Abstract:
Provided is a gas absorption spectroscopic system and gas absorption spectroscopic method capable of accurately measuring the concentration or other properties of gas even in high-speed measurements. Laser light with a varying wavelength is cast into target gas. A spectrum profile representing a change in the intensity of the laser light transmitted through the target gas with respect to wavelength is determined. For this spectrum profile, polynomial approximation is performed at each wavelength point within a predetermined wavelength width, using an approximate polynomial. Based on the coefficients of the terms in the approximate polynomial at each point, an nth order derivative curve, where n is an integer of zero or larger, of the spectrum profile is created. A physical quantity of the target gas is determined based on the thus created nth order derivative curve.

Description:
CROSS REFERENCE TO RELATED APPLICATIONS 
     This application is a National Stage of International Application No. PCT/JP2013/084741 filed Dec. 25, 2013, claiming priority based on Japanese Patent Application No. 2013-000305 filed Jan. 7, 2013, the contents of all of which are incorporated herein by reference in their entirety. 
     TECHNICAL FIELD 
     The present invention relates to a gas absorption spectroscopic system and method for measuring the concentration, temperature, pressure and other properties of target gas, based on a laser light absorption spectrum of the gas. The gas absorption spectroscopic system and method can be applied for contactless high-speed measurement of the concentration, temperature and pressure of gas in the automotive industry. It can also be used for a measurement of combustion gas within a plant furnace or similar gas in high-temperature and high-pressure environments, as well as in various other areas. 
     BACKGROUND ART 
     There are three kinds of gas absorption spectroscopy using lasers: 
     (1) DLAS (Direct Laser Absorption Spectroscopy) 
     (2) WMS (Wavelength Modulated Spectroscopy) 
     (3) CRDS (Cavity Ring Down Spectroscopy) 
     In DLAS, laser light is cast into target gas and detected with a photodetector. In this detection, the wavelength of the laser light cast into the gas is fixed at a specific value to measure the amount of absorption by the gas, or a certain range of the laser wavelength is swept to measure an absorption spectrum of the gas. In the former case, the wavelength of the laser light is fixed at an absorption wavelength of the gas and the absorbance at that wavelength is measured. In the case of sweeping the wavelength range, the wavelength of the laser light is varied over a range including the absorption wavelength of the gas to obtain a spectrum of the gas and determine the magnitude of area of the absorption peak formed by the gas (Non Patent Literature 1). 
     WMS is similar to the wavelength-sweeping mode of DLAS. However, in WMS, not only the wavelength is swept through a range, but the wavelength is also sinusoidally modulated with a cycle sufficiently shorter than the sweeping cycle (i.e. at an adequately high frequency, which is herein denoted by f). The detector is tuned to detect a higher harmonic wave of frequency f (normally, the second-order harmonic wave), whereby the absorption by the gas can be measured with higher sensitivity than by DLAS (Patent Literature 1; Non Patent Literatures 2, 3 and 4). For detection of the higher harmonic wave, lock-in amplifiers are normally used. Another method has also been proposed in which the detector signal is directly subjected to digital sampling and subsequently analyzed by FFT for synchronous detection of 2f (Non Patent Literature 5). 
     In CRDS, the target gas is placed in an optical resonator composed of at least two mirrors. As one example, a CRDS using a CW (continuous wave) laser is hereinafter described. The light which has entered the optical resonator is reflected and resonated within the optical resonator, and a large part of light with an amount of energy corresponding to the reflectance of the mirrors on both sides is trapped in the resonator. Meanwhile, light with a trace amount of energy leaks to the outside of the mirrors. Accordingly, in the steady state, a stable amount of light energy is constantly stored in the resonator, while a certain amount of light continuously leaks to the outside of the mirrors. In this state, if the laser radiation is discontinued, the light energy in the resonator decays at a rate corresponding to the amount of light lost from the resonator, which simultaneously causes a decay in the intensity of light leaking to the outside of the mirrors. The decay time depends on the amount of light absorbed by the target gas in the resonator. Using this fact, the amount of absorption by the gas is determined. Although this technique is more sensitive than WMS, it is susceptible to the contamination of the resonator, and furthermore, its dynamic range is generally narrow, since the resonator loss rapidly increases with an increase in the amount of absorption, making the measurement impossible. Additionally, a highly nerve-straining control is needed for finely mode-locking the laser in the resonator or in other tasks. 
     From the previously described facts, WMS is said to be suitable for industrial gas absorption spectroscopic systems due to its favorable balance of sensitivity and robustness (ease of measurement). By WMS, the gas concentration can be easily calculated from the intensity of the obtained absorption spectrum. Additionally, WMS can be used in an application which can measure the concentration and/or temperature of the gas by using two wavelengths even under an environment in which it is impossible to directly measure the pressure or temperature although the temperature and pressure are constantly changing (Non Patent Literature 4). 
     CITATION LIST 
     Patent Literature 
     
         
         Patent Literature 1: JP 2011-196832 A 
       
    
     Non Patent Literature 
     
         
         Non Patent Literature 1: E. D. Hinkley and P. L. Kelley, “Detection of air pollutants with tunable diode lasers,”  Science  171, 635-639 (1971) 
         Non Patent Literature 2: Reid, J. and Labrie, D., “Second-harmonic detection with tunable diode lasers-comparison of experiment and theory,”  Appl. Phys . B 26, 203-210 (1981) 
         Non Patent Literature 3: J. A. Silver, “Frequency-modulation spectroscopy for trace species detection: theory and comparison among experimental methods,” Appl. Opt.  31, 707-717 (1992) 
         Non Patent Literature 4: G. B. Rieker, J. B. Jeffries, and R. K. Hanson, “Calibration-free wavelength modulation spectroscopy for measurements of gas temperature and concentration in harsh environments,”  Appl. Opt.  29, 5546-5560 (2009) 
         Non Patent Literature 5: T. Fernholz, H. Teichert, and V. Ebert, “Digital, phase-sensitive detection for in situ diode-laser spectroscopy under rapidly changing transmission conditions,”  Appl. Phys . B 75, 229-236 (2002) 
         Non Patent Literature 6: J. T. C. Liu, “Near-infrared diode laser absorption diagnostics for temperature and species in engines,” Ph.D. dissertation, Dept. Mechanical Engineering, Stanford Univ., Stanford, Calif., 2004. (FIG. 3.12) 
         Non Patent Literature 7: “Calculation of molecular spectra with the Spectral Calculator”, [accessed on Jan. 7, 2013], the Internet 
         Non Patent Literature 8: Katsuhiko Fukuzato, Yuji Ikeda, and Tsuyoshi Nakajima, “CO 2  gas measurement by diode laser absorption spectroscopy (2 nd  Report)”,  Transactions of the Japan Society of Mechanical Engineers, Series B  68, 2901-2907 (2002) 
       
    
     SUMMARY OF INVENTION 
     Technical Problem 
     As just described, WMS is a robust and highly sensitive method. However, it has the following problems: 
     1. For high-speed measurements, WMS requires both a short sweeping cycle and a high wavelength modulation frequency. However, if an injection current control type tunable diode laser (which is the most widely used type of tunable laser) is used as the wavelength-variable laser, increasing the modulation frequency lowers the changing rate of the wavelength with respect to the injection current and makes it impossible to achieve a sufficient modulation depth (Non Patent Literature 6). 
     2. In particular, for a high-frequency modulation which exceeds MHz levels, it is difficult to accurately measure the modulation depth. That is to say, it is impossible to correctly determine the modulation depth in high-speed measurements. Therefore, the concentration, temperature or other information on the gas calculated from the measured result has a high degree of uncertainty. 
     Due to the previously described factors, the conventional WMS has the problem that the measurement of the concentration, temperature and other properties of gas becomes noticeably difficult when the measurement is performed at high speeds. 
     The problem to be solved by the present invention is to provide a gas absorption spectroscopic system and gas absorption spectroscopic method capable of correctly measuring the concentration or other properties of gas even in high-speed measurements. 
     Solution to Problem 
     The gas absorption spectroscopic system according to the present invention aimed at solving the previously described problems includes: 
     a) a wavelength-variable light source; 
     b) a light source controller for varying the wavelength of light generated by the light source; 
     c) a photodetector for detecting the intensity of light generated by the light source and transmitted through target gas; 
     d) a polynomial approximator for creating a curve approximating a change in the intensity of the light detected by the photodetector with a change in the wavelength varied by the light source controller, using an approximate polynomial at each wavelength point and within a predetermined wavelength width; 
     e) a derivative curve creator for creating an nth order derivative curve, where n is an integer of zero or larger, based on the coefficient of each term of the approximate polynomial at each of the wavelength points; and 
     f) a physical quantity determiner for determining at least one among the temperature, concentration and pressure of the target gas, based on the nth order derivative curve. 
     The “wavelength” in the present context uniquely corresponds to the “wavenumber.” Therefore, it is naturally possible to construct a similar system using the “wavenumber.” 
     In the gas absorption spectroscopic system according to the present invention, the wavelength of the light cast into the target gas (which is normally, but not necessarily, laser light) is varied (i.e. a wavelength range is swept) as in DLAS. However, the light is not modulated as in WMS. The wavelength may be varied (swept) only one time between the lowest and highest predetermined frequencies, or the sweeping may be repeated multiple times. 
     After passing through the target gas, the light is received by the photodetector and its intensity change is detected. The range of wavelengths to be swept is previously set, including the absorption wavelength of the target gas. Therefore, an absorption peak centering on a wavelength specific to the target gas appears in the spectrum profile of the light detected by the photodetector (this profile corresponds to the “curve representing a change in the intensity of the light detected by the photodetector with a change in the wavelength varied by the light source controller”). 
     In the gas absorption spectroscopic system according to the present invention, a mathematical operation similar to the WMS process is performed on this spectrum profile including the absorption peak. Specifically, an nth order polynomial approximation is performed on the spectrum profile in a section corresponding to the modulation depth of the WMS around each wavelength point, and the amplitude of the WMS signal is reproduced using the coefficients in the nth order polynomial based on the principle of Fourier transform. This principle is as follows. 
     Regarding the WMS process, it is generally known that a spectrum profile of an nth order harmonic wave obtained by synchronous detection approximately takes the form of an nth order derivative of the absorption spectrum (Non Patent Literature 2: Equation 8). Accordingly, it is possible to consider that a spectrum corresponding to the nth order synchronous detection can be obtained by nth order differentiation of the spectrum obtained by the wavelength sweeping. However, the nth order differentiation has the practical problem that the noise in the measurement data significantly affects the nth order differentiation. To avoid this problem, in the gas absorption spectroscopic system according to the present invention, mth order polynomial approximation is performed over a certain range centering on a wavelength at which the higher harmonic wave needs to be determined. The coefficients in the obtained polynomial correspond to the higher harmonic wave signal which will be obtained by the WMS process. The range over which the polynomial approximation is performed corresponds to the amplitude of modulation in the WMS process. 
     The higher the order of the approximate polynomial is, the more accurate the approximation is. Normally, the first or second order approximate polynomial is sufficient. 
     Also performed is a process for correcting a change in the amount of light associated with unwanted factors, such as a blockage of light other than absorption by the gas. 
     Advantageous Effects of the Invention 
     In the gas absorption spectroscopic system according to the present invention, since the wavelength sweeping in the light source is performed at a frequency of several hundreds of kHz or lower, the oscillation wavelength of the light source corresponding to the injection current can be accurately determined. Since the WMS process is performed by mathematical operation based on the wavelength information, a high order synchronous detection with a correct modulation depth can be performed without being affected by the non-linearity of the power source for driving the light source or that of the light source itself. 
     The use of the mathematical process allows simultaneous acquisition of WMS spectra with a plurality of modulation depths using a single light source. This makes it easier to realize a system which has only a single light source yet can perform a temperature measurement which has conventionally required two or more light sources. In temperature measurements, the modulation depth must be optimally adjusted to minimize the pressure dependency of the measured temperature. Conventional techniques require this adjustment to be made before the measurement. By contrast, according to the present invention, the modulation depth can be adjusted in an ex-post analysis. 
    
    
     
       BRIEF DESCRIPTION OF DRAWINGS 
         FIG. 1  is a schematic configuration diagram of one embodiment of the gas absorption spectroscopic system according to the present invention. 
         FIG. 2  is a flowchart showing a procedure for measuring the concentration and other properties of target gas according to the present invention. 
         FIG. 3A  is a graph showing the form of a change in the wavelength of the laser source in a conventional WMS method, and  FIG. 3B  is a corresponding graph in the case of a method according to the present invention. 
         FIG. 4  is the profile of a gas transmission spectrum used for verifying the present invention. 
         FIG. 5  is a model diagram illustrating how to represent a spectrum profile using a polynomial. 
         FIG. 6  is a graph showing a first order synchronous detection profile (broken line) and a first order derivative profile (solid line) calculated by the method according to the present invention (using a second order polynomial). 
         FIG. 7  is a graph showing a second order synchronous detection profile (broken line) and a second order derivative profile (solid line) calculated by the method according to the present invention (using a second order polynomial). 
         FIG. 8  is a spectrum profile created as a result of plotting coefficient b 0  against wavenumber “ v ”. 
     
    
    
     DESCRIPTION OF EMBODIMENTS 
     A schematic configuration of a gas absorption spectroscopic system as one embodiment of the present invention is shown in  FIG. 1 . A laser source  12  and a photodetector  13  are placed on both sides of a gas cell  11  which contains target gas or through which the target gas is passed. The laser source  12  has a variable wavelength. A light source controller  14  sweeps (varies) this wavelength between the shortest and longest predetermined wavelengths. The photodetector  13  produces an electric signal which shows the intensity of light. This signal is subjected to digital sampling by an A/D converter  15  and sent to an analyzer  16 . 
     A procedure for measuring the concentration, temperature, pressure and other properties of the target gas is as follows ( FIG. 2 ): The light source controller  14  operates the laser source  12  to radiate laser light having the shortest predetermined wavelength (Step S 1 ) and then sequentially varies the wavelength to the longest wavelength (Step S 2 ). As already noted, in the conventional WMS method, while the wavelength is varied (swept), the wavelength is modulated with a predetermined wavelength width, as shown in  FIG. 3A . In the method according to the present invention, no such modulation is performed, as shown in  FIG. 3B . The light from the laser source  12  passes through the target gas in the gas cell  11 , where the light undergoes absorption at wavelengths specific to the target gas. The intensity of the laser light transmitted through the target gas is detected by the photodetector  13 . The electric signal produced by the photodetector  13 , which shows the intensity of the light, is digitized by the A/D converter  15  and sent to the analyzer  16 . The change in this electric signal forms the aforementioned spectrum profile (Step S 3 ). Based on the data representing this spectrum profile, the analyzer  16  performs the following mathematical operations. 
     The mathematical operations performed by the analyzer  16  using a polynomial approximation of the detection signal are hereinafter described and compared to the process performed in the conventional WMS. A spectrum profile centering on an absorption peak of CO 2  obtained from the HITRAN 2008 database has been used as the gas absorption spectrum to be processed. Naturally, the following operations should actually be performed on a spectrum profile obtained in the previously described manner. 
     For this spectrum, the polynomial approximation was performed by the analyzer  16  of the gas absorption spectroscopic system according to the present invention, and the obtained result was compared with a result obtained by simulating a lock-in amplifier based on the conventional WMS process. 
       FIG. 4  shows the transmission profile used in the simulation. This has been obtained by simulating a gas cell with an optical length of 5 cm under the conditions of 3% CO 2  concentration and 1-atm pressure, paying attention to an absorption line near 2 μm (5000 cm −1 ). 
     It is generally known that an absorption peak under atmospheric pressure can be expressed by the following Lorentzian function: 
                     g   ⁡     (   v   )       =       A   π     ⁢       α   L           (     v   -     v   c       )     2     +     α   L   2                   (   1   )               
where v is the wavenumber, A is the peak area, v c  is the wavenumber of the peak, and α L  is the half width at half maximum of the Lorentz broadening.
 
     Consider the situation where incident laser light which has been modulated with amplitude a according to the WMS method is passing through gas having the aforementioned absorption profile. If synchronous detection of this gas using a lock-in amplifier is performed, the spectrum obtained by the nth order synchronous detection will be expressed by the following equation (Non Patent Literature 2): 
                         H   n     ⁡     (     v   _     )       =       1   π     ⁢       ∫     -   π     π     ⁢       τ   ⁡     (       v   _     +     a   ⁢           ⁢     cos   ⁡     (   θ   )           )       ⁢     cos   ⁡     (     n   ⁢           ⁢   θ     )       ⁢           ⁢     ⅆ   θ             ,     n   ≥   1             (   2   )               
where  v  is the wavenumber, τ is the profile of the transmission spectrum and a is the amplitude of modulation.
 
     The broken lines in  FIGS. 6 and 7  respectively show the profiles obtained by the first order (n=1; which is hereinafter referred to as “1f”) and second order (n=2; which is hereinafter referred to as “2f”) synchronous detections with a=0.1 cm −1  actually performed on the profile shown in  FIG. 4 . 
     Although equation (2) in the present form may also be used to perform a mathematical operation equivalent to the WMS process, it is too complex for practical use. Accordingly, in the present invention, a polynomial is used in the mathematical operation to perform a process equivalent to high order (including the zeroth order) detections of WMS in a faster and simpler way and then measure various physical quantities of the target gas. 
     In the method according to the present invention, it is initially assumed that a range centering on each point v with a width of 2a′, [ v −a′&lt;v&lt; v +a′], on the wavenumber axis of the profile of a spectrum obtained by DLAS is expressed by the following polynomial:
 
τ( v )= b   0   +b   1 ( v− v   )+ b   2 ( v− v   ) 2   +b   3 ( v− v   ) 3 + . . .   (3)
 
 FIG. 5  schematically illustrates this. The nth order derivative of equation (3) is:
 
                           d   n     ⁢     τ   ⁡     (   v   )           d   ⁢           ⁢     v   n         ⁢     ❘     v   =     v   _           =     b   n             (   4   )               
Meanwhile, it is generally known that the spectrum profile of an nth order harmonic wave obtained by synchronous detection in the WMS process can be approximately expressed by the following equation (Non Patent Literature 2: Equation 8):
 
                           H   n     ⁡     (     v   _     )       ≈           2     1   -   n       ⁢     τ   ⁡     (   v   )           n   !       ⁢     a   n     ⁢         d   n     ⁢     τ   ⁡     (   v   )           d   ⁢           ⁢     v   n             ⁢     ❘     v   =     v   _           ,     n   ≥   1             (   5   )               
From equations (4) and (5):
 
                         H   n     ⁡     (     v   _     )       ≈           2     1   -   n       ⁢     τ   ⁡     (   v   )           n   !       ⁢     a   n     ⁢     b   n         ,     n   ≥   1             (   6   )               
Accordingly, to calculate the WMS signal for wavenumber  V  in the DLAS spectrum, a function which fits the curve within the wavenumber range [ v −a′&lt;v&lt; v +a′] is determined by the least squares method or similar method (Step S 4 ), and the coefficients b 0 , b 1 , b 2 , b 3  . . . are determined (Step S 5 ). The profiles of the coefficients b 1  and b 2  determined by the curve fitting while sequentially changing  v  respectively correspond to the 1f and 2f WMS profiles (Step S 6 ). The value a′ representing the range of fitting corresponds to the amplitude of modulation.
 
     In the present example, for the profile shown in  FIG. 4 , the polynomial was terminated at the second order term. The solid lines in  FIGS. 6 and 7  respectively show the coefficients b 1 (1f) and b 2 (2f) plotted against the wavenumber  v . The fitting range is a′=0.11 cm −1 . 
     A comparison of the profiles obtained by equations (2) and (3) demonstrates that the two profiles have considerably similar shapes except for the difference in the scale of the vertical axis. The error due to the termination at the second order term is also adequately small. The difference in the scale is evident from equation (6). Additionally,  FIG. 8  shows the coefficient b 0  plotted against the wavenumber  v . The profile in  FIG. 8  is roughly identical to the DLAS spectrum shown in  FIG. 4 . This is evident from the fact that substituting v= v  into equation (3) gives τ( v )=b 0 . 
     In an actual measurement of target gas, the concentration, pressure, temperature and other properties of the gas are calculated based on the high order derivative curves (including the zeroth order) thus created (Step S 7 ). For example, the concentration of the target gas can be calculated from the area of the absorption peak of the zeroth order derivative curve ( FIG. 8 ). It may also be calculated from the peak height of the second order derivative curve ( FIG. 7 ). The pressure P of the target gas is known to have the following relationship with the half width at half maximum α L  of the absorption peak of the zeroth order derivative curve ( FIG. 8 ) (Non Patent Literature 7): 
                     α   L     =         α     L   ⁢           ⁢   0       ⁡     (     P     P   0       )       ⁢       (       T   0     T     )     γ               (   7   )               
where α L0  is the half width at half maximum at pressure P 0  and temperature T 0 , P 0  is the pressure of the target gas at a reference point in time, T is the temperature of the target gas at the point in time of the measurement, To is the temperature at the reference point in time, and γ is the constant representing the temperature dependency of the Lorentz width.
 
     From this equation, the pressure of the target gas can be determined. 
     As for the temperature of the target gas, it is generally known that the ratio of the sizes of two absorption peaks varies with the temperature. This relationship can be used to detect the temperature of the target gas (Non Patent Literature 8). 
     In actual measurements, the DLAS spectrum obtained by the measurement contains shot noise from the photodetector and electrical noise from the amplifier circuits. In the method according to the present invention, since the curve fitting is achieved by mathematical operations, the 1f and 2f WMS profiles as well as the DLAS spectrum can be obtained with a reduced amount of noise. 
     Next, a process for normalizing the intensity of the transmitted light is described. 
     One of the practical problems related to gas absorption spectroscopy is the change in the light intensity associated with a shift of the optical axis due to the contamination of optical parts used in the gas cell or the vibration which occurs under unfavorable environments. Therefore, a process for correcting the light intensity is required. One commonly known correction method is the normalization in which the 2f signal obtained by synchronous detection is divided by the 1f signal (Non Patent Literature 4). However, this method requires modulating the laser light as well as providing two synchronous detection circuits for 1f and 2f, respectively. 
     By contrast, the WMS-equivalent process using the polynomial approximation according to the present invention requires neither the modulation of the laser light nor the synchronous detection circuits. Furthermore, since the 1f and 2f detection signals can be simultaneously calculated in the approximation process, the normalization can be performed effortlessly. A detailed description follows. 
     Let I 0  denote the intensity of the incident light to gas. Then, the intensity of the detected light is expressed as S(v)=GI 0 τ(v), where G represents the electrical gain for the decrease (and fluctuation) in the light intensity by the optical parts and the intensity of the detected light. For an actual system, by applying the WMS process using the mathematical operation to S(v), the following equation is obtained:
 
 S ( v )= b   0   ′+b   1 ′( v− v   )+ b   2 ′( v− v   ) 2   +b   3 ′( v− v   ) 3 + . . .   (8)
 
Accordingly, the coefficients obtained in this step are:
 
 b   0   ′=GI   0   b   0   (9a)
 
 b   1   ′=GI   0   b   1   (9b)
 
 b   2   ′=GI   0   b   2   (9c)
 
A value which only depends on the transmission spectrum and is independent of the fluctuation in the light intensity can be obtained by dividing b 2 ′ (2f signal) by b 1 ′ (1f signal) or b 0 ′ as follows:
 
     
       
         
           
             
               
                 
                   
                     
                       b 
                       2 
                       ′ 
                     
                     
                       b 
                       1 
                       ′ 
                     
                   
                   = 
                   
                     
                       b 
                       2 
                     
                     
                       b 
                       1 
                     
                   
                 
               
               
                 
                   ( 
                   
                     10 
                     ⁢ 
                     a 
                   
                   ) 
                 
               
             
             
               
                 
                   
                     
                       b 
                       2 
                       ′ 
                     
                     
                       b 
                       0 
                       ′ 
                     
                   
                   = 
                   
                     
                       
                         b 
                         2 
                       
                       
                         b 
                         0 
                       
                     
                     ≈ 
                     
                       b 
                       2 
                     
                   
                 
               
               
                 
                   ( 
                   
                     10 
                     ⁢ 
                     b 
                   
                   ) 
                 
               
             
           
         
       
     
     If the absorption is low, then b 0 ˜1 (i.e. b 0  is close to 1), so that an approximation as shown by equation (10b) is available. As a result, a robust gas measurement which is independent of the light intensity is made possible. 
     REFERENCE SIGNS LIST 
     
         
           11  . . . Gas Cell 
           12  . . . Laser Source 
           13  . . . Photodetector 
           14  . . . Light Source Controller 
           15  . . . A/D Converter 
           16  . . . Analyzer