A fiber-optic vibration sensing device and method based on large amplitude phase demodulation

Abstract

The present application relates to the technical field of vibration sensing, in particular to a fiber vibration sensing device and method based on large amplitude phase demodulation. The present application separates two polarization eigenmodes output by a sensing polarization maintaining fiber through a polarization beam splitter, then recombines at least three phase diversity interference signals with a nominal 120° mutual phase offset by a polarization maintaining 3*3 coupler, converts the signals into three electrical signals through a photoelectric detection assembly, and then a signal processing unit sequentially performs singular value decomposition projection to obtain a two-dimensional signal plane projection, elliptical correction to obtain corrected orthogonal components, inverse tangent operation and phase unwrapping to recover the differential phase. By changing the readout of the differential phase from the single value mapping of the sinusoidal intensity transfer function to the direct phase extraction based on the phase diversity, when the differential phase amplitude exceeds the local linear region of the sinusoidal transfer function or even crosses multiple interference fringes, a unique phase value can still be obtained.

Description

Technical Field

[0001] This invention relates to the field of vibration sensing technology, and in particular to an optical fiber vibration sensing device and method based on large amplitude phase demodulation. Background Technology

[0002] Polarization-Sensitive Optical Fiber Sensors (POFS) infer vibration information by utilizing changes in the polarization state of the sensing fiber caused by external disturbances. They offer advantages such as resistance to electromagnetic interference and corrosion, suitability for remote and multiplexed measurements, and have broad application prospects in perimeter security, structural health monitoring, and other fields. In fading-free POFS sensors using polarization-maintaining fiber as the sensing medium, aligning the polarization initiation axis at a 45° angle to the principal axis of the polarization-maintaining fiber ensures equal-intensity excitation of the two polarization eigenmodes, thus constraining the polarization evolution to a deterministic trajectory and eliminating polarization-induced signal fading.

[0003] However, eliminating polarization fading alone cannot provide unambiguous measurements under large phase shifts. In conventional intensity-detection receivers, the detected intensity is a sinusoidal function of the differential phase of two polarization intrinsic modes. When operating near the quadrature bias point, small phase changes can provide an approximately linear response; however, when the differential phase amplitude generated by external disturbances is large, the signal may cross the extreme points of the sinusoidal transfer function or traverse multiple interference fringes, leading to non-unique phase mapping, waveform folding, and harmonic distortion. Specifically, when the differential phase amplitude approaches or exceeds approximately 3.83 rad (i.e., the first zero of the Bessel function J1), higher-order harmonics dominate, and intensity demodulation loses the fidelity of the original waveform. Especially near the zero of the Bessel function, the fundamental component is suppressed to near zero.

[0004] Therefore, overcoming the shortcomings of the existing technology is an urgent problem to be solved in this technical field. Summary of the Invention

[0005] The technical problem to be solved by this invention is that traditional intensity detection receivers are only suitable for detecting the presence and frequency of weak vibrations, and cannot achieve quantitative measurement of large amplitude waveforms.

[0006] The present invention adopts the following technical solution: In a first aspect, an optical fiber vibration sensing device based on large amplitude phase demodulation is provided, comprising a laser, a sensing polarization-maintaining fiber, a polarization beam splitter, a polarization-maintaining 3×3 coupler, and a photoelectric detection component coupled sequentially along the optical path; and further comprising a signal processing unit connected to the photoelectric detection component. The laser is used to emit polarized light, which is coupled into the sensing polarization-maintaining fiber through a 45° rotating fusion splice to excite two polarization eigenmodes of the sensing polarization-maintaining fiber with equal intensity. The two polarization eigenmodes accumulate differential phase modulated by external perturbation during propagation along the sensing polarization-maintaining fiber. The polarization beam splitter is used to separate the two polarization eigenmodes output from the polarization-maintaining sensing fiber. The polarization-maintaining 3×3 coupler is used to recombine the two polarization eigenmodes to generate at least three phase diversity interference signals, which have a nominal phase offset of 120° between them. The photoelectric detection component includes at least three photodetectors, which are used to convert the three phase diversity interference signals into three corresponding electrical signals. The signal processing unit is used to perform singular value decomposition projection on the three electrical signals to obtain a two-dimensional signal plane projection, perform elliptic correction on the two-dimensional signal plane projection to obtain corrected orthogonal components, and recover the differential phase from the corrected orthogonal components through arctangent operation and phase unwrapping.

[0007] Preferably, the main axes of the two input pigtails of the polarization-maintaining 3×3 coupler are aligned with the polarization intrinsic mode axes corresponding to the two output ports of the polarization beam splitter, respectively.

[0008] Preferably, the signal processing unit is further configured to: perform mean centering on the three electrical signals used for singular value decomposition to remove the DC component when projecting the two-dimensional signal plane projection through singular value decomposition.

[0009] Preferably, the elliptic correction performed by the signal processing unit includes: The two-dimensional signal plane is projected and fitted into a quadratic curve using the direct least squares method to obtain elliptical parameters including center coordinates, rotation angle, and semi-axis length; and translation, rotation, and normalization are performed based on the elliptical parameters to map the two-dimensional signal plane onto a unit circle.

[0010] Preferably, the signal processing unit is configured to use a fixed set of calibration parameters obtained from a single calibration record, which is suitable for measurements with differential phase amplitudes ranging from at least 0.52 rad to 15.21 rad without the need for recalibration.

[0011] In a second aspect, a fiber optic vibration sensing method based on large-amplitude phase demodulation is provided, applied to the fiber optic vibration sensing device based on large-amplitude phase demodulation as described in the first aspect, the method comprising: Polarized light is coupled into the sensing polarization-maintaining fiber through a 45° rotating fusion splice, thereby exciting the two polarization eigenmodes of the sensing polarization-maintaining fiber with equal intensity. The two polarization eigenmodes accumulate differential phase modulated by external disturbances during propagation along the sensing polarization-maintaining fiber. The two polarization eigenmodes output from the polarization-maintaining sensing fiber are separated by a polarization beam splitter. The two polarization eigenmodes after separation are recombined by a polarization-maintaining 3×3 coupler to generate at least three phase diversity interference signals, which have a nominal mutual phase offset of 120°. The three phase diversity interference signals are converted into three corresponding electrical signals using at least three photodetectors; Singular value decomposition projection is performed on the three electrical signals to obtain a two-dimensional signal plane projection. Elliptic correction is performed on the two-dimensional signal plane projection to obtain corrected orthogonal components. The differential phase is recovered from the corrected orthogonal components through arctangent operation and phase unwrapping.

[0012] Preferably, the step of performing singular value decomposition projection on the three electrical signals to obtain a two-dimensional signal plane projection specifically includes: The three electrical signals are arranged into a signal matrix X∈R^(N×3), where N is the number of sampling points, and the k-th column of X is the N sampled values ​​of the k-th electrical signal; Perform mean centering on the signal matrix X to obtain a mean-centered matrix, including subtracting the time mean of the corresponding channel from each sample value to obtain a zero-mean signal, and the mean-centered matrix. Represented as: ; in, A matrix consisting of the means of each column. It is a left singular vector matrix. It is a singular value diagonal matrix. It is a right singular vector matrix; Perform singular value decomposition on the mean-centered matrix to obtain the decomposition result, which includes the left singular vector matrix. The singular value diagonal matrix and the right singular vector matrix ; The three electrical signals are projected onto a two-dimensional signal plane defined by the first two right singular vectors of the decomposition result to obtain the two-dimensional signal plane projection. Represented as: ; in, The signal plane basis is formed by the first two columns of the right singular vector matrix V, and the projection of the two-dimensional signal plane is an N×2 matrix P, whose two columns are denoted as... and .

[0013] Preferably, performing elliptic correction on the two-dimensional signal plane projection to obtain corrected orthogonal components specifically includes: The two-dimensional signal plane projection is fitted into a general quadratic curve using the direct least squares method to obtain elliptical parameters including center coordinates, rotation angle, and semi-axis length; the equation of the general quadratic curve is: ; Where A, B, C, D and E are parameter terms, F is a constant term, and the ellipse constraint B²-4AC<0 is satisfied. The ellipse center coordinates (x0, y0), principal axis rotation angle θ, semi-major axis length a and semi-minor axis length b are analytically calculated from the fitting coefficients of the general quadratic curve. Based on the ellipse parameters, translation, rotation, and normalization are performed to project the two-dimensional signal plane onto the unit circle, thereby obtaining the coordinates on the unit circle as the corrected orthogonal components. The translation, rotation, and normalization are performed sequentially, including first eliminating center offset through translation transformation, then eliminating axis tilt through rotation transformation, and finally normalizing by dividing along both axes by the corresponding semi-axis lengths, thereby obtaining the corrected orthogonal components. ²+ The corrected orthogonal components of the relation ²≈1 , ),in and These correspond to the cosine and sine components of the differential phase, respectively.

[0014] Preferably, the step of recovering the differential phase from the corrected orthogonal components through arctangent operation and phase unwrapping specifically includes: The arctangent value of the corrected quadrature components is calculated using a two-parameter arctangent function to obtain the winding phase. : ; in, and For the corrected orthogonal components, the range of the winding phase is (-π, π]. Phase unwrapping is performed on the entangled phase to obtain the recovered differential phase. The phase unwrapping is achieved by detecting the phase jump between adjacent sampling points point by point: when the entangled phase difference between two adjacent points exceeds π, a 2π jump is determined to have occurred. The entangled phase of subsequent sampling points is corrected by accumulating or subtracting 2π, thereby unfolding the entangled phase into a continuous time series to obtain the recovered differential phase Δφ(t).

[0015] Preferably, before performing singular value decomposition projection on the three electrical signals, the method further includes: A wide-arc perturbation is applied to the sensing polarization-maintaining fiber to generate a calibration record spanning multiple interference fringes; A fixed set of calibration parameters is derived from the calibration record. This fixed set of calibration parameters is applicable to subsequent measurements with differential phase amplitudes ranging from at least 0.52 rad to 15.21 rad without the need for recalibration.

[0016] Compared with the prior art, the beneficial effects of the present invention are as follows: This invention separates the two polarization eigenmodes output from the polarization-maintaining fiber using a polarization beamsplitter. These eigenmodes are then recombined by a 3×3 polarization-maintaining coupler to generate at least three phase diversity interference signals with a nominal 120° mutual phase offset. These signals are converted into three electrical signals by a photoelectric detection component. The signal processing unit then sequentially performs singular value decomposition projection to obtain a two-dimensional signal plane projection, elliptic correction to obtain the corrected orthogonal components, arctangent operation, and phase unwrapping to recover the differential phase. By transforming the differential phase readout from a single-valued mapping of the sinusoidal intensity transfer function to direct phase extraction based on phase diversity, a unique and definite phase value can still be obtained even when the differential phase amplitude exceeds the local linear region of the sinusoidal transfer function or even crosses multiple interference fringes. This solves the technical problem of traditional intensity detection receivers being unable to achieve quantitative measurement under large-amplitude phase offsets due to non-unique mapping, waveform folding, and fundamental suppression. Attached Figure Description

[0017] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0018] Figure 1 This is a schematic diagram of an analyzer-based non-fading PMF-POFS provided in an embodiment of the present invention; Figure 2 This is a schematic diagram of the structure of an optical fiber vibration sensing device based on large amplitude phase demodulation provided in an embodiment of the present invention; Figure 3 This is a schematic flowchart of an optical fiber vibration sensing method based on large amplitude phase demodulation provided in an embodiment of the present invention; Figure 4 This is a schematic diagram of a process for obtaining differential phase according to an embodiment of the present invention; Figure 5This is a schematic diagram of an experimental setup for comparing an intensity receiver and a phase receiver, provided by an embodiment of the present invention. Figure 6 This is a schematic diagram of the complete optical and electronic configurations of two receivers and the corresponding processing chain provided in an embodiment of the present invention; Figure 7 This is a schematic diagram of the G1 intensity output and its best-fit sine wave provided by an embodiment of the present invention; Figure 8 This is a schematic diagram of a G2 phase recovery and its best-fit sine provided by an embodiment of the present invention; Figure 9 This is a schematic diagram of a G1 spectrum provided in an embodiment of the present invention; Figure 10 This is a schematic diagram of a G2 spectrum provided in an embodiment of the present invention; Figure 11 This is a schematic diagram of a time-domain waveform provided in an embodiment of the present invention; Figure 12 This is a schematic diagram of a spectrum with the residual fundamental frequency as a reference, provided by an embodiment of the present invention; Figure 13 This is a schematic diagram illustrating the waveform fidelity index of two receivers at 100 Hz, provided by an embodiment of the present invention. Figure 14 This is a schematic diagram of the correlation coefficient amplitude provided in an embodiment of the present invention; Figure 15 This is a schematic diagram of the second to tenth harmonic THD provided in an embodiment of the present invention; Figure 16 This is a schematic diagram of the projection trajectory before and after parameter correction using 150 Vpp, provided by an embodiment of the present invention. Detailed Implementation

[0019] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention.

[0020] Unless the context otherwise requires, throughout the specification and claims, the term "comprising" is interpreted as openly inclusive, meaning "including, but not limited to." In the description of the specification, terms such as "one embodiment," "some embodiments," "exemplary embodiment," "example," "specific example," or "some examples" are intended to indicate that a particular feature, structure, material, or characteristic associated with that embodiment or example is included in at least one embodiment or example of this disclosure. The illustrative representations of the above terms do not necessarily refer to the same embodiment or example. Furthermore, the specific features, structures, materials, or characteristics mentioned may be included in any suitable manner in any one or more embodiments or examples; that is, although they may be incorporated into embodiments or examples using the above terms for reasons such as order and position, it does not limit them to be incorporated in combination by a single embodiment or example.

[0021] In the description of this invention, the terms "first" and "second" are used for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the number of indicated technical features. Thus, a feature defined with "first" or "second" may explicitly or implicitly include one or more of that feature. In the description of embodiments of this disclosure, unless otherwise stated, "a plurality of" means two or more. Furthermore, for example, the description may use the prefix "A" or "B" to describe the same type of nouns as two independent entities. In this case, the corresponding features defined with "A" and "B" are used only to distinguish between similar entities and should not be construed as indicating or implying relative importance or implicitly specifying the number of indicated technical features.

[0022] In describing some embodiments, the terms "coupled," "coupled," and "connected," and their derivative expressions, may be used. For example, the term "connected" may be used in describing some embodiments to indicate that two or more components have direct physical or electrical contact with each other. Similarly, the term "coupled" may be used in describing some embodiments to indicate that two or more components have direct physical or electrical contact. However, the terms "connected" or "coupled" may also refer to two or more components that do not have direct contact with each other but still cooperate or interact with each other, such as "optical coupling," "wireless connection," etc. The embodiments disclosed herein are not necessarily limited to the scope of this invention.

[0023] Furthermore, the technical features involved in the various embodiments of the present invention described below can be combined with each other as long as they do not conflict with each other.

[0024] Example 1: Figure 1 This demonstrates existing analyzer-based fading-free PMF (Polarization) technology. Maintaining Fiber (POFS). Linearly polarized light from a DFB (Distributed Feedback Laser) laser is coupled into the sensing PMF through a 45° rotated PMF fusion splice, resulting in a roughly even distribution of optical power between the two orthogonally polarized eigenmodes. Because the principal axis and birefringence of the PMF are well-defined, polarization evolution is constrained, unlike the random walk characteristic of single-mode fibers.

[0025] External strain alters the differential phase accumulated between the two polarization modes. For a uniformly disturbed fiber segment, the dynamic phase can be written as: (1) in, The wavelength of light The change in birefringence per unit strain. For the effective interaction length, The applied strain. More generally, non-uniform disturbances can be represented by the corresponding integral along the sensing fiber.

[0026] At the receiver, the analyzer, at 45° to the PMF principal axis, converts the relative phase into an intensity change. The transmit and detect alignment determines the excitation balance and fringe visibility, while the static mode phase Φ_b is determined by accumulated birefringence and any applied phase bias. Therefore, the 45° alignment suppresses polarization-induced fading but does not itself fix the interferometric operating point.

[0027] for Figure 1 The receiver based on the analyzer detects an intensity that includes a property related to cos[Φ_b+]. The phase-dependent interference term is proportional to the DC component. After removing the DC component, the phase-dependent output can be written as: (2) Where K includes optical power, interferometric visibility, detector responsivity, and receiver gain. When the static phase is adjusted to be orthogonal, i.e., Φ_b = π / 2, the above equation becomes: (3) The intensity receiver used as the experimental reference implements the same transfer function in a balanced form. Instead of projecting the two polarization eigenmodes onto a common axis using a polarizer, it first separates them using a polarizing beam splitter (PBS), and then performs interference reconstruction using a PM2×2 coupler. The outputs of the two couplers contain complementary interference terms; the common DC component is eliminated by subtracting the two photodetector signals, resulting in the same sinusoidal dependence as equation (2), only with different overall gain and phase conventions. Therefore, Figure 1The analyzer-based receiver and the balanced receiver are different physical implementations of the same periodic intensity-phase map, and the large signal limit derived below applies to both.

[0028] When |Δφ| At 1 rad, the receiver is approximately linear because sin(Δφ) ≈ Δφ. Outside this local region, the periodic transfer function is non-monotonic. The same intensity may correspond to multiple phase values, and crossing the extreme points of the sinusoidal transfer function will reverse the response slope and produce waveform folding.

[0029] For sinusoidal phase modulation = sin(ωt), given by the Jacobi–Anger expansion: (4) Where Jm is a Bessel function of the first kind, order m. Fundamental wave and Proportional, while the third, fifth, and higher odd harmonics are respectively caused by , Awaiting decision. Near the first zero point, that is At approximately 3.83 rad, even if higher-order harmonics still exist, the fundamental component will be suppressed. This behavior is an inevitable consequence of the intensity transfer function and cannot be eliminated by simply maintaining a quadrature bias.

[0030] Based on the above analysis, in order to address the problem that traditional intensity detection receivers are only suitable for detecting the presence and frequency of weak vibrations and cannot achieve quantitative measurement of large-amplitude waveforms, this embodiment proposes a fiber optic vibration sensing device based on large-amplitude phase demodulation. In one implementation, such as... Figure 2 As shown, the device includes a laser, a sensing polarization-maintaining fiber, a polarization beam splitter (PBS), a polarization-maintaining 3×3 coupler, and a photodetector (PD) coupled sequentially along the optical path; it also includes a signal processing unit (not shown in the figure) connected to the photodetector.

[0031] The laser is used to emit polarized light. In this embodiment, the laser is a DFB laser with an output wavelength of 1550 nm, a linewidth of less than 100 kHz, and stable output power. The polarized light emitted by the laser has a definite linear polarization direction, providing a light source basis for the subsequent equal-intensity excitation of the two polarization eigenmodes of the polarization-maintaining sensing fiber.

[0032] In one embodiment, the polarized light is coupled into the sensing polarization-maintaining fiber through a 45° rotating fusion splice to excite the two polarization eigenmodes of the sensing polarization-maintaining fiber with equal intensity. Specifically, the 45° rotating fusion splice is located between the output pigtail of the laser and the input end of the sensing polarization-maintaining fiber, such that the polarization initiation axis is aligned at a 45° angle with the main axis of the polarization-maintaining fiber. This distributes the input linearly polarized light equally in power to the fast and slow axis polarization eigenmodes of the sensing polarization-maintaining fiber. By aligning the polarization initiation axis with the main axis of the polarization-maintaining fiber at a 45° angle, the two polarization eigenmodes are excited with equal intensity, thus constraining the polarization evolution to a deterministic trajectory and eliminating polarization-induced signal fading.

[0033] In one embodiment, the two polarization eigenmodes accumulate a differential phase modulated by an external disturbance as they propagate along the polarization-maintaining sensing fiber. As the sensing medium, the polarization-maintaining fiber experiences different effective refractive index changes in the fast-axis and slow-axis modes due to the elasto-optic effect and geometric deformation when subjected to external vibration disturbances. This introduces a differential phase change proportional to the vibration signal between the two polarization eigenmodes. The length of the polarization-maintaining fiber used for sensing is determined according to actual sensing requirements, and in this embodiment it ranges from tens of meters to hundreds of meters.

[0034] The polarization beam splitter is used to separate the two polarization eigenmodes output from the polarization-maintaining fiber of the sensing sensor. The polarization beam splitter has one input port and two output ports, outputting the fast-axis polarization eigenmode and the slow-axis polarization eigenmode, respectively. In this embodiment, the polarization beam splitter is a Wollaston prism type or fiber type polarization beam splitter with an extinction ratio better than 20dB, ensuring sufficiently low polarization crosstalk in the two outputs.

[0035] The polarization-maintaining 3×3 coupler is used to recombine the two polarization eigenmodes to generate at least three phase diversity interference signals, which have a nominal phase offset of 120°. The main axes of the two input pigtails of the polarization-maintaining 3×3 coupler are aligned with the polarization eigenmode axes corresponding to the two output ports of the polarization beamsplitter, respectively, to ensure that the two polarization eigenmodes are injected into the two input ports of the polarization-maintaining 3×3 coupler in a defined polarization state, maintaining polarization alignment accuracy. The polarization-maintaining 3×3 coupler is fabricated using a fused taper process, and the splitting ratio between its three output ports is close to 1:1:1. The nominal phase offset between the three output signals is 120° (i.e., 2π / 3 rad). This nominal 120° phase offset is an inherent physical characteristic of the 3×3 symmetrical coupler, ensuring that the three interference signals are uniformly distributed in the phase space, providing a complete information basis for subsequent phase diversity demodulation.

[0036] It should be noted that the polarization-maintaining 3×3 coupler in this embodiment is the core device for realizing phase diversity interferometry. In traditional intensity detection receivers, the detected intensity is a sinusoidal function of the differential phase of two polarization intrinsic modes. When operating near the quadrature bias point, small-amplitude phase changes can provide an approximately linear response; however, when the differential phase amplitude generated by external disturbances is large, the signal will cross the extreme points of the sinusoidal transfer function or pass through multiple interference fringes, resulting in non-unique phase mapping, waveform folding, and harmonic distortion. Specifically, when the differential phase amplitude approaches or exceeds approximately 3.83 rad (i.e., the first zero of the Bessel function J1), the fundamental component approaches zero, and the intensity reading completely loses its fidelity to the original waveform. The three phase diversity interferometry signals generated by the polarization-maintaining 3×3 coupler, each with a nominal 120° mutual phase offset, ensure that even when any one signal is at its lowest sensitivity point, the other two can still provide effective phase information. This fundamentally eliminates the mapping ambiguity of a single sinusoidal transfer function and provides a physical basis for the unambiguous recovery of large-amplitude differential phases.

[0037] Reference Figure 2 The photoelectric detection component includes at least three photodetectors (PD1, PD2, and PD3), which are used to convert the three phase diversity interference signals into three corresponding electrical signals. In this embodiment, the photodetectors can be InGaAs photodiodes with bandwidth covering the target vibration frequency range and responsivity consistency better than ±0.5dB. The three photodetectors correspond to the three output ports of the polarization-maintaining 3×3 coupler, respectively, converting the light intensity signal into voltage signals I1(t), I2(t), and I3(t).

[0038] The signal processing unit is used to perform singular value decomposition projection on the three electrical signals to obtain a two-dimensional signal plane projection, perform elliptic correction on the two-dimensional signal plane projection to obtain corrected orthogonal components, and recover the differential phase from the corrected orthogonal components through arctangent operation and phase unwrapping.

[0039] The signal processing unit can be implemented by a digital signal processor (DSP), a field-programmable gate array (FPGA), or a general-purpose computer, and includes an analog-to-digital conversion module and a digital computing module.

[0040] The specific processing flow of the signal processing unit is described in detail below: In one implementation, when projecting the two-dimensional signal plane using singular value decomposition (SVD), the signal processing unit performs mean centering on the three electrical signals used for SVD to remove the DC component. Specifically, the time mean of each of the three electrical signals I1(t), I2(t), and I3(t) is subtracted to obtain a zero-mean signal. This step eliminates the DC bias introduced by differences in light source power, detector dark current, and coupler insertion loss, ensuring that subsequent SVD is performed only on the AC variation components of the signal.

[0041] The three electrical signals are arranged into a signal matrix, which is an N×3 matrix where N is the number of sampling points, and the three columns correspond to the three mean-centered electrical signals. Mean centering is performed on the signal matrix to obtain a mean-centered matrix. Singular value decomposition is performed on the mean-centered matrix to obtain the decomposition result. The three electrical signals are projected onto a two-dimensional signal plane defined by the first two right singular vectors of the decomposition result to obtain the two-dimensional signal plane projection.

[0042] Since the three interference signals generated by the polarization-maintaining 3×3 coupler are essentially driven by the same differential phase Δφ(t), the trajectories of the three signals in three-dimensional space actually lie in a two-dimensional plane (ideally, the third singular value is zero). By extracting the directions of the first two principal components through singular value decomposition, the three-dimensional signal is projected onto the two-dimensional signal plane without loss. The resulting two-dimensional signal plane projection retains all the information of the differential phase while simultaneously achieving dimensionality reduction.

[0043] Elliptic correction is performed on the two-dimensional signal plane projection to obtain the corrected orthogonal components. Due to the actual polarization-maintaining 3×3 coupler's splitting ratio deviating from the ideal 1:1:1, the three-way phase offset deviating from the ideal 120°, and the inconsistent photodetector responsivity, the trajectory of the two-dimensional signal plane projection is elliptical rather than an ideal circle.

[0044] The ellipse correction specifically includes: using the direct least squares method to project and fit the two-dimensional signal plane into a general quadratic curve to obtain ellipse parameters including center coordinates, rotation angle, and semi-axis length; and performing translation, rotation, and normalization based on the ellipse parameters to project and map the two-dimensional signal plane onto a unit circle, thereby obtaining the coordinates on the unit circle as the corrected orthogonal components.

[0045] Specifically, the direct least squares method is used to fit the general quadratic curve equation ax² + bxy + cy² + dx + ey + f = 0, which satisfies elliptic constraints, to the two-dimensional projected data points (x_i, y_i). The ellipse center coordinates (x0, y0), rotation angle θ, and semi-major axis a and semi-minor axis b are extracted from the fitting coefficients. Then, translation transformations are performed to eliminate center offset, rotation transformations to eliminate axis tilt, and normalization is achieved by dividing along each axis by the corresponding semi-axis length. Finally, the elliptical trajectory is mapped to the unit circle. The coordinates (u, v) on the unit circle are the corrected orthogonal components, satisfying the relationship u² + v² ≈ 1, where u and v correspond to the cosine and sine components of the difference phase, respectively.

[0046] The differential phase is recovered from the corrected orthogonal components through arctangent operation and phase unwrapping. Specifically, this includes: calculating the arctangent value of the corrected orthogonal components using the two-parameter arctangent function atan2(v, u) to obtain the wrapped phase φ_wrapped(t), whose value range is (-π, π]; and performing phase unwrapping on the wrapped phase to obtain the recovered differential phase Δφ(t).

[0047] The phase unwrapping is achieved by detecting the phase jump between adjacent sampling points point by point: when the phase difference between two adjacent points exceeds π, a 2π jump is determined to have occurred, and subsequent points are corrected by accumulating or subtracting 2π, thereby unwrapping the wrapped phase into a continuous differential phase time series. The differential phase Δφ(t) obtained after phase unwrapping is the real phase modulation signal generated by external vibration disturbance on the sensing polarization-maintaining fiber, which can directly reflect the amplitude and waveform information of the vibration.

[0048] In one embodiment, the signal processing unit is further configured to use a fixed set of calibration parameters obtained from a single calibration record, which is applicable to measurements with differential phase amplitudes ranging from at least 0.52 rad to 15.21 rad without requiring recalibration. Specifically, during the calibration phase, a wide-arc perturbation is applied to the sensing polarization-maintaining fiber to generate a calibration record spanning multiple interference fringes. This wide-arc perturbation causes the differential phase to vary over a large range, ensuring that the trajectory of the two-dimensional signal plane projection covers a sufficient arc segment of the ellipse, thereby obtaining reliable ellipse fitting parameters. The fixed set of calibration parameters is derived from the calibration record, including the projection matrix of the singular value decomposition (the first two right singular vectors) and the ellipse correction parameters (center coordinates, rotation angle, and semi-axis length). Once obtained, this fixed set of calibration parameters remains unchanged in subsequent measurements without requiring recalibration for vibration signals of different amplitudes, and is applicable to subsequent measurements with differential phase amplitudes ranging from at least 0.52 rad to 15.21 rad without requiring recalibration. This characteristic indicates that the demodulation algorithm of this device has good adaptability to signal amplitude, and a single calibration can cover a wide dynamic range from weak vibration to strong vibration.

[0049] In summary, this embodiment separates the two polarization eigenmodes output from the polarization-maintaining fiber using a polarization beamsplitter. These eigenmodes are then recombined by a 3×3 polarization-maintaining coupler to generate at least three phase diversity interference signals with a nominal 120° mutual phase offset. After being converted into three electrical signals by a photoelectric detection component, the signal processing unit sequentially performs singular value decomposition projection to obtain a two-dimensional signal plane projection, elliptic correction to obtain the corrected orthogonal components, arctangent operation, and phase unwrapping to recover the differential phase. By transforming the differential phase readout from a single-value mapping of the sinusoidal intensity transfer function to direct phase extraction based on phase diversity, a unique and definite phase value can still be obtained even when the differential phase amplitude exceeds the local linear region of the sinusoidal transfer function or even crosses multiple interference fringes. This solves the technical problem of traditional intensity detection receivers being unable to achieve quantitative measurement under large-amplitude phase offsets due to non-unique mapping, waveform folding, and fundamental suppression.

[0050] Example 2 This embodiment provides a fiber optic vibration sensing method based on large-amplitude phase demodulation, applied to the fiber optic vibration sensing device based on large-amplitude phase demodulation described in Embodiment 1. In one implementation, as follows... Figure 3 As shown, the method includes: Step 101: The polarized light is coupled into the sensing polarization-maintaining fiber by rotating the fusion splice at 45° to excite the two polarization eigenmodes of the sensing polarization-maintaining fiber at equal intensity. The two polarization eigenmodes accumulate differential phase modulated by external disturbances during propagation along the sensing polarization-maintaining fiber.

[0051] In this step, the linearly polarized light output from the laser enters the sensing polarization-maintaining fiber through a 45° rotating fusion splice. The polarization axis is aligned 45° with the main axis of the polarization-maintaining fiber, ensuring equal excitation power for the fast and slow axis modes. When external vibrations act on the sensing polarization-maintaining fiber, a differential phase modulation Δφ(t) corresponding to the vibration signal is generated between the two polarization eigenmodes. Because the polarization-maintaining fiber is used as the sensing medium, the polarization evolution is constrained to a deterministic trajectory, eliminating polarization-induced signal fading.

[0052] Step 102: Separate the two polarization eigenmodes output from the polarization-maintaining sensing fiber using a polarization beam splitter.

[0053] The polarization beam splitter decomposes the composite polarization state at the output end of the sensing polarization-maintaining fiber into two orthogonal linear polarization components, which are output from two separate output ports. The two output ports correspond to the fast-axis polarization eigenmode and the slow-axis polarization eigenmode, respectively.

[0054] Step 103: Recombine the two separated polarization eigenmodes using a polarization-maintaining 3×3 coupler to generate at least three phase diversity interference signals, which have a nominal phase offset of 120° between them.

[0055] In this configuration, the principal axes of the two input pigtails of the polarization-maintaining 3×3 coupler are aligned with the polarization eigenmode axes corresponding to the two output ports of the polarization beam splitter, respectively. The two polarization eigenmodes interfere within the polarization-maintaining 3×3 coupler. Due to the inherent coupling phase relationship of the 3×3 symmetrical coupler, the interference signals at the three output ports have a nominal mutual phase offset of 120°. The three output light intensities can be expressed as: (5) in, DC bias, For modulation amplitude, This is the channel phase offset.

[0056] Step 104: Convert the three phase diversity interference signals into three corresponding electrical signals using at least three photodetectors.

[0057] The three photodetectors receive the optical signals from the three output ports of the polarization-maintaining 3×3 coupler, respectively, and convert them into voltage signals I1(t), I2(t), and I3(t) that are proportional to the light intensity. After analog-to-digital conversion, the signals are sent to the signal processing unit for digital processing.

[0058] Step 105: Perform singular value decomposition projection on the three electrical signals to obtain a two-dimensional signal plane projection, perform elliptic correction on the two-dimensional signal plane projection to obtain corrected orthogonal components, and recover the differential phase from the corrected orthogonal components through arctangent operation and phase unwrapping.

[0059] In one implementation, such as Figure 4 As shown, step 105 specifically includes: Step 1051: Arrange the three electrical signals into a signal matrix.

[0060] The three electrical signals are arranged into a signal matrix X∈R^(N×3), where N is the number of sampling points, and the k-th column of X contains the N sample values ​​of the k-th electrical signal.

[0061] Step 1052: Perform mean centering on the signal matrix to obtain a mean-centered matrix.

[0062] The signal matrix X is mean-centered to obtain a mean-centered matrix. Each sample value is subtracted from the time mean of the corresponding channel to obtain a zero-mean signal. The mean-centered matrix is ​​then used. Represented as: (6) in, A matrix consisting of the means of each column. It is a left singular vector matrix. It is a singular value diagonal matrix. It is a right singular vector matrix.

[0063] Step 1053: Perform singular value decomposition on the mean-centered matrix to obtain the decomposition result.

[0064] Perform singular value decomposition on the mean-centered matrix to obtain the decomposition result, which includes the left singular vector matrix. The singular value diagonal matrix and the right singular vector matrix .

[0065] Step 1054: Project the three electrical signals onto the two-dimensional signal plane defined by the first two right singular vectors of the decomposition result to obtain the projection of the two-dimensional signal plane.

[0066] The three electrical signals are projected onto a two-dimensional signal plane defined by the first two right singular vectors of the decomposition result to obtain the two-dimensional signal plane projection. Represented as: (7) in The signal plane basis is formed by the first two columns of the right singular vector matrix V, and the projection of the two-dimensional signal plane is an N×2 matrix P, whose two columns are denoted as... and .

[0067] Step 1055: Use the direct least squares method to project and fit the two-dimensional signal plane into a general quadratic curve to obtain ellipse parameters including center coordinates, rotation angle and semi-axis length.

[0068] The two-dimensional signal plane projection is fitted into a general quadratic curve using the direct least squares method to obtain elliptical parameters including center coordinates, rotation angle, and semi-axis length; the equation of the general quadratic curve is: (8) Where A, B, C, D and E are parameter terms, F is a constant term, and the ellipse constraint B²-4AC<0 is satisfied. The center coordinates (x0, y0), the principal axis rotation angle θ, the semi-major axis length a and the semi-minor axis length b are analytically calculated from the fitting coefficients of the general quadratic curve.

[0069] Step 1056: Perform translation, rotation and normalization based on the ellipse parameters to project and map the two-dimensional signal plane onto the unit circle, thereby obtaining the coordinates on the unit circle as the corrected orthogonal components.

[0070] The translation, rotation, and normalization are performed sequentially: (9) This process includes first eliminating center offset through translation transformation, then eliminating axis tilt through rotation transformation, and finally normalizing by dividing along both axes by the corresponding semi-axis length, thereby obtaining the desired result. ²+ The corrected orthogonal components of the relation ²≈1 , ),in and These correspond to the cosine and sine components of the differential phase, respectively.

[0071] Step 1057: Calculate the arctangent value of the corrected orthogonal component using the two-parameter arctangent function to obtain the winding phase.

[0072] The arctangent value of the corrected quadrature components is calculated using a two-parameter arctangent function to obtain the winding phase. : (10) in, and The corrected orthogonal component has a winding phase range of (-π, π).

[0073] Step 1058: Perform phase unwrapping on the wrapped phase to obtain the recovered differential phase.

[0074] The phase unwrapping is achieved by detecting the phase jump between adjacent sampling points point by point: when the wrapping phase difference between two adjacent points exceeds π, a 2π jump is determined to have occurred. The wrapping phase of subsequent sampling points is corrected by adding or subtracting 2π, thereby unfolding the wrapping phase into a continuous time series and obtaining the recovered differential phase Δφ(t).

[0075] The azimuth and constant phase offset are fixed once by the calibration convention. Unlike Equation (3), Equation (10) recovers the phase itself, rather than a periodic intensity function of the phase. Therefore, the available range of phase unwrapping that supports recovery across multiple interference fringes is determined by the signal-to-noise ratio, sampling rate and digitizer range, sampling rate, and the reliability of phase unwrapping. Once calibration is complete, the projection basis and ellipse correction parameters define a fixed receiver transform that can be directly applied to subsequent recordings.

[0076] By detecting phase transitions between adjacent sampling points (a 2π flip is determined when the transition exceeds π), the wound phase is unwound point by point to obtain a continuous differential phase Δφ(t). The recovered differential phase Δφ(t) is the true phase modulation caused by external vibration on the sensing polarization-maintaining fiber, and its time waveform directly reflects the amplitude, frequency, and phase information of the vibration signal.

[0077] Before performing singular value decomposition projection on the three electrical signals, the method further includes: applying a wide-arc perturbation to the sensing polarization-maintaining fiber to generate a calibration record spanning multiple interference fringes; The wide-arc perturbation can be achieved by applying a known large-amplitude mechanical deformation to a local segment of the sensing polarization-maintaining fiber, causing the differential phase to cover multiple 2π cycles, ensuring that the trajectory of the two-dimensional signal plane projection forms a complete or near-complete ellipse. A fixed calibration parameter set, including the projection matrix V2 and ellipse parameters (x0, y0, φ, a, b), is derived from the calibration record. This fixed calibration parameter set is applicable to subsequent measurements with differential phase amplitudes ranging from at least 0.52 rad to 15.21 rad without requiring recalibration.

[0078] This wide dynamic range characteristic stems from the following principle: Singular value decomposition projection and elliptic correction are essentially one-time calibrations of the system's transfer matrix and non-idealities. As long as the optical configuration of the sensing device remains unchanged (e.g., fiber optic connection status, coupler characteristics remain constant), the calibration parameters remain valid and are independent of the amplitude of the measured vibration signal. Therefore, whether it is a weak vibration with a differential phase amplitude of 0.52 rad or a strong vibration with a differential phase amplitude of 15.21 rad, the same set of fixed calibration parameters can be used for accurate demodulation.

[0079] In summary, this embodiment separates the two polarization eigenmodes output from the polarization-maintaining fiber using a polarization beamsplitter. These eigenmodes are then recombined by a 3×3 polarization-maintaining coupler to generate at least three phase diversity interference signals with a nominal 120° mutual phase offset. After being converted into three electrical signals by a photoelectric detection component, the signal processing unit sequentially performs singular value decomposition projection to obtain a two-dimensional signal plane projection, elliptic correction to obtain the corrected orthogonal components, arctangent operation, and phase unwrapping to recover the differential phase. By transforming the differential phase readout from a single-value mapping of the sinusoidal intensity transfer function to direct phase extraction based on phase diversity, a unique and definite phase value can still be obtained even when the differential phase amplitude exceeds the local linear region of the sinusoidal transfer function or even crosses multiple interference fringes. This solves the technical problem of traditional intensity detection receivers being unable to achieve quantitative measurement under large-amplitude phase offsets due to non-unique mapping, waveform folding, and fundamental suppression.

[0080] Example 3 To verify the effectiveness of the present invention, the device was experimentally tested in this embodiment.

[0081] Figure 5 The experimental setup for comparing intensity and phase receivers is shown. In G1, the PBS output is recombined using PM 2×2 couplers and detected by two PDs to achieve balanced intensity readings. In G2, the PBS output is recombined using PM 3×3 couplers and detected by three PDs to achieve phase recovery. The equipment includes an Arbitrary Waveform Generator (AWG); a Voltage Amplifier (VA); a Piezoelectric Fiber Stretcher (PZT); and a Digital Storage Oscilloscope (DSO).

[0082] The light source was an uncooled 1550nm, 5mW PM fiber-coupled DFB laser with an integrated isolator, driven by a custom electronic driver. Its output pigtail was fused to a PMF jumper cable, the input of which was rotated 45° to provide approximately equal excitation for the fast and slow axes of the sensing PMF. A 30m long PMF was wound around a piezoelectric fiber stretcher (FPM-P36-02-FA-01-00-M, Lightpromotech). An arbitrary waveform generator (AWG; AFG3252) generated a sinusoidal excitation, which was amplified approximately 30 times by a voltage amplifier (HV3012A) to drive the fiber stretcher. The PMF exiting the fiber stretcher was connected to a PM PBS (FlyinOptronics), and two optional receiver configurations were subsequently tested. Two 300 MHz PDs (LNPDM-300-D-SP, LamdaPhotonics) provide two common detection channels; a self-made 85 MHz PD provides the third channel required by the phase receiver (G2). All detector outputs are acquired synchronously via a digital storage oscilloscope (SDS824X HD).

[0083] Strength receiver (G1): The two polarization eigenmodes separated by the PBS are coupled to the two inputs of a PM 2×2 coupler and subjected to interference recombination. Their complementary outputs are detected by two 300 MHz PDs, synchronously acquired, and subtracted in software. A DC bias applied to the AWG waveform generates a static phase bias via a PZT and is adjusted to keep the receiver operating near Φ_b = π / 2. This balance is achieved with… Figure 1 The receivers based on the analyzer are optically different, but maintain the same sinusoidal phase-intensity transfer function. Therefore, their AC output follows equation (3) over the overall gain factor range.

[0084] Phase receiver (G2): The transmitter, sensor link, PBS, and data acquisition instruments remain unchanged. The two PBS outputs are instead connected to a PM 3×3 coupler, whose three outputs are detected and synchronously acquired by two 300 MHz commercial PDs and a self-made 85 MHz PD. Phase recovery follows Equations (6)–(10).

[0085] like Figure 6 The diagram summarizes the complete optical and electronic configurations of the two receivers and their corresponding processing chains.

[0086] During amplitude scanning, the excitation frequency was fixed at 100 Hz, and the sampling rate was 50 kSa / s. The AWG output varied between 0.2–5 Vpp and was amplified by approximately 30 times to obtain a PZT drive of 6–150 Vpp. The corresponding G2 recovery phase amplitude was 0.52–15.21 rad. Each record contained 50–100 modulation cycles. At the start of the measurement, a wide-arc calibration record was acquired at 150 Vpp; the resulting projection basis and elliptic correction parameters were subsequently fixed.

[0087] Waveform fidelity is evaluated using the amplitude |r| of the Pearson correlation coefficient between the measured waveform and the least-squares best-fit sine at the excitation frequency. THD is calculated based on the second to tenth harmonics. (11) Among them, A h Let A1 be the amplitude of the fast Fourier transform of the h-th harmonic, and A1 be the fundamental amplitude. |r| and THD together quantify the waveform fidelity and harmonic distortion in the amplitude scan.

[0088] To test the physical limit predicted by equation (4), Figures 7-10 The two receivers were compared at 54 Vpp (at which point the phase amplitude recovered by G2 is approximately 4.98 rad). This offset is well beyond the local monotonic segment of the sinusoidal intensity transfer function, thus providing a direct test for the recovery of large amplitude waveforms.

[0089] like Figure 7 As shown, the G1 output exhibits waveform folding and peak inversion. Its correlation coefficient with the best-fit sine is only 0.5745, and its THD is 142.4%. The vertical axis is in volts because the G1 provides a differential PD output. In contrast, as... Figure 8 As shown, the output of G2 follows the sinusoidal excitation, |r|=1.0000, and the THD is 0.3%. Its vertical axis is in radians because equation (10) recovers the unwrapped phase.

[0090] The frequency domain results are consistent with the time domain waveforms. For example... Figure 9 As shown, in G1, the third, fifth, and seventh harmonic components at 300Hz, 500Hz, and 700Hz are 0.9dBc, respectively. 1.9dBc and 15.7 dBc. Therefore, the third and fifth harmonics are equivalent to the fundamental frequency. For example... Figure 10 As shown, in G2, the measured harmonics of this record remain at Below 50 dBc. The comparison focuses on waveform distortion and harmonic content with reference to the fundamental frequency of each receiver.

[0091] A more stringent test of the intensity receiver occurs near the first zero of J1(φ_a). At 42 Vpp, the phase amplitude recovered by G2 is 3.82 rad, close to this zero. Figure 11 and Figure 12 As shown, the G1 waveform is dominated by higher harmonics at this point, with |r| = 0.0127. After normalization to the residual fundamental frequency, the third, fifth, and seventh harmonics are 37.5 dBc, 26.2 dBc, and 6.6 dBc, respectively. The fundamental normalization THD was omitted because the definition is poor when the fundamental frequency approaches zero. The direct correspondence between the predicted Bessel zero and the measured fundamental frequency collapse indicates that the loss of linearity is a result of the periodic intensity transfer function.

[0092] Figure 13 , Figure 14 and Figure 15 Amplitude sweeps at 100 Hz are summarized. The phase amplitude in the second column is recovered by G2 and increases monotonically with PZT drive. Using the same fixed calibration for all measurements, G2 maintains |r|≥0.9988 and THD within the range of 0.52–15.21 rad. 2-10 <2%. The same storage receiver transformation is applied directly to each record in the scan.

[0093] G1 performs well only at smaller phase offsets. The correlation coefficient remains above 0.95 at 1.60 rad, but drops below 0.95 at 2.14 rad, accompanied by a significant increase in harmonic distortion. G1 measurements extend to 96 Vpp across the available bias and drive range, while G2 was tested up to the 150 Vpp limit for PZT drives.

[0094] The non-monotonic variation of the G1 correlation at larger amplitudes follows the oscillating harmonic coefficients in equation (4). After the first J1 zero, the residual correlation can increase again, although the underlying intensity-phase mapping remains periodic and non-unique. In contrast, G2 directly tracks the unwrapped phase throughout the experimentally explored range, reaching 15.21 rad at the available PZT drive limit, and no decrease in waveform fidelity was observed.

[0095] Figure 16 The receiver transform derived from the 150 Vpp wide-arc calibration record was examined to be applicable to small-signal recordings without refitting. Before calibration, the calibration record forms an offset ellipse, while the minimum test signal (6 Vpp, φ_a ≈ 0.52 rad) covers only a short arc of the same underlying track. Applying the parameters derived from 150 Vpp, the calibration data can be mapped to a unit circle with radial coordinates ρ = 1.000 ± 0.020; while the 6 Vpp data is mapped to a short arc coinciding with the circle, ρ = 1.013 ± 0.012.

[0096] The consistency between independently acquired 6 Vpp records and the calibration circle confirms that the same stored signal plane basis and elliptic transformation can be used for all cases, from short-arc small signals to multi-friction records. Therefore, the amplitude scan results are obtained through a single receiver calibration, rather than fitting each amplitude separately.

[0097] Measurement results show that in POFS, polarization fading and large-signal readout are independent design problems. The PMF link stabilizes the polarization mapping by defining two sensing eigenmodes, while the phase diversity receiver resolves the periodic ambiguity that still exists when observing its differential phase through a single intensity transfer function. Together, they achieve direct recovery of the multi-fringe phase waveform without maintaining orthogonal intensity operating points.

[0098] The comparison of G1 provides a physical explanation for the large-signal transition. The small-signal slope of equation (3) is maximized by the orthogonal bias, but the response remains periodic and becomes non-unique after crossing the extremum. The measured collapse of the G1 fundamental at 3.82 rad is highly consistent with the first zero of J1, directly linking the distorted waveform to the Bessel spectral model. The subsequent partial recovery of the correlation can also be explained by the oscillating harmonic coefficients and does not recover the unique intensity-phase mapping.

[0099] A practical feature of the phase receiver is that the single wide-arc calibration remains applicable throughout the 0.52–15.21 rad amplitude scan. Figure 16 The short-arc results illustrate why this is useful. Small signal records that do not cross a complete ellipse can still be processed using the stored receiver transform. This fixed calibration implementation provides a consistent phase retrieval basis for the tested amplitudes, avoiding the need to re-estimate receiver geometry from individual records.

[0100] The reported range represents the achievable phase recovery range in this 100 Hz experiment, with its upper limit determined by the available PZT drive. Correlation and THD results establish the waveform fidelity and harmonic distortion within this range. Independent phase calibration and frequency-dependent operating limits are natural topics for further characterization.

[0101] In summary, this embodiment demonstrates a polarization-resolved phase receiver that extends fading-free PMF-POFS from local intensity readings to direct multi-fringe differential phase measurements. The PMF link defines stable sensing eigenmodes, and a PM 3×3 coupler maps their relative phases to three simultaneous phase diversity outputs. Through a single fixed receiver calibration, a measurement is achieved in the range of 0.52–15.21 rad with |r| ≥ 0.9988 and THD... 2-10The proposed receiver architecture recovers the 100 Hz phase modulation with a margin of less than 2%. In contrast, the quadrature bias intensity receiver exhibits waveform folding, strong harmonic distortion, and suppression of its fundamental frequency near the first zero of J1. Therefore, the proposed receiver architecture achieves quantitative recovery of the large-amplitude phase waveform across multiple interference fringes while maintaining the fading-free characteristics of the PMF sensing link.

[0102] For the specific process of the fiber optic vibration sensing method based on large amplitude phase demodulation, please refer to Example 2, which will not be repeated in this example.

[0103] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A fiber optic vibration sensing device based on large-amplitude phase demodulation, characterized in that, It includes a laser, a sensing polarization-maintaining fiber, a polarization beam splitter, a polarization-maintaining 3×3 coupler, and a photoelectric detection component coupled sequentially along the optical path; it also includes a signal processing unit connected to the photoelectric detection component; The laser is used to emit polarized light, which is coupled into the sensing polarization-maintaining fiber through a 45° rotating fusion splice to excite two polarization eigenmodes of the sensing polarization-maintaining fiber with equal intensity. The two polarization eigenmodes accumulate differential phase modulated by external perturbation during propagation along the sensing polarization-maintaining fiber. The polarization beam splitter is used to separate the two polarization eigenmodes output from the polarization-maintaining sensing fiber. The polarization-maintaining 3×3 coupler is used to recombine the two polarization eigenmodes to generate at least three phase diversity interference signals, which have a nominal phase offset of 120° between them. The photoelectric detection component includes at least three photodetectors, which are used to convert the three phase diversity interference signals into three corresponding electrical signals. The signal processing unit is used to perform singular value decomposition projection on the three electrical signals to obtain a two-dimensional signal plane projection, perform elliptic correction on the two-dimensional signal plane projection to obtain corrected orthogonal components, and recover the differential phase from the corrected orthogonal components through arctangent operation and phase unwrapping.

2. The fiber optic vibration sensing device based on large amplitude phase demodulation according to claim 1, characterized in that, The main axes of the two input pigtails of the polarization-maintaining 3×3 coupler are aligned with the polarization intrinsic mode axes corresponding to the two output ports of the polarization beam splitter, respectively.

3. The fiber optic vibration sensing device based on large amplitude phase demodulation according to claim 1, characterized in that, The signal processing unit is further configured to perform mean centering on the three electrical signals used for singular value decomposition to remove the DC component when projecting the two-dimensional signal plane projection through singular value decomposition.

4. The fiber optic vibration sensing device based on large-amplitude phase demodulation according to claim 1, characterized in that, The elliptic correction performed by the signal processing unit includes: The two-dimensional signal plane is projected and fitted into a quadratic curve using the direct least squares method to obtain elliptical parameters including center coordinates, rotation angle, and semi-axis length; and translation, rotation, and normalization are performed based on the elliptical parameters to map the two-dimensional signal plane onto a unit circle.

5. The fiber optic vibration sensing device based on large-amplitude phase demodulation according to claim 1, characterized in that, The signal processing unit is configured to use a fixed set of calibration parameters obtained from a single calibration record, which is suitable for measurements with differential phase amplitudes ranging from at least 0.52 rad to 15.21 rad without the need for recalibration.

6. A fiber optic vibration sensing method based on large-amplitude phase demodulation, applied to the fiber optic vibration sensing device based on large-amplitude phase demodulation as described in any one of claims 1-5, characterized in that, The method includes: Polarized light is coupled into the sensing polarization-maintaining fiber through a 45° rotating fusion splice, thereby exciting the two polarization eigenmodes of the sensing polarization-maintaining fiber with equal intensity. The two polarization eigenmodes accumulate differential phase modulated by external disturbances during propagation along the sensing polarization-maintaining fiber. The two polarization eigenmodes output from the polarization-maintaining sensing fiber are separated by a polarization beam splitter. The two polarization eigenmodes after separation are recombined by a polarization-maintaining 3×3 coupler to generate at least three phase diversity interference signals, which have a nominal mutual phase offset of 120°. The three phase diversity interference signals are converted into three corresponding electrical signals using at least three photodetectors; Singular value decomposition projection is performed on the three electrical signals to obtain a two-dimensional signal plane projection. Elliptic correction is performed on the two-dimensional signal plane projection to obtain corrected orthogonal components. The differential phase is recovered from the corrected orthogonal components through arctangent operation and phase unwrapping.

7. The fiber optic vibration sensing method based on large-amplitude phase demodulation according to claim 6, characterized in that, The step of performing singular value decomposition projection on the three electrical signals to obtain a two-dimensional signal plane projection specifically includes: The three electrical signals are arranged into a signal matrix X∈R^(N×3), where N is the number of sampling points, and the k-th column of X is the N sampled values ​​of the k-th electrical signal; Perform mean centering on the signal matrix X to obtain a mean-centered matrix, including subtracting the time mean of the corresponding channel from each sample value to obtain a zero-mean signal, and the mean-centered matrix. Represented as: ； in, A matrix consisting of the means of each column. It is a left singular vector matrix. It is a singular value diagonal matrix. It is a right singular vector matrix; Perform singular value decomposition on the mean-centered matrix to obtain the decomposition result, which includes the left singular vector matrix. The singular value diagonal matrix and the right singular vector matrix ; The three electrical signals are projected onto a two-dimensional signal plane defined by the first two right singular vectors of the decomposition result to obtain the two-dimensional signal plane projection. Represented as: ； in, The signal plane basis is formed by the first two columns of the right singular vector matrix V, and the projection of the two-dimensional signal plane is an N×2 matrix P, whose two columns are denoted as... and .

8. The fiber optic vibration sensing method based on large amplitude phase demodulation according to claim 7, characterized in that, The step of performing elliptic correction on the two-dimensional signal plane projection to obtain corrected orthogonal components specifically includes: The two-dimensional signal plane projection is fitted into a general quadratic curve using the direct least squares method to obtain elliptical parameters including center coordinates, rotation angle, and semi-axis length; the equation of the general quadratic curve is: ； Where A, B, C, D and E are parameter terms, F is a constant term, and the ellipse constraint B²-4AC<0 is satisfied. The ellipse center coordinates (x0, y0), principal axis rotation angle θ, semi-major axis length a and semi-minor axis length b are analytically calculated from the fitting coefficients of the general quadratic curve. Based on the ellipse parameters, translation, rotation, and normalization are performed to project the two-dimensional signal plane onto the unit circle, thereby obtaining the coordinates on the unit circle as the corrected orthogonal components. The translation, rotation, and normalization are performed sequentially, including first eliminating center offset through translation transformation, then eliminating axis tilt through rotation transformation, and finally normalizing by dividing along both axes by the corresponding semi-axis lengths, thereby obtaining the corrected orthogonal components. ²+ The corrected orthogonal components of the relation ²≈1 , ),in and These correspond to the cosine and sine components of the differential phase, respectively.

9. The fiber optic vibration sensing method based on large-amplitude phase demodulation according to claim 8, characterized in that, The step of recovering the differential phase from the corrected orthogonal components through arctangent operation and phase unwrapping specifically includes: The arctangent value of the corrected quadrature components is calculated using a two-parameter arctangent function to obtain the winding phase. : ； in, and The corrected orthogonal components are... Let be the phase unwinding function, and the range of the unwound phase is (-π, π]. Phase unwrapping is performed on the entangled phase to obtain the recovered differential phase. The phase unwrapping is achieved by detecting the phase jump between adjacent sampling points point by point: when the entangled phase difference between two adjacent points exceeds π, a 2π jump is determined to have occurred. The entangled phase of subsequent sampling points is corrected by accumulating or subtracting 2π, thereby unfolding the entangled phase into a continuous time series to obtain the recovered differential phase Δφ(t).

10. The fiber optic vibration sensing method based on large-amplitude phase demodulation according to claim 6, characterized in that, Before performing singular value decomposition projection on the three electrical signals, the method further includes: A wide-arc perturbation is applied to the sensing polarization-maintaining fiber to generate a calibration record spanning multiple interference fringes; A fixed set of calibration parameters is derived from the calibration record. This fixed set of calibration parameters is applicable to subsequent measurements with differential phase amplitudes ranging from at least 0.52 rad to 15.21 rad without the need for recalibration.

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