High-precision SF6 decomposition product concentration photoacoustic detection system and method

Abstract

The invention discloses a high-precision SF6 decomposition product concentration photoacoustic detection system and a high-precision SF6 decomposition product concentration photoacoustic detection method, belongs to the technical field of optical fiber sensing and measurement of power transmission and transformation equipment operation and maintenance, and solves the problem of how to improve the precision of the SF6 decomposition product concentration photoacoustic detection system. The volume of the gas chamber of the photoacoustic optical fiber sensor is reduced by half, the gas consumption is less, the gas balance time is shorter, and the processing technology is simpler; a third cylindrical mounting groove is formed in the middle non-reflecting surface of the second reflecting mirror and is used for mounting a sound wave sensitive cantilever beam diaphragm, so that the sound wave sensitive cantilever beam diaphragm is tightly attached to a photoacoustic resonance tube, the loss of sound wave signals is reduced, the Q value is increased, and the sensitivity of gas detection is improved; meanwhile, the concentration of the SF6 decomposition product gas is calculated through the ratio of a 2f signal to a 1f signal, and the 2f signal / 1f signal calibration-free function is achieved.

Description

Technical Field

[0001] The present invention belongs to the technical field of optical fiber sensing and measurement for the operation and maintenance of power transmission and transformation equipment, and relates to a high-precision photoacoustic detection system and method for the concentration of SF 6 decomposition products. Background Art

[0002] Sulfur hexafluoride (SF 6 ) gas is widely used in high-voltage power equipment such as circuit breakers, transformers, and gas-insulated switchgear (GIS) due to its excellent electrical insulation and arc extinguishing properties. However, due to long-term use, aging or overheating inside the equipment can cause partial discharge or local overheating, and under the action of these factors, SF 6 will decompose to produce a variety of gases. H 2 S is one of the important decomposition products of SF 6 , and it is a characteristic component when high-energy partial discharge or overheating fault occurs to a certain extent, which can reflect the severity of the fault. However, as an important characteristic decomposition component of the mixed insulating gas, the concentration of H 2 S is extremely low and has strong adsorption at the initial stage of equipment failure. Therefore, realizing the highly sensitive detection of the characteristic decomposition component gas H 2 S is of great significance for the fault diagnosis and evaluation of SF 6 gas-insulated equipment.

[0003] Photoacoustic spectroscopy gas detection technology is an indirect absorption spectroscopy technology. By converting the light energy absorbed by the target gas into an acoustic wave signal, and then using an acoustic wave sensor to detect the photoacoustic signal, and further measuring the concentration of the target gas. It is an absorption spectroscopy technology with almost no background, and has the advantages of no need for carrier gas, maintenance-free, fast response, and high sensitivity. The literature by Ma Fengxiang, Zhao Yue, Wang Nan, etc., "High-sensitivity detection technology of SF 6 decomposition product H 2 S based on a multi-pass photoacoustic cell" [J]. Acta Photonica Sinica, 2023, 52(3): 0352121. reported a detection system for SF 6 decomposition product H 2 S based on a resonant traditional multi-pass photoacoustic cell. By using acoustic resonance amplification technology and wavelength modulation - second harmonic (WMS-2f) detection technology, combined with a high-power fiber amplifier, it realizes the detection of trace H 6 under the background of SF 2High-sensitivity detection of S gas. However, the traditional resonant photoacoustic cell used in the above literature has disadvantages such as a large gas chamber volume, a long response time, and a large gas consumption. In the practical application of a photoacoustic spectroscopy trace gas detection instrument, there are many situations such as the aging of the laser or optical fiber, the contamination of the optical fiber end face, and the bending loss that will cause the power of the light source to change. At the same time, during the wavelength modulation process, the 2f signal absorbed by the gas is proportional to the power of the light source, which will lead to a large error in concentration measurement. Summary of the Invention

[0004] The technical solution of the present invention is used to solve the problem of how to improve the accuracy of the photoacoustic detection system for the concentration of SF 6 decomposition products.

[0005] The present invention solves the above technical problems through the following technical solutions:

[0006] The present invention provides a high-precision photoacoustic detection system for the concentration of SF 6 decomposition products, including: an excitation light source, an optical fiber collimator, a detection light source, an optical fiber circulator, a photoacoustic optical fiber sensor, a high-speed spectrometer, a signal processing circuit, and a computer; the output end of the excitation light source is connected to the input end of the optical fiber collimator, the optical fiber collimator is installed at the excitation light input end of the photoacoustic optical fiber sensor, the output end of the detection light source is connected to the first port of the optical fiber circulator, the second port of the optical fiber circulator is connected to the detection light input end of the photoacoustic optical fiber sensor by a single-mode optical fiber, the third port of the optical fiber circulator is connected to the input end of the high-speed spectrometer, the output end of the high-speed spectrometer is connected to the input end of the signal processing circuit, and the output end of the signal processing circuit is connected to the computer;

[0007] The photoacoustic fiber optic sensor comprises: an air intake buffer chamber structure and a T-type resonant photoacoustic pool structure; a buffer cavity is processed inside the air intake buffer chamber structure, a first cylindrical mounting groove is processed at one end of the buffer cavity, the first cylindrical mounting groove is used to install a first reflector, an excitation light incident hole is provided on the first reflector, the excitation light emitted by the excitation light source passes through the incident optical fiber of the optical fiber collimator and then passes through the excitation light incident hole to enter the buffer cavity, and the other end of the buffer cavity is open; an air intake hole and an air outlet hole are provided on one side of the outside of the air intake buffer chamber structure, and the air intake hole and the air outlet hole are both connected to the buffer cavity; a cylindrical connecting cavity is processed inside one end of the T-type resonant photoacoustic pool structure, one end of the connecting cavity is open, the open end of the connecting cavity is sealed and connected to the open end of the buffer cavity, and the other end of the connecting cavity is sealed and connected to the open end of the buffer cavity. A photoacoustic resonance tube is horizontally opened at the middle position of the bottom of the end, and the photoacoustic resonance tube extends horizontally to the other end of the T-type resonant photoacoustic pool structure. A second cylindrical mounting groove is opened at the other end of the T-type resonant photoacoustic pool structure, and the second cylindrical mounting groove is used for a second reflector. The reflective surface of the first reflector and the reflective surface of the second reflector are arranged opposite to each other. A detection light incident hole is opened in the middle of the second reflector, and a third cylindrical mounting groove is opened on the middle non-reflective surface of the second reflector. The third cylindrical mounting groove is used to install a sound wave sensitive cantilever beam diaphragm. There is a distance between the terminal end face of the single-mode optical fiber connected to the second port of the optical fiber circulator and the sound wave sensitive cantilever beam diaphragm, and a Fabry-Perot cavity is formed between the terminal end face of the single-mode optical fiber and the sound wave sensitive cantilever beam diaphragm.

[0008] Furthermore, the excitation light source adopts a narrow linewidth tunable laser with a central wavelength of 1574.56nm and a linewidth less than 10pm.

[0009] Furthermore, the wavelength range of the high-speed spectrometer is 1525nm-1570nm, and the frame rate is not less than 10kHz.

[0010] Furthermore, the sound wave sensitive cantilever beam diaphragm adopts a gate-shaped silicon-based cantilever beam structure.

[0011] The present invention also provides a method based on the high-precision SF 6 The detection method of the decomposition product concentration photoacoustic detection system comprises the following steps:

[0012] (1) The excitation light emitted by the excitation light source passes through the incident optical fiber of the fiber collimator and then through the excitation light incident hole into the buffer cavity. 6 The decomposition product gas absorbs the excitation light to produce a photoacoustic effect, causing the gas to expand periodically and then generate an acoustic signal, which causes the acoustic wave sensitive cantilever beam diaphragm to produce forced vibration;

[0013] (2) The detection light emitted by the detection light source passes through the fiber circulator and then passes through the single-mode optical fiber. The detection light reflected by the acoustic sensitive cantilever beam diaphragm and the detection light reflected back by the end face of the single-mode optical fiber generate interference. The interference light returns through the fiber circulator and enters the high-speed spectrometer for collection. The collected interference spectrum signal is calculated and processed by the signal processing circuit, and the processing result is transmitted to the computer in real time for display. The method of calculating and processing the interference spectrum signal by the signal processing circuit is as follows: According to the wavelength modulation spectroscopy method, when the wavelength of the excitation light source is tuned to the SF to be measured 6 The 1f signal and 2f signal are obtained at the central wavelength of the decomposition product gas absorption line, SF 6 The concentration of the decomposition product gas is calculated by the ratio of the 2f signal to the 1f signal, realizing the 2f signal / 1f signal calibration-free function.

[0014] Furthermore, the 1f signal and the 2f signal are expressed as follows:

[0015] S 1f =Pεmp w g (1)

[0016] S 2f =P(η-ε)H 2 α(v)CLcos(2Ω) (2)

[0017] In the formula, S 1f represents 1f signal, S 2f represents the 2f signal, P represents the effective power of the excitation light, η is the photoacoustic cell constant, v is the central wave number of the incident light, α(v) is the gas absorption coefficient, L is the effective absorption path length, C represents the gas concentration, ε is the photoacoustic conversion coefficient of the solid absorber, m is the modulation depth coefficient, g represents the half-height full width of the absorption line, P w is the excitation optical power coefficient of the fast modulated sinusoidal current at the modulation frequency ω, Ω represents the phase shift, H 2 is the second harmonic generation coefficient.

[0018] The advantages of the present invention are:

[0019] The SF of the present invention 6 The decomposition product concentration photoacoustic detection system adopts a T-type resonant photoacoustic cell structure. Compared with the traditional H-type resonant photoacoustic cell, the gas chamber volume of the photoacoustic optical fiber sensor of the T-type resonant photoacoustic cell structure is reduced by half, the gas consumption is less, the gas balance time is shorter, and the processing technology is simpler; the present invention provides a third cylindrical mounting groove on the middle non-reflective surface of the second reflector, and the third cylindrical mounting groove is used to install the sound wave sensitive cantilever beam diaphragm, so that the sound wave sensitive cantilever beam diaphragm is closely fitted with the photoacoustic resonance tube, the sound wave signal loss is reduced, the Q value is improved, and the sensitivity of gas detection is improved; at the same time, the SF 6The concentration of the decomposition product gas is calculated by the ratio of the 2f signal to the 1f signal, realizing the function of calibration-free for the 2f signal / 1f signal, and solving the problem that the incident optical power will change greatly in the case of laser aging, large insertion loss or bending loss, etc., and then the gas detection system will generate a large error; All in all, the present invention has the advantages of less gas consumption, short response time, high detection sensitivity, etc., and provides a highly competitive technical solution for the high-precision detection of SF 6 decomposition products. Description of the Drawings

[0020] Figure 1 Figure 1 is the structural block diagram of the high-precision photoacoustic detection system for SF 6 decomposition product concentration in the first embodiment of the present invention;

[0021] Figure 2 Figure 2 is the front perspective view of the photoacoustic fiber sensor structure of the high-precision photoacoustic detection system for SF 6 decomposition product concentration in the first embodiment of the present invention;

[0022] Figure 3 Figure 3 is the flat-sectioned oblique perspective view of the photoacoustic fiber sensor structure of the high-precision photoacoustic detection system for SF 6 decomposition product concentration in the first embodiment of the present invention;

[0023] Figure 4 Figure 4 is the flat-sectioned top perspective view of the photoacoustic fiber sensor structure of the high-precision photoacoustic detection system for SF 6 decomposition product concentration in the first embodiment of the present invention;

[0024] Figure 5 Figure 5 is the enlarged partial oblique perspective view of the flat-sectioned detection end of the photoacoustic fiber sensor structure of the high-precision photoacoustic detection system for SF 6 decomposition product concentration in the first embodiment of the present invention;

[0025] Figure 6 Figure 6 is the response fitting curve diagram of the 2f signal / 1f signal to the SF 6 decomposition product gas;

[0026] Figure 7 Figure 7 is the change trend diagram between the 2f signal / 1f signal and the excitation light source power. Detailed Embodiments

[0027] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the embodiments of the present invention. Obviously, the described embodiments are part of the embodiments of the present invention, rather than all of them. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without creative efforts shall fall within the protection scope of the present invention.

[0028] The technical solutions of the present invention will be further described below in conjunction with the accompanying drawings of the specification and specific embodiments:

[0029] Embodiment 1

[0030] As Figure 1 shown, a high-precision SF 6 photoacoustic detection system for decomposition product concentration includes: an excitation light source 1, an optical fiber collimator 2, a detection light source 3, an optical fiber circulator 4, a photoacoustic fiber sensor 5, a high-speed spectrometer 6, a signal processing circuit 7, and a computer 8; the output end of the excitation light source 1 is connected to the input end of the optical fiber collimator 2, and the optical fiber collimator 2 is installed at the excitation light input end of the photoacoustic fiber sensor 5. The output end of the detection light source 3 is connected to the first port of the optical fiber circulator 4. The second port of the optical fiber circulator 4 is connected to the detection light input end of the photoacoustic fiber sensor 5 by a single-mode optical fiber. The third port of the optical fiber circulator 4 is connected to the input end of the high-speed spectrometer 6. The output end of the high-speed spectrometer 6 is connected to the input end of the signal processing circuit 7. The output end of the signal processing circuit 7 is connected to the computer 8.

[0031] Preferably, the excitation light source 1 uses a narrow linewidth tunable laser with a central wavelength of 1574.56 nm and a linewidth less than 10 pm.

[0032] Preferably, the wavelength range of the high-speed spectrometer 6 is 1525 nm - 1570 nm, and the frame rate is not less than 10 kHz.

[0033] As Figures 2 to 5As shown in the figure, the photoacoustic fiber optic sensor 5 includes: an intake buffer chamber structure 51 and a T-shaped resonant photoacoustic cell structure 52; the intake buffer chamber structure 51 is a cuboid structure, and a cylindrical buffer cavity 511 is machined inside the cuboid structure. A first cylindrical mounting groove is machined at one end of the buffer cavity 511 for mounting a first mirror 512. An excitation light incident hole is provided on the first mirror 512. The excitation light emitted by the excitation light source 1 passes through the incident optical fiber of the fiber collimator 2 and then enters the buffer cavity 511 through the excitation light incident hole. The other end of the buffer cavity 511 is open; an intake hole 513 and an exhaust hole 514 are provided on one side of the outer part of the intake buffer chamber structure 51, and both the intake hole 513 and the exhaust hole 514 are communicated with the buffer cavity 511; the T-shaped resonant photoacoustic cell structure 52 is a cuboid structure, and a cylindrical connection cavity 521 is machined inside one end of the cuboid structure. One end of the connection cavity 521 is open, and the open end of the connection cavity 521 is hermetically communicated with the open end of the buffer cavity 511. A photoacoustic resonance tube 522 is horizontally opened at the middle position of the bottom of the other end of the connection cavity 521. The photoacoustic resonance tube 522 horizontally extends to the other end of the cuboid structure of the T-shaped resonant photoacoustic cell structure 52. A second cylindrical mounting groove is provided at the other end of the cuboid structure of the T-shaped resonant photoacoustic cell structure 52 for the second mirror 523. The reflecting surface of the first mirror 512 is arranged opposite to the reflecting surface of the second mirror 523. A detection light incident hole is provided in the middle of the second mirror 523, and a third cylindrical mounting groove is provided on the non-reflecting surface in the middle of the second mirror 523 for mounting a sound wave sensitive cantilever diaphragm 524. There is a distance between the end face of the end of the single-mode optical fiber connected to the second port of the fiber optic circulator 4 and the sound wave sensitive cantilever diaphragm 524. A Fabry-Perot cavity F-P cavity is formed between the end face of the end of the single-mode optical fiber and the sound wave sensitive cantilever diaphragm 524.

[0034] Preferably, the sound wave sensitive cantilever diaphragm 524 adopts a gate-shaped silicon-based cantilever structure.

[0035] The high-precision SF in the embodiment of the present invention 6 The working process of the photoacoustic detection system for the decomposition product concentration is as follows:

[0036] (1) The excitation light emitted by the excitation light source 1 passes through the incident optical fiber of the fiber collimator 2 and then enters the buffer cavity 511 through the excitation light incident hole. The SF to be measured 6 The decomposition product gas absorbs the excitation light to generate a photoacoustic effect, causing periodic thermal expansion of the gas, and then generating an acoustic signal, thereby causing the sound wave sensitive cantilever diaphragm 524 to generate a forced vibration.

[0037] (2) The detection light emitted by the detection light source 3 passes through the fiber optic circulator 4 and then through a single-mode fiber. The detection light reflected by the acoustic wave-sensitive cantilever diaphragm 524 and the detection light reflected back from the end face of the single-mode fiber interfere. The interference light returns through the fiber optic circulator 4 and enters the high-speed spectrometer 6 for acquisition. The acquired interference spectral signal is calculated and processed by the signal processing circuit 7, and the processing result is transmitted to the computer 8 in real time for display.

[0038] The method for calculating and processing the interference spectral signal by the signal processing circuit is as follows:

[0039] According to the wavelength modulation spectroscopy method, when the wavelength of the excitation light source is tuned to the center wavelength of the absorption line of the decomposition product gas to be measured, the 1f signal (fundamental wave signal) and the 2f signal (second harmonic signal) are obtained. The concentration of the decomposition product gas is calculated by the ratio of the 2f signal to the 1f signal, realizing the function of calibration-free for the 2f signal / 1f signal; the 1f signal and the 2f signal are respectively expressed as follows: 6 decomposition product gas absorption line to obtain the 1f signal (fundamental wave signal) and the 2f signal (second harmonic signal). The concentration of the SF 6 decomposition product gas is calculated by the ratio of the 2f signal to the 1f signal, realizing the function of calibration-free for the 2f signal / 1f signal; the 1f signal and the 2f signal are respectively expressed as follows:

[0040] S 1f = Pεmp w g(1)

[0041] S 2f = P(η - ε)H 2 α(v)CLcos(2Ω) (2)

[0042] In the formula, S 1f represents the 1f signal, S 2f represents the 2f signal, P represents the effective power of the excitation light, η is the photoacoustic cell constant, v is the central wave number of the incident light, α(v) is the gas absorption coefficient, L is the effective absorption path length, C represents the gas concentration, ε is the photoacoustic conversion coefficient of the solid absorber, m is the modulation depth coefficient, g represents the full width at half maximum of the absorption line, P w is the excitation light power coefficient of the fast modulation sine current at the modulation frequency ω, Ω represents the phase shift, H 2 is the second harmonic generation coefficient.

[0043] As Figure 6 shown, it is the response of the 2f signal / 1f signal ratio to the gas to be measured. Linear fitting is performed on it, and it is found that the linearity of the 2f signal / 1f signal is good at different gas concentrations.

[0044] As Figure 7As shown, as time changes, the power of the excitation light source is reduced by the same amount at equal time intervals. Both the 2f signal and the 1f signal gradually decline due to the influence of the excitation light source power. Compared with the changes in their individual signals, the 2f signal / 1f signal shows a stable trend from 0s to 180s and hardly changes with the change of the excitation light source power.

[0045] The above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit it; although the present invention has been described in detail with reference to the foregoing embodiments, those of ordinary skill in the art should understand that they can still modify the technical solutions described in the foregoing embodiments, or perform equivalent replacements for some of the technical features; and these modifications or replacements do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A high-precision photoacoustic detection system for SF6 decomposition product concentration, characterized in that: include: An excitation light source, an optical fiber collimator, a detection light source, an optical fiber circulator, a photoacoustic optical fiber sensor, a high-speed spectrometer, a signal processing circuit, and a computer; the output end of the excitation light source is connected to the input end of the optical fiber collimator, the optical fiber collimator is installed at the excitation light input end of the photoacoustic optical fiber sensor, the output end of the detection light source is connected to the first port of the optical fiber circulator, the second port of the optical fiber circulator is connected to the detection light input end of the photoacoustic optical fiber sensor using a single-mode optical fiber, the third port of the optical fiber circulator is connected to the input end of the high-speed spectrometer, the output end of the high-speed spectrometer is connected to the input end of the signal processing circuit, and the output end of the signal processing circuit is connected to the computer; The photoacoustic fiber optic sensor comprises: an air intake buffer chamber structure and a T-type resonant photoacoustic pool structure; a buffer cavity is processed inside the air intake buffer chamber structure, a first cylindrical mounting groove is processed at one end of the buffer cavity, the first cylindrical mounting groove is used to install a first reflector, an excitation light incident hole is provided on the first reflector, the excitation light emitted by the excitation light source passes through the incident optical fiber of the optical fiber collimator and then passes through the excitation light incident hole to enter the buffer cavity, and the other end of the buffer cavity is open; an air intake hole and an air outlet hole are provided on one side of the outside of the air intake buffer chamber structure, and the air intake hole and the air outlet hole are both connected to the buffer cavity; a cylindrical connecting cavity is processed inside one end of the T-type resonant photoacoustic pool structure, one end of the connecting cavity is open, the open end of the connecting cavity is sealed and connected to the open end of the buffer cavity, and the other end of the connecting cavity is sealed and connected to the open end of the buffer cavity. A photoacoustic resonance tube is horizontally opened at the middle position of the bottom of the end, and the photoacoustic resonance tube extends horizontally to the other end of the T-type resonant photoacoustic pool structure. A second cylindrical mounting groove is opened at the other end of the T-type resonant photoacoustic pool structure, and the second cylindrical mounting groove is used for a second reflector. The reflective surface of the first reflector and the reflective surface of the second reflector are arranged opposite to each other. A detection light incident hole is opened in the middle of the second reflector, and a third cylindrical mounting groove is opened on the middle non-reflective surface of the second reflector. The third cylindrical mounting groove is used to install a sound wave sensitive cantilever beam diaphragm. There is a distance between the terminal end face of the single-mode optical fiber connected to the second port of the optical fiber circulator and the sound wave sensitive cantilever beam diaphragm, and a Fabry-Perot cavity is formed between the terminal end face of the single-mode optical fiber and the sound wave sensitive cantilever beam diaphragm.

2. The high-precision SF6 decomposition product concentration photoacoustic detection system according to claim 1 is characterized in that: The excitation light source adopts a narrow linewidth tunable laser with a central wavelength of 1574.56nm and a linewidth of less than 10pm.

3. The high-precision photoacoustic detection system for SF6 decomposition product concentration according to claim 1 is characterized in that: The wavelength range of the high-speed spectrometer is 1525nm-1570nm, and the frame rate is not less than 10kHz.

4. The high-precision SF6 decomposition product concentration photoacoustic detection system according to claim 1 is characterized in that: The sound wave sensitive cantilever beam diaphragm adopts a gate-shaped silicon-based cantilever beam structure.

5. A detection method based on the high-precision SF6 decomposition product concentration photoacoustic detection system according to any one of claims 1 to 4, characterized in that: The following steps are involved: (1) The excitation light emitted by the excitation light source passes through the incident optical fiber of the optical fiber collimator and then through the excitation light incident hole into the buffer cavity. The decomposition product gas of the SF6 to be measured absorbs the excitation light to produce a photoacoustic effect, causing periodic thermal expansion of the gas, and then generates an acoustic signal, thereby causing the acoustic wave sensitive cantilever beam diaphragm to produce forced vibration; (2) The detection light emitted by the detection light source passes through the fiber circulator and then through the single-mode optical fiber. The detection light reflected by the acoustic sensitive cantilever beam diaphragm and the detection light reflected back by the end face of the single-mode optical fiber generate interference. The interference light returns through the fiber circulator and enters the high-speed spectrometer for collection. The collected interference spectrum signal is calculated and processed by the signal processing circuit, and the processing result is transmitted to the computer in real time for display. The method for calculating and processing the interference spectrum signal by the signal processing circuit is as follows: According to the wavelength modulation spectroscopy method, when the wavelength of the excitation light source is tuned to the central wavelength of the SF6 decomposition product gas absorption line to be measured, the 1f signal and the 2f signal are obtained. The concentration of the SF6 decomposition product gas is calculated by the ratio of the 2f signal to the 1f signal, thereby realizing the 2f signal / 1f signal calibration-free function.

6. The detection method according to claim 5, characterized in that: The 1f signal and the 2f signal are expressed as follows: S 1f =Pεmp w g (1) S 2f =P(η-ε)H2α(v)CLcos(2Ω) (2) In the formula, S 1f represents 1f signal, S 2f represents the 2f signal, P represents the effective power of the excitation light, η is the photoacoustic cell constant, v is the central wave number of the incident light, α(v) is the gas absorption coefficient, L is the effective absorption path length, C represents the gas concentration, ε is the photoacoustic conversion coefficient of the solid absorber, m is the modulation depth coefficient, g represents the half-height full width of the absorption line, P w is the excitation optical power coefficient of the fast modulated sinusoidal current at the modulation frequency ω, Ω represents the phase shift, and H2 is the second harmonic generation coefficient.

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