A Method and System for Synchronous Measurement of Length and Refractive Index of Single-Mode Fiber and Model Optimization Prediction

Abstract

This invention discloses a method and system for synchronous measurement and model optimization prediction of the length and refractive index of a single-mode optical fiber, relating to the field of optical fiber sensing technology. The method includes: S1: Performing spectral analysis on the electro-optically modulated optical signal in a Sagnac ring interference optical path, extracting a first set of concave point frequency data, and generating a first frequency interval parameter through linear fitting; S2: Connecting a standard single-mode optical fiber of known length in series in the Sagnac ring interference optical path, performing spectral analysis on the modulated optical signal, extracting a second set of concave point frequency data, and generating a second frequency interval parameter through linear fitting; S3: Calculating the length and refractive index of the single-mode optical fiber under test using a preset formula based on the difference between the first and second frequency interval parameters; S4: Adjusting the laser wavelength to obtain multiple sets of wavelength-refractive index data, constructing a Gaussian process regression model based on the data, optimizing the Sellmeier equation parameters, and generating a refractive index-wavelength prediction model. This significantly reduces the complexity of the measurement.

Description

Technical Field

[0001] This invention relates to the field of fiber optic sensing technology, and in particular to a method and system for synchronous measurement of the length and refractive index of single-mode optical fibers and for model optimization and prediction. Background Technology

[0002] Single-mode optical fiber, as a core carrier of modern information infrastructure, is widely used in long-distance high-speed communication, precision fiber optic sensing, and other fields. Among these, length and refractive index are key parameters determining the transmission performance and sensing accuracy of optical fibers: length directly affects link loss and signal delay calculations, while refractive index is related to the propagation speed, mode constraints, and dispersion characteristics of optical signals. Therefore, accurate acquisition of these two parameters is crucial for ensuring the stability of optical fiber systems and optimizing device performance.

[0003] However, existing fiber optic parameter measurement technologies have significant limitations. First, current methods cannot achieve simultaneous measurement of length and refractive index. Optical time-domain reflectometry (OTDR) suffers from near-range blind zones and long-range signal attenuation, and cannot obtain refractive index information; while femtosecond laser pulse methods offer excellent accuracy, the equipment is expensive and requires pre-calibration of the refractive index; conventional interferometry is sensitive to environmental interference and requires known refractive index to deduce length. Regarding refractive index measurement, focusing methods can only measure small local segments of fiber; near-field refraction methods are complex and inefficient; digital holography has poor real-time performance; and fiber grating methods have limited applicability. Second, traditional methods have limited measurement accuracy and efficiency, and are subject to stringent environmental conditions. Third, existing technologies lack the ability to model and predict the refractive index-wavelength relationship with high precision, cannot overcome the strong dependence of the Sellmeier equation on material composition, and fail to integrate artificial intelligence algorithms such as Gaussian process regression to quantify uncertainty, thus limiting their application in high-end fiber optic device design and system performance evaluation.

[0004] Therefore, there is an urgent need to develop a method and system for synchronous measurement of the length and refractive index of single-mode optical fibers and for model optimization and prediction. Summary of the Invention

[0005] This invention provides a method and system for synchronous measurement of the length and refractive index of a single-mode optical fiber and for model optimization and prediction, in order to solve the above-mentioned problems existing in the prior art.

[0006] To achieve the above objectives, the present invention provides the following technical solution:

[0007] A method for simultaneous measurement of the length and refractive index of a single-mode optical fiber and for model optimization and prediction includes:

[0008] S1: Perform spectral analysis on the electro-optically modulated optical signal in the Sagnac ring interference optical path, extract the first set of concave point frequency data, and generate the first frequency interval parameter through linear fitting;

[0009] S2: Connect a standard single-mode fiber of known length in series in the Sagnac ring interference optical path, perform spectrum analysis on the modulated optical signal, extract the second set of concave point frequency data, and generate the second frequency interval parameter through linear fitting.

[0010] S3: Based on the difference between the first frequency spacing parameter and the second frequency spacing parameter, the length and refractive index of the single-mode fiber under test are calculated using a preset formula.

[0011] S4: Adjust the laser wavelength to obtain multiple sets of wavelength-refractive index data, construct a Gaussian process regression model based on the data and optimize the Sellmeier equation parameters to generate a refractive index-wavelength prediction model.

[0012] Furthermore, step S1 includes:

[0013] S11: The optical signal propagating in the Sagnac ring is frequency-sweeped and modulated in the range of 600MHz to 600.5MHz by an RF signal source to generate a modulated optical signal;

[0014] S12: The interference output of the modulated optical signal is converted into an electrical signal by a photodetector, and the spectrum data is collected by a spectrum analyzer;

[0015] S13: Extract the modulation frequency corresponding to each depression point in the spectrum data, plot the relationship curve between the modulation frequency and the ordinal number of the depression point, and obtain the slope of the curve as the first frequency interval parameter through linear fitting.

[0016] Furthermore, step S2 includes:

[0017] S21: While keeping the system parameters constant, connect a standard single-mode fiber of known length in series next to the single-mode fiber under test in the Sagnac ring.

[0018] S22: Perform interference output acquisition and spectrum analysis on the modulated optical signal in the series optical path;

[0019] S23: Extract the modulation frequency corresponding to each depression point in the spectrum data, and obtain the second frequency interval parameter through linear fitting.

[0020] Furthermore, step S3 includes:

[0021] S31: Calculate the difference between the first frequency interval parameter and the second frequency interval parameter;

[0022] S32: Length-based L Formula for calculating the length of the single-mode fiber to be tested:

[0023]

[0024] Where Δ LFor standard single-mode fiber of known length, This is the first frequency spacing parameter. This is the second frequency spacing parameter;

[0025] S33: Based on refractive index n Formula for calculating the refractive index of the single-mode fiber under test:

[0026]

[0027] Where c is the speed of light in a vacuum.

[0028] Furthermore, step S4 includes:

[0029] S41: Adjust the tunable laser to output different wavelengths in the wavelength range of 1530nm to 1570nm, repeat steps S1 to S3, and obtain multiple wavelength points and corresponding refractive index data.

[0030] S42: Remove outliers with a deviation exceeding three times the standard deviation and construct a wavelength-refractive index training dataset;

[0031] S43: Using wavelength as input and refractive index as output, a Gaussian process regression model is constructed using a squared exponential kernel function, and the hyperparameters are optimized by maximizing the marginal likelihood estimate;

[0032] S44: Based on the Levenberg-Marquardt algorithm, optimize the six parameters of the Sellmeier equation to generate a prediction model adapted to the optical fiber under test.

[0033] Furthermore, step S43 includes:

[0034] S431: Using wavelength as the input variable and refractive index as the output variable, the squared exponential covariance function is selected as the kernel function;

[0035] S432: Iteratively optimize the hyperparameters of signal standard deviation, length scale, and noise standard deviation;

[0036] S433: Output refractive index-wavelength prediction curve and confidence interval.

[0037] Furthermore, step S44 includes:

[0038] S441: An equation model is constructed using the Sellmeier coefficients of standard fused silica as initial parameters. The initial Sellmeier equations based on the typical coefficients of pure silica are as follows:

[0039] ;

[0040] in, This indicates the wavelength of the incident light in a vacuum.

[0041] S442: Set parameter boundary constraints and optimization options, with the objective function being to minimize the sum of squared residuals between the predicted values ​​and the experimental data;

[0042] S443: Iterative Optimization Six parameters are used to output the optimized Sellmeier equation.

[0043] Furthermore, it also includes a model validation step:

[0044] Introduce experimental data points that were not used in training to verify whether the data points fall within the confidence interval of the Gaussian process regression model and whether the relative error with the predicted value of the optimized Sellmeier equation is within the preset range.

[0045] If the verification passes, the refractive index-wavelength prediction model is determined to be a valid model; if the verification fails, return to S4 for re-optimization.

[0046] Furthermore, a system for synchronous measurement of length and refractive index of single-mode optical fiber and for model optimization and prediction is characterized by comprising:

[0047] The Sagnac ring interferometry module includes a tunable laser, an optical isolator, a 2×2 fiber coupler, an electro-optic modulator, a single-mode fiber under test, and a photodetector, which are used to construct the Sagnac ring interferometry optical path and generate interference signals.

[0048] The signal modulation and analysis module, including an RF signal source and a spectrum analyzer, is used to perform sweep frequency modulation on the interference signal and extract the concave point frequency;

[0049] The data processing module is used to calculate the frequency interval parameter based on the indentation frequency data from two measurements, and to calculate the length and refractive index of the single-mode fiber under test using a preset formula.

[0050] The model optimization and prediction module is used to construct a Gaussian process regression model and optimize the Sellmeier equation parameters based on refractive index data at multiple wavelengths, thereby generating a refractive index-wavelength prediction model.

[0051] Compared with the prior art, the present invention has the following advantages:

[0052] High-precision synchronous measurement of single-mode fiber length and refractive index was achieved; by combining Gaussian process regression (GPR) with AI-assisted optimization of the Sellmeier equation, high-precision prediction and uncertainty quantification of fiber refractive index-wavelength relationship were realized, providing a reliable foundation for fiber dispersion characteristic analysis and device design.

[0053] Other features and advantages of the invention will be set forth in the description which follows, and will be apparent in part from the description, or may be learned by practicing the invention.

[0054] The technical solution of the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. Attached Figure Description

[0055] The accompanying drawings are provided to further illustrate the invention and form part of the specification. They are used in conjunction with embodiments of the invention to explain the invention and do not constitute a limitation thereof. In the drawings:

[0056] Figure 1 This is an integrated schematic diagram of a method for synchronous measurement of the length and refractive index of a single-mode optical fiber and for model optimization and prediction, as described in an embodiment of the present invention.

[0057] Figure 2 This is a schematic diagram of the structure of a single-mode fiber length and refractive index synchronous measurement and model optimization prediction system according to an embodiment of the present invention;

[0058] Figure 3 This is a parameter setting diagram of a tunable laser according to an embodiment of the present invention;

[0059] Figure 4 This is a parameter setting diagram of a radio frequency signal source in an embodiment of the present invention;

[0060] Figure 5 This is a waveform diagram of the spectrum analyzer during the first measurement (without a 10m single-mode fiber jumper) in a single-mode fiber length refractive index synchronous measurement and model optimization prediction system according to an embodiment of the present invention.

[0061] Figure 6 The waveform diagram of the spectrum analyzer for the second measurement (connected to a 10m single-mode fiber jumper) in a single-mode fiber length refractive index synchronous measurement and model optimization prediction system in an embodiment of the present invention.

[0062] Figure 7 The modulation frequency is used in the first measurement (without a 10m single-mode fiber jumper) of a single-mode fiber length and refractive index synchronous measurement and model optimization prediction system in an embodiment of the present invention. -Origin fitting plot of the indentation point ordinal numbers;

[0063] Figure 8 The modulation frequency for the second measurement (connected to a 10m single-mode fiber jumper) in a single-mode fiber length and refractive index synchronous measurement and model optimization prediction system in an embodiment of the present invention. Origin fitting plot of the indentation point ordinal numbers;

[0064] Figure 9This is a flowchart of the AI-assisted optimization and prediction method for the refractive index-wavelength relationship of single-mode fiber based on Sagnac ring interference and electro-optic modulation in an embodiment of the present invention.

[0065] Figure 10 This is a comparison chart of the results of AI-assisted optimization prediction of the refractive index-wavelength relationship of a G.652D single-mode fiber (Gaussian process regression and improved Sellmeier equation) in an embodiment of the present invention.

[0066] Figure 11 The figure shows the verification results of AI-assisted optimization prediction of the refractive index-wavelength relationship of G.652D single-mode fiber (Gaussian process regression and improved Sellmeier equation) for three sets of experimental data points that were not involved in the training in this embodiment of the invention. Detailed Implementation

[0067] The preferred embodiments of the present invention will be described below with reference to the accompanying drawings. It should be understood that the preferred embodiments described herein are for illustration and explanation only and are not intended to limit the present invention.

[0068] This invention provides a method for simultaneous measurement of the length and refractive index of a single-mode optical fiber and for model optimization and prediction, including:

[0069] S1: Perform spectral analysis on the electro-optically modulated optical signal in the Sagnac ring interference optical path, extract the first set of concave point frequency data, and generate the first frequency interval parameter through linear fitting;

[0070] S2: Connect a standard single-mode fiber of known length in series in the Sagnac ring interference optical path, perform spectrum analysis on the modulated optical signal, extract the second set of concave point frequency data, and generate the second frequency interval parameter through linear fitting.

[0071] S3: Based on the difference between the first frequency spacing parameter and the second frequency spacing parameter, the length and refractive index of the single-mode fiber under test are calculated using a preset formula.

[0072] S4: Adjust the laser wavelength to obtain multiple sets of wavelength-refractive index data, construct a Gaussian process regression model based on the data and optimize the Sellmeier equation parameters to generate a refractive index-wavelength prediction model.

[0073] The following is a detailed description with reference to specific embodiments.

[0074] Example 1

[0075] This embodiment provides a method for simultaneous measurement of the length and refractive index of a single-mode optical fiber and for model optimization and prediction, such as... Figure 9The diagram illustrates the complete process of AI-assisted optimization prediction, comprising four core steps: data preparation and preprocessing (outlier removal, unit standardization), Gaussian process regression (GPR) modeling (using the squared exponential kernel function, outputting 95% confidence intervals), and Sellmeier equation optimization (optimizing coefficients based on the Levenberg-Marquardt algorithm). Model validation and generalization testing (introducing untrained data points for validation).

[0076] The method includes the following steps:

[0077] S1: Perform spectral analysis on the electro-optically modulated optical signal in the Sagnac ring interference optical path, extract the first set of concave point frequency data, and generate the first frequency interval parameter through linear fitting.

[0078] Specifically, the steps include:

[0079] S11: The optical signal propagating in the Sagnac ring is frequency-sweeped and modulated within the range of 600MHz to 600.5MHz using an RF signal source to generate a modulated optical signal. For example... Figure 4 As shown, the starting frequency of the RF signal source is set to 600MHz, the ending frequency is set to 600.5MHz, the scan type is set to frequency scan, the number of scan points is set to 501, and the output level is set to 6dBm.

[0080] S12: The interference output of the modulated optical signal is converted into an electrical signal by a photodetector, and the spectrum data is acquired by a spectrum analyzer. The starting frequency of the spectrum analyzer is set to 600MHz and the ending frequency is set to 600.5MHz to match the RF signal source. The trajectory type is set to "maximum hold" mode, the reference level is adjusted to be slightly higher than the signal peak value, and the scale is set to 3dB to match the level interval for identifying the beat frequency signal dip point.

[0081] S13: Extract the modulation frequency corresponding to each indentation point in the spectrum data. Draw the modulation frequency The curve relating the indentation number to the number of the depression point. For example... Figure 5 The image shows the beat frequency signal waveform during the first measurement. Figure 5 The waveform is complete and stable, exhibiting multiple minimum interference intensity dips, each dip corresponding to a modulation frequency. The spectrum analyzer was set to a start frequency of 600MHz, an end frequency of 600.5MHz, a trace type of "maximum hold", and a reference level slightly higher than the signal peak value.

[0082] like Figure 7 As shown, the modulation frequency was plotted using Origin software. The relationship curve between the frequency and the indentation number was obtained and linearly fitted. After the waveform displayed on the spectrum analyzer was complete and stable, the modulation frequency corresponding to each indentation point with the minimum interference intensity was recorded. The slope of the curve is obtained through linear fitting. As the first frequency interval parameter Δ .

[0083] S2: Connect a standard single-mode fiber of known length in series in the Sagnac ring interference optical path, perform spectrum analysis on the modulated optical signal, extract the second set of concave point frequency data, and generate the second frequency interval parameter through linear fitting.

[0084] Specifically, the steps include:

[0085] S21: While keeping all system parameters constant, connect a known length Δ fiber in series next to the single-mode fiber under test in the Sagnac ring. L =10m standard single-mode fiber optic patch cord, the patch cord being made of the same material as the single-mode fiber under test.

[0086] S22: Perform interference output acquisition and spectrum analysis on the modulated optical signal in the series optical path, keeping all parameter settings of the RF signal source and spectrum analyzer completely consistent with step S1.

[0087] S23: Extract the modulation frequency corresponding to each indentation point in the spectrum data. Draw the modulation frequency The curve relating the indentation number to the number of the depression point. For example... Figure 6 and Figure 8 As shown, the slope of the curve is obtained through linear fitting. As the second frequency spacing parameter Δ .

[0088] S3: Based on the difference between the first frequency spacing parameter and the second frequency spacing parameter, the length and refractive index of the single-mode fiber under test are calculated using a preset formula.

[0089] Specifically, the steps include:

[0090] S31: Calculate the first frequency interval parameter Δ With the second frequency spacing parameter Δ The difference (Δ) -Δ ).

[0091] S32: Length-based L Formula for calculating the length of the single-mode fiber to be tested:

[0092]

[0093] Where, Δ LGiven the known length of a standard single-mode fiber optic patch cord (10m in this example), Δ Δ is the first frequency interval parameter. This is the second frequency spacing parameter.

[0094] S33: Based on refractive index n Formula for calculating the refractive index of the single-mode fiber under test:

[0095]

[0096] Where c is the speed of light in a vacuum (c≈3× m / s).

[0097] The calculated single-mode fiber length L Compared with nominal value Compare with 3017m to calculate the absolute and relative errors; then use the calculated single-mode fiber refractive index... n Compared with the standard refractive index of single-mode fiber at the corresponding wavelength Compare the results and calculate the absolute and relative errors.

[0098] S4: Adjust the laser wavelength to obtain multiple sets of wavelength-refractive index data, construct a Gaussian process regression model based on the data and optimize the Sellmeier equation parameters to generate a refractive index-wavelength prediction model.

[0099] Specifically, the steps include:

[0100] S41: Adjust the tunable laser to output different wavelengths within the wavelength range of 1530nm to 1570nm, with a wavelength interval of 5nm. Repeat steps S1 to S3 to obtain multiple wavelength points. and corresponding refractive index data .like Figure 3 As shown, the output wavelength is set to 1550nm and the output power is 8dBm (below 11dBm to ensure clear spectrum analyzer images), that is: the output power of the tunable laser is kept at 8dBm.

[0101] S42: Remove outliers with a deviation exceeding three times the standard deviation (judgment criteria: Construct a wavelength-refractive index training dataset (where the deviation from the dataset mean exceeds 3 standard deviations). , Ideally, about 8 sets of data should be selected for model training.

[0102] S43: with wavelength λ Input variables, refractive index nFor the output variables, a Gaussian process regression (GPR) model is constructed using the squared exponential kernel function, and the hyperparameters are optimized by maximizing the marginal likelihood estimate. Specifically, this includes:

[0103] S431: Using wavelength as the input variable and refractive index as the output variable, the squared exponential covariance function is selected as the kernel function. This embodiment is implemented using the MATLAB function `fitrgp`, with `Standardize=true` set for data standardization and `SigmaLowerBound=1e-6` to avoid excessively small variance.

[0104] S432: The training process iterates 50 times until convergence by iteratively optimizing hyperparameters such as signal standard deviation, length scale, and noise standard deviation.

[0105] S433: Outputs the refractive index-wavelength prediction curve and 95% confidence interval, quantifying prediction uncertainty. The predicted refractive index for a specific wavelength is compared with the standard refractive index corresponding to that wavelength, calculating the absolute and relative errors. After obtaining the absolute and relative errors of multiple sets of data, the overall mean absolute error and mean relative absolute error are further calculated.

[0106] S44: Based on the Levenberg-Marquardt algorithm, six parameters of the Sellmeier equation are optimized to generate a prediction model adapted to the fiber under test. Specifically, this includes:

[0107] S441: The equation model is constructed using the Sellmeier coefficients of standard fused silica as initial parameters. The initial Sellmeier equations based on the typical coefficients of pure silica are as follows:

[0108]

[0109] The initial parameters are: =0.6961663, =0.4079426, =0.8974794, =0.06840432μm², =0.11624142μm², =9.8961612μm² ~ It has a unitless coefficient. ~ (Unit: μm²) Wavelength λ It needs to be converted to μm units to meet the requirements of the equation.

[0110] S442: Set parameter boundary constraints and optimization options, with the objective function being to minimize the sum of squared residuals between the predicted values ​​and the experimental data. The Levenberg-Marquardt nonlinear least squares algorithm is implemented using MATLAB's `lsqcurvefit` function, with the parameter boundary constraints set as follows: B i ∈[0.6, 1.0], C i ∈[0.004, 100] to ensure physical rationality; optimization options include: maximum function evaluation times of 10,000, maximum iteration times of 1,000, and function tolerance. Optimal tolerance Step size tolerance This ensures the convergence and accuracy of the optimization process.

[0111] S443: Iterative Optimization The algorithm takes six parameters and outputs an optimized Sellmeier equation. The optimized equation accurately reflects the dispersion characteristics of optical fiber materials, possessing both mathematical fitting capabilities and physical interpretability. It can be used to derive dispersion characteristic parameters of optical fibers and calculate key indicators such as group velocity dispersion (GVD) and dispersion coefficient D.

[0112] Calculate the goodness-of-fit indices of the optimized Sellmeier equation: mean squared error (MSE), mean absolute error (MAE), and root mean square error (RMSE), quantify their evaluation errors, and ensure the reliability of the optimized Sellmeier equation.

[0113] like Figure 10 As shown, the comparison of the prediction results of the refractive index-wavelength relationship of G.652D single-mode fiber based on the Gaussian process regression model and the optimized Sellmeier equation is presented.

[0114] Model validation steps:

[0115] To ensure the model's generalization ability and prediction reliability, this embodiment also includes a model validation step:

[0116] Untrained experimental data points were introduced, and cross-validation was used to examine the predictive capabilities of the Gaussian process regression model and the optimized Sellmeier equation on the untrained data. The specific validation criteria were: whether the data points fell within the 95% confidence interval of the Gaussian process regression model, and whether the relative error between the predicted values ​​and those of the optimized Sellmeier equation was within a preset range.

[0117] Preferably, the preset range is set to a relative error of ≤0.05%.

[0118] If the validation passes, meaning that all three sets of experimental data points not involved in training fall within the 95% confidence interval of the GPR model and the relative error with the predicted value of the optimized Sellmeier equation is ≤0.05%, then the refractive index-wavelength prediction model is determined to be an effective model. If the validation fails, meaning that the validation set residuals increase significantly, then return to S4 to re-optimize the parameters in order to avoid underfitting and overfitting and ensure generalization ability.

[0119] like Figure 11 As shown, the results of verifying the refractive index-wavelength relationship of G.652D single-mode fiber by introducing three sets of experimental data points that were not used in the training are presented. This verifies the prediction accuracy of the GPR model and the optimized Sellmeier equation for the dispersion characteristics of G.652D fiber, ensuring the reliability and adaptability for practical applications.

[0120] Example 2

[0121] This embodiment provides a system for simultaneous measurement and model optimization prediction of single-mode fiber length and refractive index applied to the method described in Embodiment 1. For example... Figure 1 As shown, the optical path layout and key component connections of the entire measurement system are visualized. Figure 1 The following components are listed: tunable laser (wavelength range 1500-1630nm), optical isolator, 2×2 fiber coupler, electro-optic modulator (MZM), RF signal source, and single-mode fiber under test (G.652D, length...). =3017m), photodetector (PD), and spectrum analyzer. The optical path is as follows: the optical signal starts from the laser, passes through the isolator and enters the coupler, where it is split into two beams, clockwise (CW) and counterclockwise (CCW). The CW beam is first modulated by MZM and then passes through the fiber under test; the CCW beam passes through the fiber under test and then is modulated by MZM. After the two beams interfere at the coupler, they are converted into electrical signals by the PD and finally analyzed by the spectrum analyzer.

[0122] Specifically, the system includes:

[0123] The Sagnac ring interferometry module includes:

[0124] A tunable laser is used to provide a light source of a specific wavelength in the 1500-1630nm band, and the output power is adjustable from 0 to 11dBm. In this embodiment, it is set to 8dBm.

[0125] An optical isolator is connected to the laser output to ensure unidirectional transmission of optical signals and prevent backlight from interfering with the laser.

[0126] A 2×2 fiber optic coupler with input 1 connected to an isolator and two outputs 3 and 4 connected to the clockwise (CW) and counterclockwise (CCW) optical paths of a Sagnac ring, respectively, to evenly split the incident light into two beams (50% each).

[0127] An electro-optic modulator (MZM), placed in one arm of the Sagnac ring, is used for radio frequency modulation of light intensity;

[0128] The single-mode fiber under test is connected to the other arm of the Sagnac ring, forming a closed Sagnac ring together with the electro-optic modulator. In this embodiment, the single-mode fiber under test is a G.652D type single-mode fiber with a nominal length of... =3017m;

[0129] A photodetector (PD) is connected at one end to the interference signal output terminal 2 of a 2×2 fiber coupler, converting the interference optical signal output by the coupler into an electrical signal.

[0130] In the clockwise optical path, the light first passes through branch 3, is frequency modulated by an electro-optic modulator (MZM), and then passes through the single-mode fiber under test to complete the loop transmission; the counterclockwise optical path first passes through branch 4, passes through the single-mode fiber under test, and is then modulated by the MZM; the two modulated optical signals interfere when they pass through the coupler again, and are finally output to the photodetector by branch 2.

[0131] The signal modulation and analysis module includes:

[0132] The radio frequency signal source, connected to the MZM, is used to provide a sweep frequency modulation signal in the range of 600~600.5MHz, with the number of scan points set to 501 and the output level of 6dBm;

[0133] The spectrum analyzer, connected to the other end of the photodetector, is used to analyze the spectrum of the beat frequency signal and extract the frequency of the dip point. The starting frequency is set to 600MHz, the ending frequency is set to 600.5MHz, the trajectory type is set to "maximum hold", the reference level is adjusted to be slightly higher than the signal peak value, and the scale is set to 3dB.

[0134] The data processing module calculates the frequency interval parameter based on the indentation frequency data from two measurements, and calculates the length and refractive index of the single-mode fiber under test using a preset formula. The data processing module is implemented via a computer or dedicated processor and performs the following functions:

[0135] Receive the frequency data of the depression points from the first and second measurements collected by the spectrum analyzer;

[0136] Plot the curves showing the relationship between modulation frequency and the ordinal number of the depression points, and obtain the first frequency interval parameter Δ through linear fitting. Second frequency interval parameter Δ ;

[0137] The length of the single-mode optical fiber under test is calculated according to a preset formula. L and refractive index n ;

[0138] Calculate the absolute and relative errors of the measurement results.

[0139] The model optimization and prediction module is used to construct a Gaussian process regression model and optimize the Sellmeier equation parameters based on refractive index data at multiple wavelengths, generating a refractive index-wavelength prediction model. This module is implemented using a programming environment such as MATLAB or Python and performs the following functions:

[0140] Receive wavelength-refractive index data measured at different wavelengths;

[0141] Remove outliers and build a training dataset;

[0142] Use the GPR algorithm to construct a Gaussian process regression model and output the prediction curve and confidence interval;

[0143] The Levenberg-Marquardt algorithm is used to optimize the parameters of the Sellmeier equation;

[0144] Calculate the goodness-of-fit indices (MSE, MAE, RMSE);

[0145] Perform model validation and evaluate generalization ability.

[0146] In practical use, users operate this system by following these steps:

[0147] System setup: such as Figure 2 As shown, the system's structural composition is further refined, emphasizing the physical connections and signal flow of each instrument, including the laser output power setting (8dBm), the RF signal source sweep range (600-600.5MHz), and the "maximum hold" mode configuration of the spectrum analyzer. Connect each optical component according to the optical path, ensuring a secure connection, and wipe the fiber optic interface with alcohol to remove oil and dust.

[0148] Parameter settings: according to Figure 3 and Figure 4 The parameters for the tunable laser, RF signal source, and spectrum analyzer are shown in the diagram.

[0149] First measurement: Start the system and record the frequency data of the depression point after the waveform displayed by the spectrum analyzer stabilizes;

[0150] Second measurement: Connect a 10m standard single-mode fiber optic patch cord in series and repeat the measurement operation;

[0151] Parameter calculation: The fiber length and refractive index are automatically calculated through the data processing module;

[0152] Multi-wavelength measurement: Adjust the laser wavelength and repeat the above measurement process;

[0153] Model building: The GPR model is built and the Sellmeier equation is optimized through the model optimization and prediction module;

[0154] Results validation: Validation data points are introduced to evaluate model performance.

[0155] This system is built on general-purpose instruments, with readily available core components. It is compatible with mainstream single-mode optical fibers such as G.652D and can archive and save results such as fitting data and model parameters. It is suitable for promotion and application in university scientific research and teaching, industrial testing and communication engineering.

[0156] This invention achieves synchronous high-precision measurement of single-mode fiber length and refractive index using Sagnac ring interferometry and electro-optic modulation technology, significantly reducing measurement complexity. By combining Gaussian process regression and the improved Sellmeier equation, it realizes high-precision continuous prediction of the refractive index-wavelength relationship over a wide wavelength range, providing reliable technical support for fiber dispersion characteristic analysis, device design, and system performance evaluation.

[0157] Obviously, those skilled in the art can make various modifications and variations to this invention without departing from the spirit and scope of this invention.

Claims

1. A method for simultaneous measurement of the length and refractive index of a single-mode optical fiber and for model optimization and prediction, characterized in that, Including: S1: Perform spectral analysis on the electro-optically modulated optical signal in the Sagnac loop interference optical path, extract the first set of dip point frequency data, and generate the first frequency interval parameter through linear fitting; S2: In series connection with a standard single-mode fiber of known length in the Sagnac loop interference optical path, perform spectral analysis on the modulated optical signal, extract the second set of dip point frequency data, and generate the second frequency interval parameter through linear fitting; S3: Based on the difference between the first frequency interval parameter and the second frequency interval parameter, calculate and generate the length value and refractive index value of the待测 single-mode fiber through a preset formula; Step S3 includes: S31: Calculate the difference between the first frequency interval parameter and the second frequency interval parameter; S32: Length-based L Formula for calculating the length of the single-mode fiber to be tested: ； Where Δ L For standard single-mode fiber of known length, This is the first frequency spacing parameter. This is the second frequency spacing parameter; S33: Based on refractive index n Formula for calculating the refractive index of the single-mode fiber under test: ； where c is the speed of light in vacuum; S4: Adjust the wavelength of the laser to obtain multiple sets of wavelength-refractive index data, construct a Gaussian process regression model based on the data, and optimize the parameters of the Sellmeier equation to generate a refractive index-wavelength prediction model.

2. The method for synchronous measurement of single-mode fiber length and refractive index and model optimization prediction according to claim 1, characterized in that, Step S1 includes: S11: Use a radio frequency signal source to perform frequency sweep modulation on the optical signal propagating in the Sagnac loop within the range of 600 MHz to 600.5 MHz to generate a modulated optical signal; S12: Convert the interference output of the modulated optical signal into an electrical signal through a photodetector, and collect spectral data by a spectrum analyzer; S13: Extract the modulation frequencies corresponding to each dip point in the spectral data, plot the relationship curve between the modulation frequency and the dip point ordinal number, and obtain the curve slope as the first frequency interval parameter through linear fitting.

3. The method for synchronous measurement of single-mode fiber length and refractive index and model optimization prediction according to claim 1, characterized in that, Step S2 includes: S21: Under the condition of keeping the system parameters unchanged, serially connect a standard single-mode fiber of known length beside the待测 single-mode fiber in the Sagnac loop; S22: Collect and perform spectral analysis on the interference output of the modulated optical signal in the optical path after series connection; S23: Extract the modulation frequencies corresponding to each dip point in the spectral data, and obtain the second frequency interval parameter through linear fitting.

4. The method for synchronous measurement of the length and refractive index of single-mode optical fiber and model optimization prediction according to claim 1, characterized in that, Step S4 includes: S41: Adjust the tunable laser to output different wavelengths within the wavelength range of 1530 nm to 1570 nm, repeat steps S1 to S3, and obtain multiple wavelength points and corresponding refractive index data; S42:剔除 the outliers whose deviation exceeds three standard deviations, and construct a wavelength-refractive index training data set; S43: Use the wavelength as the input and the refractive index as the output, construct a Gaussian process regression model with a squared exponential kernel function, and optimize the hyperparameters through maximizing the marginal likelihood estimation; S44: Optimize the six parameters of the Sellmeier equation based on the Levenberg-Marquardt algorithm to generate a prediction model adapted to the待测 fiber.

5. The method for synchronous measurement of single-mode fiber length and refractive index and model optimization prediction according to claim 4, characterized in that, Step S43 includes: S431: Use the wavelength as the input variable and the refractive index as the output variable, and select the squared exponential covariance function as the kernel function; S432: Iteratively optimize the hyperparameters of the signal standard deviation, length scale, and noise standard deviation; S433: Output the refractive index-wavelength prediction curve and the confidence interval.

6. The method for synchronous measurement of single-mode fiber length and refractive index and model optimization prediction according to claim 4, characterized in that, Step S44 includes: S441: An equation model is constructed using the Sellmeier coefficients of standard fused silica as initial parameters. The initial Sellmeier equations based on the typical coefficients of pure silica are as follows: ； S442: Set parameter boundary constraints and optimization options, with the objective function being to minimize the sum of squared residuals between the predicted values ​​and the experimental data; S443: Iterative Optimization Six parameters are used to output the optimized Sellmeier equation.

7. The method for synchronous measurement of single-mode fiber length and refractive index and model optimization prediction according to claim 1, characterized in that, It also includes a model validation step: Introduce experimental data points that were not used in training to verify whether the data points fall within the confidence interval of the Gaussian process regression model and whether the relative error with the predicted value of the optimized Sellmeier equation is within the preset range. If the verification passes, the refractive index-wavelength prediction model is determined to be a valid model; if the verification fails, return to S4 for re-optimization.

8. A system for synchronous measurement of the length and refractive index of single-mode optical fiber and for model optimization and prediction as described in any one of claims 1 to 7, characterized in that, include: The Sagnac ring interferometry module includes a tunable laser, an optical isolator, a 2×2 fiber coupler, an electro-optic modulator, a single-mode fiber under test, and a photodetector, which are used to construct the Sagnac ring interferometry optical path and generate interference signals. The signal modulation and analysis module, including an RF signal source and a spectrum analyzer, is used to perform sweep frequency modulation on the interference signal and extract the concave point frequency; The data processing module is used to calculate the frequency interval parameter based on the indentation frequency data from two measurements, and to calculate the length and refractive index of the single-mode fiber under test using a preset formula. The model optimization and prediction module is used to construct a Gaussian process regression model and optimize the Sellmeier equation parameters based on refractive index data at multiple wavelengths, thereby generating a refractive index-wavelength prediction model.

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