CN114791294A - Optical fiber sensor and method based on Mach-Zehnder interference - Google Patents

Optical fiber sensor and method based on Mach-Zehnder interference Download PDF

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CN114791294A
CN114791294A CN202210465674.3A CN202210465674A CN114791294A CN 114791294 A CN114791294 A CN 114791294A CN 202210465674 A CN202210465674 A CN 202210465674A CN 114791294 A CN114791294 A CN 114791294A
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optical fiber
fiber
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bending
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刘博�
吴泳锋
任建新
毛雅亚
毛贝贝
吴翔宇
孙婷婷
赵立龙
戚志鹏
李莹
王凤
哈特
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Nanjing University of Information Science and Technology
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    • 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
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Abstract

The invention discloses an optical fiber sensor and a method based on Mach-Zehnder interference in the field of optical fiber sensing, which comprises an input single-mode optical fiber, a first micro-bending conical optical fiber, a second micro-bending conical optical fiber and an output single-mode optical fiber which are sequentially connected; the pointed conical parts of the first micro-bending conical optical fiber and the second micro-bending conical optical fiber are spliced to form an S shape; light is transmitted to the first micro-bending conical optical fiber through the fiber core of the input single-mode optical fiber, and the light is transmitted to the second micro-bending conical optical fiber through the first micro-bending conical optical fiber; the light transmitted by the high-order mode enters the fiber core through the cladding coupling in the second micro-bending conical fiber, interferes with the light transmitted by the fundamental mode, and is output through the output single-mode fiber; the invention can excite more high-order modes in the light transmission process, improves the refractive index of the high-order modes, effectively improves the strain sensitivity and the refractive index sensitivity of the optical fiber sensor, and simultaneously has simple manufacture of the optical fiber sensor and lower cost.

Description

Optical fiber sensor and method based on Mach-Zehnder interference
Technical Field
The invention belongs to the field of optical fiber sensing, and particularly relates to an optical fiber sensor and a method based on Mach-Zehnder interference.
Background
The optical fiber sensor has the advantages of compact structure, strong external interference resistance, sensitive sensing signal, large dynamic range and the like, so that the optical fiber sensor is widely applied to the sensing field such as temperature sensing, humidity sensing, strain sensing, transverse pressure sensing, refractive index sensing and the like. Among a series of optical fiber sensors, the optical fiber Mach-Zehnder interference sensor has unique advantages, such as the requirements of temperature insensitivity, strain high sensitivity, refractive index high sensitivity and the like can be realized, and the stability is relatively good. Therefore, the optical fiber Mach-Zehnder interferometer sensor is developed rapidly and widely applied. Among them, the measurement of strain and solution refractive index is one of the important application fields of the optical fiber Mach-Zehnder interferometer sensor.
The sensing mechanism of the optical fiber Mach-Zehnder interferometer is based on intermode interference, and the intermode interference is a phenomenon that modes in an optical waveguide are mutually coupled and interfered in the transmission process. In the optical fiber Mach-Zehnder interferometer sensor, the effective refractive indexes of different modes in the optical fiber are different, so that phase difference is generated, and interference among the different modes is realized. When the external environment changes (such as external refractive index and strain), the effective refractive index of the optical fiber changes to enable the mode to be recombined, the output interference waveform changes along with the mode, and the change of the environmental parameters can be measured by detecting the change, so that sensing is realized.
At present, the preparation method of the optical fiber sensing structure comprises dislocation fusion, fused biconical taper, optical fiber etching and the like, and in the prior art, a few high-order modes are excited in the optical transmission process, the refractive index of the high-order modes is low, the manufacturing cost is high, and the manufacturing procedure is complex.
Disclosure of Invention
The invention aims to provide an optical fiber sensor based on Mach-Zehnder interference and a method thereof.
In order to achieve the purpose, the technical scheme adopted by the invention is as follows:
the invention provides an optical fiber sensor based on Mach-Zehnder interference, which comprises an input single-mode optical fiber, a first micro-bending conical optical fiber, a second micro-bending conical optical fiber and an output single-mode optical fiber which are sequentially connected; the pointed cone parts of the first micro-bending cone-shaped optical fiber and the second micro-bending cone-shaped optical fiber are spliced to form an S shape;
light is transmitted into the first micro-bending conical fiber through the fiber core of the input single-mode fiber, the light is transmitted into the first micro-bending conical fiber and divided into two parts, one part of light is transmitted along the fiber core of the first micro-bending conical fiber in a fundamental mode, and the other part of light is coupled into the cladding of the first micro-bending conical fiber by the fiber core of the first micro-bending conical fiber and is excited into high-order mode transmission; the light is transmitted to a second micro-bending cone-shaped optical fiber through the first micro-bending cone-shaped optical fiber; light transmitted by a high-order mode in the second micro-bending conical fiber enters a fiber core of the second micro-bending conical fiber through the cladding of the second micro-bending conical fiber, and interferes with light transmitted by a fundamental mode in the fiber core of the second micro-bending conical fiber to form interference light, and the interference light is output through the output single-mode fiber.
Preferably, the bending angles of the input single mode fiber and the first, second and output single mode fibers are 30 to 60 degrees.
Preferably, the input single-mode fiber, the first microbend tapered fiber, the second microbend tapered fiber and the output single-mode fiber are communication single-mode fibers or small-diameter single-mode fibers or single-mode photonic crystal fibers.
Preferably, the core of the first microbend cone fiber and the core of the second microbend cone fiber are welded in a staggered manner.
Preferably, the high-order modes include cone-excited high-order modes and dislocation-excited high-order modes.
The second aspect of the present invention provides a method for manufacturing an optical fiber sensor based on Mach-Zehnder interference, including:
pretreating two single-mode fibers and carrying out dislocation fusion to obtain fusion fibers;
detecting the fusion spliced optical fiber through a spectrum analyzer to obtain a qualified fusion spliced optical fiber of which the extinction ratio, the free spectrum and the light intensity of the transmission spectrum meet a set range;
connecting one end of the qualified fusion spliced optical fiber with a broadband light source, connecting the other output end of the qualified fusion spliced optical fiber with a spectral frequency analyzer, and detecting the change condition of the transmission spectrum through the spectral frequency analyzer;
discharging, melting and heating the welding position of the qualified fusion spliced optical fiber, stretching and twisting the welding position of the qualified fusion spliced optical fiber to form an S shape, and acquiring an optical fiber sensor with a transmission spectrum meeting a set range;
and (4) carrying out solution refraction interference resistance detection and stress interference resistance detection on the S-shaped optical fiber sensor to obtain a qualified optical fiber sensor.
Preferably, the method for pretreating two single-mode optical fibers comprises the following steps: the fiber stripper is used for stripping the coating layers at one ends of the two single-mode fibers respectively, absorbent cotton is used for dipping alcohol and then repeatedly wiping the part stripped from the coating layers on the two single-mode fibers so as to remove residues of the coating layers, and then the fiber cutter is used for cutting the end faces of the two single-mode fibers stripped from one ends of the coating layers respectively, so that the end faces are smooth.
Preferably, the method for performing the dislocation welding on the two pretreated single-mode optical fibers comprises the following steps:
one end of each of the two single mode fibers, the coating of which is stripped, is respectively placed on two fiber clamps in the optical fiber fusion splicer and fixed;
and moving the optical fiber clamp in the horizontal direction to form a staggered state, and carrying out fiber staggered welding on the two single-mode optical fibers by using an optical fiber welding machine.
Preferably, the formula for calculating the light intensity of the transmission spectrum is:
Figure BDA0003623949360000041
in the formula, I m Is the light intensity of the mth order mode; I.C. A n Is the light intensity of the nth order mode;
Figure BDA0003623949360000042
is the phase difference between the mth order mode and the nth order mode, and I is the intensity of the interference light.
Preferably, the method for detecting the refractive index of the solution of the S-shaped optical fiber sensor includes:
fixing the optical fiber sensor on a glass sheet straightly;
connecting one end of an optical fiber sensor with a broadband light source, and connecting the other output end of the optical fiber sensor with a spectral frequency analyzer;
and sequentially placing the glass sheets in the water mixed solution with gradually increased concentration of the glycerol, and detecting the change condition of the transmission spectrum by using a spectral frequency analyzer to obtain the optical fiber sensor with the solution refractive index in accordance with the set range.
Preferably, the method for detecting stress interference resistance of the S-shaped optical fiber sensor comprises:
fixing two ends of the optical fiber sensor on a micro-operation platform respectively;
connecting one end of an optical fiber sensor with a broadband light source, and connecting the other output end of the optical fiber sensor with a spectral frequency analyzer;
stress is applied to the optical fiber sensor by adjusting a micro-displacement platform at one end of the optical fiber sensor, the applied stress is gradually increased to a set value, and the change condition of the transmission spectrum is detected by the spectrum frequency analyzer to obtain the optical fiber sensor with the solution refractive index in accordance with the set range.
Compared with the prior art, the invention has the beneficial effects that:
the pointed cone parts of the first micro-bending cone-shaped optical fiber and the second micro-bending cone-shaped optical fiber are spliced to form an S shape; the light is transmitted in the first micro-bending conical fiber and divided into two parts, one part of light is transmitted along the fiber core of the first micro-bending conical fiber in a fundamental mode, and the other part of light is coupled by the fiber core of the first micro-bending conical fiber and enters the cladding of the first micro-bending conical fiber to be excited into high-order mode transmission; light transmitted by a high-order mode in the second micro-bending conical fiber is coupled into a fiber core of the second micro-bending conical fiber through a cladding of the second micro-bending conical fiber and interferes with light transmitted by a fundamental mode in the fiber core of the second micro-bending conical fiber; more high-order modes can be excited in the optical transmission process, the refractive index of the high-order modes is improved, and the strain sensitivity and the refractive index sensitivity of the optical fiber sensor can be effectively improved.
The method comprises the steps of pretreating two single-mode fibers and carrying out dislocation fusion to obtain fusion-spliced fibers; discharging, melting and heating the welding position of the qualified fusion spliced optical fiber, stretching and twisting the welding position of the qualified fusion spliced optical fiber to form an S shape, and acquiring an optical fiber sensor with a transmission spectrum meeting a set range; the manufacturing procedure of the optical fiber sensor is simple, and the manufacturing cost of the optical fiber sensor is reduced.
Drawings
Fig. 1 is a structural diagram of an optical fiber sensor based on Mach-Zehnder interference according to an embodiment of the present invention;
FIG. 2 is a flow chart of a method for cleaving an end face of a single mode optical fiber according to an embodiment of the present invention;
FIG. 3 is a flow chart of single mode fiber splicing according to an embodiment of the present invention;
FIG. 4 is a block diagram of a qualified fusion spliced optical fiber according to an embodiment of the present invention;
FIG. 5 is a flow chart of a method for manufacturing an optical fiber sensor according to an embodiment of the present invention;
FIG. 6 is a flow chart of the detection of the solution-resistant refractive index disturbance according to an embodiment of the present invention;
FIG. 7 is a flowchart of the anti-stress interference detection provided by the embodiment of the invention.
In the figure: 101 cladding, 102 core, 11 input single mode fiber, 12 first micro-bending cone fiber, 13 second micro-bending cone fiber, 14 output single mode fiber.
Detailed Description
The invention is further described below with reference to the accompanying drawings. The following examples are only for illustrating the technical solutions of the present invention more clearly, and the protection scope of the present invention is not limited thereby.
Example one
As shown in fig. 1, the fiber bundle comprises an input single-mode fiber 11, a first microbend tapered fiber 12, a second microbend tapered fiber 13 and an output single-mode fiber 14 which are connected in sequence; the input single-mode fiber 11, the first micro-bending tapered fiber 12, the second micro-bending tapered fiber 13 and the output single-mode fiber 14 are communication single-mode fibers or small-diameter single-mode fibers or single-mode photonic crystal fibers; the pointed cone parts of the first micro-bending cone-shaped optical fiber 12 and the second micro-bending cone-shaped optical fiber 13 are spliced to form an S shape; the fiber core 101 of the first micro-bending cone-shaped optical fiber 12 and the fiber core 101 of the second micro-bending cone-shaped optical fiber 13 are welded in a staggered mode; the bending angles of the input single-mode fiber 11, the first micro-bending tapered fiber 12, the second micro-bending tapered fiber 13 and the output single-mode fiber 14 are 30 to 60 degrees.
Light is transmitted to the first microbending cone-shaped optical fiber 12 through the fiber core 101 of the input single-mode optical fiber 11, the light is propagated in the first microbending cone-shaped optical fiber 12 and divided into two parts, one part of light is propagated in a fundamental mode along the fiber core of the first microbending cone-shaped optical fiber 12, and the other part of light is coupled by the fiber core 101 of the first microbending cone-shaped optical fiber 12 and enters the cladding 102 of the first microbending cone-shaped optical fiber 12 to be excited into a high-order mode for propagation; the high-order modes comprise cone-excited high-order modes and dislocation-excited high-order modes.
The light is transmitted to the second micro-bending cone-shaped optical fiber 13 through the first micro-bending cone-shaped optical fiber 12; the light propagating in the second microbend tapered fiber 13 in the high-order mode is coupled into the fiber core 101 of the second microbend tapered fiber 13 by the cladding 102 of the second microbend tapered fiber 13, and interferes with the light propagating in the fiber core 102 of the second microbend tapered fiber 13 in the fundamental mode to form interference light, and the interference light is output through the output single-mode fiber 14.
Example two
As shown in fig. 1 to 7, a method for manufacturing an optical fiber sensor based on Mach-Zehnder interference according to a first embodiment includes:
pretreating two single-mode optical fibers, wherein the method comprises the following steps:
the fiber stripper is used for stripping the coating layers at one ends of the two single-mode fibers respectively, absorbent cotton is used for dipping alcohol and then repeatedly wiping the part stripped from the coating layers on the two single-mode fibers so as to remove residues of the coating layers, and then the fiber cutter is used for cutting the end faces of the two single-mode fibers stripped from one ends of the coating layers respectively, so that the end faces are smooth.
The method for carrying out dislocation fusion on the two pretreated single-mode fibers comprises the following steps:
one end of each of the two single mode fibers, the coating of which is stripped, is respectively placed on two fiber clamps in the optical fiber fusion splicer and fixed;
moving the optical fiber clamp in the horizontal direction to form a staggered state, and carrying out fiber staggered fusion on the two single-mode optical fibers by using an optical fiber fusion splicer; a fusion spliced optical fiber is obtained.
Detecting the fusion spliced optical fiber through a spectrum analyzer to obtain a qualified fusion spliced optical fiber of which the extinction ratio, the free spectrum and the light intensity of the transmission spectrum meet a set range;
the formula for calculating the light intensity of the transmission spectrum is as follows:
Figure BDA0003623949360000071
in the formula, I m Is the light intensity of the mth order mode; I.C. A n Is the light intensity of the nth order mode;
Figure BDA0003623949360000072
is the phase difference between the mth order mode and the nth order mode, and I is the intensity of the interference light.
Connecting one end of the qualified fusion-spliced optical fiber with a broadband light source, connecting the other output end of the qualified fusion-spliced optical fiber with a spectral frequency analyzer, and detecting the change condition of the transmission spectrum through the spectral frequency analyzer;
discharging, melting and heating the welding position of the qualified fusion spliced optical fiber, stretching and twisting the welding position of the qualified fusion spliced optical fiber to form an S shape, and obtaining an optical fiber sensor with a transmission spectrum in accordance with a set range; a first micro-bending conical optical fiber 102 and a second micro-bending conical optical fiber 103 are respectively formed at the welding position of the optical fiber sensor; the two ends of the fiber sensor are respectively formed as an input single-mode fiber 101 and an input single-mode fiber 104.
And (4) carrying out solution refraction interference resistance detection and stress interference resistance detection on the S-shaped optical fiber sensor to obtain a qualified optical fiber sensor.
The optical fiber sensor is fixed on the glass sheet straightly;
connecting one end of an optical fiber sensor with a broadband light source, and connecting the other output end of the optical fiber sensor with a spectral frequency analyzer;
and sequentially placing the glass sheets in the water mixed solution with gradually increased concentration of the glycerol, and detecting the change condition of the transmission spectrum by using a spectral frequency analyzer to obtain the optical fiber sensor with the solution refractive index meeting the set range.
The method for detecting the stress interference resistance of the S-shaped optical fiber sensor comprises the following steps:
under the conditions that the room temperature is 25 ℃ and other external environments are not changed, two ends of the optical fiber sensor are respectively fixed on the micro-operation table;
connecting one end of an optical fiber sensor with a broadband light source, and connecting the other output end of the optical fiber sensor with a spectral frequency analyzer;
stress is applied to the optical fiber sensor by adjusting a micro-displacement platform at one end of the optical fiber sensor, the applied stress is gradually increased to a set value, and the change condition of the transmission spectrum is detected by the spectrum frequency analyzer, so that the optical fiber sensor with the solution refractive index in a set range is obtained.
The present application is described with reference to flowchart illustrations and/or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the application. It will be understood that each flow and/or block of the flow diagrams and/or block diagrams, and combinations of flows and/or blocks in the flow diagrams and/or block diagrams, can be implemented by computer program instructions. These computer program instructions may be provided to a processor of a general purpose computer, special purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, create means for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.
These computer program instructions may also be stored in a computer-readable memory that can direct a computer or other programmable data processing apparatus to function in a particular manner, such that the instructions stored in the computer-readable memory produce an article of manufacture including instruction means which implement the function specified in the flowchart flow or flows and/or block diagram block or blocks.
These computer program instructions may also be loaded onto a computer or other programmable data processing apparatus to cause a series of operational steps to be performed on the computer or other programmable apparatus to produce a computer implemented process such that the instructions which execute on the computer or other programmable apparatus provide steps for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.
The above description is only a preferred embodiment of the present invention, and it should be noted that, for those skilled in the art, several modifications and variations can be made without departing from the technical principle of the present invention, and these modifications and variations should also be regarded as the protection scope of the present invention.

Claims (10)

1. An optical fiber sensor based on Mach-Zehnder interference is characterized by comprising an input single-mode optical fiber, a first micro-bending cone-shaped optical fiber, a second micro-bending cone-shaped optical fiber and an output single-mode optical fiber which are sequentially connected; the pointed cone parts of the first micro-bending cone-shaped optical fiber and the second micro-bending cone-shaped optical fiber are spliced to form an S shape;
light is transmitted into the first micro-bending conical fiber through the fiber core of the input single-mode fiber, the light is transmitted into the first micro-bending conical fiber and divided into two parts, one part of light is transmitted along the fiber core of the first micro-bending conical fiber in a fundamental mode, and the other part of light is coupled into the cladding of the first micro-bending conical fiber from the fiber core of the first micro-bending conical fiber and is excited into high-order mode transmission; the light is transmitted to a second micro-bending conical optical fiber through a first micro-bending conical optical fiber; light transmitted by a high-order mode in the second micro-bending conical fiber enters a fiber core of the second micro-bending conical fiber through the cladding of the second micro-bending conical fiber, and is interfered with light transmitted by a fundamental mode in the fiber core of the second micro-bending conical fiber to form interference light, and the interference light is output through the output single-mode fiber.
2. A Mach-Zehnder interference based optical fiber sensor in accordance with claim 1 wherein the bending angles of the input single mode fiber with the first microbend cone type fiber, the second microbend cone type fiber and the output single mode fiber are 30 to 60 degrees.
3. A Mach-Zehnder interference based optical fiber sensor in accordance with claim 1, wherein the input single mode fiber, the first microbend cone type fiber, the second microbend cone type fiber and the output single mode fiber are communication single mode fibers or small diameter single mode fibers or single mode photonic crystal fibers.
4. A Mach-Zehnder interference based optical fiber sensor in accordance with claim 1 wherein the fiber core of the first microbend cone fiber is fusion spliced with the fiber core of the second microbend cone fiber in a staggered manner; the high-order modes comprise cone-excited high-order modes and dislocation-excited high-order modes.
5. A manufacturing method of an optical fiber sensor based on Mach-Zehnder interference is characterized by comprising the following steps:
pretreating two single-mode fibers and carrying out dislocation fusion to obtain fusion fibers;
detecting the fusion spliced optical fiber through a spectrum analyzer to obtain a qualified fusion spliced optical fiber of which the extinction ratio, the free spectrum and the light intensity of the transmission spectrum meet a set range;
connecting one end of the qualified fusion spliced optical fiber with a broadband light source, connecting the other output end of the qualified fusion spliced optical fiber with a spectral frequency analyzer, and detecting the change condition of the transmission spectrum through the spectral frequency analyzer;
discharging, melting and heating the welding position of the qualified fusion spliced optical fiber, stretching and twisting the welding position of the qualified fusion spliced optical fiber to form an S shape, and acquiring an optical fiber sensor with a transmission spectrum meeting a set range;
and carrying out anti-solution refraction interference detection and anti-stress interference detection on the S-shaped optical fiber sensor to obtain a qualified optical fiber sensor.
6. The method for manufacturing an optical fiber sensor based on Mach-Zehnder interference as defined in claim 1, wherein the method for pre-processing two single-mode optical fibers comprises: the fiber peeling pliers are used for peeling the coating layers at one ends of the two single-mode fibers respectively, absorbent cotton is used for dipping alcohol and then repeatedly wiping the part, stripped of the coating layers, of the two single-mode fibers so as to remove residues of the coating layers, and the fiber cutting knife is used for cutting the end faces, stripped of one ends of the coating layers, of the two single-mode fibers respectively, so that the end faces are smooth.
7. The manufacturing method of the optical fiber sensor based on Mach-Zehnder interference as claimed in claim 6, wherein the method for performing the dislocation fusion of the two pretreated single-mode optical fibers comprises:
one end of each of the two single mode fibers, the coating of which is stripped, is respectively placed on two fiber clamps in the optical fiber fusion splicer and fixed;
and moving the optical fiber clamp in the horizontal direction to form a staggered state, and carrying out fiber staggered welding on the two single-mode optical fibers by using an optical fiber welding machine.
8. The manufacturing method of an optical fiber sensor based on Mach-Zehnder interference as defined in claim 1, wherein the light intensity calculation formula of the transmission spectrum is:
Figure FDA0003623949350000031
in the formula, I m Is the light intensity of the mth order mode; I.C. A n Is the light intensity of the nth order mode;
Figure FDA0003623949350000032
is the phase difference between the m-th order mode and the n-th order mode, and I is the intensity of the interference light.
9. The manufacturing method of the optical fiber sensor based on Mach-Zehnder interference as claimed in claim 1, wherein the method for detecting the solution refractive index of the S-shaped optical fiber sensor comprises:
the optical fiber sensor is fixed on the glass sheet straightly;
connecting one end of an optical fiber sensor with a broadband light source, and connecting the other output end of the optical fiber sensor with a spectral frequency analyzer;
and sequentially placing the glass sheets in the water mixed solution with gradually increased concentration of the glycerol, and detecting the change condition of the transmission spectrum by using a spectral frequency analyzer to obtain the optical fiber sensor with the solution refractive index in accordance with the set range.
10. The manufacturing method of the optical fiber sensor based on Mach-Zehnder interference as claimed in claim 1, wherein the method for detecting the stress interference resistance of the S-shaped optical fiber sensor comprises:
fixing two ends of the optical fiber sensor on a micro-operation platform respectively;
connecting one end of an optical fiber sensor with a broadband light source, and connecting the other output end of the optical fiber sensor with a spectral frequency analyzer;
stress is applied to the optical fiber sensor by adjusting a micro-displacement platform at one end of the optical fiber sensor, the applied stress is gradually increased to a set value, and the change condition of the transmission spectrum is detected by the spectrum frequency analyzer, so that the optical fiber sensor with the solution refractive index in a set range is obtained.
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