A SHUPE error evaluation and suppression method for optical fiber rings based on distributed circumferential strain

Abstract

This invention belongs to the field of fiber optic gyroscope technology, specifically relating to a method for evaluating and suppressing SHUPE errors in fiber optic rings based on distributed circumferential strain. By testing the isothermal distributed circumferential strain of the fiber optic ring, this invention establishes a correspondence between the strain and the SHUPE error of the fiber optic ring, enabling the evaluation of the variable-temperature performance of the fiber optic ring. Furthermore, based on the geometric parameters of each component of the fiber optic ring and the material parameters at different temperature points, SHUPE errors can be suppressed during the forward design stage of the fiber optic ring, thereby effectively improving the variable-temperature performance of the fiber optic ring.

Description

Technical Field

[0001] This invention belongs to the field of fiber optic gyroscope technology, specifically relating to a method for evaluating and suppressing the error of a fiber optic loop SHUPE based on distributed circumferential strain. Background Technology

[0002] The fiber optic loop is the sensitive core component of a fiber optic gyroscope; in principle, its performance determines the gyroscope's performance. Since fiber optic gyroscope applications often involve variable temperature environments, the performance of the fiber optic loop in these environments is particularly crucial. The fiber optic loop operates based on the Sagnac effect. Limited by its structure, fiber materials, and manufacturing processes, changes in the environmental field alter the internal characteristics of the sensitive fiber, ultimately introducing a non-reciprocal phase difference that affects the gyroscope's accuracy. This asymmetric temperature disturbance causes a non-reciprocal phase shift in the fiber optic loop, known as the "SHUPE error." In fact, the "SHUPE error" in the fiber optic loop is not comprehensive. Thermal strain and stress caused by temperature, according to the photoelastic effect, can also affect the core refractive index, generating a thermally induced non-reciprocal error (SHUPE error). This is similar to the strain and stress mechanism in stress-type polarization-maintaining fibers, becoming a significant factor limiting the high-precision application of fiber optic gyroscopes.

[0003] For example, the fiber optic ring bonding performance evaluation method based on Brillouin time-domain stress analysis described in CN202311812700.6 only considers process improvement from the perspective of fiber optic ring bonding and does not establish the relationship between fiber optic ring strain and SHUPE error; the method for testing the temperature distribution of fiber optic ring in fiber optic gyroscope described in CN201811116125.5 does not actually use the strain curve for fiber optic ring performance evaluation; the temperature compensation method for fiber optic gyroscope described in CN201811237609.5 can only be compensated by algorithm through temperature variation test after the fiber optic ring is connected to the fiber optic gyroscope system. Summary of the Invention

[0004] The technical problem solved by this invention is to propose a quantitative evaluation and suppression method for thermally induced zero-bias error (SHUPE error), which is a major factor affecting gyroscope performance. By measuring the distributed circumferential strain of the fiber optic ring at a specific temperature point, the zero-bias error can be calculated through modeling. Based on the established model, the influence of different material properties on the zero-bias error can be studied. Furthermore, by analyzing and optimizing the material properties, the SHUPE error can be suppressed.

[0005] The technical solution of this invention:

[0006] A method for evaluating and suppressing the error of a fiber optic loop SHUPE based on distributed circumferential strain, the method comprising the following steps:

[0007] Step 1: Calculate the total length L of the sensitive fiber of the fiber ring, the length of each layer of sensitive fiber, and the outer diameter based on the number of layers, number of turns, inner radius, and size parameters of the fiber used.

[0008] Step 2: Measure the distributed circumferential strain of the fiber optic ring at different temperature points using BOTDA. After baseline calibration and subtraction of strain curves at adjacent temperature points, obtain the circumferential distributed strain difference per unit temperature. ;

[0009] Step 3: Treat each layer of optical fiber as a micro-segment Considering constant slope and varying temperature conditions Calculate the phase difference between adjacent layers ;

[0010] Step 4: Using the phase difference between adjacent layers Solving for the zero bias error of adjacent layers; finally, the fiber optic gyroscope SHUPE error generated by the fiber optic loop. It equals the sum of the zero-bias errors of each adjacent fiber layer;

[0011] Step 5: Calculate the circumferential distributed strain difference per unit temperature Following steps 3 and 4, the SHUPE error is calculated to establish the correspondence between strain difference and SHUPE error. Then, the SHUPE error is suppressed by changing the material properties.

[0012] Furthermore, in step 1,

[0013] The radius Ri of the i-th layer of sensitive fiber is calculated using the following formula:

[0014]

[0015] The length of the i-th layer of sensitive optical fiber is: M layer The number of turns for each layer of the fiber optic ring

[0016] N coil The sum of the lengths of the layers of sensitive optical fibers is denoted as the total length L of the sensitive optical fibers in the optical fiber ring.

[0017] Furthermore, in step 2,

[0018] BOTDA center frequency variation Temperature change of optical fiber and strain change They are directly proportional, establishing the following linear correlation:

[0019] in, The strain coefficient representing frequency shift, with units of MHz / με; Represents the temperature coefficient, with units of MHz / °C;

[0020] The distributed circumferential strain at adjacent temperature points is subtracted, and then divided by the difference between the temperature points to obtain the strain difference curve under unit temperature change. This leads to the strain difference slope curve, and ultimately, the strain difference data between adjacent layers at a specific temperature point. .

[0021] Furthermore, in step 3,

[0022] according to Calculate the phase difference between adjacent layers Where L is the fiber loop length in meters (m); λ is the average wavelength of the optical signal in meters (m); c is the optical signal velocity in meters per second (m / s); and n is the effective refractive index of the optical fiber. For the m-th infinitesimal segment coordinates Regarding the unit temperature-dependent strain difference of the symmetrical infinitesimal segment at the midpoint.

[0023] Furthermore, in step 4,

[0024] Thermally induced zero bias error of fiber optic gyroscope generated by fiber optic loop :

[0025]

[0026] The average diameter of the fiber optic ring sensitive fiber. The phase difference between adjacent fiber layers sum.

[0027] Furthermore, thermally induced zero bias error The smaller the fiber optic ring, the better its performance.

[0028] Furthermore, in step 5,

[0029] A model is established, and the average temperature slope of adjacent layers is selected based on the geometric parameters of each component of the sensitive optical fiber material and the material parameters under different temperature conditions. The length of each layer of optical fiber is calculated by using the radius and number of turns of each layer of the sensitive optical fiber in the optical fiber ring as a micro-element segment.

[0030] The circumferential distributed strain difference per unit temperature was calculated. Following steps 3 and 4, the SHUPE error is calculated to determine the influence of each material parameter on the SHUPE error, establish the correspondence between strain difference and SHUPE error, and then suppress the SHUPE error by changing the material properties.

[0031] Furthermore, the circumferential distributed strain difference per unit temperature was calculated. Specifically:

[0032] The final dimensions of the fiber optic ring are obtained by superimposing the dimensional parameters after radial translation and the dimensional parameters after four-way expansion. These final dimensions include at least the change in the outer diameter of the fiber optic ring. and inner diameter change Combined with the change in the outer diameter of the fiber optic ring and inner diameter change The strain difference data between adjacent layers at a single temperature is obtained, and then the strain difference data between adjacent layers at all specific temperature points is obtained. : .

[0033] The beneficial effects of the present invention are as follows:

[0034] This invention evaluates the impact of material parameter variations on the SHUPE error of fiber optic rings, providing a simple evaluation method to suppress SHUPE errors and improve variable-temperature performance. By testing the isothermal distributed circumferential strain of the fiber optic ring, a correlation can be established between the strain and the SHUPE error, enabling the evaluation of the variable-temperature performance of the fiber optic ring. Furthermore, based on the geometric parameters of each component of the fiber optic ring and the material parameters at different temperature points, SHUPE errors can be suppressed during the forward design phase of the fiber optic ring, thereby effectively improving its variable-temperature performance. Attached Figure Description

[0035] Figure 1 A flowchart of an error evaluation and suppression method for fiber optic loop SHUPE based on distributed circumferential strain;

[0036] Figure 2 Test the circumferentially distributed strain connection device for BOTDA;

[0037] 1-Industrial control computer, 2-BOTDA, 3-Fiber optic patch cord, 4-Fiber optic ring, 5-High and low temperature test chamber

[0038] Figure 3 This diagram shows the arrangement of sensitive optical fibers inside the optical fiber ring and an enlarged view of the inside of the optical fiber.

[0039] 6-Wrapping adhesive, 7-Outer coating, 8-Inner coating, 9-Fiber cladding. Detailed Implementation

[0040] The technical solution of the present invention will be described in detail with reference to the accompanying drawings.

[0041] This invention establishes a correlation between the isothermal distributed circumferential strain of the fiber optic ring and the SHUPE error of the fiber optic ring by testing the isothermal distributed circumferential strain, thereby enabling the evaluation of the variable temperature performance of the fiber optic ring. Furthermore, based on the geometric parameters of each component of the fiber optic ring and the material parameters at different temperature points, the SHUPE error can be suppressed during the forward design stage of the fiber optic ring, thus effectively improving the variable temperature performance of the fiber optic ring.

[0042] Based on the above analysis, the present invention aims to provide a method for evaluating and suppressing the SHUPE error of an optical fiber ring based on distributed circumferential strain, in order to solve the problem of suppressing the SHUPE error in the forward design of an optical fiber ring.

[0043] A specific embodiment of the present invention discloses a method for evaluating and suppressing the SHUPE error of an optical fiber loop based on distributed circumferential strain, such as... Figure 1 As shown, it includes the following steps:

[0044] Step 1: Taking a certain type of fiber ring as an example, perform the calculation. A panda-type polarization-maintaining fiber with a cladding diameter d1 = 60 μm, an inner coating diameter d2 = 80 μm, and an outer coating diameter (outer diameter) d = 100 μm is wound into a ring using an orthogonal octagonal symmetric winding method. The inner diameter of the fiber ring is D = 47.5 mm, and the number of fiber ring layers is N. coil =40 layers, M corresponding to each layer of the fiber optic ring layer =83 turns, the total length of the sensitive fiber in the fiber ring is calculated to be L=531.7m, and the radius Ri of the i-th layer of sensitive fiber can be calculated using the following formula:

[0045]

[0046] The outer diameter D of the fiber optic ring out =R 40 +1 / 2×D, fiber optic loop height H coil =M layer ×d;

[0047] The length of the i-th layer of sensitive optical fiber is:

[0048]

[0049] N coil The sum of the lengths of the layers of sensitive optical fibers is denoted as the total length L of the sensitive optical fibers in the optical fiber ring.

[0050] Step 2: Schematic diagram of the circumferential distributed strain connection device for BOTDA testing (see figure) Figure 2The fiber optic ring is secured to a tray with high-temperature tape and placed in a high-low temperature test chamber. The fiber optic loop's pigtail is extended 30cm, marked with ends A and B, and extends from the side hole of the test chamber. The remaining pigtail is coiled and secured to the tray with high-temperature tape. The high-low temperature test chamber controls the fiber optic ring to operate within a specific temperature environment. The fiber optic patch cord's pigtail is also extended 30cm, marked with ends A' and B'. Polarization-maintaining fusion splices are then applied to ends A and A' using a polarization-maintaining fusion splice, and to ends B and B' using the same splice. After splicing, the interface at end A' of the fiber optic patch cord is connected to the BOTDA pump output connector, and the interface at end B' is connected to the BOTDA probe output connector. The BOTDA is controlled by an industrial control computer via a data line for distributed circumferential strain curve acquisition.

[0051] The fiber optic patch cord is a polarization-maintaining fiber in the 1550nm band.

[0052] The micro-strain analyzer BOTDA is NBX-6055(PM) and has two fiber optic ports.

[0053] The industrial control computer is connected to BOTDA via a data cable.

[0054] The high and low temperature test chamber has a temperature range of -70 to +150℃, with specific temperature points including -45℃, -25℃, -5℃, 15℃, 35℃, 55℃, and 75℃. Each temperature point is held for 50 minutes, and the distributed circumferential strain data of the fiber optic ring is collected starting at 45 minutes.

[0055] After the distributed circumferential strain data acquisition is completed, the data is processed.

[0056] (1) Baseline calibration

[0057] The BOTDA testing principle is based on the stimulated Brillouin amplification effect generated between the pump pulse light and the continuous probe light. By scanning the frequency difference between the two light sources and recording the magnitude of energy transfer along the fiber at each frequency difference, the Brillouin gain spectrum along the fiber can be obtained. Lorentz fitting of the Brillouin gain spectrum yields the Brillouin frequency shift distribution along the fiber, thus achieving fully distributed sensing of fiber strain.

[0058] BOTDA center frequency variation Temperature change of optical fiber and strain change They are directly proportional, and the following linear correlation can be established.

[0059]

[0060] in, The strain coefficient representing frequency shift, with units of MHz / με; This represents the temperature coefficient, measured in MHz / °C. During the test, the instrument will use the calibration values ​​for calculations. Typically 0.04970MHz / με, Typically 1.07000MHz / °C, during calibration, the temperature-dependent values ​​are assumed to be under strain-free conditions. Calibration is performed. By aligning the baseline, the temperature term can be eliminated, thereby allowing demodulation of strain value changes.

[0061] The pigtails on both sides of the fiber optic ring are stress-free fibers. Therefore, the strain values ​​of the pigtails on both sides of the fiber optic ring only change with temperature, and the corresponding strain values ​​are within a flat region. Using the stress-free fibers on both sides of the fiber optic ring as a reference, the baseline of the distributed circumferential strain of the fiber optic ring at each temperature point can be aligned at the zero strain value, thus obtaining the distributed circumferential strain curves at each temperature point of the fiber optic ring that reflect the internal stress state of the fiber optic ring.

[0062] (2) Calculation of strain difference slope

[0063] The strain difference between distributed circumferential strains at adjacent temperature points is calculated, and then divided by the temperature difference between the points to obtain the strain difference curve under unit temperature change. For example, in the ranges of -45℃, -25℃, -5℃, 15℃, 35℃, 55℃, and 75℃, the strain curve at -45℃ is subtracted from the strain curve at -25℃, and the difference is then divided by the temperature difference of 20℃ to obtain the strain difference slope curve. This yields the strain difference data between adjacent layers at a specific temperature point. .

[0064] Evaluation criteria for fiber optic ring performance: the variance of the strain difference slope at each temperature point should be as close to 0 as possible, the mean value of the strain difference slope should be as close to 0 as possible, and the overlap of the strain difference curves should be as high as possible.

[0065] A good fiber optic ring requires that the curves of the distributed circumferential strain difference under a unit temperature difference completely overlap throughout the entire operating temperature range, so that the zero bias error of the fiber optic ring is constant in the temperature slope stable region, thereby achieving optimal temperature slope compensability for variable temperature zero bias.

[0066] Step 3: Treat each layer of optical fiber as a micro-segment Considering constant slope and varying temperature values The phase difference between adjacent fiber layers It can be calculated using the formula.

[0067]

[0068] Where L is the total length of the sensitive fiber, in meters; λ is the average wavelength of the optical signal (in vacuum), in meters; c is the speed of the optical signal (in vacuum), in meters per second; and n is the effective refractive index of the fiber. For the m-th infinitesimal segment coordinates Regarding the unit temperature-dependent strain difference of the symmetrical infinitesimal segment at the midpoint.

[0069] Step 4: Combining the zero-bias calculation formula, the phase difference between adjacent fiber layers is used to determine the zero-bias calculation method. Solve for the zero-bias error of adjacent fiber layers. The final fiber loop generates a fiber optic gyroscope with thermally induced zero-bias error. It equals the cumulative zero-bias error of each adjacent fiber layer, in ° / h / (℃ / min).

[0070]

[0071] The average diameter of the fiber optic ring sensitive fiber. The phase difference between adjacent fiber layers sum.

[0072] Thermally induced zero bias error The smaller the value, the better the performance of the fiber optic ring.

[0073] Step 5: Based on the geometric parameters of each component of the sensitive optical fiber material and the material parameters at different temperature points, select a constant slope temperature variation value. The unit is ℃ / s (temperature change per second). The length of each fiber layer is calculated by considering the radius and number of turns of each layer in the fiber loop. Each fiber layer is treated as a micro-segment, with the unit being meters (m). The slope of the strain difference between adjacent layers per degree Celsius (με / ℃) is confirmed through model formulas at different temperature points.

[0074] like Figure 3 As shown, the winding method is equivalent to a "hexagonal closed encapsulation array" of optical fibers, with the gaps filled with wrapping adhesive 6. Assuming the individual optical fibers are closely packed, the areas and proportions of the cladding 9, inner coating 8, outer coating 7, and wrapping adhesive 6 are as follows:

[0075] Fiber cladding (including fiber core): , accounting for 32.65%

[0076] Inner coating layer: , accounting for 25.39%

[0077] Outer coating: , accounting for 32.65%

[0078] Circular adhesive: , accounting for 9.31%

[0079] Therefore, the volume percentage of each part is: fiber cladding volume percentage V f =32.65%; Inner coating volume percentage V pi =32.65%; Outer coating volume percentage V po =32.65%; Volume percentage of wrap-around adhesive V g =32.65%.

[0080] Material parameters of the fiber cladding, inner coating, outer coating, and wrapping adhesive were obtained at temperatures of -55℃, -35℃, -15℃, 0℃, 20℃, 40℃, 60℃, and 85℃. These parameters included Young's modulus, Poisson's ratio, and linear coefficient of thermal expansion. Young's modulus of the fiber cladding, inner coating, outer coating, and wrapping adhesive at any given temperature was obtained by performing full-temperature spline interpolation fitting on the tested parameters from -55℃ to 85℃. , , and To obtain the Poisson's ratio of the fiber cladding, inner coating, outer coating, and filament wrapping adhesive at any given temperature point. , , and The linear thermal expansion coefficients of the fiber cladding, inner coating, outer coating, and epoxy resin at any given temperature point were obtained. , , and .

[0081] Based on the finite element method, the entire fiber optic ring is considered as a homogeneous composite material, and its mechanical and thermal parameters are homogeneously equivalent. By treating the fiber optic ring as a microscopic mechanical component of composite materials, the longitudinal Young's modulus of the fiber optic ring composite material can be obtained as follows: :

[0082]

[0083] The transverse Young's modulus of the fiber ring composite material is :

[0084]

[0085] in , , and These represent the Young's modulus of the cladding layer, inner coating layer, outer coating layer, and ring wrapping adhesive, respectively. , , and These represent the volume fractions of the fiber cladding, inner coating, outer coating, and wrapping adhesive, respectively.

[0086] Longitudinal Poisson's ratio of fiber ring composite materials :

[0087]

[0088] Transverse Poisson's ratio of fiber ring composite materials :

[0089]

[0090] in , , and These represent the Poisson's ratios of the cladding layer, inner coating layer, outer coating layer, and cyclopentadiene, respectively.

[0091] Longitudinal linear thermal expansion coefficient of fiber ring composite material :

[0092]

[0093] Transverse linear thermal expansion coefficient of fiber ring composite material :

[0094]

[0095] in, , , and These represent the linear thermal expansion coefficients of the cladding layer, inner coating layer, outer coating layer, and cyclopentadiene, respectively.

[0096] Select constant slope temperature value The unit is 1 / 60℃ / s. Based on the geometric parameters of each component of the sensitive optical fiber material and the material parameters at a specific temperature point, the dimensional parameters of the fiber ring after radial translation can be calculated using the longitudinal Young's modulus, longitudinal Poisson's ratio, and longitudinal linear thermal expansion coefficient. The dimensional parameters of the fiber ring after four-way expansion are obtained using the transverse Young's modulus, transverse Poisson's ratio, and transverse linear thermal expansion coefficient. The final dimensional parameters of the fiber ring are obtained by superimposing the dimensional parameters after radial translation and the dimensional parameters after four-way expansion. The final dimensional parameters include at least the change in the outer diameter of the fiber ring. and inner diameter change Combined with the change in the outer diameter of the fiber optic ring and inner diameter change The strain difference data between adjacent layers at a single temperature is obtained, and then the strain difference data between adjacent layers at all specific temperature points is obtained. .

[0097]

[0098] Perform thermally induced zero bias error calculation according to steps (3) and (4), determine the influence of each material parameter on the SHUPE error, and then suppress the SHUPE error by changing the material properties.

[0099] This invention evaluates the impact of material parameter variations on the SHUPE error of fiber optic rings, providing a simple evaluation method to suppress SHUPE errors and improve variable-temperature performance. By testing the isothermal distributed circumferential strain of the fiber optic ring, a correlation can be established between the strain and the SHUPE error, enabling the evaluation of the variable-temperature performance of the fiber optic ring. Furthermore, based on the geometric parameters of each component of the fiber optic ring and the material parameters at different temperature points, SHUPE errors can be suppressed during the forward design phase of the fiber optic ring, thereby effectively improving its variable-temperature performance.

Claims

1. A method for evaluating and suppressing SHUPE errors in fiber optic loops based on distributed circumferential strain, characterized in that, The method includes the following steps: Step 1: Calculate the total length L of the sensitive fiber of the fiber ring, the length of each layer of sensitive fiber, and the outer diameter based on the number of layers, number of turns, inner radius, and size parameters of the fiber used. Step 2: Measure the distributed circumferential strain of the fiber optic ring at different temperature points using BOTDA. After baseline calibration and subtraction of strain curves at adjacent temperature points, obtain the circumferential distributed strain difference per unit temperature. ; Step 3: Treat each layer of optical fiber as a micro-segment Considering constant slope and varying temperature conditions Calculate the phase difference between adjacent layers ; Step 4: Using the phase difference between adjacent layers Solving for the zero bias error of adjacent layers; finally, the fiber optic gyroscope SHUPE error generated by the fiber optic loop. This equals the sum of the zero-bias errors of each adjacent fiber layer; in step 4, Thermally induced zero bias error of fiber optic gyroscope generated by fiber optic loop : The average diameter of the fiber optic ring sensitive fiber. The phase difference between adjacent fiber layers sum; Step 5: Calculate the circumferential distributed strain difference per unit temperature Following steps 3 and 4, SHUPE error is calculated to establish the correspondence between strain difference and SHUPE error. Then, by altering material properties, SHUPE error can be suppressed. In step 5, A model is established, and the average temperature slope of adjacent layers is selected based on the geometric parameters of each component of the sensitive optical fiber material and the material parameters under different temperature conditions. The length of each layer of optical fiber is calculated by using the radius and number of turns of each layer of the sensitive optical fiber in the optical fiber ring as a micro-element segment. The circumferential distributed strain difference per unit temperature was calculated. SHUPE error is calculated according to steps 3 and 4 to determine the influence of each material parameter on SHUPE error, establish the correspondence between strain difference and SHUPE error, and then suppress SHUPE error by changing material properties. The circumferential distributed strain difference per unit temperature was calculated. Specifically: The final dimensions of the fiber optic ring are obtained by superimposing the dimensional parameters after radial translation and the dimensional parameters after four-way expansion. These final dimensions include at least the change in the outer diameter of the fiber optic ring. and inner diameter change Combined with the change in the outer diameter of the fiber optic ring and inner diameter change The strain difference data between adjacent layers at a single temperature is obtained, and then the strain difference data between adjacent layers at all specific temperature points is obtained. : .

2. The method for evaluating and suppressing the SHUPE error of an optical fiber loop based on distributed circumferential strain according to claim 1, characterized in that, In step 1, The radius Ri of the i-th layer of sensitive fiber is calculated using the following formula: D is the inner diameter of the fiber optic ring, d is the diameter of the outer coating layer, and the length of the i-th sensitive fiber layer is: M layer To represent the number of turns for each layer of the fiber optic ring, let N... coil The sum of the lengths of the layers of sensitive optical fibers is denoted as the total length L of the sensitive optical fibers in the optical fiber ring.

3. The method for evaluating and suppressing the SHUPE error of an optical fiber loop based on distributed circumferential strain according to claim 2, characterized in that, In step 2, BOTDA center frequency variation Temperature change of optical fiber and strain change They are directly proportional, establishing the following linear correlation: in, The strain coefficient representing frequency shift, with units of MHz / με; Represents the temperature coefficient, with units of MHz / °C; The distributed circumferential strain at adjacent temperature points is subtracted, and then divided by the difference between the temperature points to obtain the strain difference curve under unit temperature change. This leads to the strain difference slope curve, and ultimately, the strain difference data between adjacent layers at a specific temperature point. .

4. The method for evaluating and suppressing SHUPE errors in fiber optic loops based on distributed circumferential strain according to claim 3, characterized in that, In step 3, according to Calculate the phase difference between adjacent layers Where L is the fiber loop length in meters (m); λ is the average wavelength of the optical signal in meters (m); c is the optical signal velocity in meters per second (m / s); and n is the effective refractive index of the optical fiber. For the m-th infinitesimal segment coordinates Regarding the unit temperature-dependent strain difference of the symmetrical infinitesimal segment at the midpoint.

5. The method for evaluating and suppressing the SHUPE error of an optical fiber loop based on distributed circumferential strain according to claim 1, characterized in that, Thermally induced zero bias error The smaller the fiber optic ring, the better its performance.

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