- Email: [email protected]
A dual-tone modulation method to reduce the background fluctuation in tunable diode laser absorption spectroscopy
Optik 142 (2017) 608–614
Contents lists available at ScienceDirect
Optik journal homepage: www.elsevier.de/ijleo
Original research article
A dual-tone modulation method to reduce the background fluctuation in tunable diode laser absorption spectroscopy Rendi Yang a,b , Xiaozhou Dong a , Yunfeng Bi a , Lifang Fang a , Tieliang Lv a,∗ a b
School of Mechanical, Electrical & Information Engineering, Shandong University (Weihai), Weihai, China School of Electromechanical Automobile Engineering, Yantai University, Yantai, China
a r t i c l e
i n f o
Article history: Received 1 March 2017 Accepted 30 May 2017 Keywords: Etalon effects Dual-tone modulation Harmonic detection Tunable diode laser absorption spectroscopy (TDLAS)
a b s t r a c t Optical interference fringe, known as etalon effect, is the main factor which causes background fluctuation in trace gas concentration detection based on tunable diode laser absorption spectroscopy(TDLAS). The fringes make the background signal present a sinusoidal oscillation, which reduces the system’s detection ability on the gas of more low concentration. To reduce the background fluctuations, a dual-tone modulation (DTM) method is introduced to the model based on Beer-Lambert law and etalon effects. According to the results of simulation and actual experiments, the DTM method can significantly reduce the background fluctuations. More specifically, the standard deviation (STD) value of background fluctuations decreased from 2.6239 parts-per-million (ppm) to 0.19 ppm in our experiments, where the STD of 0.19 ppm is corresponding to absorption of 6.224*10−6 Hz−1/2 with effective optical path length of 2.8 m and integral time of 0.1 s. The results of long-term detection experiment further demonstrated the stability of DTM in reducing the background fluctuations and the reliability of trace gas concentration detection. © 2017 Elsevier GmbH. All rights reserved.
1. Introduction Tunable diode laser absorption spectroscopy (TDLAS) is a widely used technique in environmental gas monitoring, atmospheric science, and spectral measurement areas, especially in trace gas concentration detection due to its many merits such as no-contact, high-sensitivity, high-precision, good-selectivity and fast-response time [1,2]. TDLAS measures the gas concentration by studying the laser intensity variation when laser pass through the target gas. However, almost all TDLAS system suffer from background fluctuation which significantly hinder the system’s ability on low-concentration gas detection. Therefore it is important to find an approach to reduce the background fluctuation in trace gas detection. The main factor causing background fluctuations in the detection of trace gas concentration is optical interference fringe. The fringes, also called etalon effects, are caused by multiple reflections upon surfaces in the optical path. The fringes can obscure the weak absorption signals especially when the free spectral range (FSR) of the optical fringes is in the same order as the line width of the absorption signal. These fringes cause an oscillation of the photo current during wavelength scanning, which may be regarded as an absorption signal incorrectly in the absence of absorbers. In the past decades, several techniques have been introduced to reduce the influence of optical interference fringes [3]. Besides using anti-reflection coating and wedged optical components in optical system [4], frequency modulation(FM)
∗ Corresponding author. E-mail address: [email protected] (T. Lv). http://dx.doi.org/10.1016/j.ijleo.2017.05.112 0030-4026/© 2017 Elsevier GmbH. All rights reserved.
R. Yang et al. / Optik 142 (2017) 608–614
609
manipulation, improvements in device and post-detection filtering also have been used [5]. Among them, FM methods are complicated and highly dependent on the performances of the laser diode (LD) applied. Improvements in device include mechanical vibration modulation, dithering or rotating various optical components [6–8] and double-beam techniques[3,9]. Most of these device improvements are effective, but they add the complexity and the cost of the detection system, and some types of optical fringes still exist (for example, the fringes coming from beam steering optics and LD inside). Post-detection filtering often use high-pass filters or low-pass filters [10], but this technique affects the response time of system and is not effective when the free spectral range (FSR) of fringes is comparable to the gas absorption line-width. In addition, for the measurement of lower absorption, these methods mentioned above are limited in the ability on reducing interference fringes, because such fringes can arise in various parts of the optical apparatus. In this paper, a dual-tone modulation (DTM) method is proposed to reduce the background fluctuation, which can be applied to any analytical absorption system. The main feature of the method is to combine wavelength modulation spectroscopy (WMS) with harmonic detection and to put dual sinusoidal injection currents in the LD to modulate the center frequency. The DTM method can reduce the influence of fringes on the output signal at the detection frequency. 2. Theory and method 2.1. TDLAS According to the Beer-Lambert law, when a narrow-band light with a frequency of v passes through a gas cell filled with an absorbing gas [11], the transmitted intensity I(v) is given by: I(v) = I0 (v) exp[−a(v)CL]
(1)
where I0 (v) is the incident intensity of the narrow-band light, C is the gas concentration, L is the path length through the gas, and a(v) is the absorption coefficient of the gas at frequency v. When the sample has a small optical thickness, i.e. a(v)CL « 1, the transmitted intensity can be approximated as follows [12–14]. I(v) ≈ I0 (v)[1 − a(v)CL]
(2)
When the experiment environment is 1 atm at room temperature, the collision broadening dominates. Then a(v) can be described by normalized Lorentz function [14,15], that is, a(v) =
a0 1 + ( v−vc )
2
(3)
where ␣0 is the absorption coefficient at center absorption frequency vc , and is the half width at the half maximum of the absorption line. In real-time gas measurements, the laser frequency is usually kept near the center of the molecular transition of interest by adjusting the laser temperature. The frequency of the LD is then tuned by injecting current. Different types of current modulation define different methods of absorption spectroscopy. Among them, the technique usually used is WMS. The laser injection current is swept over a transition of interest at a low frequency. Meanwhile, a high frequency sinusoidal modulation signal is superimposed. When the LD is modulated by a sinusoidal injection current of frequency w, the instantaneous frequency can be defined as
v(t) = vc + va cos(wt)
(4)
where vc is the center laser frequency and va is the modulation amplitude of the laser. When the LD is modulated through injection current, the transmitted intensity and absorption line shape profile are modulated at the same time [12]. Hence the transmitted intensity can be revised as I = (I0 + I0 cos wt) exp[−a(vc + va cos wt)CL]
(5)
where I0 is the modulation amplitude of intensity. Then the transmitted intensity at the center frequency can be further expressed in terms of cosine Fourier series. It is an even function and can be written as I(vc , t) =
∞
An (vc ) cos(nwt)
(6)
n=0
where An (vc ) is the nth Fourier component of the modulated absorption coefficient at the center frequency. 2.2. Etalon effects The trace gas measurement system based on TDLAS usually includes two parts: detection circuit and optical system. In the optical system, the surfaces of optical component reflect the light when the laser passes through the gas cell. The reflected lights are generally weak in light intensity [16], but they are mutual superposition and make the light’s transmissivity be
610
R. Yang et al. / Optik 142 (2017) 608–614
changed. Thus the interference fringes caused by these reflected lights are formed, which also called etalon effects. Interference fringes may be originated from various parts of the optical path, including the laser, collimator, lens, photoelectric detector (PD), etc. Even if using anti-reflection coated and wedged optical components, the interference fringes generated in the interior of laser or PD cannot be eliminated completely, some method must be found to reduce the impact of interference fringes on gas detection. In WMS, the transmission of monochromatic light between two low reflecting surfaces can be represented by an etalon with a small coefficient of finesse [17]. The coefficient of finesse F can be defined as F=
4R
(7)
(1 − R)2
where R is the reflectivity of the surface. When the coefficient of finesse is sufficiently small, the transmission of monochromatic light of frequency v between two optical surfaces in the system can be defined as T (v) =
1
1 + F sin2
ϕ(v) 2
(8)
where T(v) is the transmission function, (v) is the normalized laser frequency of FSR, (v) = 2v/vFSR . Here vFSR = c/2l is the free spectral range of the etalon, c is the velocity of light and l is the length of etalon. For the fringes of low-finesse, Eq. (8) can be expanded by Taylor series and written as T (v) ≈ 1 −
F F F F + cos[ϕ(v)] = 1 − + cos 2 2 2 2
4lv c
(9)
According to Eq. (9), we can see that the optical transmission T follows a periodical pattern. 2.3. DTM method Because the etalon effects will affect the results of trace gas concentration detection, the detection model based on Beer-Lambert law, that is Eq. (2), can be revised as I(v) ≈ I0 (v)T (v)[1 − a(v)CL]
(10)
When LD is modulated by injection current, the transmitted intensity is then changed to I(v) = (I0 + I0 cos wt)T (vc + va cos wt)[1 − a(vc + va cos wt)CL]
(11)
The transmitted intensity at the center frequency can be expressed in terms of cosine Fourier series and the nth Fourier component are deduced as An (vc ) =
2
= −
2
(I0 + I0 cos )T (vc + va cos )(1 − a(vc + va cos )CL) cos(n)d 0
2CL
(I0 + I0 cos )T (vc + va cos ) cos(n)d
0
(12)
(I0 + I0 cos )T (vc + va cos )a(vc + va cos ) cos(n)d 0
= SBG,n (vc ) + SAS,n (vc ) where = wt. The nth Fourier components An (vc ) can be selected by a lock-in amplifier (LIA). In Eq. (12), An (vc ) is decomposed into two parts: a background signal SBG,n (vc ) and an analytical signal SAS,n (vc ) which is proportional to the trace gas concentration. It can be seen from Eq. (12), the background signal SBG,n (vc ) is defined as 2 SBG,n (vc ) =
(I0 + I0 cos )T (vc + va cos ) cos(n)d
(13)
0
SBG,n (vc ) is related with the wavelength modulation and the transmission function of etalon. The second harmonic of background signal can be calculated according to Eq. (13) and is shown in Fig. 1. From Fig. 1 we can see that the background is nonzero in the absence of absorbers and presents an oscillation in the form of sine wave, which is in accordance with the viewpoints in the literature. Because the background fluctuation present the form of sinusoidal oscillation, if a method can be found to raise the frequency of oscillation, then the background fluctuation will be averaged out and its amplitude will be reduced. Based on
R. Yang et al. / Optik 142 (2017) 608–614
611
Fig. 1. Second harmonic of background signal.
Reflector
PD Collimator
lens
Optical fiber Temperature controller
LD
w
Amplifier
3w
Current driver Reference signals Processor unit
Waveform generator
Controller
Computer
Fig. 2. Schematic diagram of detection system.
this idea, a DTM method is proposed in this paper, that is, the laser frequency is modulated by two sinusoidal signals, thus the instantaneous frequency of the modulated laser can be defined as
v(t) = vc + va cos(wt) + vb cos(w1 t)
(14)
where va and vb respectively represent the first and the second modulation amplitude. w and w1 are two modulate frequencies. The second harmonic is widely used in the measurement of gas concentration due to its relatively higher signal noise ratio (SNR) compared with other orders of harmonics and its large peak value at the absorption line center [18]. The frequency of the second modulation signal is chosen as 3w in our work, because it has several contributions to the harmonic signal at 2w. The second harmonic signals can be obtained by w + w, w1 -w, 5w-w1 , 2w1 -4w, and etc. Thus the instantaneous frequency of the modulated laser can be written as
v(t) = vc + va cos(wt) + vb cos(3wt)
(15)
3. Design of the detection system Fig. 2 is the schematic of the designed detection system, which is composed of electrical and optical subsystem. In the detection system, a distributed feedback (DFB) laser diode emitting around 1653.72 nm region is used as a light source. The LD is mounted on a copper block that is temperature stabilized by a thermistor sensor and a thermo-electric cooler (TEC). The LD can be modulated by varying temperature and injection current. The temperature and current tuning rates of the laser are about 0.1 nm/K and 0.01 nm/mA, respectively. The light emitted is collimated by collimator and passed through a self-made cell of 1.4 m. The optical length is 2.8 m. The transmitted light is then collected and converted into electric signal by a PD. In order to weaken the influence of etalon effects, an anti-reflection coating is applied in all optical components, and the components are mounted at a slight wedged angle. The frequency and amplitude of sinusoidal modulation signals used in system were synthesized by a FPGA controller.
612
R. Yang et al. / Optik 142 (2017) 608–614
Fig. 3. Values of background fluctuation varies with the amplitude ratio of two modulation signals.
A LIA is used for phase-sensitive detection at the second harmonic and the first harmonic of the fundamental modulation frequency. The outputs from LIA are digitized by an A/D converter. The result data signal is then recorded and processed by the personal computer. In the optical system, the optical path is opened and placed in a stable environment, that is the system temperature and pressure are kept constant when the experiment is made. This can significantly reduce the error introduced by environment temperature, pressure, and improve detection accuracy. 4. Experiment results and discussion 4.1. Determination of amplitude of second modulated signal According to the theory mentioned above, the background fluctuation can be reduced if the DTM is introduced to the system, and the reduction degree of background fluctuation is related with the amplitude of second modulation signal. In order to find the optimal amplitude of the second modulation signal, an experiment that the background fluctuation varied with amplitude of second modulation was made. In the experiment, the frequency of two modulation signal were respectively set as 1 kHz and 3 kHz, and the amplitude of first modulation signal was set 1.7 mA, then we analyzed the variation of the background fluctuation when the amplitude ratio of two modulated signals (vb /va ) was changed from 0 to 1. The result is shown in Fig. 3. As can be seen in Fig. 3, the amplitude of background fluctuation varies with the amplitude ratio of two modulation signals, and the minimum of background fluctuation can be gotten when the ratio of two modulation signals is 0.2. Thus in the following experiments, the amplitude ratio of two modulation signals will be adopted as the value of 0.2. 4.2. Validation of DTM method In order to verify the performance of DTM, a simulation experiment was conducted in MathCAD 15.0 to compare the performance of DTM with that of single tone modulation (STM). In DTM method, the frequencies of two sinusoidal signals were respectively set as 1 kHz and 3 kHz, with the signal amplitude of 1 mA and 0.2 mA. In STM method, the frequency and the amplitude of modulation signal were 1 kHz and 1 mA respectively. The simulation results are shown in Fig. 4. In Fig. 4, the red solid line and the blue dotted line are respectively the background fluctuation signal in STM and DTM. The peak to peak (P-P) values of the two background signal are about 3*10−4 and 2*10−5 , respectively. As can be seen from Fig. 4, the amplitude of background signal is greatly reduced after DTM method was applied to the detection system. 4.3. The effectiveness of DTM method In order to test the effectiveness of DTM on the background fluctuation reduction, a contrast experiment was also conducted in the designed detection system. In the experiment, we made the gas cell with no target gas. In the mode of DTM, the frequency of two modulation signal were respectively set as 1 kHz and 3 kHz, and the amplitude of 1.7 mA and 0.34 mA. The integral time of the detection system is 0.1s. In the mode of STM, the frequency and the amplitude of modulation signal were 1 kHz and 1.7 mA respectively. The experiments of STM and DTM were both made on the condition of 1 atm and constant temperature. After the background fluctuation signals of STM and DTM were recorded, a comparison was made. Results showed that the background fluctuations were significantly reduced in DTM. As an example, parts of the background signals are given in Fig. 5. Fig. 5 (a) and (b) respectively present the background signal in STM and DTM. The P-P value and the standard deviation (STD) value of the signal shown in Fig. 5(a) were computed and they are about 8.627 parts-per-million (ppm) and 2.6239 ppm respectively. In the same way, the P-P value and the STD value of the signal shown in Fig. 5(b) are respectively about 1.072 ppm
R. Yang et al. / Optik 142 (2017) 608–614
613
Fig. 4. The amplitude comparison of simulated background signals in DTM and STM.
Fig. 5. The background signals in STM and DTM are respectively presented in (a) and (b). Moreover, the two signals are connected and given in a same panel (c) to make the amplitude comparison more obviously.
and 0.19 ppm. The STD of 0.19 ppm is corresponding to absorption of 6.224*10−6 Hz−1/2 with effective optical path length of 2.8 m and integral time of 0.1s. These results illustrate that DTM can effectively reduce the background fluctuation and the reduction of background fluctuation is about 13 times that of STM. Moreover, the two signals shown in Fig. 5(a) and (b) are connected and given in Fig. 5(c) to make the amplitude comparison more clearly. Obviously, the amplitude of the background signal in DTM is much lower than that in STM. 4.4. The stability of DTM method To test DTM method’s stability in reducing background fluctuation, long-term experiments were conducted based on STM and DTM methods respectively. In the experiments, we made the gas cell with no target gas. Meanwhile, the pressure and temperature of the detection environment keep constant. The integral time of system was adopted as 0.1 s. We recorded the data of 100000 points in each modulation mode and divided the data into 10 equal length sections. The STD values of every section are shown in Fig. 6. From Fig. 6, we can see that the STD values have a bigger fluctuation in the mode of STM and range from 1.833 ppm to 2.697 ppm with the average STD value of 2.01768 ppm. However, the STD values of the background signal decrease obviously after using DTM in the detection system and fluctuate in the range of 0.1921 ppm to 0.3876 ppm, with the average STD value of 0.2641 ppm. Statistically significant difference was also found in the STD value between the data of DTM and STM by one-way analysis of variance (p < 0.05).The results show that the DTM mode has a better stability and repeatability in long-term trace gas concentration detection.
614
R. Yang et al. / Optik 142 (2017) 608–614
Fig. 6. STD values of background fluctuation signals in STM and DTM long-term experiments.
5. Conclusion In this paper, a DTM method is proposed and applied to the real-time detection system. The results of simulation and experiments showed that the DTM method can reduce the background fluctuation significantly and the reduction of background fluctuation was about 13 times that of STM. The results of long-term test further verified the stability of DTM in reducing the background fluctuation signal. After DTM method was introduced in TDLAS system, the reliability of trace gas concentration detection thus can be improved greatly. In addition, the frequency and amplitude of the modulation signals used in this paper were synthesized by a FPGA controller, thus there is no need for any additional hardware in the detection system. Therefore this method can be applied in both laboratory and industrial detection system. Acknowledgements This work was supported by the National Natural Science Foundation of China [grant no. 41503063]. References [1] I. Linnerud, P. Kaspersen, T. Jaeger, Gas monitoring in the process industry using diode laser spectroscopy, Appl. Phys. B 67 (1998) 297–305. [2] C.G. Li, L. Dong, C.T. Zheng, F.K. Tittel, Compact TDLAS based optical sensor for ppb-level ethane detection by use of a 3.34 um room-temperature CW interband cascade laser, Sens. Actuators B 232 (2016) 188–194. [3] L. Persson, F. Andersson, M. Andersson, S. Svanberg, Approach to optical interference fringes reduction in diode laser absorption spectroscopy, Appl. Phys. B 87 (2007) 523–530. [4] V.V. Liger, Optical fringes reduction in ultrasensitive diode laser absorption spectroscopy, Spectrochim. Acta A 55 (1999) 2021–2026. [5] A. Hartmann, R. Strzoda, R. Schrobenhauser, R. Weigel, Ultra compact TDLAS humidity measurement cell with advanced signal processing, Appl. Phys. B 115 (2014) 263–268. [6] J. Hodgkinson, D. Masiyano, R.P. Tatam, Gas cells for tunable diode laser absorption spectroscopy employing optical diffusers. Part 1: single and dual pass cells, Appl. Phys. B 100 (2010) 291–302. [7] C.R. Webster, Brewster-plate spoiler: a novel method for reducing the amplitude of interference fringes that limit tunable-laser absorption sensitivities, J. Opt. Soc. Am. B 2 (1985) 1464–1470. [8] J.A. Silver, A.C. Stanton, Optical interference fringe reduction in laser absorption experiments, Appl. Opt. 27 (1988) 1914–1916. [9] X. Zhu, D.T. Cassidy, Electronic subtracter for trace-gas detection with InGaAsP diode lasers, Appl. Opt. 34 (1995) 8303–8308. [10] C.B. Carlisle, D.E. Cooper, H. Preier, Quantum noise-limited FM spectroscopy with a lead-salt diode laser, Appl. Opt. 28 (1989) 2567–2576. [11] J. Yan, C. Zhai, X.N. Wang, W.P. Huang, The research of oxygen measurement by TDLAS based on Levenberg-Marquardt nonlinear fitting, Spectrosc. Spect. Anal. 35 (2015) 1497–1500. [12] P. Kluczynski, O. Axner, Theoretical description based on Fourier analysis of wavelength-modulation spectrometry in terms of analytical and background signals, Appl. Opt. 38 (1999) 5803–5815. [13] P. Kluczynski, A.M. Lindberg, O. Axner, Background signals in wavelength-modulation spectrometry with frequency-doubled diode-laser light. I, theory, Appl. Opt. 40 (2001) 783–793. [14] J. Westberg, J.Y. Wang, O. Axner, Fast and non-approximate methodology for calculation of wavelength-modulated Voigt line-shape functions suitable for real-time curve fitting, J. Quant. Spectrosc. Radiat. Transfer 113 (2012) 2049–2057. [15] J. Reid, D. Labrie, Second-harmonic detection with tunable diode lasers-comparison of experiment and theory, Appl. Phys. B 26 (1981) 203–210. [16] D. Chen, Z.L. Jia, Signal analysis of tunable diode laser based wavelength modulation spectroscopy, J. Atmos. Environ. Opt. 3 (2008) 193–198. [17] D.T. Cassidy, J. Reid, Harmonic detection with tunable diode lasers two tone modulation, Appl. Phys. B 29 (1982) 279–285. [18] R.B. Qi, Z.H. Du, D.Y. Gao, J.Y. Li, K.X. Xu, Wavelength modulation spectroscopy based on quasi-continuous-wave diode lasers, Chin. Opt. Lett. 10 (2012) 033001.
Contents lists available at ScienceDirect
Optik journal homepage: www.elsevier.de/ijleo
Original research article
A dual-tone modulation method to reduce the background fluctuation in tunable diode laser absorption spectroscopy Rendi Yang a,b , Xiaozhou Dong a , Yunfeng Bi a , Lifang Fang a , Tieliang Lv a,∗ a b
School of Mechanical, Electrical & Information Engineering, Shandong University (Weihai), Weihai, China School of Electromechanical Automobile Engineering, Yantai University, Yantai, China
a r t i c l e
i n f o
Article history: Received 1 March 2017 Accepted 30 May 2017 Keywords: Etalon effects Dual-tone modulation Harmonic detection Tunable diode laser absorption spectroscopy (TDLAS)
a b s t r a c t Optical interference fringe, known as etalon effect, is the main factor which causes background fluctuation in trace gas concentration detection based on tunable diode laser absorption spectroscopy(TDLAS). The fringes make the background signal present a sinusoidal oscillation, which reduces the system’s detection ability on the gas of more low concentration. To reduce the background fluctuations, a dual-tone modulation (DTM) method is introduced to the model based on Beer-Lambert law and etalon effects. According to the results of simulation and actual experiments, the DTM method can significantly reduce the background fluctuations. More specifically, the standard deviation (STD) value of background fluctuations decreased from 2.6239 parts-per-million (ppm) to 0.19 ppm in our experiments, where the STD of 0.19 ppm is corresponding to absorption of 6.224*10−6 Hz−1/2 with effective optical path length of 2.8 m and integral time of 0.1 s. The results of long-term detection experiment further demonstrated the stability of DTM in reducing the background fluctuations and the reliability of trace gas concentration detection. © 2017 Elsevier GmbH. All rights reserved.
1. Introduction Tunable diode laser absorption spectroscopy (TDLAS) is a widely used technique in environmental gas monitoring, atmospheric science, and spectral measurement areas, especially in trace gas concentration detection due to its many merits such as no-contact, high-sensitivity, high-precision, good-selectivity and fast-response time [1,2]. TDLAS measures the gas concentration by studying the laser intensity variation when laser pass through the target gas. However, almost all TDLAS system suffer from background fluctuation which significantly hinder the system’s ability on low-concentration gas detection. Therefore it is important to find an approach to reduce the background fluctuation in trace gas detection. The main factor causing background fluctuations in the detection of trace gas concentration is optical interference fringe. The fringes, also called etalon effects, are caused by multiple reflections upon surfaces in the optical path. The fringes can obscure the weak absorption signals especially when the free spectral range (FSR) of the optical fringes is in the same order as the line width of the absorption signal. These fringes cause an oscillation of the photo current during wavelength scanning, which may be regarded as an absorption signal incorrectly in the absence of absorbers. In the past decades, several techniques have been introduced to reduce the influence of optical interference fringes [3]. Besides using anti-reflection coating and wedged optical components in optical system [4], frequency modulation(FM)
∗ Corresponding author. E-mail address: [email protected] (T. Lv). http://dx.doi.org/10.1016/j.ijleo.2017.05.112 0030-4026/© 2017 Elsevier GmbH. All rights reserved.
R. Yang et al. / Optik 142 (2017) 608–614
609
manipulation, improvements in device and post-detection filtering also have been used [5]. Among them, FM methods are complicated and highly dependent on the performances of the laser diode (LD) applied. Improvements in device include mechanical vibration modulation, dithering or rotating various optical components [6–8] and double-beam techniques[3,9]. Most of these device improvements are effective, but they add the complexity and the cost of the detection system, and some types of optical fringes still exist (for example, the fringes coming from beam steering optics and LD inside). Post-detection filtering often use high-pass filters or low-pass filters [10], but this technique affects the response time of system and is not effective when the free spectral range (FSR) of fringes is comparable to the gas absorption line-width. In addition, for the measurement of lower absorption, these methods mentioned above are limited in the ability on reducing interference fringes, because such fringes can arise in various parts of the optical apparatus. In this paper, a dual-tone modulation (DTM) method is proposed to reduce the background fluctuation, which can be applied to any analytical absorption system. The main feature of the method is to combine wavelength modulation spectroscopy (WMS) with harmonic detection and to put dual sinusoidal injection currents in the LD to modulate the center frequency. The DTM method can reduce the influence of fringes on the output signal at the detection frequency. 2. Theory and method 2.1. TDLAS According to the Beer-Lambert law, when a narrow-band light with a frequency of v passes through a gas cell filled with an absorbing gas [11], the transmitted intensity I(v) is given by: I(v) = I0 (v) exp[−a(v)CL]
(1)
where I0 (v) is the incident intensity of the narrow-band light, C is the gas concentration, L is the path length through the gas, and a(v) is the absorption coefficient of the gas at frequency v. When the sample has a small optical thickness, i.e. a(v)CL « 1, the transmitted intensity can be approximated as follows [12–14]. I(v) ≈ I0 (v)[1 − a(v)CL]
(2)
When the experiment environment is 1 atm at room temperature, the collision broadening dominates. Then a(v) can be described by normalized Lorentz function [14,15], that is, a(v) =
a0 1 + ( v−vc )
2
(3)
where ␣0 is the absorption coefficient at center absorption frequency vc , and is the half width at the half maximum of the absorption line. In real-time gas measurements, the laser frequency is usually kept near the center of the molecular transition of interest by adjusting the laser temperature. The frequency of the LD is then tuned by injecting current. Different types of current modulation define different methods of absorption spectroscopy. Among them, the technique usually used is WMS. The laser injection current is swept over a transition of interest at a low frequency. Meanwhile, a high frequency sinusoidal modulation signal is superimposed. When the LD is modulated by a sinusoidal injection current of frequency w, the instantaneous frequency can be defined as
v(t) = vc + va cos(wt)
(4)
where vc is the center laser frequency and va is the modulation amplitude of the laser. When the LD is modulated through injection current, the transmitted intensity and absorption line shape profile are modulated at the same time [12]. Hence the transmitted intensity can be revised as I = (I0 + I0 cos wt) exp[−a(vc + va cos wt)CL]
(5)
where I0 is the modulation amplitude of intensity. Then the transmitted intensity at the center frequency can be further expressed in terms of cosine Fourier series. It is an even function and can be written as I(vc , t) =
∞
An (vc ) cos(nwt)
(6)
n=0
where An (vc ) is the nth Fourier component of the modulated absorption coefficient at the center frequency. 2.2. Etalon effects The trace gas measurement system based on TDLAS usually includes two parts: detection circuit and optical system. In the optical system, the surfaces of optical component reflect the light when the laser passes through the gas cell. The reflected lights are generally weak in light intensity [16], but they are mutual superposition and make the light’s transmissivity be
610
R. Yang et al. / Optik 142 (2017) 608–614
changed. Thus the interference fringes caused by these reflected lights are formed, which also called etalon effects. Interference fringes may be originated from various parts of the optical path, including the laser, collimator, lens, photoelectric detector (PD), etc. Even if using anti-reflection coated and wedged optical components, the interference fringes generated in the interior of laser or PD cannot be eliminated completely, some method must be found to reduce the impact of interference fringes on gas detection. In WMS, the transmission of monochromatic light between two low reflecting surfaces can be represented by an etalon with a small coefficient of finesse [17]. The coefficient of finesse F can be defined as F=
4R
(7)
(1 − R)2
where R is the reflectivity of the surface. When the coefficient of finesse is sufficiently small, the transmission of monochromatic light of frequency v between two optical surfaces in the system can be defined as T (v) =
1
1 + F sin2
ϕ(v) 2
(8)
where T(v) is the transmission function, (v) is the normalized laser frequency of FSR, (v) = 2v/vFSR . Here vFSR = c/2l is the free spectral range of the etalon, c is the velocity of light and l is the length of etalon. For the fringes of low-finesse, Eq. (8) can be expanded by Taylor series and written as T (v) ≈ 1 −
F F F F + cos[ϕ(v)] = 1 − + cos 2 2 2 2
4lv c
(9)
According to Eq. (9), we can see that the optical transmission T follows a periodical pattern. 2.3. DTM method Because the etalon effects will affect the results of trace gas concentration detection, the detection model based on Beer-Lambert law, that is Eq. (2), can be revised as I(v) ≈ I0 (v)T (v)[1 − a(v)CL]
(10)
When LD is modulated by injection current, the transmitted intensity is then changed to I(v) = (I0 + I0 cos wt)T (vc + va cos wt)[1 − a(vc + va cos wt)CL]
(11)
The transmitted intensity at the center frequency can be expressed in terms of cosine Fourier series and the nth Fourier component are deduced as An (vc ) =
2
= −
2
(I0 + I0 cos )T (vc + va cos )(1 − a(vc + va cos )CL) cos(n)d 0
2CL
(I0 + I0 cos )T (vc + va cos ) cos(n)d
0
(12)
(I0 + I0 cos )T (vc + va cos )a(vc + va cos ) cos(n)d 0
= SBG,n (vc ) + SAS,n (vc ) where = wt. The nth Fourier components An (vc ) can be selected by a lock-in amplifier (LIA). In Eq. (12), An (vc ) is decomposed into two parts: a background signal SBG,n (vc ) and an analytical signal SAS,n (vc ) which is proportional to the trace gas concentration. It can be seen from Eq. (12), the background signal SBG,n (vc ) is defined as 2 SBG,n (vc ) =
(I0 + I0 cos )T (vc + va cos ) cos(n)d
(13)
0
SBG,n (vc ) is related with the wavelength modulation and the transmission function of etalon. The second harmonic of background signal can be calculated according to Eq. (13) and is shown in Fig. 1. From Fig. 1 we can see that the background is nonzero in the absence of absorbers and presents an oscillation in the form of sine wave, which is in accordance with the viewpoints in the literature. Because the background fluctuation present the form of sinusoidal oscillation, if a method can be found to raise the frequency of oscillation, then the background fluctuation will be averaged out and its amplitude will be reduced. Based on
R. Yang et al. / Optik 142 (2017) 608–614
611
Fig. 1. Second harmonic of background signal.
Reflector
PD Collimator
lens
Optical fiber Temperature controller
LD
w
Amplifier
3w
Current driver Reference signals Processor unit
Waveform generator
Controller
Computer
Fig. 2. Schematic diagram of detection system.
this idea, a DTM method is proposed in this paper, that is, the laser frequency is modulated by two sinusoidal signals, thus the instantaneous frequency of the modulated laser can be defined as
v(t) = vc + va cos(wt) + vb cos(w1 t)
(14)
where va and vb respectively represent the first and the second modulation amplitude. w and w1 are two modulate frequencies. The second harmonic is widely used in the measurement of gas concentration due to its relatively higher signal noise ratio (SNR) compared with other orders of harmonics and its large peak value at the absorption line center [18]. The frequency of the second modulation signal is chosen as 3w in our work, because it has several contributions to the harmonic signal at 2w. The second harmonic signals can be obtained by w + w, w1 -w, 5w-w1 , 2w1 -4w, and etc. Thus the instantaneous frequency of the modulated laser can be written as
v(t) = vc + va cos(wt) + vb cos(3wt)
(15)
3. Design of the detection system Fig. 2 is the schematic of the designed detection system, which is composed of electrical and optical subsystem. In the detection system, a distributed feedback (DFB) laser diode emitting around 1653.72 nm region is used as a light source. The LD is mounted on a copper block that is temperature stabilized by a thermistor sensor and a thermo-electric cooler (TEC). The LD can be modulated by varying temperature and injection current. The temperature and current tuning rates of the laser are about 0.1 nm/K and 0.01 nm/mA, respectively. The light emitted is collimated by collimator and passed through a self-made cell of 1.4 m. The optical length is 2.8 m. The transmitted light is then collected and converted into electric signal by a PD. In order to weaken the influence of etalon effects, an anti-reflection coating is applied in all optical components, and the components are mounted at a slight wedged angle. The frequency and amplitude of sinusoidal modulation signals used in system were synthesized by a FPGA controller.
612
R. Yang et al. / Optik 142 (2017) 608–614
Fig. 3. Values of background fluctuation varies with the amplitude ratio of two modulation signals.
A LIA is used for phase-sensitive detection at the second harmonic and the first harmonic of the fundamental modulation frequency. The outputs from LIA are digitized by an A/D converter. The result data signal is then recorded and processed by the personal computer. In the optical system, the optical path is opened and placed in a stable environment, that is the system temperature and pressure are kept constant when the experiment is made. This can significantly reduce the error introduced by environment temperature, pressure, and improve detection accuracy. 4. Experiment results and discussion 4.1. Determination of amplitude of second modulated signal According to the theory mentioned above, the background fluctuation can be reduced if the DTM is introduced to the system, and the reduction degree of background fluctuation is related with the amplitude of second modulation signal. In order to find the optimal amplitude of the second modulation signal, an experiment that the background fluctuation varied with amplitude of second modulation was made. In the experiment, the frequency of two modulation signal were respectively set as 1 kHz and 3 kHz, and the amplitude of first modulation signal was set 1.7 mA, then we analyzed the variation of the background fluctuation when the amplitude ratio of two modulated signals (vb /va ) was changed from 0 to 1. The result is shown in Fig. 3. As can be seen in Fig. 3, the amplitude of background fluctuation varies with the amplitude ratio of two modulation signals, and the minimum of background fluctuation can be gotten when the ratio of two modulation signals is 0.2. Thus in the following experiments, the amplitude ratio of two modulation signals will be adopted as the value of 0.2. 4.2. Validation of DTM method In order to verify the performance of DTM, a simulation experiment was conducted in MathCAD 15.0 to compare the performance of DTM with that of single tone modulation (STM). In DTM method, the frequencies of two sinusoidal signals were respectively set as 1 kHz and 3 kHz, with the signal amplitude of 1 mA and 0.2 mA. In STM method, the frequency and the amplitude of modulation signal were 1 kHz and 1 mA respectively. The simulation results are shown in Fig. 4. In Fig. 4, the red solid line and the blue dotted line are respectively the background fluctuation signal in STM and DTM. The peak to peak (P-P) values of the two background signal are about 3*10−4 and 2*10−5 , respectively. As can be seen from Fig. 4, the amplitude of background signal is greatly reduced after DTM method was applied to the detection system. 4.3. The effectiveness of DTM method In order to test the effectiveness of DTM on the background fluctuation reduction, a contrast experiment was also conducted in the designed detection system. In the experiment, we made the gas cell with no target gas. In the mode of DTM, the frequency of two modulation signal were respectively set as 1 kHz and 3 kHz, and the amplitude of 1.7 mA and 0.34 mA. The integral time of the detection system is 0.1s. In the mode of STM, the frequency and the amplitude of modulation signal were 1 kHz and 1.7 mA respectively. The experiments of STM and DTM were both made on the condition of 1 atm and constant temperature. After the background fluctuation signals of STM and DTM were recorded, a comparison was made. Results showed that the background fluctuations were significantly reduced in DTM. As an example, parts of the background signals are given in Fig. 5. Fig. 5 (a) and (b) respectively present the background signal in STM and DTM. The P-P value and the standard deviation (STD) value of the signal shown in Fig. 5(a) were computed and they are about 8.627 parts-per-million (ppm) and 2.6239 ppm respectively. In the same way, the P-P value and the STD value of the signal shown in Fig. 5(b) are respectively about 1.072 ppm
R. Yang et al. / Optik 142 (2017) 608–614
613
Fig. 4. The amplitude comparison of simulated background signals in DTM and STM.
Fig. 5. The background signals in STM and DTM are respectively presented in (a) and (b). Moreover, the two signals are connected and given in a same panel (c) to make the amplitude comparison more obviously.
and 0.19 ppm. The STD of 0.19 ppm is corresponding to absorption of 6.224*10−6 Hz−1/2 with effective optical path length of 2.8 m and integral time of 0.1s. These results illustrate that DTM can effectively reduce the background fluctuation and the reduction of background fluctuation is about 13 times that of STM. Moreover, the two signals shown in Fig. 5(a) and (b) are connected and given in Fig. 5(c) to make the amplitude comparison more clearly. Obviously, the amplitude of the background signal in DTM is much lower than that in STM. 4.4. The stability of DTM method To test DTM method’s stability in reducing background fluctuation, long-term experiments were conducted based on STM and DTM methods respectively. In the experiments, we made the gas cell with no target gas. Meanwhile, the pressure and temperature of the detection environment keep constant. The integral time of system was adopted as 0.1 s. We recorded the data of 100000 points in each modulation mode and divided the data into 10 equal length sections. The STD values of every section are shown in Fig. 6. From Fig. 6, we can see that the STD values have a bigger fluctuation in the mode of STM and range from 1.833 ppm to 2.697 ppm with the average STD value of 2.01768 ppm. However, the STD values of the background signal decrease obviously after using DTM in the detection system and fluctuate in the range of 0.1921 ppm to 0.3876 ppm, with the average STD value of 0.2641 ppm. Statistically significant difference was also found in the STD value between the data of DTM and STM by one-way analysis of variance (p < 0.05).The results show that the DTM mode has a better stability and repeatability in long-term trace gas concentration detection.
614
R. Yang et al. / Optik 142 (2017) 608–614
Fig. 6. STD values of background fluctuation signals in STM and DTM long-term experiments.
5. Conclusion In this paper, a DTM method is proposed and applied to the real-time detection system. The results of simulation and experiments showed that the DTM method can reduce the background fluctuation significantly and the reduction of background fluctuation was about 13 times that of STM. The results of long-term test further verified the stability of DTM in reducing the background fluctuation signal. After DTM method was introduced in TDLAS system, the reliability of trace gas concentration detection thus can be improved greatly. In addition, the frequency and amplitude of the modulation signals used in this paper were synthesized by a FPGA controller, thus there is no need for any additional hardware in the detection system. Therefore this method can be applied in both laboratory and industrial detection system. Acknowledgements This work was supported by the National Natural Science Foundation of China [grant no. 41503063]. References [1] I. Linnerud, P. Kaspersen, T. Jaeger, Gas monitoring in the process industry using diode laser spectroscopy, Appl. Phys. B 67 (1998) 297–305. [2] C.G. Li, L. Dong, C.T. Zheng, F.K. Tittel, Compact TDLAS based optical sensor for ppb-level ethane detection by use of a 3.34 um room-temperature CW interband cascade laser, Sens. Actuators B 232 (2016) 188–194. [3] L. Persson, F. Andersson, M. Andersson, S. Svanberg, Approach to optical interference fringes reduction in diode laser absorption spectroscopy, Appl. Phys. B 87 (2007) 523–530. [4] V.V. Liger, Optical fringes reduction in ultrasensitive diode laser absorption spectroscopy, Spectrochim. Acta A 55 (1999) 2021–2026. [5] A. Hartmann, R. Strzoda, R. Schrobenhauser, R. Weigel, Ultra compact TDLAS humidity measurement cell with advanced signal processing, Appl. Phys. B 115 (2014) 263–268. [6] J. Hodgkinson, D. Masiyano, R.P. Tatam, Gas cells for tunable diode laser absorption spectroscopy employing optical diffusers. Part 1: single and dual pass cells, Appl. Phys. B 100 (2010) 291–302. [7] C.R. Webster, Brewster-plate spoiler: a novel method for reducing the amplitude of interference fringes that limit tunable-laser absorption sensitivities, J. Opt. Soc. Am. B 2 (1985) 1464–1470. [8] J.A. Silver, A.C. Stanton, Optical interference fringe reduction in laser absorption experiments, Appl. Opt. 27 (1988) 1914–1916. [9] X. Zhu, D.T. Cassidy, Electronic subtracter for trace-gas detection with InGaAsP diode lasers, Appl. Opt. 34 (1995) 8303–8308. [10] C.B. Carlisle, D.E. Cooper, H. Preier, Quantum noise-limited FM spectroscopy with a lead-salt diode laser, Appl. Opt. 28 (1989) 2567–2576. [11] J. Yan, C. Zhai, X.N. Wang, W.P. Huang, The research of oxygen measurement by TDLAS based on Levenberg-Marquardt nonlinear fitting, Spectrosc. Spect. Anal. 35 (2015) 1497–1500. [12] P. Kluczynski, O. Axner, Theoretical description based on Fourier analysis of wavelength-modulation spectrometry in terms of analytical and background signals, Appl. Opt. 38 (1999) 5803–5815. [13] P. Kluczynski, A.M. Lindberg, O. Axner, Background signals in wavelength-modulation spectrometry with frequency-doubled diode-laser light. I, theory, Appl. Opt. 40 (2001) 783–793. [14] J. Westberg, J.Y. Wang, O. Axner, Fast and non-approximate methodology for calculation of wavelength-modulated Voigt line-shape functions suitable for real-time curve fitting, J. Quant. Spectrosc. Radiat. Transfer 113 (2012) 2049–2057. [15] J. Reid, D. Labrie, Second-harmonic detection with tunable diode lasers-comparison of experiment and theory, Appl. Phys. B 26 (1981) 203–210. [16] D. Chen, Z.L. Jia, Signal analysis of tunable diode laser based wavelength modulation spectroscopy, J. Atmos. Environ. Opt. 3 (2008) 193–198. [17] D.T. Cassidy, J. Reid, Harmonic detection with tunable diode lasers two tone modulation, Appl. Phys. B 29 (1982) 279–285. [18] R.B. Qi, Z.H. Du, D.Y. Gao, J.Y. Li, K.X. Xu, Wavelength modulation spectroscopy based on quasi-continuous-wave diode lasers, Chin. Opt. Lett. 10 (2012) 033001.