some gas sample in the cavity, then what happens is that the light
decays more rapidly compared to the empty cavity as a result of absorption of the
gas sample and now the ring-down time can described by the following equation [4]:
τ =
1
c
[
L
(1 − R) + α.d
]
(4)
Here, τ is the ring-down time (RDT) in presence of sample in optical cavity,
d actually corresponds to the physical length (L) of the cavity containing the gas
sample. α is known as the absorption coefficient which is the product of wavelength
dependent absorption cross-section (σ λ ) and concentration of the sample ([X]):
α = σ λ .[X]
(5)
However, it is clear that RDT is linked with the reflectivity of the cavity mirrors,
length of the cavity and absorption coefficient and thus devoid of any intensity
fluctuations of the laser beam. Therefore, the measurements are done in the time
domain.
In a typical CRDS experiment, if we record the ring-down times with respect to
laser frequency, the absorption co-efficient of the gas sample can be determined in
the following way:
α = σ λ .[X] =
k
c
; where k =
1
τ
−
1
τ 0
(6)
As it is already mentioned that CRDS is a high sensitive cavity-enhanced technique
method, the sensitivity is represented by the minimum absorption coefficient (α min )
in the following manner:
α min =
1
cτ 0
τ min
τ 0
(7)
In the above equation, τ min indicates the minimum detectable change in RDTs
and (τ min /τ 0 ) represents the relative errors of the experimentally determined RDTs.
However, the sensitivity typically lies in the range between 10
–8 cm
−1 and 10
–10 cm
−1 .
It is noteworthy to mention that minimum detectable concentration ([X min ]) can be
also determined using the following equation:
[X min ] =
α min
σ λ
(8)
It suggests that if the absorption cross-section is high at particular wavelength,
we can then detect much lower concentration of the gas-phase molecules. Moreover, in this connection, there are two important parameters, termed as mixing ratios
sometimes used to indicate the detection limit of a CRDS setup: ppbv (parts per
A. Maity et al.
Now, let us put some gas sample in the cavity, then what happens is that the light
decays more rapidly compared to the empty cavity as a result of absorption of the
gas sample and now the ring-down time can described by the following equation [4]:
τ =
1
c
[
L
(1 − R) + α.d
]
(4)
Here, τ is the ring-down time (RDT) in presence of sample in optical cavity,
d actually corresponds to the physical length (L) of the cavity containing the gas
sample. α is known as the absorption coefficient which is the product of wavelength
dependent absorption cross-section (σ λ ) and concentration of the sample ([X]):
α = σ λ .[X]
(5)
However, it is clear that RDT is linked with the reflectivity of the cavity mirrors,
length of the cavity and absorption coefficient and thus devoid of any intensity
fluctuations of the laser beam. Therefore, the measurements are done in the time
domain.
In a typical CRDS experiment, if we record the ring-down times with respect to
laser frequency, the absorption co-efficient of the gas sample can be determined in
the following way:
α = σ λ .[X] =
k
c
; where k =
1
τ
−
1
τ 0
(6)
As it is already mentioned that CRDS is a high sensitive cavity-enhanced technique
method, the sensitivity is represented by the minimum absorption coefficient (α min )
in the following manner:
α min =
1
cτ 0
τ min
τ 0
(7)
In the above equation, τ min indicates the minimum detectable change in RDTs
and (τ min /τ 0 ) represents the relative errors of the experimentally determined RDTs.
However, the sensitivity typically lies in the range between 10
–8 cm
−1 and 10
–10 cm
−1 .
It is noteworthy to mention that minimum detectable concentration ([X min ]) can be
also determined using the following equation:
[X min ] =
α min
σ λ
(8)
It suggests that if the absorption cross-section is high at particular wavelength,
we can then detect much lower concentration of the gas-phase molecules. Moreover, in this connection, there are two important parameters, termed as mixing ratios
sometimes used to indicate the detection limit of a CRDS setup: ppbv (parts per