CN107741243A - A kind of BOTDR system and the method for lifting the lifetime of system - Google Patents
A kind of BOTDR system and the method for lifting the lifetime of system Download PDFInfo
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01D—MEASURING 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
- G01D5/00—Mechanical 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
- G01D5/26—Mechanical 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
- G01D5/32—Mechanical 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
- G01D5/34—Mechanical 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
- G01D5/353—Mechanical 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
- G01D5/35338—Mechanical 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
- G01D5/35354—Sensor working in reflection
- G01D5/35358—Sensor working in reflection using backscattering to detect the measured quantity
- G01D5/35364—Sensor 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 kind of BOTDR system and the method for lifting the lifetime of system, BOTDR system includes light source module, the first coupler, Electro-optical Modulation module, pulse generating module, Optical pulse amplification module, circulator, light polarization disturbance module, the second coupler, the 3rd coupler, the first optical detection module, scan module, signal processing module, the second optical detection module, feedback module and current control module.The present invention is by increasing feedback module, measure the different piece of whole piece sensor fibre by several times using different launched powers, and the fiber segment close to light source incidence end is deliberately made to produce stimulated Brillouin scattering phenomenon in the measurement process away from luminous source optical fiber section, by the fitting respectively to gradation measurement result and overall splicing, effective Brillouin's crest frequency spectral line of whole piece sensor fibre is obtained.The present invention solves the problems, such as that measurement distance is reduced caused by radiation-induced loss increase, adds service life of the BOTDR system under space radiation environment.
Description
Technical field
The invention belongs to distributed fiberoptic sensor technical field, more particularly to a kind of BOTDR system and lift this and be
The method in system life-span.
Background technology
Brillouin light time domain reflection technology (BOTDR) is a kind of Distributed Optical Fiber Sensing Techniques, and its principle is based on from issue
In deep pool scattering.System source injects pulsed light from one end of optical fiber, and from same one end direct impulse light backwards to spontaneous Brillouin
Scattering spectra.Heat transfer agent on optical fiber can be obtained by analyzing the spectral line.Brillouin scattering is to be lured by the light field in optical fiber with it
Caused by the interaction for the sound field led, Brillouin scattering has the skew in a frequency relative to incident light, referred to as cloth
In deep frequency displacement.And BOTDR then utilizes Brillouin shift analysis heat transfer agent：Brillouin shift and fiber optic temperature and it is suffered should
Become relevant, and the temperature change and suffered axial strain of frequency displacement size and optical fiber are proportional.
With the progressively development of space industry science and technology, the monitoring and protecting of space flight device is also got under severe space environment
More to be paid attention to.However, traditional sensing technology means are but difficult to meet the field to the light-weighted requirement of space flight equipment.
The advantages that BOTDR technologies have electromagnetism interference, in light weight, and error is small, high resolution, lay simply, and cost is cheap.Its is earliest
Applied to space industry, it is applied to the monitoring in the directions such as electric power, communication, engineering successively in developed country.From the nineties, I
State begins to carry out the application study of optical fiber sensing technology.And in all Distributed Optical Fiber Sensing Techniques, BOTDR relies on its energy
Measurement temperature, strain and other a variety of physical quantitys, while also there is the advantages such as spatial resolution is high, distance sensing is remote, can be in time
It was found that the problem of in large-scale structure and hidden danger, thus be widely used in safety monitoring.
Under the severe radiation environment in universe, ionising radiation produces radiation effect to be influenceed on BOTDR system, can be by light
The reinforcing of electrical part improves, but optical fiber must be exposed under radiation environment for a long time as the sensing element of BOTDR system.
Under the influence of radiation, inside of optical fibre can produce colour center, and this can produce certain influence, obvious shadow to the sensing capability of optical fiber
Sound is exactly the increase being lost.Although the pulse width of light or the method for power can be detected to improve into fine optical signal by increasing
Energy, so as to increase the sensing scope of system, but the width for increasing light pulse can cause the spatial resolution of system to decline；
And for improving incident optical power, the presence that Brillouin is excited threshold value is limited to, when detection of optical power is less than Brillouin's stimulated threshold
During value, the energy of Brillouin's rear orientation light and the energy for detecting light are linear.It is excited when detection of optical power exceedes in cloth
When threshold value is excited in deep pool, detection light energy is transferred to Brillouin's stokes light, increases the energy of Brillouin's stokes light, and
Detection light energy can decay rapidly, and the dynamic range for ultimately resulting in system declines.Therefore there is an urgent need to research and propose a kind of raising
The method of BOTDR service lifes under radiation environment.
The content of the invention
In order to solve the technical problem that above-mentioned background technology proposes, the present invention is intended to provide a kind of BOTDR system and lifting
The method of the lifetime of system, solve because space radiation environment causes optical fiber to produce colour center effect, and damage the transmission of sensor fibre
Consumption increase, BOTDR system distance sensing reduce.
In order to realize above-mentioned technical purpose, the technical scheme is that：
A kind of BOTDR system worked under space radiation environment, including light source module, the first coupler, Electro-optical Modulation
Module, pulse generating module, Optical pulse amplification module, circulator, light polarization disturbance module, the second coupler, the 3rd coupler,
First optical detection module, scan module, signal processing module, the second optical detection module, feedback module and current control module；Light
Source module sends continuous light, and the continuous light is divided into the continuous light of two-way that energy do not wait by the first coupler, and wherein energy is higher
Continuous light input Electro-optical Modulation module all the way, the relatively low light continuous all the way of energy is as relevant local oscillator light input light polarization scrambling mould
Block, Electro-optical Modulation module pulse electrical signal according to caused by pulse generating module believe the continuous light modulation of input into pulsed light
Number, pulsed optical signals injection fibre after the amplification of Optical pulse amplification module, obtained by circulator along the backward of fiber distribution
Brillouin scattering optical signal, the backward Brillouin scattering optical signal that the second coupler exports circulator and light polarization disturbing signal
The local oscillator optical signal of the random distribution of module output carries out coupling and is concerned with, and exports Brillouin scattering optical signal, and the 3rd coupler will
The Brillouin scattering optical signal is divided into the two ways of optical signals that energy does not wait, and wherein the higher optical signal of energy is through the first optical detection mould
Brillouin scattering electric signal is obtained after the opto-electronic conversion of block, then through scan module frequency sweep, signal processing module filter and amplification, is obtained
Corresponding backward Brillouin scattering electric signal, the relatively low optical signal of another way energy is through the second optical detection module input feedback mould
Block, feedback module realize the control of the light signal power sent to light source module by control electric current control module.
Further, the course of work of the feedback module is as follows：
(a) when light source power is not lifted, cut-point A is obtained：The power of Brillouin spectrum increases and reduced with distance,
When the power of certain opening position Brillouin spectrum is close to background noise power, i.e., when can not be normal through Lorentz fit, by this
Position mark is A；
(b) control source current to lift light source power, and in this process, judge whether A points are excited：If A points
Phenomenon is excited in generation, then the power near A points is not by fixed attenuation coefficient attenuation, but produces violent shake, when A points are sent out
Life is excited after phenomenon to be excited until A points do not produce, it is necessary to adjust back light source power；
(c) after lifting light source power, judge that the solstics B of testing distance whether there is effective brillouin scattering signal：
If the signal power at B is not flooded by noise, i.e., it can correctly carry out Lorentz fit, then it represents that now exist at B effective
Transducing signal.
Further, the continuous light that the first coupler sends light source module is divided into energy ratio for 9:The 1 continuous light of two-way.
Further, the Brillouin scattering optical signal of input is divided into energy ratio for 95 by the 3rd coupler:5 two-way light letter
Number.
Further, the first optical detection module uses APD avalanche diodes.
A kind of method for lifting the above-mentioned BOTDR system life-span, comprises the following steps：
(1) spectrum of cut-point A and first paragraph optical fiber is obtained using BOTDR system：
If O points are the signal incidence end of optical fiber, the power of detecting optical pulses is P0, B points are the distalmost end for requiring detection, just
Beginning light source power P0 will ensure do not produce be excited phenomenon on the premise of lifted as far as possible, to lift sensing effect；Before irradiation
The maximum range of system is OC, and after system is radiated, the loss of sensor fibre can increase, and cause system not receive
The effective brillouin scattering signal of B points, now first keep incident optical power P0Constant, record can now obtain effective Brillouin
The solstics A of scattered signal, while obtain the Brillouin spectral lines backwards of OA section optical fiber；
(2) Brillouin spectral lines of the OA section optical fiber to being obtained in step (1) are fitted processing, so as to obtain the section
Brillouin's crest frequency of optical fiber；
(3) incident optical signal power is lifted, obtains the spectrum of second segment optical fiber after A points：
Gradually lifting light source power, until that can ensure：Stimulated Brillouin scattering is not produced at point A, and there are at B points
The brillouin scattering signal of effect；Now stop lifting light source power, and measured using the power using BOTDR system, obtain A points
Effective sensing data of fine section between B points；
(4) processing is fitted backwards to Brillouin spectral lines to the AB fiber segments that are obtained in step (3), so as to obtain
The crest frequency of the Brillouin spectral line of this section of optical fiber；
(5) crest frequency of the Brillouin spectral line to being obtained in step (2) and step (4) carries out splicing, so as to
To whole section of sensor fibre OB Brillouin's peak frequency information；
(6) light source power is adjusted back to former power P 0, return to step (1).
Further, in step (3), if after lifting light source power, OA section optical fiber is not also excited phenomenon, then may be used
The measurement of crest frequency is carried out with the Brillouin spectral lines of the full section optical fiber OB after hoisting power.
The beneficial effect brought using above-mentioned technical proposal：
The present invention is measured by several times by adding feedback module in traditional BOTDR system, using different launched powers
The different piece of whole piece sensor fibre, and deliberately light of the order close to light source incidence end in the measurement process away from luminous source optical fiber section
Fine section produces stimulated Brillouin scattering phenomenon.It is whole so as to obtain by the fitting respectively to gradation measurement result and overall splicing
Effective Brillouin's crest frequency spectral line of bar sensor fibre, according to Brillouin shift and temperature or the relational implementation of strain to temperature
Degree or the sensing of strain.
Brief description of the drawings
Fig. 1 is the block diagram of system of the present invention；
Fig. 2 is the schematic diagram that optical fiber attenuation converts with dose of radiation；
Fig. 3 is the relation schematic diagram of Brillouin spectrum power and distance sensing；
Fig. 4 is the schematic diagram for lifting incident optical signal power.
Embodiment
Below with reference to accompanying drawing, technical scheme is described in detail.
Fig. 1 be the present invention BOTDR system structural representation, including light source module, the first coupler, light polarization disturbance mould
Block, Electro-optical Modulation module, pulse generating module, Optical pulse amplification module, circulator, the second coupler, the first optical detection module,
Scan module, signal processing module, the 3rd coupler, the second optical detection module, feedback module and current control module, wherein light
Source module is connected with the first coupler, and the narrow linewidth laser in light source module sends continuous light, is divided into by the first coupler
The continuous light of two-way：The continuous light of the first via and the second road continuous light (energy ratio 9:1), wherein the continuous light of the first via is sent into electric light tune
Molding block, the continuous light in the second road is as relevant local oscillator light；Electro-optical Modulation module pulse telecommunications according to caused by pulse generating module
Number by the continuous light modulation of the first via into pulsed optical signals, the pulsed optical signals pass through injection light after the amplification of Optical pulse amplification module
Fibre, the backward Brillouin scattering optical signal along fiber distribution is obtained by circulator；Second coupler is defeated by circulator again
The backward Brillouin scattering optical signal gone out carries out coupling relevant, acquisition Brillouin scattering respectively with the local oscillator optical signal of random distribution
Optical signal.
Brillouin scattering optical signal is divided into two-way via the 3rd coupler, wherein the optical signal of 95% energy is through all the way
After the opto-electronic conversion of one optical detection module obtains Brillouin scattering electric signal, carry out frequency sweep, filter and amplification, gather corresponding to acquisition
Backward Brillouin scattering electric signal, analyzing and processing is obtained along the Brillouin shift at the every bit of fiber distribution, according to the cloth
In deep frequency displacement obtain the change of optical fiber environment temperature or strain；The optical signal of the energy of another way 5% is by entering the second optical detection
In module, the information then composed containing Power of Brillouin along optical fiber can be passed to feedback module, and feedback module passes through control electric current
Control module realizes the control to light source power.
The function that feedback control module needs to realize includes：
A. when light source power is not lifted, cut-point A is obtained：The power of Brillouin spectrum increases and reduced with distance,
It is point A by this position mark when the power of Brillouin spectrum is close to background noise power (can not be normal through Lorentz fit)；
B. control source current to lift light source power, and in this process, judge whether A points are excited：If A points
Phenomenon is excited in generation, then the power near A points is not by fixed attenuation coefficient attenuation, but produces violent shake.When A points are sent out
Life is excited after phenomenon to be excited until A is not produced, it is necessary to adjust back light source power；
C. after lifting light source power, judge that the solstics B of testing distance whether there is effective brillouin scattering signal：If
Signal power at this is not flooded by noise and (can correctly be carried out Lorentz fit), then it represents that is now existed at B and is effectively passed
Feel signal.
Fig. 2 is the schematic diagram for radiating induced attenuation, and the loss of sensor fibre can increase with the increase of dose of radiation, that is, pass
The maximum detectable range of sensing system can be reduced with the increase of radiation length；If on the premise of distance sensing is constant, when
After dose of radiation increase to a certain extent, the brillouin scattering signal of optical fiber connector is eventually flooded by noise, cause BOTDR without
Method normal work.
The step of present invention lifting BOTDR system life-span, is as follows.
Step 1, the spectrum of cut-point A and first paragraph optical fiber is obtained using BOTDR system：
Fig. 3 is the relation schematic diagram of Brillouin spectrum power and distance sensing, and O points are the signal incidence end of optical fiber, detect light
The power of pulse is P0, B points are the distalmost end for requiring detection.Primary light source power P 0 will be before ensureing not producing and be excited phenomenon
Put and lifted as far as possible, to lift sensing effect.The maximum range of system is OC before irradiation, but when system is by one
After the radiation for determining dosage, the loss of sensor fibre can increase, and cause system not receive the effective brillouin scattering signal of B points
(being flooded by noise).Now first keep incident optical power P0Constant, the farthest sensing location A points recorded now (can obtain effectively
The solstics of brillouin scattering signal)；The Brillouin spectral lines backwards of OA section optical fiber are obtained simultaneously.
It is noted that with the increase of dose of radiation, the determination of A points is the dose of radiation dynamic change being subject to according to system
's.It is embodied in：It in light source power is P that A points, which are,0Farthest effective distance sensing when (not having hoisting power).
A points are obtained by the feedback control module of system；It is embodied in：Before light source power is lifted, Brillouin spectrum
Power with distance increase and reduce, when the power of Brillouin spectrum (can not be intended close to background noise power normal through Lorentz
Close) when, it is point A by this position mark.
Step 2, the Brillouin spectral line of the OA section optical fiber to being obtained in step 1 is fitted processing, so as to obtain the Duan Guang
Fine Brillouin's crest frequency.
Step 3, incident optical signal power is lifted, obtains the spectrum of second segment optical fiber after A points：
Fig. 4 is the schematic diagram for lifting incident optical signal power.Gradually lifting light source power, until that can ensure：(1) point A
Place, which is not produced at stimulated Brillouin scattering (2) B points, has effective brillouin scattering signal.Now stop lifting light source power,
And measured using the power using BOTDR system, obtain effective sensing data of fine section between A points and B points.In view of radiating ring
Border may have an impact to the threshold value of optical fiber, if after lifting light source power in step 3, OA sections optical fiber is not also excited existing
As, then it can use the Brillouin spectral lines of the full section optical fiber OB after hoisting power to carry out the measurement of crest frequency, it is more preferable to obtain
Brillouin spectral lines.
It is noted that with the increase of dose of radiation, the lifting amplitude of incident optical power is according to the reflection specific work(of spectral line
Rate and dynamic change.It is embodied in：The power ascension of light source will ensure that A points do not produce simultaneously and be excited phenomenon, and B points are present
Effective transducing signal.
The current control module that the lifting of light source power is controlled by feedback module regulates and controls.
Whether A points are excited to be judged by feedback control module；It is embodied in：During light source power is lifted,
If A points, which produce, is excited phenomenon, the power near A points is not by fixed attenuation coefficient attenuation, but produces violent shake.When
A points are excited after phenomenon to be excited until A is not produced, it is necessary to adjust back light source power.
B points are judged with the presence or absence of effective brillouin scattering signal by feedback control module；It is embodied in：When lifting light
After source power, if the signal power of B points is not flooded by noise and (can correctly be carried out Lorentz fit), then it represents that now B points
In the presence of effective transducing signal.
In addition, it is contemplated that the power of stimulated scattering is bigger, to ensure system normal operation, will be divided into by the 3rd coupler
The optical signal of two-way is separately detected using different optical detection modules, it is proposed that the first optical detection module uses APD avalanche diodes.
Step 4, processing is fitted backwards to Brillouin spectral lines to the AB fiber segments that are obtained in step 3, so as to
To the crest frequency of the Brillouin spectral line of this section of optical fiber.
Step 5, the crest frequency of the Brillouin spectral line to being obtained in step 2 and step 4 carries out splicing, so as to obtain
Whole section of sensor fibre OB Brillouin's peak frequency information.
Step 6, readjustment light source power to former power P 0, repeat step 1 measures.
The technological thought of embodiment only to illustrate the invention, it is impossible to protection scope of the present invention is limited with this, it is every according to
Technological thought proposed by the present invention, any change done on the basis of technical scheme, each falls within the scope of the present invention.
Claims (7)
- A kind of 1. BOTDR system worked under space radiation environment, it is characterised in that：Including light source module, the first coupler, Electro-optical Modulation module, pulse generating module, Optical pulse amplification module, circulator, light polarization disturbance module, the second coupler, the Three couplers, the first optical detection module, scan module, signal processing module, the second optical detection module, feedback module and electric current control Molding block；Light source module sends continuous light, and the continuous light is divided into the continuous light of two-way that energy do not wait by the first coupler, wherein can The higher light continuous all the way input Electro-optical Modulation module of amount, the relatively low light continuous all the way of energy are inclined as relevant local oscillator light input light Shake disturbance module, Electro-optical Modulation module according to caused by pulse generating module pulse electrical signal by the continuous light modulation of input into arteries and veins Pulsed light signal, pulsed optical signals injection fibre after the amplification of Optical pulse amplification module, is obtained along fiber distribution by circulator Backward Brillouin scattering optical signal, the second coupler disturbs the backward Brillouin scattering optical signal that circulator exports with light polarization The local oscillator optical signal of the random distribution of dynamic signaling module output carries out coupling and is concerned with, and exports Brillouin scattering optical signal, the 3rd coupling Clutch by the Brillouin scattering optical signal be divided into energy not wait two ways of optical signals, the wherein higher optical signal of energy is through the first light Brillouin scattering electric signal is obtained after the opto-electronic conversion of detecting module, then is put through scan module frequency sweep, signal processing module filtering Greatly, backward Brillouin scattering electric signal corresponding to acquisition, the relatively low optical signal of another way energy input through the second optical detection module Feedback module, feedback module realize the control of the light signal power sent to light source module by control electric current control module.
- 2. the BOTDR system under space radiation environment is worked according to claim 1, it is characterised in that：The feedback mould The course of work of block is as follows：(a) when light source power is not lifted, cut-point A is obtained：The power of Brillouin spectrum increases and reduced with distance, when certain The power of opening position Brillouin spectrum is close to background noise power, i.e., when can not be normal through Lorentz fit, by this position Labeled as A；(b) control source current to lift light source power, and in this process, judge whether A points are excited：If A points produce Be excited phenomenon, then the power near A points is not by fixed attenuation coefficient attenuation, but produces violent shake, when A points occur by It is excited after swashing phenomenon, it is necessary to adjust back light source power until A points do not produce；(c) after lifting light source power, judge that the solstics B of testing distance whether there is effective brillouin scattering signal：If at B Signal power do not flooded by noise, i.e., can correctly carry out Lorentz fit, then it represents that now at B exist effectively sensing believe Number.
- 3. the BOTDR system according to claim 1 or claim 2 worked under space radiation environment, it is characterised in that：First coupling The continuous light that device sends light source module is divided into energy ratio for 9:The 1 continuous light of two-way.
- 4. the BOTDR system according to claim 1 or claim 2 worked under space radiation environment, it is characterised in that：3rd coupling The Brillouin scattering optical signal of input is divided into energy ratio for 95 by device:5 two ways of optical signals.
- 5. the BOTDR system according to claim 1 or claim 2 worked under space radiation environment, it is characterised in that：Described first Optical detection module uses APD avalanche diodes.
- A kind of 6. method for lifting the BOTDR system life-span described in claim 2, it is characterised in that comprise the following steps：(1) spectrum of cut-point A and first paragraph optical fiber is obtained using BOTDR system：If O points are the signal incidence end of optical fiber, the power of detecting optical pulses is P0, B points be require detection distalmost end, initial light Source power P0 will ensure do not produce be excited phenomenon on the premise of lifted as far as possible, to lift sensing effect；System before irradiation Maximum range be OC, after system is radiated, the loss of sensor fibre can increase, and cause system not receive B points Effective brillouin scattering signal, now first keep incident optical power P0Constant, record can now obtain effective Brillouin and dissipate The solstics A of signal is penetrated, while obtains the Brillouin spectral lines backwards of OA section optical fiber；(2) Brillouin spectral lines of the OA section optical fiber to being obtained in step (1) are fitted processing, so as to obtain this section of optical fiber Brillouin's crest frequency；(3) incident optical signal power is lifted, obtains the spectrum of second segment optical fiber after A points：Gradually lifting light source power, until that can ensure：Stimulated Brillouin scattering is not produced at point A, and is existed at B points effective Brillouin scattering signal；Now stop lifting light source power, and measured using the power using BOTDR system, obtain A points and B Effective sensing data of fine section between point；(4) processing is fitted backwards to Brillouin spectral lines to the AB fiber segments that are obtained in step (3), so as to obtain the section The crest frequency of the Brillouin spectral line of optical fiber；(5) crest frequency of the Brillouin spectral line to being obtained in step (2) and step (4) carries out splicing, whole so as to obtain Section sensor fibre OB Brillouin's peak frequency information；(6) light source power is adjusted back to former power P 0, return to step (1).
- 7. method according to claim 6, it is characterised in that：In step (3), if after lifting light source power, OA section light Fibre is not also excited phenomenon, then can use the Brillouin spectral lines of the full section optical fiber OB after hoisting power to carry out crest frequency Measurement.
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Citations (9)
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