Wavelength Modulation Spectroscopy
345
5 Calibration-Free WMS
In general the signal of interest in n
th harmonic WMS is dominated by the n
th Fourier
component scaled by the laser intensity. The challenge in real-life measurements
is that the strength of the n
th harmonic signal is liable to vary significantly due
to several external factors that are unrelated to the gas parameters and which the
user cannot directly control. This happens mainly due to fluctuations in the system’s
optical throughput caused by variable coupling that could be the result of mechanical
vibrations and contamination of optical surfaces by dust, dirt and excessive moisture
in the environment. The bottom line is that the recovered electrical signal level
may vary significantly due to reasons other than changes in the mole fraction. This is
what made calibration necessary in traditional WMS applications. Although repeated
calibration may be acceptable in laboratory environments, it is clearly impractical and
undesirable in field measurements. Calibration of measurement systems is a critical
operational aspect. WMS systems are often pre-calibrated in the laboratory for a
wide range of concentration, pressure and temperature values before deployment.
Calibration allows one to convert the detected voltage level to the corresponding
mole fraction of the unknown sample. Only a few distinct calibration-free WMS
techniques have been successfully demonstrated [6, 49–53]. These are described in
the following sections.
5.1 Calibration-Free 1f WMS: RAM and PD Methods
The first calibration-free techniques to be demonstrated are the closely related Residual Amplitude Modulation (RAM) method [50] and the Phasor Decomposition (PD)
method [51]. The distinctive feature of both methods is that although they use laser
modulation, they recover the absolute gas absorption line shape from the 1f WMS
signal components just as in direct detection. Both techniques exploit the higher sensitivity of WMS while retaining the simplicity of signal processing of direct detection.
These techniques were initially limited to low m-values (m < 0.7) but subsequent
research [54, 55] extended them to high m-values. For ease of understanding we
restrict ourselves to low m-values for which the line shape may be expanded using a
Taylor series formulation. For low m-values and for lasers with predominantly linear
IM, the first three relevant terms are given by, [50],
I out = I 1 (λ c ) cos ω m t − I 1 (λ c )α(λ c )CL cos ω m t − I (λ c )
d α(λ c )
d (λ c )
δλCL cos(ω m t − ψ 1 )
(28)
Here C is the concentration and L is the path length. The first term is the concentrationindependent background RAM signal that arises due to the laser IM and is usually
large for edge-emitting lasers. It is undesirable because it saturates the detection
345
5 Calibration-Free WMS
In general the signal of interest in n
th harmonic WMS is dominated by the n
th Fourier
component scaled by the laser intensity. The challenge in real-life measurements
is that the strength of the n
th harmonic signal is liable to vary significantly due
to several external factors that are unrelated to the gas parameters and which the
user cannot directly control. This happens mainly due to fluctuations in the system’s
optical throughput caused by variable coupling that could be the result of mechanical
vibrations and contamination of optical surfaces by dust, dirt and excessive moisture
in the environment. The bottom line is that the recovered electrical signal level
may vary significantly due to reasons other than changes in the mole fraction. This is
what made calibration necessary in traditional WMS applications. Although repeated
calibration may be acceptable in laboratory environments, it is clearly impractical and
undesirable in field measurements. Calibration of measurement systems is a critical
operational aspect. WMS systems are often pre-calibrated in the laboratory for a
wide range of concentration, pressure and temperature values before deployment.
Calibration allows one to convert the detected voltage level to the corresponding
mole fraction of the unknown sample. Only a few distinct calibration-free WMS
techniques have been successfully demonstrated [6, 49–53]. These are described in
the following sections.
5.1 Calibration-Free 1f WMS: RAM and PD Methods
The first calibration-free techniques to be demonstrated are the closely related Residual Amplitude Modulation (RAM) method [50] and the Phasor Decomposition (PD)
method [51]. The distinctive feature of both methods is that although they use laser
modulation, they recover the absolute gas absorption line shape from the 1f WMS
signal components just as in direct detection. Both techniques exploit the higher sensitivity of WMS while retaining the simplicity of signal processing of direct detection.
These techniques were initially limited to low m-values (m < 0.7) but subsequent
research [54, 55] extended them to high m-values. For ease of understanding we
restrict ourselves to low m-values for which the line shape may be expanded using a
Taylor series formulation. For low m-values and for lasers with predominantly linear
IM, the first three relevant terms are given by, [50],
I out = I 1 (λ c ) cos ω m t − I 1 (λ c )α(λ c )CL cos ω m t − I (λ c )
d α(λ c )
d (λ c )
δλCL cos(ω m t − ψ 1 )
(28)
Here C is the concentration and L is the path length. The first term is the concentrationindependent background RAM signal that arises due to the laser IM and is usually
large for edge-emitting lasers. It is undesirable because it saturates the detection