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A new type of continuous-wave cavity ringdown spectrometer based on the control of cavity reflection for trace gas detection was designed and evaluated. The technique separated the acquisitions of the ringdown event and the trigger signal to optical switch by detecting the cavity reflection and transmission, respectively. A detailed description of the time sequence of the measurement process was presented. In order to avoid the wrong extraction of ringdown time encountered accidentally in fitting procedure, the laser frequency and cavity length were scanned synchronously. Based on the statistical analysis of measured ringdown times, the frequency normalized minimum detectable absorption in the reflection control mode was 1.7 × 10−9cm−1Hz-1/2, which was 5.4 times smaller than that in the transmission control mode. However the signal-to-noise ratio of the absorption spectrum was only 3 times improved since the etalon effect existed. Finally, the peak absorption coefficients of the C2H2 transition near 1530.9nm under different pressures showed a good agreement with the theoretical values.
©2013 Optical Society of America
1. Introduction
Cavity ringdown spectroscopy (CRDS) is a kind of highly sensitive direct absorption spectroscopy (DAS) technique, which is based on the measurement of the changes in relaxation time of the high-finesse cavity with absorption species contained. Since the absorption is deduced by the temporal behavior of the signal, it is independent of pulse-to-pulse fluctuations of the laser intensity. Furthermore, owing to the near unit reflectivity of cavity mirrors, a very long effective optical path length could be reached with an enhancement factor of 2 × finesse/π, even though the cavity length is rather short. Another attractive property is its simplicity since few instruments can construct a CRDS setup and the lock of laser frequency to cavity mode is not needed. These advantages make CRDS remarkable as a quantitative method for molecular spectroscopy [1–3] and trace gas detection [4, 5].
The original motivation of the development of CRDS is to accurately characterize the reflectivity of mirrors. By the early 1980s, mirror coating techniques have improved to a point where the conventional measurement techniques were insufficient to precisely determine the mirror reflectivity. In 1980, Herberlin et al. performed an optical cavity phase shift technique to measure the reflectivity of mirrors [6], which set up a relationship between the ringdown time of cavity and the mirror reflectivity in the first time. In 1984, the exponential decay time of the laser intensity was used for the purpose of measuring the mirror reflectivity directly by Anderson et al. [7]. Then CRDS was in its first time demonstrated by O’Keefe and Deacon in 1988 for gaseous spectroscopy [8], and they showed that the absorption spectrum of medium inside the cavity could be given by the measurements of the cavity ringdown times utilizing a tunable, pulsed laser source. The earliest implementations of CRDS technique by using pulsed laser sources [9–11] with linewidth usually much larger than the free spectral range (FSR) of ringdown cavity showed a relatively low spectral resolution. In 1997, Romanini et al. demonstrated the continuous wave CRDS (CW-CRDS) technique by using a single-frequency ring-dye laser near 570 nm [12] and an external-cavity diode laser (ECDL) near 785 nm [13], respectively. The results indicated that the spectrum of CW-CRDS provided several advantages over pulsed CRDS, including high repetition rate, high spectral resolution and high signal-to-noise ratio (SNR). Consequently, many applications of CW-CRDS were developed based on the CW laser sources [14–18]. In order to improve the scan frequency precision of laser and detection sensitivity, Hodges et al. proposed a frequency stabilized cavity ringdown spectroscopy (FS-CRDS), in which the length of ringdown cavity was stabilized to an external absolute frequency reference [19, 20].
Compared to CRDS based on pulse laser sources, the CW-CRDS can achieve higher spectral resolution and also higher couple efficiency of laser intensity to ringdown cavity. However, a passage interruption of the laser light through the ringdown cavity is necessary for CW-CRDS, which can be realized by any of the following schemes [21]:
- (a) the employment of a fast optical switch (AOM or EOM);
- (b) driving current interruption of the laser source;
- (c) rapidly detuning of cavity mode or laser frequency by electronic control of the cavity length or laser source.
The commonly used interruption strategy in previous CW-CRDS is based on scheme (a), combined with proper modulation of cavity length and laser frequency to ensure periodic, occasional coincidences of laser frequency with cavity modes. Once such resonances appear, the laser beam will be interrupted quickly. Thereafter the decay time of the near-resonance light is measured and an absorption coefficient of medium inside the cavity at this laser frequency is obtained.
Considering the application of an optical switch used for the interruption of laser beam in CW-CRDS, the trigger signal to it is always extracted by splitting the detected signal in cavity transmission and the left part is used to determine the ringdown time. When the transmitted laser intensity reaches a preset value, the trigger signal is produced to shut off the laser beam with the help of an external threshold circuit. This scheme can be named as transmission control (TC) mode. In this working mode, the ringdown event could be decreased its amplitude and distorted its decay shape since the threshold circuit always has input resistance and capacitance. In this paper, in order to circumvent this problem, a new reflection control (RC) mode is suggested. The acquisitions of the trigger signal and ringdown event are separated by detecting the cavity reflection and transmission, respectively. As we know, it is the first time to produce the trigger signal to optical switch from the cavity reflection. This scheme not only makes full use of the cavity reflection, but increases the SNR of the ringdown event.
2. Principles
2.1 Theoretical description of CRDS
The incident laser light is injected into a high-finesse optical cavity which consists of a pair of highly reflective mirrors. A small amount of light entered into the cavity propagates back and forth lots of times between the two mirrors. For each path the laser intensity will be attenuated in a certain extent because of the mirror transmission and medium absorption. When the cavity loss exists, the laser intensity inside the cavity decays exponentially as a function of time, which can be observed by a fast response photo detector behind the output mirror. The decay time is defined as the 1/e time of the decay [22], which can be determined by fitting the recorded ringdown signal. Therefore the absorption coefficient of the medium inside the cavity can be determined by the two decay times with and without absorption loss.
The exponential decay of the light intensity transmitted from the output mirror can be expressed as
where I0 is the incident light intensity, τ is the ringdown time of cavity. For a cavity absorption cell consisted of two mirrors with the same reflectivity R, τ can be defined aswhere α is the absorption coefficient of the medium inside cavity, L is the cavity length, c is the speed of light. According the Eq. (2), τ depends on the mirror reflectivity R, the cavity length L and the absorption coefficient α of medium inside the cavity. If the cavity is empty, the expression of τ can be simplified asAccording to Eqs. (2) and (3), the absorption coefficient of medium can be calculated as
In order to evaluate the minimum detectable absorption (MDA) validly by τ, the variation of absorption Δα related to the variation of ringdown time Δτ can be expressed as [12, 18]
2.2 The principle of CW-CRDS based on the control of cavity reflection
Reviewing the previous investigations on CW-CRDS, the detected signal after the output cavity mirror is usually divided into two sections, one of which is used to monitor the intensity variation of transmitted light and the other part is used to obtain the trigger signal to optical switch. In order to get a ringdown event with high amplitude, the incident laser beam should be shut off when the light buildup inside the cavity is enough. When the laser frequency is coincident with one of the cavity modes, the light buildup starts and the transmitted light intensity will increase rapidly. At the time that the transmitted signal reaches the preset voltage value, the trigger signal to optical switch is produced and the incident laser beam is cutoff with the help of an external threshold circuit. Meanwhile the other part of the transmitted signal is recorded and works as a ringdown event. However the threshold circuit always has the characteristic of input resistance and capacitance. If an input resistance is in the order of magnitude of the output resistance of detector, the amplitude of ringdown event will be decreased. Moreover, the discharge process of the input capacitor can produce an exponential electronic signal which will be superposed to the ringdown event, therefore the ringdown signal can be distorted and high-amplitude noise will be introduced to the measurement of ringdown time. To circumvent these problems in the TC working mode, we suggest that the reflected light could be used to produce the trigger signal to optical switch, and then the ringdown event is provided by the full cavity transmission.
A typical time response of cavity reflection and transmission is shown in Fig. 1, which was simulated according to Eq. (10) in [23]. The oscillatory behavior residing in the curves could be understood in terms of the dynamic response of CW coherent radiation to an optical cavity whose length is swept rapidly and continuously. The reflected signal shows a laser intensity dependent offset and an amplitude oscillation with a decrease first, and the transmitted signal shows a zero background and also an amplitude oscillation with increase first. The times at the first valley bottom of reflection and the first peak of transmission give the related light buildup times, and the former is earlier than the latter in the order of μs which depends on the cavity finesse and the scan rate. If the selection criterion of threshold level is defined as the same percentage of dip depth or peak value, the trigger time in the RC mode is earlier than that in the TC mode. Meanwhile a slightly amplitude decrease of the ringdown event exists in the RC mode, the influence of which is much less on the determination of ringdown time. The trigger signal to optical switch can be active when the transmitted signal increases or the reflected signal decreases to the preset value which is determined by the amount of laser light buildup inside the cavity.
Fig. 1 Theoretical simulated cavity mode signals of (a) cavity reflection and (b) cavity transmission.
In order to understand the dynamic response of cavity reflection and transmission at different intracavity absorption losses, a series of simulations under the conditions of 99.95% of reflectivity, 394mm of cavity length, 5kHz of dither frequency were performed. The maximum peak value of transmission and the maximum dip depth of reflection as a function of intracavity loss are shown in Fig. 2, respectively. Since the absorption loss inside the cavity is generally much less than the total empty cavity loss in cavity enhanced absorption spectroscopy, the single pass absorption loss in the simulation was limited to 0.001. As can be seen, both of the two curves have similar decreasing trend but the decreasing rate of reflection is less than half of that of transmission. Moreover, the peak value of transmission is rather small when the single pass absorption loss is near 0.001, while the maximum dip depth of the cavity reflection is still higher than the initial peak value of transmission. However the slow changes of the dip depth of reflection can increase the dynamic range of gas concentration measurement, which makes the application of cavity reflection to CRDS even superior.
Fig. 2 The maximum dip depth of cavity reflection and maximum peak value of cavity transmission under different absorption loss.
3. Experimental procedure
3.1 Experimental setup
The experimental design of our CW-CRDS setup based on the control of cavity reflection is shown schematically in Fig. 3. The system was based on a commercial erbium-doped fiber laser (Koheras Adjustik E15 PztS PM) with a free running linewidth of 1 kHz over 120ms and a tuning range from 1530.8nm to 1531.6nm through temperature control. A fiber pigtailed acousto-optic modulator (AOM) (AA Opto-Electronic, MT110-IIR20-Fio-PM0.5-J1-A) with its first order deflection emission was employed to switch on and off the laser beam. The driver of the AOM (AA Opto-Electronic, MODA110-B51k-34) was controlled by an integrated digital TTL source. When the input voltage of TTL source was larger than 1.2V, the RF output with the power of 1.8W was on, and then the laser beam was switched on. On the contrary, the laser beam was cutoff while the input voltage was lower than 1.2V.
Fig. 3 Schematic diagram of the experimental setup for CW-CRDS based on the control of cavity reflection.AOM – acousto-optic modulator; PD – photo detector; ML – match lens; FG – function generator; PC – personal computer; HVA – high voltage amplifier.
A fiber circulator included one input port, one output port and one reflection port was used to extract the cavity reflected signal. The input port was connected with the fiber AOM and the reflected light from the ringdown cavity was guided and output from the reflection port. The light from the output port was mode matched to the TEM00 mode of cavity by a lens with a focus length of 50cm to avoid the multi-exponential decays and the interference effects caused by multiple longitudinal and transverse mode excitations [14]. The ringdown cavity consisted of two mirrors (Layertec) which were spaced by a low thermal expansion material (Zerodur, Microbas Precision AB, Sweden) with its length of 394mm. Both the flat input mirror and the concave output mirror were mounted on ring shaped low-voltage piezoelectric translators (PZT) (Piezomechanik GmbH, HPSt 150/20-15/25) which were used to modulate the cavity length. The radius of curvature of the concave mirror was 1m and the reflectivity of the two mirrors was 99.95%. A voltage amplified 100Hz triangle wave was applied to the PZT near the input mirror by a three-channel high voltage amplifier HVA1 (Piezomechanik GmbH, SVR 200/3). The dither amplitude of cavity length was larger enough to ensure that the frequency dither range was wider than the FSR of the cavity, and therefore always at least one cavity mode was observed in per dither range. The transmitted light of cavity was focused on a photo detector PD1 with 150MHz response bandwidth (Thorlabs, PDA10CF-EC). The light from the reflection port of circulator was detected by PD2 (Thorlabs, PDA10CF-EC). The obtained signal was feedback to the AOM driver together with a fixed duty cycle pulse signal which was used to switch on the laser beam at the beginning. The amplitude, frequency and pulse width of the pulse signal were 4V, 200Hz and 5μs, respectively.
All the signals were digitized and recorded by a 10MHz 12bits data acquisition (DAQ) card (NI Corporation, PCI 6115). The trigger signal to the DAQ process came from the synchronous TTL signal of triangle wave applied to the cavity PZT. Since the action of interruption was quite fast, the detector with bandwidth in the order of hundred MHz still cannot follow the fast amplitude change and an integration effect existed in the beginning of a ringdown event. Therefore the start point of exponential fitting was five data later than the maximum of cavity transmitted signal, which was realized by a Labview program. However, under this data processing scheme a wrong extraction of the ringdown event could be encountered accidentally when the cavity mode appeared in the time range of pulse signal. Such a problem could be solved by scanning the laser frequency and cavity length synchronously. For each ringdown signal 500 data points were acquired at a time interval of 100ns between the adjacent data.
The wavelength range of the fiber laser used in this work overlapped with part of the strong ν1 + ν3 overtone band of C2H2, one transition of which was used to evaluate the performance of the system. For each measurement series, the cavity was first evacuated down to a pressure of 10−5 Torr by a Turbo pump (Leybold, PT50) before it was filled with the 500 ppm C2H2 gas balanced with nitrogen. The pressure inside the cavity was monitored by a capacitive sensor (Leybold, Ceravac CRT 90) that covered a pressure range from 10−5 to 10 Torr. All measurements were performed at room temperature.
3.2 Time sequence
Since the transmitted light from AOM was its first order deflection, the laser beam was usually interrupted. In order to switch on the laser beam at the beginning, a pulse signal of 4V was applied. The detailed description of the time sequence of CW-CRDS based on the control of cavity reflection is shown in Fig. 4. From Figs. 4(a) to 4(d), the solid curves show the pulse signal, the cavity reflected signal, the trigger signal to AOM and the cavity transmitted signal in turn. In time range A, the laser beam was cutoff and there was no signal in cavity reflection and transmission. In time range B, the AOM was triggered by the summation of pulse signal and cavity reflected signal. The pulse signal was only used to switch on the laser beam since the laser beam was interrupted at the beginning. In order to decrease the influence of pulse signal on the trigger process, its pulse width should be as narrow as possible. As a result of the time response of the AOM system, there was about 400ns of time delay between the pulse signal and the reflected signal. The summation electronic circuit illustrated in the inset of Fig. 4(c) only decreased the amplitude of sum signal, but no more time delay added. Fortunately, these time delays only put off the occurrence of the ringdown event in time domain and its intrinsic characteristic was not affected. In time range C, the AOM was triggered by the reflected signal uniquely, the amplitude of which should be preset to higher than 1.2V and the valley bottom lower than 1.2V by the adjustment of amplification gain. In the transition between C and D, the laser frequency was near resonant with the cavity mode, and then the amplitude of the reflected signal started to decrease. When its amplitude decreased to less than 1.2V, the laser beam was cutoff and a ringdown event occurred. During the time of ringdown decay, the intracavity laser frequency was constant and had the same frequency as the laser was interrupted. Along with the dithering of cavity length, the longitude mode of cavity would pass through the laser frequency in a short period of time, which was only a fraction of the decay time. However the requirement of near resonance was only for the light buildup inside the cavity in the technique of CW-CRDS. The decay of intracavity laser intensity was a non-coherent process and would not be influenced by the status of resonance.
Fig. 4 The time sequence of the realization of CW-CRDS based on the control of cavity reflection. (a) The pulse signal. (b) The cavity reflected signal. (c) The trigger signal to AOM with a summation electronic inserted. (d) The cavity transmitted signal.
3.3 The optimization of the data acquisition
In order to obtain an absorption spectrum of the target gas, the laser frequency should be scanned in a certain range. Under this condition the cavity mode would move continuously back and forth during the dither period of cavity length because of the asynchronous scan. However, a data acquisition and fitting problem was encountered when a pulse signal was used to switch on the laser. The production process of the problem is shown in Fig. 5. From Figs. 5(a) to 5(d), the curves still show the pulse signal, the cavity reflected signal, the trigger signal to AOM and the cavity transmitted signal orderly. As can be seen, when the center position of the transmitted cavity mode appeared in the time range of pulse signal, the peak value was larger than the amplitude of the following ringdown event during a dither period of PZT. Therefore, our designed Labview program would only recognize the first peak, and a fake signal was acquired and fitted by the exponential expression. This problem would cause a wrong ringdown time at this laser frequency and result in a break in the absorption spectrum. Since the pulse signal was synchronous with the dither signal of cavity length, the problem only possibly existed in the beginning of each dither period. In order to avoid such a problem, a part of laser scan signal was added to the PZT near the output mirror with an adjustment of amplification gain to make sure the cavity mode close to the middle of the cavity length dithering. Based on this operation the ringdown event was kept in the range of 30MHz when a 1.7GHz of laser frequency was scanned. Consequently, the problem encountered in the data acquisition and fitting process was solved.
Fig. 5 Explanation for the wrong extraction of ringdown event. (a) The pulse signal. (b) The cavity reflected signal. (c) The trigger signal to AOM. (d) The cavity transmitted signal.
4. Experimental results
For the CRDS technique, the ringdown time τ can be obtained by fitting the transient ringdown event with single exponential expression [8]. In the experiment, a 100Hz triangle wave was used to dither the cavity length and the dither frequency range was around 100MHz. The ringdown times could be obtained at a rate of 12 Hz which depended on the operational speed of computer and the DAQ card. Since the measurement of CRDS is absolute and similar to the direct absorption, the MDA can be assessed by the statistical analysis of a series of τ without medium absorption [12, 18]. To demonstrate the features of our new spectrometer, the measurement of CW-CRDS based on the RC mode and the TC mode were performed, respectively. Under the TC working mode, the threshold circuit was based on the monostable design. The input resistance and capacitance were in the order of thousands of Ω and tens of pF.
The 2000 times measurements of the ringdown events and the statistic distribution with fixed laser frequency based on two control modes are shown in Figs. 6(a), (b) and 6(c), 6(d), respectively. As can be seen, the statistical analysis of the ringdown times in the RC working mode yields <t> = 2.513ms and Δτ = 1.12 × 10−3ms, while <t> = 2.536ms and Δτ = 6.16 × 10−3ms for the TC working mode. The difference of the mean value between these two working modes is 0.023ms, which corresponds to an error of 4ppm in mirror reflectivity. The amplitude of background noise in the TC working mode is more than five times larger than that in the RC working mode, the reason of which came from the discharge process of input capacitor of threshold circuit in the TC working mode. According to Eq. (5), the frequency normalized MDA of the RC working mode can be calculated to be 1.7 × 10−9cm−1Hz-1/2, which is 5.4 times smaller than 9.2 × 10−9cm−1Hz-1/2 obtained based on the TC mode. Therefore the CW-CRDS in the RC working mode can provide a better detectability.
Fig. 6 The 2000 times measurements of ringdown events and the corresponding statistic distribution. (a), (b) Based on the RC mode. (c), (d) Based on the TC mode.
In order to evaluate the performance of our CW-CRDS spectrometer used for trace gas detection, the absorption profile of Pe(10) transition in ν1 + ν3 overtone band [24] near 1530.9nm was measured. The laser frequency was tuned by a 0.1Hz triangle wave through the laser PZT with a tuning range of about 1.7GHz. Since the total gas pressure was set to less than 10Torr, the absorption lineshape was mainly dominated by the Doppler broadening. The Doppler broadened lineshape of C2H2 under the total sample pressure of 1Torr in the unit of absorption coefficient is shown in Fig. 7, in which the frequency calibration was made by utilizing the transmitted modes of the evacuated ringdown cavity after measurements. The dotted curves in Figs. 7(a) and 7(c) show the ten times averaged experimental data collected based on the RC mode and the TC mode, respectively, and the solid curves show the corresponding fits. The fitting residuals for each working mode are shown in Figs. 7(b) and 7(d). As can be seen there is a little difference for the absorption coefficients of both transitions, which was caused by the high-amplitude noise in the TC working mode. From the fitting residuals we know that the SNR of the absorption spectrum in the RC working mode is almost 3 times larger than that in the TC working mode since a slightly etalon effect originated in the optical path existed in the measurement. Theoretical fitting to the experimental data was based on the Voigt lineshape function.
Fig. 7 Voigt lineshape fitting of the absorption spectrum of C2H2 near 1530.9nm under the sample pressure of 1Torr, together with the fitting residual. (a), (b) Based on the RC mode. (c), (d) Based on the TC mode.
The dots and the solid curve in Fig. 8 represent the measured and theoretical calculated peak absorption coefficients at given total pressures, respectively. A good agreement can be obtained and the minor error comes from the measurement of the gas pressure and the fitting process. The total pressure range was from 0.09Torr to 7.12Torr, which was limited by the measuring range of the pressure gauge. In this total pressure range, the peak absorption coefficients show a linear dependence on it with a slope of 0.33cm−1/Torr, which is mainly because of no collision broadening included.
Fig. 8 A comparison between the measured and calculated peak absorption coefficients under different total pressure in RC working mode.
5. Conclusions
CW-CRDS is a rather useful tool for trace gas detection, in which the optical switch is generally triggered by a signal extracted from the cavity transmission. In this TC working mode, the ringdown event could be decreased its amplitude and distorted its decay shape since the threshold circuit always has input resistance and capacitance. A new type of CW-CRDS spectrometer in RC working mode for trace gas detection was designed and evaluated in this paper. The technique separated the acquisitions of the ringdown event and the trigger signal to optical switch by detecting the cavity reflection and transmission, respectively.
In order to realize this new method, a detailed description of the time sequence in principle was presented. In the RC working mode, a problem in data acquisition and fitting process was encountered accidentally when the cavity mode appeared in the time range of pulse signal. In order to circumvent this problem, the ringdown event was kept in the range of 30MHz by scanning the cavity length with a signal came from part of the laser scan signal. The statistical analysis of the 2000 times measurements of the ringdown times in the RC working mode yielded a frequency normalized MDA of 1.7 × 10−9cm−1Hz-1/2, which was 5.4 times smaller than that obtained in the TC working mode. To evaluate the performance of our new spectrometer for trace gas detection, the absorption spectrum of C2H2 near 1530.9nm under the pressure of 1Torr was measured, and the results indicated that the SNR of the absorption spectrum in the RC working mode was almost 3 times larger than that in the TC working mode since a slightly etalon effect originated in the optical path existed in the measurement. Finally, the measured peak absorption coefficients of the C2H2 transition under different total pressures showed a good agreement with the theoretical calculations. This technique will work as a necessary supplement to the family of CRDS.
Acknowledgments
The work was supported by the 973 program of China (Grant No. 2012CB921603), the National Natural Science Foundation of China (Grant Nos. 61127017, 61178009, 61108030, 60908019, 61275213 and 61205216), and the Shanxi Natural Science Foundation (Grant Nos. 2010021003-3, 2012021022-1).
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