CN113702294A - Low-speed sampling-based ring-down cavity high-speed ring-down signal coefficient extraction method - Google Patents
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Abstract
The invention discloses a low-speed sampling-based ring-down cavity high-speed ring-down signal coefficient extraction method, which comprises the following steps: the device comprises a laser, an optical ring-down cavity, a photoelectric detector, a low-pass filter, a low-speed digital-to-analog converter and a computer. The ring-down signal emitted by the optical ring-down cavity is incident to a photoelectric detector and then converted into an electric signal, the electric signal is subjected to low-pass filtering through a low-pass filter and then is acquired through a low-speed digital-to-analog converter, finally, the acquired digital signal is processed on a computer, and the attenuation coefficient of the ring-down signal emitted by the ring-down cavity is acquired by a system parameter identification method. The invention filters the high-frequency noise interference in the ring-down signal by using the low-pass filter, obtains the attenuation coefficient by using the system identification method through fitting, can greatly reduce the requirement on the sampling rate of the sampling system, and improves the integration level and the real-time performance of the ring-down cavity data acquisition system.
Description
Technical Field
The invention relates to a low-speed sampling-based method for extracting a high-speed ring-down signal coefficient of a ring-down cavity, which is used for a ring-down cavity trace gas detection system and belongs to the technical field of trace gases.
Background
Close to each otherOver the years, the continuous improvement of industrial production efficiency brings great economic benefits to human society, but also brings inevitable pollution to the atmospheric environment, and the atmospheric composition is rapidly changing in an unprecedented way. The most obvious of these changes are not the nitrogen and oxygen levels in the atmospheric constituents, which are always high, but the so-called trace gas species and concentrations. For example, sulfur dioxide SO2The increase of (B) can lead to acid rain and nitrogen oxide NOxExcessive amounts form photochemical smog, and methane CH4Nitrogen monoxide N2O, etc. will aggravate the greenhouse effect. In the biomedical field, gases generated by physiological processes, such as acetone, propanol, etc., which have volatility, although in extremely low amounts, can be used for the diagnosis of specific diseases. Therefore, the detection of the concentration of the trace gas can effectively evaluate the industrial process and can ensure the safety of health and property through real-time monitoring.
The gas concentration detection techniques are classified into conventional gas concentration detection techniques mainly based on electrochemical and electrical gas concentration analysis methods and spectroscopic gas concentration detection techniques using laser techniques. The traditional electrochemical measurement technology generally adopts a contact measurement method, which is not only easily influenced by environmental change and air disturbance in the measurement process, but also inevitably causes product aging due to the consumption of reactants, so that the service life of the product is greatly limited, and the requirements on the stability of measurement parameters such as humidity, temperature and pressure are high. The measurement result of the electrical measurement method is easy to drift, and online real-time monitoring cannot be realized. The laser absorption spectroscopy is a non-contact measurement method, can ensure that detection equipment has longer service life and stable working performance, and is divided into a direct absorption spectroscopy, a modulation spectroscopy and a ring-down cavity spectroscopy. The direct absorption spectrum technology has simple light path and convenient operation, but the measurement process is easily influenced by the intensity fluctuation of the background light. The modulation spectrum technology can effectively inhibit the influence of noise in the measurement process so as to improve the signal-to-noise ratio, but is not suitable for the measurement of low-concentration gas and weak peak-absorption. The ring-down cavity spectroscopy technology increases the equivalent absorption optical path of light by adding a high-reflection mirror at the two ends of the gas pool, so that the physical length of the measuring system is reduced, and the whole measuring device is more compact and achieves high sensitivity.
Cavity-down spectroscopy (CRDS) can be classified into Pulsed-CRDS, continuous-CRDS, and Cavity-enhanced absorption spectroscopy (CEAS). In the Scientific Instrument Review 59, Vol.12, pp.2544 and 2551 (Review of Scientific Instruments), decay Cavity spectrometer based on the measurement of the absorptivity of a pulse laser (Cavity-down optical spectrometer for absorption measurement using pulse laser), O' Keefe and Anthony were published in 1988, and oxygen O was measured using a pulse light source2The transition spectral line proves that the sensitivity of the Pulsed-CRDS method can reach 10-6cm-1However, the line width of the pulse laser is wide and generally larger than the frequency interval between the longitudinal mode and the transverse mode of the cavity, so that the outgoing signal contains different gas spectrum absorption rates corresponding to a plurality of light frequencies, so that the light intensity ring-down signal presents a multi-exponential curve and a beat frequency phenomenon, and the frequency resolution of the measurement system is limited.
Compared with a pulse laser, the continuous light laser has a narrower line width (generally several MHz), is convenient for selecting different frequency points in the same absorption spectrum line range for experiment, and has higher optical spectrum resolution and light intensity coupling efficiency. The Cavity Enhanced Absorption Spectroscopy (CEAS) technique measures the transmitted optical cavity signal integrated over time rather than measuring the ring-down time of the attenuated signal, thus using continuous light as the light source and eliminating the need for external equipment to turn off the incident light. Engeln et al, 1998, published in Scientific Instruments Review 69, Vol.11, 3763, page 3769 (Review of Scientific Instruments), in Cavity enhanced absorption and Cavity enhanced magnetic rotation spectroscopy, which ensures that the coupling efficiency of the resonator and the laser is as constant as possible throughout the scan, either by means of fast scanning the laser frequency or by means of fast scanning the laser at slow scanning speed and fast scanning the Cavity length. In 2001, Paul et al, published in Applied Optics 40 vol.27, 4904 (Applied Optics) paper, "Ultrasensitive absorption spectroscopy of optical resonators based on off-axis high finesse (ultrasensibility absorption spectroscopy with a high-definition optical cavity and off-axis alignment), light incident off-axis will reduce the equivalent free spectral range of the resonator, and the variation of the coupling coefficient of incident light to the resonator in the frequency axis can be controlled to a small range by designing the parameters of the cavity and the mirrors. In 2014, Sun et al published in the fast laser diagnosis of shock tube dynamics study using cavity enhanced absorption spectroscopy (Sensitive and rapid laser absorption spectroscopy) paper of "Optics rapid report" volume 22, No. 8, 9291 (Optics Express), a reflective lens with a reflectivity of 98.8% was used, the lower limit of acetylene measurement at room temperature was 20ppm, and the requirement of CEAS system for the lower limit of detector measurement was proposed to be reduced. Because the CEAS measures the shape of light transmitted from the cavity along with the frequency scanning of an absorption peak, the CEAS has the advantages that an external light modulator is not needed to cut off incident light, but in order to enable the response of the ring-down cavity to the incident light on the frequency interval of a measurement spectral line to be basically consistent, the special design is needed to be carried out on the parameters of the cavity and the off-axis angle of the incident light.
Continuous laser ring-down cavity absorption spectroscopy (CW-CRDS) technology adopts continuous laser as a light source, and can obtain a measurement result with higher spectral resolution due to the narrow line width of the laser, and can obtain measurement with higher signal-to-noise ratio under the condition of single longitudinal mode excitation due to the relative concentration of laser energy on a frequency domain. In 1997, Romanini was published in "continuous light ring-down cavity spectroscopy" at volume 264, phase 316-322 (Chemical Physics Letters), page 3-4, the continuous light was used as a light source, PZT was used to drive and modulate the physical length of the ring-down cavity, so that the frequency of the laser and the mode of the ring-down cavity coincide at a certain time in each scanning period, when the transmitted light intensity exceeded a predetermined threshold, the incident light was cut off by an acousto-optic modulator (AOM), the detector received the attenuation signal, and the transition line of HCCH at 570nm was measured. In 2000 He and or published in "ring-down cavity enhanced absorption spectroscopy using continuous wave tunable diode laser and fast swept optical cavity" (ring down and cavity-wave tunable laser and a rapid swept optical cavity) at volume 1, 131 and 137 pages (Chemical Physics Letters) of "physical chemistry promissory" 319, energy is rapidly accumulated in the cavity and rapidly departs from the resonant state when the resonant frequency of the cavity rapidly passes through the frequency of the laser by rapidly sweeping the cavity length instead of an external optical or electrical switching circuit. In 2014, Bostrom et al published in Optical interference detuning for ring down cavity (Optics Letters) at 4227 and 4230 pages (Optics Letters) of Optical quick report 39 volume 14, and adopt a second interference pulse light to be incident into a main laser to shift the light frequency, so as to realize the detuning process of an Optical heterodyne feedback ring down cavity, and keep the resonance state when the pulse is removed. In 2019, sons vibration source et al, published in "Random vibration-driven calibration-free continuous wave ring-down cavity trace gas measurement system based on Random vibration-driven" (Random vibration-driven) at page 3, 746-749, volume 45, Optics Letters, proposes to use a narrow-linewidth laser to generate two laser frequencies as incident light, and to change the cavity length by the Random vibration in the measurement process in the order of nanometer to micrometer, thereby changing the position of the resonant cavity mode distribution on the frequency domain, realizing the time-sharing screening of single-frequency light, and realizing the measurement of gas concentration without calibrating the cavity parameters.
At present, in the aspect of detecting the concentration of trace gas based on a ring-down cavity, with the continuous and deep research of scholars at home and abroad on the ring-down cavity spectrum technology, the technology obtains certain achievements in the practical application of gas detection in industry, medical treatment and atmospheric environment. On the other hand, how to obtain accurate and reliable gas concentration information in a complicated measurement environment, and to gradually realize integration and miniaturization also become a problem of great attention of scholars. In order to realize miniaturization and integration, the length of a cavity of a ring-down cavity is not too large, the optical path is small due to the small cavity length under the condition that the reflectivity of a reflector is certain, the ring-down signal duration is short, and generally only a few microseconds is needed, so that in order to collect a relatively accurate ring-down signal for subsequent processing, the conventional trace gas measurement system based on the ring-down cavity has high requirements on hardware of a collection part, and a high-speed analog-to-digital converter (hundreds of MHz) is often needed for sampling, which puts high requirements on the collection system. The frequency domain distribution of the ring-down signal mainly exists in a low-frequency part and mainly is noise interference in a high-frequency part by carrying out spectrum analysis on the ring-down signal emitted by the optical ring-down cavity. In order to avoid spectrum aliasing, the ring-down signal needs to pass through a low-pass filter and then be sampled by using a low-speed analog-to-digital converter, and the method can greatly reduce the requirement on an acquisition system.
Disclosure of Invention
The invention discloses a low-speed sampling-based method for extracting a high-speed ring-down signal coefficient of a ring-down cavity. The ring-down signal emitted by the optical ring-down cavity is incident to the photoelectric detector and then converted into an electric signal, the electric signal is processed by the low-pass filter and then is acquired by the low-speed analog-to-digital converter, finally, the digital signal is processed on a computer, and the attenuation coefficient of the ring-down signal emitted by the ring-down cavity is acquired by a system parameter identification method. The invention filters the high-frequency noise interference in the ring-down signal by using the low-pass filter, obtains the attenuation coefficient by using the system identification method through fitting, can greatly reduce the requirement on the sampling rate of the sampling system, and is convenient for the integration of the ring-down cavity data acquisition system.
The elements used include: the device comprises a laser, an optical ring-down cavity, a photoelectric detector, a low-pass filter, a low-speed analog-to-digital converter and a computer.
The technical scheme of the invention is as follows: after the optical path of the ring-down cavity is adjusted, the laser which is periodically turned off is incident on the ring-down cavity, so that the light intensity signal emitted from the cavity is attenuated along with time, namely the ring-down signal emitted from the ring-down cavity. After function fitting and Laplace transformation are carried out on the ring-down signal, the ring-down signal is multiplied by a transfer function of a first-order RC low-pass filter in a complex frequency domain s domain, and then Laplace inverse transformation is carried out on the multiplied function to obtain a preliminary time domain expression of the ring-down signal after passing through the low-pass filter; analyzing the step signal at the initial point of the ring-down signal to obtain a time domain expression of the step signal, and performing supplementary correction on the preliminary time domain expression; finally, a complete time domain expression of the ring-down signal after passing through a low-pass filter is obtained, the expression is used for solving the signal obtained under the sampling condition of the low-speed analog-to-digital converter by a numerical method, and the attenuation coefficient beta of the corresponding ring-down cavity emergent signal is obtained, and the method comprises the following steps:
the method comprises the following steps: the ring-down signal emerging from the ring-down cavity is incident on a photodetector with a function I (t) equal to A.e-βt+ B to fit the ring down cavity exit ring down signal, where a represents the intensity amplitude coefficient, β represents the attenuation coefficient of the ring down signal, B is a constant term, and t represents time, laplace transform is performed on the signal i (t), and the formula is:
the transfer function expression of the first-order RC filter is as follows:
wherein:
the Laplace transformed I(s) of the ring-down signal I (t) is multiplied by a low-pass filter transfer function H(s) in a complex frequency domain, and the expression is as follows:
performing inverse Laplace transform on G(s), wherein the time domain expression is as follows:
it should be noted that the amplitude of the time domain expression at the time point 0 is 0, which is not consistent with the actual situation, and needs to be subjected to supplementary correction;
step two: the step signal K (t) with K as the amplitude is subjected to laplace transform, and the formula is expressed as:
the step signal is multiplied by a low-pass filter transfer function in a complex frequency domain after Laplace transformation, and the expression is as follows:
performing inverse laplacian transform on j(s), wherein a time domain expression of the step signal after low-pass filtering is represented as:
in practical cases, the amplitude of the interception starting point of the ring-down signal is K, and the amplitude of the step signal existing at the interception starting time is not from 0 to K but from K to 0, so that the time domain expression of the step signal at the ring-down signal starting point can be represented as K · e-ωtAnd J (t) K-K · e-ωtIs symmetrical about a line y-K/2;
combining the formula G (t) in the first step, finally obtaining a time domain expression L (t) of the ring-down signal after passing through a first-order low-pass filter, wherein the time domain expression L (t) is as follows:
step three: and sampling the signal subjected to low-pass filtering under the sampling condition of the low-speed analog-to-digital converter, and performing nonlinear fitting on the signal obtained by sampling under the condition that the cut-off frequency omega of the low-pass filter is known to obtain an attenuation coefficient beta under the low-speed sampling condition, namely an unknown number a (2) in the formula.
The invention has the advantages that: the time domain representation of the ring-down signal emitted by the optical ring-down cavity may be expressed by the function i (t) a.e-βtAnd+ B represents that the low-pass filter and the low-speed analog-to-digital converter are introduced in the data acquisition process, the knowledge of system identification is utilized, the signals acquired after filtering are fitted by using the complete time domain expression in the technical scheme, and the attenuation coefficient beta of the ring-down cavity emergent ring-down signal under the high-speed sampling condition can be approximately obtained under the low-speed sampling condition.
Drawings
The invention is further described with reference to the following figures and detailed description.
Figure 1 is a flow chart of an implementation.
Fig. 2 is a schematic structural diagram of the present invention.
The figures are numbered: 101. laser 102, optical ring-down cavity 103, photodetector 104, low-pass filter 105, low-speed analog-to-digital converter 106 and computer
Detailed Description
Taking an experiment of water vapor of a gas to be detected as an example, the specific implementation mode of the method is explained, and the method comprises the following steps:
the method comprises the following steps: the optical ring-down cavity consists of two high-reflectivity reflectors which are 14cm away from each other, the reflectivity of the reflectors is 99.95%, the curvature radius is 100mm, and a narrow-linewidth laser with the central wavelength of 1342.5nm is used as an incident light source. After the coaxial adjustment of the optical path of the ring-down cavity system is finished, the size of an emergent light spot passing through the lens group is the same as that of a waist light spot of a central basic mode of the cavity by adjusting the adjustable-focus collimating lens so as to meet the matching of incident light and a transverse mode of the resonant cavity; and then the cavity length of the ring-down cavity is changed in a micron-scale length by utilizing mechanical vibration, so that the cavity length is equal to integral multiple of half wavelength of incident laser, and the longitudinal mode matching condition is met. In order to enable a light intensity signal emitted from the cavity to have an attenuation process, laser which is periodically broken and is incident to the ring-down cavity needs to be subjected to light interruption, and the specific mode is that a signal generator is adopted to generate a pulse waveform with the frequency of 100kHz and the duty ratio of 20% to drive the electro-optic modulator, so that the electro-optic modulator is used for periodically modulating space light in a pulse mode. Ideally, there will be an incident light on-time of 2 μ s for 10 μ s per modulation cycle, and the incident light is completely turned off for the remaining 8 μ s, to obtain a ring down signal. The ring-down signal is transmitted to a photoelectric detector and then converted into an electric signal, the electric signal is processed by a first-order RC low-pass filter, a low-speed analog-to-digital converter is used for signal acquisition, and finally, the digital signal is processed on a computer.
Step two: the ring-down signal emitted from the ring-down cavity is an exponential signal decaying along with time, and the function I (t) is equal to A.e-βt+ B represents the ring-down signal, where a represents the intensity amplitude coefficient, β represents the attenuation coefficient of the ring-down signal, B is a constant term, and t represents time, and the function i (t) is laplace transformed, as shown in the equation:
the first-order RC filter consists of a capacitor and a resistor, and low-pass filters with different cut-off angular frequencies omega can be obtained by selecting the sizes of the capacitor and the resistor. The resistor R used in the experiment was 2.5k Ω, the capacitor C was 32pF, and the transfer function expression of the first order RC filter was:
since the ring-down signal enters the photodetector and passes through the low-pass filter, the low-pass filtered signal cannot be directly used as i (t) ═ a · e-βt+ B, in the foregoing technical solution, we have obtained a time domain expression l (t) of the ring-down signal after passing through the first-order RC low-pass filter by using a system identification method:
step three: in the equation (14), the cutoff angular frequency ω of only the low-pass filter is known, and ω is 8 × 1e-8rad/s, the remaining parameters A, beta, C, K are unknown, and the low-pass filtered signal is fitted nonlinearly as shown in equation (15):
and (3) after low-pass filtering, the attenuation coefficient beta under the condition of low-speed sampling, namely an unknown number a (2) in the formula.
In order to verify the feasibility and effectiveness of the method, the results of low-speed sampling and high-speed sampling are compared in an experiment, specifically, a signal output by a photoelectric detector is divided into two parts, one part of the signal is subjected to low-speed sampling after passing through a first-order RC low-pass filter, the sampling rate is 12.5MHz, the other part of the signal is subjected to direct high-speed sampling, and the sampling rate is 125 MHz. For the low-pass filtered signal, we fit it with equation (15), and the high-speed sampling of the signal uses the function i (t) ═ a · e-βt+ B direct fitting to obtain the attenuation coefficient beta under two conditions: the attenuation coefficient at low-speed sampling is 1347895, and at high-speed samplingThe lower attenuation coefficient is 1359074. The result is the average value of hundreds of attenuation coefficients under the same group of water vapor concentration, and the relative error of the measurement result of the water vapor concentration under the low sampling condition and the measurement result of the water vapor concentration under the high sampling condition is calculated to be 0.3 percent.
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 (2)
1. A ring-down cavity high-speed ring-down signal coefficient extraction method based on low-speed sampling is characterized in that ring-down signals emitted by an optical ring-down cavity are converted into electric signals after being incident on a photoelectric detector, the electric signals are processed by a low-pass filter and then are acquired by a low-speed analog-to-digital converter, finally, the digital signals are processed on a computer, the attenuation coefficient of the ring-down cavity emitted ring-down signals is obtained by a system parameter identification method, and the implementation device comprises a laser light source, the optical ring-down cavity, the low-pass filter, the low-speed analog-to-digital converter and the computer.
2. The method for extracting the coefficient of the ring-down cavity high-speed ring-down signal based on the low-speed sampling as claimed in claim 1, wherein the ring-down signal is subjected to laplace transform, then multiplied by a transfer function of a first-order RC low-pass filter in a complex frequency domain s domain, and then subjected to laplace inverse transform to obtain a preliminary time domain expression of the ring-down signal after passing through the low-pass filter; analyzing the step signal at the initial point of the ring-down signal to obtain a time domain expression of the step signal, and performing supplementary correction on the preliminary time domain expression; finally, a complete time domain expression of the ring-down signal after passing through the low-pass filter is obtained, and the attenuation coefficient beta of the corresponding ring-down cavity emergent signal is obtained by a method of solving the signal obtained under the sampling condition of the low-speed analog-to-digital converter by using the expression by using a numerical value, the method can reduce the requirement on the sampling rate of an experimental acquisition device, and the method comprises the following steps:
the method comprises the following steps: the ring-down signal emerging from the ring-down cavity is incident on a photodetector with a function I (t) equal to A.e-βt+ B to fit the ring down cavity exit ring down signal, where a represents the light intensity amplitude coefficient, β represents the attenuation coefficient of the ring down signal, B is a constant term, and t represents time, and laplace transform is performed on the signal i (t), and the formula is:
the transfer function expression of the first-order RC filter is as follows:
the Laplace transformed I(s) of the ring-down signal I (t) is multiplied by a low-pass filter transfer function H(s) in a complex frequency domain, and the expression is as follows:
performing inverse Laplace transform on G(s), wherein the time domain expression is as follows:
it should be noted that the amplitude of the time domain expression at the time point 0 is 0, which is not consistent with the actual situation, and needs to be subjected to supplementary correction;
step two: the step signal K (t) with K as the amplitude is subjected to laplace transform, and the formula is expressed as:
after the step signal is subjected to Laplace transform, the step signal is multiplied by a low-pass filter transfer function in a complex frequency domain, and the expression is as follows:
performing inverse Laplace transform on J(s), wherein a time domain expression of the step signal after low-pass filtering is represented as:
in practical cases, the amplitude of the interception starting point of the ring-down signal is K, and the amplitude of the step signal existing at the interception starting time is not from 0 to K but from K to 0, so that the time domain expression of the step signal at the ring-down signal starting point can be represented as K · e-ωtAnd J (t) K-K · e-ωtIs symmetrical about a line y-K/2;
combining the formula G (t) in the first step, finally obtaining a time domain expression L (t) of the ring-down signal after passing through a first-order low-pass filter, wherein the time domain expression L (t) is as follows:
step three: by using a numerical solving method, the attenuation coefficient beta under the sampling condition of the low-speed analog-to-digital converter can be obtained:
in the case where the cutoff frequency ω is known, the attenuation coefficient is the unknown a (2) in the above-described nonlinear fitting equation.
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