2017 4th International Conference on Information Science and Control Engineering
Parametric Simulation and Analysis of Oxygen Detection Based on Wavelength Modulation Spectroscopy Gaofeng Zhu Yun Cheng Yanlei Zhang School of Information, Hunan University of Humanities, Science and Technology Loudi, China email:
[email protected] obtained by the modulation of the lock-in amplifier is the function of laser frequency and modulation degree. The amplitude of each point of its spectral line is associated with its wavelength and modulation degree of the system. As another example, if the scanning range of low- frequency sawtooth wave is too small, the absorbed signals cannot be covered completely; However, in the case the scanning range of low-frequency sawtooth wave is too wide, the interference arising from the nearby absorption line appear and may even cause some damage to the laser. Relevant literatures present these parameters based on practical system and fail to discuss the settings and change of the parameter according to theory and numerical simulation[9,10]. Therefore, by taking oxygen as the object, a systematic simulation method was put forward in the paper, and the simulation model of relevant detecting systems was designed. By combining the results of numerical simulation, the paper analyzed the influence of relevant parameters on oxygen detection to provide theory basis for the gas detection system using wavelength modulation spectroscopy.
Abstract—Modulation parameters are main factors of wavelength modulation spectroscopy (WMS) technique because they can influence both performance and accuracy of the detection system by changing absorption signal characteristics. Absorption spectroscopy parameters of oxygen near 760nm were obtained through the HIRTAN database, simulation model of oxygen detection system was designed with the second harmonic linear expressions, and process of wavelength modulation spectroscopy and second harmonic signal extraction were simulated. Simulation results show that the best center wavelength is 760.885 nm and the best wavelength offset is 20 pm, which can obtain by adjusting the laser’s DC bias current and scanning current respectively, and the modulation index is chosen between 1 and 2.2. This simulation test is very helpful to giving pertinent parameters of the real oxygen detection system. Keywords- Wavelength Modulation Spectroscopy; Second Harmonic Signal; Parameters Simulation; Modulation Index; Oxygen
I.
INTRODUCTION
With the development of the semiconductor laser, the wavelength modulation spectroscopy(WMS) has been widely applied in industrial process and gas detection owing to its advantages including in-situ non-destruction detection, strong anti-interference ability, high sensitivity and so on[1,2,3]. It mainly changes laser emission wavelengths by adjusting the working current of the tunable semiconductor laser, and superimposes a small high-frequency sinusoidal signal on low-frequency sawtooth current signal. On this basis, the output frequency and the intensity of the laser can be modulated so as to inhibit intensity noise of the laser and 1/f noise of the detector. The light beams modulated are absorbed selectively when passing the gases. Then, the intensity of the transmitting laser can be measured, meanwhile, the characteristic value of the second harmonic signals which are extracted and analyzed, such as the peak value and area, are used to conduct inversion on physical quantities like the concentration and temperature of the gas[3,4,5,6]. The gas detection is considered a process of weak signal. The performance and precision of the system are primarily determined by the wavelength modulation process of the tunable laser. Meanwhile, relevant parameters involving in the modulation process can affect the interaction between laser and gas, and therefore change the characteristics of signals absorbed based on the detection mechanism[7,8].For example, the N times harmonic signal 978-1-5386-3013-6/17 $31.00 © 2017 IEEE DOI 10.1109/ICISCE.2017.226
II.
MATHEMATICAL MODEL OF HARMONIC DETECTION
Since the frequency and intensity of the light generated by laser source are controlled by the injection current, they are influenced by DC bias-current, low-frequency sawtooth current and high-frequency sinusoidal current in this system, the output wavelength and light intensity of the laser show linear changes with the intensity of the injected current. By ignoring the phase modulation, the paper supposed v0 as the center frequency of the oxygen absorption peak, which was caused by DC bias-current of the injected current. Kv is the relationship between light frequency and low-frequency sawtooth wave; A is the current amplitude of the sawtooth wave; f is frequency of the modulated sinusoidal signal; vm is the modulation amplitude, which can be called modulation intensity. Therefore, the output frequency v(t), and light intensity I0 (t) of the laser are as follows: v (t ) = v0 + AK v t + vm sin( 2πft ) ˄1˅ ˄2˅ I 0 (t ) = I 0' (t )[1 + α sin( 2πft )]
I 0' (t ) signifies the average changes of the output light intensity caused by the low-frequency current; while Į represents modulation coefficients of light intensity caused by high-frequency sinusoidal current . According to the Beer-Lambert law, the incident light with the frequency v and intensity I0 is absorbed by gas, the intensity of the transmitted light is as follows: 1085
13142.583cm-˅ˈthe intensity of the absorption line was the maximum, so the point was the optimum wavelength point theoretically. The systematic simulation model was established through theoretical derivation to analyze relationships among parameters. Furthermore, it was used to simulate each work module of system plan to determine methods of gas concentration detection. The model consisted of three parts: light source module, gas chamber module and data detection module.
˄3˅ I (t ) = I 0 (t ) exp[− S (T ) NLPg (v)] S(T) is the intensity of the absorption line, and merely serves as a function of the temperature T, its units is cm-1/ ˄molecule*cm-2); N is the volume concentration of the gas absorbed and its unit is mol·cm-3·Pa-1; L is the optical path length in absorption with the unit of cm; P is the total pressure of the gas under the static state with the unit of atm; g(v) is the linear function of the absorption line. Absorbance is often used to describe the photoelectric absorption characteristics of gas: ln(
I 0 (t ) ) = S (T ) NLPg (v ) I (t )
˄4˅ In industrial application, Lorentz line is utilized to fit the absorption line. The types of absorption line of the oxygen molecular described by the Lorenz curve is as follows. g (v ) =
Δvc 1 2π (v − v ) 2 + ( Δvc ) 2 0 2
˄5˅ ǻvc represents full width at half maximum(FWHM), m and x are defined as: m = vm , x = v − v0 . m is called Δvc / 2 Δvc / 2 the modulation coefficient or modulation degree. Due to 6 7 1/3J Y ϜĮϜ, after the light passes through the sample, the intensity of the transmission laser is as follows: I (t ) = I 0' (t )[1 + α sin( 2πft )] exp[− S (T ) NLPg (v)] ˄˅ = I 0' (t )[1 + α sin(2πft ) − S (T ) NLPg (v)] = I 0' (t )[1 + α sin(2πft ) − S (T ) NLP
2
1
πΔv 1 + [ x + m sin(2πft )]2
]
If I(t) is developed into Fourier series, then the coefficient of the second harmonic is as follows: I 2 f = I 0' H 2 ( x, m) ˄7 ˅ In equation (7), H 2 ( x, m) = +
M 2 + 4 x2 − M
4 2x m
2 NLPS (T ) 2 ( M + 1 − x 2 ) M + M 2 + 4 x 2 ( πΔvc m2 M 2 + 4x2
2
M 2 + 4x2
−
2 ) m2
˄8 ˅ 2
2
In equation (8), M = 1 - x + m DŽ III.
SIMULATION EXPERIMENT
By investigating the absorption lines and parameters of the oxygen in the HITRAN database, researchers founded that oxygen showed stronger absorption spectra in the range from 759 to 768 QP. In this period, the electrons transited from ground-state energy levels to excited levels and they were likely to form an absorption band with the rotation and transition of molecular, as shown in figure 1(Taking 296 K as the reference temperature). Up to date, other gases with its absorption spectrum which falls within this range have not been found yet, so the absorption band to detect oxygen will present a better resolving power. Meanwhile, when the oxygen was found at the point of 760.885 nm ˄
Figure 1. Absorption spectroscopy of oxygen near 760 nm
The input parameters of light source module include: frequency and amplitude of the sinusoidal wave; frequency and amplitude of the sawtooth wave; center frequency(v0) of the absorption peak of oxygen ˄ 13142.58cm-1 ˅ . The output parameters of light source module are composed of: frequency (v) and the output light intensity (I0) of the laser. The input parameters of Lorentz function model in gas chamber module include: frequency (v) of the incident light; center frequency (v0) of oxygen absorption lines;full width (ǻvc) at half maximum ( ). The output parameter of Lorentz function model is linear function (g(v)). The input parameters of gas chamber module includes: linear function (g(v)); intensity (I0) of the input light; optical path length (L);gas pressure(P);concentration of oxygen (N); intensity (S(T)) of spectral line. The output parameter of gas chamber module is intensity (It) of the output light. The input parameters of data detection module include: intensity (I0) of the input light; intensity (It) of the output light; frequency (v) of the incident light; center frequency (v0) of the absorption peak of oxygen; intensity (S(T)) of spectral line; linear function (g(v)); optical path (L); gas pressure (P); concentration of oxygen (N). The output parameters of data detection module are composed of: the second-harmonic signal (I2f) and the absorption curve ( ln(
I 0 ). Schematic of simulation system is shown in ) It
figure 2. IV.
RESULTS AND ANALYSIS
Based on the parameters regarding oxygen in the HITRAN database, the research found that oxygen exhibited the maximum intensity of absorption line at the point of 760.885nm. As shown in figure 3, by taking this wavelength point as the center, the absorption spectral line within the
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range of 40 pm around can be fully shown. Moreover, there were no other absorption lines of the oxygen being found in this range. Therefore, the amplitude range of sawtooth current should be moderate, the interference resulting from nearby absorption lines tends to occur in the case of great change of current, and it will reduce lifespan of the laser. So, the wavelength shift of 20 pm is regarded as the standard. -C-
Vm
I0
I0
c3 100
I0'
V
V
c1 0.5
Coeff
a
V0
V0
Light source
parameter. To a certain extent, it reflects the changing trend of the signal-to-noise ratio.
5
L
L 0.21
N
N 1
P
P -C-
S(T)
P1
It
Gas chamber
Figure 4. Absorption line of gas
I0 It L
log(I0/It)
A
N P S V
I2f
V0
B
Detection part
Figure 2. Schematic of simulation system
Figure 5. Second harmonic signal
Figure 3. Absorption line of oxygen near 760 .885nm Figure 6. Relationship between modulation index and amplitude values of second harmonic signal
Supposed the initial condition is known, the systematic simulation results of the gas absorption curve and second harmonic wave are shown in figures 4 and 5, which reflect the actual absorption of the gas chamber. Figure4 shows that absorption ability of the gas was strongest when the sample point lied in the center of the scanning period. Moreover, the amplitude of the second harmonic reached the maximum by using the phase sensitive detection. In practical measuring system, the wavelength of the light source caused by DC bias-current of the injection laser was required to align the central wavelength of the gas, so as to obtain and process the maximum signal. In figure 5, P is defined as the maximum spectral line intensity at the center of the second harmonic wave and it is the most common characteristic value of the second harmonic signal. N is defined as the peak negative excursion of the 2f lineshape from the baseline, and R is the ratio P/N. This ratio is defined as an very important experimental
Figure 7. Second harmonic signals of different modulation indexes
According to the equation 8, the second harmonic mainly depends on modulation degree(m) when the object, condition and absorption line of the gas molecular are
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research determined the condition of oxygen at 760.885 nm ˄ 13142.583cm- ˅ , Numerical simulation showed that the absorption line within the range of 40 pm are able to fully reflect the absorption condition by taking this wavelength point as the center. The paper conducted to calculate linear expression of the second harmonic, etc, and simulate the process of extracting wavelength modulating absorption and second harmonic signals. Meanwhile, the paper analyzed peak value, width and SNR of the second harmonic. It was determined that the appropriate value of modulation degree requires to be selected in the range between 1 and 2.2. The analysis provides parameter settings involving in the practical system with theory basis and also has important guiding significance to the hardware development and software design in practical system.
2 determined. Supposing Q = 2 ( 2 + m − 2) , under the 2 m 1 + m2 given condition, when m is 2.20, the maximum value of Q is 0.1716. That is to say, the amplitude value of the second harmonic reaches the maximum theoretically. As shown in figure 6, in the case of 0
