CN101832832A - Optical fiber Fabry-Perot pressure sensor and production method thereof - Google Patents

Optical fiber Fabry-Perot pressure sensor and production method thereof Download PDF

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CN101832832A
CN101832832A CN 201010185466 CN201010185466A CN101832832A CN 101832832 A CN101832832 A CN 101832832A CN 201010185466 CN201010185466 CN 201010185466 CN 201010185466 A CN201010185466 A CN 201010185466A CN 101832832 A CN101832832 A CN 101832832A
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optical fiber
sensor body
perot
flexible sheet
fabry
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CN101832832B (en
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江俊峰
刘铁根
刘琨
姜丽娟
刘宇
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Tianjin University
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Abstract

The invention relates to an optical fiber Fabry-Perot pressure sensor and a production method thereof. The sensor can be used for detecting relative pressure and absolute pressure of liquid and gas and can also be used for probing acoustic and ultrasonic signal signals and the like. The structure mainly consists of three parts of an optical fiber, an elastic diaphragm and a sensor body. A Fabry-Perot cavity can be formed by adopting two ways. The elastic diaphragm is directly connected with the optical fiber, and the optical fiber is inserted in a hole on the sensor body, when the external pressure changes for causing the deformation of the elastic diaphragm, the optical fiber can move axially in the sensor body, thereby changing the length of the optical fiber Fabry-Perot cavity; and the cavity length change can be extracted by scanning the light spectrum in the optical fiber Fabry-Perot pressure sensor or extracting low coherence interferometric fringes after being accessed into a broadband light source, thereby obtaining the pressure information. The structure can avoid the defect that the deformation of the diaphragm of the traditional optical fiber Fabry-Perot sensor can not be excessive, and further obtain higher measurement precision.

Description

Optical fibre Fabry-perot pressure transducer and preparation method thereof
[technical field]: the present invention relates to the fibre optic compression sensor field, this sensor can be used for the relative pressure and the absolute pressure of tracer liquid, gas, also can be used for sound wave, the detection of ultrasonic signal etc.
[background technology]:
The optical fibre Fabry-perot pressure transducer is a kind of in the fibre optic compression sensor, it is usually by fiber end face and diaphragm end face mechanics Fabry-Perot-type micro-resonant cavity, when pressure acts on the diaphragm, will make diaphragm deformation, and make changing of Fa-Po cavity long hair, thereby realize sensing.Some design proposals have been proposed in recent years, as (DonC.Abeysinghe such as calendar year 2001 Don C.Abeysinghe, Samhita Dasgupta, Joseph T.Boyd, Howard E.Jackson, A Novel MEMSpressure sensor fabricated on an optical fiber, IEEE Photonics Technology Letters, 2001,13 (9): 993-995) be respectively 200 microns and 400 microns in cladding diameter, core diameter is that the multimode optical fiber end face of 190 microns and 360 microns etches microcavity, constitutes sensor at this straight end-face key silicon chip that closes then; (Juncheng Xu such as Juncheng Xu in 2005, Xingwei Wang, Kristie L.Cooper, Anbo Wang, Miniature all-silicafiber optic pressure and acoustic sensors, Optics Letters, 2005,30 (24): 3269-3271) utilize the silica fibre of the big core diameter of hydrofluoric acid etch to obtain quartz diaphragm, quartz diaphragm is fused to the kapillary end, and the single-mode fiber end face of cutting extend in this kapillary and just constituted the optical fibre Fabry-perot pressure transducer with quartz diaphragm; (Xiaodong Wang such as Xiaodong Wang in 2006, Baoqing Li, Onofrio L.Russo, et.al., Diaphragm design guidelines and an optical pressure sensor based on MEMStechnique, Journal of microelectronics, 2006,37:50-56) at the little microcavity body that processes of the Pyrex of 500 micron thickness glass, wafer bonding is on glass at Pyrex then, and has constituted the optical fibre Fabry-perot chamber with the fiber end face that stretches into cavity; (Wang Ming, Chen Xuxing, Ge Yixian etc. such as Wang Ming in 2006, Fabry-Perot type optical fiber pressure transducer and preparation method thereof, number of patent application: 200610096596.5) utilize monocrystalline silicon piece, glass round tube, optical fiber ring flange and Optical fiber plug have made up the optical fibre Fabry-perot chamber.But be out of shape when excessive as the silicon chip of pressure-sensitive diaphragm, silicon chip can not keep the plane, and cause bigger optical energy loss, have influence on the performance of Fabry-Perot-type cavity.Therefore when reality was used, Fabry-Perot-type cavity was limited in more among a small circle, and the silicon chip distortion does not often allow excessive, for example can not be greater than 25% of thickness.In order to improve the measuring accuracy of measuring full scale, we need be under same pressure limit, and the diaphragm deformation scope is bigger, and this just makes diaphragm on-plane surface problem on deformation to consider and to overcome.In order to overcome this problem points, we propose the optical fibre Fabry-perot sensor of new structure.
[summary of the invention]: the present invention seeks to overcome the above-mentioned problems in the prior art, a kind of novel optical fibre Fabry-perot pressure transducer and preparation method thereof is provided.This sensor can be avoided the defective that traditional fiber Fabry-Perot sensor diaphragm distortion can not be excessive, can obtain higher measuring accuracy.
First kind of optical fibre Fabry-perot pressure transducer provided by the invention comprises 3 parts:
Sensor body: the optical fibre Fabry-perot pressure sensor body is the supporting construction of sensor and the optical fiber guide structure when sliding, its shape can be cylindrical or cuboid, the two ends relative position of sensor body respectively has a blind hole, and the outer end of one of them blind hole has a pit and forms shoulder hole; The manufacturing materials of sensor body can be Pyrex glass or fused silica material;
Flexible sheet: be used for experiencing the variation of pressure, one side bonds of flexible sheet has one section optical fiber, the end face of this optical fiber is as the required reflecting surface of Fabry-Perot-type cavity, the flexible sheet that is bonded with optical fiber is inserted in the pit of sensor body one end and is fixing, and the end face of optical fiber does not contact the mechanics Fabry-Perot-type cavity with bottom surface, blind hole hole; The material of flexible sheet can be a monocrystalline silicon piece, quartzy thin slice, polymer flake, and metallic membrane.
Transmission Fibers: be positioned in the blind hole of the sensor body other end and fixing, this Transmission Fibers end face closely contacts with bottom surface, blind hole hole, and bonding optical fiber can be single-mode fiber on Transmission Fibers and the flexible sheet, also can be multimode optical fiber.Fiber end face can be that directly use the cutting back, also can plate reflectance coating.
Second kind of optical fibre Fabry-perot pressure transducer provided by the invention comprises 3 parts equally:
Sensor body: the optical fibre Fabry-perot pressure sensor body is the supporting construction of sensor and the optical fiber guide structure when sliding, it is shaped as cylindrical or cuboid, have a through hole in the middle of the sensor body, an end of through hole has a pit and forms shoulder hole;
Flexible sheet: be used for experiencing the variation of pressure, a side bonds of flexible sheet has one section optical fiber, and the end face of optical fiber is as the required reflecting surface of Fabry-Perot-type cavity, and the flexible sheet that is bonded with optical fiber is inserted in the pit of sensor body one end and be fixing;
Transmission Fibers: be positioned over the through hole and fixing from the sensor body other end, do not contact with the mechanics Fabry-Perot-type cavity between the end face of bonding optical fiber on this Transmission Fibers end face and the flexible sheet.
First kind of optical fibre Fabry-perot pressure transducer among the present invention is produced as follows, and is example with monocrystalline silicon piece and Pyrex glass material:
1, flexible sheet is made: utilize cut to go out the silicon diaphragm of required size, and make small striped with laser on the silicon diaphragm two sides, to destroy the reflection of this face, diaphragm thickness can be 10 μ m~300 μ m according to pressure measurement range;
2, the fiber end face that utilizes fiber cut cutter cutting optical fibre to obtain, then with the pen type cutter microscopically cut optical fiber to Len req (about 1~3mm), utilize epoxide-resin glue to be vertically fixed on the diaphragm this segment optical fiber;
3, the making of sensor body: utilize Pyrex glass or fused silica material to make sensor body, with the Pyrex glass material is example, at first sensor body being made external diameter is 1mm~5mm, length is the right cylinder of 5~15mm, get out the blind hole that diameter is 127 μ m respectively from sensor body two, further that the processing of blind hole end face is smooth subsequently, be about 500 μ m in working depth of sensor body, diameter is the shallow hole of 0.6~4.5mm, as the stressed support of flexible sheet;
4, to be stained with the flexible sheet of segment optical fiber from the blind hole of an insertion of the sensor body diameter 127 μ m of band shallow hole, this moment, fiber end face did not contact with blind hole hole bottom face on the sensor body, the mechanics Fabry-Perot-type cavity, another root optical fiber inserts from the other end of sensor body as Transmission Fibers, with utilize epoxide-resin glue to fix after blind hole end face in the sensor body closely contacts, so that input/output signal light passes through, utilize the control in real time of spectrometer or low coherence interferometer to be bonded at the insertion depth of the optical fiber on the silicon diaphragm, when arriving design attitude (fiber end face of this section optical fiber apart from glass column in hole end surface 20~400 μ m places), silicon diaphragm is fixed on the shallow hole of glass column by the mode of glue bond.Solidified one hour under 60 ℃ the temperature in electrocaloric effect, or solidified 24 hours under the normal temperature, sensor promptly completes.
Second kind of optical fibre Fabry-perot pressure transducer among the present invention is produced as follows, and is example with monocrystalline silicon piece and Pyrex glass material:
1, flexible sheet is made: utilize cut to go out the silicon diaphragm of required size, and make small striped with laser on the silicon diaphragm two sides, to destroy the reflection of this face, diaphragm thickness can be 10 μ m~300 μ m according to pressure measurement range;
2, the fiber end face that utilizes fiber cut cutter cutting optical fibre to obtain, then with the pen type cutter microscopically cut optical fiber to Len req (about 1~3mm), utilize epoxide-resin glue to be vertically fixed on the diaphragm this segment optical fiber;
3, the making of sensor body: utilize Pyrex glass or fused silica material to make sensor body, with the Pyrex glass material is example, at first sensor body being made external diameter is 1mm~5mm, length is the right cylinder of 5~15mm, on sensor body, get out the through hole that diameter is 127 μ m, be 500 μ m in working depth of sensor body then, diameter is the shallow hole of 0.6~4.5mm, as the stressed support of flexible sheet;
4, the flexible sheet that will be stained with segment optical fiber inserts the through hole of diameter 127mm from one of the sensor body of band shallow hole, and the mode by glue bond or anode linkage is fixed on flexible sheet on the shallow hole of sensor body; Then another root optical fiber is inserted from the hole, other end of sensor body as Transmission Fibers, the fiber end face of two sections optical fiber does not contact with the mechanics Fabry-Perot-type cavity, utilize spectrometer or low coherence interferometer to control the insertion depth of optical fiber in real time, when two sections fiber end face distances reach the design attitude of 20~400 μ m, utilize epoxide-resin glue to fix, solidified one hour under 60 ℃ the temperature in electrocaloric effect, or solidified 24 hours under the normal temperature, the optical fibre Fabry-perot pressure transducer promptly completes.
The course of work of optical fibre Fabry-perot pressure transducer is as follows:
When pressure is done the time spent, flexible sheet (as silicon chip) deforms, flexible sheet will drive in the sticking hole of segment optical fiber on the cylinder shape sensor body thereon and slide, thereby change the distance between this fiber end face and the Transmission Fibers end face, and promptly the chamber of Fabry-Perot-type cavity is long.Behind the access band light source,, can extract the long variation in chamber, thereby obtain pressure information by to the spectral scan of optical fibre Fabry-perot pressure transducer or the extraction of low coherence interference striped.
Advantage of the present invention and good effect:
1. the optical fibre Fabry-perot sensor that proposes of the present invention allows flexible sheet to have bigger distortion and does not influence the performance of Fabry-Perot-type cavity.For traditional Fabry-Perot-type cavity, the pressure of experiencing when flexible sheet changes inhomogeneous or distortion greatly the time, and the distortion of diaphragm will destroy the planar process Fabry-Perot-type cavity, thereby influences sensing accuracy.Flexible sheet does not play the reflecting surface effect among the present invention, reflecting surface is provided by the short section of optical fiber that bonds together with it, therefore in whole diaphragm elastic deformation process, two reflectings surface in optical fibre Fabry-perot chamber remain parallel, have reduced greatly because the measuring error that the Fabry-Perot-type cavity performance descends and causes.
2. structure of the present invention is small and exquisite flexibly, sensor outer dia size can be as small as 1mm, and because two reflectings surface in optical fibre Fabry-perot chamber remain parallel, under the situation of not plating reflectance coating, the Fabry-Perot-type cavity that allows also is 550 μ m, and this just makes sensor production get up to be easy to.
3. the optical fibre Fabry-perot sensor of Ti Chuing can adopt full quartz material structure, it is quartz diaphragm, the quartz transducer body, optical fiber, each several part all can adopt laser bonding and realize not having glue encapsulation this moment, can be used on to require high and to the application of electromagnetic radiation sensitivity to the sensor temperature characteristic.
[description of drawings]:
Fig. 1 is a kind of optical fibre Fabry-perot pressure transducer synoptic diagram among the present invention;
Fig. 2 is an another kind of optical fibre Fabry-perot pressure transducer synoptic diagram among the present invention;
Fig. 3 is the demodulating system signal of optical fibre Fabry-perot pressure transducer;
Fig. 4 is the low coherence interference figure that obtains;
[embodiment]:
Embodiment 1: a kind of embodiment of optical fibre Fabry-perot pressure transducer
A kind of optical fibre Fabry-perot pressure transducer as shown in Figure 1, it is by flexible sheet 1, sensor body 6, optical fiber 2 and Transmission Fibers 7 are formed.Flexible sheet 1 adopts monocrystalline silicon piece to be formed by Laser Processing, and optical fiber 2 adopts the single-mode fiber cutting to form, and optical fiber 2 is fixed on the flexible sheet 1 by epoxide-resin glue.Sensor body 6 adopts the Pyrex glass processings, get out blind hole 8 and blind hole 9 thereon after, process plane 4 and plane 5, one 500 μ m shallow hole 10 of sensor body 6 left sides processing in the drawings again is as the support of flexible sheet 1.Optical fiber 2 is inserted in the blind hole 9 by the left side of sensor body 6, the end face 3 of optical fiber 2 and the plane 4 mechanics Fabry-Perot-type cavities of sensing body 6, the long initial length in chamber is measured in real time by spectral scan or low coherence interference striped and is determined, after the chamber reaches design length, flexible sheet 1 usefulness glue is fixed on the sensor body 6.Optical fiber 7 fits tightly with the plane 5 of sensor body 6, is used for the input and output of flashlight.When pressure effect flexible sheet 1, flexible sheet 1 deforms, and drive optical fiber 2 and in the blind hole 9 of sensor body 6, slide, thus the distance between the plane 4 of the end face 3 of change optical fiber 2 and sensor body 6, promptly the Fabry-Perot-type cavity chamber is long.Thereby pressure information is converted into chamber long pass sense information.
In the optical fibre Fabry-perot pressure transducer of the present invention
1. flexible sheet also can adopt quartzy thin slice, polymer flake, or metallic membrane;
2. sensor body also can adopt fused silica material;
3. optical fiber also can adopt standard multimode fiber, or other large core fiber.
Embodiment 2: the embodiment of another kind of optical fibre Fabry-perot pressure transducer
Another kind of optical fibre Fabry-perot pressure transducer as shown in Figure 2, it is by flexible sheet 1, sensor body 6, optical fiber 2 and Transmission Fibers 7 are formed.Flexible sheet 1 adopts monocrystalline silicon piece to be formed by Laser Processing, and optical fiber 2 adopts the single-mode fiber cutting to form, and optical fiber 2 is fixed on the flexible sheet 1 by epoxide-resin glue.Sensor body 6 adopts the Pyrex glass processing, gets out through hole 12 thereon, and sensor body 6 left sides process one 500 μ m shallow hole 10 in the drawings again, as the support of flexible sheet 1.Optical fiber 2 is inserted in the through hole 12 by the left side of sensor body 6, then flexible sheet 1 usefulness glue is fixed on the sensor body 6.Transmission Fibers 7 forms end face 11 through cutting, insert from the right side of sensor body 6, this moment optical fiber 2 the end face 11 mechanics Fabry-Perot-type cavities of end face 3 and optical fiber 7, the long length in chamber is measured in real time by spectral scan or low coherence interference striped and is determined, after the chamber reaches design length, optical fiber 7 usefulness glue are fixed on the sensor body 6.Optical fiber 7 also is used for the input and output of flashlight simultaneously.When pressure effect flexible sheet 1, flexible sheet 1 deforms, and drive optical fiber 2 and in the through hole 12 of sensor body 6, slide, thus the distance between the end face 11 of the end face 3 of change optical fiber 2 and optical fiber 7, promptly the Fabry-Perot-type cavity chamber is long.Thereby pressure information is converted into chamber long pass sense information.
In the optical fibre Fabry-perot pressure transducer of the present invention
1. flexible sheet also can adopt quartzy thin slice, polymer flake, or metallic membrane;
2. sensor body also can adopt fused silica material or stupalith;
3. optical fiber also can adopt standard multimode fiber, or other large core fiber.
Embodiment 3: the cavity length demodulating of optical fibre Fabry-perot pressure transducer
The sensor-based system of optical fibre Fabry-perot pressure transducer as shown in Figure 3, the light that cavity length demodulating wideband light source 13 sends is divided into two-beam by fiber coupler 14, wherein one the tunnel directly by 15 reflections of optical fiber faraday polariscope, other one the road is reflected by optical fiber faraday polariscope 16 through optical-fibre delay line 17 earlier again, the two-way reflected light closes bundle through fiber coupler 14 again, incide optical fibre Fabry-perot pressure transducer 20 through circulator 21, the light signal of optical fibre Fabry-perot pressure transducer 20 reflected backs arrives detector 19 through circulator 21, carries out analog to digital conversion and data processing by TT﹠C system 18.TT﹠C system is carried out optical path scanning at 18 control optical-fibre delay lines 17, thereby obtain the low coherence interference striped, by measuring the peak distance of zero order interference fringe envelope and 1 grade of interference fringe envelope, the chamber long letter breath of optical fibre Fabry-perot pressure transducer can be obtained, and then pressure information can be converted into.Fig. 4 adopts thick to be the gas pressure measurement result of optical fibre Fabry-perot pressure transducer when pressurization and decompression process of 30 μ m silicon diaphragms and single-mode fiber, better linearity degree and repeatability are arranged.

Claims (7)

1. optical fibre Fabry-perot pressure transducer is characterized in that this sensor comprises following three parts:
Sensor body: the optical fibre Fabry-perot pressure sensor body is the supporting construction of sensor and the optical fiber guide structure when sliding, it is shaped as cylindrical or cuboid, the two ends relative position of sensor body respectively has a blind hole, and the outer end of one of them blind hole has a pit and forms shoulder hole;
Flexible sheet: be used for experiencing the variation of pressure, one side bonds of flexible sheet has one section optical fiber, the end face of this optical fiber is as the required reflecting surface of Fabry-Perot-type cavity, the flexible sheet that is bonded with optical fiber is inserted in the pit of sensor body one end and is fixing, and the end face of optical fiber does not contact the mechanics Fabry-Perot-type cavity with bottom surface, blind hole hole;
Transmission Fibers: be positioned in the blind hole of the sensor body other end and fixing, this Transmission Fibers end face closely contacts with bottom surface, blind hole hole.
2. optical fibre Fabry-perot pressure transducer is characterized in that this sensor comprises following three parts:
Sensor body: the optical fibre Fabry-perot pressure sensor body is the supporting construction of sensor and the optical fiber guide structure when sliding, it is shaped as cylindrical or cuboid, have a through hole in the middle of the sensor body, an end of through hole has a pit and forms shoulder hole;
Flexible sheet: be used for experiencing the variation of pressure, a side bonds of flexible sheet has one section optical fiber, and the end face of optical fiber is as the required reflecting surface of Fabry-Perot-type cavity, and the flexible sheet that is bonded with optical fiber is inserted in the pit of sensor body one end and be fixing;
Transmission Fibers: be positioned over the through hole and fixing from the sensor body other end, do not contact with the mechanics Fabry-Perot-type cavity between the end face of bonding optical fiber on this Transmission Fibers end face and the flexible sheet.
3. optical fibre Fabry-perot pressure transducer according to claim 1 and 2, the material that it is characterized in that described flexible sheet is a monocrystalline silicon piece, quartzy thin slice, polymer flake or metallic membrane; The two sides of flexible sheet is manufactured with small striped, to destroy the reflection of this face.
4. optical fibre Fabry-perot pressure transducer according to claim 1 and 2, the material that it is characterized in that described sensor body is Pyrex glass or fused silica material.
5. optical fibre Fabry-perot pressure transducer according to claim 1 and 2, it is characterized in that optical fiber bonding on described Transmission Fibers and the flexible sheet is single-mode fiber or multimode optical fiber, fiber end face can be that directly use the cutting back, also can plate reflectance coating.
6. the method for making of the described optical fibre Fabry-perot pressure transducer of claim 1 is characterized in that this method comprises the steps:
1st, flexible sheet is made: utilize cut to go out the silicon diaphragm of required size, and make small striped with laser on the silicon diaphragm two sides, to destroy the reflection of this face, diaphragm thickness is 10 μ m~300 μ m according to pressure measurement range;
2nd, the fiber end face that utilizes fiber cut cutter cutting optical fibre to obtain cuts optical fiber to Len req with the pen type cutter at microscopically then, utilizes epoxide-resin glue to be vertically fixed on the flexible sheet this segment optical fiber;
3rd, the making of sensor body: utilize Pyrex glass or fused silica material to make sensor body, at first sensor body being made external diameter is that 1mm~5mm, length are the right cylinder of 5~15mm, get out the blind hole that diameter is 127 μ m respectively from sensor body two, further that the processing of blind hole end face is smooth subsequently, in working depth of sensor body is 500 μ m, diameter is the shallow hole of 0.6~4.5mm, as the stressed support of flexible sheet;
The 4th, to be stained with the flexible sheet of segment optical fiber from an insertion of the sensor body blind hole of band shallow hole, this moment, fiber end face did not contact with blind hole hole bottom face, the mechanics Fabry-Perot-type cavity, another root optical fiber inserts from the other end of sensor body as Transmission Fibers, with utilize epoxide-resin glue to fix after hole end surface in the sensor body closely contacts, so that input/output signal light passes through, utilize spectrometer or low coherence interferometer to control the optical fiber insertion depth that is bonded on the flexible sheet in real time, when the design attitude at blind hole bottom surface 20~400 μ m places of fiber end face on sensor body of this section optical fiber, the mode by glue bond is fixed on flexible sheet on the shallow hole of sensor body; Solidified one hour under 60 ℃ the temperature in electrocaloric effect, or solidified 24 hours under the normal temperature, the optical fibre Fabry-perot pressure transducer promptly completes.
7. the method for making of the described optical fibre Fabry-perot pressure transducer of claim 2 is characterized in that this method comprises the steps:
1st, flexible sheet is made: utilize cut to go out the silicon diaphragm of required size, and make small striped with laser on the silicon diaphragm two sides, to destroy the reflection of this face, diaphragm thickness is 10 μ m~300 μ m according to pressure measurement range;
2nd, the fiber end face that utilizes fiber cut cutter cutting optical fibre to obtain cuts optical fiber to Len req with the pen type cutter at microscopically then, utilizes epoxide-resin glue to be vertically fixed on the flexible sheet this segment optical fiber;
3rd, the making of sensor body: utilize Pyrex glass or fused silica material to make sensor body, at first sensor body being made external diameter is that 1mm~5mm, length are the right cylinder of 5~15mm, on sensor body, get out the through hole that diameter is 127 μ m, be 500 μ m in working depth of sensor body then, diameter is the shallow hole of 0.6~4.5mm, as the stressed support of flexible sheet;
4th, the flexible sheet that will be stained with segment optical fiber inserts the through hole from one of the sensor body of band shallow hole, and the mode by glue bond or anode linkage is fixed on flexible sheet on the shallow hole of sensor body; Then another root optical fiber is inserted from the hole, other end of sensor body as Transmission Fibers, the fiber end face of two sections optical fiber does not contact with the mechanics Fabry-Perot-type cavity, utilize spectrometer or low coherence interferometer to control the insertion depth of optical fiber in real time, when two sections fiber end face distances reach the design attitude of 20~400 μ m, utilize epoxide-resin glue to fix, solidified one hour under 60 ℃ the temperature in electrocaloric effect, or solidified 24 hours under the normal temperature, the optical fibre Fabry-perot pressure transducer promptly completes.
CN2010101854665A 2010-05-28 2010-05-28 Optical fiber Fabry-Perot pressure sensor and production method thereof Expired - Fee Related CN101832832B (en)

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