We report a multi-pass tunable diode laser absorption spectrometer based on the frequency-modulation spectroscopy (FMS) technique. It has the advantage of high scan speed and is immune to the etalon effect. A multi-pass Herriott-type cell was used in the spectrometer to increase the effective optical length to 17.5 m and compact the physical dimensions of the spectrometer to 60×30×30 cm3. Noise due to low-frequency fluctuation of the laser power and the 1/f noise in the rapid detection are sufficiently reduced by FMS. Interference fringes are effectively suppressed when the modulation frequency equals to integer or half-integer times of their free spectral range (FSR). An absorption line of C2H2 around 1.51 µm was recorded with the spectrometer to demonstrate its capabilities. The response frequency of the spectrometer is up to 100 kHz (10 µs) thanks to the high modulation frequency of FMS. The detection sensitivity of the spectrometer is about 240 ppb (3σ) at 100 kHz measurement repetition rate. The amplitude of the absorption signal is highly linear to the C2H2 concentration in the range of 300 ppb -100 ppm. Based on the Allan variation, the detection limit was determined to be 18 ppb with a detection time of 166 s.
© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
Tunable diode laser absorption spectroscopy (TDLAS), known for its high sensitivity, non-intrusive nature, and selectivity, is widely used for real-time quantitative detection of trace gases, including atmospheric pollutants, indicator gas of industrial processes, and chemical intermediates in combustion [1–4]. However, in many cases, traditional direct-absorption techniques are still not sensitive enough to detect trace gas, especially in the near infrared region . There are two methods for improving the detection sensitivity. One of them is to increase the effective optical path, and the other is by using modulation technologies combined with lock-in amplification. The latter technique reduces low-frequency noise and eliminates the background signal. These two techniques can be combined to further improve the signal-to-noise ratio. For example, noise-immune cavity-enhanced optical heterodyne molecular spectroscopy (NICE-OHMS), combined frequency-modulation spectroscopy (FMS) with cavity enhancement, can reduce the detection limit of absorptance into the 10−11–10−10 cm−1 range [6–8]. However, NICE-OHMS is unsuitable for in-situ trace gas monitoring due to its requirements for high mechanical stability and complex laser/cavity locking . Compared with resonant cavity enhanced spectroscopy techniques, e.g., cavity ring-down spectroscopy  and off-axis integrated cavity output spectroscopy [11,12], multi-pass absorption spectroscopy is more suitable for in-suit measurement because of its high robustness and stable performance . Therefore, it has been extensively employed. However, optical fringes due to the etalon effect tend to cause difficulties in multi-pass absorption spectroscopy and limit its sensitivity . The etalon effect can be reduced by employing wavelength-modulation spectroscopy (WMS), a phase-sensitive detection technique [15–17]. In WMS, the detection regime is displaced into regions where the laser diode amplitude noise is negligible. It is one of the most common techniques used in TDLAS [18,19].
WMS is implemented by superimposing a small sinusoidal modulation to the internal injection current of the laser diode. Generally, the maximal modulation frequency for phase-sensitive detection is about 100 kHz limited by the commercial lock-in speed and internal response of the diode laser. At a modulation frequency higher than 100 kHz, the residual amplitude modulation in WMS rapidly increases and the performance of diode laser decreases . Recently, Goldenstein et al. and Li et al. developed a WMS spectrometer with a modulation frequency above several hundred kHz to determine temperature and water concentration in a shock tube [20,21]. Typically the upper limit of the measurement bandwidth for WMS is 100 kHz and high frequency sinusoid modulation is less than 1 MHz . Thus, WMS is restricted in detecting spectral parameters of transient varying and dynamics.
Many laser spectrometers, particularly those for multi-pass absorption spectroscopy, suffer from undesirable etalon fringes . Several approaches have been introduced to remove etalon noise. In general, anti-reflection coated or wedged optical components can be used to alleviate the fringe noise [23,24], although usually incompletely. In addition, optical fringes can be reduced by applying mechanical modulation of the etalon spacing, modifying modulation schemes, background subtraction and post-detection signal processing [14,17,24–27]. Recently, Ehlers et al. used a special distance to reduce the influence of background signals in FMS and NICE-OHMS . FMS was accomplished by an external phase modulator driven at radio frequencies, and the noise of the laser source was significantly reduced through shifting detection to high frequency. Therefore, the spectrometer is capable of measuring absorption lines with high sensitivity [29–31]. Furthermore, combinated with a rapidly tuned laser, FMS can be used for measuring transient spectra and dynamical properties of gaseous samples [29,32–34].
In this work, we developed a compact multi-pass absorption spectrometer based on FMS. It effectively suppresses the optical interference fringe and is featured with a high-speed response (up to 100 kHz). The optimum modulation frequency based on both theoretical simulation and experimental measurement was chosen to suppress the etalon effect. The capability of the spectrometer for rapid detection was demonstrated by recording C2H2 absorption lines around 1.51 µm. Intensity linearity of the spectrometer was verified by measuring spectra of C2H2 with different concentrations. Its stability was tested in an Allan variance analysis.
2. Principles of FMS and suppression of the etalon effect
When TDLAS is combined with FMS, an electro-optic modulator (EOM) driven by a radio frequency (rf) field is used to modulate the laser frequency. With a low modulation index M, the modulated signal can be expressed as 
Here, αn is the absorption coefficient of the sample, L is the effective path length, η is the refractive coefficient, ωc and ωm are the carrier frequency and the modulation frequency, respectively. In Eqs. (2) and (3), the subscripts n = 0, ±1 designates parameters for the carrier frequency ωc and the sideband frequencies (ωc ± ωm).
FMS is capable of measuring both absorption and dispersion of the sample. When θ approaches 0 or π, the detected signal is predominantly due to absorption. The rf beat signal arises from FM sidebands with the carrier frequency, thus the signal in no absorption region can be perfectly canceled due to the upper sideband beating against the carrier equal to the lower sideband beating against the carrier.
The optical etalon effect arises from multiple reflections of the laser beam between surfaces in the optical system. It can be considered as a Fabry-Perot interference with low-finesse since reflectivity R of these surfaces is usually low. The amplitude of transmission, EFP, decays exponentially with respect to the number of reflections and can be written as a function of the phase shift of the transmission [28,35]:Fig. 1.
The interference signal demodulated at the first harmonic can be written as Eq.s (5) and (6) into Eq. (7), the etalon signal will be vanished according to Eq. (7) when Fig. 1). When superimposed, the modulated signals at these two sidebands cancel each other out if the relation in Eq. (8) is satisfied.
A schematic diagram of the high-speed multi-pass tunable diode laser absorption spectrometer is depicted in Fig. 2(a). It consists of the optical, electrical and gas cell sub-systems. In the optical part, a distributed feedback (DFB) laser (NTT Electronics Corporation) emitting around 1.51 µm was used as the light source. The laser can achieve the tuning spectral range of 15 cm−1 by tuning the temperature and injection current of laser diode. Its frequency resolution is ~2 MHz and wavelength stability is better than 100 MHz per hour. A built-in optical isolator in the DFB laser blocks any back reflection. The output laser beam was modulated by a fiber-type EOM (Photline, MPX-LN-0.5) in the rf regime. The spectral range of the spectrometer can be extended through replacing the laser diode, along with an EOM and other optical components that whose wavelength window matches the laser frequency. Output from the EOM was coupled into free space by a GRIN lens, collimated, and fed into a 0.3-m Herriott-type absorption cell. The beam entered the cell through a small hole in the front mirror and was then reflected 58 times in the cell, resulting in an effective optical path length of about 17.5 m. The beam exited from the same hole and was focused onto a high-bandwidth photodetector (Electro-Optics Technology, ET-3010). The optical path was carefully aligned to avoid multiple reflections between any parallel surfaces of the optics. In addition, a wedged window was employed in the Herriott cell to prevent the etalon effect.
In the electrical part, a homemade laser driver was used to control the current and temperature of the DFB laser. Rapid tuning of the laser frequency was realized by sending a triangular signal from a function generator to the current driver of the laser. The rf signal was generated by a local oscillator with adjustable frequency. The optical signal was detected by the detector and sent to an rf amplifier (Mini-Circuits, ZRL-700+) before it was demodulated by a double-balanced mixer (DBM). The reference rf signal from the function generator was sent to the DBM (Mini-Circuits, ZLW-1) for demodulation after being phase-shifted. The demodulated signal was acquired with a high-speed digital oscilloscope (Tektronix-MDO3104, 1 GHz) and then sent to a PC for data analysis.
A vacuum pump was used to keep the gas pressure and refresh the sample inside the cell. The flow rate of sample gas was controlled by a mass flow controller. Pressure in the gas cell was monitored by a pressure gauge. Fig. 2(b) shows the architecture of the spectrometer. It was compacted into a physical size of 60×30×30 cm3, and the elements were partitioned into two floors.
4. Optimization and assessments of the spectrometer
The R(21) line of C2H2 at 6601.6617 cm−1 was recorded for verifying the feasibility of the spectrometer. Due to the quadrature relationship of the absorption and dispersion signals, the phase angle θ was set to 0 for detection of the absorption signal. The amplitude of the obtained FMS absorption spectra is relevant to the modulation frequency, the modulation index and the gas pressure. The relationship between the spectral linewidth and the modulation frequency spacing is quantized by a parameter ΔR = ωm/(ΔΩ/2), where ΔΩ is the full width at half maximum of spectral line. To avoid line profile distortion or even splitting and to enhance the FM absorption signal, ΔR is chosen to be between 0.6 and 1.6 . In the case of small modulation index (M<0.5), signals are approximately proportional to the modulation index . A home-made etalon with an FSR of 1.5 GHz was used to obtain the amplitudes of both carrier frequency and sidebands. The modulation index of FMS was determined by the ratio between the sideband and carrier. In the current experiment, the signal from a local oscillator source was set to a rms power level of 12 dBm, yielding a modulation index of 0.3. The recorded line has a first-derivative Voigt line shape, which is affected by both the modulation index and the gas pressure (10-200 Torr).
The observed line width, determined mainly by Doppler and pressure broadenings, is a crucial factor for signal optimization. In our measurement, the Doppler width is a constant since temperature is not varied. Therefore, the gas pressure is a key parameter that governs the spectral line width. The gas pressure was appropriately chosen to achieve the maximum FM signal. Absorption signal of 20 ppm C2H2 in N2 was measured in the pressure range of 10 to 200 Torr at the interval of 10 Torr. The amplitude of the signal is plotted as a function of the total gas pressure in Fig. 3. The maximum signal was reached at 70 Torr.
4.2. Suppression of the etalon effect
Etalon fringes can be effectively suppressed using the mechanism outlined in Section 2 and illustrated in Fig. 1. Interference fringes recorded in our experiment are plotted in Fig. 4(a), and their FSR is about 29.04 MHz as shown in Fig. 4(a). The measured FSR matches that of the Herriott cell. Therefore, it is deduced that the fringes was caused by the overlap of images. A series of modulation frequencies, from 317 MHz to 350 MHz, was used to search the optimum frequency for the elimination of the optical fringes. Fig. 4(b) illustrates the relationship between the magnitude of the fringes (black squares) and the modulation frequency. The experimental data points are fit to Eq. (7) (red line). The intensity of optical interference depends significantly on the modulation frequency. As shown in Fig. 4(b), when the modulation frequencies are set at 319 MHz, 334 MHz and 348 MHz, corresponding to 11, 11.5, and 12 times of the measured FSR, the interference is essentially eliminated. It is worth noting that the modulation frequency of FMS imposes an upper limit (~1 GHz) on the FSR of the etalon fringes that can be suppressed.
As an example, recorded scans without the absorber with three modulation frequencies: 342, 345, and 348 MHz are illustrated in Fig. 4(c). Minimal etalon effect was observed when the modulation frequency was set at 12×FSR (ωm=348 MHz). Absorption lines recorded with aforementioned modulation frequencies are illustrated in Fig. 5. All demonstrate the first-derivative absorption lineshape with similar amplitudes. The low-frequency fluctuation of the laser power and the 1/f noise are reduced due to FMS. In particularly, the noise level with 348 MHz modulation frequency is about an order of magnitude lower than the other two.
4.3. Rapid scanning performance
To assess the performance of the spectrometer for rapid detection, the absorption signal of 20 ppm C2H2 was recorded with the scan frequency of laser in the range of 0.1 Hz to 100 kHz. The observed spectral signals at 1 Hz and 100 kHz are plotted in the inserts of Fig. 6(a). As illustrated in Fig. 6(a), although in general the intensity of the absorption signal decreases monotonously as a function of the scan frequency, it varies little when between 1 Hz to 1 kHz scan frequency. It shows that the signal at 100 kHz is even more than 200 mV and is acquired by a high-speed digital oscilloscope. At this scan frequency, the SNR is about 252, which implies a detection limit of about 240 ppb (3σ) at 100 kHz measurement repetition rate. Compared to state-of-the-art TDLAS sensors with low measurement repetition rate , the sensitivity of our system is better. Moreover, the bandwidth of ours is broader than previously reported for rapid WMS technologies . In particular, the signal amplitude of our spectrometer does not drastically decrease at measurement repetition rate up to 100 kHz.
To verify the intensity linearity of the spectrometer, absorption spectra of a series of calibrated concentrations of C2H2 balanced by N2 were recorded. The total pressure was set to 70 Torr, while the concentration of C2H2 were varied between 300 ppb and 100 ppm. Both 1 Hz and 100 kHz scan frequencies were used. The observed signal amplitudes as a function of the C2H2 concentration are illustrated in Fig. 6(b). A good linear relationship is observed for both 1 Hz and 100 kHz scan frequencies. Each error bar presented in Fig. 6(b) is zoomed by twenty times.
4.4. Stability of spectrometer
The absorption signal of 20 ppm C2H2 was recorded for three thousand seconds to determine the sensitivity and stability of the system. The raw data is shown in the upper panel of Fig. 7, and Allan variance as a function of the measurement time is plotted in the lower panel of Fig. 7. The plot indicates that the optimal averaging time is about 166 s, corresponding to a minimum detection limit of 18 ppb.
We report a compact multi-pass absorption spectrometer with physical dimensions of 62 × 32 × 30 cm3. Suppression of the etalon effect and the capability of rapid detection were achieved by employing the FMS technique. As an example, the absorption R(21) line of C2H2 at 6601.6617 cm−1 was recorded with the spectrometer. The maximum absorption amplitude was reached when the total gas pressure was 70 Torr. The optical interference could be effectively suppressed when the modulation frequency is integer or half-integer times of the recorded FSR. The scan frequency could be varied in a wide range (0.1 Hz – 100 kHz) without significant decrease of the detected signal. A good linear relationship between the signal amplitude and the concentration of the absorber was recorded for both low and high scan frequencies. The Allan variance suggests that the lowest detection limit is 18 ppb with a measurement time of 166 s. The detection sensitivity of the spectrometer is about 240 ppb (3σ) at 100 kHz measurement repetition rate.
As a matter of fact, the technique can be applied to measure other gas samples by changing laser diodes of different wavelengths. It even can be extended to the mid-infrared (MIR) region as well with MIR optical components and laser sources. The minimum detection limit of the spectrometer can be significantly improved when it is applied in the MIR region, where stronger molecular absorptions are present. Furthermore, it can be used to detect transient variations of the gas sample (e.g. concentration changes of free radicals, such as OH and HO2).
National Natural Science Foundation of China (11504256, U1610117, 61675122); State Key Laboratory of Organic Geochemistry (GIGCAS) (SKLOG-201715).
We are grateful to Prof. Jinjun Liu (University of Louisville) for his careful reading of the manuscript and many useful suggestions.
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