Micropore array grating temperature and pressure sensor and preparation method and test calibration method thereof

By designing a micro-aperture array grating and a microcavity array grating in parallel in an optical waveguide, temperature and pressure are measured separately, solving the problem of stringent requirements for constant environmental parameters in existing technologies and achieving high-precision measurement in high-temperature environments.

CN119533532BActive Publication Date: 2026-03-17SHENZHEN UNIV
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Patent Information

Authority / Receiving Office
CN · China
Patent Type
Patents(China)
Current Assignee / Owner
Filing Date
2024-10-14
Publication Date
2026-03-17

AI Technical Summary

Technical Problem

Existing micro-pore array grating sensors struggle to accurately measure both temperature and pressure simultaneously in high-temperature environments, requiring the control of another environmental parameter to remain constant, which limits their measurement accuracy in practical applications.

Method used

A micropore array grating temperature and pressure sensor is designed by arranging a micropore array grating and a microcavity array grating side by side in an optical waveguide. The micropore array grating is connected to the external environment, while the microcavity array grating is isolated from the external environment. The temperature and pressure are measured separately by utilizing the wavelength changes of the reflection peaks of the different gratings, thus avoiding mutual interference between the ambient temperature and pressure.

Benefits of technology

It enables simultaneous measurement of temperature and pressure in high-temperature environments, and features high reliability, high sensitivity, and easy serial multiplexing, solving the problem of stringent environmental parameter requirements in existing technologies.

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Abstract

The application discloses a micro-hole array grating temperature and pressure sensor, which comprises an optical waveguide, a micro-hole array grating and a micro-cavity array grating, the optical waveguide has an optical transmission channel inside, the micro-hole array grating and the micro-cavity array grating are formed in the optical transmission channel of the optical waveguide in parallel, the micro-hole array grating is communicated with the outside environment, and the micro-cavity array grating is isolated from the outside environment. The micro-hole array grating temperature and pressure sensor can avoid the mutual influence of the environment temperature and the environment pressure during measurement, so that the different environment temperatures and the different environment pressures can be measured simultaneously. The application further provides a preparation method and a test calibration method of the micro-hole array grating temperature and pressure sensor.
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Description

Technical Field

[0001] This invention relates to grating sensing technology, and more particularly to a micro-pore array grating temperature and pressure sensor, its fabrication method, and its testing and calibration method. Background Technology

[0002] Real-time in-situ measurement of multiple parameters (temperature, pressure, strain, vibration) at high temperatures is of great significance for solving the "bottleneck" problems in the development of major equipment such as hypersonic vehicles, aero engines, gas turbines, and shock tunnels in my country. In the field of high-temperature pressure measurement, electronic high-temperature pressure sensors are the main type, achieving stable and reliable pressure measurement by detecting changes in parameters such as capacitance and resistance. However, due to the limitations of the high-temperature resistance of electronic components, existing electronic sensors cannot achieve high-temperature pressure measurement.

[0003] Current fiber optic high-temperature pressure sensors primarily rely on fiber optic Fabry-Perot (FPI) interferometers for pressure measurement. Their structure is a diaphragm-fiber endface type, where a pressure-sensitive diaphragm is bonded to the fiber endface using adhesive or fusion splicing to form the pressure sensing head, with the fiber serving as the optical signal transmission carrier. This structure suffers from the problem of the pressure-sensitive diaphragm easily detaching or loosening under high-temperature operation, and it also makes quasi-distributed measurement difficult.

[0004] A microaperture array (MAP) is a fiber optic grating formed by creating an array of microapertures inside an optical fiber that communicates with the external environment. Because the microaperture array is connected to the external environment, the air medium inside the microaperture array can freely circulate with the air medium in the external environment. When the refractive index of the air in the external environment changes, the refractive index of the air in the microaperture array also changes accordingly, thus causing a change in the effective refractive index of the microaperture array grating. By demodulating the wavelength of the reflection peak of the microaperture array grating, the refractive index of the air in the external environment can be measured. However, the refractive index of the air is affected by both ambient temperature and ambient pressure. When using the microaperture array grating as a temperature sensor, it is necessary to control the ambient pressure to keep it constant to avoid the air refractive index being affected by changes in ambient pressure, which would then affect the accuracy of the ambient temperature measurement. Similarly, when using the microaperture array grating as a pressure sensor, it is necessary to control the ambient temperature to keep it constant to avoid the air refractive index being affected by changes in ambient temperature, which would then affect the accuracy of the ambient pressure measurement.

[0005] As can be seen from the above, when the microporous array grating is used as a temperature sensor or a pressure sensor, it is necessary to keep another environmental parameter constant. The requirements for the measurement environment are very stringent. Currently, the microporous array grating can only measure the ambient temperature or pressure by keeping another environmental parameter constant in the laboratory. However, in practical applications, it is almost impossible to achieve the measurement of ambient temperature or pressure by keeping another environmental parameter constant. Summary of the Invention

[0006] To address the shortcomings of the prior art, this invention provides a micro-pore array grating temperature and pressure sensor that avoids the mutual interference between ambient temperature and ambient pressure during measurement, thereby enabling simultaneous measurement of different ambient temperatures and different ambient pressures.

[0007] The present invention also provides a method for fabricating and testing / calibrating the above-mentioned microporous array grating temperature and pressure sensor.

[0008] The technical problem to be solved by the present invention is achieved through the following technical solution:

[0009] A micropore array grating temperature and pressure sensor includes an optical waveguide, a micropore array grating, and a microcavity array grating. The optical waveguide has an internal optical transmission channel. The micropore array grating and the microcavity array grating are formed side by side in the optical transmission channel of the optical waveguide. The micropore array grating is connected to the external environment, while the microcavity array grating is isolated from the external environment.

[0010] Furthermore, the optical waveguide is an integrated optical waveguide or a cylindrical optical waveguide, and its waveguide material is glass, sapphire, lutetium oxide, or ceramic; wherein, the integrated optical waveguide includes planar (thin film) dielectric waveguides and strip dielectric waveguides, and the cylindrical optical waveguide includes optical fiber.

[0011] Furthermore, the micro-aperture array includes multiple open micro-apertures, each of which is distributed along the optical transmission direction of the optical waveguide and is connected to the external environment.

[0012] Furthermore, the microcavity array grating includes multiple enclosed microcavities, each of which is distributed along the optical transmission direction of the optical waveguide and isolated from the external environment.

[0013] Furthermore, the closed microcavity is formed by the induced local refractive index change of the internal medium of the optical waveguide, whereby this part of the internal medium is completely ablated or the refractive index undergoes a permanent change; the closed microcavity is a hollow microcavity, with its interior being a vacuum, air, or a vaporized medium material, or the closed microcavity is a solid microcavity, with its interior being a medium material with a changed refractive index.

[0014] Furthermore, the micropore array grating has a first center wavelength, and the microcavity array grating has a second center wavelength.

[0015] Furthermore, the ambient pressure P and the air refractive index n sensed by the microporous array grating are... tp The relationship between the ambient temperature t sensed by the microcavity array grating and the ambient temperature t satisfies the following formula:

[0016]

[0017] n s ×10 -8 =8342.54+2406147×[130-σ 2 ] -1 +15998×[38.9-σ 2 ] -1

[0018] The above formula is the dispersion formula for standard dry air, n s σ is the tail of the air refractive index under standard conditions, and σ is the wavenumber.

[0019] The fabrication method of the above-mentioned microporous array grating temperature and pressure sensor includes the following steps:

[0020] Step 100: Design the structural parameters of the micro-aperture array grating and the micro-cavity array grating respectively;

[0021] Step 200: The micro-aperture array grating and the microcavity array grating are sequentially etched in the optical transmission channel of the optical waveguide using a femtosecond laser to obtain the micro-aperture array grating temperature and pressure sensor.

[0022] Furthermore, following step 200, the following steps are also included:

[0023] Step 300: Etch the micro-aperture array grating using an etching solution.

[0024] Furthermore, following step 300, the following steps are also included:

[0025] Step 400: Perform high-temperature annealing on the micropore array grating temperature and pressure sensor.

[0026] Furthermore, in step 200, the step of sequentially etching the micro-aperture array grating and the micro-cavity array grating in the optical transmission channel of the optical waveguide using a femtosecond laser is as follows:

[0027] Step 210: Construct a femtosecond laser writing system. The femtosecond laser writing system includes an optical subsystem and a motion subsystem. The optical subsystem is used to shape the femtosecond laser, and the motion subsystem is used to drive the optical waveguide to move. The optical subsystem includes a femtosecond laser, a power attenuator, a polarization controller, a mechanical shutter, a beam splitter, a Michelson interferometer, a spatial light modulator, a focusing lens, a dichroic mirror, a focusing objective lens, and a CCD camera. The Michelson interferometer has a first interferometer arm and a second interferometer arm. The first interferometer arm includes a first reflector, and the second interferometer arm includes a second reflector and a one-dimensional... The displacement platform comprises a femtosecond laser, a power attenuator, a polarization controller, a mechanical shutter, a beam splitter, a spatial light modulator, a focusing lens, a dichroic mirror, and a focusing objective, arranged sequentially along the propagation path of the femtosecond laser. The first and second reflecting mirrors of the Michelson interferometer are respectively positioned on the two beam-splitting paths of the beam splitter. The CCD camera is located on the side of the dichroic mirror facing away from the focusing objective. The motion subsystem includes a rotating clamp, a six-axis pitch platform, and a precision displacement platform. The rotating clamp is positioned on the six-axis pitch platform, and the six-axis pitch platform is positioned on the precision displacement platform.

[0028] Step 220: Clamp and fix the optical waveguide onto the rotating fixture;

[0029] Step 230: Load the desired cone lens phase map into the spatial light modulator;

[0030] Step 240: Control the femtosecond laser to emit a single-pulse femtosecond laser, so that the single-pulse femtosecond laser is shaped by the Michelson interferometer and the spatial light modulator to form a double-pulse Bessel beam, and focus the double-pulse Bessel beam in the optical transmission channel of the optical waveguide;

[0031] Step 250: The six-axis pitch platform and the precision displacement platform drive the rotating fixture to pitch and move, thereby adjusting the writing posture of the optical waveguide so that the dual-pulse Bessel beam can write the micro-aperture array grating in the optical transmission channel of the optical waveguide.

[0032] Step 260: Block the first or second interferometer arm of the Michelson interferometer and do not load any cone lens phase map in the spatial light modulator;

[0033] Step 270: Control the femtosecond laser to emit the single-pulse femtosecond laser again, and focus the single-pulse femtosecond laser into the optical transmission channel of the optical waveguide;

[0034] Step 280: The six-axis pitch platform and the precision displacement platform drive the rotating fixture to pitch and move, thereby adjusting the writing pose of the optical waveguide so that the single-pulse femtosecond laser can write the microcavity array grating in the optical transmission channel of the optical waveguide.

[0035] The test and calibration method for the aforementioned microporous array grating temperature and pressure sensor includes the following steps:

[0036] Step S1: Under normal pressure environment P0, the micropore array grating temperature and pressure sensor is placed in different temperature environments to obtain the first reflection peak wavelength of the micropore array grating in different temperature environments and the second reflection peak wavelength of the microcavity array grating at different temperatures. The ambient temperature-first reflection peak wavelength response relationship of the micropore array grating under normal pressure P0 and the ambient temperature-second reflection peak wavelength response relationship of the microcavity array grating are respectively fitted.

[0037] Step S2: Under different temperature environments, the microporous array grating temperature and pressure sensor is placed in different pressure environments, and the first reflection peak wavelength of the microporous array grating under different pressure environments is obtained. The environmental pressure-first reflection peak wavelength response relationship and pressure sensitivity of the microporous array grating under different temperature environments are then fitted respectively.

[0038] Step S3: Place the microcavity array grating temperature and pressure sensor in the calibration environment, and calculate the ambient temperature T1 of the calibration environment based on the second reflection peak wavelength of the microcavity array grating in the calibration environment and the ambient temperature-second reflection peak wavelength response formula.

[0039] Step S4: Based on the relationship between ambient pressure and wavelength response of the first reflection peak under different temperature environments, calculate the total wavelength shift Δλ of the micro-aperture array grating when it changes from a normal temperature and pressure environment to the calibration environment. Also, based on the relationship between ambient temperature and wavelength response of the first reflection peak under normal pressure environment P0, calculate the wavelength shift component Δλ caused by the change in ambient temperature when the micro-aperture array grating changes from a normal temperature and pressure environment to the calibration environment. T Then, the total wavelength drift Δλ of the micro-aperture array grating is subtracted from its wavelength drift component Δλ. T The wavelength shift component Δλ caused by the change in environmental pressure when the micro-aperture array is changed from a normal temperature and pressure environment to the calibration environment is obtained. p ;

[0040] Step S5: Calculate the ambient pressure of the calibration environment: P = P0 + Δλ P / S P,T1 , of which SP,T1 The pressure sensitivity of the micropore array grating at ambient temperature T1 is given.

[0041] The present invention has the following beneficial effects: This patent simultaneously fabricates the micro-aperture array grating and the microcavity array grating in the optical waveguide. The micro-aperture array grating and the microcavity array grating can respectively sense and detect the air refractive index and ambient temperature of the external environment. Finally, the ambient pressure is calculated based on the air refractive index and ambient temperature of the external environment. When the microcavity array grating senses and detects ambient temperature, it is not affected by ambient pressure. When the micro-aperture array grating senses and detects ambient pressure, it can use the ambient temperature detected by the microcavity array grating to calculate the ambient pressure, avoiding the mutual influence between ambient temperature and ambient pressure during measurement. It can realize the simultaneous sensing of different ambient temperatures and different ambient pressures, and has the advantages of high reliability, high sensitivity, and easy serial multiplexing. Attached Figure Description

[0042] Figure 1 This is a schematic diagram of the radial cross-section of the micropore array grating temperature and pressure sensor provided by the present invention.

[0043] Figure 2 for Figure 1 The diagram shows an axial cross-section of a microporous array grating temperature and pressure sensor.

[0044] Figure 3 A radial cross-sectional schematic diagram of another micropore array grating temperature and pressure sensor provided by the present invention.

[0045] Figure 4 for Figure 3 The diagram shows an axial cross-section of a microporous array grating temperature and pressure sensor.

[0046] Figure 5 The schematic diagram of the femtosecond laser writing system provided by the present invention.

[0047] Figure 6 A flowchart illustrating the steps of the fabrication method of the micropore array grating temperature and pressure sensor provided by the present invention.

[0048] Figure 7 This is a step-by-step flowchart of step 200 in the fabrication method of the micropore array grating temperature and pressure sensor provided by the present invention.

[0049] Figure 8 This is a step-by-step flowchart of step 300 in the fabrication method of the micropore array grating temperature and pressure sensor provided by the present invention.

[0050] Figure 9 This is a flowchart illustrating the steps of the test and calibration method for the micropore array grating temperature and pressure sensor provided by the present invention. Detailed Implementation

[0051] The present invention will now be described in detail with reference to the accompanying drawings and embodiments, examples of which are shown in the drawings, wherein the same or similar reference numerals denote the same or similar elements or elements having the same or similar functions throughout. The embodiments described below with reference to the accompanying drawings are exemplary and intended to explain the present invention, and should not be construed as limiting the present invention.

[0052] In the description of this invention, it should be understood that the terms "length", "width", "upper", "lower", "front", "rear", "left", "right", "vertical", "horizontal", "top", "bottom", "inner", "outer", etc., indicate the orientation or positional relationship based on the orientation or positional relationship shown in the accompanying drawings. They are only for the convenience of describing this invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation. Therefore, they should not be construed as limitations on this invention.

[0053] Furthermore, the terms "first," "second," and "third" are used for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the number of technical features indicated. Thus, a feature defined as "first," "second," or "third" may explicitly or implicitly include one or more of that feature. In the description of this invention, "multiple" means two or more, unless otherwise explicitly specified.

[0054] In this invention, unless otherwise explicitly specified and limited, the terms "installation," "connection," "linking," "fixing," and "setting," etc., should be interpreted broadly. For example, they can refer to a fixed connection, a detachable connection, or an integral part; they can refer to a mechanical connection or an electrical connection; they can refer to a direct connection or an indirect connection through an intermediate medium; and they can refer to the internal communication of two components or the interaction between two components. Those skilled in the art can understand the specific meaning of the above terms in this invention according to the specific circumstances.

[0055] Example 1

[0056] like Figure 1-4 As shown, a micro-aperture array temperature and pressure sensor includes an optical waveguide 110, a micro-aperture array 120, and a microcavity array 130. The optical waveguide 110 has an internal optical transmission channel. The micro-aperture array 120 and the microcavity array 130 are formed side by side in the optical transmission channel of the optical waveguide 110. The micro-aperture array 120 is connected to the external environment, while the microcavity array 130 is isolated from the external environment.

[0057] During sensing, the detection optical signal is coupled into the optical transmission channel of the optical waveguide 110, and then the reflected optical signal reflected back by the micro-aperture array grating 120 and the micro-cavity array grating 130 is received to obtain the reflection spectrum of the reflected optical signal. Since the micro-aperture array grating 120 and the micro-cavity array grating 130 have different center wavelengths, they can reflect different wavelength portions of the detection optical signal back. Therefore, the reflection spectrum has a first reflection peak corresponding to the micro-aperture array grating 120 and a second reflection peak corresponding to the micro-cavity array grating 130. Because the micro-aperture array grating 120 is connected to the external environment, the air medium inside it can freely circulate with the air medium in the external environment. Therefore, the effective refractive index of the micro-aperture array grating 120 is subject to environmental pressure and environmental factors, just like the refractive index of the air in the external environment. The effect of temperature: When the refractive index of the air in the external environment changes, the effective refractive index of the micro-aperture array grating 120 also changes, causing a wavelength shift in the first reflection peak. The refractive index of the air in the external environment can be obtained by demodulating the wavelength of the first reflection peak. Since the microcavity array grating 130 is isolated from the external environment, the air medium inside it cannot flow with the air medium in the external environment. Therefore, the effective refractive index of the microcavity array waveguide 110 is only affected by the ambient temperature. When the ambient temperature changes, the effective refractive index of the microcavity array grating 130 also changes, causing a wavelength shift in the second reflection peak. The ambient temperature can be obtained by demodulating the wavelength of the second reflection peak. Finally, the ambient pressure is calculated based on the refractive index of the air and the ambient temperature.

[0058] This patent simultaneously fabricates the micro-aperture array grating 120 and the microcavity array grating 130 in the optical waveguide 110. The micro-aperture array grating 120 and the microcavity array grating 130 can respectively sense and detect the air refractive index and ambient temperature of the external environment. Finally, the ambient pressure is calculated based on the air refractive index and ambient temperature of the external environment. When sensing ambient temperature, the microcavity array grating 130 is not affected by ambient pressure, while when sensing ambient pressure, the micro-aperture array grating 120 can use the ambient temperature detected by the microcavity array grating 130 to calculate the ambient pressure. This avoids the mutual interference between ambient temperature and ambient pressure during measurement, and enables simultaneous sensing of different ambient temperatures and different ambient pressures. It has advantages such as high reliability, high sensitivity, and easy serial multiplexing.

[0059] The ambient pressure P and the air refractive index n sensed by the microporous array grating 120 tp The following formula applies between the ambient temperature t sensed by the microcavity array grating 130 and the ambient temperature t:

[0060]

[0061] n s ×10 -8 =8342.54+2406147×[130-σ 2 ] -1 +15998×[38.9-σ 2 ] -1

[0062] The above formula is the dispersion formula for standard dry air, n s σ is the tail of the air refractive index under standard conditions, and σ is the wavenumber.

[0063] The micro-aperture array grating 120 and the micro-cavity array grating 130 are arranged as centrally as possible in the optical transmission channel. For example, they can be located on opposite sides of the axis of the optical transmission channel and at the same distance from the axis of the optical transmission channel. Alternatively, one of them can be located at the axis of the optical transmission channel and the other can be located on one side of the axis of the optical transmission channel.

[0064] The optical waveguide 110 can be an integrated optical waveguide or a cylindrical optical waveguide, and its waveguide material can be, but is not limited to, glass, sapphire, lutetium oxide, or ceramics; wherein, the integrated optical waveguide includes planar (thin film) dielectric optical waveguides and strip dielectric optical waveguides, and the cylindrical optical waveguide includes optical fiber.

[0065] like Figure 1 and 2 As shown, the optical waveguide 110 can be a dual-dielectric or multi-dielectric structure with a central dielectric layer 111 and an outer dielectric layer 112, such as a buried strip waveguide or a single-mode fiber. For this type of optical waveguide 110, due to the refractive index difference between the central dielectric layer 111 and the outer dielectric layer 112, the optical signal in the central dielectric layer 111 can undergo total internal reflection at the interface between the two layers, thus maintaining forward transmission within the central dielectric layer 111, which serves as the optical transmission channel.

[0066] like Figure 3 and 4 As shown, the optical waveguide 110 can also be a single-medium structure, using external air as the outer medium, such as sapphire optical fiber. For this type of optical waveguide 110, the entire interior of the optical waveguide 110 is the optical transmission channel.

[0067] The micro-aperture array grating 120 is located at the axis of the optical transmission channel, and the micro-cavity array grating 130 is located on one side of the axis of the optical transmission channel. Alternatively, the micro-aperture array grating 120 and the micro-cavity array grating 130 are located on both sides of the axis of the optical transmission channel and are equidistant from the axis of the optical transmission channel.

[0068] Preferably, if the optical waveguide 110 is a dual-dielectric or multi-dielectric structure, the micro-aperture array grating 120 is located at the axis of the central dielectric layer 111, and the microcavity array grating 130 is located on one side of the axis of the central dielectric layer 111. If the optical waveguide 110 is a single-dielectric structure, the micro-aperture array grating 120 and the microcavity array grating 130 are located on both sides of the axis of the optical waveguide 110 and are equidistant from the axis of the optical waveguide 110.

[0069] The micro-aperture array grating 120 includes a plurality of open micro-apertures 131, each of which is distributed along the light transmission direction of the optical waveguide 110 and is connected to the external environment. The arrangement of the micro-aperture array can be changed to form one of Bragg grating, phase shift grating or chirped grating.

[0070] Specifically, the open micropore 131 may be, but is not limited to, a cylindrical micropore, a conical micropore, or a trapezoidal micropore; at least one end of the open micropore 131 extends outside the optical waveguide 110, thereby communicating with the external environment.

[0071] In this embodiment, the extension direction of the open microaperture 131 is perpendicular to the light transmission direction of the optical waveguide 110. In a specific implementation, the extension direction of the open microaperture 131 may also be set at an inclined angle to the light transmission direction of the optical waveguide 110.

[0072] The microcavity array grating 130 includes multiple closed microcavities 131, each of which is distributed along the light transmission direction of the optical waveguide 110 and isolated from the external environment. The arrangement of the microcavity array can be changed to form one of the following: Bragg grating, phase-shift grating, or chirped grating.

[0073] Specifically, the closed microcavity 131 can be, but is not limited to, a spherical or ellipsoidal microcavity, etc. It may not have an extension direction (such as spherical), or it may be similar to the open micropore 131, having an extension direction (such as ellipsoidal) and its extension direction is perpendicular to or at an inclined angle to the light transmission direction of the optical waveguide 110, or it may be parallel to the extension direction of the open micropore 131; none of the directions of the closed microcavity 131 extend to the outside of the optical waveguide 110, thereby isolating it from the external environment.

[0074] It should be noted that the closed microcavity 131 is formed by a local refractive index change induced by external energy such as femtosecond laser to the internal medium of the optical waveguide 110. This part of the internal medium is eventually completely ablated or the refractive index changes permanently. Therefore, the interior of the closed microcavity 131 can be either a hollow microcavity (with a vacuum, air or vaporized medium material inside) or a solid microcavity (with a medium material with a changed refractive index inside).

[0075] The micro-aperture array grating 120 has a first center wavelength, and the microcavity array grating 130 has a second center wavelength, so that the reflection spectrum can form a first reflection peak corresponding to the micro-aperture array grating 120 and a second reflection peak corresponding to the microcavity array grating 130 at different wavelength positions.

[0076] Example 2

[0077] like Figure 6 As shown, a method for fabricating a microporous array grating temperature and pressure sensor is provided for fabricating the microporous array grating temperature and pressure sensor described in Example 1.

[0078] The preparation method includes the following steps:

[0079] Step 100: Design the structural parameters of the micro-aperture array grating 120 and the micro-cavity array grating 130 respectively.

[0080] In step 100, the structural parameters of the micro-aperture array grating 120 and the micro-cavity array grating 130 correspond to their respective grating parameters. The structural parameters of the micro-aperture array grating 120 and the micro-cavity array grating 130 can be obtained through simulation and design based on the required grating parameters.

[0081] The refractive index modulation pattern of the micro-aperture array grating 120 differs from that of the traditional ultraviolet laser-written optical waveguide grating 110 with a sinusoidal refractive index modulation pattern in the following two important ways: 1) The refractive index modulation of the micro-aperture array grating 120 is a square wave pattern with a large refractive index difference; 2) The refractive index modulation region of the micro-aperture array grating 120 is composed of open micro-apertures 131 with a high aspect ratio, covering only the central region of the optical transmission channel. Therefore, the Rouard algorithm and the transfer matrix method are combined to simulate and design the micro-aperture array grating 120. The structural parameters of the micro-aperture array grating 120 are obtained through simulation. The aperture of the open micro-apertures 131 corresponds to the width of the refractive index modulation region of the micro-aperture array grating 120, and the spacing between the open micro-apertures 131 corresponds to the grating period, duty cycle, number of periods, and grating order of the micro-aperture array grating 120. On the other hand, the influence of the micro-aperture offset of the open micro-aperture 131 on the overlapping integral is studied through simulation, that is, the influence on the reflectivity of the micro-aperture array grating 120.

[0082]

[0083] In the above formula, R0, S0, R M S M These are the complex amplitudes of the forward and reverse transmission modes at the beginning and end of the micro-aperture array grating 120, respectively; M is the number of open micro-apertures 131 set in the simulation; and F... M Let be the transmission matrix of the Mth open micropore 131.

[0084]

[0085] Each open microaperture 131 can be considered as a uniform weak grating, and its transmission matrix is ​​shown in the formula above, where κ is the AC coupling coefficient; σ is the DC coupling coefficient; Δz is the microaperture spacing of the microaperture array grating 120; γ B The value is defined as the square root of the difference between the squares of the AC coupling coefficient and the DC coupling coefficient. On the other hand, the open microaperture 131 only covers a portion of the optical transmission channel, and the overlapping integral η of the microaperture array grating 120... v The coupling coefficient κ varies depending on the location and diameter of the open micropore 131. Therefore, the coupling coefficient κ for each mode order changes. v The relationship between the location and the size of the open micropore 131 is κ. v =η v πΔn / λB, where Δn is the refractive index modulation amount, and λ B ν is the wavelength of the first reflection peak of the micro-aperture array grating 120, and v is the optical frequency of the detected optical signal.

[0086] Step 200: The micro-aperture array grating 120 and the microcavity array grating 130 are sequentially etched in the optical transmission channel of the optical waveguide 110 using a femtosecond laser to obtain the micro-aperture array grating temperature and pressure sensor.

[0087] In step 200, a femtosecond laser writing system is used to modulate the refractive index inside the optical waveguide 110 to sequentially form the micro-aperture array grating 120 and the microcavity array grating 130.

[0088] like Figure 5 As shown, the femtosecond laser marking system includes an optical subsystem and a motion subsystem. The optical subsystem is used to shape the femtosecond laser, and the motion subsystem is used to drive the optical waveguide 110 to move. The optical subsystem includes a femtosecond laser 1, a power attenuator 2, a polarization controller 3, a mechanical shutter 4, a beam splitter 5, a Michelson interferometer 5, a spatial light modulator 7, a focusing lens 8, a dichroic mirror 9, a focusing objective lens 10, and a CCD camera 11. The Michelson interferometer 5 has a first interferometer arm and a second interferometer arm. The first interferometer arm includes a first reflector 61, and the second interferometer arm includes a second reflector 62 and a one-dimensional displacement platform 63. The femtosecond laser... Optical device 1, power attenuator 2, polarization controller 3, mechanical shutter 4, beam splitter 5, spatial light modulator 7, focusing lens 8, dichroic mirror 9, and focusing objective lens 10 are arranged sequentially along the propagation path of the femtosecond laser. The first reflecting mirror 61 and the second reflecting mirror 62 of the Michelson interferometer 5 are respectively arranged on the two beam splitting paths of the beam splitter 5. The CCD camera 11 is located on the side of the dichroic mirror 9 facing away from the focusing objective lens 10. The motion subsystem includes a rotating clamp 12, a six-axis pitch platform 13, and a precision displacement platform 14. The rotating clamp 12 is arranged on the six-axis pitch platform 13, and the six-axis pitch platform 13 is arranged on the precision displacement platform 14.

[0089] The single-pulse femtosecond laser emitted by the femtosecond laser 1 passes sequentially through the power attenuator 2, polarization controller 3, and mechanical shutter 4 for power attenuation adjustment, polarization state adjustment, and optical path on / off control before entering the beam splitter 5. The beam splitter 5 splits the single-pulse femtosecond laser into two mutually perpendicular femtosecond laser beams at a 1:1 ratio. One femtosecond laser beam enters the first interferometer arm of the Michelson interferometer 5 and is reflected back into the beam splitter 5 by the first reflector 61. The other femtosecond laser beam enters the second interferometer arm of the Michelson interferometer 5 and is reflected back into the beam splitter 5 by the second reflector 62. The one-dimensional displacement platform 63 moves the second reflector 62 to adjust the distance between the second reflector 62 and the beam splitter 5, creating an optical path difference between the two femtosecond laser beams, thereby generating... Pulse delay is used to convert the single-pulse femtosecond laser into a dual-pulse femtosecond laser, achieving pulse shaping in timing. Then, the dual-pulse femtosecond laser is re-emitted onto the spatial light modulator 7, and modulated by the phase map of the conical lens loaded in the spatial light modulator 7 to convert the dual-pulse femtosecond laser from a Gaussian beam into a Bessel beam, achieving pulse shaping in space. After reflection, transmission, and focusing by the focusing lens 8, dichroic mirror 9, and focusing objective lens 10, the dual-pulse Bessel beam is focused into the optical transmission channel of the optical waveguide 110. Meanwhile, the six-axis pitch platform 13 and the precision displacement platform 14 drive the rotating fixture 12 to pitch and displacement during the writing process of the micro-aperture array grating 120 and the micro-cavity array grating 130, thereby adjusting the writing pose of the optical waveguide 110.

[0090] Specifically, such as Figure 7 As shown, in step 200, the steps of sequentially etching the micro-aperture array grating 120 and the microcavity array grating 130 in the optical transmission channel of the optical waveguide 110 using a femtosecond laser are as follows:

[0091] Step 210: Build the femtosecond laser writing system described above.

[0092] Step 220: Clamp and fix the optical waveguide 110 on the rotating clamp 12.

[0093] Step 230: Load the desired cone lens phase map into the spatial light modulator 7.

[0094] Step 240: Control the femtosecond laser 1 to emit a single-pulse femtosecond laser, so that the single-pulse femtosecond laser is shaped by the Michelson interferometer 5 and the spatial light modulator 7 to form a double-pulse Bessel beam, and focus the double-pulse Bessel beam in the optical transmission channel of the optical waveguide 110.

[0095] Step 250: The six-axis pitch platform 13 and the precision displacement platform 14 drive the rotating fixture 12 to pitch and move, thereby adjusting the writing pose of the optical waveguide 110 so that the dual-pulse Bessel beam can write the micro-aperture array grating 120 in the optical transmission channel of the optical waveguide 110.

[0096] Step 260: Block the first or second interferometer arm of the Michelson interferometer 5 and do not load any cone lens phase map in the spatial light modulator 7.

[0097] Step 270: Control the femtosecond laser 1 to emit the single-pulse femtosecond laser again, and focus the single-pulse femtosecond laser in the optical transmission channel of the optical waveguide 110.

[0098] Step 280: The six-axis pitch platform 13 and the precision displacement platform 14 drive the rotating fixture 12 to pitch and move, thereby adjusting the writing pose of the optical waveguide 110 so that the single-pulse femtosecond laser can write the microcavity array grating 130 in the optical transmission channel of the optical waveguide 110.

[0099] During the writing process, the repetition rate of the femtosecond laser 1 and the moving speed of the optical waveguide 110 can be adjusted to flexibly control the grating period of the micro-aperture array grating 120 and the micro-cavity array grating 130. The CCD camera 11 can then perform real-time imaging of the optical waveguide 110 through the focusing objective lens 10 to observe the grating morphology of the micro-aperture array grating 120 and the micro-cavity array grating 130 in real time.

[0100] Step 300: Etch the micro-hole array grating 120 using an etching solution.

[0101] In step 300, because the inner wall of the open micro-orifice 131 etched by femtosecond laser is relatively rough, the spectral quality of the micro-orifice array grating 120 is poor. To ensure the smoothness of the inner wall of the micro-orifice of the micro-orifice array grating 120 and improve its spectral quality, a chemical etching method is used to reduce the insertion loss of the device. Simultaneously, etching can finely control the aperture of the micro-orifice array grating 120 and flexibly adjust its duty cycle to regulate and optimize its refractive index sensitivity. Furthermore, since the closed microcavity 131 of the microcavity array grating 130 is not connected to the outside, the etching solution will not enter the closed microcavity 131 of the microcavity array grating 130 when etching the inner wall of the open micro-orifice 131 of the microcavity array grating 120, thus preventing damage to the microcavity array grating 130.

[0102] Specifically, such as Figure 8 As shown, in step 300, the etching process of the micro-aperture array grating 120 of the optical waveguide 110 using an etching solution is as follows:

[0103] Step 310: Place the micro-pore array grating temperature and pressure sensor into the etching solution.

[0104] In step 310, the etching solution can be contained in a sealed container made of plastic or glass, and the sealed container containing the etching solution can be heated by a resistance wire to accelerate the etching speed.

[0105] If the optical waveguide 110 is made of quartz, the etching solution is preferably, but not limited to, 5% hydrofluoric acid, and the sealed container is made of plastic; if the optical waveguide 110 is made of sapphire, the etching solution is preferably, but not limited to, a mixture of sulfuric acid and phosphoric acid with a molar ratio of 3:1, and the sealed container is made of glass.

[0106] When etching the sapphire waveguide 110, the temperature of the etching solution can be maintained at around 330°C. At the same time, a glass sleeve is used to protect the waveguide 110 outside the sealed container to prevent sulfate from being deposited on the part of the waveguide 110 outside the sealed container due to the influence of the etching solution.

[0107] Step 320: Connect the microporous array grating temperature and pressure sensor to the spectral monitoring system, and obtain the reflection spectrum of the microporous array grating temperature and pressure sensor in real time through the spectral monitoring system.

[0108] In step 320, the spectral monitoring system includes a detection laser, a spectrometer, and a circulator. The circulator has an incident end, a reflecting end, and a transmitting end. The incident end is connected to the detection laser, the reflecting end is connected to the spectrometer, and the transmitting end is connected to the micropore array grating temperature and pressure sensor. The detection light signal emitted by the detection laser is coupled into the micropore array grating temperature and pressure sensor via the circulator. The reflected light signal reflected back by the micropore array grating temperature and pressure sensor is coupled to the spectrometer via the circulator. The spectrometer collects and outputs the reflection spectrum of the reflected light signal, thereby obtaining the first reflection peak and the second reflection peak corresponding to the micropore array grating 120 and the microcavity array grating 130 on the reflection spectrum, respectively.

[0109] Step 330: Observe the reflection spectrum of the micro-pore array grating temperature and pressure sensor. When the first reflection peak corresponding to the micro-pore array grating 120 in the reflection spectrum gradually becomes smooth and the loss is minimal, remove the micro-pore array grating temperature and pressure sensor from the etching solution.

[0110] Step 340: Clean the micropore array grating temperature and pressure sensor.

[0111] In step 340, the micropore array grating temperature and pressure sensor can be immersed in distilled water and then ultrasonically cleaned in isopropanol solution to thoroughly remove the residual etching solution on the micropore array grating temperature and pressure sensor.

[0112] Step 400: Perform high-temperature annealing on the micropore array grating temperature and pressure sensor.

[0113] In step 400, in order to release the internal residual stress of the micropore array grating 120 and the microcavity array grating 130 and increase the thermal stability and reliability of the micropore array grating 120 and the microcavity array grating 130, the fabricated micropore array grating temperature and pressure sensor is placed in a high-temperature furnace for long-term annealing. During the annealing process, the spectral monitoring system is used to monitor and record the reflection spectrum of the micropore array grating temperature and pressure sensor in real time until the wavelengths of the first and second reflection peaks of the reflection spectrum tend to stabilize.

[0114] Specifically, during high-temperature annealing, if the optical waveguide 110 is made of quartz, the annealing temperature is gradually increased from room temperature (20°C) to 900°C. If the optical waveguide 110 is made of sapphire, the annealing temperature is gradually increased from room temperature (20°C) to 1500°C. The heating rate is 10°C / min, and the temperature is kept stable for one hour after each 100°C increase. After the wavelength of the reflected spectrum stabilizes, the temperature is increased again.

[0115] Example 3

[0116] like Figure 9 As shown, a test and calibration method for a microporous array grating temperature and pressure sensor is provided for testing and calibrating the microporous array grating temperature and pressure sensor described in Example 1.

[0117] The test and calibration method for the aforementioned microporous array grating temperature and pressure sensor includes the following steps:

[0118] Step S1: Under normal pressure environment P0, the micro-aperture array grating temperature and pressure sensor is placed in different temperature environments to obtain the first reflection peak wavelength of the micro-aperture array grating 120 in different temperature environments and the second reflection peak wavelength of the micro-cavity array grating 130 at different temperatures. The ambient temperature-first reflection peak wavelength response relationship of the micro-aperture array grating 120 under normal pressure P0 and the ambient temperature-second reflection peak wavelength response relationship of the micro-cavity array grating 130 are respectively fitted.

[0119] In step S1, the spectral monitoring system is used to detect the reflection spectrum of the micro-aperture array grating temperature and pressure sensor at different temperatures under normal pressure environment P0. When the micro-aperture array grating 120 and the microcavity array grating 130 are at different temperatures, the effective refractive index of the micro-aperture array grating 120 and the microcavity array grating 130 changes due to the photothermal effect, which causes the wavelength shift of the first reflection peak and the second reflection peak. Then, a polynomial fitting function is used to linearly fit the wavelength of the first reflection peak of the micro-aperture array grating 120 at different temperatures and the wavelength of the second reflection peak of the microcavity array grating 130 at different temperatures, respectively, to obtain the ambient temperature-first reflection peak wavelength response relationship and the ambient temperature-second reflection peak wavelength response relationship under normal pressure P0.

[0120] Step S2: Under different temperature environments, the microporous array grating temperature and pressure sensor is placed in different pressure environments, and the first reflection peak wavelength of the microporous array grating 120 under different pressure environments is obtained. The environmental pressure-first reflection peak wavelength response relationship and pressure sensitivity of the microporous array grating 120 under different temperature environments are then fitted respectively.

[0121] In step S2, the spectral monitoring system is used to detect the reflection spectrum of the microporous array grating temperature and pressure sensor under different pressure environments. When the microporous array grating 120 is under different temperature and pressure environments, the effective refractive index of the microporous array grating 120 is affected by both ambient temperature and ambient pressure, which will change and cause the wavelength of the first reflection peak to drift. Then, a polynomial fitting function is used to linearly fit the wavelength of the first reflection peak of the microporous array grating 120 under different temperature and pressure environments to obtain the ambient pressure-first reflection peak wavelength response relationship and pressure sensitivity (slope of the response relationship) at different ambient temperatures.

[0122] Step S3: Place the microcavity array grating temperature and pressure sensor in the calibration environment, and calculate the ambient temperature T1 of the calibration environment based on the second reflection peak wavelength of the microcavity array grating 130 in the calibration environment and the ambient temperature-second reflection peak wavelength response formula.

[0123] In step S3, since the effective refractive index of the microcavity array grating 130 is not affected by the ambient pressure, the ambient temperature T1 of the calibration environment can be calculated by substituting the second reflection peak wavelength of the microcavity array grating 130 in the calibration environment into the ambient temperature-second reflection peak wavelength response formula.

[0124] Step S4: Based on the relationship between ambient pressure and wavelength response of the first reflection peak under different temperature environments, calculate the total wavelength shift Δλ of the micro-aperture array grating 120 when it changes from a normal temperature and pressure environment to the calibration environment. Also, based on the relationship between ambient temperature and wavelength response of the first reflection peak under normal pressure environment P0, calculate the wavelength shift component Δλ caused by the change in ambient temperature when the micro-aperture array grating 120 changes from a normal temperature and pressure environment to the calibration environment. T Then, the total wavelength drift Δλ of the micro-aperture array grating 120 is subtracted from its wavelength drift component Δλ. T The wavelength shift component Δλ caused by the change in ambient pressure when the micro-aperture array grating 120 changes from a normal temperature and pressure environment to the calibration environment is obtained. p .

[0125] In step S4, the wavelength of the first reflection peak of the micro-aperture array grating 120 under normal temperature and pressure is found by using the environmental pressure-first reflection peak wavelength response relationship of the micro-aperture array grating 120 under different temperature environments. Then, the wavelength of the first reflection peak of the micro-aperture array grating 120 under normal temperature and pressure is subtracted from the wavelength of the first reflection peak of the micro-aperture array grating 120 under the calibration environment to obtain the total wavelength drift Δλ of the micro-aperture array grating 120.

[0126] Similarly, by using the relationship between ambient temperature and the wavelength of the first reflection peak of the micro-aperture array grating 120 under normal pressure P0, the wavelength of the first reflection peak of the micro-aperture array grating 120 under normal pressure P0 and temperature T1 can be found. Then, by subtracting the wavelength of the first reflection peak of the micro-aperture array grating 120 under normal pressure P0 and temperature T1 from the wavelength of the first reflection peak under the calibration environment, the wavelength shift component Δλ caused by the change in ambient temperature when the micro-aperture array grating 120 changes from the normal temperature and pressure environment to the calibration environment can be obtained. T .

[0127] Step S5: Calculate the ambient pressure of the calibration environment: P = P0 + Δλ P / S P,T1 , of which S P,T1 The pressure sensitivity of the micropore array grating at ambient temperature T1 is given.

[0128] In step S5, the calculated value of the ambient pressure of the calibration environment is compared with its actual value to determine the sensing error of the micro-pore array grating temperature and pressure sensor to the ambient pressure. Then, the error correction coefficient is calculated and written into the demodulation device of the micro-pore array grating temperature and pressure sensor.

[0129] Preferably, the test calibration method of this patent can be performed in the high-temperature annealing step of the micropore array grating temperature and pressure sensor, and is completed together with the high-temperature annealing step.

[0130] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the embodiments of the present invention and not to limit them. Although the embodiments of the present invention have been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can still be made to the technical solutions of the embodiments of the present invention, and these modifications or equivalent substitutions cannot cause the modified technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A microcell array optical grating temperature pressure sensor, characterized by, The application relates to a micro-hole array grating and a micro-cavity array grating, and a micro-hole array grating temperature and pressure sensor.

2. The microcell array optical grating temperature pressure sensor of claim 1, wherein, The light waveguide is an integrated light waveguide or a cylindrical light waveguide, and the waveguide material is glass, sapphire, lutetium oxide or ceramic; wherein the integrated light waveguide comprises a planar medium light waveguide and a strip-shaped medium light waveguide, and the cylindrical light waveguide comprises an optical fiber.

3. The microcell arrayed grating temperature pressure sensor of claim 1, wherein, The environmental pressure P and the air refractive index n sensed by the microwell array grating tp The environmental temperature t sensed by the microwell array grating satisfies the following formula: The above equation is the dispersion equation for standard dry air, n s is the mantissa of the refractive index of air at standard conditions, and σ is the wave number.

4. The method of claim 1, wherein the microcell array optical grating temperature pressure sensor is prepared by the steps of: The application further relates to a method for manufacturing a micro-hole array grating temperature and pressure sensor. After step 200, the following steps are further included: Step 300: etching the micro-hole array grating by using an etching liquid.

5. The method for fabricating a microporous array grating temperature and pressure sensor according to claim 4, characterized in that, After step 300, the following steps are further included: Step 400: high-temperature annealing the micro-hole array grating temperature and pressure sensor.

6. The method for fabricating a microporous array grating temperature and pressure sensor according to claim 5, characterized in that, In step 200, the steps of sequentially writing the micro-hole array grating and the micro-cavity array grating in the light transmission channel of the light waveguide by using a femtosecond laser are as follows: ​ 7. The method for fabricating a microporous array grating temperature and pressure sensor according to claim 4, characterized in that, ​ Step 210: build a femtosecond laser writing system, the femtosecond laser writing system comprising an optical subsystem and a motion subsystem, the optical subsystem being used for shaping femtosecond laser, the motion subsystem being used for driving the optical waveguide to move; the optical subsystem comprises a femtosecond laser, a power attenuator, a polarization controller, a mechanical shutter, a beam splitter, a Michelson interferometer, a spatial light modulator, a focusing lens, a dichroic mirror, a focusing objective and a CCD camera, the Michelson interferometer having a first interference arm and a second interference arm, the first interference arm comprising a first mirror, the second interference arm comprising a second mirror and a one-dimensional displacement platform; wherein the femtosecond laser, the power attenuator, the polarization controller, the mechanical shutter, the beam splitter, the spatial light modulator, the focusing lens, the dichroic mirror and the focusing objective are sequentially arranged along the propagation path of the femtosecond laser, the first mirror and the second mirror of the Michelson interferometer are respectively arranged on the two light splitting paths of the beam splitter, and the CCD camera is located on the side of the dichroic mirror away from the focusing objective; the motion subsystem comprises a rotary clamp, a six-axis tilt platform and a precision displacement platform, the rotary clamp is arranged on the six-axis tilt platform, and the six-axis tilt platform is arranged on the precision displacement platform; Step 220: clamping and fixing the optical waveguide on the rotary clamp; Step 230: loading the required tapered lens phase pattern in the spatial light modulator; Step 240: controlling the femtosecond laser to emit a single pulse femtosecond laser, making the single pulse femtosecond laser form a double pulse Bessel beam after shaping by the Michelson interferometer and the spatial light modulator, and focusing the double pulse Bessel beam in the light transmission channel of the optical waveguide; Step 250: adjusting the writing position of the optical waveguide by tilting and displacing the rotary clamp through the six-axis tilt platform and the precision displacement platform, so that the double pulse Bessel beam is written in the light transmission channel of the optical waveguide to form the micro-hole array grating; Step 260: shielding the first interference arm or the second interference arm of the Michelson interferometer, and not loading any tapered lens phase pattern in the spatial light modulator; Step 270: controlling the femtosecond laser to emit the single pulse femtosecond laser again, and focusing the single pulse femtosecond laser in the light transmission channel of the optical waveguide; Step 280: adjusting the writing position of the optical waveguide by tilting and displacing the rotary clamp through the six-axis tilt platform and the precision displacement platform, so that the single pulse femtosecond laser is written in the light transmission channel of the optical waveguide to form the micro-cavity array grating.

8. The method of testing and calibrating a microcell array optical grating temperature pressure sensor of claim 1, wherein, Comprising the following steps: Step S1: placing the micro-hole array grating temperature and pressure sensor in different temperature environments under normal pressure environment P0 to obtain the first reflection peak wavelength of the micro-hole array grating in different temperature environments and the second reflection peak wavelength of the micro-cavity array grating at different temperatures, and respectively fitting to obtain the ambient temperature-first reflection peak wavelength response formula of the micro-hole array grating under normal pressure P0 and the ambient temperature-second reflection peak wavelength response formula of the micro-cavity array grating; Step S2: placing the micro-hole array grating temperature and pressure sensor in different pressure environments under different temperature environments, and obtaining the first reflection peak wavelength of the micro-hole array grating in different pressure environments, and respectively fitting to obtain the ambient pressure-first reflection peak wavelength response formula and the pressure sensitivity of the micro-hole array grating under different temperature environments; Step S3: placing the micro-hole array grating temperature and pressure sensor in a calibration environment, and calculating the ambient temperature T1 of the calibration environment according to the second reflection peak wavelength of the micro-cavity array grating in the calibration environment and the ambient temperature-second reflection peak wavelength response formula; Step S4: according to the environmental pressure-first reflection peak wavelength response relationship of the microwell array grating at different temperature environments, the wavelength shift total amount Δλ of the microwell array grating changing from normal temperature and pressure environment to the calibration environment is calculated, and according to the environmental temperature-first reflection peak wavelength response relationship of the microwell array grating at the normal pressure environment P0, the wavelength shift component Δλ caused by the change of the environmental temperature of the microwell array grating changing from normal temperature and pressure environment to the calibration environment is calculated T Then, the wavelength shift total amount Δλ of the microwell array grating is subtracted by the wavelength shift component Δλ, and the wavelength shift component Δλ caused by the change of the environmental pressure of the microwell array grating changing from normal temperature and pressure environment to the calibration environment is obtained T p ;​ Step S5: calculating the environmental pressure of the calibration environment P = P0+ Δλ P / S P, T1 where S P, T1 is the pressure sensitivity of the microwell array grating at the environmental temperature T1.

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