CN110702148B - Preparation method and application of optical fiber sensing device capable of simultaneously distinguishing and measuring three parameters - Google Patents
Preparation method and application of optical fiber sensing device capable of simultaneously distinguishing and measuring three parameters 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
- G01D5/268—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 using optical fibres
Abstract
A three-parameter simultaneous differential measurement optical fiber sensor preparation method and application, a section of standard single mode fiber Bragg grating with the total length of a grid region about 15mm, which is inscribed by 193nm excimer laser, is cut into two small sections in the grid region by an optical fiber cutter, so that the grating with uniform refractive index modulation is damaged; respectively fixing two small sections of gratings on a left optical fiber fixing clamp and a right optical fiber fixing clamp of a fusion splicer, and aligning the two sections of gratings in a manual adjusting mode of the fusion splicer and adjusting the two sections of gratings to a proper interval; another section of optical fiber is taken, the tail end of the optical fiber is stripped off a distance coating layer and cleaned by alcohol, and then a small drop of photosensitive glue is dipped and dropped into the gap between the two fixed sections of optical gratings; and irradiating the photosensitive glue by using an ultraviolet curing lamp to cure the photosensitive glue to form a photosensitive glue cavity, thereby introducing structural phase shift. The invention can effectively realize the distinguishing measurement of temperature, pressure and refractive index according to the spectral characteristics of the structural phase shift, and the method has simple operation process and lower cost.
Description
Technical Field
The invention relates to the technical field of optical fiber sensing devices, in particular to a preparation method and application of an optical fiber sensor capable of distinguishing and measuring three parameters simultaneously.
Background
When the optical fiber is used as a sensing device, it can directly or indirectly measure a plurality of physical quantities such as tensile force, pressure, temperature, refractive index, humidity, and the like. However, with the increasing complexity of the surrounding environment, the detection of changes in a single physical quantity has not been able to meet the measurement needs of people. Therefore, designing and manufacturing a sensing device capable of realizing multiple parameters and multiple functions has become a research hotspot of the optical fiber sensing technology.
An interference type optical fiber sensor, especially an optical fiber Fabry-Perot interferometer (FPI), manufactured based on an optical interference principle is widely applied to the fields of optical fiber sensing detection and the like due to the advantages of flexible and various structures, high reflectivity, low loss and the like. The type of the method for manufacturing the fiber interference type Fabry-Perot structure can be divided into an intrinsic type interferometer (IFPI) with an all-fiber F-P cavity structure and an extrinsic type interferometer (EFPI) with an F-P cavity structure formed by other materials or objects (such as capillary tubes, ceramic sleeve cores and the like). At present, the technology for simultaneously distinguishing and measuring double parameters of temperature and pressure, temperature and refractive index, temperature and displacement, temperature and humidity and the like by using an integrated structure sensor based on an all-fiber FPI and a fiber grating is mature, but the response sensitivity is only limited to the level of the fiber, and the manufacturing cost is high. The principle of the above dual-parameter distinguishing measurement mostly adopts a temperature compensation method, i.e. the structure in the integrated sensor, namely the fiber grating, is insensitive to pressure intensity, refractive index and the like, and can be used for temperature compensation during measurement. Meanwhile, double or multiple parameters are used for distinguishing measurement, and the cross sensitivity effect is an intrinsic problem.
Disclosure of Invention
In order to solve the technical problems, the invention aims to provide a preparation method and application of a three-parameter simultaneous differential measurement optical fiber sensor.
In order to achieve the purpose, the invention adopts the technical scheme that:
a preparation method of an optical fiber sensor capable of simultaneously distinguishing and measuring three parameters comprises the following steps;
the method comprises the following steps: a standard single-mode fiber Bragg grating with the total length of a grid region of 15mm, which is inscribed by a 193nm excimer laser, is cut into two small sections in the grid region by a fiber cutter, so that the grating with uniform refractive index modulation is damaged;
step two: respectively fixing two small sections of gratings on a left optical fiber fixing clamp and a right optical fiber fixing clamp of a fusion splicer, aligning the two sections of gratings through a manual adjustment mode of the fusion splicer, and adjusting the distance to be 50-100 um so as to obtain a better interference spectrogram;
step three: another section of optical fiber is taken, the tail end of the optical fiber is stripped off a distance of the coating layer and cleaned by alcohol, and then a small drop of photosensitive glue is dipped and dropped in the gap of the two fixed sections of gratings (as described in the second step);
step four: and irradiating the photosensitive emulsion by using an ultraviolet curing lamp to cure the photosensitive emulsion to form a photosensitive emulsion cavity, thereby introducing structural phase shift and obtaining the integrated sensor based on the extrinsic FPI and the phase shift grating.
The ultraviolet curing lamp irradiates the photosensitive adhesive for 5 minutes to improve the strength of the photosensitive adhesive cavity.
The optical fiber cutter is cut into two small sections at the position of the middle of the grid area.
The device is applied to the simultaneous differential measurement of three parameters, namely temperature, pressure and refractive index;
the optical fiber sensor is provided with two reflecting surfaces, namely a reflecting surface 1 and a reflecting surface 2 which are both interfaces of optical fibers and photosensitive adhesive, incident light is partially reflected through an optical fiber grating, the rest light continuously propagates forwards and reaches the reflecting surface 1 to be reflected again, the rest light continuously propagates forwards and then is partially reflected by the reflecting surface 2 through a photosensitive adhesive cavity with the refractive index of about 1.5 and the length of about 57um, the rest light continuously propagates forwards and is reflected by the optical fiber grating, after being reflected by the two reflecting surfaces of the closed EFPI, the phase delay caused by different optical path differences is different, an interference pattern is generated at an output end, and because the reflectivity of the reflecting surfaces is lower, the multi-beam reflection can be ignored, the output light intensity is approximate to the interference formed in the two cavities, and the output light intensity is:
wherein I is the output light intensity; i is1And I2The reflected light intensities of the incident light at the end face of the sealed EFPI cavity are respectively;
is the initial phase of the interference; n is the refractive index of the closed EFPI cavity; λ is the optical wavelength; l is the cavity length of the enclosed EFPI, therefore, the optical length of the cavity can be calculated as:
in the formula, λ1And λ2To encapsulate the wavelengths of two adjacent valleys in the EFPI interference spectrum, the Free Spectral Range (FSR) in the encapsulated EFPI spectrum can be expressed as:
the transmission matrix method is widely applied to the calculation of the optical wave field of non-uniform fiber gratings such as phase-shifting fiber gratings, and the like, so the method is adopted to analyze the spectral characteristics in the process of introducing the structural phase shift by manufacturing the closed EFPI in the gate area.
In the formula
Represents the magnitude of the phase shift amount;
by measuring the wavelength shift (Δ λ) of the closed EFPI spectrumEFPI) Power change (Δ K) of structure phase shift spectrumPS) And wavelength shift (Δ λ)PS) The sensitivity coefficient matrix can be used to realize the simultaneous differential measurement of the three parameters of temperature, pressure and refractive index, and if the variation of temperature, pressure and refractive index is Δ T, Δ P and Δ n, the sensitivity matrix can be expressed as:
in the formula, S1n、S1TAnd S1PThe sensitivity of the wavelength drift of the sealed EFPI along with the change of refractive index, temperature and pressure is obtained; s2n、S2TAnd S2PSensitivity of the structure phase shift wavelength drift along with the measured change; s, S3n、S3TAnd S3PIs a structureSensitivity of phase shift power drift to changes in measurement values. The variation of the three measured physical quantities obtained by the inverse operation of the matrix is:
in the formula
Is a determinant of a sensitivity coefficient matrix;
by substituting the above experimental measurement results into formula (6), it is possible to obtain:
therefore, the three parameters of temperature, pressure and refractive index can be effectively distinguished and measured simultaneously.
The invention has the beneficial effects that:
firstly, the closed EFPI manufactured by the method is formed by curing photosensitive resist, and breaks through the problem that the sensitivity of an optical fiber sensor is only limited to optical fibers; secondly, a new idea is provided for manufacturing a phase shift grating by introducing structural phase shift by preparing an EFPI structure in a gate region; thirdly, the length of the F-P cavity is determined by adjusting the gap between two small sections of gratings fixed at the left end and the right end of the fixing clamp of the welding machine, so that the length of the cavity can be flexibly and accurately controlled. Fourthly, the three parameters of temperature, pressure and refractive index can be distinguished and measured simultaneously, the sensitivity is high, the cost is low, and the method has important research significance in the field of optical fiber sensing detection.
Drawings
Figure 1 is a schematic diagram of a standard single mode fiber grating cut approximately in the middle of the grating region.
FIG. 2 is a schematic view of the attachment of a two-segment cut grating to an optical fiber retaining clip of a fusion splicer.
FIG. 3 is a schematic diagram of another single-mode fiber dipped with photosensitive glue and dropped into the gap between two segments of gratings.
FIG. 4 is a schematic diagram of curing a photoresist of a two-segment grating gap by irradiation of an ultraviolet curing lamp.
Fig. 5 is a microscopic image of an integrated sensor.
Fig. 6 is a schematic diagram of an integrated sensor measurement experiment apparatus.
FIG. 7 is a graph of the response of an integrated sensor to temperature.
FIG. 8 is a reflection spectrum of a phase shift grating of a structure magnified at 25 ℃.
FIG. 9 is a reflection spectrum of a phase shift grating of a structure magnified at 40 ℃.
FIG. 10 is a reflection spectrum of a phase shift grating of a structure magnified at 50 ℃.
FIG. 11 is a linear fit plot of encapsulated EFPI wavelength drift as a function of temperature.
FIG. 12 is a graph of a linear fit of the wavelength shift of the phase shift of the structure as a function of temperature.
FIG. 13 is a linear fit plot of the structure phase shift power drift as a function of temperature.
FIG. 14 is a spectral plot of the response of an integrated sensor to pressure.
FIG. 15 is a reflection spectrum of a phase shift grating of a structure magnified when pressure is increased.
FIG. 16 is a linear fit plot of encapsulated EFPI wavelength drift as a function of pressure.
FIG. 17 is a graph of the response of an integrated sensor to refractive index.
FIG. 18 is a reflection spectrum of an enlarged structured phase-shift grating having a refractive index of 1.3342.
FIG. 19 is a reflection spectrum of an enlarged structured phase-shift grating having a refractive index of 1.3388.
FIG. 20 is a reflection spectrum of an enlarged structured phase-shift grating having a refractive index of 1.3478.
FIG. 21 is a linear fit plot of encapsulated EFPI wavelength drift as a function of refractive index.
FIG. 22 is a linear fit graph of the power drift of a structured phase-shifted grating as a function of refractive index.
Detailed Description
The present invention will be described in further detail with reference to the accompanying drawings.
The technical scheme for preparing the sensor comprises the following four steps:
the method comprises the following steps: a standard single mode fiber bragg grating having a total grating length of about 15mm written using a 193nm excimer laser is cut into two small segments at about the middle of the grating by a fiber cutter (FITEL S326), resulting in the destruction of the uniform index modulated grating, as shown in fig. 1. (ii) a
Step two: two small sections of gratings are respectively fixed on a left optical fiber fixing clamp and a right optical fiber fixing clamp of a fusion splicer (Guhe FIELS 177), and then the two sections of gratings are aligned and adjusted to a proper distance through a manual adjustment mode of the fusion splicer. Since the FPI free-normal range is inversely proportional to the cavity length, the smaller cavity length is adjusted to be about L57 um, as shown in fig. 2;
step three: another section of the optical fiber is taken, the end of the optical fiber is stripped of a distance of the coating layer and cleaned by alcohol, and then a small drop of photosensitive resist (AUSBONDA332) is dipped and dropped in the gap between the two fixed sections of the gratings (as described in the second step), as shown in FIG. 3;
step four: the photoresist was irradiated using an ultraviolet curing lamp for about 5 minutes to cure the photoresist to form a photoresist cavity, introducing a structural phase shift, as shown in fig. 4. Fig. 8 shows a micrograph of the integrated sensor seen under an optical microscope, in which the structural phase shift image is not visible.
The invention provides a preparation method of an optical fiber sensor capable of simultaneously distinguishing and measuring three parameters. The optical fiber is common standard single mode optical fiber; the writing grid equipment is a 193nm excimer laser; the fusion splicer is used for aligning the two small segments of cut gratings and adjusting and determining the length of the F-P cavity, and plays a role of a micro-displacement adjusting platform without being used for fusing optical fiber gratings; in the experiment, the sealed EFPI is made of photosensitive emulsion AUSBONDA332 with high transparency and high strength; the demodulation equipment in the experiment is an SM125 demodulator, which is produced by micron optics International.
The sensitivity of the all-fiber FPI is limited to the level of the optical fiber, so that the EFPI is formed by curing the photosensitive adhesive, and the measurement sensitivity of the F-P cavity of the optical fiber can be effectively improved; the EFPI is manufactured in the middle of the grating region of the fiber grating with the uniform refractive index modulation, so that the introduction of structural phase shift caused by the uniform refractive index modulation of the grating is broken, and the EFPI has certain significance on the research and manufacture of phase shift gratings; the optical fiber sensor prepared by the invention has low cost, but the prepared sensing spectrum has high quality, and is equivalent to the spectrum of a standard F-P cavity; the invention provides a preparation technology of an EFPI integrated optical fiber sensor for manufacturing a grid region, preliminarily tests the temperature, the pressure and the refractive index with higher sensitivity, further realizes the simultaneous distinguishing and measurement of the three physical quantities, and provides certain technical support for the development of an optical fiber sensing device with higher sensitivity, which can realize the simultaneous distinguishing and measurement of three parameters.
The preparation process of the integrated sensor provided by the invention particularly needs to be noticed as follows: firstly, the photosensitive resist has high transparency, namely high reflectivity, so that in order to successfully introduce a better structural phase shift spectrum, the grating is cut off at the approximate middle position of the grating area to manufacture a photosensitive resist cavity; secondly, although the photosensitive emulsion can be cured quickly, the curing time can be increased properly for improving the curing strength, and is about 5 minutes; when the gap distance between two sections of cut gratings, namely the length of the cavity, is adjusted through a manual adjusting mode of a welding machine, the gap distance is not too long on the premise of obtaining an F-P interference spectrum so as to avoid damaging a photosensitive adhesive cavity;
sensing principle and differential measurement:
the basic working principle of the sensor is that the length of the sealed EFPI cavity is changed due to the change of external environment parameters, such as the change of physical parameters of temperature, pressure intensity, refractive index and the like, so that the position of a phase shift point or the size of a phase shift quantity influencing the structural phase shift is changed, the final result is that the reflection spectrum of the sealed EFPI reflected by an experimental spectrum generates drift, the wavelength and the power of the structural phase shift also generate certain linear changes, the sensing effect is achieved, and the three-parameter distinguishing measurement is realized.
The integrated optical fiber sensor prepared by the invention is characterized in that a section of complete optical fiber grating is cut into two small sections of gratings at the approximate middle position of a grating area, then the two small sections of gratings are fixed on a welding machine, and the gap between the two small sections of gratings, namely the cavity length, can be conveniently controlled through a manual adjusting mode, so that the number of free spectrums required by an experiment is realized, and the gap is filled with photosensitive glue and cured to form the closed EFPI.
The following laboratory data was all built on the sensors as shown in figure 5,
the optical fiber sensor has two reflecting surfaces, which are the interfaces of the optical fiber and the photosensitive glue. Incident light is partially reflected by the fiber grating, the rest light continues to propagate forwards, reaches the reflecting surface 1 and is partially reflected again, the rest light continues to propagate forwards and then is partially reflected by the reflecting surface 2 through the photosensitive rubber cavity with the refractive index of about 1.5 and the length of about 57um, and the rest light continues to propagate forwards and is partially reflected by the fiber grating. After light is reflected by the two closed EFPI reflecting surfaces, interference patterns are generated at the output end due to different phase delays caused by different optical path differences. Multiple beam reflections can be neglected due to the lower reflectivity of the reflective surface. Thus, the output light intensity is approximately the interference formed in the two cavities, the output light intensity being:
wherein I is the output light intensity; i is1And I2The reflected light intensities of the incident light at the end face of the sealed EFPI cavity are respectively;
is the initial phase of the interference; n is the refractive index of the closed EFPI cavity; λ is the optical wavelength; l is the length of the closed EFPI chamber. Thus, the optical length of the cavity can be calculated as:
in the formula, λ1And λ2The wavelengths of two adjacent wave troughs in the closed EFPI interference spectrum are disclosed. Free Spectral Range (FSR) in closed EFPI SpectrumExpressed as:
the transmission matrix method is widely applied to the calculation of the optical wave field of non-uniform fiber gratings such as phase-shifting fiber gratings, and the like, so the method is adopted to analyze the spectral characteristics in the process of introducing the structural phase shift by manufacturing the closed EFPI in the gate area.
In the formula
Indicating the magnitude of the phase shift.
As shown in FIG. 6, one end of an SM125 demodulator with the measurement precision of 1pm is connected with a computer, and the other end of the SM125 demodulator is connected with a sensor. When the sensor is placed in different measuring environments, the spectral change of the sensor can be acquired by a computer.
FIG. 10 is a reflectance spectrum of the sensor at atmospheric pressure with temperature changes of 25 deg.C, 30 deg.C, 35 deg.C, 40 deg.C, 45 deg.C and 50 deg.C, in which a red shift of the closed EFPI spectrum can be clearly seen. In order to observe the effect of temperature changes on the structural phase shift significantly, several spectra representative at 25 deg.C, 40 deg.C and 50 deg.C were selected and magnified as shown in FIGS. 11, 12 and 13, and the wavelength right shift and power reduction of the transmission window of the structural phase shift was seen. As shown in FIGS. 14, 15 and 16, the linear fitting is performed on the spectrum drift amounts at different temperatures, so that the wavelength drift of the sealed EFPI spectrum has a response sensitivity to temperature of 0.3076 nm/DEG C, the response sensitivity to temperature is improved by more than 30 times compared with that of a bare fiber F-P, and the wavelength drift and the power change of the structure phase shift also show response sensitivities of 6.2 pm/DEG C and-0.2299 dB/DEG C to temperature.
FIG. 17 shows the reflection spectrum of the sensor at pressures varying from 0MPa to 1.2 MPa. The inset is an enlarged spectrum of the sealed EFPI, where the spectrum can be seen to gradually move towards the long-wave direction, demonstrating that the sensor can also work normally in high pressure environments. FIG. 18 is an enlarged spectrum of the phase shift of the structure after the sensor is applied to pressure. It can be seen that there is little change in the structural phase shift spectrum when pressure is applied to the sensor, since the change in refractive index produced by the applied pressure does not cause a change in the amount of phase shift. The wavelength drift of the sealed EFPI spectrum under different applied pressures was subjected to linear fitting, and the response sensitivity to pressure was found to be 0.81nm/MPa, as shown in FIG. 19.
The change of the structural phase shift is finally attributed to the change of the refractive index, so that the integrated sensor is subjected to the refractive index test again. The response spectra of the sensors obtained by placing the sensors in a series of sucrose solutions with refractive index values 1.3342, 1.3360,1.3373, 1.3388, 1.3408, 1.3418,1.3438, 1.3438, 1.3450, 1.3466 and 1.3478 are shown in fig. 20. The inset shows the spectrum of the sealed EFPI enlarged, and it can be seen that the reflectance spectrum also shifts in the long-wavelength direction. In addition, in order to observe the influence of sucrose solutions of different concentrations on the structural phase shift spectrum, the spectra with representative structural phase shifts at refractive indices of 1.3342, 1.3388, and 1.3478 were selected and enlarged, as shown in fig. 21 and 22. It can be seen that the power of the phase shifted spectrum of the structure is gradually reduced, but its wavelength is hardly shifted. And performing linear fitting on the wavelength drift of the closed EFPI spectrum when the solutions with different refractive indexes change to obtain the response sensitivity of the closed EFPI spectrum to the solution with the refractive index of 355.03 nm/RIU. Furthermore, the response sensitivity of the power change of the phase shift of the structure to the refractive index was 319.82 dB/nm.
By measuring the wavelength shift (Δ λ) of the closed EFPI spectrumEFPI) Power change (Δ K) of structure phase shift spectrumPS) And wavelength shift (Δ λ)PS) The sensitivity coefficient matrix can be used for realizing the simultaneous distinguishing measurement of the three parameters of temperature, pressure and refractive index. Assuming that the temperature, pressure and refractive index change amounts are Δ T, Δ P and Δ n, the sensitivity matrix can be expressed as:
in the formula, S1n、S1TAnd S1PThe sensitivity of the wavelength drift of the sealed EFPI along with the change of refractive index, temperature and pressure is obtained; s2n、S2TAnd S2PSensitivity of the structure phase shift wavelength drift along with the measured change; s, S3n、S3TAnd S3PThe sensitivity of the structure phase shift power drift with the change of the measured value. The variation of the three measured physical quantities obtained by the inverse operation of the matrix is:
in the formula
Is a determinant of a sensitivity coefficient matrix.
By substituting the above experimental measurement results into formula (6), it is possible to obtain:
therefore, the three parameters of temperature, pressure and refractive index can be effectively distinguished and measured simultaneously.
On the basis of the manufacturing method of the traditional double-parameter measuring sensor, the invention uses the photosensitive glue to manufacture the closed F-P cavity at the approximate middle position of one fiber grating. Thus, the fiber grating having uniform refractive index modulation is destroyed, and a structural phase shift is introduced. The response characteristics of the integrated sensor to temperature, pressure and refractive index are verified through experiments. The result shows that compared with the all-fiber FPI, the sensitivity of the closed FPI made of the photosensitive glue is obviously improved. More importantly, in the experimental process, the structural phase shift also shows the response characteristics of a certain rule to the temperature, the pressure and the refractive index, so that the problem of cross sensitivity can be effectively solved, and the three parameters can be distinguished and measured simultaneously.
Claims (1)
1. A three-parameter simultaneous differential measurement optical fiber sensor preparation method is characterized by comprising the following steps;
the method comprises the following steps: a standard single-mode fiber Bragg grating with the total length of a grid region of 15mm, which is inscribed by a 193nm excimer laser, is cut into two small sections in the grid region by a fiber cutter, so that the grating with uniform refractive index modulation is damaged;
step two: respectively fixing two small sections of gratings on a left optical fiber fixing clamp and a right optical fiber fixing clamp of a fusion splicer, aligning the two sections of gratings in a manual adjustment mode of the fusion splicer, and adjusting the distance between the two sections of gratings to be 50-100 um;
step three: another section of optical fiber is taken, the tail end of the optical fiber is stripped off a distance coating layer and cleaned by alcohol, and then a small drop of photosensitive resist is dipped and dropped into the gap between the two fixed sections of gratings (as described in the second step);
step four: irradiating the photosensitive glue by using an ultraviolet curing lamp, so that the photosensitive glue is cured to form a photosensitive glue cavity, and introducing structural phase shift;
the ultraviolet curing lamp irradiates the photosensitive adhesive for 5 minutes to improve the strength of the photosensitive adhesive cavity;
the optical fiber cutter is cut into two small sections at the middle position of the grid area;
the device prepared by the method is applied to the simultaneous distinguishing and measurement of three parameters of temperature, pressure and refractive index;
the optical fiber sensor is provided with two reflecting surfaces which are a first reflecting surface (1) and a second reflecting surface (2) respectively and are interfaces of optical fibers and photosensitive adhesives, incident light is partially reflected through an optical fiber grating, the rest light continuously propagates forwards and reaches the first reflecting surface (1) to be reflected again, the rest light continuously propagates forwards and then is reflected by the second reflecting surface (2) through a photosensitive adhesive cavity with the refractive index of about 1.5 and the length of about 57um, the rest light continuously propagates forwards and is partially reflected by the optical fiber grating, after being reflected by the two reflecting surfaces of the closed EFPI, interference patterns are generated at an output end due to different phase delays caused by different optical path differences, the reflection of multiple beams can be ignored due to the lower reflectivity of the reflecting surfaces, therefore, the output light intensity is approximate to the interference formed in the two cavities, and the output light intensity is:
wherein I is the output light intensity; i is1And I2The reflected light intensities of the incident light at the end face of the sealed EFPI cavity are respectively;
is the initial phase of the interference; n is the refractive index of the closed EFPI cavity; λ is the optical wavelength; l is the cavity length of the closed EFPI, therefore, the optical length of the cavity can be calculated as:
in the formula, λ1And λ2To encapsulate the wavelengths of two adjacent valleys in the EFPI interference spectrum, the Free Spectral Range (FSR) in the encapsulated EFPI spectrum can be expressed as:
the transmission matrix method is widely applied to the calculation of the optical wave field of non-uniform fiber gratings such as phase-shifting fiber gratings, and the like, so the method is adopted to analyze the spectral characteristics in the process of introducing the structural phase shift by manufacturing the closed EFPI in the gate area, and because the phase is relatively delayed when the structural phase shift is introduced, a negative sign needs to be added before the phase shift of the grating, and the phase-shifting matrix is as follows:
in the formula
Represents the magnitude of the phase shift amount;
by measuring the wavelength shift (Δ λ) of the closed EFPI spectrumEFPI) Power change (Δ K) of structure phase shift spectrumPS) And wavelength shift (Δ λ)PS) The sensitivity coefficient matrix can be used to realize the simultaneous differential measurement of the three parameters of temperature, pressure and refractive index, and if the variation of temperature, pressure and refractive index is Δ T, Δ P and Δ n, the sensitivity matrix can be expressed as:
in the formula, S1n、S1TAnd S1PSensitivity of wavelength drift of the sealed EFPI along with changes of refractive index, temperature and pressure; s2n、S2TAnd S2PSensitivity of the structure phase shift wavelength drift along with the measured change; s3n、S3TAnd S3PFor the sensitivity of the structure phase shift power drift along with the change of the measured value, the change quantity of the three measured physical quantities can be obtained through the inverse operation of the matrix as follows:
in the formula
Is a determinant of a sensitivity coefficient matrix;
by substituting the above experimental measurement results into formula (6), it is possible to obtain:
the three parameters of temperature, pressure and refractive index can be simultaneously measured in a distinguishing way.
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