Cavity ringdown spectroscopy is an efficient gas-sensing method, but improvement in measurement speed is required before this method can be applied to the analysis of fast phenomena. We present a new continuous-wave cavity ringdown design, involving fast tuning of the laser frequency and a rapidly swept optical cavity, to allow high-speed sensing with spectral resolution refinement. This approach, which provides a simple and versatile instrument, is investigated numerically and experimentally. By performing detection of a forbidden transition of molecular oxygen near 766 nm during a 2-ms single sweep of the laser frequency, we show that our system fulfils the requirements for probing rapid chemical processes.
©2005 Optical Society of America
Nonintrusive optical sensing tools are needed to perform fast, sensitive, and local gas analysis of transient flows generated in blowdown hypersonic wind tunnels. In particular, monitoring of trace molecular oxygen (O2) is of high interest, since this substance is deeply involved in many chemical processes occurring in those flows, including dissociation and recombination effects. Cavity ringdown spectroscopy (CRDS) has proved to be an accurate way to probe a wide range of gas environments [1,2] and is a promising candidate for realizing such measurements. This laser-based absorption spectroscopy technique directly deduces the absolute value of optical losses in a high-finesse stable resonator from its measured photon lifetime. The ringdown cavity is created by positioning two highly reflective mirrors (typically reflecting more than 99.9%) around the medium of interest. The light source is coupled to the ringdown cavity, resulting in a rapid buildup of the intensity of radiation trapped inside. After abruptly stopping the laser injection, the stored light propagates back and forth within the cavity and, at each pass, gradually leaks out through the mirrors. The transmitted intensity I(t) is an exponential decay of the initial intensity I 0 given by the equation
where τ is the ringdown time of the cavity. The loss rate per distance is then given by
with c the speed of light, L the cavity length, R the reflectivity of the mirrors, A the diffraction losses of the mirrors, and α the medium absorption coefficient. For small laser frequency tuning ranges, the first term on the right-hand side of Eq. (2) is slowly frequency dependent and appears as a baseline offset that can be measured when the cavity is empty. A plot of the loss rate α as a function of the laser frequency is a CRDS spectrum. The basic principle of a CRDS setup with a continuous-wave (cw) laser is illustrated in Fig. 1.
Compared with traditional absorption spectroscopic techniques, CRDS exhibits the major advantages of long effective absorption path lengths (many kilometers) combined with intrinsic insensitivity to source-intensity fluctuations, thus offering great sensitivity. It uses either pulsed [1,3] or cw lasers [4–6], but, since CRDS with cw lasers (cw CRDS) is particularly well suited for the realization of efficient, compact, and low-cost gas detectors, we focus on the use of tunable diode lasers as light sources for our applications. In conventional cw CRDS several strategies can be adopted to produce the exponential decay of light transmitted by the cavity. The cavity length can be either scanned [4–6] or locked  to the laser wavelength, or the laser frequency can be swept through the successive modes of a fixed ringdown cavity . In all cases a rapid extinction of the laser beam permits exponential free photon decay when the cavity has stored sufficient energy. Averaging procedures are generally applied on ringdown signals to record absorption spectra with improved sensitivity, thus giving long integration times.
In addition to serving as a means of atmospheric monitoring, cw CRDS is an efficient tool for probing chemical processes at remote sites and in hostile environments; however, measurements in blowdown hypersonic wind tunnels impose additional temporal constraints. Indeed, the flows we are targeting are generated during short gusts, typically 200 ms long, with aerodynamic conditions changing by 1% ms-1. Another difficulty arises from the low gas pressures encountered in such media (absorption linewidths are one tenth smaller than at atmospheric pressure). The crucial goal therefore is to develop cw CRDS as a fast and high-resolution method to measure trace gas, especially O2, in hypersonic flows.
It has been shown that a ringdown signal can be obtained during a rapid and continuous sweep of the cavity length, the cavity injection being obtained while passing through the resonance condition, without any optical switch [9,10]. Recently, another cw CRDS scheme has been demonstrated in which an absorption spectrum is recorded during a single rapid sweep of the laser frequency . Nevertheless, the free spectral range of the fixed cavity represents in this approach a limit on the frequency resolution that the technique can achieve and the only way to increase resolution is to increase the cavity length.
In this paper we present an alternative cw CRDS design based on fast tuning of the laser frequency and an additional simultaneous sweep of the cavity length. This method permits high-speed measurements and also presents an interesting potential for increasing spectral resolution when low-pressure features are monitored. The principle of operation of our system is demonstrated numerically and experimentally. By performing detection of a forbidden transition of O2 (near 766 nm) during a 2-ms single sweep, with a detection limit of 2×10-7 cm-1, we show that our simplified CRDS setup offers adequate performance for fast-sensing applications.
2. Theoretical Study of CRDS by Simultaneous Laser and Cavity Tuning
2.1. Principle of Operation
The basic principle behind our cw CRDS approach is based on physical properties that are well known in terms of the response of a high-finesse Fabry-Perot resonator to cw laser input [12–14]. In the following we consider only selective excitation of the TEM00 cavity longitudinal modes, obtained by accurate transverse mode matching, which increases the ringdown signal-to-noise ratio, avoids transverse mode beating , and allows unambiguous determination of the ringdown time. Injection of the ringdown cavity, followed by its relaxation, can be accomplished either by a continuous sweep of the cavity modes while the laser frequency is fixed or by a continuous scan of the laser frequency over the motionless cavity modes. In both cases, the buildup of the intracavity energy occurs as soon as the resonance condition between the laser and a cavity mode is satisfied. The subsequent light decay occurs as the laser frequency moves through the cavity bandwidth, or, inversely, when the cavity mode frequency is tuned. A sufficiently fast sweep through resonance leads to asymmetric temporal profiles that exhibit nearly exponential decays with smoothed superimposed oscillations, caused by beating between the stored intracavity field and the progressively detuned incoming field [9,14].
When a rapidly swept laser source and a static cavity of length L 0 are used [8,11], the maximum achievable frequency resolution corresponds to its free spectral range (FSR=c/2L 0). Hence, for our 50-cm-long cavity, the separation between ringdown events is 0.01 cm-1 (0.3 GHz). We overcome this limitation by using a novel cw CRDS design that involves synchronous laser and cavity tuning to combine rapidity of absorption measurements and resolution enhancement. Here absorption features are rapidly recorded during a single scan of the laser frequency through the probed absorption line as the cavity-resonance frequencies are synchronously swept in the opposite direction by scanning the cavity length. This leads to faster relative frequency changes, and the number of frequency-matched events between the laser and the cavity is increased. The ringdown events, corresponding to the successive resonances of the cavity, are thus separated by a distance smaller than the cavity’s FSR. The above-described principle of cavity injection is depicted in Fig. 2.
To confirm this behavior, the dynamic response of a rapidly swept Fabry-Perot cavity to a frequency-scanned electromagnetic field is simulated by use of a superposition of multiply reflected plane-wave fields that enter the cavity at times separated by the cavity round-trip time. Assuming that the laser is well mode matched to the cavity, we consider the process of excitation of the successive cavity’s TEM00 longitudinal modes while they move through the frequency-tuned laser line. Unlike in previous works [12–14], here both the changes in cavity length and in laser frequency are simultaneously taken into account by updating the amplitude and phase of the reflected plane waves at each round trip. The cavity field is propagated around the cavity, reflected from the moving end mirror, and combined at the input mirror with the next transmitted incident beam. This gives a recursive relationship that relates the cavity field to both the input field and the cavity field existing one round trip before, including all effects responsible for phase changes in the intracavity field, and that can be extended to any integer number n of later round trips.
To simulate the laser frequency scan over an absorption line at atmospheric pressure, within 2 ms a 0.4-cm-1 (12-GHz) positive and continuous laser sweep is combined with a synchronized positive cavity sweep. Considering a 5-µm modulation, the cavity and laser tuning rates are u mode=-1.96 THz s-1 and u las=6 THz s-1, resulting in an effective frequency sweep of ~8 THz s-1. Relevant parameters used in the simulation are the 50-cm cavity length, the 99.97% mirror reflectivity, and the 3×10-7-cm-1 absorption coefficient, giving a 5.3-µs ringdown time. The cavity has a typical finesse of 104 and is coupled to an external-cavity diode laser (ECDL) with a typical full width at half-maximum (FWHM) linewidth of 100 kHz for the short time scales. In Fig. 3 we show calculated transmission events for increasingly faster passes through resonance, with the total amplitude of the piezo-electrical cavity sweep going from 0 to 10 µm. These events are observed during a 0.02-cm-1 fraction of the overall sweep. When no PZT sweep is applied, the 0.01-cm-1 FSR for a 50-cm cavity is recovered [Fig. 3(a)]. For higher-amplitude cavity-length modulation, calculated distances between successive ringdown events are smaller than the fixed-cavity FSR [Fig. 3(b)].
2.2. Further Analysis of Resolution Refinement through Cavity-Length Tuning
A brief demonstration is given here of the derivation of the analytical expression for the new value of the frequency resolution when the laser and cavity frequencies are simultaneously swept. Considering a ringdown cavity with one mirror translated at a constant velocity u, the cavity length is a function of time given by L(t)=L 0+ ut, where L 0 is the initial fixed-cavity length at t=0. The successive cavity-resonance frequencies are indexed by a positive integer m and expressed as νm (t)=mc/[2L(t)]. As a direct consequence of the dependence from L(t), a linear frequency sweep of the cavity modes is induced, as shown in Fig. 2. The frequency-tuning speed of the longitudinal cavity modes u mode is obtained from a time derivative:
The frequency-tuned laser is represented by a progressive plane-wave field with a linear frequency sweep expressed as ν las(t)=ν0 +u las t, where ν0 is the laser frequency at t=0 and ulas the laser frequency scanning speed. Let t 1 be the time at which the first resonance match occurs between the laser frequency and the m-indexed cavity mode frequency. The resonance condition ν las(t 1)=ν m(t 1) leads to
where ν 0 and νm (0), respectively, are the initial frequencies of the laser and the cavity mode. In the same way, the next resonance condition is satisfied when the laser frequency is matched with the next moving cavity mode at the later time t 2, which leads to
We thus immediately identify the first term as the frequency space between two successive resonances and ν m+1(0)-νm (0) as the initial FSR of the fixed cavity, while u las-u mode represents the equivalent frequency scanning speed, accounting for the laser sweep plus the opposite cavity mode tuning effect. Hence the new spectral resolution can be expressed as
We conclude, from the last expression in Eq. (7), that the necessary condition for observing a diminution of the frequency space between consecutive resonances is u mode/u las <0. It is also shown that it is reduced when the ratio |u mode/u las| is increased, through an increase in |u mode|, with higher cavity sweep ranges [Fig. 4(a)], or through a decrease in |u las|, with smaller laser frequency excursions [Fig. 4(b)]. Indeed, for low-pressure features, a 0.1-cm-1 laser sweep range is sufficient to determine the absorption line shape.
In addition, reducing the cavity length can lead to a relative greater increase of the frequency resolution, since |u mode| is inversely proportional to L 0 [Eq. (3)]. As an example, a 25-cm cavity length and a 5-µm cavity sweep give a 0.00554 cm-1 resolution, corresponding to a 3.6 enhancement factor over the 0.02-cm-1 resolution for a static cavity. It is thus possible to recover satisfying resolutions with a shorter cavity, in spite of its FSR increase.
New perspectives for the development of compact cw CRDS instruments are thus provided, since it is not necessary to use very long cavities to increase spectral resolution. Unfortunately, the technique suffers from low injection levels when the frequency tuning rate is increased, as is seen in Fig. 3, and the detection noise may become a limiting factor. It must also be pointed out that the resolution enhancement seems limited by the fact that the decay of each ringdown event must be complete before the next event builds up. This does not concern us here, since we work with rather short ringdown times (<4 µs), but it must be taken into account if longer ringdown times have to be used to increase sensitivity.
Another limitation to this technique could be the accumulation of Doppler-type shifts on the laser frequency that occur with each reflection from a moving mirror. After injection of the cavity, the intracavity laser frequency ν 0 is progressively shifted, following the continuous change of the cavity-resonance frequency as the cavity length is swept, by an amount νD (t)=-ν 0 ut/L 0. Different frequencies that experience different absorption losses are generated and can yield nonexponential cavity decay signals, leading to errors in the ringdown time determination. It has been shown that for relatively long cavity mirror displacements the influence of intracavity Doppler effects could result in significant frequency shifts of absorption features . However, since the time rate of the Doppler shift is given by ν′ D (t)=-ν 0 u/L 0, the effective intracavity shift introduced in a ringdown signal having a time decay τ is τνD ′(t). In our experience, considering a moderate cavity sweep range (<10 µm) and the time scale of the ringdown time (<4 µs), the total frequency excursion can be estimated to be less than 15 MHz, which is small compared with the absorption linewidth.
3. Experimental Procedures and Results
The experimental setup devoted to the record of molecular oxygen spectra in room air is depicted in Fig. 5. We use an external-cavity diode laser (Toptica) emitting at ~766 nm as a narrow-linewidth cw light source. After propagation through a Faraday optical isolator (Isowave) and a single-mode fiber with FC–APC connectors, a 2-mW laser beam is TEM00-mode-matched by use of a 6-mm-focal lens and two injection mirrors. The 50-cm-long ringdown cavity is formed by two concave mirrors (Layertec) with a specified reflectivity of 99.97% at 765 nm and a 1-m radius of curvature. The air sample is confined in a metallic tube that is placed between the mirrors, providing sufficient isolation from perturbations of the atmosphere. One of the cavity mirrors is mounted on a piezoelectric translator (PZT) (Polytec) for cavity length modulation. The cavity light leak is monitored with a direct detection approach by an amplified silicon avalanche photodetector (APD) (Hamamatsu).
The laser frequency is rapidly modulated over almost 0.6 cm-1 with a 280-Hz triangular scan pattern that controls a PZT within the ECDL. The voltage generator synchronously controls the 5-µm modulation of the PZT placed on the cavity mirror (driven with a 1000-V ramp). An additional phase delay provides the adequate laser-cavity relative frequency change. For wavelength calibration we perform saturated absorption in a gas cell filled with potassium (K) to get a well-defined frequency reference, and we use a 23.5-cm vacuum-spaced Fabry-Perot low-finesse cavity. The photodetectors’ outputs and the PZT triangular voltage are recorded by a 12-bit, 20-MS/s digitizer board (ADLink PCI-9812). As the laser frequency is widely swept over the O2 absorption line, a sequence of ringdown events corresponding to successive passes through cavity resonances is recorded. Each ringdown decay is then numerically processed in Labview by a nonlinear Levenberg-Marquart fit method. After measuring the empty cavity decay time, here τ 0=3.9 µs, the calculated ringdown times are converted to linear absorptions α. Spectra are obtained as a function of the diode laser frequency because of the relative calibration system. Ringdown events situated at extremities of the laser modulation ramp are not taken into account because neither the laser nor the cavity sweeps are linear in these regions. Typical signals recorded in less than 2 ms during a single positive-going scan of the laser current are displayed in Fig. 6. This minimum recording time is determined by the higher achievable tuning rate of the swept-frequency laser, while mode-hope-free operation is maintained. It can be seen from Fig. 6 that an additional 5-µm modulation of the cavity length leads to an increased number of ringdown events and thus to an increased frequency resolution.
Our cw CRDS apparatus is demonstrated by use of the A band of molecular oxygen, corresponding to the (0, 0) vibrational transition of the weak electronic transition, around 765 nm. Absorption profiles corresponding to the PQ(21) line at 766.6978 nm (13042.9487 cm-1) are measured after a single fast (<2 ms) laser scan with no averaging. At atmospheric pressure, the A band of O2 exhibits Lorentzian absorption features with a FWHM near 0.1 cm-1, while the cavity FSR is 0.01 cm -1. The number of points between half-maximum intensities is then sufficient to determine the peak shape and intensity of the absorption feature. As an example, Fig. 7 shows an absorption profile generated within a single fast sweep of the laser frequency, exhibiting absorbance values sampled at intervals defined by the cavity’s FSR. Right above the spectrum are given the corresponding absorption-dependent ringdown times that are measured at successive cavity-resonance frequencies. At lower pressures, an additional 5-µm cavity sweep is used for spectral resolution refinement. Measured absorption spectra at atmospheric and low pressures are shown in Fig. 8. In Fig. 8(a), 66 ringdown points are recorded from almost 13042.66 cm-1 to 13043.21 cm-1, resulting in an estimated frequency resolution of 0.00833 cm-1. An 83% reduction factor of the fixed-cavity FSR is thus observed, in rather good agreement with the theoretical prediction in Eq. (9).
The minimum detectable absorption coefficient in CRDS depends on the cavity loss rate and the accuracy obtainable in the determination of the ringdown time τ, as α min=Δτ/(τL eq), where L eq=cτ is the equivalent absorption path length . The shot-to-shot fluctuations Δτ/τ are measured from the baseline noise of the recorded ringdown times and are found to be ~2.5%. The detection limit, corresponding to the (rms) noise-equivalent absorption, is then estimated to be 2×10-7 cm-1, or 1×10-5 per pass through the 50-cm-long cavity.
The oxygen mixing-ratio retrieval is based on a nonlinear least-squares fit to the full molecular line shape, with molecular parameters provided by the HITRAN96 database. At 295 K and atmospheric pressure, from spectra displayed in Fig. 7 and Fig. 8(a), we measure respective concentrations of 5.1×1018 molecules cm-3 and 5.2×1018 molecules cm-3. The corresponding retrieved oxygen mixing ratios are then 20.81% and 21.22%. Around 20 mbar, the spectra recorded in Fig. 8(b) gives a concentration of 1.4×1017 molecules cm-3. While the baseline noise achieved in the recorded spectra allows a minimal 2.5% uncertainty, other contributions also have to be added, mainly errors in wavelength calibration and errors in baseline determination. The previous results are in rather good agreement with the expected values, with an inaccuracy in the concentration retrieval ranging from 2% to 5%.
4. Sensitivity Analysis and Discussion
The minimum detectable absorption coefficient achieved by use of our rapidly swept cw CRDS setup has been estimated to 2×10-7 cm-1 for a single 2-ms laser scan. This value represents a respectable performance, considering the ringdown time of less than 4 µs, the high laser frequency-scanning rate (~9 THz s-1), and the high temporal resolution. As almost 70 ringdown events are recorded during a 1.7-ms laser scan, resulting in a data-acquisition rate of 40,000 points/s, the bandwidth-normalized detection limit is ~1×10-9 cm-1 Hz-1/2, which falls within the typical performances of cw CRDS. An averaging over 1000 spectra (2 s) would decrease the detection limit down to 6×10-9 cm -1, but we emphasize that our objective is mainly to develop a simple design with a very short detection period. Thus other instrumental aspects have to be improved, namely, by the use of more stable lasers, longer path lengths, or mirrors with higher reflectivity and the achievement of superior mechanical stability and higher injected intensity levels. The baselines of the recorded spectra are not perfectly flat and exhibit oscillations that can be attributed to the cavity mirrors, which are not sufficiently wedged, or to weak optical feedback to the laser from some optical element. Fluctuations on the baseline are also attributed to erroneous determinations of the ringdown times, attributed to transverse modes overlapping with the tail of the ringdown decay signals, thus showing that the cavity transverse-mode suppression must be improved. Other extrinsic factors can degrade the detection sensitivity, including the noise introduced by the laser and the detector, the resolution of the digitizing electronics, and the fitting method. Here the effects of shot noise are considered to be small compared with the effects described above, which are the main sources of errors in our setup.
More complicated forms of cw CRDS instruments have obtained lower detection limits, ranging from 10-9 to 10-10 cm-1, mainly by means of higher integration times, improved detection schemes, or higher input powers . In terms of a bandwidth-normalized detection limit, sensitivities of 10-10-10-11 cm-1 Hz-1/2 have been reported by a few research groups. However, fast response is an essential feature of our cw CRDS system performance when it is compared with other schemes. As a more appropriate reference, we should consider the previous study in which a detection limit of 1.1×10-9 cm-1 Hz-1/2 was demonstrated by recording an absorption spectrum during a rapid laser frequency sweep and using heterodyne detection . Our performance compares favorably with that result, considering our higher acquisition rate, the use of a simple direct detection approach and the additional ability to increase spectral resolution. Other sensitive absorption-based laser techniques are available, including direct-absorption spectroscopy or cavity-enhanced absorption spectroscopy (CEAS). With a rapidly swept diode laser, a CEAS setup has demonstrated a 3×10-8 cm-1 Hz-1/2 sensitivity . Tunable diode laser absorption spectroscopy (TDLAS) with long-path multipass cells is also an efficient tool for gas analysis and is often an appropriate benchmark technique. An instrument based on differential absorption spectroscopy with diode lasers was reported , offering a minimum detectable absorption of ~10-4, on a spectra recorded in 8 ms. Our 10-5 minimum detectable single-pass absorption, obtained during a 2-ms scan, thus compares favorably with this result.
In this paper we have presented a theoretical and experimental investigation of a novel cw CRDS scheme that combines rapid and continuous tuning of the laser frequency and a synchronous, opposite frequency-sweep of the cavity modes. In addition to the ability of the laser tuning approach to yield high-speed measurements, we have shown that the additional cavity-sweep configuration is an efficient way to increase spectral resolution when scanning an absorption profile. The performance of the spectrometer has been successfully demonstrated by achieving rapid detection (in less than 2 ms) in the molecular oxygen A band, with a detection limit of 2×10-7 cm-1. The potential for resolution refinement by synchronous laser and cavity tuning has been demonstrated experimentally with an almost 0.6-cm-1 laser frequency sweep and a 5-µm cavity sweep range. This is only a first step toward resolution enhancement, but more spectacular changes may be obtained for higher cavity tuning rates, smaller laser-sweep ranges for low-pressure features, or shorter cavities.
Through this approach adequate performance will then become available to probe fast chemical processes in various gas environments. In particular, our cw CRDS setup is devoted to high-speed O2 measurements in hypersonic transient flows. The obtained absorption line profiles will allow one not only to get the species concentration but also to characterize the medium of interest in terms of pressure and temperature. As a spectrum is recorded in a time less than 2 ms, more than a hundred spectra will be recorded during one short gust in a blowdown wind tunnel, which is sufficient to analyze the transitory aerodynamic conditions.
Until now we have focused on trying to achieve high-speed and increased-resolution measurements with minimal instrumental complexity, rather than achieving the highest possible detection sensitivity. Indeed, our cw CRDS system provides a simplified instrument for gas sensing, which does not requires acousto- or electro-optic switches or special signal processing equipment and uses a direct detection method. Future experimental work will be carried out to improve the performance of our setup while maintaining the high temporal resolution and the conceptual and practical simplicity of the current approach.
References and Links
1. G. Berden, R. Peeters, and G. Meijer, “Cavity ring-down spectroscopy: experimental schemes and applications,” Int. Rev. Phys. Chem. 19, 565–607 (2000). [CrossRef]
2. K. W. Busch and M. A. Busch, ed., “Cavity-Ringdown Spectroscopy - An Ultratrace-Absorption Measurement Technique” (Oxford U. Press, Washington, D.C., 1999).
3. A. O’Keefe and D. A. G. Deacon, “Cavity ring-down optical spectrometer for absorption measurements using pulsed laser sources,” Rev. Sci. Instrum. 59, 2544 (1988). [CrossRef]
4. D. Romanini, A. A. Kachanov, N. Sadeghi, and F. Stoeckel, “Cw cavity ring down spectroscopy,” Chem. Phys. Lett. 264, 316–322 (1997). [CrossRef]
5. D. Romanini, A. A. Kachanov, and F. Stoeckel, “Diode laser cavity ring down spectroscopy,” Chem. Phys. Lett. 270, 538–545 (1997). [CrossRef]
6. D. Romanini, A. A. Kachanov, and F. Stoeckel, “Cavity ringdown spectroscopy: broad band absolute absorption measurements,” Chem. Phys. Lett. 270, 546–550 (1997). [CrossRef]
7. B. A. Paldus, C. C. Harb, T. G. Spence, B. Wilke, J. Xie, J. S. Harris, and R. N. Zare, “Cavity-locked ringdown spectroscopy,” J. Appl. Phys. 83, 3991–3997 (1998). [CrossRef]
8. K. J. Schulz and W. R. Simpson, “Frequency-matched cavity ring-down spectroscopy,” Chem. Phys. Lett. 297, 523–529 (1998). [CrossRef]
9. Y. He and B. J. Orr, “Ringdown and cavity-enhanced absorption spectroscopy using a continuous-wave tunable diode laser and a rapidly swept optical cavity,” Chem. Phys. Lett. 319, 131–137 (2000). [CrossRef]
10. Y. He and B. J. Orr, “Optical heterodyne signal generation and detection in cavity ringdown spectroscopy based on a rapidly swept cavity,” Chem. Phys. Lett. 335, 215–220 (2001). [CrossRef]
11. Y. He and B. J. Orr, “Rapid measurement of cavity ringdown absorption spectra with a swept-frequency laser,” Appl. Phys. B 79, 941–945 (2004). [CrossRef]
13. M. J. Lawrence, B. Willke, M. E. Husman, E. K. Gustafson, and R. L. Byer, “Dynamic response of a Fabry-Perot interferometer,” J. Opt. Soc. Am. B 16, 523–532 (1999). [CrossRef]
15. K. K. Lehmann and D. Romanini, “The superposition principle and cavity ring-down spectroscopy,” J. Chem. Phys. 105, 10263–10277 (1996). [CrossRef]
16. J. Y. Lee and J. W. Hahn, “Theoretical investigation on the intracavity Doppler effect in continuous wave swept-cavity ringdown spectroscopy,” Appl. Phys. B 79, 371–378 (2004). [CrossRef]
17. B. Bakowski, L. Corner, G. Hancock, R. Kotchie, R. Peverall, and G. A. D. Ritchie, “Cavity-enhanced absorption spectroscopy with a rapidly swept diode laser,” Appl. Phys. B 75, 745–750 (2002). [CrossRef]
18. G. Durry, I. Pouchet, N. Amarouche, T. Danguy, and G. Megie, “Shot-noise-limited dual-beam detector for atmospheric trace-gas monitoring with near-infrared diode lasers,” Appl. Opt. 39, 5609–5619 (2000). [CrossRef]