CN111220189B - Brillouin optical time domain analysis sensing device and non-local effect compensation method - Google Patents

Brillouin optical time domain analysis sensing device and non-local effect compensation method Download PDF

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CN111220189B
CN111220189B CN202010052968.4A CN202010052968A CN111220189B CN 111220189 B CN111220189 B CN 111220189B CN 202010052968 A CN202010052968 A CN 202010052968A CN 111220189 B CN111220189 B CN 111220189B
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brillouin
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CN111220189A (en
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闫连山
刘灿
何海军
周银
张信普
潘炜
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Anjie Guangtong Technology Chengdu Co ltd
Southwest Jiaotong University
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Southwest Jiaotong University
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    • G01DMEASURING NOT SPECIALLY ADAPTED FOR A SPECIFIC VARIABLE; ARRANGEMENTS FOR MEASURING TWO OR MORE VARIABLES NOT COVERED IN A SINGLE OTHER SUBCLASS; TARIFF METERING APPARATUS; MEASURING OR TESTING NOT OTHERWISE PROVIDED FOR
    • G01D5/00Mechanical means for transferring the output of a sensing member; Means for converting the output of a sensing member to another variable where the form or nature of the sensing member does not constrain the means for converting; Transducers not specially adapted for a specific variable
    • G01D5/26Mechanical means for transferring the output of a sensing member; Means for converting the output of a sensing member to another variable where the form or nature of the sensing member does not constrain the means for converting; Transducers not specially adapted for a specific variable characterised by optical transfer means, i.e. using infrared, visible, or ultraviolet light
    • G01D5/32Mechanical means for transferring the output of a sensing member; Means for converting the output of a sensing member to another variable where the form or nature of the sensing member does not constrain the means for converting; Transducers not specially adapted for a specific variable characterised by optical transfer means, i.e. using infrared, visible, or ultraviolet light with attenuation or whole or partial obturation of beams of light
    • G01D5/34Mechanical means for transferring the output of a sensing member; Means for converting the output of a sensing member to another variable where the form or nature of the sensing member does not constrain the means for converting; Transducers not specially adapted for a specific variable characterised by optical transfer means, i.e. using infrared, visible, or ultraviolet light with attenuation or whole or partial obturation of beams of light the beams of light being detected by photocells
    • G01D5/353Mechanical means for transferring the output of a sensing member; Means for converting the output of a sensing member to another variable where the form or nature of the sensing member does not constrain the means for converting; Transducers not specially adapted for a specific variable characterised by optical transfer means, i.e. using infrared, visible, or ultraviolet light with attenuation or whole or partial obturation of beams of light the beams of light being detected by photocells influencing the transmission properties of an optical fibre
    • G01D5/35338Mechanical means for transferring the output of a sensing member; Means for converting the output of a sensing member to another variable where the form or nature of the sensing member does not constrain the means for converting; Transducers not specially adapted for a specific variable characterised by optical transfer means, i.e. using infrared, visible, or ultraviolet light with attenuation or whole or partial obturation of beams of light the beams of light being detected by photocells influencing the transmission properties of an optical fibre using other arrangements than interferometer arrangements
    • G01D5/35354Sensor working in reflection
    • G01D5/35358Sensor working in reflection using backscattering to detect the measured quantity
    • G01D5/35364Sensor working in reflection using backscattering to detect the measured quantity using inelastic backscattering to detect the measured quantity, e.g. using Brillouin or Raman backscattering

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Abstract

The invention discloses a Brillouin optical time domain analysis sensing device and a non-local effect compensation method.A continuous light output by a tunable laser is divided into an upper branch and a lower branch after passing through a coupler; continuous light in the upper branch enters the sensing optical fiber after sequentially passing through the polarization controller, the intensity modulator, the first erbium-doped optical fiber amplifier and the first optical circulator; continuous light in the lower branch passes through an acousto-optic modulator to realize optical pulse modulation, and then sequentially passes through a second erbium-doped optical fiber amplifier, a polarization scrambler and a second optical circulator and then enters a sensing optical fiber; the detection light enters a third optical circulator and a first photoelectric detector through a third port of the second optical circulator and then is sent to an upper computer through a data acquisition card; pulse light enters the adjustable attenuator through a third port of the first optical circulator, then passes through a second photoelectric detector and then is sent to an upper computer through a data acquisition card; the invention has simple structure, can effectively improve the performance of the sensing device and improve the compensation quality and precision.

Description

Brillouin optical time domain analysis sensing device and non-local effect compensation method
Technical Field
The invention relates to a distributed optical fiber sensing technology, in particular to a Brillouin optical time domain analysis sensing device and a non-local effect compensation method.
Background
In the last thirty years, with the rapid development of oil and gas pipelines, subways (high-speed railways), large buildings and the like, the safety of the pipelines is more and more emphasized by people. The distributed optical fiber sensing technology can use a common communication optical cable as a sensing medium, has the advantages of long sensing distance, more sensing nodes and the like, and is widely applied to infrastructure safety detection. The Brillouin optical time domain analysis technology is an important component of the distributed optical fiber sensing technology. The method is mainly applied to the fields of oil and gas pipelines, bridge structure health monitoring and the like at present. The brillouin optical time domain analysis technique obtains brillouin frequency shift (the parameter is in a linear relation with the temperature stress of the optical fiber) by measuring brillouin gain spectrum. The overall performance of the brillouin optical time domain analysis system is directly related to the signal-to-noise ratio of the brillouin gain. The signal-to-noise ratio is in turn directly proportional to the power of the continuous probe light input to the system. To mitigate non-local effects, the power of the continuous light in conventional single sideband gain configured systems is limited to-13 dBm. The current techniques for overcoming non-local effects are mainly classified into the following categories: 1. symmetric double-sideband detection light, which raises the detection light power to about-6 dBm; 2. the power of the detection light is raised to +5dBm by the symmetrical double-sideband detection light-scanning pulse light; 3. scanning the wavelength of a light source, and lifting the detection light to about-6.3 dBm; 4. modulating the frequency of the detection light, and increasing the power of the detection light to about-6 dBm; 5. the average Brillouin gain spectrum and the attenuation spectrum are used for increasing the detection light to 0 dBm; 6. the reflected rayleigh signal can be used to boost the probe light to about +2 dBm; the method 1 has a simple structure, but can only improve the detection optical power to-6 dBm; the methods 2 to 6 have complex structure configuration, and the signal-to-noise ratio of the compensation signal of the method 6 is low.
Disclosure of Invention
Aiming at the problems in the prior art, the invention provides a simple and high-performance Brillouin optical time domain analysis sensing device for compensating the non-local effect and a non-local effect compensation method.
The technical scheme adopted by the invention is as follows:
a Brillouin optical time domain analysis sensing device comprises an upper branch circuit and a lower branch circuit, wherein the upper branch circuit is used for generating continuous probe light, and the lower branch circuit is used for generating pulsed light; continuous light output by the tunable laser is divided into an upper branch and a lower branch after passing through the coupler; continuous light in the upper branch enters the sensing optical fiber after sequentially passing through the polarization controller, the intensity modulator, the first erbium-doped optical fiber amplifier and the first optical circulator; continuous light in the lower branch passes through an acousto-optic modulator to realize optical pulse modulation, and then sequentially passes through a second erbium-doped optical fiber amplifier, a polarization scrambler and a second optical circulator and then enters a sensing optical fiber; the intensity modulator is driven by a microwave source, and the acousto-optic modulator is driven by a pulse generator; after the stimulated Brillouin action in the sensing optical fiber, the detection light enters a third optical circulator through a third port of the second optical circulator, then enters a first photoelectric detector and then is sent to an upper computer through a data acquisition card; after the stimulated Brillouin action in the sensing optical fiber, the pulse light enters the adjustable attenuator through the third port of the first optical circulator, then passes through the second photoelectric detector and is sent to the upper computer through the data acquisition card.
Further, the third optical circulator is connected with an optical filter.
Further, the optical filter filtering window corresponds to an upper sideband of the double sidebands generated by the intensity modulator.
Further, the bandwidth of the first photoelectric detector is larger than the lowest sampling rate; the bandwidth of the second photodetector is greater than twice the frequency of the corresponding rising or falling edge of the pulse.
A non-local effect compensation method of a Brillouin optical time domain analysis sensing device comprises the following steps:
step 1: the probe light and the pulse light after undergoing the brillouin effect are expressed as formulas (1) and (3), and the probe light and the pulse light without the brillouin effect are expressed as formulas (2) and (4):
Figure GDA0002927407470000021
PSo(v,z)=Pise-α(L-z)e-αz (2)
Pp(v,z)=PiPe-αz(1-d(v,z)) (3)
Ppo(v,z)=PiPe-αz (4)
in the formula: pS(v, z) is the power of the probe light with energy transfer, PSo(v, z) is the power of the probe light without energy transfer; pp(v, z) is the power of the pulsed light with energy transfer, Ppo(v, z) is the power of the pulsed light without energy transfer; v is the difference between the frequencies of the detection light and the pulse light, z is the interaction position of the detection light and the pulse light, and delta z is the length of the interaction position of the detection light and the pulse light; l is the total length of the sensing fiber, alpha is the fiber loss coefficient, PisFor detecting the power of light input into the sensing fibre, PiPFor pulsed light input into the sensing fiber, gB(v, z) is the linear gain of Brillouin, AeffA nonlinear effective area that is a light sensing mode; d (v, z) is the pulse consumption due to energy transfer from the 0 to z position due to the stimulated brillouin scattering effect;
step 2: probe light in z1The power gained by the location is as follows:
Figure GDA0002927407470000022
and step 3: assuming pulsed light in z1The position gives the probe light energy, which is carried to the z position by the pulsed light and also due to the propagation z-z1Distance and loss of energy; further assuming that the pulse light does not impart probe light energy at the 0 to z positions, then these energies, i.e. the energy E consumed by the pulsed(v,z):
Figure GDA0002927407470000031
Namely:
Ed(v,z)=(PPo(v,z)-PP(v,z))Δz=d(v,z)PiPΔze-αz (7)
and 4, step 4: the following formula can be obtained from formulas (6) and (7):
Figure GDA0002927407470000032
namely:
Figure GDA0002927407470000033
in the formula: pS(v,z)、PSo(v, z) and z are obtained according to the first photoelectric detector (14), and k is a consumption coefficient of pulsed light measured by the second photoelectric detector at the tail end of the optical fiber;
and 5: the power of the pulse at the fiber pigtail with and without energy transfer is as follows:
PP(v,z=L)=LssPiPe-αL(1-d(v,z=L)) (10)
PPo(v,z=L)=LssPiPe-αL (11)
in the formula: l isssIs a fixed loss factor; pP(v, z ═ L) is the power of the pulse at the fiber pigtail end with energy transfer, PPo(v, z ═ L) is the power of the pulse at the fiber pigtail end without energy transfer;
step 6: solving according to equations (10) and (11) yields d (v, z ═ L):
Figure GDA0002927407470000034
and 7: d (v, z) is obtained by substituting formula (12) for formula (9):
Figure GDA0002927407470000035
and 8: the original Brillouin gain can be obtained according to the formulao(v, z) and the compensated Brillouin gainc(v,z):
Figure GDA0002927407470000036
Figure GDA0002927407470000041
The invention has the beneficial effects that:
(1) the invention has simple structure and good compensation performance;
(2) the invention has high compensation signal quality, can effectively ensure the compensated precision, and has high precision of the measurement result;
(3) the invention has obviously improved performance, and can improve the detection light from-13 dBm to +2dBm under the condition of avoiding Brillouin error.
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FIG. 1 is a schematic view of the structure of the present invention.
Fig. 2 is a schematic structural diagram of the principle of the present invention.
Fig. 3 is a schematic diagram of a measurement result of pulsed light at the tail end of an optical fiber according to an embodiment of the present invention.
FIG. 4 is a d (v, z) distribution diagram in example.
FIG. 5 is a graphical comparison of Brillouin gain without compensation and compensated by the method of the present invention; a is a pulse consumption graph, b is an original Brillouin gain spectrum, and c is the compensated Brillouin gain spectrum by the method.
Fig. 6 is a comparison graph of the hot spot test results at 45 ℃, wherein a is an original brillouin frequency shift result graph, and b is a compensated brillouin frequency shift result graph.
In the figure: 1-tunable laser, 2-coupler, 3-polarization controller, 4-intensity modulator, 5-first erbium-doped fiber amplifier, 6-first optical circulator, 7-sensing fiber, 8-second optical circulator, 9-polarization scrambler, 10-acousto-optic modulator, 11-second erbium-doped fiber amplifier, 12-optical filter, 13-third optical circulator, 14-first photoelectric detector, 15-data acquisition card, 16-upper computer, 17-second photoelectric detector and 18-adjustable attenuator.
Detailed Description
The invention is further described with reference to the following figures and specific embodiments.
As shown in fig. 1, in a brillouin optical time domain analysis sensing device, continuous light output by a tunable laser 1 is divided into an upper path and a lower path through a coupler 2; continuous light in the upper branch sequentially passes through a polarization controller 3 to adjust the light polarization state, then is subjected to carrier suppression double-sideband modulation through an intensity modulator 4 driven by a microwave source, is improved in light power through a first erbium-doped fiber amplifier 5, and enters a sensing fiber 7 through a first optical circulator 6 to serve as detection light.
Continuous light in the lower branch is subjected to light pulse modulation through an acousto-optic modulator 10 driven by a pulse generator, then is amplified through a second erbium-doped fiber amplifier 11 in sequence, then is disturbed in the polarization state of the pulse light through a polarization scrambler 9, and is injected into a sensing fiber 7 through a second optical circulator 8 to serve as interaction of the pulse light and the detection light.
The detection light after the stimulated Brillouin effect in the sensing optical fiber 7 enters a third optical circulator 13 through a third port of a second optical circulator 8, the upper side band of the light is filtered by an optical filter 12, then the detection light enters a first photoelectric detector 14 for photoelectric conversion, and then the detection light is sent to an upper computer 16 through a data acquisition card 15 for data processing.
After being subjected to the stimulated Brillouin action in the sensing optical fiber 7, the pulse light enters the adjustable attenuator 18 through the third port of the first optical circulator 6 to adjust the light intensity, then is subjected to photoelectric conversion through the second photoelectric detector 17, and then is sent to the upper computer 20 through the data acquisition card 15 to be subjected to data processing.
The filter window of the optical filter 12 corresponds to the upper one of the double side bands generated by the intensity modulator 4. The bandwidth of the first photoelectric detector 14 is greater than the lowest sampling rate (the lowest sampling rate is 100MHz corresponding to the optical fiber spatial resolution 1m corresponding to the pulse light width 10 ns); the second photodetector 17 has a bandwidth greater than twice the frequency of the rising or falling edges of the pulses (10 ns for a rising edge corresponds to a frequency of 200 MHz).
The driving frequency of the intensity modulator 4 of the upper branch of the invention is the frequency sweep frequency fsThe frequency sweep range of the fiber needs to cover the Brillouin gain region of the sensing fiber; the acousto-optic modulator 10 of the lower branch circuit not only producesThe pulse-generating light also introduces a frequency shift that allows the lower sideband of the probe light to avoid the brillouin loss region of the sensing fiber. And describing the distribution condition of pulse consumption in the optical fiber by adopting a continuous optical signal, and using the pulse at the tail end of the optical fiber to assist in calculating the pulse consumption coefficient.
A non-local effect compensation method of a Brillouin optical time domain analysis sensing device comprises the following steps:
step 1: the probe light and the pulse light after undergoing the brillouin effect are expressed as formulas (1) and (3), and the probe light and the pulse light without the brillouin effect are expressed as formulas (2) and (4):
Figure GDA0002927407470000051
PSo(v,z)=Pise-α(L-z)e-αz (2)
Pp(v,z)=PiPe-αz(1-d(v,z)) (3)
Ppo(v,z)=PiPe-αz (4)
in the formula: pS(v, z) is the power of the probe light with energy transfer, PSo(v, z) is the power of the probe light without energy transfer; pp(v, z) is the power of the pulsed light with energy transfer, Ppo(v, z) is the power of the pulsed light without energy transfer; v is the difference between the frequencies of the detection light and the pulse light, z is the interaction position of the detection light and the pulse light, and delta z is the length of the interaction position of the detection light and the pulse light; l is the total length of the sensing fiber 7, alpha is the fiber loss coefficient, PisFor detecting the power, P, of light input into the sensing fibre 7iPFor pulsed light input into the power of the sensing fiber 7, gB(v, z) is the linear gain of Brillouin, AeffA nonlinear effective area that is a light sensing mode; d (v, z) is the pulse consumption due to energy transfer from the 0 to z position due to the stimulated brillouin scattering effect;
step 2: probe light in z1The power gained by the location is as follows:
Figure GDA0002927407470000061
and step 3: assuming pulsed light in z1The position gives the probe light energy, which is carried to the z position by the pulsed light and also due to the propagation z-z1Distance and loss of energy; further assuming that the pulse light does not impart probe light energy at the 0 to z positions, then these energies, i.e. the energy E consumed by the pulsed(v,z):
Figure GDA0002927407470000062
Namely:
Ed(v,z)=(PPo(v,z)-PP(v,z))Δz=d(v,z)PiPΔze-αz (7)
and 4, step 4: the following formula can be obtained from formulas (6) and (7):
Figure GDA0002927407470000063
namely:
Figure GDA0002927407470000064
in the formula: pS(v,z)、PSo(v, z) and z are obtained according to the first photodetector 14, and k is the consumption coefficient of the pulsed light measured by the second photodetector 17 at the tail end of the optical fiber; z is ct/2, c is the propagation velocity of light in the fiber, the only parameter to be determined in equation (9) is k, and the fiber loss coefficient is α-1=22×103m。
And 5: the power of the pulse at the fiber pigtail with and without energy transfer is as follows:
PP(v,z=L)=LssPiPe-αL(1-d(v,z=L)) (10)
PPo(v,z=L)=LssPiPe-αL (11)
in the formula: l isssA fixed loss factor introduced for the first optical circulator 6 and the adjustable attenuator 18; pP(v, z ═ L) is the power of the pulse at the fiber pigtail end with energy transfer, PPo(v, z ═ L) is the power of the pulse at the fiber pigtail end without energy transfer;
step 6: solving according to equations (10) and (11) yields d (v, z ═ L):
Figure GDA0002927407470000065
and 7: d (v, z) is obtained by substituting formula (12) for formula (9):
Figure GDA0002927407470000071
and 8: the original Brillouin gain can be obtained according to the formulao(v, z) and the compensated Brillouin gainc(v,z):
Figure GDA0002927407470000072
Figure GDA0002927407470000073
It can be seen from the above equation that the non-local effects of the pulse loss can be eliminated.
In practice, the frequency range needs to cover the fiber brillouin shift by the microwave source sweeping the frequency. FIGS. 3 and 4 are graphs of the results of tests using the apparatus of the present invention, using 39.1km of fiber. Fig. 3 is a graph showing the measurement result of the pulse light at the end of the optical fiber, and fig. 4 is a d (v, z) distribution graph. Pulse consumption plots at the proximal end of 6km and at the end of the fibre of 39.105km are also shown. It can be seen that the d (v, z) signal-to-noise ratio is high, thus ensuring the post-compensation measurement accuracy.
FIG. 5 is a graph of Brillouin gain versus Brillouin gain without compensation in accordance with the present invention; under the condition that the detection light is +2 dBm; a is the pulse consumption graph, b is the original brillouin gain spectrum, and c is the compensated brillouin gain spectrum. Comparing the graphs b and c can show that the line width of the gain spectrum before compensation is inconsistent with the Brillouin frequency shift, and the line width after compensation is highly consistent with the Brillouin frequency shift.
Fig. 6 is a comparison graph of the hot spot test results at 45 ℃, wherein a is an original brillouin frequency shift result graph, and b is a compensated brillouin frequency shift result graph. It can be seen from the graph that the original brillouin frequency shift at the hot spot is not consistent, and the compensated brillouin frequency shift is basically consistent.
The invention uses continuous detecting light to draw the distribution condition of pulse consumption in the optical fiber, and uses the pulse consumption value to compensate the non-local effect, thereby improving the performance and accuracy of the whole system. The system has a simple structure, only needs the configuration of the most basic Brillouin analysis system, and effectively improves the detection light from-13 dBm to +2dBm under the condition of avoiding the Brillouin error, thereby improving the performance of the sensing system; and the quality compensation signal can be improved, thereby ensuring the compensated precision.

Claims (5)

1. A Brillouin optical time domain analysis sensing device is characterized by comprising an upper branch circuit and a lower branch circuit, wherein the upper branch circuit is used for generating continuous probe light, and the lower branch circuit is used for generating pulsed light; continuous light output by the tunable laser (1) is divided into an upper branch and a lower branch after passing through the coupler (2); continuous light in the upper branch enters a sensing optical fiber (7) after sequentially passing through a polarization controller (3), an intensity modulator (4), a first erbium-doped optical fiber amplifier (5) and a first optical circulator (6); continuous light in the lower branch passes through an acousto-optic modulator (10) to realize optical pulse modulation, then sequentially passes through a second erbium-doped optical fiber amplifier (11), a polarization scrambler (9) and a second optical circulator (8) and then enters a sensing optical fiber (7); the intensity modulator (4) is driven by a microwave source, and the acousto-optic modulator (10) is driven by a pulse generator; after being subjected to stimulated Brillouin action in the sensing optical fiber (7), the detection light enters a third optical circulator (13) through a third port of a second optical circulator (8), then enters a first photoelectric detector (14) and then is sent to an upper computer (16) through a data acquisition card (15); after being subjected to the stimulated Brillouin action in the sensing optical fiber (7), the pulse light enters the adjustable attenuator (18) through the third port of the first optical circulator (6), then passes through the second photoelectric detector (17) and then is sent to the upper computer (16) through the data acquisition card (15).
2. A brillouin optical time domain analysis sensing apparatus according to claim 1, wherein said third optical circulator (13) is connected to an optical filter (12).
3. A brillouin optical time domain analysis sensing apparatus according to claim 2, wherein the filter window of the optical filter (12) corresponds to an upper one of the double sidebands produced by the intensity modulator (4).
4. A brillouin optical time domain analysis sensing apparatus according to claim 1, wherein said first photodetector (14) has a bandwidth greater than a lowest sampling rate; the bandwidth of the second photodetector (17) is greater than twice the corresponding frequency of the rising or falling edge of the pulse.
5. The non-local effect compensation method adopting the Brillouin optical time domain analysis sensing device as claimed in any one of claims 1 to 4, characterized by comprising the following steps:
step 1: the probe light and the pulse light after undergoing the brillouin effect are expressed as formulas (1) and (3), and the probe light and the pulse light without the brillouin effect are expressed as formulas (2) and (4):
Figure FDA0002927407460000011
PSo(v,z)=Pise-α(L-z)e-αz (2)
Pp(v,z)=PiPe-αz(1-d(v,z)) (3)
Ppo(v,z)=PiPe-αz (4)
in the formula: pS(v, z) is the power of the probe light with energy transfer, PSo(v, z) is the power of the probe light without energy transfer; pp(v, z) is the power of the pulsed light with energy transfer, Ppo(v, z) is the power of the pulsed light without energy transfer; v is the difference between the frequencies of the detection light and the pulse light, z is the interaction position of the detection light and the pulse light, and delta z is the length of the interaction position of the detection light and the pulse light; l is the total length of the sensing fiber (7), alpha is the fiber loss coefficient, PisFor detecting the power, P, of light input into the sensing fibre (7)iPFor the pulsed light input into the power of the sensing fiber (7), gB(v, z) is the linear gain of Brillouin, AeffA nonlinear effective area that is a light sensing mode; d (v, z) is the pulse consumption due to energy transfer from the 0 to z position due to the stimulated brillouin scattering effect;
step 2: probe light in z1The power gained by the location is as follows:
Figure FDA0002927407460000021
and step 3: assuming pulsed light in z1The position gives the probe light energy, which is carried to the z position by the pulsed light and also due to the propagation z-z1Distance and loss of energy; further assuming that the pulse light does not impart probe light energy at the 0 to z positions, then these energies, i.e. the energy E consumed by the pulsed(v,z):
Figure FDA0002927407460000022
Namely:
Ed(v,z)=(PPo(v,z)-PP(v,z))Δz=d(v,z)PiPΔze-αz (7)
and 4, step 4: the following formula can be obtained from formulas (6) and (7):
Figure FDA0002927407460000023
namely:
Figure FDA0002927407460000024
in the formula: pS(v,z)、PSo(v, z) and z are obtained according to the first photoelectric detector (14), and k is a consumption coefficient of pulsed light measured by the second photoelectric detector (17) at the tail end of the optical fiber;
and 5: the power of the pulse at the fiber pigtail with and without energy transfer is as follows:
PP(v,z=L)=LssPiPe-αL(1-d(v,z=L)) (10)
PPo(v,z=L)=LssPiPe-αL (11)
in the formula: l isssIs a fixed loss factor; pP(v, z ═ L) is the power of the pulse at the fiber pigtail end with energy transfer, PPo(v, z ═ L) is the power of the pulse at the fiber pigtail end without energy transfer;
step 6: solving according to equations (10) and (11) yields d (v, z ═ L):
Figure FDA0002927407460000034
and 7: d (v, z) is obtained by substituting formula (12) for formula (9):
Figure FDA0002927407460000031
and 8: the original Brillouin gain can be obtained according to the formulao(v, z) and the compensated Brillouin gainc(v,z):
Figure FDA0002927407460000032
Figure FDA0002927407460000033
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