An optimal matching method for the length of delay fiber in an auxiliary interferometer

Abstract

This invention proposes an optimal matching method for the length of the delayed fiber in an auxiliary interferometer, belonging to the field of laser measurement instruments. This method derives the optimal matching condition between the length difference between the main and auxiliary interferometer arms and the resampled residual phase noise in fiber strain measurement using optical frequency domain reflection (OFDR) technology. For applications requiring high-precision strain measurement across the entire distance scale, segmented matching and demodulation followed by splicing can ensure optimal strain testing accuracy for each fiber segment. This method offers advantages of low spatial resolution and high strain accuracy, and can be widely applied to high-precision testing of fiber optic devices.

Description

Technical Field

[0001] This invention relates to an optimal matching method for the length of the delay fiber in an auxiliary interferometer for a distributed strain sensing system in the optical frequency domain, belonging to the field of laser measuring instruments. Background Technology

[0002] Optical frequency domain reflectometry (OFDR) technology was first proposed by W. Eickhoff et al. in 1981. It uses continuously swept light emitted from a narrow-linewidth laser as the probe light. The spatial resolution of the overall system is directly determined by the tuning range of the probe light. This technology mainly uses Rayleigh scattering light in fiber optic devices for coherent detection. The frequency of the coherent light is proportional to the distance between Rayleigh scattering points in the fiber. By analyzing the spectrum of the coherent light, distributed sensing information in the fiber can be obtained. Compared with other distributed fiber optic sensing technologies, OFDR systems have significant advantages in terms of spatial resolution and dynamic range.

[0003] In the field of fiber optic inductive strain measurement, OFDR sensing systems have been applied to structural health monitoring of bridges and buildings, three-dimensional shape sensing, and aircraft structural monitoring due to their advantages such as high spatial resolution, large data limit, no measurement dead zone, and single-end detection. However, in some special monitoring scenarios, such as aircraft wing shape monitoring and satellite solar panel structural health monitoring, where extremely high strain accuracy is required, a test length of hundreds of meters, a test sensitivity of με, and a measurement range of thousands of με are usually needed, while maintaining a demodulation spatial resolution of millimeters.

[0004] Due to the influence of the nonlinearity of the frequency sweep of the tunable light source, the auxiliary interferometer has become an essential component for high-precision testing of current optical frequency domain reflection systems, and there is a matching relationship between the delay fiber length of the auxiliary interferometer and the optimal test distance of the fiber under test.

[0005] In 2004, LUNA Corporation of the United States proposed using an auxiliary interferometer to correct errors generated by a laser with non-ideal tuning characteristics in an optical frequency domain reflection system (Apparatus and method for correcting errors generated by a laser with non-ideal tuning characteristics, US6900897B2), which greatly improved the testing accuracy of the OFDR system. However, they did not find a matching correspondence between the arm length difference of the auxiliary interferometer and the arm length difference of the main interferometer.

[0006] Wang Feng et al. from Nanjing University published a compensation method (CN111397644B) for the nonlinear tuning effect of lasers in optical frequency domain reflectometers. This method involves connecting an acousto-optic frequency shifter (AOM) to one interferometer arm of an OFDR auxiliary interferometer to shift the frequency of the light wave, increasing the beat frequency signal of the auxiliary interferometer. The zero-crossing point of this signal is then used as a reference point to correct the measurement signal of the main interferometer. However, the acousto-optic frequency shifting scheme suffers from noise interference from the AOM itself and does not consider the matching problem between the time delay of the auxiliary interferometer and the time delay of the main interferometer, resulting in the final strain demodulation result failing to reach the ideal optimal value.

[0007] Zhang Lixun et al. from the University of Electronic Science and Technology of China published a system and method for reducing the influence of nonlinear phase of OFDR light sources (CN112461276B). This method uses a test fiber as the reference fiber for an auxiliary interferometer to achieve long-distance and high spatial resolution signal detection. Since there is an optimal matching relationship between the time delay of the auxiliary interferometer and the time delay of the main interferometer, directly using the device under test (DUT) as the delay fiber of the main interferometer cannot achieve the best strain testing accuracy.

[0008] Wuhan Haoheng Technology Co., Ltd. disclosed a device and method for long-distance measurement using OFDR segmented acquisition (CN111578971B). This method employs an auxiliary interferometer, whose generated beat frequency signal serves as the external clock for the data acquisition card, enabling equal-frequency interval sampling of the main interferometer's beat frequency signal. Simultaneously, the optical fiber under test is divided into N segments for segmented testing. While measuring the fiber under test in shorter segments effectively suppresses the accumulation of residual phase noise, this method does not consider the matching relationship between the arm length difference of the auxiliary interferometer and the arm length difference of the main interferometer, resulting in the final test results failing to meet expectations.

[0009] Anritsu Corp. of Japan disclosed that it used an auxiliary interferometer to calibrate the influence of frequency sweep nonlinearity of OFDR system light source and found that its correction effect depends on the difference in reference arm length between the main interferometer and the auxiliary interferometer, i.e., the length of the delay fiber of the auxiliary interferometer reference arm (Optical frequency domain reflection measurement device and optical frequency domain reflection measurement method, JP2017181115A). However, it did not accurately calculate the optimal matching relationship between the difference in arm length between the auxiliary interferometer and the main interferometer, and could not realize the adaptive dynamic matching technology of the delay fiber of the auxiliary interferometer.

[0010] This invention provides a method for optimal matching of the fiber delay loop length in an auxiliary interferometer for optical frequency domain reflection systems. This method determines the optimal matching relationship between the maximum measurement distance and the delay fiber length by deriving an analytical expression for the residual phase noise variance. For test conditions with relatively low strain accuracy requirements, the optimal delay fiber length can be dynamically matched based on the desired maximum measurement distance. For test conditions with relatively high strain accuracy requirements, the device under test (DUT) can be segmented, and after independent optimal delay fiber matching in an auxiliary interferometer, the segments can be spliced ​​and reassembled. This allows for strain measurement accuracy better than 1.5 με with a spatial resolution of 2 mm over the entire 101-meter range. This method can be widely used in the field of fiber optic inductive strain measurement. Summary of the Invention

[0011] 1.1. An optimal matching method for the length of the delay fiber of an auxiliary interferometer, characterized in that: by deriving the analytical expression of the variance of residual phase noise, the optimal matching relationship between the maximum measurement distance of the optical frequency domain reflection system and the length of the delay fiber of the auxiliary interferometer is determined; by controlling the length of the delay fiber of the auxiliary interferometer, the resampled residual phase noise is made to approach the shot noise limit, thereby achieving the optimal strain test conditions. The specific process includes the following steps:

[0012] Step 1.501: To achieve optimal strain test results, the test of the device under test will be performed in two steps. The first step is a rough measurement to obtain the approximate length of the device under test, followed by a second high-precision measurement. First, the length of the fiber optic device under test is initially estimated to obtain the predicted length of the fiber optic cable.

[0013] Step 2 502: Based on the preliminary estimated length of the fiber to be tested, select a standard single-mode fiber that is close to the predicted length as the delay fiber of one arm of the auxiliary interferometer in the high-precision optical frequency domain reflection system.

[0014] Step 3.503: After calibrating the auxiliary interferometer for time delay, perform preliminary testing on the device under test. Once the scattering spectrum information of the device under test is obtained, the precise length of the device under test can be calculated based on the calibrated time delay.

[0015] Step 4.504: Based on the precise length of the device under test obtained in Step 3.503 and the minimum residual phase noise requirement, determine whether segmented matching measurement is necessary. After testing the device under test using the OFDR system, the residual phase noise of the obtained signal after equal-frequency interval resampling correction can be expressed by the formula:

[0016]

[0017] In the formula τ M The time delay of the master interferometer, τ RTo account for the interferometer's time delay, φ(t) follows a Wiener process, and its increment Δφ(t) = φ(t + Δt) - φ(t) follows a Gaussian normal distribution with a mean of 0 and a variance of 2πΔvΔt, where Δv is the linewidth of the tunable laser. To minimize the residual phase noise term after resampling, the master interferometer's time delay τ is further analyzed. M With time delay τ of auxiliary interferometer R The relationship between the two factors leads to the derivation of the residual phase noise. The variance expression is:

[0018]

[0019] During OFDR system testing, after selecting the fiber optic device under test, the time delay τ of the master interferometer... M The path length is determined by the difference between the optical path length of the fiber under test and the optical path length of the reference arm of the main interferometer, and remains constant; when τ M <τ R At that time, the resampled residual phase noise increases with the time delay τ of the master interferometer. M The increase of τ exhibits a concave function trend, and the extreme values ​​of this growth trend are related to the time delay τ of the auxiliary interferometer. R Positive correlation. Equation (2) shows that when the delay of the main interferometer is exactly equal to the delay of the auxiliary interferometer, i.e. τ M =τ R When the residual phase noise variance is minimized, the optimal test effect for strain demodulation is achieved. However, to achieve high-precision testing at all locations within the overall measurement range, after determining the longest test distance, the maximum value D of the residual phase noise within the maximum test distance range should be minimized. max Minimize it as much as possible. Assume the equivalent fiber length of the device under test is L. max That is, the test length range is 0 to L. max L max The corresponding master interferometer delay is make D(τ M ) in τ M ∈(0,τ R The extreme points within the range are The corresponding maximum value is When τ M >τ R hour To minimize the residual phase noise of the optical fiber under test over the entire measurement range, the following condition must be met:

[0020]

[0021] Simplifying equation (3) yields:

[0022]

[0023] Solving equation (4) yields the optimal auxiliary interferometer delay:

[0024]

[0025] From equation (5), it can be seen that when the time delay of the auxiliary interferometer is Under the condition of a time delay of times that of the main interferometer, the entire fiber under test can achieve the minimum resampling residual phase noise result; that is, when the test result achieves the best strain accuracy, the relationship between the length of the auxiliary interferometer delay fiber and the length of the fiber under test is:

[0026]

[0027] Step 505: If the equivalent fiber length of the device under test is short or the requirement for the distributed strain accuracy of the device under test is not high, the length of the delay fiber of the auxiliary interferometer can be calculated according to formula (6) after obtaining the accurate length of the fiber under test through Step 1 501 to Step 3 503.

[0028] Step 6.506: After replacing the delay fiber of the OFDR system auxiliary interferometer reference arm with the delay fiber calculated in Step 5.505, perform a second high-precision distributed strain test to obtain the final distributed accurate strain result and complete the test.

[0029] Step 7.507: If high strain accuracy is required, the fiber under test can be divided into multiple independent units to further improve the strain sensing accuracy within the measurement distance range. Each segment of the device under test is individually matched with the optimal auxiliary interferometer delay fiber length to obtain extremely low residual phase noise within each unit. Assuming the device under test is divided into n independent length units, the residual phase noise at the boundaries of adjacent units must be equal. Thus, the division formula can be obtained:

[0030]

[0031] In the formula (LM) i ,LM i+1 ) is used to divide the length of the fiber under test into intervals, LR i This method divides the length of the delay fiber in the auxiliary interferometer into intervals. It enables longer devices under test to achieve optimal testing accuracy across the entire range, thereby suppressing accuracy degradation around the optimal point.

[0032] Step 8 508: After dividing the device under test into n independent units according to the segmentation criteria of the device under test in Step 7 507, repeat Step 5 505 according to the segmentation interval to match the corresponding auxiliary interferometer delay fiber length. Replace the matched auxiliary interferometer delay fiber in the segmentation order and then perform the test.

[0033] Step 9.509: For devices under test (DUTs) that do not require segmented testing, replace the auxiliary interferometer with the delayed fiber for a second high-precision test, and then directly perform strain demodulation on the entire fiber segment. If the DUT requires high full-range strain accuracy or is long, segment the fiber under test, perform segmented delayed fiber matching, and then perform a second high-precision test on each segment separately. The demodulation results from the segmented matching tests are then spliced ​​together sequentially to obtain the full-range distributed high-precision strain test results for the entire fiber under test.

[0034] Compared with the prior art, the advantages of the present invention are as follows:

[0035] This method can not only improve the full-size distance strain sensing accuracy of OFDR, but also guide the optimal segmented demodulation of long-distance fiber optic testing. By minimizing residual phase noise, it matches the optimal auxiliary interferometer delay fiber length, thereby approaching the theoretical accuracy limit of strain testing.

[0036] This method minimizes residual phase noise at the hardware level by guiding the delay fiber of the auxiliary interferometer, thus eliminating the need for additional data processing;

[0037] This method determines the optimal matching relationship between the maximum measurement distance of the OFDR system and the length of the delay fiber, satisfying the various requirements of the optical frequency domain reflection system for measurement distance, strain accuracy and demodulation time. Attached Figure Description

[0038] Figure 1 This is a flowchart of a method for optimal matching of the delay fiber loop length in an auxiliary interferometer.

[0039] Figure 2 This is a schematic diagram of the overall structure of the high-precision OFDR testing device used in this method.

[0040] Figure 3 The optimal strain demodulation result near the matching point.

[0041] Figure 4 Segmented matching of strain demodulation results within the shortest distance.

[0042] Figure 5 Long-distance segmented matching optimal auxiliary interferometer delayed fiber splicing strain demodulation results. Detailed Implementation

[0043] To clearly illustrate the optimal matching method for the delay fiber loop length of an auxiliary interferometer according to the present invention, the present invention will be further described in conjunction with embodiments and accompanying drawings, but this should not be construed as limiting the scope of protection of the present invention. Specific implementation method one:

[0045] like Figure 2The figure shows the optical frequency domain distributed strain sensing system used in this embodiment. The selection and parameters of the main optoelectronic devices of the system are as follows:

[0046] The light source 101 is a narrow linewidth tunable laser source with a wavelength scanning range of 154nm (1483nm-1637nm), a scanning speed of 200nm / s, and a scanning time of 0.77s.

[0047] The maximum detection bandwidth of the first balanced photodetector 208, the second balanced detector 305, and the third balanced detector 306 is 200MHz.

[0048] The sampling rate of the acquisition card 401 is set to 90MHz / s;

[0049] The auxiliary interferometer uses a 207 standard single-mode fiber with a refractive index n = 1.456 as the delay fiber. The delay fiber is calculated and replaced according to the optimal matching method of this invention to ensure optimal strain testing results.

[0050] The splitting ratio of the first coupler 102 and the third coupler 301 is 1:99, and the splitting ratio of the second coupler 202 and the fourth coupler 304 is 50:50.

[0051] Here, a 101m long 307 sensing fiber was used. Two measurements were quickly performed without external environmental interference. Then, strain demodulation with a spatial resolution of 2mm was performed on the fiber under test.

[0052] Since the time interval between the two measurements is very short and no strain is applied to the optical fiber during this process, the strain fluctuation relative to the zero-strain condition can be approximately equivalent to the strain demodulation accuracy of the system, thus characterizing the magnitude of the residual phase noise.

[0053] The test fiber length in the experiment was 101m, and calculations showed that the optimal delay fiber length for the auxiliary interferometer was 83.7m.

[0054] The test results obtained using this calculation method show that when the delay fiber of the auxiliary interferometer is configured at its optimal length, the worst strain accuracy over the entire 10¹m range of the fiber under test is 3.1 με. The strain demodulation results are as follows: Figure 3 As shown.

[0055] To further improve the strain accuracy across the entire measurement distance, the optical fiber under test was divided into multiple independent sections. The optimal auxiliary interferometer delay fiber length for each independent section was calculated to ensure that the residual phase noise of each section was below the required specifications.

[0056] However, when the length of the delayed fiber is less than or equal to 24m, the residual phase noise within the optimal measurement distance range is close to the critical value, and the value of the phase noise is close to the optical shot noise.

[0057] When optical particle noise dominates among all noises, the system noise reaches its theoretical minimum. Under the experimental conditions in this study, when optical particle noise is dominant, the strain accuracy can reach its theoretical optimal value. Figure 4 The results of measuring a 29m fiber under test using a 24m delay fiber are shown, with the worst strain accuracy being 1.2με (close to the theoretical best accuracy limit of 1με).

[0058] To make the variance of the residual phase noise as close as possible to the photoelastic noise, the lengths of the delay fiber in the auxiliary interferometer were set to 24m, 32m, 39m, 46.5m, 56.75m, 62m, 69m, 76.5m, 83.5m, 91.5m, and 98.5m. The final segmented splicing test results are as follows: Figure 5 As shown.

Claims

1. A method for optimal matching of the delay fiber length in an auxiliary interferometer, characterized by: By deriving the analytical expression for the residual phase noise variance, the optimal matching relationship between the maximum measurement distance of the optical frequency domain reflection system and the length of the delay fiber of the auxiliary interferometer was determined. By controlling the length of the delay fiber of the auxiliary interferometer, the resampled residual phase noise is made to approach the shot noise limit, thereby achieving the optimal strain test conditions. The specific process includes the following steps: Step 1 (501): To achieve the best strain test results, the test of the device under test will be performed in two steps. The first rough measurement will be used to obtain the approximate length of the device under test, followed by a second high-precision measurement. First, the length of the fiber optic device under test will be preliminarily estimated to obtain the predicted length of the fiber optic device under test. Step 2 (502): Based on the preliminary estimated length of the fiber to be tested, select a standard single-mode fiber that is close to the predicted length as the delay fiber of one arm of the auxiliary interferometer in the high-precision optical frequency domain reflection system. Step 3 (503): After calibrating the time delay of the auxiliary interferometer, perform preliminary testing on the device under test, obtain the scattering spectrum information of the device under test, and calculate the precise length of the device under test based on the time delay obtained from the calibration. Step 4 (504): Based on the precise length of the device under test obtained in Step 3 (503) and the minimum residual phase noise condition required for the test, determine whether segmented matching high-precision measurement is necessary; after testing the device under test using the OFDR system, the residual phase noise of the obtained signal after equal-frequency interval resampling correction is expressed by the formula: In the formula τ M The time delay of the master interferometer, τ R To assist the interferometer's time delay, It follows a Wiener process, and its increment The laser follows a Gaussian normal distribution with a mean of 0 and a variance of 2πΔvΔt, where Δv is the linewidth of the tunable laser. To minimize the residual phase noise term after resampling, the time delay τ of the master interferometer is further analyzed. M With time delay τ of auxiliary interferometer R The relationship between the two factors leads to the derivation of the residual phase noise. The variance expression is: During OFDR system testing, after selecting the fiber optic device under test, the time delay τ of the master interferometer... M The path length is determined by the difference between the optical path length of the fiber under test and the optical path length of the reference arm of the main interferometer, and remains constant; when τ M <τ R At that time, the resampled residual phase noise increases with the time delay τ of the master interferometer. M The increase of τ exhibits a concave function trend, and the extreme values ​​of this trend are related to the time delay τ of the auxiliary interferometer. R Positive correlation; Formula (2) shows that when the delay of the main interferometer is exactly equal to the delay of the auxiliary interferometer, i.e. τ M =τ R When the residual phase noise variance is minimized, the optimal test effect of strain demodulation is achieved. However, to achieve high-precision testing at all locations within the overall measurement range, after determining the longest test distance, the maximum value D of the residual phase noise within the maximum test distance range should be minimized. max As small as possible; assume the equivalent fiber length of the device under test is L. max That is, the test length range is 0 to L. max L max The corresponding master interferometer delay is make D(τ M ) in τ M ∈(0,τ R The extreme points within the range are The corresponding maximum value is When τ M >τ R hour To minimize the residual phase noise of the optical fiber under test over the entire measurement range, the following condition must be met: Simplifying equation (3) yields: Solving equation (4) yields the optimal auxiliary interferometer delay: From equation (5), it can be seen that when the time delay of the auxiliary interferometer is Under the condition of a time delay of times that of the main interferometer, the entire fiber under test can achieve the minimum resampling residual phase noise result; that is, when the test result achieves the best strain accuracy, the relationship between the length of the auxiliary interferometer delay fiber and the length of the fiber under test is: Step 5 (505): If the equivalent fiber length of the device under test is short or the distributed strain accuracy requirement of the device under test is not high, the length of the delay fiber of the auxiliary interferometer is calculated according to formula (6) after obtaining the accurate length of the fiber under test through Step 1 (501) to Step 3 (503). Step 6 (506): After replacing the delay fiber of the OFDR system auxiliary interferometer reference arm with the delay fiber calculated in Step 5 (505), perform a second high-precision distributed strain test to obtain the final distributed accurate strain result and complete the test. Step 7 (507): If the strain accuracy requirement is high, the fiber under test is divided into multiple independent units to further improve the strain sensing accuracy within the measurement distance range. Each segment of the device under test is individually matched with the optimal auxiliary interferometer delay fiber length to obtain extremely low residual phase noise in each unit. Assuming the device under test is divided into n independent length units, the residual phase noise at the boundaries of adjacent units must be equal, resulting in the division formula: In the formula (LM) i ,LM i+1 ) is used to divide the length of the fiber under test into intervals, LR i To divide the length of the delay fiber in the auxiliary interferometer into intervals, this method enables longer devices under test to achieve optimal testing accuracy across the entire range, thereby suppressing the problem of accuracy degradation on both sides of the optimal point. Step 8 (508): After dividing the device under test into n independent units according to the segmentation criteria of the device under test in Step 7 (507), repeat Step 5 (505) according to the segmentation interval to match the corresponding auxiliary interferometer delay fiber length. Replace the matched auxiliary interferometer delay fiber in the segmentation order and then perform the test. Step 9 (509): For devices under test that do not require segmented testing, replace the auxiliary interferometer with the delay fiber for a second high-precision test, and then directly perform strain demodulation of the entire fiber. If the full-range strain accuracy requirement of the device under test is high or the length of the device under test is long, then after segmented delay fiber matching, each fiber segment is individually tested twice with high precision, and the demodulation results after segmented matching tests are spliced ​​together in sequence to obtain the full-range distributed high-precision strain test results of the entire fiber under test.

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