CN111579532A - Laser absorption spectrum tomography method based on frequency division multiplexing and main peak scanning - Google Patents

Laser absorption spectrum tomography method based on frequency division multiplexing and main peak scanning Download PDF

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CN111579532A
CN111579532A CN202010495274.8A CN202010495274A CN111579532A CN 111579532 A CN111579532 A CN 111579532A CN 202010495274 A CN202010495274 A CN 202010495274A CN 111579532 A CN111579532 A CN 111579532A
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temperature
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曹章
黄昂
徐立军
赵文帅
张宏宇
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Beihang University
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    • G01—MEASURING; TESTING
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    • G01N21/00—Investigating or analysing materials by the use of optical means, i.e. using sub-millimetre waves, infrared, visible or ultraviolet light
    • G01N21/17—Systems in which incident light is modified in accordance with the properties of the material investigated
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    • G01N21/31—Investigating relative effect of material at wavelengths characteristic of specific elements or molecules, e.g. atomic absorption spectrometry
    • G01N21/39—Investigating relative effect of material at wavelengths characteristic of specific elements or molecules, e.g. atomic absorption spectrometry using tunable lasers
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    • G01K11/006—Measuring temperature based upon physical or chemical changes not covered by groups G01K3/00, G01K5/00, G01K7/00 or G01K9/00 using measurement of the effect of a material on microwaves or longer electromagnetic waves, e.g. measuring temperature via microwaves emitted by the object

Abstract

The invention provides a laser absorption spectrum tomography method based on frequency division multiplexing and main peak scanning, belongs to the technical field of tunable diode laser absorption spectrum, and is used for rapid measurement of two-dimensional distribution of temperature and molecular concentration of gas to be measured. The method replaces the time division multiplexing technology with the frequency division multiplexing technology, and a plurality of absorption spectrums and each projection angle are simultaneously scanned and measured by different lasers through wavelength, so that the scanning time is shortened, and the measurement frame rate is improved; the full waveform scanning technology is replaced by the main peak scanning technology, so that the scanning length is shortened, the scanning time is further shortened, and the measurement frame rate is improved. Meanwhile, the method is suitable for hardware implementation and has wide prospect in the aspect of real-time monitoring of gas parameters.

Description

Laser absorption spectrum tomography method based on frequency division multiplexing and main peak scanning
Technical Field
The invention provides a laser absorption spectrum tomography method based on frequency division multiplexing and main peak scanning, and belongs to the technical field of tunable diode laser absorption spectrum. The method is used for rapid measurement of two-dimensional distribution of gas temperature and molecular concentration to be measured by using laser absorption spectroscopy.
Background
Tunable Diode Laser Absorption Spectroscopy (TDLAS) technology due to its non-invasive natureThe method has the advantages of quick response, high sensitivity, accurate measurement, low cost, strong anti-interference capability and the like, and is widely applied to measurement of the temperature and the molecular concentration of a combustion field. Laser absorption spectroscopy (lased spectroscopy) often uses a distributed feedback laser to generate a light source, and there are two measurement methods, Direct Absorption Spectroscopy (DAS) and Wavelength Modulation Spectroscopy (WMS). The direct absorption method scans the wavelength linearly, extracts the absorption spectrum directly from the transmitted light intensity, and is widely applied to single-path average temperature, concentration and two-dimensional distribution measurement. In 2017, Wenyang king et al published in IEEE Journal of Sensors (IEEE Sensors Journal) 17, vol.24, 8215, page 8223, a reconfigurable Parallel Data Acquisition System for Tunable Diode laser absorption Spectroscopy Tomography (autoregressive Tomography), designed a Tomography Parallel Acquisition System based on a direct absorption method, measured two-dimensional distributions of temperature and water molecule concentration in flame of an acoustically-excited Bunsen burner, and highly matched 120Hz frequency component extracted from temperature distribution reconstructed from the laser absorption Spectroscopy Tomography System with acoustic excitation frequency. In 2018, S V Kireev et al, published in Laser Physics Letters (Laser Physics Letters) No. 15, 95701-95704, the paper of improving the level of exhaled air in human body by using tunable Laser absorption spectroscopy13C16O2Kalman method of on-line measurement of precision (Kalman's method to advance accuracy of online)13C16O2measurement in the amplified human breakthrough using tunable diode absorption spectroscopy) applying Kalman filtering to processing laser absorption spectroscopy experimental signals can significantly improve13C16O2The measurement accuracy of (2). The direct absorption method has the advantages of intuition, simplicity and capability of extracting a complete absorption spectrum, but is weak in noise resistance and not suitable for industrial measurement in severe environments.
The wavelength modulation method utilizes harmonic waves in the modulated light intensity signal to effectively suppress noise and avoid baseline fitting required by a direct absorption method, and can adapt to a more severe field environment. In 2016, an article "detecting gaseous elemental mercury by using a frequency-doubling green diode laser" (Detection of gaseous elemental mercury using a frequency-doubled green diode laser) published by Xiutao Lou et al at 24 th volume 24 and 27509 pages 27520 of optics express (optics express) proposes a second harmonic Detection method for detecting gaseous elemental mercury by using a green diode laser, and the measurement accuracy of mercury concentration is improved by a wavelength modulation technique. In 2018, Chuanliang Li et al published in optical quick report (optics express) volume 26, No. 22, No. 29330 and No. 29339, High-speed multi-pass tunable diode laser absorption spectrometer (High-speed multi-pass tunable on-frequency-modulation spectroscopy) based on frequency modulation spectrum was designed and implemented for the frequency modulation-based laser absorption spectrometer, the lower limit of concentration measurement reached 18ppb, but the measurement speed was slow, and the response time required 166 seconds. In 2018, Cunguang Zhu et al published in IEEE journal of Sensors (IEEE Sensorsjournal) 18, No. 7513 and No. 7519, a study on Non-absorption transmission Loss Signal Recovery in Wavelength Modulation Spectroscopy (analysis on the Signal Recovery From the Non-absorption transmission Loss Spectroscopy) proposed a Signal Recovery method of automatic gain closed-loop control, which adds a closed-loop automatic gain control module in a traditional Wavelength system to eliminate the influence of Non-absorption transmission Loss of a Wavelength Modulation method. An article published by Chenguang Yang et al in 2019, volume 27, phase 9, 12137 and 12146, which uses the Wavelength modulation spectroscopy by the first harmonic phase angle method to extract absorption spectrum information from the first harmonic phase of Wavelength modulation, has stronger noise suppression capability than the conventional second harmonic. For measuring the concentration and temperature distribution, at least two absorption lines of the same target molecule are required. A typical wavelength modulation method uses a Time Division multiplexing technology, and in 2014, Alexander Klein et al, a single-path temperature and water molecule concentration measurement method based on Time Division multiplexing of a wavelength modulation method is designed in a Rapid, Time Division multiplexing, Direct Absorption and wavelength modulation spectrum (Rapid, Time-Division multiplexing, Direct Absorption-and wavelength modulation-Spectroscopy) paper which is published in a sensor (Sensors) 14, 11 th, 21497 th, 21513 th page, and a measurement frame rate is limited by Time Division scanning of a plurality of Absorption lines. In 2018, a paper published by Wei Chen et al in "Spectroscopy Letters" volume 51, pages 1, 61-66, entitled "demodulation method independent of Broadening of wavelength modulation spectra based on even harmonics" (spreading-independent demodulation method for wavelength modulation spectra based on even harmonics) proposes a method for calculating average temperature of a single path by using second harmonics and fourth harmonics of a wavelength modulation method, wherein the method is independent of linear Broadening, but utilizes the fourth harmonics with smaller signal occupation ratio, thereby reducing noise suppression capability. However, since the bandwidth of the distributed feedback laser used in the wavelength modulation method is limited, it is difficult for the laser to scan a spectrum at a speed of several kHz or more, and in order to further increase the system measurement speed, the measurement frame rate can be increased using the frequency division multiplexing technique instead of the time division multiplexing technique.
The wavelength modulation technology based on frequency division multiplexing uses a plurality of lasers to scan different absorption spectral lines, and each laser simultaneously emits the same low-frequency scanning light and high-frequency modulation light with different modulation frequencies, and the scanning light and the high-frequency modulation light are coupled into a beam and pass through target gas. The absorption spectrum is separated by demodulation, and the calculation of temperature and concentration is realized by table lookup, so that the calculation complexity is increased instead of an optical structure, and the method is suitable for laser absorption spectrum tomography. Frequency division multiplexing has been used in single path laser absorption spectroscopy. In 2013, Zhirong Zhang et al published in European Physics Letters at 104 th stage 44002 and 44009 page 44009, a multi-frequency wavelength modulation spectroscopy method for simultaneously detecting concentrations of multiple gases (a frequency division multiplexing method based on wavelength modulation) proposes a method for simultaneously detecting concentrations of two gases and considers the indoor temperature as a constant. In 2007, the paper "diode laser sensor for rapid and sensitive Measurement of gas temperature and water vapor concentration under high temperature and high pressure conditions" (a diode laser for rapid, sensitive Measurement of gas temperature and water vapor concentration) published by g.b. rieker et al in Measurement Science and Technology "suggests another single-path wavelength modulation system using frequency division multiplexing method for rapid shock wave Measurement. The designed system successfully captured the average temperature and water vapor concentration changes of the shock wave within 0.1 milliseconds. However, in the frequency division multiplexing method the entire absorption spectrum is scanned, which also limits the scanning rate. The main peak scanning strategy can be used for frequency division multiplexing to further increase the frame rate. In addition, laser absorption spectroscopy tomography has not used a frequency division multiplexing method.
Based on the background, the invention provides a laser absorption spectrum tomography method based on frequency division multiplexing and main peak scanning, which can quickly obtain the peak value of normalized second harmonic of a plurality of absorption spectral lines. The method replaces the time division multiplexing technology with the frequency division multiplexing technology, and a plurality of absorption spectrums and each projection angle are simultaneously scanned and measured by different lasers through wavelength, so that the scanning time is shortened, and the measurement frame rate is improved; the full waveform scanning technology is replaced by the main peak scanning technology, the scanning length is shortened, the scanning time is further shortened, and the measurement frame rate is improved. And (4) under the same conditions of the experiment, simulating a manufactured temperature and concentration lookup table, and looking up the table to obtain the temperature and molecular concentration values. When a plurality of path projections are measured in a measured field, the two-dimensional distribution measurement of the temperature and the concentration in the measured field is realized by combining with the hard field tomography Landeweber.
Disclosure of Invention
Aiming at the two-dimensional distribution measurement of temperature molecules and concentration of gas to be measured, the invention discloses a laser absorption spectrum tomography method based on frequency division multiplexing and main peak scanning. And the rapid reconstruction of the two-dimensional distribution of temperature and concentration is realized by combining a hard field tomography technology.
The method isA laser absorption spectrum tomography sensor with M projection angle, n single-angle projection, M total projection M × n and R inner diameter is manufactured, and Q lasers are used to simultaneously use modulation frequency f1，f2，…，fQExciting and scanning main peak parts of Q absorption spectral lines of detected gas molecules, detecting transmission light intensity of different projections by M detectors, demodulating and extracting normalized second harmonic peak values of the Q spectral line absorption spectra, dividing a detected field into N grids, reconstructing local normalized second harmonic by using a Landeweber tomography reconstruction method, and finally obtaining two-dimensional distribution of temperature and molecular concentration by searching a lookup table of the temperature, the concentration and the normalized second harmonic, wherein the method comprises the following specific steps:
step one, calculating a peak value A of normalized second harmonic by adopting an excitation and demodulation method based on frequency division multiplexing and main peak scanningq(1. ltoreq. Q. ltoreq.Q), wherein Q is the laser number and Q is the total number of lasers; all Q lasers scan the wavelength simultaneously, and for the Q laser, according to the Lambert beer law, when the frequency is vq[cm-1]Is passed through a collimated laser beam having a thickness of L cm]When the measured area is absorbed by the target gas, the transmission coefficient is expressed as:
Figure BDA0002522601770000041
wherein i (v)q) And I (v)q) Respectively incident and transmitted light intensity, P atm]Is the total pressure of the measured area, C (l) is the mole fraction of the measured gas, T (l) K]Is the temperature, S, of the gas to be measuredq[T(l)]Is the temperature dependent molecular transition line strength, phiq(νq) Is a linear function at frequency vqThe value of (a) and thus the output wavelength of the qth time-varying laser is expressed as:
Figure BDA0002522601770000042
wherein the content of the first and second substances,
Figure BDA0002522601770000043
is a slowly varying average wavelength, aqIs the modulation depth, fqIs the modulation frequency. The transmitted light intensity can be rewritten as a fourier cosine series:
Figure BDA0002522601770000044
wherein
Figure BDA0002522601770000045
Comprises the following steps:
Figure BDA0002522601770000046
wherein θ is 2 π fqt, k are non-negative integers, n is 2 when k is 0, and k is not negative>When n is 1at 0, the fourier component of the k-th harmonic is expressed as when weakly absorbed (less than 5%)
Figure BDA0002522601770000047
Wherein
Figure BDA0002522601770000048
The output light intensity varies with periodicity
Figure BDA0002522601770000049
Wherein
Figure BDA00025226017700000410
Is a slowly varying average light intensity, bqThe laser light intensity modulation coefficient is that the laser light output by Q lasers is coupled into a single mode fiber, passes through the target gas after being collimated by a collimating mirror and is absorbed, and the incident light intensity I (t) and the transmission light intensity I detected by a detectorm(t) are respectively:
Figure BDA0002522601770000051
wherein G isqIs the photoelectric amplification coefficient of the photoelectric detector to the laser wavelength,
extraction of I by quadrature demodulationm(t) at fqAnd 2fqAt a frequency component, i.e. the first harmonic Aq,1And the second harmonic Aq,2Obtaining:
Figure BDA0002522601770000052
wherein the symbol | | represents absolute value, in order to increase scanning speed by using a main peak scanning mode, the scanning range of the main peak needs to be determined, and the normalized second harmonic A of an absorption spectrum line is obtained by simulation by using a HITRAN2016 databaseq,2/Aq,1Calculating Aq,2/Aq,1And selecting a part of the derivative which monotonically decreases at the main peak as a scanning wavelength scanned by the main peak. The laser is used for selecting the scanning range to realize main peak scanning and normalizing the second harmonic Aq,2/Aq,1At peak of AqIs provided with
Figure BDA0002522601770000053
Thus, it is possible to provide
Figure BDA0002522601770000054
Completion of Aq(Q is more than or equal to 1 and less than or equal to Q).
Step two, obtaining a local normalized second harmonic matrix by utilizing tomography
Figure BDA0002522601770000055
According to formula (11), AqBecause of the path integral quantity, the two-dimensional distribution reconstruction of parameters such as temperature and concentration can be realized by combining a hard field tomography technology, the detected area is divided into N grids, and if the concentration and the temperature in each grid are uniform, the ith path passes through the local normalized second harmonic of the jth grid
Figure BDA0002522601770000056
Comprises the following steps:
Figure BDA0002522601770000057
then the normalized second harmonic A of the ith path in the measured areaq,iCan be expressed as
Figure BDA0002522601770000061
Wherein li,jIs the absorption length of the ith path through the jth mesh, equation (13) can be rewritten as a matrix:
Figure BDA0002522601770000062
wherein
Figure BDA0002522601770000063
Wherein]TRepresenting the transpose of a matrix, the projection matrix L being defined as
Figure BDA0002522601770000064
Locally normalizing the second harmonic for reconstruction
Figure BDA0002522601770000065
Using Landweber iterative algorithm to reconstruct:
Figure BDA0002522601770000066
wherein
Figure BDA0002522601770000067
Is the reconstruction distribution of local normalized second harmonic in the s-th iteration, and is not less than 1i≤M,1≤j≤N,λ(s)Is the relaxation factor for the s-th iteration:
Figure BDA0002522601770000068
wherein<>The inner product is represented by the sum of the two,
Figure BDA0002522601770000069
is defined as:
Figure BDA00025226017700000610
stopping iteration when a reconstruction error condition is met, wherein the reconstruction error condition is as follows:
Figure BDA00025226017700000611
where σ is the maximum allowable error of the setting, thus completing the locally normalized second harmonic matrix
Figure BDA00025226017700000612
And (4) calculating.
Step three, searching a temperature concentration lookup table to reconstruct temperature distribution T and concentration distribution X; for single path measurements, the temperature T will be referencedrefConcentration XrefEqually spaced into D parts:
Figure BDA0002522601770000071
wherein, TminAnd TmaxRespectively the lowest lower limit and the highest upper limit of the average temperature of the set measured area, XminAnd XmaxSetting T as the lowest limit and the highest limit of the average concentration of the measured area respectivelyrefAnd XrefCombining the values one by one, combining with a HITRAN2016 database, simulating and calculating transmission signals of all spectral lines of Q lasers, and substituting the transmission signals into the A calculated and simulated in the step oneqPreparing a two-dimensional table A of temperature and concentrationq(Tref,Cref) Because A isq(T(k),Cref) Is about CrefIs strictly monotonically increasing function, thus for TrefIn a certain T (k), a C can be foundq(k) Such that the difference | A of the measured normalized second harmonic and the value in the look-up tableq-Aq(T(k),Cq(k) ) is minimum, then vector C is calculatedq＝[Cq(1),Cq(2),…,Cq(D)]，C1，C2，…，CqCross point (k) of1,Cq(k1) I.e. finding the target position, the average temperature T ═ T (k) of the measured area1) The average concentration C ═ C of the measured areaq(k1) (ii) a The local normalized second harmonic value A measured by each laser in the jth grid1,j、A2,j…AQ,jLooking up the table to obtain the average temperature T in the jth grid as a single measurement resultjConcentration XjCalculating the average temperature and concentration values in all grids, and writing the values into a matrix form
Figure BDA0002522601770000072
T and X are the two-dimensional distribution of the temperature and the concentration which are respectively obtained and have the same resolution with the divided grids.
Drawings
Fig. 1 is a numerical simulation given distribution.
FIG. 2 is a flow chart of temperature and concentration extraction.
FIG. 3 is a block diagram of an exemplary frequency division multiplexed and main peak scanned laser absorption spectroscopy tomography system, consisting of: the device is composed of the following parts: the device comprises a laser group (101), an optical fiber beam combiner (102), a collimating mirror (103), a Powell prism (104), a field absorption gas to be measured (105), a photoelectric detector array (106), a data acquisition system (107), an upper computer (108) and a pressure gauge (109).
FIG. 4 is a normalized second harmonic peak vector A1And A2。
FIG. 5 is a locally normalized second harmonic matrix
Figure BDA0002522601770000073
And
Figure BDA0002522601770000074
fig. 6 is a reconstructed temperature distribution T and a water molecule concentration distribution X.
Detailed Description
The present invention is further illustrated by the following examples.
In this example, the absorption line 7185cm of water molecule is measured with water molecule as the measured object, Q2-1And 7444cm-1. Firstly, a circular region to be measured and a central circular high-temperature high-water-molecule concentration region are given. The projection angle number of the laser absorption spectrum tomography sensor is M-5, the single-angle projection number is n-12, the total projection number is M-60, and the inner diameter is R-100 mm. Numerical simulation given a distribution as shown in fig. 1, the gas pressure was 1atm, the high temperature and high water vapor molar concentration region was a circle with a diameter of 80mm, and the distribution was uniform. The temperature of the high temperature in the center is 900K, and the temperature of the low temperature in the periphery is 300K, namely room temperature. The water concentration in the center was 0.05 at a high concentration, and the water concentration in the periphery was 0.001 at a low concentration. The method comprises the following steps that laser at each angle penetrates through gas to be measured, then transmitted light intensity of a selected laser absorption spectral line after passing through the gas to be measured after wavelength modulation and main peak scanning is calculated by using a HITRAN database theory as measurement data, and finally frequency components are extracted through orthogonal demodulation, wherein a temperature and concentration extraction flow chart is shown in figure 2 and comprises the following steps:
step one, calculating a peak value A of normalized second harmonic by adopting an excitation and demodulation method based on frequency division multiplexing and main peak scanning1And A2. A typical structure diagram of a frequency division multiplexed and main peak scanned laser absorption spectroscopy tomography system is shown in fig. 3, and is composed of the following parts: the device comprises a laser group (101), an optical fiber beam combiner (102), a collimating mirror (103), a Powell prism (104), a field absorption gas to be measured (105), a photoelectric detector array (106), a data acquisition system (107), an upper computer (108) and a pressure gauge (109). Q is 2, and the lasers in the laser group are 7185cm in length-1And 7444cm-1The central absorption spectrum line is simultaneously scanned with main wavelength peak, and is respectively modulated as f1＝371.7kHz，f2100 kHz. The emergent laser is combined by the optical fiber beam combiner, passes through the gas to be detected after being collimated by the collimating mirror and is received by the photoelectric detector array with 12 detectors, and the total pressure of the gas is initially detected to be 1atm by using a pressure gauge. Calculate 7185cm for all 60 detectors-1And 7444cm-1Normalized second harmonic peak component vector A of spectral line1And A2As shown in fig. 4.
Step two, A is1And A2Bringing the Landeweber tomography method into to obtain a local normalized second harmonic matrix
Figure BDA0002522601770000081
And
Figure BDA0002522601770000082
as shown in fig. 5.
And step three, calculating the two-dimensional temperature distribution T and the two-dimensional concentration distribution X by table lookup. T ismin＝273K，Tmax＝1500K，Xmin＝0，XmaxWhen D is 50, T is equal to 0.1refAnd XrefThe values in the step (A) are combined one by one, and a normalized second harmonic peak value lookup table is manufactured by numerical simulation by using the same method of the step (A). For local normalized second harmonic matrix
Figure BDA0002522601770000083
And
Figure BDA0002522601770000084
look-up tables for each value in (a) to obtain a reconstructed temperature distribution T and a water molecule concentration distribution X, as shown in fig. 6.
The above description of the invention and its embodiments is not intended to be limiting, and the illustrations in the drawings are intended to represent only one embodiment of the invention. Without departing from the spirit of the invention, it is within the scope of the invention to design structures or embodiments similar to the technical solution without creation.

Claims (4)

1. A laser absorption spectrum tomography method based on frequency division multiplexing and main peak scanning utilizes Q lasers to excite and scan main peak parts of Q absorption spectral lines of a measured target gas molecule at different modulation frequencies respectively, the lasers are coupled into a single mode fiber through a fiber coupler and then are divided into M laser beams with equal intensity through a fiber beam splitter, each laser beam is widened into a fan-shaped laser beam through a prism and enters a measured field containing target molecules from different angles, the lasers penetrate through the measured field and then are detected by M detectors to transmit light intensity signals, a normalized second harmonic peak value of the Q spectral line absorption spectrum is demodulated and extracted from the transmitted light intensity, an iterative image reconstruction method is used to reconstruct local normalized second harmonic, and finally a lookup table of temperature, concentration and normalized second harmonic is established through numerical simulation, the table is searched for the value with the minimum deviation to obtain the two-dimensional distribution of the temperature and the molecular concentration.
2. The laser absorption spectrum tomography method based on frequency division multiplexing and main peak scanning as claimed in claim 1, characterized in that the peak value A of the normalized second harmonic is calculated by using the excitation and demodulation method based on frequency division multiplexing and main peak scanningq(1. ltoreq. Q. ltoreq.Q), wherein Q is the laser number and Q is the total number of lasers; all Q lasers scan the wavelength simultaneously, and for the Q laser, according to the Lambert beer law, when the frequency is vq[cm-1]Is passed through a collimated laser beam having a thickness of L cm]When the measured area is absorbed by the target gas, the transmission coefficient is expressed as:
Figure FDA0002522601760000011
wherein i (v)q) And I (v)q) Respectively incident and transmitted light intensity, P atm]Is the total pressure of the measured area, C (l) is the mole fraction of the measured gas, T (l) K]Is the temperature, S, of the gas to be measuredq[T(l)]Is the temperature dependent molecular transition line strength, phiq(νq) Is a linear function at frequency vqThe value of (c), and therefore,the output wavelength of the qth time-varying laser is represented as:
Figure FDA0002522601760000012
wherein, t is a time,
Figure FDA0002522601760000013
is a slowly varying average wavelength, aqIs the modulation depth, fqIs the modulation frequency. The transmitted light intensity can be rewritten as a fourier cosine series:
Figure FDA0002522601760000014
wherein
Figure FDA0002522601760000015
Comprises the following steps:
Figure FDA0002522601760000016
wherein θ is 2 π fqt, k are non-negative integers, n is 2 when k is 0, and k is not negative>When n is 1at 0, the fourier component of the k-th harmonic is expressed as when weakly absorbed (less than 5%)
Figure FDA0002522601760000017
Wherein
Figure FDA0002522601760000021
At this time, the output light intensity also changes periodically
Figure FDA0002522601760000022
Wherein
Figure FDA0002522601760000023
Is a slowly varying average light intensity, bqThe laser light intensity modulation coefficient is that the laser light output by Q lasers is coupled into a single mode fiber, passes through the target gas after being collimated by a collimating mirror and is absorbed, and the incident light intensity I (t) and the transmission light intensity I detected by a detectorm(t) are respectively:
Figure FDA0002522601760000024
wherein G isqIs the photoelectric amplification coefficient of the photoelectric detector to the laser wavelength,
extraction of I by quadrature demodulationm(t) at fqAnd 2fqAt a frequency component, i.e. the first harmonic Aq,1And the second harmonic Aq,2Obtaining:
Figure FDA0002522601760000025
wherein the symbol | | represents absolute value, in order to increase scanning speed by using a main peak scanning mode, the scanning range of the main peak needs to be determined, and the normalized second harmonic A of an absorption spectrum line is obtained by simulation by using a HITRAN2016 databaseq,2/Aq,1Calculating Aq,2/Aq,1Selecting the part of the derivative which monotonically decreases at the main peak as the scanning wavelength of the main peak scanning, selecting the scanning range by using a laser to realize the main peak scanning, and normalizing the second harmonic Aq,2/Aq,1At peak of AqIs provided with
Figure FDA0002522601760000026
Thus, it is possible to provide
Figure FDA0002522601760000027
Completion of Aq(Q is more than or equal to 1 and less than or equal to Q).
3. A laser absorption spectroscopy tomography method based on frequency division multiplexing and main peak scanning as claimed in claim 1, characterized in that the local normalized second harmonic matrix is obtained by tomography
Figure FDA0002522601760000031
A laser absorption spectrum tomography sensor with M projection angle, n single-angle projection, M total projection, M × n total projection diameter and R inner diameter is used, and Q lasers are respectively used to simultaneously modulate frequency f1，f2，…，fQExciting and scanning main peak part of Q absorption lines of detected gas molecules according to formula (11), AqBecause of the path integral quantity, the two-dimensional distribution reconstruction of parameters such as temperature and concentration can be realized by combining a hard field tomography technology, the detected area is divided into N grids, and if the concentration and the temperature in each grid are uniform, the ith path passes through the local normalized second harmonic of the jth grid
Figure FDA0002522601760000032
Comprises the following steps:
Figure FDA0002522601760000033
then the normalized second harmonic A of the ith path in the measured areaq,iCan be expressed as
Figure FDA0002522601760000034
Wherein li,jIs the absorption length of the ith path through the jth mesh, equation (13) can be rewritten as a matrix:
Figure FDA0002522601760000035
wherein
Figure FDA0002522601760000036
Wherein]TRepresenting the transpose of a matrix, the projection matrix L being defined as
Figure FDA0002522601760000037
Locally normalizing the second harmonic for reconstruction
Figure FDA0002522601760000038
Using Landweber iterative algorithm to reconstruct:
Figure FDA0002522601760000039
wherein
Figure FDA00025226017600000310
Is the reconstruction distribution of local normalized second harmonic in the s-th iteration, i is more than or equal to 1 and less than or equal to M, j is more than or equal to 1 and less than or equal to N, and lambda(s)Is the relaxation factor for the s-th iteration:
Figure FDA00025226017600000311
wherein<>The inner product is represented by the sum of the two,
Figure FDA00025226017600000312
is defined as:
Figure FDA00025226017600000313
stopping iteration when a reconstruction error condition is met, wherein the reconstruction error condition is as follows:
Figure FDA0002522601760000041
where σ is the maximum allowable error of the setting, thus completing the locally normalized second harmonic matrix
Figure FDA0002522601760000042
And (4) calculating.
4. The laser absorption spectrum tomography method based on frequency division multiplexing and main peak scanning as claimed in claim 1, characterized in that a temperature concentration lookup table is searched to reconstruct a temperature distribution T and a concentration distribution X; for single path measurements, the temperature T will be referencedrefConcentration XrefEqually spaced into D parts:
Figure FDA0002522601760000043
wherein, TminAnd TmaxRespectively the lowest lower limit and the highest upper limit of the average temperature of the set measured area, XminAnd XmaxSetting T as the lowest limit and the highest limit of the average concentration of the measured area respectivelyrefAnd XrefCombining the values one by one, combining with a HITRAN2016 database, simulating and calculating transmission signals of all spectral lines of Q lasers, and calculating simulated AqPreparing a two-dimensional table A of temperature and concentrationq(Tref,Cref) Because A isq(T(k),Cref) Is about CrefIs strictly monotonically increasing function, thus for TrefIn a certain T (k), a C can be foundq(k) Such that the difference | A of the measured normalized second harmonic and the value in the look-up tableq-Aq(T(k),Cq(k) ) is minimum, then vector C is calculatedq＝[Cq(1),Cq(2),…,Cq(D)]，C1，C2，…，CqCross point (k) of1,Cq(k1) I.e. finding the target position, the average temperature T ═ T (k) of the measured area1) The average concentration C ═ C of the measured areaq(k1) (ii) a The local normalized second harmonic value A measured by each laser in the jth grid1,j、A2,j…AQ,jLooking up the table to obtain the average temperature T in the jth grid as a single measurement resultjConcentration XjCalculating the average temperature and concentration values in all grids, and writing the values into a matrix form
Figure FDA0002522601760000044
T and X are the two-dimensional distribution of the temperature and the concentration which are respectively obtained and have the same resolution with the divided grids.
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