338
A. L. Chakraborty and A. Roy
it is not possible to recover the n
th harmonic signal in complete isolation from the
distorting effect of the laser IM. The systematic distortion must be characterized for
a given laser and taken into account while modelling the n
th harmonic signal to fit it
to the n
th harmonic signal obtained from experiments for gas parameter extraction.
A key parameter in WMS is the modulation index given by m = ν/γ, where γ
is the half-width at half-maximum (HWHM) of the absorption line. The parameter
m represents the depth of modulation and it directly influences the strength of the
harmonic signal components. Figure 7c shows the first three Fourier components
(H 1 , H 2 , H 3 ) of the gas line shape (assumed to be Lorentzian for simplicity) for
increasing values of m. The Fourier components become stronger and wider as m
increases. The form (shape and symmetry) of the harmonic components is completely
determined by the line shape being probed. A characteristic feature is that the odd
harmonic components (H 1 and H 3 ) pass through zero at the line centre while the
even harmonic components (H 0 , H 2 etc) reach their peak values there. Note that
H 1 is always the dominant component. Although H 1 would seem to be the natural
choice for gas measurements, it is not necessarily the case because the linear IM
(I 1 ) introduces a typically large non-absorbing background component on which
the concentration-dependent signal appears, and which limits the sensitivity. The
laser IM also distorts the shape of the harmonic signals but that discussion is deferred
to a later section for the sake of clarity. Figure 7c shows that the H 1 component is
maximized at m = 2.0 while the H 2 component is maximized at m = 2.2. Note that
H 1 and H 2 vary slowly with m around these values. WMS systems are invariably
operated at these m-values to ensure that the signal strengths are influenced only by
changes in the mole fraction rather than by changes in pressure that cause unintended
changes in the m-value. This however requires the laser to be sufficiently frequency
agile at the operating frequency. The frequency agility of a laser is quantified by the
tuning coefficient (ξ = δν/δi, GHz/mA). It is always preferable to use a laser that
has a large value of ξ so that a small current modulation gives rise to the amount of
FM (ν) required to attain m = 2.2 for a given value of γ at the operating pressure.
Clearly both DC and AC characterization of the laser are important in WMS.
4.2 Laser Characterization and Implications for WMS
Semiconductor lasers differ greatly in their output power, current requirement, wavelength tuning range and modulation behaviour. It is necessary to accurately characterize the laser parameters to optimize the operation of a WMS system. These system
parameters must also be taken into account while generating the simulated n
th harmonic signal at the post-processing stage. Table 1 shows a comparison of some of
the main properties of a 2004 nm vertical cavity surface emitting laser (VCSELVL-2004-1-SQA5), a 4312 nm QCL (HHL513) and a 4559 nm QCL (HHL490)
that are used to detect CO 2 , CO 2 and N 2 O respectively. The noticeable features are
that the VCSEL has a very low threshold current and that the wavelength can be
current-tuned over ten times wider a range compared to the QCLs, which shows
A. L. Chakraborty and A. Roy
it is not possible to recover the n
th harmonic signal in complete isolation from the
distorting effect of the laser IM. The systematic distortion must be characterized for
a given laser and taken into account while modelling the n
th harmonic signal to fit it
to the n
th harmonic signal obtained from experiments for gas parameter extraction.
A key parameter in WMS is the modulation index given by m = ν/γ, where γ
is the half-width at half-maximum (HWHM) of the absorption line. The parameter
m represents the depth of modulation and it directly influences the strength of the
harmonic signal components. Figure 7c shows the first three Fourier components
(H 1 , H 2 , H 3 ) of the gas line shape (assumed to be Lorentzian for simplicity) for
increasing values of m. The Fourier components become stronger and wider as m
increases. The form (shape and symmetry) of the harmonic components is completely
determined by the line shape being probed. A characteristic feature is that the odd
harmonic components (H 1 and H 3 ) pass through zero at the line centre while the
even harmonic components (H 0 , H 2 etc) reach their peak values there. Note that
H 1 is always the dominant component. Although H 1 would seem to be the natural
choice for gas measurements, it is not necessarily the case because the linear IM
(I 1 ) introduces a typically large non-absorbing background component on which
the concentration-dependent signal appears, and which limits the sensitivity. The
laser IM also distorts the shape of the harmonic signals but that discussion is deferred
to a later section for the sake of clarity. Figure 7c shows that the H 1 component is
maximized at m = 2.0 while the H 2 component is maximized at m = 2.2. Note that
H 1 and H 2 vary slowly with m around these values. WMS systems are invariably
operated at these m-values to ensure that the signal strengths are influenced only by
changes in the mole fraction rather than by changes in pressure that cause unintended
changes in the m-value. This however requires the laser to be sufficiently frequency
agile at the operating frequency. The frequency agility of a laser is quantified by the
tuning coefficient (ξ = δν/δi, GHz/mA). It is always preferable to use a laser that
has a large value of ξ so that a small current modulation gives rise to the amount of
FM (ν) required to attain m = 2.2 for a given value of γ at the operating pressure.
Clearly both DC and AC characterization of the laser are important in WMS.
4.2 Laser Characterization and Implications for WMS
Semiconductor lasers differ greatly in their output power, current requirement, wavelength tuning range and modulation behaviour. It is necessary to accurately characterize the laser parameters to optimize the operation of a WMS system. These system
parameters must also be taken into account while generating the simulated n
th harmonic signal at the post-processing stage. Table 1 shows a comparison of some of
the main properties of a 2004 nm vertical cavity surface emitting laser (VCSELVL-2004-1-SQA5), a 4312 nm QCL (HHL513) and a 4559 nm QCL (HHL490)
that are used to detect CO 2 , CO 2 and N 2 O respectively. The noticeable features are
that the VCSEL has a very low threshold current and that the wavelength can be
current-tuned over ten times wider a range compared to the QCLs, which shows