Gas absorption spectroscopic system and gas absorption spectroscopic method

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.

Claims

1. A gas absorption spectroscopic system, comprising: a) a wavelength-variable light source; b) a light source controller for varying a wavelength of light generated by the light source; c) a photodetector for detecting an 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 a plurality of discrete approximate polynomials, each of the plurality of approximate polynomials being centered at a respective wavelength point within a predetermined wavelength width, the predetermined wavelength width corresponding to a modulation depth of a Wavelength Modulation Spectroscopy—WMS—signal; e) a derivative curve creator for creating an nth order derivative curve, where n is an integer of zero or larger, based on a 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′.

2. The gas absorption spectroscopic system according to claim 1, wherein the approximate polynomials used in the polynomial approximator are second order polynomials.

3. The gas absorption spectroscopic system according to claim 2, wherein a zeroth order derivative curve is used in the polynomial approximator and the derivative curve creator, and the concentration of the target gas is determined from a peak area of the zeroth order derivative curve in the physical quantity determiner.

4. The gas absorption spectroscopic system according to claim 2, wherein the created nth order derivative curve is a second order derivative curve, and the concentration of the target gas is determined from a peak height of the second order derivative curve in the physical quantity determiner.

5. The gas absorption spectroscopic system according to claim 1, wherein a zeroth order derivative curve is used in the polynomial approximator and the derivative curve creator, and the concentration of the target gas is determined from a peak area of the zeroth order derivative curve in the physical quantity determiner.

6. The gas absorption spectroscopic system according to claim 1, wherein a second order derivative curve is used in the polynomial approximator and the derivative curve creator, and the concentration of the target gas is determined from a peak height of the second order derivative curve in the physical quantity determiner.

7. The gas absorption spectroscopic system according to claim 6, wherein a normalization for correcting a fluctuation in an amount of light is performed on the second order derivative curve in the derivative curve creator by dividing the coefficient of the second order term of the approximate polynomial at each of the wavelength points by the coefficient of the first order term or the coefficient of the zeroth order term.

8. A gas absorption spectroscopic method, comprising steps of: a-1) casting light with a varying wavelength into target gas; a-2) detecting an intensity of light transmitted through the target gas; b) performing a polynomial approximation of creating a curve approximating a change in the intensity of the light transmitted through the target gas with respect to the wavelength, using a plurality of discrete approximate polynomials, each of the plurality of approximate polynomials being centered at a respective wavelength point within a predetermined wavelength width, the predetermined wavelength width corresponding to a modulation depth of a Wavelength Modulation Spectroscopy—WMS—signal; c) creating an nth order derivative curve, where n is an integer of zero or larger, based on a coefficient of each term of the approximate polynomial at each of the wavelength points; and d) determining a physical quantity of the target gas based on the nth order derivative curve.

9. The gas absorption spectroscopic method according to claim 8, further comprising a step of performing a normalization process for correcting a fluctuation in an amount of light by dividing the coefficient of the second order term of the approximate polynomial at each of the wavelength points by the coefficient of the first order term or the coefficient of the zeroth order term, wherein the nth order derivative curve is a second order derivative curve and the normalization process is performed on the second order derivative curve.

Description

BRIEF DESCRIPTION OF DRAWINGS

(1) FIG. 1 is a schematic configuration diagram of one embodiment of the gas absorption spectroscopic system according to the present invention.

(2) FIG. 2 is a flowchart showing a procedure for measuring the concentration and other properties of target gas according to the present invention.

(3) 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.

(4) FIG. 4 is the profile of a gas transmission spectrum used for verifying the present invention.

(5) FIG. 5 is a model diagram illustrating how to represent a spectrum profile using a polynomial.

(6) 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).

(7) 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).

(8) FIG. 8 is a spectrum profile created as a result of plotting coefficient b.sub.0 against wavenumber “v”.

DESCRIPTION OF EMBODIMENTS

(9) 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.

(10) 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 S1) and then sequentially varies the wavelength to the longest wavelength (Step S2). 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 S3). Based on the data representing this spectrum profile, the analyzer 16 performs the following mathematical operations.

(11) 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.sub.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.

(12) 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.

(13) 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.sub.2 concentration and 1-atm pressure, paying attention to an absorption line near 2 μm (5000 cm.sup.−1).

(14) It is generally known that an absorption peak under atmospheric pressure can be expressed by the following Lorentzian function:

(15) $\begin{array}{cc}g\left(v\right)=\frac{A}{\pi }\frac{{\alpha }_L}{{\left(v-v_c\right)}^2+{\alpha }_L^2}& \left(1\right)\end{array}$
where v is the wavenumber, A is the peak area, v.sub.c is the wavenumber of the peak, and α.sub.L is the half width at half maximum of the Lorentz broadening.

(16) 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):

(17) $\begin{array}{cc}{H}_n\left(\stackrel{\_}{v}\right)=\frac{1}{\pi }{\int }_{-\pi }^{\pi }\tau \left(\stackrel{\_}{v}+a\cos \left(\theta \right)\right)\cos \left(n\theta \right)d\theta ,n\ge 1& \left(2\right)\end{array}$
where v is the wavenumber, τ is the profile of the transmission spectrum and a is the amplitude of modulation.

(18) 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.sup.−1 actually performed on the profile shown in FIG. 4.

(19) 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.

(20) 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′<v<v+a′], on the wavenumber axis of the profile of a spectrum obtained by DLAS is expressed by the following polynomial:
τ(v)=b.sub.0+b.sub.1(v−v)+b.sub.2(v−v).sup.2+b.sub.3(v−v).sup.3+ . . .   (3)
FIG. 5 schematically illustrates this. The nth order derivative of equation (3) is:

(21) $\begin{array}{cc}\frac{d^n\tau \left(v\right)}{d{v}^n}{.Math.}_{v=\stackrel{\_}{v}}=b_n& \left(4\right)\end{array}$
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):

(22) $\begin{array}{cc}{H}_n\left(\stackrel{\_}{v}\right)\approx \frac{2^{1-n}\tau \left(v\right)}{n!}{a}^n\frac{d^n\tau \left(v\right)}{d{v}^n}{.Math.}_{v=\stackrel{\_}{v}},n\ge 1& \left(5\right)\end{array}$
From equations (4) and (5):

(23) $\begin{array}{cc}{H}_n\left(\stackrel{\_}{v}\right)\approx \frac{2^{1-n}\tau \left(v\right)}{n!}{a}^n{b}_n,n\ge 1& \left(6\right)\end{array}$
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′<v<v+a′] is determined by the least squares method or similar method (Step S4), and the coefficients b.sub.0, b.sub.1, b.sub.2, b.sub.3 . . . are determined (Step S5). The profiles of the coefficients b.sub.1 and b.sub.2 determined by the curve fitting while sequentially changing v respectively correspond to the 1f and 2f WMS profiles (Step S6). The value a′ representing the range of fitting corresponds to the amplitude of modulation.

(24) 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.sub.1(1f) and b.sub.2(2f) plotted against the wavenumber v. The fitting range is a′=0.11 cm.sup.−1.

(25) 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.sub.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.sub.0.

(26) 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 S7). 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.sub.L of the absorption peak of the zeroth order derivative curve (FIG. 8) (Non Patent Literature 7):

(27) $\begin{array}{cc}{\alpha }_L={\alpha }_{L0}\left(\frac{P}{P_0}\right){\left(\frac{T_0}{T}\right)}^{\gamma }& \left(7\right)\end{array}$
where α.sub.L0 is the half width at half maximum at pressure P.sub.0 and temperature T.sub.0, P.sub.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.

(28) From this equation, the pressure of the target gas can be determined.

(29) 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).

(30) 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.

(31) Next, a process for normalizing the intensity of the transmitted light is described.

(32) 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.

(33) 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.

(34) Let I.sub.0 denote the intensity of the incident light to gas. Then, the intensity of the detected light is expressed as S(v)=GI.sub.0τ(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.sub.0′+b.sub.1′(v−v)+b.sub.2′(v−v).sup.2+b.sub.3′(v−v).sup.3+ . . .   (8)
Accordingly, the coefficients obtained in this step are:
b.sub.0′=GI.sub.0b.sub.0  (9a)
b.sub.1′=GI.sub.0b.sub.1  (9b)
b.sub.2′=GI.sub.0b.sub.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.sub.2′ (2f signal) by b.sub.1′ (1f signal) or b.sub.0′ as follows:

(35) $\begin{array}{cc}\frac{b_2^{\prime }}{b_1^{\prime }}=\frac{b_2}{b_1}& \left(10a\right)\\ \frac{b_2^{\prime }}{b_0^{\prime }}=\frac{b_2}{b_0}\approx b_2& \left(10b\right)\end{array}$

(36) If the absorption is low, then b.sub.0˜1 (i.e. b.sub.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

(37) 11 . . . Gas Cell 12 . . . Laser Source 13 . . . Photodetector 14 . . . Light Source Controller 15 . . . A/D Converter 16 . . . Analyzer