Tunable diode laser absorption spectroscopy

The basic principle behind the TDLAS technique is simple. The focus here is on a single absorption line in the absorption spectrum of a particular species of interest. To start, the wavelength of a diode laser is tuned over a particular absorption line of interest and the intensity of the transmitted radiation is measured. The transmitted intensity can be related to the concentration of the species present by the Beer-Lambert law, which states that when a radiation of wavenumber ${\displaystyle ({\tilde {\nu }})}$ passes through an absorbing medium, the intensity variation along the path of the beam is given by,[6]

${\displaystyle I({\tilde {\nu }})=I_{0}({\tilde {\nu }})\exp(-\alpha ({\tilde {\nu }})L)=I_{0}({\tilde {\nu }})\exp(-\sigma ({\tilde {\nu }})NL)}$

where,

${\displaystyle I({\tilde {\nu }})}$ is the transmitted intensity of the radiation after it has traversed a distance ${\displaystyle L}$ through the medium,

${\displaystyle I_{0}({\tilde {\nu }})}$ is the initial intensity of the radiation,

${\displaystyle \alpha ({\tilde {\nu }})=\sigma ({\tilde {\nu }})N=S(T)\phi ({\tilde {\nu }}-{\tilde {\nu }}_{0})}$ is the absorbance of the medium,

${\displaystyle \sigma ({\tilde {\nu }})}$ is the absorption cross-section of the absorbing species,

${\displaystyle N\!}$ is the number density of the absorbing species,

${\displaystyle S(T)\!}$ is the line strength (i.e. the total absorption per molecule) of the absorbing species at temperature ${\displaystyle T}$,

${\displaystyle \phi ({\tilde {\nu }}-{\tilde {\nu }}_{0})}$ is the lineshape function for the particular absorption line. Sometimes also represented by ${\displaystyle g({\tilde {\nu }}-{\tilde {\nu }}_{0})}$,

${\displaystyle {\tilde {\nu }}_{0}}$ is the center frequency of the spectrum.

The above relation requires that the temperature ${\displaystyle T\!}$ of the absorbing species is known. However, it is possible to overcome this difficulty and measure the temperature simultaneously. There are number of ways to measure the temperature. A widely applied method, which can measure the temperature simultaneously, uses the fact that the line strength ${\displaystyle S(T)\!}$ is a function of temperature alone. Here two different absorption lines for the same species are probed while sweeping the laser across the absorption spectrum, the ratio of the integrated absorbance, is then a function of temperature alone.

${\displaystyle R=\left({\frac {S_{1}}{S_{2}}}\right)_{T}=\left({\frac {S_{1}}{S_{2}}}\right)_{T_{0}}\exp \left[-{\frac {hc(E_{1}-E_{2})}{k}}\left({\frac {1}{T}}-{\frac {1}{T_{0}}}\right)\right]}$

where,

${\displaystyle T_{0}\!}$ is some reference temperature at which the line strengths are known,

${\displaystyle \Delta E=(E_{1}-E_{2})\!}$ is the difference in the lower energy levels involved in the transitions for the lines being probed.

Another way to measure the temperature is by relating the FWHM of the probed absorption line to the Doppler line width of the species at that temperature. This is given by,

${\displaystyle FWHM(\Delta {\tilde {\nu }}_{D})={\tilde {\nu }}_{0}{\sqrt {\frac {8kT\ln 2}{mc^{2}}}}={\tilde {\nu }}_{0}(7.1623{\mbox{x}}10^{-7}){\sqrt {\frac {T}{M}}}}$

where,

${\displaystyle m}$ is the weight of one molecule of the species, and

${\displaystyle M}$ is the molecular weight of the species.

Note: In the last expression, ${\displaystyle T}$ is in kelvins and ${\displaystyle M}$ is in g/mol. However, this method can be used, only when the gas pressure is low (of the order of few mbar). At higher pressures (tens of millibars or more), pressure or collisional broadening becomes important and the lineshape is no longer a function of temperature alone.

The effect of a mean flow of the gas in the path of the laser beam can be seen as a shift in the absorption spectrum, also known as Doppler shift. The shift in the frequency spectrum is related to the mean flow velocity by,

${\displaystyle \Delta {\tilde {\nu }}_{D}={\frac {V}{c}}{\tilde {\nu }}_{0}\cos \theta }$

where,

${\displaystyle \theta }$ is the angle between the flow direction and the laser beam direction.

Note : ${\displaystyle \Delta {\tilde {\nu }}_{D}}$ is not the same as the one mentioned before where it refers to the width of the spectrum. The shift is usually very small (3×10⁻⁵ cm⁻¹ ms⁻¹ for near-IR diode laser) and the shift-to-width ratio is of the order of 10⁻⁴.

Modulation techniques make use of the fact that technical noise usually decreases with increasing frequency (which is why it is often referred to as 1/f noise) and improve the signal to noise ratio by encoding and detecting the absorption signal at a high frequency, where the noise level is low. The most common modulation techniques are wavelength modulation spectroscopy (WMS) and frequency modulation spectroscopy (FMS).

In WMS the wavelength of the light is continuously scanned across the absorption profile, and the signal is detected at a harmonic of the modulation frequency.

In FMS, the light is modulated at a much higher frequency but with a lower modulation index. As a result, a pair of sidebands separated from the carrier by the modulation frequency appears, giving rise to a so-called FM-triplet. The signal at the modulation frequency is a sum of the beat signals of the carrier with each of the two sidebands. Since these two sidebands are fully out of phase with each other, the two beat signals cancel in the absence of absorbers. However, an alteration of any of the sidebands, either by absorption or dispersion, or a phase shift of the carrier, will give rise to an unbalance between the two beat signals, and therefore a net-signal.

Although in theory baseline-free, both modulation techniques are usually limited by residual amplitude modulation (RAM), either from the laser or from multiple reflections in the optical system (etalon effects). If these noise contributions are held low, the sensitivity can be brought into the 10⁻⁵ – 10⁻⁶ range or even better.

In general the absorption imprints are generated by a straight line light propagation through a volume with the specific gas. To further enhance the signal, the pathway of the light travel can be increased with multi-pass cells. There is however a variety of the WMS-technique that utilizes the narrow line absorption from gases for sensing even when the gases are situated in closed compartments (e.g. pores) inside solid materia. The technique is referred to as gas in scattering media absorption spectroscopy (GASMAS).

The second way of improving the detectability of TDLAS technique is to extend the interaction length. This can be obtained by placing the species inside a cavity in which the light bounces back and forth many times, whereby the interaction length can be increased considerably. This has led to a group of techniques denoted as cavity enhanced AS (CEAS). The cavity can either be placed inside the laser, giving rise to intracavity AS, or outside, when it is referred to as an external cavity. Although the former technique can provide a high sensitivity, its practical applicability is limited because of all the non-linear processes involved.

External cavities can either be of multi-pass type, i.e. Herriott or White cells, of non- resonant type (off-axis alignment), or of resonant type, most often working as a Fabry–Pérot (FP) etalon. Multi-pass cells, which typically can provide an enhanced interaction length of up to ~2 orders of magnitude, are nowaday common together with TDLAS.

Resonant cavities can provide a much larger path length enhancement, in the order of the finesse of the cavity, F, which for a balanced cavity with high reflecting mirrors with reflectivities of ~99.99–99.999% can be ~ 10⁴ to 10⁵. It should be clear that if all this increase in interaction length can be utilized efficiently, this vouches for a significant increase in detectability. A problem with resonant cavities is that a high finesse cavity has very narrow cavity modes, often in the low kHz range (the width of the cavity modes is given by FSR/F, where FSR is the free-spectral range of the cavity, which is given by c/2L, where c is the speed of light and L is the cavity length). Since cw lasers often have free-running linewidths in the MHz range, and pulsed even larger, it is non-trivial to couple laser light effectively into a high finesse cavity.

The most important resonant CEAS techniques are cavity ring-down spectrometry (CRDS), integrated cavity output spectroscopy (ICOS) or cavity enhanced absorption spectroscopy (CEAS), phase-shift cavity ring-down spectroscopy (PS-CRDS) and Continuous wave Cavity Enhanced Absorption Spectrometry (cw-CEAS), either with optical locking, referred to as (OF-CEAS),[7] as has been demonstrated Romanini et al.[8] or by electronic locking.,[8] as for example is done in the Noise-Immune Cavity-Enhanced Optical-Heterodyne Molecular Spectroscopy (NICE-OHMS) technique.[9][10][11] or combination of frequency modulation and optical feedback locking CEAS, referred to as (FM-OF-CEAS).[12]

The most important non-resonant CEAS techniques are off-axis ICOS (OA-ICOS)[13] or off-axis CEAS (OA-CEAS), wavelength modulation off-axis CEAS (WM-OA-CEAS),[14] off-axis phase-shift cavity enhanced absorption spectroscopy (off-axis PS-CEAS).[15]

These resonant and non-resonant cavity enhanced absorption techniques have so far not been used that frequently with TDLAS. However, since the field is developing fast, they will presumably be more used with TDLAS in the future.