Patent Publication Number: US-11650155-B2

Title: Gas analysis system and gas analysis method

Description:
BACKGROUND 
     Technical Field 
     The present invention generally relates to a gas analysis system and a gas analysis method. 
     Related Art 
     Among gas analysis systems that analyze a measurement target gas, there is one that measures a concentration of a measurement target gas based on an absorbance of light irradiated to the measurement target gas. In such a gas analysis system, to increase measurement precision (sensitivity), wavelength-modulation spectroscopy is sometimes used. Wavelength-modulation spectroscopy is a technique of irradiating a laser light modulated by a modulation frequency f to a measurement target gas and measuring a concentration of the measurement target gas based on a second-order harmonic component (2f component) obtained by detecting the laser light upon its transmission through the measurement target gas. 
     In wavelength-modulation spectroscopy, the concentration of the measurement target gas is often measured upon calculating a ratio of the 2f component to a component (1f component) of the modulation frequency f that is detected and standardizing a light reception amount. This is to reduce an effect of fluctuations in the light reception amount of the laser light due to factors other than the measurement target gas. Note that wavelength-modulation spectroscopy is also sometimes referred to as 2f detection. Patent literature 1 below discloses one example of a conventional gas analysis system that uses wavelength-modulation spectroscopy to measure a gas concentration. 
     PATENT LITERATURE 
     
         
         Patent Literature 1: WO 2017/014097 A1 
       
    
     Now, in the above gas analysis system, optical interference noise may be generated when the laser light passes through a lens or other optical element, a window, a thin film, or the like. This optical interference noise arises due to, for example, interference caused by the laser light upon undergoing multiple reflection inside an optical element or the like, and a magnitude thereof changes periodically depending on a wavelength of the laser light. For example, just as a transmittance of a Fabry-Pérot etalon becomes periodic relative to wavelength, the magnitude of the optical interference noise also becomes periodic relative to the wavelength. When there is such optical interference noise, there is a problem of a worsened detection limit of the concentration of the measurement target gas. 
     SUMMARY 
     One or more embodiments provide a gas analysis system and a gas analysis method that can improve a detection limit of a concentration of a measurement target gas. 
     According to one or more embodiments, a gas analysis system ( 1 ) includes: a light-emitting element ( 13 ) that emits a laser light modulated by a predetermined modulation frequency (f); a light-receiving element ( 17 ) that receives the laser light upon the laser light passing through a measurement target gas (GS); and a signal processing device ( 20 ) that calculates a concentration of the measurement target gas based on a magnitude of a third component obtained by removing, from a first component that is a component having an N-frequency, meaning a frequency n times (n being an integer no less than 2) the modulation frequency included in a received signal output from the light-receiving element, a second component that is a component, of the same frequency as the first component, of optical interference noise arising on an optical path of the laser light from the light-emitting element to the light-receiving element. 
     Furthermore, the gas analysis system according to one or more embodiments is provided with a detector ( 19 ) that detects an amplitude (R 2f ) and a phase (θ 2f ) of the first component included in the received signal, and the signal processing device is provided with a storage ( 21 ) that stores an amplitude (R 0 , R 02f ) and a phase (θ 0 , θ 02f ) of the second component and a processor that calculates the third component by using the amplitude and the phase of the first component detected by the detector and the amplitude and the phase of the second component stored in the storage to perform a computation of removing the second component from the first component. 
     Furthermore, in the gas analysis system according to one or more embodiments, the detector detects, in addition to the first component, a fundamental component that is a component having the same frequency as the modulation frequency included in the received signal, and the processor calculates the concentration of the measurement target gas based on a ratio (R′ 2f /R 1f ) of an amplitude (R′ 2f ) of the third component to an amplitude (R 1f ) of the fundamental component. 
     Furthermore, in the gas analysis system according to one or more embodiments, the amplitude and the phase of the second component stored in the storage are an amplitude and a phase of the first component detected by the detector at a time when the measurement target gas is not present on the optical path of the laser light or a state where the concentration of the measurement target gas on the optical path of the laser light is sufficiently low. 
     Alternatively, in the gas analysis system according to one or more embodiments, the amplitude and the phase of the second component stored in the storage are an amplitude and a phase obtained by performing a predetermined computation using an amplitude and a phase of the first component detected by the detector at a time when the measurement target gas is present on the optical path of the laser light at a known first concentration and an amplitude and a phase of the first component detected by the detector at a time when the measurement target gas is present on the optical path of the laser light at a known second concentration. 
     Alternatively, in the gas analysis system according to one or more embodiments, the amplitude and the phase of the second component stored in the storage are an amplitude and a phase of the first component detected by the detector at a time when an optical path length of the laser light is set to a reference length prescribed in advance, and the processor calculates the third component by performing a computation of removing the second component from the first component upon correcting, based on a difference between a phase of the fundamental component detected by the detector at a time when the optical path length of the laser light is not set to the reference length and a phase of the fundamental component detected by the detector at the time when the optical path length of the laser light is set to the reference length, a phase of the first component detected by the detector at the time when the optical path length of the laser light is not set to the reference length. 
     A gas analysis method according to one or more embodiments has: a first step of emitting a laser light modulated by a predetermined modulation frequency (f); a second step of obtaining a received signal by receiving the laser light upon the laser light passing through a measurement target gas (GS); a third step (S 14 , S 25 ) of obtaining a third component by removing, from a first component that is a component having an N-frequency that is n times (n being an integer no less than 2) the modulation frequency included in the received signal, a second component that is a component, of the same frequency as the first component, of optical interference noise arising on an optical path of the laser light; and a fourth step (S 15 , S 26 ) of calculating a concentration of the measurement target gas based on a magnitude of the third component. 
     Furthermore, the gas analysis method according to one or more embodiments further includes: a step (S 11 , S 12 , S 21 , S 22 ) of calculating the second component in advance, prior to measuring the measurement target gas. 
     One or more embodiments can improve a detection limit of a concentration of a measurement target gas. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG.  1    is a block diagram illustrating a configuration of main parts of a gas analysis system according to a first embodiment. 
         FIG.  2    is a diagram for describing a process performed in a processor in the first embodiment. 
         FIG.  3    is a flowchart illustrating a gas analysis method according to the first embodiment. 
         FIGS.  4 A and  4 B  are diagrams illustrating measurement results of the gas analysis system according to the first embodiment. 
         FIG.  5    is a diagram for describing a method of calculating a 2f noise component in a second embodiment. 
         FIG.  6    is a flowchart illustrating a gas analysis method according to a third embodiment. 
     
    
    
     DETAILED DESCRIPTION 
     Gas analysis systems and gas analysis methods according to one or more embodiments of the present invention are described in detail below with reference to the drawings. In the following, first, an overview of the present embodiments is described. Afterward, details of each embodiment are described. 
     [Overview] 
     One or more embodiments enable an improvement of a detection limit of a concentration of a measurement target gas. For example, they enable high-precision measurement of a concentration of a measurement target gas even when the concentration of the measurement target gas is low. That is, they enable high-precision measurement of the concentration of the measurement target gas even near a detection limit that is found theoretically. 
     In wavelength-modulation spectroscopy, a magnitude of an amplitude of a second-order harmonic component (2f component) that is detected is represented by formula (1) below.
 
[Math. 1]
 
 I   s =√{square root over (2)} sP   dc   k   2 α 0   C   R   (1)
 
     In formula (1) above, I S  is the magnitude (RMS: root mean square) of the amplitude of the 2f component. Moreover, s is a coefficient indicating a sensitivity of a light-receiving element, P dc  is a received power of a laser light, and k 2  is a constant determined by a modulation frequency of the laser light. Moreover, α 0  is an absorbance at a center wavelength of a measurement target gas, and C R  is a gas concentration of the measurement target gas. 
     Furthermore, noise I N  of the 2f component that is detected is represented by formula (2) below. 
     
       
         
           
             
               
                 
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     In formula (2) above, RIN is relative intensity noise of a laser light source, and I dark  is a dark current of the light-receiving element. Moreover, e is the elementary charge, k B  is the Boltzmann constant, T is a temperature of the light-receiving element, R sh  is a shunt resistance of the light-receiving element, and Δt is a time constant of a lock-in amplifier used to detect the 2f component. 
     A detection limit C R   limit  of the concentration of the measurement target gas when a signal-to-noise ratio (SN ratio: signal-noise ratio) is “1” is indicated by formula (3) below. 
     
       
         
           
             
               
                 
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     Here, in formula (2) above indicating the noise I N  of the 2f component and formula (3) above indicating the detection limit C R   limit  of the concentration of the measurement target gas, optical interference noise is not taken into consideration. Optical interference noise is generated when the laser light passes through a lens or other optical element, a window, a thin film, or the like. For example, optical interference noise arises due to interference caused by the laser light upon undergoing multiple reflection inside an optical element or the like, and a magnitude thereof changes periodically depending on a wavelength of the laser light or a thickness of the optical element or the like. As such, for example, when a full width at half maximum of the optical interference noise and a full width at half maximum of an absorption spectrum of the measurement target gas are at the same level due to the thickness of the optical element or the like, it is difficult to separate the optical interference noise and the absorption spectrum of the measurement target gas. 
     Such optical interference noise can be removed (or reduced) by, for example, applying the following measures (optical measures).
         Forming an antireflective film (AR film) on an incidence face and an emission face of the optical element or the like that is the cause   Inclining the incidence face and the emission face of the optical element or the like that is the cause relative to an optical path of the laser light   Designing the FWHM (full width at half maximum) of the absorption spectrum and a period of optical interference to not be the same level       

     However, applying these measures involves demerits such as increased costs, a complicated configuration, reduced freedom in design, and cumbersome adjustment. 
     In one or more embodiments, first, a laser light modulated by a predetermined modulation frequency is emitted, and a received signal is obtained by receiving the laser light upon its passing through a measurement target gas. Next, from a first component, which is a component having an N-frequency that is n times (n being an integer no less than 2) the modulation frequency included in the received signal, a second component, which is a component of the same frequency as the first component of optical interference noise arising on an optical path of the laser light, is removed to obtain a third component. Then, a concentration of the measurement target gas is found based on a magnitude of the third component. This enables improvement of a detection limit of the concentration of the measurement target gas without giving rise to demerits such as increased costs, a complicated configuration, reduced freedom in design, and cumbersome adjustment. 
     First Embodiment 
     &lt;Gas Analysis System&gt; 
       FIG.  1    is a block diagram illustrating a configuration of main parts of a gas analysis system according to a first embodiment. As illustrated in  FIG.  1   , a gas analysis system  1  of the present embodiment is provided with a gas analysis device  10  and a signal processing device  20 , which is referred to as a processing unit, and uses wavelength-modulation spectroscopy to measure a concentration of a measurement target gas GS. For example, the gas analysis system  1  of the present embodiment irradiates a laser light modulated by a modulation frequency f to the measurement target gas GS and measures the concentration of the measurement target gas GS based on a second-order harmonic component (2f component) that is detected. 
     The gas analysis device  10  is provided with a signal generator  11 , a drive circuit  12 , a semiconductor laser  13  (light-emitting element), an optical amplifier  14 , a lens  15 , a lens  16 , a photodetector  17  (light-receiving element), an amplifier  18 , and a lock-in amplifier  19  (detector). Such a gas analysis device  10  performs emission of the laser light irradiated to the measurement target gas GS, reception of the laser light via the measurement target gas GS, detection of a component of the modulation frequency f (1f component) and the 2f component included in a received signal, and the like. 
     As controlled by the signal processing device  20 , the signal generator  11  outputs a control signal CS for controlling the drive circuit  12  and a reference signal RS used in the lock-in amplifier  19 . The reference signal RS output from the signal generator  11  is synchronized with the control signal CS output from the signal generator  11 . As this signal generator  11 , for example, an arbitrary waveform generator or a function generator can be used. 
     Based on the control signal CS output from the signal generator  11 , the drive circuit  12  outputs a drive signal for driving the semiconductor laser  13 . The drive signal output from the drive circuit  12  is, for example, a signal wherein an alternating current of the modulation frequency f is superimposed on a direct current having a certain magnitude (amplitude). Note that the alternating current of the modulation frequency f may be, for example, sinusoidal or non-sinusoidal. 
     The semiconductor laser  13  is driven by the drive signal output from the drive circuit  12  and emits the laser light irradiated to the measurement target gas GS. The laser light emitted from the semiconductor laser  13  is, for example, a laser light wherein a center wavelength of modulation is a center wavelength of an absorption spectrum of the measurement target gas GS and a wavelength modulation width (modulation frequency f) is 2.2 times a FWHM of the absorption spectrum of the measurement target gas GS. The wavelength modulation width (modulation frequency f) of the laser light emitted from the semiconductor laser  13  may be no less than 1 time, no less than 2 times, or no less than 10 times the FWHM of the absorption spectrum of the measurement target gas GS. Note that as the semiconductor laser  13 , for example, a QCL (quantum cascade laser) or an ICL (interband cascade laser) can be used. 
     The optical amplifier  14  amplifies the laser light emitted from the semiconductor laser  13 . As this optical amplifier  14 , for example, an optical fiber amplifier or a semiconductor optical amplifier can be used. The lens  15  converts the laser light passed through the optical amplifier  14  into parallel light. As such a lens  15 , a collimating lens can be used. Note that another optical element (for example, a parabolic mirror) can also be used instead of the lens  15  as long as it can convert the laser light passed through the optical amplifier  14  into parallel light. 
     The laser light collimated by the lens  15  is irradiated to the measurement target gas GS. Of the laser light irradiated to the measurement target gas GS, a portion that is transmitted through the measurement target gas GS is reflected by a scatterer SM such as a wall. Afterward, it is again transmitted through the measurement target gas GS and becomes incident on the lens  16 . Note that a distance between the gas analysis device  10  and the scatterer SM may be any distance but is set to, for example, no greater than about 100 [m]. 
     The lens  16  condenses the laser light passed through the measurement target gas GS onto the photodetector  17 . As such a lens  16 , a condensing lens can be used. Note that another optical element (for example, a parabolic mirror) can also be used instead of the lens  16  as long as it can condense the laser light passed through the measurement target gas GS onto the photodetector  17 . The photodetector  17  converts the laser light condensed by the lens  16  into an electrical signal and outputs this as the received signal. As this photodetector  17 , for example, a PD (photodiode) can be used. 
     The amplifier  18  amplifies the received signal output from the photodetector  17 . An amplification rate of the amplifier  18  is set to an appropriate amplification rate in response to, for example, an intensity of the laser light incident on the photodetector  17 . When the photodetector  17  is a PD, as the amplifier  18 , an IV conversion circuit that converts a photocurrent output as the received signal from the photodetector  17  into a voltage can be used. 
     The lock-in amplifier  19  uses the reference signal RS output from the signal generator  11  to detect a specific frequency component from the received signal amplified by the amplifier  18 . For example, the lock-in amplifier  19  uses the reference signal RS output from the signal generator  11  to perform phase-sensitive detection and detects the 1f component (fundamental component) and the 2f component (first component) from the received signal amplified by the amplifier  18 . 
     The signal processing device  20  is provided with a storage  21 , a processor  22 , and an output unit  23 . It controls operations of the gas analysis device  10  and uses a detection result of the gas analysis device  10  (detection result of the lock-in amplifier  19 ) to measure the concentration of the measurement target gas GS. The signal processing device  20  is realized by, for example, a computer such as a personal computer. 
     The storage  21  stores a predetermined component (second component) of optical interference noise arising on an optical path of the laser light from the semiconductor laser  13  to the photodetector  17 . For example, the storage  21  stores an amplitude R 0  and a phase θ 0  of a component, among components of the optical interference noise, of the same frequency as the 2f component (referred to as a “2f noise component” hereinbelow). Note that the phase θ 0  is a phase whose basis is a phase of the reference signal RS output from the signal generator  11 . Here, the amplitude R 0  and the phase θ 0  stored in the storage  21  is, for example, an amplitude and a phase of the 2f component detected by the lock-in amplifier  19  at a time when the measurement target gas GS is not present on the optical path of the laser light emitted from the gas analysis device  10  (or a concentration of the measurement target gas GS on the optical path of the laser light is sufficiently low). Here, “a concentration of the measurement target gas GS [being] sufficiently low” refers to a concentration of the measurement target gas GS on the optical path of the laser light being sufficiently lower than a concentration of the measurement target gas GS on the optical path of the laser light at a time of concentration measurement; this concentration may be lower than a detection limit of the gas analysis system  1 . 
     The processor  22  uses the detection result of the gas analysis device  10  (detection result of the lock-in amplifier  19 ) and the amplitude R 0  and the phase θ 0  of the 2f noise component stored in the storage  21  to calculate the concentration of the measurement target gas GS. For example, the processor  22  performs a computation of removing the amplitude R 0  and the phase θ 0  of the 2f noise component stored in the storage  21  from an amplitude R 2f  and a phase θ 2f  of the 2f component detected by the lock-in amplifier  19 . The processor  22  thereby calculates an amplitude R′ 2f  of a component wherein the 2f noise component is removed from the 2f component (referred to as a “noise-removed 2f component” hereinbelow; third component). 
     For example, the processor  22  performs the computation indicated in formula (4) below to calculate the amplitude R′ 2f  of the noise-removed 2f component.
 
[Math. 4]
 
 R′   2f =√{square root over (( R   2f  cos θ− R   0  cos θ 0 ) 2 +( R   2f  sin θ− R   0  sin θ 0 ) 2 )}  (4)
 
       FIG.  2    is a diagram for describing a process performed in the processor in the first embodiment. The graph illustrated in  FIG.  2    is a graph wherein a horizontal axis is an X output of the lock-in amplifier  19  and a vertical axis is a Y output thereof. Note that the graph illustrated in  FIG.  2    can also be seen as a graph of a complex plane wherein the horizontal axis is a real axis and the vertical axis is an imaginary axis. In  FIG.  2   , the 2f component is represented as vector V 2f , and the 2f noise component is represented as vector V 0 . Moreover, the noise-removed 2f component is represented as vector V′ 2f . 
     Note that a length of vector V 2f  indicates an amplitude R of the 2f component and that a counterclockwise rotation angle of vector V 2f  relative to the positive real axis indicates a phase θ of the 2f component. Moreover, a length of vector V 0  indicates the amplitude R 0  of the 2f noise component, and a counterclockwise rotation angle of vector V 0  relative to the positive real axis indicates the phase θ 0  of the 2f component. Likewise, a length of vector V′ 2f  indicates the amplitude R′ 2f  of the noise-removed 2f component, and a counterclockwise rotation angle of vector V′ 2f  relative to the positive real axis indicates a phase of the noise-removed 2f component. 
     As illustrated in  FIG.  2   , the 2f component detected by the lock-in amplifier  19  (vector V 2f  in  FIG.  2   ) is represented as a sum of the noise-removed 2f component (vector V′ 2f  in  FIG.  2   ) and the 2f noise component (vector V 0 ). Note that the noise-removed 2f component (vector V′ 2f  in FIG.  2 ) is the original 2f component unaffected by the 2f noise component. The processor  22  uses formula (4) above to subtract vector V 0  from the 2f component detected by the lock-in amplifier  19  (vector V 2f  in  FIG.  2   ) to calculate a length (amplitude R′ 2f  of the noise-removed 2f component) of the original 2f component (vector V′ 2f  in  FIG.  2   ). 
     Furthermore, the processor  22  measures the concentration of the measurement target gas GS based on a ratio of the amplitude R′ 2f  of the noise-removed 2f component relative to an amplitude R 1f  of the 1f component detected by the lock-in amplifier  19  (R′ 2f /R 1f ). Here, the concentration of the measurement target gas GS is measured based on the above ratio in order to reduce an effect of fluctuations in a light reception amount of the laser light due to factors other than the measurement target gas. 
     The output unit  23  outputs a computation result of the processor  22  to the outside. For example, the output unit  23  outputs information indicating the concentration of the measurement target gas GS measured by the processor  22 . Note that the output unit  23  may output, other than the information indicating the concentration of the measurement target gas GS, information indicating the 2f component, information indicating the 1f component, information indicating the 2f noise component, and other various information. The output unit  23  may output to the outside a signal indicating the above information or perform output to the outside by displaying the above information. 
     &lt;Gas Analysis Method&gt; 
       FIG.  3    is a flowchart illustrating a gas analysis method according to the first embodiment. First, prior to measuring the measurement target gas GS, a process of acquiring the amplitude R 0  and the phase θ 0  of the 2f noise component is performed. 
     For example, at the time when the measurement target gas GS is not present, a process of emitting the laser light modulated by the modulation frequency f, detecting the laser light reflected by the scatterer SM by the photodetector  17 , and detecting the received signal output from the photodetector  17  by the lock-in amplifier  19  is performed in the gas analysis device  10 . Then, a process of acquiring an amplitude and a phase of the 2f component detected by the lock-in amplifier  19  (step S 11 ) and storing the acquired amplitude and phase of the 2f component as the amplitude R 0  and the phase θ 0  in the storage  21  is performed in the signal processing device  20  (step S 12 ). 
     Next, the measurement target gas GS is measured. For example, in a state where the measurement target gas GS is present, a process of emitting the laser light modulated by the modulation frequency f (first step), obtaining the received signal by detecting the laser light passed through the measurement target gas GS by the photodetector  17  (second step), and detecting the received signal by the lock-in amplifier  19  is performed in the gas analysis device  10 . Then, a process of acquiring the amplitude R 1f  of the 1f component and the amplitude R 2f  and phase θ 2f  of the 2f component of the measurement target gas detected by the lock-in amplifier  19  is performed in the signal processing device  20  (step S 13 ). 
     Next, a process of performing the computation indicated by formula (4) above to calculate the amplitude R′ 2f  of the noise-removed 2f component is performed in the processor  22  (step S 14 ; third step). For example, a process of calculating the amplitude R′ 2f  of the noise-removed 2f component by substituting the amplitude R 0  and the phase θ 0  stored in the storage  21  at step S 12  and the amplitude R 2f  and the phase θ 2f  of the 2f component acquired at step S 13  into formula (4) above is performed in the processor  22 . 
     Next, a process of calculating the concentration of the measurement target gas GS by calculating the ratio of the amplitude R′ 2f  of the noise-removed 2f component relative to the amplitude R 1f  of the 1f component obtained at step S 13  (R′ 2f /R 1f ) is performed in the processor  22  (step S 15 ; fourth step). Then, the information indicating the concentration of the measurement target gas GS measured by the processor  22  is output from the output unit  23 . Subsequently, the processes of steps S 13  to S 15  are repeatedly performed at certain time intervals prescribed in advance. 
       FIG.  4    is a diagram illustrating a measurement result of the gas analysis system according to the first embodiment. The measurement results illustrated in  FIG.  4    are results of measuring methane (CH 4 ) gas as the measurement target gas; (a) in  FIG.  4    is a diagram illustrating the measurement result of the gas analysis system  1  of the present embodiment, and (b) in  FIG.  4    is a diagram illustrating a measurement result of a conventional gas analysis system. Note that the measurement result illustrated in (a) in  FIG.  4    indicates a relationship between, on one hand, the amplitude ratio between the noise-removed 2f component and the 1f component (R′ 2f /R 1f ) and, on the other, a concentration of the methane gas, and the measurement result illustrated in (b) in  FIG.  4    indicates a relationship between, on one hand, an amplitude ratio between the 2f component and the 1f component (R 2f /R 1f ) and, on the other, the concentration of the methane gas. 
     Referring to the measurement result illustrated in (b) in  FIG.  4   , when the concentration is no greater than 100 [ppmm], the linearity of the graph illustrating the relationship between, on one hand, the amplitude ratio between the 2f component and the 1f component (R 2f /R 1f ) and, on the other, the concentration of the methane gas is disrupted. It is thereby understood that conventionally, the concentration of the measurement target gas is not being able to be precisely measured when the concentration is no greater than 100 [ppmm]. In contrast, referring to the measurement result illustrated in (a) in  FIG.  4   , the linearity of the graph illustrating the relationship between, on one hand, the amplitude ratio between the noise-removed 2f component and the 1f component (R′ 2f /R 1f ) and, on the other, the concentration of the methane gas is maintained even if the concentration is no greater than 100 [ppmm]. It is thereby understood that in the present embodiment, the concentration of the measurement target gas is being able to be precisely measured even if the concentration of the measurement target gas is low. 
     As above, in the present embodiment, first, the laser light modulated by the predetermined modulation frequency f is emitted, and the received signal is obtained by receiving the laser light passed through the measurement target gas GS. Next, the 2f noise component arising on the optical path of the laser light is removed from the 2f component included in the received signal to obtain the noise-removed 2f component. Then, the concentration of the measurement target gas GS is found based on a magnitude of the noise-removed 2f component. This enables improvement of a detection limit of the concentration of the measurement target gas GS without giving rise to demerits such as increased costs, a complicated configuration, reduced freedom in design, and cumbersome adjustment. 
     In this manner, by using not only amplitude information but also phase information, the present embodiment can remove a component having a set phase, such as optical interference noise. This enables precise measurement of the concentration of the measurement target gas GS up to a detection-limit level determined by RIN (relative intensity noise) of the semiconductor laser  13  and white noise of circuits such as the amplifier  18 . 
     Second Embodiment 
     Next, a second embodiment is described. The gas analysis system in the present embodiment has a configuration similar to the gas analysis system  1  illustrated in  FIG.  1   . The present embodiment and the first embodiment above differ in an acquisition method of the amplitude R 0  and the phase θ 0  of the 2f noise component. That is, the present embodiment and the first embodiment differ in processes of steps S 11 , S 12  illustrated in  FIG.  3   . 
     In the first embodiment above, in the process of step S 11  illustrated in  FIG.  3   , the amplitude and the phase of the 2f component detected by the lock-in amplifier  19  are acquired at the time when the measurement target gas GS is not present on the optical path of the laser light emitted from the gas analysis device  10 . Then, in the process of step S 11  illustrated in  FIG.  3   , the acquired amplitude and phase of the 2f component are stored in the storage  21  as the amplitude R 0  and the phase θ 0  of the 2f noise component. 
     In contrast, the present embodiment acquires an amplitude and a phase of the 2f component detected by the lock-in amplifier  19  at a time when the measurement target gas GS is present on the optical path of the laser light at a known first concentration. It also acquires an amplitude and a phase of the 2f component detected by the lock-in amplifier  19  at a time when the measurement target gas GS is present on the optical path of the laser light at a known second concentration. Then, using the two amplitudes and phases that are acquired and the concentrations of the measurement target gas GS (first concentration, second concentration), the amplitude R 0  and the phase θ 0  of the 2f noise component are found by computation. 
     When calculating the amplitude R 0  and the phase θ 0  of the 2f noise component, two types of gas cells where the measurement target gas GS is enclosed on the optical path of the laser light may be disposed. For example, the amplitudes and the phases of the 2f component detected by the lock-in amplifier  19  may be acquired by alternatingly disposing on the optical path of the laser light a gas cell wherein the measurement target gas GS is enclosed at the first concentration above and a gas cell wherein the measurement target gas GS is enclosed at the second concentration above. 
       FIG.  5    is a diagram for describing the method of calculating the 2f noise component in the second embodiment. Note that in  FIG.  5   , like  FIG.  2   , the horizontal axis is the X output of the lock-in amplifier  19 , and the vertical axis is the Y output thereof. Note that like  FIG.  2   , the graph illustrated in  FIG.  5    can also be seen as a graph of a complex plane wherein the horizontal axis is a real axis and the vertical axis is an imaginary axis. 
     In  FIG.  5   , the 2f component detected by the lock-in amplifier  19  at the time when the measurement target gas GS is present on the optical path of the laser light at the known first concentration is represented as vector V 1   2f . Moreover, the 2f component detected by the lock-in amplifier  19  at the time when the measurement target gas GS is present on the optical path of the laser light at the known second concentration is represented as vector V 2   2f . Moreover, the 2f noise component is represented as vector V 0 . 
     Note that vector V 1 ′ 2f  in  FIG.  5    indicates the original 2f component unaffected by the 2f noise component at the time when the measurement target gas GS is present at the first concentration. Moreover, vector V 2 ′ 2f  indicates the original 2f component unaffected by the 2f noise component at the time when the measurement target gas GS is present at the second concentration. A length (amplitude) of vector V 1 ′ 2f  is a length according to the first concentration of the measurement target gas GS. Likewise, a length (amplitude) of vector V 2 ′ 2f  is a length according to the second concentration of the measurement target gas GS. The first concentration of the measurement target gas GS is referred to as d1, and the second concentration of the measurement target gas GS is referred to as d2. 
     The signal processing device  20  calculates the 2f noise component (vector V 0 ) by performing the computation indicated in formula (5) below. 
     
       
         
           
             
               
                 
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     Note that the length of vector V 0  is the amplitude R 0  of the 2f noise component, and the counterclockwise rotation angle of vector V 0  relative to the positive real axis is the phase θ 0  of the 2f noise component. The amplitude R 0  and the phase θ 0  of the 2f noise component found in this manner are stored in the storage  21 . 
     As above, the present embodiment and the first embodiment above only differ in the acquisition method of the amplitude R 0  and the phase θ 0  of the 2f noise component. In the present embodiment as well, like the first embodiment, the 2f noise component arising on the optical path of the laser light is removed from the 2f component included in the received signal to obtain the noise-removed 2f component, and the concentration of the measurement target gas GS is found based on the magnitude of the noise-removed 2f component. This enables improvement of a detection limit of the concentration of the measurement target gas GS without giving rise to demerits such as increased costs, a complicated configuration, reduced freedom in design, and cumbersome adjustment. 
     Third Embodiment 
     Next, a third embodiment is described. The gas analysis system in the present embodiment has a configuration similar to the gas analysis system  1  illustrated in  FIG.  1   . The present embodiment and the first embodiment above differ in an acquisition method of the amplitude R 0  and the phase θ 0  of the 2f noise component and a process of calculating the amplitude R′ 2f  of the noise-removed 2f component performed by the processor  22 . The present embodiment is for a situation wherein a modulation frequency is high and a measurement distance (optical path length of the laser light) changes variously. 
     When the modulation frequency is high and the measurement distance (optical path length of the laser light) changes variously, the phase of the laser light (laser light detected by the photodetector  17 ) relative to the reference signal RS used in the lock-in amplifier  19  changes. The present embodiment enables an improved detection limit of the concentration of the measurement target gas GS by correcting such a phase change. 
     In the present embodiment, the storage  21  stores a phase θ 01f  of the 1f component and an amplitude R 01f  and phase θ 02f  of the 2f noise component from when the optical path length of the laser light is set to a reference length prescribed in advance (for example, 0 [m]). Note that in the present embodiment, the amplitude and the phase of the 2f noise component are written as “amplitude R 02f ” and “phase θ 02f ” so as to be differentiated from the amplitude R 0  and the phase θ 0  of the 2f noise component in the first and second embodiments. The phases θ 01f , θ 02f  are phases whose basis is the phase of the reference signal RS output from the signal generator  11 . 
     In the present embodiment, the processor  22  calculates a phase difference φ between the phase θ 1f  of the 1f component obtained when the optical path length of the laser light is not set to the reference length and the phase θ 01f  of the 1f component obtained when the optical path length of the laser light is set to the reference length. Moreover, the processor  22  uses the detection result of the gas analysis device  10  (detection result of the lock-in amplifier  19 ) and the amplitude R 01f  and the phase θ 02f  of the 2f noise component stored in the storage  21  to calculate the concentration of the measurement target gas GS. 
     For example, the processor  22  performs a computation of removing the amplitude R 01f  and the phase θ 02f  of the 2f noise component stored in the storage  21  from the amplitude Ref and the phase θ 2f  of the 2f component detected by the lock-in amplifier  19 . At this time, the processor  22  corrects the phase θ 2f  of the 2f component in consideration of the above phase difference φ of the 1f component. 
     For example, the processor  22  performs the computation indicated in formula (6) below to calculate the amplitude R′ 2f  of the noise-removed 2f component.
 
[Math. 6]
 
 R′   2f =√{square root over ({ R   2f  cos(θ 2f −φ)− R   02f  cos θ 02f } 2   +{R   2f  sin(θ 2f −φ)− R   02f  sin θ 02f } 2 )}  (6)
 
       FIG.  6    is a flowchart illustrating the gas analysis method according to the third embodiment. First, prior to measuring the measurement target gas GS, a process of acquiring the phase θ 01f  of the 1f component and the amplitude R 02f  and phase θ 02f  of the 2f noise component from when the optical path length of the laser light is set to the reference length is performed. Note that as a method of setting the optical path length of the laser light to the reference length, for example, a method of disposing a jig on the optical path of the laser light can be mentioned. 
     A process of emitting the laser light modulated by the modulation frequency f in a state where the optical path length of the laser light is set to the reference length; detecting the laser light, upon its being reflected by, for example, the jig, by the photodetector  17 ; and detecting the received signal output from the photodetector  17  by the lock-in amplifier  19  is performed in the gas analysis device  10 . Then, a process of acquiring a phase of the 1f component and an amplitude and phase of the 2f component detected by the lock-in amplifier  19  is performed in the signal processing device  20  (step S 21 ). Moreover, a process of storing the acquired phase of the 1f component as the phase θ 01f  in the storage  21  and storing the acquired amplitude and phase of the 2f component as the amplitude R 02f  and the phase θ 02f  in the storage  21  is performed in the signal processing device  20  (step S 22 ). 
     Next, the measurement target gas GS is measured. For example, in a state where the above jig is removed from the optical path of the laser light and the measurement target gas GS is present on the optical path of the laser light, a process of emitting the laser light modulated by the modulation frequency f (first step), obtaining the received signal by detecting the laser light passed through the measurement target gas GS by the photodetector  17  (second step), and detecting the received signal by the lock-in amplifier  19  is performed in the gas analysis device  10 . Then, a process of acquiring the amplitude R 1f  and the phase θ 1f  of the 1f component and the amplitude Ref and the phase θ 2f  of the 2f component of the measurement target gas detected by the lock-in amplifier  19  is performed in the signal processing device  20  (step S 23 ). 
     Next, a process of calculating the phase difference φ between the phase θ 1f  of the 1f component acquired at step S 23  and the phase θ 01f  of the 1f component stored in the storage  21  is performed in the processor  22  (step S 24 ). Next, a process of performing the computation indicated by formula (6) above to calculate the amplitude R′ 2f  of the noise-removed 2f component in consideration of the phase difference φ of the 1f component is performed in the processor  22  (step S 25 ; third step). For example, a process of calculating the amplitude R′ 2f  of the noise-removed 2f component by substituting the amplitude R 02f  and the phase θ 02f  stored in the storage  21  at step S 22 , the amplitude Ref and the phase θ 2f  of the 2f component acquired at step S 23 , and the phase difference φ calculated at step S 14  into formula (6) above is performed in the processor  22 . 
     Next, a process of calculating the concentration of the measurement target gas GS by calculating the ratio of the amplitude R′ 2f  of the noise-removed 2f component relative to the amplitude R 1f  of the 1f component obtained at step S 23  (R′ 2f /R 1f ) is performed in the processor  22  (step S 26 ; fourth step). Then, the information indicating the concentration of the measurement target gas GS measured by the processor  22  is output from the output unit  23 . Subsequently, the processes of steps S 23  to S 26  are repeatedly performed at certain time intervals prescribed in advance. 
     As above, the present embodiment and the first embodiment above only differ in the acquisition method of the amplitude R 02f  and the phase θ 02f  of the 2f noise component and the process of calculating the amplitude R′ 2f  of the noise-removed 2f component performed by the processor  22 . In the present embodiment as well, like the first embodiment, the 2f noise component arising on the optical path of the laser light is removed from the 2f component included in the received signal to obtain the noise-removed 2f component, and the concentration of the measurement target gas GS is found based on the magnitude of the noise-removed 2f component. This enables improvement of a detection limit of the concentration of the measurement target gas GS without giving rise to demerits such as increased costs, a complicated configuration, reduced freedom in design, and cumbersome adjustment. 
     Furthermore, the present embodiment calculates the phase difference y between the phase θ 1f  of the 1f component obtained when the optical path length of the laser light is not set to the reference length and the phase θ 01f  of the 1f component obtained when the optical path length of the laser light is set to the reference length and corrects the phase θ 2f  of the 2f component. This enables improvement of the detection limit of the concentration of the measurement target gas GS even when the modulation frequency is high and the measurement distance (optical path length of the laser light) changes variously. 
     The gas analysis systems and the gas analysis methods according to one or more embodiments are described above. However, the present invention is not limited to the above embodiments and can be freely modified within the scope of the present invention. For example, the above embodiments describe a situation of measuring the concentration of the measurement target gas GS based on the second-order harmonic component (2f component) of the modulation frequency f of the laser light. However, the concentration of the measurement target gas GS may be measured based on an nth-order harmonic component (n being an integer no less than 3) of the modulation frequency f of the laser light. 
     Furthermore, the above embodiments describe an example of detecting the 1f component and the 2f component included in the received signal output from the photodetector  17  by the lock-in amplifier  19 . However, the lock-in amplifier  19  may be omitted, and the signal processing device  20  may be equipped with the functions of the lock-in amplifier  19  so a signal processing unit detects the 1f component and the 2f component included in the received signal. Alternatively, the signal processing device  20  may be equipped with an FFT (fast Fourier transform) function instead of the functions of the lock-in amplifier  19  so a signal processing unit detects the 1f component and the 2f component included in the received signal. 
     Note that the functions of the signal processing device  20  provided in the gas analysis systems of the above embodiments may be realized as software by installing a program that realizes these functions on a computer. That is, the functions of the signal processing device  20  may be realized by cooperation between software and hardware resources. Note that the functions of the signal processing device  20  may be realized using hardware such as an FPGA (field-programmable gate array), LSI (large-scale integration), or an ASIC (application-specific integrated circuit). 
     Although the disclosure has been described with respect to only a limited number of embodiments, those skilled in the art, having benefit of this disclosure, will appreciate that various other embodiments may be devised without departing from the scope of the present invention. Accordingly, the scope of the invention should be limited only by the attached claims.
           1  Gas analysis system     13  Semiconductor laser     17  Photodetector     19  Lock-in amplifier     20  Signal processing device     21  Storage     22  Processor   f Modulation frequency   GS Measurement target gas