BOTDR error estimation method based on bending condition of single-mode fiber

Abstract

The invention discloses a BOTDR (Brillouin Optical Time Domain Reflectometry) error estimation method based on a bending condition of a single-mode optical fiber. Firstly, a Brillouin scattering spectrum bending loss calculation formula considering the bending radius and length of an optical fiber is obtained through theoretical analysis, and theoretical derivation is verified through experimental data. Besides, by analyzing simulation and experimental data, an estimation formula of Brillouin frequency shift errors after the optical fiber is bent is provided, and the Brillouin frequency shift errors can be estimated according to the refractive index of an optical fiber cladding, the refractive index of an optical fiber core, the radius of the fiber core, the bending radius, the bending length and the wavelength of a laser. And calculating the Brillouin frequency shift standard deviation under the bending condition according to the Brillouin frequency shift standard deviation under the non-bending condition so as to evaluate the BOTDR precision.

Description

Technical Field

[0001] This invention relates to a BOTDR error estimation method based on the bending condition of single-mode optical fiber, belonging to the field of measurement technology. Background Technology

[0002] When light propagates in an optical fiber, scattering phenomena occur, including Rayleigh scattering, Brillouin scattering, and Raman scattering. Among these, the Brillouin gain spectrum (BGS) is sensitive to both temperature and strain. Therefore, Brillouin optical time domain reflectometry (BOTDR) has been widely used for temperature and strain monitoring. In some monitoring scenarios, it is necessary to bend the optical fiber around the object being measured. However, due to the characteristics of light transmission, when the bending radius of a section of the fiber is too small, the transmission of light in that section will be accompanied by significant loss. Therefore, how to calculate the power loss of the Brillouin spectrum and assess the impact of fiber bending on the accuracy of BOTDR are key problems that need to be solved.

[0003] The existing relevant patents are as follows: Patent document CN119779631A, entitled "A Method for Detecting Bending Loss of an Optical Fiber Ribbon," includes: configuration of the testing equipment; testing the initial loss value; testing the bending loss value by wrapping the portion between the two ends of the optical fiber ribbon no more than 10 times around a circular rod to obtain the bending loss value of each fiber from a strain gauge; determining the bending loss value of the optical fiber ribbon by selecting the bending loss value with the maximum strain from the obtained bending loss values ​​of each fiber as the bending loss test value of the optical fiber ribbon under test. Its advantages are: it can simultaneously detect the bending loss of multiple optical fibers in an optical fiber ribbon, making the invention simple and easy to implement, and can accurately and repeatedly simulate the bending state of the optical fiber, providing a basis for accurate testing; it can also reflect the maximum bending loss value under the same environment, having a better inclusive effect and making the detection value more accurate. Patent CN120415561B, entitled "Optical Fiber Bending Loss Testing System and Method Based on Spectral Analysis," discloses an optical fiber bending loss testing system and method based on spectral analysis, relating to the field of optical fiber testing technology. This application utilizes multi-wavelength scanning to acquire power values ​​and interference signals, and transmits at least two measurement data in parallel within one transmission cycle. Data is written to a storage array based on wavelength index and batch identifier. If alignment inaccuracies are detected, the process pauses and corrects the data. After corrections are completed, transmission resumes, and distributed loss information is calculated. This approach balances data integrity, transmission throughput, and real-time loss calculation accuracy in large-scale measurement environments, effectively avoiding the prolonged measurement cycle and index confusion inherent in conventional linear probing or fixed-offset methods, significantly improving the efficiency and reliability of fiber optic loss testing.

[0004] The aforementioned invention patent effectively solves the problem of how to detect fiber bending loss. However, fiber bending can also occur during the use of BOTDR systems, causing attenuation of BGS power and a decrease in the BGS spectral signal-to-noise ratio, thus increasing the demodulated Brillouin frequency shift (BFS) error. This reduces the accuracy of the BOTDR system, making its evaluation scheme essential, but currently no invention patent proposes a solution. Summary of the Invention

[0005] To address the shortcomings of existing technologies, this invention proposes a BOTDR error estimation method based on single-mode fiber bending. The aim is to fill the gap in BOTDR accuracy assessment schemes under fiber bending conditions, enabling the evaluation of the impact of fiber bending on the BOTDR system based on known information.

[0006] To achieve the above objectives, the technical solution adopted by the present invention is as follows:

[0007] A method for estimating BOTDR error based on the bending condition of single-mode optical fiber is characterized in that the method calculates the BFS standard deviation under bending conditions based on the optical fiber parameters (including the fiber cladding refractive index, fiber core refractive index, and core radius), the optical fiber bending conditions (including bending radius and bending length), the laser parameters in the BOTDR (including the laser wavelength), the BFS standard deviation of the fiber in the unbent condition, and the BFS standard deviation calculation formula under bending conditions, thereby evaluating the accuracy of the BOTDR.

[0008] Furthermore, the formula for calculating the standard deviation of BFS under bending conditions proposed in this invention is as follows:

[0009]

[0010] In the formula, σ is the BFS standard deviation under bending conditions, σ0 is the BFS standard deviation under unbent conditions, κ is the radially normalized phase constant, γ is the radially normalized loss constant, β is the axial propagation constant, V is the normalized frequency, a is the fiber core radius, R is the bending radius, and K... v Here, π is the v-th order Bessel function, and π is the mathematical constant pi. The above variables can be calculated using the following formula:

[0011]

[0012]

[0013]

[0014]

[0015]

[0016] In the formula, n1 and n2 are the refractive indices of the fiber core and cladding, respectively, k is the wave number of the electromagnetic wave in free space, and λ is the wavelength of the incident light.

[0017] The beneficial effects of this invention are as follows:

[0018] This invention, through theoretical derivation combined with extensive experiments and simulations, proposes a formula for calculating the BFS standard deviation under bending conditions. Based on this formula, the BFS standard deviation under bending conditions can be calculated using the fiber cladding refractive index, fiber core refractive index, core radius, bending radius, bending length, laser wavelength, and the BFS standard deviation under unbent conditions. The accuracy of the BOTDR is then evaluated using the BFS standard deviation. This invention fills the gap in BOTDR accuracy evaluation schemes under fiber bending conditions, enabling the assessment of the impact of fiber bending on the BOTDR system based on known information. Attached Figure Description

[0019] The present invention will now be described in further detail with reference to the accompanying drawings;

[0020] Figure 1 This is a schematic diagram of an optical fiber bending experiment;

[0021] Figure 2 It is the change in the attenuation of the Brillouin scattering spectrum with the bending length;

[0022] Figure 3 It is the trend of the change in signal-to-noise ratio with the change in Brillouin scattering spectrum power;

[0023] Figure 4 It is the trend of the relative value of the Brillouin frequency shift standard deviation as a function of the signal-to-noise ratio;

[0024] Figure 5 It is the standard deviation of BFS for a bending length of 10 mm;

[0025] Figure 6 It is the BFS standard deviation for a bending length of 11.5 mm. Detailed Implementation

[0026] The present invention will now be described in further detail with reference to the accompanying drawings.

[0027] 1. Power attenuation in Brillouin scattering spectrum caused by fiber bending

[0028] When an optical fiber is bent, the optical propagation mode changes due to the altered geometry. Specifically, bending the fiber causes the propagation constants of certain modes to no longer satisfy the condition for total internal reflection, resulting in some light energy leakage through the cladding and thus loss. Assuming the cladding is infinitely large, meaning the cladding and coating have no effect on the fiber's transmission, and the loss is entirely due to bending, the change in optical power can be expressed as:

[0029] (1)

[0030] In the formula, P0 and P1 are the incident light power before and after bending attenuation, respectively; 2α is the bending loss coefficient of the incident light; and L is the bending length.

[0031] The bending loss coefficient in a single-mode fiber can be calculated using equation (2).

[0032] (2)

[0033] In the formula, κ is the radially normalized phase constant, γ is the radially normalized loss constant, β is the axial propagation constant, V is the normalized frequency, a is the fiber core radius, R is the bending radius, and K is the axial propagation constant. v Here, π is the v-th order Bessel function, and π is the mathematical constant pi. The above variables can be calculated using the following formula:

[0034] (3)

[0035] (4)

[0036] (5)

[0037] (6)

[0038] (7)

[0039] In the formula, n1 and n2 are the refractive indices of the fiber core and cladding, respectively, k is the wave number of the electromagnetic wave in free space, and λ is the wavelength of the incident light.

[0040] It is important to note that BOTDR detects backscattered Brillouin light, therefore, for Brillouin scattering, there are two instances of fiber attenuation. That is, the power of the incident light attenuates as it propagates forward, and the power of the Brillouin scattered light also attenuates as it propagates backward. Since Brillouin scattered light is essentially light, only with a frequency shift of about 10.8 GHz compared to the incident light, the attenuation magnitude of the Brillouin scattered light during backward propagation can also be calculated using equation (1).

[0041] In BOTDR, the laser wavelength is typically 1550 nm, or 193.5 THz. Because the frequency shift of the Brillouin scattering light is much smaller than the laser wavelength (the difference is approximately 10 THz), the frequency shift of the laser is significantly less than the wavelength of the laser. 4 (The wavelength of the Brillouin scattered light is approximately equal to that of the laser, which is twice that of the laser).

[0042] In summary, the power variation of the Brillouin scattering spectrum caused by fiber bending can be obtained as shown in equation (8).

[0043] (8)

[0044] In the formula P B0 and P B1 These represent the Brillouin scattering spectral power before and after bending attenuation, respectively. It should be noted that since existing literature does not define Brillouin scattering spectral power, and the photodetector in a BOTDR converts the optical signal into an electrical signal, which is characterized by Brillouin gain, this power is defined as the Brillouin scattering spectral power.

[0045] To verify the reliability of the above conclusions, a Brillouin spectrum of a single-mode fiber (model: G.652D) wound around a cylinder was acquired using a BOTDR system (model: 6419A, manufacturer: Ceyear Technology Co., Ltd., China). The attenuation of the Brillouin scattering power under different bending lengths and radii was observed by varying the winding length and the radius of the cylinder. The experimental circuit diagram is shown below. Figure 1 As shown. The basic parameters of the single-mode fiber are as follows: n1=1.4683; n2=1.4633; a=4.5 μm; the wavelength of the laser in the BOTDR is λ=1550 nm, obtained through experimental calculation. The BOTDR settings are as follows: incident light pulse width is 10 ns, and the average number of superpositions is 2. 12 The scan start frequency was 10.74 GHz, the end frequency was 10.94 GHz, the scan step size was 2 MHz, the number of scan points was 101, and the sampling resolution was set to 0.2 m.

[0046] Depend on Figure 1 As can be seen, the single-mode fiber is divided into three parts. The middle section of the single-mode fiber is wound around a cylinder. When the incident light and the Brillouin scattered light pass through this section of fiber, optical power attenuation occurs. We take the Brillouin gain spectrum of the third section of fiber, namely the 50m single-mode fiber, as the research object. The Brillouin gain peak values ​​at all spatial points in this section of fiber are averaged to obtain the Brillouin scattering spectrum power of this section of fiber. In addition, for the reliability of the data, the experiment was repeated 8 times, and the average of the 8 results was used as the final Brillouin scattering spectrum power. The experimental results and the theoretical results calculated by equation (8) are presented together in Figure 2 middle.

[0047] Depend on Figure 2 It can be seen that when the bending radius is 10 mm and 11.5 mm, the theoretical results are basically consistent with the experimental results, which verifies the reliability of the theoretical derivation and the experimental results.

[0048] 2. Decreased BOTDR accuracy due to power attenuation in Brillouin scattering spectra

[0049] BOTDR accuracy can be evaluated through BFS error, which is related to the signal-to-noise ratio (SNR). To obtain the trend of SNR variation with Brillouin scattering power, a large number of Brillouin spectra with different scattering powers need to be measured. The amount of data obtained through bent optical fibers is insufficient to meet the analytical requirements. Therefore, this study analyzes the variation of SNR with Brillouin scattering power in ultra-long-distance optical fibers. Measurements were performed on a 45 km single-mode optical fiber (model: G.652D) using a BOTDR. The experimental setup for the BOTDR was as follows: incident pulse width 250 ns, average number of superpositions 2... 14 The scanning start frequency was 10.75 GHz, the end frequency was 10.95 GHz, the sweep step size was 5 MHz, the number of sweep points was 41, the sampling resolution was set to 4 m, and the incident light wavelength was 1550 nm. The Brillouin scattering spectra at different Brillouin powers were obtained at 10925 spatial points. To increase data stability, the following processing was performed: 1) The measurement was repeated 11 times, and the Brillouin scattering spectrum power and signal-to-noise ratio (SNR) data of all data were calculated. Data from the same spatial point were averaged. 2) After averaging, 25 Brillouin spectra with similar Brillouin scattering power were grouped together, and the data within each group were averaged. The Brillouin scattering spectrum power and SNR data after the above processing were statistically analyzed. Finally, the trend of the Brillouin scattering spectrum SNR as the Brillouin power decayed was obtained, as shown in the figure. Figure 3 In order to be more applicable, the trends of Brillouin power and signal-to-noise ratio are expressed as relative values.

[0050] Figure 3 The relative attenuation of the Brillouin spectrum signal-to-noise ratio and the Brillouin scattering spectrum power is calculated using equations (9) and (10), respectively. It should be noted that the power here does not refer to the signal power, but rather the optical power converted by the photodetector, which is essentially a current. Furthermore, the Brillouin scattering spectrum power before attenuation in this data is the same as the Brillouin scattering spectrum power at the beginning of the optical fiber; the Brillouin scattering spectrum power after attenuation is the same as the Brillouin scattering spectrum power after attenuation as the light propagates through the optical fiber.

[0051] (9)

[0052] (10)

[0053] In the formula, S is the signal-to-noise ratio, and R is... B P represents the relative attenuation of the Brillouin scattering spectrum power. n1 The steps for obtaining noise power are as follows: 1) Perform pseudo-Voigt fitting on the Brillouin scattering spectrum and reconstruct the ideal Brillouin spectrum based on the fitting results; 2) Subtract the measured Brillouin spectrum from the ideal spectrum to obtain the noise; 3) Calculate the standard deviation of the noise at different spatial locations for each frequency point; 4) Perform pseudo-Voigt fitting on the standard deviation of the noise, and sum the peak gain of the Lorentz model and the peak gain of the Gaussian model obtained from the fitting, using this as the noise power. Figure 3 It can be seen that the change in signal-to-noise ratio and the relative attenuation of Brillouin scattering spectrum power exhibit an exponential function relationship as shown in equation (11).

[0054] (11)

[0055] To obtain the influence of bending loss on Brillouin frequency shift error, it is necessary to further analyze the variation law of Brillouin frequency shift error with signal-to-noise ratio. For this purpose, a large number of Brillouin spectra with different signal-to-noise ratios were generated numerically based on the pseudo-Voigt model. The Brillouin frequency shift was calculated using a fitting algorithm based on the pseudo-Voigt model, and their Brillouin frequency shift errors were statistically analyzed. Without loss of generality, the parameters of the numerically generated spectrum were set as follows: Lorentz model gain and Gaussian model gain were both 0.5; Brillouin linewidth was 40 MHz; sweep frequency range was 10.74 GHz to 10.94 GHz; sweep frequency interval was 2 MHz; Brillouin frequency shift was 10.84 GHz; signal-to-noise ratio was 10 dB to 40 dB, and step size was 1 dB. 2000 sets of Brillouin spectra were randomly generated for each signal-to-noise ratio. The applied noise was Gaussian white noise with a noise amplitude proportional to the Brillouin gain and an expectation of 0. The relative value of the standard deviation of the Brillouin frequency shift was calculated by equation (12).

[0056] (12)

[0057] In the formula σ R Let be the relative value of the Brillouin frequency shift standard deviation; σ is the Brillouin frequency shift standard deviation under different signal-to-noise ratios, and σ0 is the Brillouin frequency shift standard deviation at the maximum signal-to-noise ratio. The relative value of the Brillouin frequency shift standard deviation changes with the signal-to-noise ratio as follows: Figure 4 As shown.

[0058] Depend on Figure 4 The fitting results show that the relative value of the Brillouin frequency shift standard deviation and the change in signal-to-noise ratio have a linear relationship as shown in equation (13).

[0059] (13)

[0060] In summary, by substituting equations (2), (8), (10), (11) and (13) into equation (12), the relationship between the standard deviation of the Brillouin frequency shift before and after the fiber bending can be obtained based on the fiber bending length and bending radius, as shown in equation (14).

[0061] (14)

[0062] Equation (14) was verified using experimental data from the bending experiment, and the results are as follows: Figure 5 and Figure 6 As shown.

[0063] To make it more intuitive, the errors of the proposed formulas under different bending radii are shown in Tables 1 and 2.

[0064] Table 1 Error of Equation (14) when R=10 mm Bending length (m) Absolute error (MHz) relative error 0.1 0.0334 14.46% 0.2 0.0228 6.16% 0.3 0.1156 21.21% 0.4 0.2357 15.21%

[0065] Table 2 shows the error of equation (14) when R = 11.5 mm. Bending length (m) Absolute error (MHz) relative error 0.1 0.0056 2.54% 0.2 0.0039 1.67% 0.3 0.0349 15.68% 0.4 0.0044 1.57% 0.5 0.0121 3.69%

[0066] Depend on Figure 5 , Figure 6 As shown in Tables 1 and 2, the overall error of the proposed method is within an acceptable range. For R = 10 mm, the maximum relative error is 21.21%, and the average relative error is 14.26%; for R = 11.5 mm, the maximum relative error is 15.68%, and the average relative error is 5.03%. When R = 10 mm and L = 0.5 m, the Brillouin spectral power is only 0.08% of its pre-attenuation value, and the signal-to-noise ratio (SNR) of the Brillouin spectrum calculated using Equation (9) is only 3.36 dB. At this point, the SNR is too low, the calculated Brillouin frequency shift error is very unstable, and the calculation results are unreliable. Therefore, the case of L = 0.5 m is not shown for R = 10 mm.

[0067] In summary, the advantages of this invention are as follows: 1) Through theoretical derivation and analysis, a formula for attenuation of Brillouin spectrum power under different fiber bending radii and bending lengths is proposed for the first time, and its reliability is verified by experiments. 2) Combining the conclusions of theoretical derivation, simulation, and experiments, a formula for calculating Brillouin spectrum error caused by fiber bending is proposed for the first time. The BFS standard deviation under bending conditions can be calculated based on the fiber cladding refractive index, fiber core refractive index, core radius, bending radius, bending length, laser wavelength, and the BFS standard deviation under the unbent condition.

[0068] The above embodiments are merely illustrative of the principles and effects of the present invention and are not intended to limit the invention. Any person skilled in the art can modify or alter the above embodiments without departing from the spirit and scope of the present invention. Therefore, all equivalent modifications or alterations made by those skilled in the art without departing from the spirit and technical concept disclosed in the present invention should still be covered by the claims of the present invention.

Claims

1. A BOTDR error estimation method based on single-mode fiber bending, characterized in that, The method describes how to calculate the BFS standard deviation under bending conditions based on the fiber parameters (including fiber cladding refractive index, fiber core refractive index, and core radius), fiber bending conditions (including bending radius and bending length), laser parameters in the BOTDR (including laser wavelength), the Brillouin frequency shift (BFS) standard deviation of the fiber in its unbent state, and the BFS standard deviation calculation formula under bending conditions. This calculation is then used to evaluate the accuracy of the BOTDR.

2. The BOTDR error estimation method based on single-mode fiber bending as described in claim 1, characterized in that, The formula for calculating the standard deviation of BFS under bending conditions proposed in this invention is as follows: In the formula, σ is the BFS standard deviation under bending conditions, σ0 is the BFS standard deviation under unbent conditions, κ is the radially normalized phase constant, γ is the radially normalized loss constant, β is the axial propagation constant, V is the normalized frequency, a is the fiber core radius, R is the bending radius, and K... v Here, π is the v-th order Bessel function, and π is the mathematical constant pi. The above variables can be calculated using the following formula: In the formula, n1 and n2 are the refractive indices of the fiber core and cladding, respectively, k is the wave number of the electromagnetic wave in free space, and λ is the wavelength of the incident light.

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