A distance expansion method of ultra-weak fiber grating optical frequency domain analyzer

Abstract

A distance expansion method of ultra-weak fiber grating optical frequency domain analyzer, comprising: preparing a fiber grating array with a center wavelength of; setting the wavelength scanning range of optical frequency domain reflection, entering the reference scanning mode, using the adaptive Gaussian fitting algorithm to analyze the grating interval ratio of the grating length of the fiber grating array, and calculating the power spectral density dynamic threshold; enter the data acquisition mode, according to the starting position and spectrum information of each section of the fiber grating array obtained in the reference scanning mode, remove the data redundancy of different fiber grating array sections, complete the data splicing framing; based on 3σ criterion dynamic cutting fiber grating spectrum fitting area, realize fast wavelength demodulation. The method introduces time division / wavelength division multiplexing optical path architecture, uses adaptive PSD threshold calibration algorithm combined with grating physical parameters, eliminates the cumulative error generated when scanning a large range of light sources, effectively expands the capacity and measurement distance of the sensing system, and realizes accurate and robust positioning of the ultra-weak grating array.

Description

Technical Field

[0001] This invention relates to the field of fiber optic sensing and demodulation technology, and in particular to a distance extension method for an ultra-weak fiber Bragg grating optical frequency domain analyzer. Background Technology

[0002] Traditional optical frequency domain reflectance (OFDR) systems use ordinary single-mode optical fiber as the sensing unit. This fiber exhibits low backscattered Rayleigh light intensity and poor directionality, making it susceptible to environmental interference. As the scanning range and sensing distance increase, the system's signal-to-noise ratio drops sharply, severely limiting the system's measurement distance and dynamic range. Furthermore, nonlinear frequency sweeping and phase noise from large-scale light sources further degrade system performance, making it difficult to exceed the hundred-meter range in actual measurement distances.

[0003] To improve the sensing distance of optical frequency domain reflectance (OFDR) systems, various technical solutions have been proposed in recent years. In 2023, Shen Zhen et al. proposed an external modulation OFDR system in their paper "Research on improving the spatial resolution of external modulation OFDR by frequency domain interpolation and window width optimization [J]. Journal of Sensor Technology, 2023, 36(10): 1615-1621." By reducing the data processing window width, the spatial resolution can be improved. However, if the window width is too small, it will cause the "false peak" problem in sensing and positioning. This constraint between spatial resolution and positioning accuracy is more prominent in long-distance measurement.

[0004] In 2023, Dang Hong et al. achieved a spatial resolution of 5 mm by using Kalman prediction and local optimization methods in “A method to improve the performance of distributed optical fiber sensing based on Kalman prediction [J]. Acta Optica Sinica, 2024, 44(01):315-323”, but the sensing distance was also limited to within 50 meters.

[0005] Although the real-time STF-VCFIR filter system proposed by Shuai Luwei et al. in “OFDR Harmonic Noise Elimination Based on Real-time STF-VCFIR Filter System [J]. Chinese Journal of Lasers, 2025, 52(2): 0206002” can reduce harmonic noise to below -102.7 dB, its effective operating distance is still limited.

[0006] While the aforementioned work has made some progress in improving spatial resolution, it generally sacrifices measurement distance; as the sensing distance increases, the system's spatial resolution still deteriorates sharply. In terms of commercialization, the French company APEX's OFDR-AP6 series achieves a sampling resolution of 42μm on 244m of fiber, but it cannot achieve sensing detection. The American company LUNA's ODiSI7100 series achieves a temperature / strain resolution of 0.1℃ / 1με on 50m of fiber, but its high price limits its widespread application.

[0007] Existing optical frequency domain reflectance (OFDR) systems still face fundamental technical obstacles in long-distance measurement: nonlinear cumulative errors during large-scale light source scanning; and reliance on imported core light sources and key electronic components, which restricts their application in scenarios such as on-site inspection. Achieving high spatial resolution and dynamic demodulation in OFDR systems under long-distance measurement conditions has become an urgent technical challenge to be solved. Summary of the Invention

[0008] This invention provides a distance extension method for an ultra-weak fiber grating optical frequency domain analyzer. This method introduces a time-division / wavelength-division multiplexing optical path architecture and adopts an adaptive PSD threshold calibration algorithm that combines grating physical parameters. This eliminates the cumulative error generated during large-scale light source scanning, effectively expands the capacity and measurement distance of the sensing system, and achieves accurate and robust positioning of ultra-weak grating arrays.

[0009] The technical solution adopted in this invention is as follows:

[0010] A distance extension method for an ultra-weak fiber Bragg grating optical frequency domain analyzer includes the following steps: Step 1: Prepare a center wavelength of Fiber Bragg grating array; Step 2: When the center wavelength is When the fabrication length of the fiber grating array reaches 100 meters, a 100-meter-long fiber grating array with a center wavelength of [missing information] is fabricated. Fiber Bragg grating array i =2,… n, n The termination value of the center wavelength sequence is determined based on the required detection distance. Step 3: Set the wavelength scanning range of optical frequency domain reflectance (OFDR), enter the reference scanning mode, use the adaptive Gaussian fitting algorithm to analyze the ratio of grating length to grating spacing of the fiber grating array, calculate the dynamic threshold of power spectral density (PSD), and achieve accurate positioning of wavelength division multiplexing gratings. Step 4: Set the wavelength scanning range of optical frequency domain reflectance (OFDR), enter the data acquisition mode, obtain the starting position and spectral information of each fiber grating array segment according to the reference scanning mode, remove redundancy from the data of different fiber grating array segments, and complete the data splicing into frames. Step 5: Dynamically trim the fiber grating spectral fitting region based on the 3σ criterion to achieve fast wavelength demodulation.

[0011] In step 1, a femtosecond laser or phase mask method is used to prepare a material with a reflectivity of less than 0.1% and a center wavelength of [missing value]. A dense fiber grating array.

[0012] In step 2, 100-meter-long optical fibers with a center wavelength of [missing information] are sequentially fabricated on a single optical fiber. Fiber Bragg grating array i =2,… n ; The total length of the ultra-weak fiber grating array fabricated on a single optical fiber does not exceed the coherence length of the swept frequency light source; In step 3, in the reference scan mode, when greater than Continuous frequency sweeping was performed within the range to acquire the auxiliary interferometer signal I. aux The polarization component signal I of the main interferometer P p and the polarization component signal I of the main interferometer s .

[0013] In step 3, an equal-phase resampling algorithm is used for nonlinear compensation, and an adaptive power spectral density (PSD) threshold is used to identify the spatial location of the first-end ultra-weak fiber grating in each wavelength band. With tail-end ultra-weak fiber optic grating This is designated as the reference grating for that wavelength channel, where the subscript n represents the nth wavelength segment, and the subscript m represents the mth grating within the nth wavelength segment. Specifically: 3.1: The acquired auxiliary interferometer signal I aux The phase is obtained by performing a Hilbert transform. The expression for the Hilbert transform is: (1); In formula (1): The Hilbert transform operator is used to transform functions; The input is the real-valued signal of the auxiliary interferometer; It is a time variable; To measure the time delay difference between the test light and the reference light; By constructing an analytical signal: Z(t) = I aux (t) + j H{I aux (t)}(2; In equation (2): Z(t) is the analytic signal constructed from the original signal and its Hilbert transform; j is the imaginary unit; The instantaneous phase of the auxiliary interferometer signal can be obtained: φ aux (t) = arctan( H{I aux (t)} / I aux (t) )(3; In equation (3): φ aux (t) represents the instantaneous phase of the auxiliary signal; Using the instantaneous phase obtained by demodulation by the auxiliary interferometer as a scale, the polarization component signal of the main interferometer is analyzed by the following formula (4). , Perform resampling: (4); In equation (4): φ aux (t) represents the instantaneous phase of the auxiliary interferometer; and These are the real-valued signals of the two orthogonal polarization components of the main interferometer acquired at the corresponding time points; This represents the selected interpolation algorithm; For sequence index, ; The set uniform phase interval; and This refers to the new signal sequence obtained after resampling on a uniform phase axis.

[0014] φ aux (t) represents the instantaneous phase of the auxiliary signal; The distance domain is obtained by performing a Fast Fourier Transform (FFT) on the interpolated and resampled signal using the following formula (5): (5); In equation (5): This is the total length of the resampled signal; For the index of the distance domain, ; The imaginary unit; and That is, the range domain signal of the two polarization components; The polarization-depolarized range domain signal is obtained by signal processing using the following formula (6). : (6).

[0015] 3.2: Based on the statistical characteristics of the power spectral density in the local space near the positioning point, and the length of the ultra-weak fiber grating grating region. Length of grating spacing Parameters, dynamically matched with adaptive power spectral density (PSD) thresholds based on weights. Its expression is: (5); In equation (5): and These are the statistical mean and standard deviation of the power spectral density (PSD) amplitude, respectively. For adjustment coefficients; For and The weight function is a parameter.

[0016] The weight function expression is: (6); In formula (6): Spacing-to-gate length ratio; α represents the gate length duty cycle; β represents the weighting coefficients.

[0017] Ultra-weak fiber grating grating length Length of grating spacing satisfy ≥ .

[0018] 3.3: Establish the spatial correspondence between the measurement group fiber Bragg grating array and the reference group fiber Bragg grating array, as follows: For the reference state range domain signal L sig_ref and the measurement state distance domain signal L sig_meas All UW-FBG reflection peaks were identified using the adaptive PSD thresholding algorithm in step 3.2, resulting in two location arrays: Z ref = [z refj [j=1,2…M] and Z meas = [z measi [i=1,2…M]; Among them, Z ref It is an array consisting of the center positions of all ultra-weak fiber grating reflection peaks identified under the reference state; z refj Z represents the center position of the reflection peak of the j-th ultra-weak fiber grating in the reference state; j is the index number of the grating position array in the reference state; M is the total number of identified ultra-weak fiber gratings; Z meas It is an array consisting of the center positions of all ultra-weak fiber grating reflection peaks identified under measurement conditions; z measi It represents the center position coordinates of the i-th ultra-weak fiber grating reflection peak under the measurement state; The reference position z is calculated using the following formula (7). refj With measurement position z measi Absolute distance: (7); In equation (7): d ij This represents the absolute distance between the reference position and the measurement position. The reference position z with the smallest distance refj Determined to be related to z measi The corresponding physical grating.

[0019] For wavelength division multiplexing systems, this process needs to be performed independently in each wavelength channel.

[0020] In step 4, based on the sampling rate F s With gate length Calculate the minimum number of consecutive sampling points required for a single complete gate region. The grating region is precisely located and IFFT demodulation is performed to obtain the grating spectrum. Details are as follows: 4.1: Calculate the minimum number of consecutive sampling points : (8); In equation (8): It is a rounding function; The refractive index of the optical fiber; The speed of light; This represents the effective frequency scanning range of the laser.

[0021] 4.2: Calculation of depolarized range domain signal The power spectral density (PSD) is given by the formula: where n = 1, 2, 3…N, and N is the number of signal points. (9); In equation (9): The power spectral density amplitude at the k-th sampling point in the polarization-depolarized distance domain signal; Represents the Discrete Fourier Transform; To take the square of the amplitude; Spatial sampling rate, unit: sampling points / meter; Number of signal points; When continuous Power spectral density amplitude at each sampling point Above the dynamic threshold When identified as an ultra-weak fiber grating unit, the polarization distance domain signal will be eliminated. Threshold identification is performed on all N signal points to obtain grating array information.

[0022] In step 5, spectral data regions deviating from the ±3σ range of the center wavelength are dynamically trimmed based on the 3σ criterion, retaining only the effective region of the main peak for Gaussian fitting to obtain the optimized center wavelength. The grating wavelength array is obtained by traversing the distance domain.

[0023] The steps include: S5.1: Establish a Gaussian function model for the ultra-weak fiber grating spectrum by inverting the grating spectrum using IFFT: (10); In formula (10): This represents a Gaussian function model of the reflectance spectrum of a single UW-FBG. Peak intensity; It is the independent variable, representing wavelength; For the Bragg wavelength; Spectral width; It is a natural exponential function.

[0024] S5.2: Taking the natural logarithm of the Gaussian function model of the ultra-weak fiber grating spectrum, we expand it into a quadratic polynomial: (11); S5.3: Solve the parameters using the least squares method to obtain the optimized center wavelength peak value. : (12); In equation (12): Indicates at wavelength The UW-FBG reflectance spectral intensity measured at the location; This represents the wavelength value represented by the i-th sampling point in the UW-FBG reflectance spectrum; Indicates the number of signal points; S5.4: Let the maximum spectral amplitude S max The corresponding wavelength is Calculate the full width at half maximum (FWHM) as follows: Find the peak S on the spectral curve. max Half of, i.e., S half = S max / 2; at peak wavelength λ peak On the left, find the spectral intensity value equal to S. half The corresponding wavelength is denoted as λ. left ; in λ peak On the right side, find the spectral intensity value equal to S. half The corresponding wavelength is denoted as λ. right The formula for calculating the full width at half maximum (FWHM) is: FWHM = λ right - λ left (13); S5.5: Let the wavelength sampling interval be... x and σ0 are the initial standard deviations. The range of ±3σ from the center wavelength is selected as the fitting window, and the number of fitting points m0 is: (14); S5.6: According to formula (13) in S5.5, calculate the number of corresponding fitting points for the spectrum of different fiber gratings to achieve adaptive grating demodulation.

[0025] In step 6, after wavelength demodulation of each grating in the ultra-weak fiber grating array (UW-FBGs) is completed, a Bragg wavelength array {λ} corresponding to the spatial position order of the gratings is obtained. i , i=1,2,...}, where: i is the raster index; Save the reference Bragg wavelength array {λ} measured under default conditions. i_ref , i=1,2,...}, and the measured Bragg wavelength array {λ} measured under sensing conditions. i_ Subtracting the values ​​of i=1,2,..., from the values ​​of i=1,2,..., we obtain the change in wavelength. .

[0026] This invention provides a distance extension method for an ultra-weak fiber Bragg grating optical frequency domain analyzer, with the following technical advantages: 1) The sensing distance is increased by orders of magnitude. By using a wavelength division multiplexing ultra-weak fiber grating array, the "first grating" in all wavelength channels is identified and matched, and a global spatial mapping relationship between the measurement group and the reference group grating array can be automatically established to achieve rapid self-calibration, thereby increasing the sensing distance of OFDR from hundreds of meters to kilometers.

[0027] 2) High cost-effectiveness. Currently, kilometer-scale OFDR systems require high-performance imported light sources, and the demodulation algorithms are complex, resulting in huge engineering application costs. This invention only requires the use of mature ultra-weak grating fabrication technology for time-division / wavelength-division array fabrication, combined with the 3σ criterion to dynamically trim the grating spectral fitting region, to achieve high-performance demodulation. This method, without sacrificing accuracy, offers a simple and cost-effective system, while also improving computational efficiency and demodulation robustness. Attached Figure Description

[0028] The present invention will be further described below with reference to the accompanying drawings and examples; Figure 1 This is a diagram of the optical path structure of the present invention.

[0029] Figure 2 This is a schematic diagram of the grating PSD threshold calibration of the present invention.

[0030] Figure 3 This is a comparison diagram of the 3σ criterion spectral clipping fitting region and the full spectrum of the present invention.

[0031] Figure 4 This is a diagram illustrating the strain sensing effect of the present invention. Detailed Implementation

[0032] This invention relates to the optimized design of optical frequency domain reflectance (OFDR) sensing systems, specifically addressing key technical bottlenecks such as short measurement distance and power degradation caused by numerous grating points, and providing a long-distance, high-resolution OFDR architecture.

[0033] A distance extension method for an ultra-weak fiber Bragg grating optical frequency domain analyzer includes: fabricating a fiber Bragg grating with a reflectivity of less than 0.1% and a center wavelength of [missing information - likely a specific wavelength range]. A dense grating array, fabricated at a single wavelength, is used to prepare a 100-meter-long [structure / structure]. The array is fabricated sequentially on individual optical fibers, each 100 meters long. (i=1,2,…n) array; set the wavelength scanning range of OFDR, enter the reference scanning mode, adopt the adaptive Gaussian fitting algorithm, and calculate the dynamic threshold of power spectral density (PSD) by analyzing the ratio of grating area length to grating spacing of the grating array to achieve accurate positioning of wavelength division multiplexing grating; enter the data acquisition mode, according to the starting position and spectral information of each array segment obtained during the reference scan, remove redundancy from the data of different array segments, complete the data stitching into frames, and use the 3σ criterion to dynamically trim the grating spectral fitting area to achieve fast wavelength demodulation.

[0034] A schematic diagram of grating PSD threshold calibration is shown below. Figure 2 As shown, a distance extension method for an ultra-weak fiber grating optical frequency domain reflectometer is demonstrated to improve the threshold calibration effect on an ultra-weak fiber grating array. The method involves traversing the distance domain to identify the grating and determine its position. A comparison of the 3σ criterion spectral clipping fitting region and the full spectrum, as shown in the figure. Figure 3 As shown, the spectra of different UW-FBGs are dynamically cropped, and the spectral characterization region retained is only 6.5%-14.5% of the complete spectrum, which reduces the data volume by nearly 10 times compared with traditional algorithms. Strain sensing effect reference diagram, such as Figure 4 The figure shows the calibration curves of a distance extension method for an ultra-weak fiber grating optical frequency domain reflectometer in a strain sensing experiment. The horizontal axis represents the load weight G, and the vertical axis represents the strain demodulation amount με. This figure verifies that there is an excellent linear relationship R between the demodulation result and the strain change. 2 =0.99999, which verifies that the method of the present invention has distributed measurement capability and good dynamic response characteristics, and can accurately and synchronously acquire the status information of each point on the sensing link, thus meeting the real-time monitoring requirements.

[0035] In summary, this invention effectively expands the capacity and measurement distance of the sensing system by introducing a wavelength division multiplexing optical path architecture; it achieves accurate and robust positioning of ultra-weak grating arrays by employing an adaptive PSD threshold calibration algorithm that combines grating physical parameters; and it overcomes the challenge of rapid demodulation of long-distance, high-density array spectra by utilizing parallelized IFFT spectral reconstruction and dynamic clipping fitting technology based on the 3σ criterion.

[0036] Experiments have verified that the long-distance ultra-weak fiber optic grating OFDR system can achieve kilometer-scale distributed sensing measurements, with spatial resolution up to the millimeter level, strain measurement accuracy better than ±1με, and linearity R0.2 =0.99999, suitable for long-distance, high-precision sensing applications such as health monitoring of large infrastructure and safety testing of new energy equipment.

Claims

1. A distance extension method for an ultra-weak fiber grating optical frequency domain analyzer, characterized in that... Includes the following steps: Step 1: Prepare a center wavelength of Fiber Bragg grating array; Step 2: When the center wavelength is When the fabrication length of the fiber grating array reaches 100 meters, a 100-meter-long fiber grating array with a center wavelength of [missing information] is fabricated. Fiber Bragg grating array i =2,… n, n This is the termination value of the center wavelength sequence; Step 3: Set the wavelength scanning range of optical frequency domain reflection, enter the reference scanning mode, use the adaptive Gaussian fitting algorithm to analyze the ratio of grating length to grating spacing of the fiber grating array, calculate the dynamic threshold of power spectral density, and realize the accurate positioning of wavelength division multiplexing gratings. Step 4: Set the wavelength scanning range of optical frequency domain reflection, enter the data acquisition mode, obtain the starting position and spectral information of each fiber grating array segment according to the reference scanning mode, remove redundancy from the data of different fiber grating array segments, and complete the data splicing into frames. Step 5: Dynamically trim the fiber grating spectral fitting region based on the 3σ criterion to achieve fast wavelength demodulation.

2. The distance extension method for an ultra-weak fiber optic frequency domain analyzer according to claim 1, characterized in that: In step 2, 100-meter-long optical fibers with a center wavelength of [missing information] are sequentially fabricated on a single optical fiber. Fiber Bragg grating array i =2,… n ; The total length of an ultra-weak fiber grating array fabricated on a single optical fiber does not exceed the coherence length of the swept frequency light source.

3. The distance extension method for an ultra-weak fiber optic grating optical frequency domain analyzer according to claim 2, characterized in that: In step 3, in the reference scan mode, when greater than Continuous frequency sweeping was performed within the range to acquire the auxiliary interferometer signal I. aux The polarization component signal I of the main interferometer P p and the polarization component signal I of the main interferometer s .

4. The distance extension method for an ultra-weak fiber optic grating optical frequency domain analyzer according to claim 3, characterized in that: In step 3, an equal-phase resampling algorithm is used for nonlinear compensation, and an adaptive power spectral density (PSD) threshold is used to identify the spatial location of the first-end ultra-weak fiber grating in each wavelength band. With tail-end ultra-weak fiber optic grating This is then marked as the reference grating for that wavelength channel.

5. The distance extension method for an ultra-weak fiber optic grating optical frequency domain analyzer according to claim 4, characterized in that: In step 3: The acquired auxiliary interferometer signal I aux The phase is obtained by performing a Hilbert transform. The expression for the Hilbert transform is: （1）； In formula (1): The Hilbert transform operator is used to transform functions; The input is the real-valued signal of the auxiliary interferometer; It is a time variable; To measure the time delay difference between the test light and the reference light; By constructing an analytical signal: Z(t) = I aux (t) + j H{I aux (t)}(2); In equation (2): Z(t) is the analytic signal constructed from the original signal and its Hilbert transform; j is the imaginary unit; The instantaneous phase of the auxiliary interferometer signal can be obtained: φ aux (t) = arctan( H{I aux (t)} / I aux (t) )(3); In equation (3): φ aux (t) represents the instantaneous phase of the auxiliary signal; Using the instantaneous phase obtained by demodulation by the auxiliary interferometer as a scale, the polarization component signal of the main interferometer is analyzed by the following formula (4). , Perform resampling: （4）； In equation (4): φ aux (t) represents the instantaneous phase of the auxiliary interferometer; and These are the real-valued signals of the two orthogonal polarization components of the main interferometer acquired at the corresponding time points; This represents the selected interpolation algorithm; For sequence indexing; The set uniform phase interval; and That is, the new signal sequence obtained after resampling on the uniform phase axis; φ aux (t) represents the instantaneous phase of the auxiliary signal; The distance domain is obtained by performing a Fast Fourier Transform (FFT) on the interpolated and resampled signal using the following formula (5): （5）； In equation (5): This is the total length of the resampled signal; For the index of the distance domain, ; The imaginary unit; and That is, the range domain signal of the two polarization components; The polarization-depolarized range domain signal is obtained by signal processing using the following formula (6). : （6）。 6. The distance extension method for an ultra-weak fiber optic grating optical frequency domain analyzer according to claim 5, characterized in that: In step 3: based on the statistical characteristics of the power spectral density of the local space near the positioning point, and the length of the ultra-weak fiber grating region... Length of grating spacing Parameters, dynamically matched with weighted adaptive power spectral density (PSD) thresholds Its expression is: （5）； In equation (5): and These are the statistical mean and standard deviation of the power spectral density (PSD) amplitude, respectively. For adjustment coefficients; For and Weighting function for parameters; The weight function expression is: （6）； In formula (6): The spacing-to-gate length ratio; α is the gate length duty cycle; β are weighting coefficients. Ultra-weak fiber grating grating length Length of grating spacing satisfy ≥ .

7. The distance extension method for an ultra-weak fiber optic frequency domain analyzer according to claim 6, characterized in that: In step 3: establishing the spatial correspondence between the measurement group fiber grating array and the reference group fiber grating array, as detailed below: For the reference state range domain signal L sig_ref and the measurement state distance domain signal L sig_meas All UW-FBG reflection peaks were identified using an adaptive PSD thresholding algorithm, resulting in two location arrays: Z ref = [z refj [j=1,2…M] and Z meas =[z measi [i=1,2…M]; Among them, Z ref It is an array consisting of the center positions of all ultra-weak fiber grating reflection peaks identified under the reference state; z refj Z represents the center position of the reflection peak of the j-th ultra-weak fiber grating in the reference state; j is the index number of the grating position array in the reference state; M is the total number of identified ultra-weak fiber gratings; Z meas It is an array consisting of the center positions of all ultra-weak fiber grating reflection peaks identified under measurement conditions; z measi It represents the center position coordinates of the i-th ultra-weak fiber grating reflection peak under the measurement state; The reference position z is calculated using the following formula (7). refj With measurement position z measi Absolute distance: （7）； In equation (7): d ij The absolute distance between the reference position and the measurement position; the reference position z with the smallest distance. refj Determined to be related to z measi The corresponding physical grating.

8. The distance extension method for an ultra-weak fiber optic grating optical frequency domain analyzer according to claim 7, characterized in that: In step 4, based on the sampling rate F s With gate length Calculate the minimum number of consecutive sampling points required for a single complete gate region. The grating region is precisely located and IFFT demodulation is performed to obtain the grating spectrum; the details are as follows: 4.1: Calculate the minimum number of consecutive sampling points : （8）； In equation (8): It is a rounding function; The refractive index of the optical fiber; The speed of light; This refers to the effective frequency scanning range of the laser. 4.2: Calculation of depolarized distance domain signal The power spectral density (PSD) is given by the formula: where n = 1, 2, 3…N, and N is the number of signal points. （9）； In equation (9): The power spectral density amplitude at the k-th sampling point in the polarization-depolarized distance domain signal; Represents the Discrete Fourier Transform; To take the square of the amplitude; Spatial sampling rate, unit: sampling points / meter; Number of signal points; When continuous Power spectral density amplitude at each sampling point Above the dynamic threshold When identified as an ultra-weak fiber grating unit, the polarization distance domain signal will be eliminated. Threshold identification is performed on all N signal points to obtain grating array information.

9. The distance extension method for an ultra-weak fiber optic frequency domain analyzer according to claim 8, characterized in that: In step 5, spectral data regions deviating from the ±3σ range of the center wavelength are dynamically trimmed based on the 3σ criterion, retaining only the effective region of the main peak for Gaussian fitting to obtain the optimized center wavelength. The grating wavelength array is obtained by traversing the distance domain. ; Includes the following steps: S5.1: Establish a Gaussian function model for the ultra-weak fiber grating spectrum by inverting the grating spectrum using IFFT: （10）； In formula (10): This represents a Gaussian function model of the reflectance spectrum of a single UW-FBG. Peak intensity; It is the independent variable, representing wavelength; For the Bragg wavelength; Spectral width; It is a natural exponential function; S5.2: Taking the natural logarithm of the Gaussian function model of the ultra-weak fiber grating spectrum, we expand it into a quadratic polynomial: （11）； S5.3: Solve the parameters using the least squares method to obtain the optimized center wavelength peak value. : （12）； In equation (12): Indicates at wavelength The UW-FBG reflectance spectral intensity measured at the location; This represents the wavelength value represented by the i-th sampling point in the UW-FBG reflectance spectrum; Indicates the number of signal points; S5.4: Let the maximum spectral amplitude S max The corresponding wavelength is Calculate the full width at half maximum (FWHM) as follows: Find the peak S on the spectral curve. max Half of, i.e., S half = S max / 2; at peak wavelength λ peak On the left, find the spectral intensity value equal to S. half The corresponding wavelength is denoted as λ. left ; in λ peak On the right side, find the spectral intensity value equal to S. half The corresponding wavelength is denoted as λ. right The formula for calculating the full width at half maximum (FWHM) is: FWHM = λ right - l left (13); S5.5: Let the wavelength sampling interval be... x and σ0 are the initial standard deviations. The range of ±3σ from the center wavelength is selected as the fitting window, and the number of fitting points m0 is: （14）； S5.6: According to formula (14) in S5.5, calculate the number of corresponding fitting points for the spectrum of different fiber gratings to achieve adaptive grating demodulation.

10. The distance extension method for an ultra-weak fiber optic grating optical frequency domain analyzer according to claim 8, characterized in that: In step 6, after wavelength demodulation of each grating in the ultra-weak fiber grating array (UW-FBGs) is completed, a Bragg wavelength array {λ} corresponding to the spatial position order of the gratings is obtained. i , i=1,2,...}, where: i is the raster index; Save the reference Bragg wavelength array {λ} measured under default conditions. i_ref , i=1,2,...}, and the measured Bragg wavelength array {λ} measured under sensing conditions. i_ Subtracting the values ​​of i=1,2,..., from the values ​​of i=1,2,..., we obtain the change in wavelength. .

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