CN109696416A - A kind of measurement method of the absorption coefficient based on cavity attenuation and vibration technique - Google Patents
A kind of measurement method of the absorption coefficient based on cavity attenuation and vibration technique Download PDFInfo
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- G01N21/41—Refractivity; Phase-affecting properties, e.g. optical path length
- G01N21/45—Refractivity; Phase-affecting properties, e.g. optical path length using interferometric methods; using Schlieren methods
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- G01N21/41—Refractivity; Phase-affecting properties, e.g. optical path length
- G01N21/45—Refractivity; Phase-affecting properties, e.g. optical path length using interferometric methods; using Schlieren methods
- G01N2021/451—Refractivity; Phase-affecting properties, e.g. optical path length using interferometric methods; using Schlieren methods for determining the optical absorption
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Abstract
A kind of measurement method of the absorption coefficient based on cavity attenuation and vibration technique, this method obtains periodically variable ring-down time by the way of scanning laser frequency, then Fast Fourier Transform (FFT) is carried out to it, and the Fourier coefficient of selected characteristic frequency, ring-down time can be reconstructed by being substituted into Fourier space;Interferometer measurement laser frequency is used later, starts against the relationship of ring-down time and laser frequency, and then obtain absorption coefficient.The present invention property of can choose eliminates various intrinsic frequency noises, restores the absorption coefficient of more high s/n ratio;And interferometer carries out one-shot measurement to optical maser wavelength, is not only restricted to the measurement accuracy and measurement rate of wavemeter;With the laser that scanning mode works, it is not necessarily to high-precision laser controller, reduces the influence of the randomized jitter of optical maser wavelength.
Description
Technical field
The present invention relates to a kind of measurement method of absorption coefficient based on cavity attenuation and vibration technique, be suitable for gas temperature,
The measurement of pressure, concentration and spectrum parameter, belongs to field of measuring technique.
Background technique
Absorption coefficient can determine temperature, pressure, concentration and many spectrum parameters of gas.Cavity ring-down spectroscopy
One kind that (Cavity ring-down spectroscopy, abbreviation CRDS) has proved to be characterization absorption coefficient is accurate
Method is a kind of up-and-coming method for realizing spectrum parameter precise measurement.Its advantage first is that, the equivalent optical path of CRDS can
To be easily reached several kilometers even tens kilometers, therefore tested spectrum has very high signal-to-noise ratio.Another advantage is to adopt
Have with the cavity ring-down spectroscopy (Continuous wave CRDS, abbreviation CW-CRDS) of the relatively narrow continuous-wave laser of line width
Very high spectral resolution.In brief, this absorption spectroscopy techniques based on laser pass through photon lifetime for measuring or
Ring-down time determines the absolute value of optical loss in high-accuracy stable chamber;These losses include gas absorption, specular transmission, auspicious
Benefit scattering etc..In relatively narrow wave-length coverage, only with wavelength shift, remaining loss is constant for the absorption of gas;It therefore, can be with
By measurement ring-down time come reproducible absorption coefficient.
In actual measurement, there are still some problems by CW-CRDS.First is that wavelength need to be used while measuring ring-down time
Meter measurement optical maser wavelength is limited by wavemeter measurement delay, and measurement is spaced in several hundred milliseconds, thus entire absorption spectrum every time
Need a few minutes even time of dozens of minutes;Second is that this process proposes the measurement accuracy of wavemeter and the stability of laser
Very high requirement is gone out, and the system intrinsic noise during this can not be ignored.For the former, we can be used more smart
True wavemeter and laser more stable, that line width is narrower;Or carry out stabilized lasers frequency using more complicated technology, as light is anti-
Present frequency stabilization cavity ring down spectroscopy technology and Pound-Drever-Hall (abbreviation PDH) cavity ring down spectroscopy technology;Or we can
To increase cavity ring-down time, and in the longer time it is averaged spectrum to promote signal-to-noise ratio.And for the latter, due to
System noise frequency be it is fixed, the fine tuning of system is the current best practice for reducing system noise.In CW-CRDS technology,
In view of system noise is fixed frequency, then this noise can be eliminated in frequency domain.Therefore, length scanning can be passed through
Mode allow ring-down time become a periodic signal changed over time.Since the acquisition rate of ring-down time can achieve 20Hz
More than, it is realized so the program is not too much difficult.But here there are still two problems have it is to be solved: one, wavemeter typically measures
Rate is 1~10Hz, measurement accuracy 0.001cm-1, therefore wavelength sweep rate highest must not exceed the measurement rate of wavemeter,
To limit wavelength sweep rate;Two, if not using wavemeter, it is difficult to directly obtain wavelength and ring-down time corresponding relationship.
Therefore, spectral signal-noise ratio is further increased in order to eliminate system noise, it is necessary to design the optical cavity ring-down based on length scanning
Spectral measurement method extracts characteristic frequency by Fourier transformation and reconstructs ring-down time, eliminates system noise from frequency domain, and then obtain
To the higher absorption coefficient of precision.
Summary of the invention
It is an object of the invention to eliminate CW-CRDS system noise to further increase spectral signal-noise ratio, one kind is proposed
The measurement method of absorption coefficient based on cavity attenuation and vibration technique.The core of this method is: 1, by the way of length scanning
Obtain periodically variable ring-down time;2, Fourier transformation is carried out to ring-down time, extracts the Fourier coefficient of characteristic frequency,
Ring-down time is reconstructed using Fourier space;3, using interferometer measurement laser frequency, obtain laser frequency calibration coefficient;4, root
The relationship of ring-down time and wavelength can be obtained according to the formula of derivation, and then obtain the absorption coefficient of gas.
To achieve the above object, technical scheme is as follows:
1) according under test gas type, corresponding absorption spectrum spectral line is chosen from spectra database;Its centre frequency is
ν0, line intensity is S;
2) it acquires ring-down time τ: as shown in Figure 1, using semiconductor laser with tunable as light source, being fixed in laser frequency
When, the laser beam of semiconductor laser with tunable output successively passes through optoisolator, acousto-optic modulator, optical collimator, device it
Between connected using optical fiber, light beam the first plano-concave reflecting mirror of collimated arrival swings chamber, the second plano-concave reflecting mirror by declining, then lead to
On excess convexity lens focus to photodetector;The signal of photodetector is divided into two-way, acquires all the way via capture card, and will adopt
The signal of collection is input in main control computer, and another way generates pulse signal via digital delay generator and is input to acousto-optic tune
Device processed.Piezoelectric ceramics is tightly attached on the second plano-concave reflecting mirror, generates low frequency triangular signal and defeated by function signal generator
Enter high-voltage drive, drive piezoelectric ceramics with scan decline swing chamber chamber it is long;Sweep length is slightly larger than optical maser wavelength, to realize incidence
It optical maser wavelength and declines and swings the pattern match of chamber eigen mode, incident laser, which can effectively be coupled to decline, at this time swings intracavitary, photodetection
The light intensity that device receives is maximum;When the signal of photodetector reaches 0.9V, digital delay generator can generate a pulse
Signal, rising edge can turn off acousto-optic modulator in nanosecond order moment;Since light source is cut off, photodetection is reached at this time
The light intensity of device is in single exponent ring-down;This deamplification is acquired by capture card and deamplification is fitted by computer
Calculate corresponding ring-down time τ under the wavelength;
3) temperature and electric current that semiconductor laser with tunable is controlled by computer make laser frequency in core frequency
Rate ν0The step-scan in the form of triangular wave nearby, scan frequency f;Corresponding ring-down time is acquired in each stepped intervals
τ to get arrive periodically variable ring-down time τ (t);Fast Fourier Transform (FFT) is carried out to τ (t) and obtains Fourier coefficient, therefrom
Take out Fourier coefficient corresponding to characteristic frequency kf, real part Ak, imaginary part Bk;Again by AkAnd BkFourier space is substituted into,
Periodically variable ring-down time τ ' (t) reconstructed:
Wherein, τ ' (t) is the periodically variable ring-down time of reconstruct, AkAnd BkRespectively in corresponding Fu of characteristic frequency
Leaf system number real and imaginary parts;ω is the angular frequency of triangular wave, and f is the scan frequency of triangular wave, then has the π of ω=2 f;P is characterized frequency
Rate total number, k=0,1,2..., p, t are sweep time;
4) laser frequency ν (t) is measured using interferometer 18, makes laser frequency in core frequency ν0Nearby with triangular wave
Form scanning, scan frequency f are respectively fitted the rising edge of laser frequency and failing edge using polynomial of degree n:
Wherein, νOn(t) laser frequency of rising edge, ν are indicatedUnder(t) laser frequency of failing edge is indicated;aiFor rising edge
I term coefficient, biFor failing edge i-th term coefficient, i=0,1,2..., n, n is polynomial order;L represents periodicity, T tri-
Angle wave period, and T=1/f;
5) relationship of ν (t) Yu τ ' (t) are established: enabling θ=ω (t-lT)=ω t-2 π l, wherein 0 < θ < π, l indicates the period
Number;According to the expression formula of step 4) laser frequency, t is replaced to obtain following formula with θ:
According to the expression formula of τ ' (t) in step 3), obtains the periodically variable of rising edge and failing edge reconstruct and decline when swinging
Between τ 'OnWith τ 'Under:
By intermediate variable θ, make νOnWith τ 'OnSimultaneous, νUnderWith τ 'UnderSimultaneous is to get the periodically variable τ ' for arriving reconstructOn
(ν) and τ 'Under(ν);The periodically variable ring-down time τ ' (ν) of the reconstruct changed with laser frequency is obtained after the two is average;
6) it asks absorption coefficient α (ν): τ ' (ν) is substituted into following formula:
Obtain absorption coefficient α (ν);Wherein, R be plano-concave reflecting mirror reflectivity, L be decline swing chamber chamber it is long, c is
The light velocity.
The present invention compared with the conventional method, has the following advantages that and the technical effect of high-lighting: 1. being obtained using the method
Ring-down time be the cyclical signal changed over time, by Fourier transformation extract characteristic frequency reconstruct ring-down time, can
Various intrinsic frequency noises are eliminated with selectivity, and restore the absorption coefficient of more high s/n ratio.2. without making in measurement process
With wavemeter, only one-shot measurement need to be carried out to optical maser wavelength using interferometer, be no longer limited by the measurement of wavemeter itself
Error and measurement rate.3. the method is the frequency of scanning laser compared with CW-CRDS method, therefore is no longer required for laser frequency
Rate keeps stable in a long time, is not necessarily to high-precision laser controller, and reduce the randomized jitter of optical maser wavelength to survey
The influence of amount.
Detailed description of the invention
Fig. 1 is system structure schematic diagram of the invention.
Fig. 2 is the system structure schematic diagram of interferometer measurement laser frequency in the present invention.
Fig. 3 is laser current measured by experiment of the invention, laser frequency, periodically variable ring-down time and its Fu
In leaf transformation coefficient.
Fig. 4 is absorption coefficient measured by experiment of the invention and its regression criterion figure.
In figure: 1- tunable laser;2- optoisolator;3- acousto-optic modulator;4- optical fiber;5- optical collimator;6- first
Plano-concave reflecting mirror;7-, which declines, swings chamber;8- the second plano-concave reflecting mirror;9- piezoelectric ceramics;10- high-voltage drive;11- function signal occurs
Device, 12- convex lens;13- photodetector;14- high-speed collection card;15- computer;16- laser controller;17- digital delay
Generator;18- interferometer.
Specific embodiment
The present invention will be further described below with reference to the drawings.
1) according under test gas type, corresponding absorption spectrum spectral line is chosen from spectra database, centre frequency is
ν0, the intensity of spectral line S.
It 2) is light source with semiconductor laser with tunable 1, as shown in Figure 1, when laser frequency is fixed, tunable semiconductor
The laser beam that laser 1 exports successively passes through optoisolator 2, acousto-optic modulator 3, optical collimator 5, uses optical fiber 4 between device
Connection, light beam the first plano-concave reflecting mirror 6 of collimated arrival swing chamber 7, the second plano-concave reflecting mirror 8 by declining, then pass through convex lens
12 focus on photodetector 13;The signal of photodetector 13 is divided into two-way, acquires all the way via capture card 14, and will adopt
The signal of collection is input in main control computer 15, and another way generates pulse signal via digital delay generator 17 and is input to sound
Optical modulator 4.Piezoelectric ceramics 9 is tightly attached on the second plano-concave reflecting mirror 8, generates low frequency triangular wave by function signal generator 11
Signal simultaneously inputs high-voltage drive 10, drive piezoelectric ceramics 9 with scan decline swing chamber chamber it is long;Sweep length is slightly larger than laser wave
It is long, the pattern match of chamber eigen mode is swung to realize laser wavelength of incidence and decline, incident laser effectively can be coupled to decline and swing at this time
Intracavitary, the light intensity that photodetector 13 receives is maximum;When the signal of photodetector 13 reaches 0.9V, digital delay occurs
Device 17 can generate a pulse signal, and rising edge can turn off acousto-optic modulator 3 moment in nanosecond order;Since light source is cut
Disconnected, the light intensity for reaching photodetector 13 at this time is in single exponent ring-down;This deamplification is acquired by capture card 14 and by calculating
Machine 15, which is fitted deamplification, can calculate corresponding ring-down time τ under the wavelength.
3) temperature and electric current that semiconductor laser with tunable is controlled by computer make laser frequency in core frequency
Rate ν0The step-scan in the form of triangular wave nearby, scan frequency f;Corresponding ring-down time is acquired in each stepped intervals
τ to get arrive periodically variable ring-down time τ (t);Fast Fourier Transform (FFT) is carried out to τ (t) and obtains Fourier coefficient, therefrom
Take out Fourier coefficient corresponding to characteristic frequency kf, real part Ak, imaginary part Bk;Again by AkAnd BkFourier space is substituted into,
Periodically variable ring-down time τ ' (t) reconstructed:
Wherein, τ ' (t) is the periodically variable ring-down time of reconstruct, AkAnd BkRespectively in corresponding Fu of characteristic frequency
Leaf system number real and imaginary parts;ω is the angular frequency of triangular wave, and f is the scan frequency of triangular wave, then has the π of ω=2 f;P is characterized frequency
Rate total number, k=0,1,2..., p, t are sweep time;
4) laser frequency ν (t) is measured using interferometer 18, makes laser frequency in core frequency ν0Nearby with triangular wave
Form scanning, scan frequency f are respectively fitted the rising edge of laser frequency and failing edge using polynomial of degree n:
Wherein, νOn(t) laser frequency of rising edge, ν are indicatedUnder(t) laser frequency of failing edge is indicated;aiFor rising edge
I term coefficient, biFor failing edge i-th term coefficient, i=0,1,2..., n, n is polynomial order;L represents periodicity, T tri-
Angle wave period, and T=1/f;
5) relationship of ν (t) Yu τ ' (t) are established: enabling θ=ω (t-lT)=ω t-2 π l, wherein 0 < θ < π, l indicates the period
Number;According to the expression formula of step 4) laser frequency, t is replaced to obtain following formula with θ:
According to the expression formula of τ ' (t) in step 3), obtains the periodically variable of rising edge and failing edge reconstruct and decline when swinging
Between τ 'OnWith τ 'Under:
By intermediate variable θ, make νOnWith τ 'OnSimultaneous, νUnderWith τ 'UnderSimultaneous is to get the periodically variable τ ' for arriving reconstructOn
(ν) and τ 'Under(ν);The periodically variable ring-down time τ ' (ν) of the reconstruct changed with laser frequency is obtained after the two is average;
6) it asks absorption coefficient α (ν): τ ' (ν) is substituted into following formula:
Obtain absorption coefficient α (ν);Wherein, R be plano-concave reflecting mirror reflectivity, L be decline swing chamber chamber it is long, c is
The light velocity.
α (ν) is fitted using suitable linear function (linear functions such as Voigt, Galatry) to get gas is arrived
Concentration, pressure, temperature and spectral line physical parameter.
Embodiment:
1) with CO2With N2For mixed gas, absorption spectrum spectral line, center frequency are chosen from HITRAN spectra database
Rate ν0For 6526.374cm-1, the intensity of spectral line is 8 × 10-25cm-1/(molec·cm-2);Mixed gas temperature is 23 DEG C, pressure
20kPa, CO2Concentration 1%;
It 2) is light source with semiconductor laser with tunable 1, when laser frequency is fixed, semiconductor laser with tunable 1 is defeated
Laser beam out successively passes through optoisolator 2, acousto-optic modulator 3, optical collimator 5, is connected between device using optical fiber 4, light beam
The first plano-concave reflecting mirror 6 of collimated arrival swings chamber 7, the second plano-concave reflecting mirror 8 by declining, then is focused on by convex lens 12
On photodetector 13;The signal of photodetector 13 is divided into two-way, acquires all the way via capture card 14, and by the signal of acquisition
It is input in main control computer 15, another way generates pulse signal via digital delay generator 17 and is input to acousto-optic modulator
4.Piezoelectric ceramics 9 is tightly attached on the second plano-concave reflecting mirror 8, generates low frequency triangular signal and defeated by function signal generator 11
Enter high-voltage drive 10, drive piezoelectric ceramics 9 with scan decline swing chamber chamber it is long;Sweep length is slightly larger than optical maser wavelength, to realize
It laser wavelength of incidence and declines and swings the pattern match of chamber eigen mode, incident laser, which can effectively be coupled to decline, at this time swings intracavitary, photoelectricity
The light intensity that detector 13 receives is maximum;When the signal of photodetector 13 reaches 0.9V, digital delay generator 17 can be produced
A raw pulse signal, rising edge can turn off acousto-optic modulator 3 moment in nanosecond order;Since light source is cut off, arrive at this time
Light intensity up to photodetector 13 is in single exponent ring-down;This deamplification is acquired by capture card 14 and is decayed by 15 Duis of computer
Signal, which is fitted, can calculate corresponding ring-down time under the wavelength.Wherein, it declines and swings a length of L=50cm of chamber of chamber, plano-concave
Reflectance of reflector R=0.999975;Chamber long scan range is more than 2 μm, scan period 50Hz;
3) temperature and electric current that laser is controlled by computer program, make laser frequency in core frequency ν0Near
It is gradually scanned in the form of triangular wave, laser frequency such as Fig. 3 (b) is shown in solid, and laser current is as shown in Fig. 3 (b) dotted line;At this time
Corresponding ring-down time is also altered in steps, this process has obtained periodically variable ring-down time, if Fig. 3 (a) is shown in solid,
About 38 μ s of ring-down time at centre frequency, the ring-down time of baseline are about 51 μ s.Wherein, triangular voltage sweep frequency f=16Hz swashs
Light device current scanning range ± 15mA, central current 80mA, temperature are stablized at 36.632 DEG C, corresponding wavelength scanning range about ±
0.2cm-1;Fast Fourier Transform (FFT) is carried out to τ (t) and obtains Fourier coefficient, is taken out in Fu corresponding to characteristic frequency kf
Leaf system number, real part Ak, imaginary part Bk;Again by AkAnd BkFourier space is substituted into decline to get to the periodically variable of reconstruct
Swing time τ ' (t):
Wherein, τ ' (t) is the periodically variable ring-down time of reconstruct, AkAnd BkRespectively in corresponding Fu of characteristic frequency
Leaf system number real and imaginary parts;ω is the angular frequency of triangular wave, and f is the scan frequency of triangular wave, then has the π of ω=2 f;P is characterized frequency
Rate total number takes p=100, i.e. k=0 here, and 1,2..., 100, t be detection time;
4) laser frequency ν (t) is measured using interferometer 18, makes laser frequency in core frequency ν0Nearby with triangular wave
Form scanning, scan frequency f=16Hz respectively intend the rising edge of laser frequency and failing edge using polynomial of degree n
It closes:
Wherein, νOn(t) laser frequency of rising edge, ν are indicatedUnder(t) laser frequency of failing edge is indicated;aiFor rising edge
I term coefficient, biFor failing edge i-th term coefficient, i=0,1,2..., n, n=2;L represents periodicity, and T is triangle wave period,
And T=1/f;Calibration coefficient a is obtained by fitting2=9.00 × 10-4,a1=0.0637, a0=0.0198, b2=8.98 × 10-4,b1=-0.0925, b0=1.2683.
5) relationship of ν (t) Yu τ ' (t) are established: enabling θ=ω (t-lT)=ω t-2 π l, wherein 0 < θ < π, l indicates the period
Number;According to the expression formula of laser frequency in formula (2), t can be replaced to obtain following formula with θ:
According to the expression formula of τ ' (t) in step 3), obtains the periodically variable of rising edge and failing edge reconstruct and decline when swinging
Between τ 'OnWith τ 'Under:
Due to νOnWith τ 'OnIt is corresponded with intermediate variable θ, the cyclically-varying of simultaneous (3) and (4) available reconstruct
τ 'On(ν), the periodically variable τ ' that can be similarly reconstructedUnder(ν);It is obtained after the two is average with laser frequency variation
The periodically variable ring-down time τ ' (ν) of reconstruct;Wherein, intermediate variable θ is spaced 0.025 from 0 to 1 and gradually increases, total to count
401。
6) it asks absorption coefficient α (ν): τ ' (ν) is substituted into following formula:
Obtain absorption coefficient α (ν);Wherein, R is the reflectivity of reflecting mirror, and R=0.999975, L are to decline to swing chamber
Chamber is long, L=50cm, and c is the light velocity, c=3 × 108m/s;As shown in figure 4, black open squares are the absorption coefficients of experiment measurement,
As described in step 5), 401 are always counted;Solid line is using Voigt linear fitting result, it is possible to find its regression criterion has apparent
" W " type structure, root-mean-square error are larger;This is because background gas N2To CO2Collision narrow spectral line both wings, and Voigt line style
The inherent structure of this spectral line itself can not be eliminated.This shows that this method has very high spectral signal-noise ratio, can measure light
The fine structure of spectrum.In order to obtain more accurately as a result, using the Galatry linear fitting based on soft collision model, such as Fig. 4 void
Shown in line;" W " type structure has been not present in its regression criterion, and root-mean-square error is obviously reduced.It is carried out using Galatry linear function
Fitting, obtained spectral line line differ 4% with HITRAN2016 database by force, are much smaller than database assigned error range (> 20%);
Wherein, air ceofficient of spread differs only by 1.31%, is less than database assigned error range (2~5%).
Claims (1)
1. a kind of measurement method of the absorption coefficient based on cavity attenuation and vibration technique, it is characterised in that this method includes following step
It is rapid:
1) according under test gas type, corresponding absorption spectrum spectral line is chosen from spectra database;Its centre frequency is ν0, spectrum
Line intensity is S;
2) acquire ring-down time τ: with semiconductor laser with tunable (1) for light source, when laser frequency is fixed, laser successively leads to
It crosses optoisolator (2), acousto-optic modulator (3), optical collimator (5) and declines and swing chamber (7), finally received by photodetector (13);
Using piezoelectric ceramics scanning decline swing chamber chamber it is long, so that zlasing mode is matched with cavity mold formula, at this time photodetector reception light intensity
It is maximum;Shutdown laser then obtains the light intensity signal of single index formula decaying, is fitted to this signal and obtains ring-down time τ;
3) temperature and electric current that semiconductor laser with tunable is controlled by computer, make laser frequency in core frequency ν0
The step-scan in the form of triangular wave nearby, scan frequency f;Corresponding ring-down time τ is acquired in each stepped intervals, i.e.,
Obtain periodically variable ring-down time τ (t);Fast Fourier Transform (FFT) is carried out to τ (t) and obtains Fourier coefficient, is taken out
Fourier coefficient corresponding to characteristic frequency kf, real part Ak, imaginary part Bk;Again by AkAnd BkSubstitute into Fourier space to get
To periodically variable ring-down time τ ' (t) of reconstruct:
Wherein, τ ' (t) is the periodically variable ring-down time of reconstruct, AkAnd BkThe respectively corresponding Fourier system of characteristic frequency
Number real and imaginary parts;ω is the angular frequency of triangular wave, and f is the scan frequency of triangular wave, then has the π of ω=2 f;It is total that p is characterized frequency
Number, k=0,1,2..., p, t are sweep time;
4) using interferometer (18) measurement laser frequency ν (t), make laser frequency in core frequency ν0Nearby with triangular waveform
Formula scanning, scan frequency f are respectively fitted the rising edge of laser frequency and failing edge using polynomial of degree n:
Wherein, νOn(t) laser frequency of rising edge, ν are indicatedUnder(t) laser frequency of failing edge is indicated;aiFor rising edge i-th item
Coefficient, biFor failing edge i-th term coefficient, i=0,1,2..., n, n is polynomial order;L represents periodicity, and T is triangular wave
Period, and T=1/f;
5) relationship of ν (t) Yu τ ' (t) are established: enabling θ=ω (t-lT)=ω t-2 π l, wherein 0 < θ < π, l indicates periodicity;Root
According to the expression formula of step 4) laser frequency, t is replaced to obtain following formula with θ:
According to the expression formula of τ ' (t) in step 3), the periodically variable ring-down time τ ' of rising edge and failing edge reconstruct is obtainedOn
With τ 'Under:
By intermediate variable θ, make νOnWith τ 'OnSimultaneous, νUnderWith τ 'UnderSimultaneous is to get the periodically variable ring-down time for arriving reconstruct
τ'On(ν) and τ 'Under(ν);The periodically variable ring-down time τ ' of the reconstruct changed with laser frequency is obtained after the two is average
(ν);
6) it asks absorption coefficient α (ν): τ ' (ν) is substituted into following formula:
Obtain absorption coefficient α (ν);Wherein, R be plano-concave reflecting mirror reflectivity, L be decline swing chamber chamber it is long, c is light
Speed.
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