CN103697920A - Optical fiber sensing head and optical fiber sensing system and method for measuring liquid refractivity based on sensing head - Google Patents

Abstract

The invention discloses an optical fiber sensing head and an optical fiber sensing system and method for measuring liquid refractivity based on the sensing head, belongs to the field of optical fiber sensing systems, and aims to solve the problem of influence on the reflectivity due to a small distance between the FP cavity of the conventional optical fiber sensing head and the tail end of an optical fiber. By adopting the optical fiber sensing head and the optical fiber sensing system and method for measuring the liquid refractivity based on the sensing head, the simultaneous influence of liquid to be tested on the reflectivity of two interfaces of the FP cavity is avoided by forming an air channel on the optical fiber, changing the direction of a light path and taking an optical fiber cladding as the FP cavity. When light entering the sensing head is in an S-polarized state, the maximum sensitivity of the measured refractivity is up to -298.3dB/RIU. When the light entering the sensing head is in a P-polarized state, the maximum sensitivity of the measured refractivity is up to -597.1dB/RIU. The system and the method are suitable for measuring the refractivity of liquid.

Description

Optical fiber sensing system and the method for a kind of optical fiber sensor head and the measurement liquid refractivity based on this sensing head

Technical field

The invention belongs to optical fiber sensing system field.

Background technology

Due to the low cost of optical fiber, anticorrosive, the high good characteristic such as responsive, optical fiber obtains very large concern and has extensively applied to the fields such as biological, chemical aspect refractive index sensing in recent years.Optic fibre refractive index sensor mainly can be divided into two classes by detecting light spectrum, transmission-type Fibre Optical Sensor and reflective optical sensor.With respect to reflective optical sensor, the sensor-based system of transmission-type Fibre Optical Sensor takes up space relatively large, has limited it and has carried out in vivo direct refractive index detection.For reflective optical sensor, conventionally use optical fiber in conjunction with outer fiber Fabry-Perot(FP) chamber or inside of optical fibre FP chamber survey the variation of refractive index; And outside FP chamber is faced with the sensing head relatively large problem that takes up space equally.Thereby compare, the sensor based on inside of optical fibre FP chamber is wider aspect the Application in Sensing of refractive index.Although yet traditional Fibre Optical Sensor size based on inner FP chamber is little, distance is large, due to the close together of FP chamber apart from optical fiber tail end, when test liquid, liquid is except exerting an influence to the reflectivity of FP reflecting surface, and the reflectivity to optical fiber tail end exerts an influence, both affect sensing can occur to intersect, thereby cause the reflective light intensity that spectrometer records cannot be monotone variation for testing liquid refractive index, can only in one section of very narrow ranges of indices of refraction, present monotone variation, and monotone area changes along with the variation of testing liquid refractive index.Thereby greatly limited Fibre Optical Sensor based on inner FP chamber in the application aspect refractometry.

Summary of the invention

The present invention is in order to solve existing fiber sensing head FP chamber apart from the close together of optical fiber tail end, and then the problem that reflectivity is exerted an influence, and a kind of optical fiber sensing system and the method for optical fiber sensor head and the measurement liquid refractivity based on this sensing head is now provided.

An optical fiber sensor head, it comprises: optical fiber and reflecting material;

Described optical fiber comprises: fibre cladding and fiber core;

Fibre cladding is wrapped in the outside of fiber core; On fiber core, have the air duct of four prism type, the cross section of this air duct is isosceles trapezoid, and the waist place plane of this isosceles trapezoid and the angle of fiber axis are 45 degree, this isosceles trapezoid high in the diameter of fiber core, the length range on the short base of this isosceles trapezoid is between 10 μ m to 20 μ m, the length of air duct equals the diameter of optical fiber, and the corresponding fibre cladding outside, short base of this isosceles trapezoid is fixed with reflecting material.

An optical fiber sensing system of measuring liquid refractivity, it comprises: light source, three-dB coupler, polarizer, sensing head, spectrometer and signal processing module;

The light that light source sends transfers in polarizer through three-dB coupler, polarizer regulates and transfers in sensing head through this light, sensing head reflexes to this light in polarizer, polarizer transfers to the light of sensing head reflection in three-dB coupler, three-dB coupler transfers to this light in spectrometer, and the spectral signal output terminal of spectrometer connects the spectral signal input end of signal processing module;

Described signal processing module comprises with lower unit:

The reflectance spectrum obtaining in collection spectrometer is in the unit of the reflectance spectrum intensity at 1550nm place;

Obtain the unit of the reflectivity R of air duct and fiber core surface of contact;

Obtain the refractive index n of testing liquid ₂unit;

Described sensing head comprises: optical fiber and reflecting material;

Described optical fiber comprises: fibre cladding and fiber core;

Fibre cladding is wrapped in the outside of fiber core; On fiber core, have the air duct of four prism type, the cross section of this air duct is isosceles trapezoid, and the waist place plane of this isosceles trapezoid and the angle of fiber axis are 45 degree, this isosceles trapezoid high in the diameter of fiber core, the length range on the short base of this isosceles trapezoid is between 10 μ m to 20 μ m, the length of air duct equals the diameter of optical fiber, and the corresponding fibre cladding outside, short base of this isosceles trapezoid is provided with reflecting material.

Measure a method for liquid refractivity, the method realizes based on following apparatus,

Described device comprises: light source, three-dB coupler, polarizer, sensing head and spectrometer;

The light that light source sends transfers in polarizer through three-dB coupler, polarizer regulates and transfers in sensing head through this light, sensing head reflexes to this light in polarizer, and polarizer transfers to the light of sensing head reflection in three-dB coupler, and three-dB coupler transfers to this light in spectrometer;

Described sensing head comprises: optical fiber and reflecting material;

Described optical fiber comprises: fibre cladding and fiber core;

Fibre cladding is wrapped in the outside of fiber core; On fiber core, have the air duct of four prism type, the cross section of this air duct is isosceles trapezoid, and the waist place plane of this isosceles trapezoid and the angle of fiber axis are 45 degree, this isosceles trapezoid high in the diameter of fiber core, the length range on the short base of this isosceles trapezoid is between 10 μ m to 20 μ m, the length of air duct equals the diameter of optical fiber, and the corresponding fibre cladding outside, short base of this isosceles trapezoid is provided with reflecting material;

A kind of method of measuring liquid refractivity based on said apparatus comprises the following steps:

Step 1: regulate polarizer, the light that makes to incide in sensing head is the light under a kind of polarization state; Then perform step two;

Step 2: keep sensing head not immerse in liquid, utilize spectrometer to obtain reflectance spectrum in the reflectance spectrum intensity reference value I at 1550nm place ₀, then perform step three;

Step 3: sensing head is immersed in testing liquid, make testing liquid enter air duct, utilize spectrometer to obtain reflectance spectrum at the reflectance spectrum intensity level I at 1550nm place ₁, then perform step four;

Step 4: utilize reflectance spectrum intensity reference value I ₀with reflectance spectrum intensity level I ₁, obtain and be filled with the air duct of testing liquid and the reflectivity R of fiber core surface of contact, then perform step five;

Step 5: utilize and be filled with the air duct of testing liquid and the reflectivity R of fiber core surface of contact, obtain the refractive index n of testing liquid ₂.

Optical fiber sensing system and the method for a kind of optical fiber sensor head of the present invention and the measurement liquid refractivity based on this sensing head, overcome in prior art, adopt existing fiber sensing head that the intrinsic thinking in FP chamber is set in outer fiber, but by open an air duct on optical fiber, changed the direction of light path, thereby using fibre cladding as FP chamber, avoided the testing liquid impact on two of FP chamber boundary reflection rates simultaneously.Light in inciding sensing head is when S polarization, and the peak response of measuring refractive index can be up to-298.3dB/RIU, and when P polarization, the peak response of measuring refractive index can be up to-597.1dB/RIU.

Optical fiber sensing system and the method for a kind of optical fiber sensor head of the present invention and the measurement liquid refractivity based on this sensing head, be applicable to the refractive index of liquid to measure.

Accompanying drawing explanation

Fig. 1 is a kind of cross-sectional view of optical fiber sensor head;

Fig. 2 is a kind of principle schematic of measuring the optical fiber sensing system of liquid refractivity;

Fig. 3 is a kind of process flow diagram of measuring the optical fiber sensing method of liquid refractivity;

When Fig. 4 is S polarization, sensing head reflectance spectrum is for the spectrum change figure of refractive index;

When Fig. 5 is P polarization, sensing head reflectance spectrum is for the spectrum change figure of refractive index.

Embodiment

Embodiment one: with reference to Fig. 1, illustrate present embodiment, a kind of optical fiber sensor head described in present embodiment, it comprises: optical fiber and reflecting material 4-3;

Described optical fiber comprises: fibre cladding 4-1 and fiber core 4-2;

Fibre cladding 4-1 is wrapped in the outside of fiber core 4-2; On fiber core 4-2, have the air duct 4-4 of four prism type, the cross section of this air duct 4-5 is isosceles trapezoid, and the waist place plane of this isosceles trapezoid and the angle of fiber axis are 45 degree, this isosceles trapezoid high in the diameter of fiber core 4-2, the length range on the short base of this isosceles trapezoid is between 10 μ m to 20 μ m, the length of air duct 4-5 equals the diameter of optical fiber, and the corresponding fibre cladding 4-1 outside, short base of this isosceles trapezoid is fixed with reflecting material 4-3.

Embodiment two: present embodiment is that a kind of optical fiber sensor head described in embodiment one is described further, in present embodiment, described optical fiber is single-mode fiber.

Embodiment three: present embodiment is that a kind of optical fiber sensor head described in embodiment one is described further, in present embodiment, described optical fiber is multimode optical fiber.

Embodiment four: present embodiment is that a kind of optical fiber sensor head described in embodiment one is described further, and in present embodiment, the material of described reflecting material 4-3 is identical with the material of fiber core 4-2.

Embodiment five: illustrate present embodiment with reference to Fig. 2, a kind of optical fiber sensing system of measuring liquid refractivity described in present embodiment, it comprises: light source 1, three-dB coupler 2, polarizer 3, sensing head 4, spectrometer 5 and signal processing module 6;

The light that light source 1 sends transfers in polarizer 3 through three-dB coupler 2, polarizer 3 regulates and transfers in sensing head 4 through this light, sensing head 4 reflexes to this light in polarizer 3, polarizer 3 transfers to the light of sensing head 4 reflections in three-dB coupler 2, three-dB coupler 2 transfers to this light in spectrometer 5, and the spectral signal output terminal of spectrometer 5 connects the spectral signal input end of signal processing module 6;

Described signal processing module 6 comprises with lower unit:

Gather the reflectance spectrum of acquisition in spectrometer 5 in the unit of the reflectance spectrum intensity at 1550nm place;

Obtain the unit of the reflectivity R of air duct 4-5 and fiber core 4-2 surface of contact;

Obtain the refractive index n of testing liquid ₂unit;

Described sensing head 4 comprises: optical fiber and reflecting material 4-3;

Described optical fiber comprises: fibre cladding 4-1 and fiber core 4-2;

Fibre cladding 4-1 is wrapped in the outside of fiber core 4-2; On fiber core 4-2, have the air duct 4-4 of four prism type, the cross section of this air duct 4-5 is isosceles trapezoid, and the waist place plane of this isosceles trapezoid and the angle of fiber axis are 45 degree, this isosceles trapezoid high in the diameter of fiber core 4-2, the length range on the short base of this isosceles trapezoid is between 10 μ m to 20 μ m, the length of air duct 4-5 equals the diameter of optical fiber, and the corresponding fibre cladding 4-1 outside, short base of this isosceles trapezoid is provided with reflecting material 4-3.

Embodiment six: present embodiment is that a kind of optical fiber sensing system of measuring liquid refractivity described in embodiment five is described further, in present embodiment, described light source 1 is Gauss's light source.

Embodiment seven: with reference to Fig. 3, illustrate present embodiment, a kind of method of measuring liquid refractivity described in present embodiment, the method realizes based on following apparatus,

Described device comprises: light source 1, three-dB coupler 2, polarizer 3, sensing head 4 and spectrometer 5;

The light that light source 1 sends transfers in polarizer 3 through three-dB coupler 2, polarizer 3 regulates and transfers in sensing head 4 through this light, sensing head 4 reflexes to this light in polarizer 3, polarizer 3 transfers to the light of sensing head 4 reflections in three-dB coupler 2, and three-dB coupler 2 transfers to this light in spectrometer 5;

Described sensing head 4 comprises: optical fiber and reflecting material 4-3;

Described optical fiber comprises: fibre cladding 4-1 and fiber core 4-2;

Fibre cladding 4-1 is wrapped in the outside of fiber core 4-2; On fiber core 4-2, have the air duct 4-4 of four prism type, the cross section of this air duct 4-5 is isosceles trapezoid, and the waist place plane of this isosceles trapezoid and the angle of fiber axis are 45 degree, this isosceles trapezoid high in the diameter of fiber core 4-2, the length range on the short base of this isosceles trapezoid is between 10 μ m to 20 μ m, the length of air duct 4-5 equals the diameter of optical fiber, and the corresponding fibre cladding 4-1 outside, short base of this isosceles trapezoid is provided with reflecting material 4-3;

A kind of method of measuring liquid refractivity based on said apparatus comprises the following steps:

Step 1: regulate polarizer 3, the light that makes to incide in sensing head 4 is the light under a kind of polarization state; Then perform step two;

Step 2: keep sensing head 4 not immerse in liquid, utilize spectrometer 5 to obtain reflectance spectrum at the reflectance spectrum intensity reference value I0 at 1550nm place, then perform step three;

Step 3: sensing head 4 is immersed in testing liquid, make testing liquid enter air duct (4-5), utilize spectrometer 5 to obtain reflectance spectrum at the reflectance spectrum intensity level I1 at 1550nm place, then perform step four;

Step 4: utilize reflectance spectrum intensity reference value I ₀with reflectance spectrum intensity level I ₁, the reflectivity R of acquisition air duct 4-5 and fiber core 4-2 surface of contact, then performs step five;

Step 5: utilize and be filled with the air duct 4-5 of testing liquid and the reflectivity R of fiber core 4-2 surface of contact, obtain the refractive index n of testing liquid ₂.

Embodiment eight: present embodiment is that a kind of method of measuring liquid refractivity described in embodiment seven is described further, in present embodiment, according to following formula, obtain and be filled with the air duct 4-5 of testing liquid and the reflectivity R of fiber core 4-2 surface of contact

lg(I ₁/I ₀)=lg(R)。

Embodiment nine: present embodiment is that a kind of method of measuring liquid refractivity described in embodiment seven is described further, in present embodiment, in step 1, regulate polarizer 3, when making to incide light in sensing head 4 and being S polarization, according to following formula, obtain the refractive index n of testing liquid ₂,

$\left\{\begin{array}{c}R={\left(\frac{n\cos {\mathrm{\θ}}_1-\cos {\mathrm{\θ}}_2}{n\cos {\mathrm{\θ}}_1+\cos {\mathrm{\θ}}_2}\right)}^2\\ n=n_1/n_2\end{array}\right.,$

Wherein, n ₁for the refractive index of fiber core 4-2, θ ₁for inciding light in sensing head 4 and the angle of air duct 4-5 and fiber core 4-2 surface of contact place plane, θ ₂refraction angle while there is refraction for inciding light in sensing head 4 on air duct 4-5 and fiber core 4-2 surface of contact.

Embodiment ten: present embodiment is that a kind of method of measuring liquid refractivity described in embodiment seven is described further, in present embodiment, in step 1, regulate polarizer 3, when making to incide light in sensing head 4 and being P polarization, according to following formula, obtain the refractive index n of testing liquid ₂,

$\left\{\begin{array}{c}R={\left(\frac{-n\cos {\mathrm{\θ}}_2+\cos {\mathrm{\θ}}_1}{n\cos {\mathrm{\θ}}_2+\cos {\mathrm{\θ}}_1}\right)}^2\\ n=n_1/n_2\end{array}\right.,$

Wherein, n ₁for the refractive index of fiber core 4-2, θ ₁for inciding light in sensing head 4 and the angle of air duct 4-5 and fiber core 4-2 surface of contact place plane, θ ₂refraction angle while there is refraction for inciding light in sensing head 4 on air duct 4-5 and fiber core 4-2 surface of contact.

Fibre cladding 4-1 can be regarded as Fabry-Perot(FP function) chamber, flashlight can constantly reflect in FP chamber, because the reflectivity on light beam two sides on FP chamber is equal and lower, thereby the reflectance spectrum of this sensing probe can directly simply represent with two-beam interference.That is:

Wherein, R is the reflectivity on air duct 4-5 inclined-plane; I ₁for catoptrical light intensity on the reflecting surface of one, FP chamber, I ₂for catoptrical light intensity on another reflecting surface of FP chamber; λ is the light intensity of the light that sends of light source 1, n ₃refractive index for fibre cladding 4-1; L is that the chamber in FP chamber is long, is the thickness of fibre cladding 4-1,

for initial phase.

Setting incident light is Gauss's light source, bandwidth is 200nm, spectral range is that 1200nm is to 1600nm, centre wavelength is 1500nm, testing liquid refractive index is selected generally conventional 1.33(water)-1.44, regulate polarizer, allow flashlight when S polarization, from measured reflectance spectrum, extract the data result of communication window 1550nm, the measurement result obtaining after processing as shown in Figure 4, along with refractive index constantly increases, more and more approach fiber core refractive index, transmitted light constantly increases, and reflected light constantly reduces, and is monotone variation.The refractive index sensitivity of sensing head is minimum is-73.6dB/RIU, and peak response can, up to-298.3dB/RIU, have the ability to carry out refractive index sensing completely.

In like manner, regulate polarizer, allow flashlight when P polarization, other parameters arrange identical, and the measurement result obtaining as shown in Figure 5, along with refractive index constantly increases, more and more approaches fiber core refractive index, and reflected light constantly reduces, and is monotone variation.And, by calculating, to find, the refractive index sensitivity of this sensing head is minimum is-148.0dB/RIU, peak response can, up to-597.1dB/RIU, have the ability to carry out refractive index sensing completely.

Claims (10)

1. an optical fiber sensor head, is characterized in that, it comprises: optical fiber and reflecting material (4-3);

Described optical fiber comprises: fibre cladding (4-1) and fiber core (4-2);

Fibre cladding (4-1) is wrapped in the outside of fiber core (4-2); On fiber core (4-2), have the air duct (4-4) of four prism type, the cross section of this air duct (4-5) is isosceles trapezoid, and the waist place plane of this isosceles trapezoid and the angle of fiber axis are 45 degree, this isosceles trapezoid high in the diameter of fiber core (4-2), the length range on the short base of this isosceles trapezoid is between 10 μ m to 20 μ m, the length of air duct (4-5) equals the diameter of optical fiber, and the corresponding fibre cladding in short base (4-1) outside of this isosceles trapezoid is fixed with reflecting material (4-3).

2. a kind of optical fiber sensor head according to claim 1, is characterized in that, described optical fiber is single-mode fiber.

3. a kind of optical fiber sensor head according to claim 1, is characterized in that, described optical fiber is multimode optical fiber.

4. a kind of optical fiber sensor head according to claim 1, is characterized in that, the material of described reflecting material (4-3) is identical with the material of fiber core (4-2).

5. an optical fiber sensing system of measuring liquid refractivity, is characterized in that, it comprises: light source (1), three-dB coupler (2), polarizer (3), sensing head (4), spectrometer (5) and signal processing module (6);

The light that light source (1) sends transfers in polarizer (3) through three-dB coupler (2), polarizer (3) regulates and transfers in sensing head (4) through this light, sensing head (4) reflexes to this light in polarizer (3), polarizer (3) transfers to the light of sensing head (4) reflection in three-dB coupler (2), three-dB coupler (2) transfers to this light in spectrometer (5), and the spectral signal output terminal of spectrometer (5) connects the spectral signal input end of signal processing module (6);

Described signal processing module (6) comprises with lower unit:

Gather the reflectance spectrum of acquisition in spectrometer (5) in the unit of the reflectance spectrum intensity at 1550nm place;

Obtain the unit of the reflectivity R of air duct (4-5) and fiber core (4-2) surface of contact;

Obtain the refractive index n of testing liquid ₂unit;

Described sensing head (4) comprising: optical fiber and reflecting material (4-3);

Described optical fiber comprises: fibre cladding (4-1) and fiber core (4-2);

Fibre cladding (4-1) is wrapped in the outside of fiber core (4-2); On fiber core (4-2), have the air duct (4-4) of four prism type, the cross section of this air duct (4-5) is isosceles trapezoid, and the waist place plane of this isosceles trapezoid and the angle of fiber axis are 45 degree, this isosceles trapezoid high in the diameter of fiber core (4-2), the length range on the short base of this isosceles trapezoid is between 10 μ m to 20 μ m, the length of air duct (4-5) equals the diameter of optical fiber, and the corresponding fibre cladding in short base (4-1) outside of this isosceles trapezoid is provided with reflecting material (4-3).

6. a kind of optical fiber sensing system of measuring liquid refractivity according to claim 5, is characterized in that, described light source (1) is Gauss's light source.

7. a method of measuring liquid refractivity, is characterized in that, the method realizes based on following apparatus,

Described device comprises: light source (1), three-dB coupler (2), polarizer (3), sensing head (4) and spectrometer (5);

The light that light source (1) sends transfers in polarizer (3) through three-dB coupler (2), polarizer (3) regulates and transfers in sensing head (4) through this light, sensing head (4) reflexes to this light in polarizer (3), polarizer (3) transfers to the light of sensing head (4) reflection in three-dB coupler (2), and three-dB coupler (2) transfers to this light in spectrometer (5);

Described sensing head (4) comprising: optical fiber and reflecting material (4-3);

Described optical fiber comprises: fibre cladding (4-1) and fiber core (4-2);

Fibre cladding (4-1) is wrapped in the outside of fiber core (4-2); On fiber core (4-2), have the air duct (4-4) of four prism type, the cross section of this air duct (4-5) is isosceles trapezoid, and the waist place plane of this isosceles trapezoid and the angle of fiber axis are 45 degree, this isosceles trapezoid high in the diameter of fiber core (4-2), the length range on the short base of this isosceles trapezoid is between 10 μ m to 20 μ m, the length of air duct (4-5) equals the diameter of optical fiber, and the corresponding fibre cladding in short base (4-1) outside of this isosceles trapezoid is provided with reflecting material (4-3);

A kind of method of measuring liquid refractivity based on said apparatus comprises the following steps:

Step 1: regulate polarizer (3), the light that makes to incide in sensing head (4) is the light under a kind of polarization state; Then perform step two;

Step 2: keep sensing head (4) not immerse in liquid, utilize spectrometer (5) to obtain reflectance spectrum in the reflectance spectrum intensity reference value I at 1550nm place ₀, then perform step three;

Step 3: sensing head (4) is immersed in testing liquid, make testing liquid enter air duct (4-5), utilize spectrometer (5) to obtain reflectance spectrum at the reflectance spectrum intensity level I at 1550nm place ₁, then perform step four;

Step 4: utilize reflectance spectrum intensity reference value I ₀with reflectance spectrum intensity level I ₁, obtain and be filled with the air duct (4-5) of testing liquid and the reflectivity R of fiber core (4-2) surface of contact, then perform step five;

Step 5: utilize and be filled with the air duct (4-5) of testing liquid and the reflectivity R of fiber core (4-2) surface of contact, obtain the refractive index n of testing liquid ₂.

8. a kind of method of measuring liquid refractivity according to claim 7, is characterized in that, according to following formula, obtain and be filled with the air duct (4-5) of testing liquid and the reflectivity R of fiber core (4-2) surface of contact,

lg(I ₁/I ₀)=lg(R)。

9. a kind of method of measuring liquid refractivity according to claim 7, is characterized in that, regulates polarizer (3) in step 1, when making to incide light in sensing head (4) and being S polarization, obtains the refractive index n of testing liquid according to following formula ₂,

$\left\{\begin{array}{c}R={\left(\frac{n\cos {\mathrm{\θ}}_1-\cos {\mathrm{\θ}}_2}{n\cos {\mathrm{\θ}}_1+\cos {\mathrm{\θ}}_2}\right)}^2\\ n=n_1/n_2\end{array}\right.,$

Wherein, n ₁for the refractive index of fiber core (4-2), θ ₁for inciding the angle of light in sensing head (4) and air duct (4-5) and fiber core (4-2) surface of contact place plane, θ ₂refraction angle while there is refraction for inciding light in sensing head (4) on air duct (4-5) and fiber core (4-2) surface of contact.

10. a kind of method of measuring liquid refractivity according to claim 7, is characterized in that, regulates polarizer (3) in step 1, when making to incide light in sensing head (4) and being P polarization, obtains the refractive index n of testing liquid according to following formula ₂,

$\left\{\begin{array}{c}R={\left(\frac{-n\cos {\mathrm{\θ}}_2+\cos {\mathrm{\θ}}_1}{n\cos {\mathrm{\θ}}_2+\cos {\mathrm{\θ}}_1}\right)}^2\\ n=n_1/n_2\end{array}\right.,$

Wherein, n ₁for the refractive index of fiber core (4-2), θ ₁for inciding the angle of light in sensing head (4) and air duct (4-5) and fiber core (4-2) surface of contact place plane, θ ₂refraction angle while there is refraction for inciding light in sensing head (4) on air duct (4-5) and fiber core (4-2) surface of contact.

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