Method for demodulating a fiber interferometer measuring vibration with reference to a two-frequency phase-modulated interferometer

Abstract

The application provides a fiber interferometer vibration measurement demodulation method based on reference interferometer double-frequency phase modulation, and relates to the technical field of fiber interferometer measurement, and the method comprises the following steps: obtaining reference and detection interference signals modulated by inner and outer double frequencies; performing phase generation carrier demodulation on the reference interference signal, demodulating the reference phase after correction by elliptical fitting; performing phase generation carrier demodulation on the detection interference signal, and correcting the amplitude by using reference elliptical parameters; based on the reference phase, performing polynomial fitting on the Lissajous circle center trajectory of the detection quadrature signal pair, and eliminating parasitic interference zero point drift; performing arctangent and unwrapping on the signal pair after secondary correction, and obtaining an initial detection phase; based on the inner modulation depth ratio, eliminating laser noise from the initial detection phase, and obtaining a target vibration phase. The application suppresses light source noise and parasitic light interference, and improves the precision of non-cooperative target vibration detection.

Description

Technical Field

[0001] This invention relates to the field of fiber optic interferometry technology, and in particular to a fiber optic interferometric vibration demodulation method based on dual-frequency phase modulation of a reference interferometer. Background Technology

[0002] Vibration is one of the most prevalent physical phenomena in nature, and its accurate measurement plays a crucial foundational role in fields such as mechanical fault diagnosis, structural health monitoring, precision manufacturing, and voice information acquisition. Traditional vibration measurement methods are mainly divided into two categories: contact and non-contact. Contact sensors, such as accelerometers, are widely used, but they require a rigid connection to the object being measured, resulting in inherent drawbacks such as large cumulative errors and installation limitations. They are particularly unsuitable for applications involving high temperatures, high pressures, strong electromagnetic interference, or situations where sensor installation is impossible. All-fiber vibration sensors, such as those based on fiber Bragg gratings, overcome electromagnetic interference problems to some extent, but they typically still require the fiber to be bonded to the surface of the object being measured, and their application flexibility and convenience still need improvement.

[0003] Laser interferometry, due to its advantages of being non-contact, highly accurate, and traceable to wavelength references, is considered the most accurate method for displacement measurement and a common means of calibrating vibration sensors. Various interferometers based on the principles of laser heterodyne or null difference, through optimized optical structures and signal demodulation, can achieve non-contact measurement of target objects, i.e., non-cooperative target measurement, which gives them significant advantages in complex application scenarios. Among them, the sinusoidal phase modulation interferometer, by introducing high-speed phase modulation into the reference arm, loads the measurement information onto the phase carrier sideband, and combines it with a phase generation carrier demodulation algorithm, combining the compact structure of a null difference interferometer with the high accuracy and strong anti-interference capability of a heterodyne interferometer, and has become an important implementation form for fiber optic hydrophones and fiber optic vibration sensors. Currently, research on sinusoidal phase modulation interferometers mainly focuses on handling various non-ideal factors, such as light intensity disturbances, carrier phase delays, and modulation depth fluctuations, to improve the measurement stability and accuracy of the system.

[0004] However, applying sinusoidal phase-modulated interferometers to detect vibrations of non-cooperative targets at long distances or on low-reflectivity surfaces presents even greater challenges. In such applications, the probe light must be emitted to the target via an optical antenna, and its weak backscattered return light is then received by the antenna and coupled back to the fiber optic system. This transmission and reception process results in extremely low return light power and severely degraded signal-to-noise ratio. Even more problematic is the parasitic light generated by reflections from the end faces of the optical components in the system, which undergoes complex multi-beam mixing with the weak probe return light and the reference light, forming parasitic interference. This parasitic interference, superimposed on the target detection signal, severely interferes with the phase-generating carrier demodulation process, causing zero-point drift in orthogonal signal pairs, resulting in severe distortion of the Lissajous figure, ultimately leading to demodulation failure or significant errors. How to stably and accurately extract target vibration information from complex mixed signals under extremely low signal-to-noise ratios and strong parasitic light interference is a critical problem that urgently needs to be solved to achieve high-sensitivity non-cooperative target detection.

[0005] Furthermore, the inherent frequency jitter noise of semiconductor lasers, used as coherent detection sources, is converted into phase noise, which is directly superimposed on the detection results, limiting the system's detection sensitivity and resolution. Although increasing optical power or optimizing the optical path can improve the signal-to-noise ratio to some extent, conventional signal processing methods struggle to effectively suppress the laser's own low-frequency phase noise. Especially in non-cooperative target detection, where the return light power is already extremely weak, the impact of laser noise becomes even more pronounced, becoming another bottleneck restricting system performance improvement.

[0006] In summary, existing technologies face two major technical challenges in detecting non-cooperative targets: first, the phase noise of the laser itself is difficult to suppress effectively, which limits the improvement of system sensitivity; second, parasitic light interference generated by reflection from the device end face is severe, resulting in unstable signal demodulation, low accuracy, or even demodulation failure. Summary of the Invention

[0007] To address the technical problems in the prior art, this invention provides a fiber optic interferometric vibration demodulation method based on dual-frequency phase modulation of a reference interferometer.

[0008] The technical solution provided by this invention is as follows:

[0009] The fiber optic interferometric vibration demodulation method based on dual-frequency phase modulation of a reference interferometer provided by this invention includes:

[0010] S1: Acquire a reference interference signal and a probe interference signal, wherein both the reference interference signal and the probe interference signal contain an external modulation phase carrier and an internal modulation phase term;

[0011] S2: Perform phase generation carrier demodulation on the reference interference signal to obtain a reference orthogonal signal pair, and perform amplitude correction on the reference orthogonal signal pair based on the ellipse fitting algorithm;

[0012] S3: Obtain the reference phase based on the demodulation of the corrected reference quadrature signal pair;

[0013] S4: Perform phase generation carrier demodulation on the probe interference signal to obtain probe orthogonal signal pairs;

[0014] S5: The amplitude correction parameters of the reference quadrature signal pair are used to perform amplitude correction on the probe quadrature signal pair to obtain the corrected probe quadrature signal pair;

[0015] S6: Based on the reference phase, perform polynomial fitting on the Lissajous figure circle center trajectory of the corrected probe orthogonal signal pair to eliminate the zero-point drift introduced by parasitic interference and obtain the probe orthogonal signal pair after secondary correction.

[0016] S7: Perform arctangent and unwrapping operations on the second-corrected detection orthogonal signal pair to obtain an initial detection phase containing the target vibration phase, laser noise phase, and internal modulation phase;

[0017] S8: Based on the ratio of the reference phase to the internal modulation depth in the initial detection phase, the laser noise phase and the internal modulation phase are eliminated from the initial detection phase to obtain the target vibration phase.

[0018] Further, in step S1, the reference interference signal and the probe interference signal are represented by the following formula:

[0019]

[0020] in, For the reference interference signal amplitude, To detect the amplitude of the interference signal, For the depth of external modulation, The externally modulated angular frequency, The internal modulation angular frequency, The depth of the internal modulation in the reference signal. To detect the depth of internal modulation in the signal, The phase noise is caused by laser frequency jitter in the reference signal. To detect phase noise caused by laser frequency jitter in the signal, The phase to be demodulated is generated by the target vibration.

[0021] Furthermore, the elliptic fitting and amplitude correction of the reference orthogonal signal pair described in step S2 further includes the following sub-steps:

[0022] S201: The following elliptic equation is used to apply to the reference orthogonal signal pair. and Perform fitting:

[0023]

[0024] in, For the reference orthogonal components of the orthogonal signal pair, For the reference quadrature signal pair in-phase component, and These are the parameters of the ellipse equation;

[0025] S202: The ellipse parameters are calculated using the following formula based on the least squares principle. and :

[0026]

[0027] in, Let i be the reference orthogonal signal pair orthogonal component value at the i-th sampling point. Let i be the reference quadrature signal pair in-phase component value at the i-th sampling point. This represents summing over all sample points;

[0028] S203: Using the elliptic parameters, the amplitude of the reference orthogonal signal pair is corrected using the following formula to obtain the corrected reference orthogonal signal pair, and then demodulated to obtain the reference phase. :

[0029]

[0030] in, As a reference phase, For phase unwrapping operation. For arctangent operation, For the reference orthogonal components of the orthogonal signal pair, For the reference quadrature signal pair in-phase component, and These are the parameters of the ellipse equation.

[0031] Furthermore, the step S5, which involves using the amplitude correction parameters of the reference quadrature signal pair to perform amplitude correction on the probe quadrature signal pair, includes:

[0032] S501: Using the ellipse parameters obtained in S203 and The following formula is used to detect orthogonal signal pairs. and Perform amplitude correction:

[0033]

[0034] in, To detect the orthogonal components of orthogonal signal pairs, To detect the in-phase components of quadrature signal pairs, and These are the parameters of the ellipse equation. and These are the corrected detection orthogonal signal pairs.

[0035] Furthermore, the polynomial fitting of the Lissajous figure center trajectory of the corrected probe orthogonal signal pair described in step S6 further includes the following sub-steps:

[0036] S601: Establish a model of probed orthogonal signal pairs that includes the effects of parasitic interference, and denote the reference phase. It is expressed by the following formula:

[0037]

[0038]

[0039] in, For the corrected detection orthogonal signal pairs of orthogonal components, For the corrected detection quadrature signal pairs in-phase components, To detect the amplitude of the in-phase component of a quadrature signal pair, To detect the amplitude of the quadrature components of quadrature signal pairs, The amplitude of the in-phase component of the parasitic interference quadrature signal pair. The amplitudes of the orthogonal components of the parasitic interference orthogonal signal pair are given. As a scaling factor, It is the ratio of the modulation depth within the parasitic interference to the modulation depth within the reference signal. To detect the depth of internal modulation in the signal, The depth of the internal modulation in the reference signal. The depth of internal modulation in the parasitic interference signal. As a reference phase, The target vibration phase;

[0040] S602: Represent the probed quadrature signal pair as about the reference phase The function, and denoted as , The function of the circle's center trajectory is expressed by the following formula. and :

[0041]

[0042] Where x represents the quadrature component of the corrected probe quadrature signal pair, and y represents the in-phase component of the corrected probe quadrature signal pair. For reference phase The orthogonal component center locus function, For reference phase The in-phase component's circular center trajectory function, where E is a constant;

[0043] S603: Using a second-order polynomial function to plot the center trajectory and The following formula is used for fitting:

[0044]

[0045]

[0046] in, The polynomial coefficients are the center locus functions of the orthogonal components. denoted by , where z is the polynomial coefficient of the in-phase component's circular trajectory function, and z is the reference phase;

[0047] S604: Calculate the coefficients of the polynomial according to the least squares principle.

[0048] Furthermore, the elimination of zero-point drift introduced by parasitic interference in step S6 further includes:

[0049] S605: Zero-point correction of the probed orthogonal signal pairs is performed using the following formula based on the fitted circle center trajectory function:

[0050]

[0051]

[0052] in, For the corrected detection orthogonal signal pairs of orthogonal components, For the corrected detection quadrature signal pairs in-phase components, The function is the locus of the center of the orthogonal components. Let z be the trajectory function of the center of the in-phase component, and z be the reference phase. and These are the orthogonal detection signal pairs after secondary correction.

[0053] Furthermore, the elimination of laser noise and internal modulation phase based on the ratio of the internal modulation depth in the reference phase to the initial probe phase in step S8 further includes the following sub-steps:

[0054] S801: Reference Phase Perform a Fast Fourier Transform to extract the internal modulation frequency. The amplitude at that point, i.e., the modulation depth of the internal modulation, is determined using the following formula:

[0055]

[0056] in, As a reference phase, For Fast Fourier Transform, The internal modulation angular frequency, The depth corresponding to the internal modulation frequency in the reference phase;

[0057] S802: Initial detection phase Perform a Fast Fourier Transform to extract the internal modulation frequency. The amplitude at that point is determined using the following formula:

[0058]

[0059] in, For the initial detection phase, For Fast Fourier Transform, The internal modulation angular frequency, The depth corresponding to the internal modulation frequency in the initial probe phase;

[0060] S803: Calculate the proportionality coefficient using the following formula:

[0061]

[0062] in, The depth corresponding to the internal modulation frequency in the initial probe phase. The depth corresponding to the internal modulation frequency in the reference phase, where 'a' is the scaling factor;

[0063] S804: Laser noise and internal modulation phase are eliminated from the initial probe phase using the following formula:

[0064]

[0065] in, The initial detection phase is denoted by 'a', where 'a' is the scaling factor. As a reference phase, The target vibration phase.

[0066] Furthermore, the external modulation is achieved by an electro-optic phase modulator or a fiber PZT modulator, with a modulation frequency higher than the target vibration frequency; the internal modulation is achieved by periodically changing the injection current of the DFB semiconductor laser, with a modulation frequency lower than the external modulation frequency.

[0067] Furthermore, the reference interference signal and the probe interference signal are obtained by a Mach-Zehnder interferometer optical path sharing a reference arm, the reference arm being externally modulated, and the probe interference signal containing parasitic light interference generated by reflection from the end face of the optical device.

[0068] Furthermore, the method further includes step S9: demodulating the target vibration phase. Combined with laser operating wavelength Converted to vibration displacement The following formula is used:

[0069]

[0070] in, The laser operating wavelength, For the target vibration phase, This represents the vibration displacement.

[0071] The beneficial effects of the technical solution provided by this invention include at least the following:

[0072] (1) In this invention, a reference interferometer is introduced and internal modulation is applied to the light source, which serves as an indicator of laser jitter noise. Since the internal modulation depth is proportional to the optical path difference of the interferometer, the magnitude of laser noise in the probe signal can be accurately estimated by obtaining the ratio of the internal modulation depth in the reference interference signal to that in the probe interference signal. Furthermore, the noise component is subtracted from the probe phase using the reference phase, thereby effectively suppressing the influence of light source noise on the measurement results and significantly improving the signal-to-noise ratio and sensitivity of the detection system.

[0073] (2) In this invention, to address the problem of zero-point drift caused by parasitic light interference in the detection of orthogonal signal pairs, a method based on Lissajous figure center trajectory fitting and correction is proposed. This method first uses a reference interference signal to correct for non-ideal modulation factors, and then performs polynomial fitting on the center drift trajectory of the orthogonal components of the detection signals based on the reference phase. By subtracting the fitted center trajectory function from the detection orthogonal signals, the zero-point drift introduced by parasitic interference is effectively eliminated, and a pure orthogonal signal pair is recovered. This ensures the accuracy and robustness of the arctangent phase demodulation, significantly improving the measurement stability of the system under strong parasitic light interference.

[0074] (3) In this invention, a complete high-robustness signal demodulation scheme is constructed through the coordinated design of internal and external dual-frequency modulation and the introduction of a reference interferometer. This scheme not only solves the two core problems that restrict the detection performance of non-cooperative targets—laser noise and parasitic light interference—but also ensures the high dynamic range of the system through external modulation. Ultimately, it achieves accurate and stable demodulation of target vibration under weak echo signal conditions, providing a feasible technical approach for vibration measurement of long-distance, low-reflectivity targets and practical applications such as voice signal interception. Attached Figure Description

[0075] Figure 1 This is a schematic diagram of the Ref-DFPMI optical path in the fiber optic interferometric vibration demodulation method with dual-frequency phase modulation of the reference interferometer provided in the embodiments of the present invention;

[0076] Figure 2 A schematic diagram of the process for obtaining orthogonal signal pairs in the fiber optic interferometric vibration demodulation method of dual-frequency phase modulation of a reference interferometer provided in the embodiments of the present invention;

[0077] Figure 3 This is a schematic diagram of the Ref-PGC-CTC-Arctan demodulation algorithm in the fiber optic interferometric vibration demodulation method with dual-frequency phase modulation of the reference interferometer provided in the embodiments of the present invention;

[0078] Figure 4 Figure z shows the Lissajous figures before and after correction of the orthogonal signal pairs under different parasitic light intensity ratios in the fiber interferometric vibration demodulation method of dual-frequency phase modulation of the reference interferometer provided in the embodiments of the present invention.

[0079] Figure 5 SINAD and THD of the demodulation results of three algorithms under different parasitic light intensity ratios in the fiber interferometric vibration demodulation method of dual-frequency phase modulation of reference interferometer provided in the embodiments of the present invention;

[0080] Figure 6 This is a diagram of the Ref-DFPMI experimental system in the fiber optic interferometric vibration demodulation method with dual-frequency phase modulation of a reference interferometer provided in the embodiments of the present invention;

[0081] Figure 7 The above are the IQ signal correction results of different parasitic light intensities in the fiber interferometric vibration demodulation method of dual-frequency phase modulation of reference interferometer provided in the embodiments of the present invention;

[0082] Figure 8 The demodulation results of different parasitic light intensity signals in the fiber optic interferometric vibration demodulation method with dual-frequency phase modulation of the reference interferometer provided in the embodiments of the present invention;

[0083] Figure 9The measurement results of nanometer displacement of the fiber optic interferometric vibration demodulation method with dual-frequency phase modulation of the reference interferometer provided in the embodiments of the present invention;

[0084] Figure 10 SINAD of the demodulated signals under different external modulation voltages in the fiber optic interferometric vibration demodulation method of dual-frequency phase modulation of the reference interferometer provided in the embodiments of the present invention;

[0085] Figure 11 The THD of the demodulated signal under different external modulation voltages in the fiber optic interferometric vibration demodulation method of dual-frequency phase modulation of the reference interferometer provided in the embodiments of the present invention;

[0086] Figure 12 The fiber optic interferometric vibration demodulation method using dual-frequency phase modulation of a reference interferometer provided in this embodiment of the invention employs four different schemes to demodulate vibration signals of different frequencies using SINAD.

[0087] Figure 13 The fiber optic interferometric vibration demodulation method using dual-frequency phase modulation of a reference interferometer provided in this embodiment of the invention employs four different schemes to demodulate the THD of vibration signals at different frequencies;

[0088] Figure 14 The background noise levels of three different methods in the fiber optic interferometric vibration demodulation method with dual-frequency phase modulation of the reference interferometer provided in the embodiments of the present invention;

[0089] Figure 15 The demodulation results of the audio signal listening experiment in the fiber optic interferometric vibration demodulation method with dual-frequency phase modulation of the reference interferometer provided in the embodiments of the present invention.

[0090] Figure 1 Medium: ISO: Isolator; CL: Collimating Lens; FC: Focusing Lens; DFB: Distributed Feedback Semiconductor Laser; BPD: Balanced Photodetector; EOM: Electro-Optic Modulator;

[0091] Figure 2 In Chinese: MUL: Multiplier; LPF: Low-pass filter;

[0092] Figure 3Medium: EF: Ellipse Fitting; EC: Ellipse Correction; CFT: Center Trajectory Fitting; CTC: Center Trajectory Correction; DIV: Divider; MUL: Multiplier; SUB: Subtractor;

[0093] Figure 15 (a) This text system; (b) The microphone. Detailed Implementation

[0094] The technical solution of the present invention will now be described with reference to the accompanying drawings.

[0095] This invention provides a fiber optic interferometric vibration demodulation method based on dual-frequency phase modulation of a reference interferometer. The processing flow may include:

[0096] The optical path of the non-cooperative target vibration detection system proposed in this embodiment of the invention is as follows: Figure 1 As shown, a reference interferometer is introduced based on a conventional internally modulated sinusoidal phase-modulated interferometer. Both the probe and reference interferometers are based on Mach-Zehnder interference structures. The two interferometers share a reference arm, and a high-speed phase modulation of the reference beams in both interferometers is achieved using an electro-optic phase modulator. The system uses a DFB semiconductor laser as the light source and employs a semiconductor laser driver to perform internal phase modulation of the laser (essentially modulating the laser wavelength by changing the driving current). The laser output from the DFB laser is split into two beams by a 1×2 coupler after passing through an isolator. This coupler is designed with a special splitting ratio; the beam with lower intensity serves as the reference beam, and the beam with higher intensity serves as the probe beam. The reference beam, after passing through the electro-optic modulator (with its phase modulated at a high frequency), is split into two beams by the 1×2 coupler. One beam is used for the reference interferometer, and the other for the probe interferometer. The probe beam, after passing through the 1×2 coupler with a special splitting ratio, has its higher-power beam used to probe the actual target after passing through a circulator and an optical transceiver antenna; the other beam is input to the reference interferometer. Two interferometers each obtain two optical interference signals with a phase difference of π using 2×2 couplers (a total of 4 optical interference signals). After passing through two balanced photodetectors, common-mode suppressed reference interference signal and probe interference signal are obtained, respectively. In this embodiment of the invention, the system is referred to as a reference-introduced dual-frequency phase-modulated laser interferometer, denoted as Ref-DFPMI.

[0097] according to Figure 1As shown in the diagram, the phases of the reference and probe interferometer signals contain both externally modulated phase carriers and internally modulated phase terms. The depth and frequency of the external modulation depend on the electro-optic modulator and its driving circuit; therefore, the external modulation terms in the two signal phases are completely identical. According to the principle of internal modulation, the depth of internal modulation in the phases of the two interferometer signals mainly depends on the optical path difference between the two arms of the interferometer. Ignoring the initial phases of the internal and external modulations, the reference and probe signals obtained after eliminating common-mode components using a balanced detector can be expressed as:

[0098] (1)

[0099] In the formula, A r and A d C represents the amplitudes of the reference interferometer signal and the probe interferometer signal, respectively. e and ω e For the depth and angular frequency of external modulation, ω i C is the angular frequency of the internal modulation. ri and C di These represent the depths of internal modulation in the reference signal and the probe signal, respectively. and These are the phase noises caused by laser frequency jitter in the reference signal and the probe signal, respectively. The phase generated by the target vibration, i.e. the target phase to be demodulated, can be expressed by the following formula:

[0100] (2)

[0101] In the formula, ΔL r and ΔL d Let $\frac{ ...

[0102] (3)

[0103] For non-cooperative target detection, the Doppler echo from the detection interferometer is often extremely weak. Therefore, the influence of parasitic echoes generated by reflections from the end faces of the optical antenna devices on the interferometric detection signal must be considered. Taking into account the effect of parasitic light and neglecting higher-order terms of interference between parasitic cavities, the detection interferometric signal can be rewritten as:

[0104] (4)

[0105] In the formula A d1 A d2 A d3 These are the amplitudes of the three aliased AC components of the interference signal. It is the phase of the parasitic beam relative to the reference beam, including source noise, ΔL p Optical path difference between the parasitic beam and the reference beam; C pi The depth of the internal modulation in the parasitic interference signal is proportional to ΔL. p Compared to the absence of parasitic light intensity, the presence of parasitic interference greatly affects the accuracy of phase demodulation, and may even lead to demodulation failure of the probe signal.

[0106] Phase generated carrier (PGC) demodulation has the advantages of good stability and high accuracy, and is a commonly used signal demodulation method in sinusoidal phase modulation interferometers. For example... Figure 2 As shown, the core of PGC demodulation is to utilize the carrier Gcos(ω) e t) and its second harmonic signal Hcos(2ω) e t) The signals are mixed with the interference signals to be demodulated, and then low-pass filtered to obtain a pair of orthogonal interference signal components, which are referred to as orthogonal signal pairs in this embodiment of the invention. After obtaining the orthogonal interference signal pairs, the signal phase can be demodulated using the arctangent & phase unwrapping algorithm or the differential cross-multiplication algorithm (DCM).

[0107] use Figure 2 The process (1) refers to the reference interference signal S of the Ref-DFPMI. r (t) yields the following orthogonal signal pairs (referred to as reference orthogonal signal pairs in this embodiment of the invention):

[0108] (5)

[0109] In the formula, The phase delay between the acquired carrier signal and the actual phase carrier of the interference signal is given by J1 and J2, which are the first and second order Bessel functions of the first kind, respectively. As can be seen from equation (5), the amplitudes of the reference orthogonal signal pairs are not consistent. In order to achieve more accurate phase demodulation, normalization of their amplitudes is a common operation. The main methods are divided into two categories: one is the analog adjustment method, which adjusts the carrier modulation depth and carrier phase delay through the carrier signal source and driver to make the amplitudes of the two signals equal. From the Lissajous figure formed by the orthogonal signal pairs, we can observe that the Lissajous figure changes from an ellipse to a standard circle, which completes the normalization of the amplitude of the orthogonal signal pairs; the other is the digital processing algorithm, which uses the ellipse fitting algorithm to fit the Lissajous ellipse formed by the orthogonal signal pairs to obtain the lengths of its major and minor axes (corresponding to the amplitudes of the orthogonal signal pairs). The normalization of the orthogonal signal pairs is achieved by using division. To ensure the stability of the normalization, this method requires that the arc of the Lissajous ellipse formed by the orthogonal signal pairs be no less than 1 / 4 of the entire circumference.

[0110] use Figure 2 The processing algorithm detects the interference signal S d After processing (t), the following signal pairs (abbreviated as probe orthogonal signal pairs) can be obtained:

[0111] (6)

[0112] As shown in equation (6), under the interference of parasitic light, the probe signal cannot obtain an ideal orthogonal interference signal pair after PGC demodulation. The orthogonal component Q d (t) and in-phase component I d In addition to the component containing the target vibration phase, (t) also contains the component generated by the mixing of parasitic light and reference light. Directly performing arctangent or DCM phase demodulation on the signal pair described in equation (6) will produce large errors and distortions.

[0113] Further observation of equation (6) reveals that when the optical path of the parasitic light is equal to that of the reference light, the internal modulation depth C in the parasitic interference component... pi and laser noise phase When the parasitic interference equals 0, it has no effect on the demodulation of the probe signal. However, in actual system setup, it is difficult to control the optical path of the parasitic light to be precisely equal to that of the reference light. In fact, the source of the parasitic light is not singular. Therefore, in practice, the fiber length of the reference light can only be adjusted as much as possible to reduce the influence of parasitic interference. Since the frequency of the internal modulation is relatively small compared to the vibration of the target being measured, under short-time observation conditions, parasitic interference has a significant impact on the demodulation of the probe orthogonal signal Q. d (t) and I dThe effect of (t) manifests as a zero-point drift, causing the Lissajous figure formed by the probed orthogonal signal pairs to appear as a non-closed circular arc with an unstable center point. To address this center-point drift caused by parasitic interference, this invention proposes a method for estimating and correcting the center trajectory based on linear function fitting.

[0114] To suppress the effects of laser noise and parasitic interference, this invention proposes a PGC demodulation scheme based on Lissajous figure center point trajectory estimation and correction, namely the Ref-PGC-CTC-Arctan algorithm. This demodulation scheme mainly includes the following processing:

[0115] (1) The amplitude of the probe interferometric orthogonal signal pair is corrected by estimating the non-ideal factors of external modulation through the reference interferometric signal;

[0116] (2) Use the linear function fitting method to estimate the circle center trajectory of the Lissajous figure of the probe orthogonal signal pair and correct the zero drift of the probe orthogonal signal pair;

[0117] (3) The phase demodulation of the reference interference signal and the corrected probe signal is realized by using the arctangent and phase unwrapping algorithm. The ratio of the internal modulation depth of the two signals is obtained by Fourier spectrum analysis. The demodulation result of the reference signal multiplied by the ratio coefficient is removed from the demodulation result of the probe signal, thereby eliminating laser noise and internal modulation phase.

[0118] The flowchart of the Ref-PGC-CTC-Arctan demodulation algorithm proposed in this embodiment of the invention is as follows: Figure 3 As shown, it is mainly divided into three functional modules, including Lissajous figure ellipse fitting and correction, Lissajous circle center point trajectory fitting and correction, and light source noise compression.

[0119] Let z(t) = C be the sum of the internal modulation phase and the light source noise phase in the reference interference signal. ri cos(ω i t)+Δφ r The formulas (5) and (6) for the reference interferometer and the measuring interferometer signals are rewritten as follows:

[0120] (7)

[0121] (8)

[0122] In the formula, the scaling factor a = C di / C ri =ΔL d / ΔL r b=C pi / C ri =ΔL p / ΔL r Arq A ri A dq A di A pq A pi The amplitudes of the reference orthogonal signal pair, the amplitude of the probe orthogonal signal pair, and the amplitude of the parasitic interference orthogonal signal pair are respectively, and they satisfy the relationship described in equation (9). Inspired by this equation, the ratio of the amplitudes of the reference orthogonal signal pair can be used to correct the amplitude of the probe orthogonal signal pair.

[0123] (9)

[0124] According to equation (7), the orthogonal signal pairs of the reference interferometer satisfy the equation of an ellipse:

[0125] (10)

[0126] In the formula, (r1, r2) are the parameters of the ellipse equation, which can be used to correct the ellipse and normalize orthogonal signal pairs. According to the least squares principle, the calculation formulas for these two parameters are as follows:

[0127] (11)

[0128] After obtaining the elliptic parameters (r1, r2) of the reference orthogonal signal, the reference orthogonal signal pair Q is then... r (t) and I r The amplitude of z(t) is corrected, and then the phase of the reference interference signal z(t) is obtained by performing arctangent operation and unwrapping on the corrected quadrature signal pair:

[0129] (12)

[0130] When the optical path of the parasitic light is adjusted to be close to that of the reference light, the effect of parasitic interference manifests as the detection of the zero-point drift of orthogonal signal pairs, denoted as (ΔQ). d , ΔI d Similar amplitude correction is performed on the probe orthogonal signal pair using the elliptic parameters (r1, r2) of the reference signal. The corrected probe orthogonal signal pair [Q′] can then be obtained. d (t), I′ d (t)]:

[0131] (13)

[0132] Detecting the zero-point drift (ΔQ) of orthogonal signal pairs d , ΔI dThese are not constant values; they are functions of the reference signal phase z, and their frequency of change is approximately equal to the internal modulation frequency. Since the internal modulation is designed as a low-frequency modulation, it can be expressed as a linear function [f] within a short observation time scale. q (z), f i [(z)] is used to characterize the trajectory of the orthogonal signal pair at the zero point (i.e., the trajectory of the center of the circle in the Lissajous figure). For ease of description, let [Q′] be the probe signal pair. d (t), I′ d If the quadrature component (t) is x and the in-phase component is y, then according to the aforementioned conditions, they satisfy the following equation:

[0133] (14)

[0134] In the formula, this embodiment of the invention uses two second-order linear functions to fit the zero-point trajectory of the orthogonal signal. The aforementioned equation contains a total of seven undetermined coefficients (α...). x , β x , γ x , α y , β y , γ y After obtaining the probe orthogonal signal pair (x, y) and the phase demodulation result z of the reference interferometric signal, the calculation formulas for the parameters of the aforementioned 7 equations can be obtained according to the least squares principle:

[0135] (15)

[0136] The parameters (α) of the trajectory equation of the center point of the Lissajous figure circle for the detection of orthogonal signals are obtained by solving equation (15). x , β x , γ x , α y ,β y , γ y Using these parameters, construct the locus function of the center point [f] q (z), f i (z)], and the detection of orthogonal signal pairs [Q′ d (t),I′ d Zero-point correction is performed on the (t)] and then arctangent and phase unwrapping operations are performed on the corrected quadrature signal pair to obtain the demodulation result containing the measured vibration, light source noise phase and internal modulation, as shown in Equation (16).

[0137] (16)

[0138] From equation (16), it can be seen that once the scaling factor a is determined, combined with the demodulation result z(t) of the reference interference signal, it is easy to eliminate the non-measured vibration phase from the demodulation result of the probe signal, that is, to eliminate the light source noise phase and the internal modulation phase. The scaling factor a is equal to the ratio of the internal modulation depth in the probe signal to the internal modulation depth in the reference signal. Since the internal modulation frequency is fixed, it is easy to think of using Fast Fourier Transform (FFT) to extract the internal modulation depth (that is, the amplitude corresponding to the modulation frequency in the Fourier frequency domain) from the demodulation results of the two signal phases. Therefore, the final demodulation result of the probe signal is:

[0139] (17)

[0140] In the formula, abs() is the modulus length operation. By combining this with the operating wavelength of the laser, the phase demodulation result can be converted into vibration displacement.

[0141] To verify the accuracy of the demodulation principle of the Ref-PGC-CTC-Arctan algorithm, this embodiment of the invention conducts numerical simulation research. The focus is on testing the effectiveness of the correction methods for the probe orthogonal signal pairs, including methods for correcting the amplitude of the probe orthogonal signals using elliptic fitting of the reference signal and methods for correcting the zero-point drift trajectory of the probe orthogonal signals. Comparing the Lissajous figures of the probe orthogonal signals before and after correction under different intensities of parasitic interference allows for a direct verification of the effectiveness of the probe orthogonal signal amplitude and zero-point drift correction methods. Two interference signals are constructed according to equations (5) and (6): a reference interference signal and a probe interference signal. The main simulation parameters are shown in Table 1. The main simulation parameters are shown in Table 1. In the table, f... s ω is the sampling frequency. c This is the cutoff frequency of the low-pass filter. In the simulation, the vibration amplitude of the target under test is 27 nm (corresponding to a phase modulation depth of 0.22 rad in the interference signal), and the frequency is 600 Hz.

[0142] Table 1 Simulation Parameter Settings

[0143] The proportion of parasitic light intensity reflected from the device end face in the total return light intensity of the interferometer varies, resulting in different correction effects from detecting orthogonal signals. The ratio of parasitic light intensity to total return light intensity is defined as R. Six different R values, ranging from 0 to 50%, were designed based on the possible proportions of parasitic light intensity in actual experiments. Figure 4 The figure shown is a Lissajous figure of the simulated probe signal amplitude and the orthogonal signal pairs before and after zero-point drift correction (red line is before correction, blue line is after correction). Figure 4 (a) With the parasitic light intensity designed to be 0, this figure reflects the effectiveness of using Lissajous ellipse fitting of the reference interference signal to correct the amplitude of the probed orthogonal signal. The Lissajous trajectory of the probed orthogonal signal is corrected from an ellipse to a circle. Figure 4 (a) Compared to no parasitic interference, Figure 4 In (bf), as the proportion of parasitic light intensity increases, the centrifugal distortion of the Lissajous figure of the detection signal becomes increasingly severe, even to the point of failing to form a closed ellipse. From Figure 4 In the study, it can be observed that when the proportion of parasitic light intensity is less than 40%, the correction method described in this embodiment of the invention can still effectively correct the severely distorted Lissajous figure into a closed circle, that is, realize the correction of the zero-point drift of the detection orthogonal signal pair.

[0144] To demonstrate the superiority of the demodulation scheme described in this embodiment, simulated detection signals with different parasitic light intensity ratios were demodulated. Phase demodulation of the detection signals was performed using three methods: conventional PGC-Arctan, Ref-PGC-EFA-Arctan, and the Ref-PGC-CTC-Arctan method proposed in this embodiment. The total harmonic distortion and signal-to-susceptibility distortion ratio were calculated from the demodulation results, as shown below. Figure 5 As shown in the figure, the performance of all three demodulation schemes decreases with increasing parasitic light intensity, and the Ref-PGC-EFA-Arctan method even exhibits significant demodulation failure. Whether evaluated by total harmonic distortion (THD) or signal-to-susceptibility distortion ratio (SINAD), the demodulation scheme described in this embodiment of the invention demonstrates optimal performance.

[0145] To further verify the feasibility of the detection scheme proposed in the embodiments of the present invention, its detection performance and application potential were investigated. Based on the proposed Ref-DFPMI optical path principle, a set of... Figure 6 The experimental system shown uses a DFB semiconductor laser with a center wavelength of 1550 nm and an output power of 10 mW as the light source. A low-frequency internal phase modulation of 20 Hz is applied using its driver (CLD1015, Thorlabs). The DFB laser output is split into two beams by a coupler with a splitting ratio of 98:2 after passing through an isolator. The lower-power beam serves as the reference beam shared by the reference and detector interferometers. This reference beam is then phase-modulated by an electro-optic phase modulator (APE PM-50-005, JDSU) to generate a high-frequency carrier wave. The half-wave voltage of the electro-optic phase modulator is 3.5 V @ 1550 nm. To match the subsequent data acquisition module, its modulation frequency is designed to be 50 kHz, and the modulation signal waveform is a sine wave. After external modulation, the reference beam is split into two beams of equal power by a 1:1 splitting coupler, which then enter the reference and detector interferometers, respectively. After the initial beam splitting, the high-power laser beam is further divided into two beams by a 98:2 beam splitter. The higher-power beam serves as the probe beam for the probe interferometer (measured power is approximately 9.3mW), while the other beam is input to the reference interferometer. The probe beam is then focused onto the target object by an optical antenna after passing through a circulator.

[0146] The optical antenna consists of a lens group. It collimates the light output from the fiber optic pigtail before focusing it onto the target. The collimated light spot diameter is 24 mm. The focal length of the focusing lens is adjusted according to different experimental requirements. The effective detection aperture (ENA) of the optical antenna is defined as follows in this embodiment of the invention:

[0147] (18)

[0148] In the formula, n0 is the refractive index of air, θ is half the focusing angle of the probe light, and f is the focal length of the antenna focusing mirror. A larger effective numerical aperture results in a stronger ability to receive the probe return light, but also means a smaller depth of focus. When the displacement scale of the measured target is large, it is easy to cause defocusing. Therefore, the experiment needs to balance the size of the effective aperture and the focusing distance. Based on different experimental requirements, two types of measured targets are designed: a surface acoustic wave composed of a loudspeaker and white paper (target A in the figure) and a piezoelectric displacement stage providing stable vibration (target B in the figure, NF15AP25\M, Thorlabs). The optical antenna receives the Doppler scattered return light from the target. The return light passes through a circulator and a 2×2 coupler and is optically mixed with an externally modulated reference light. Two balanced detectors (PDB470C, Thorlabs) with high common-mode rejection ratios convert the reference interference signal and the probe interference signal into voltage signals. These signals are then passed through an anti-aliasing filter with a cutoff frequency of 500kHz and acquired by a data acquisition module (JYUSB-61210, JYTEK) before being sent to a host computer processing platform. The sampling rate is 1MSps, and the sampling resolution is 16 bits. In the host computer, the improved digital signal demodulation scheme described in this embodiment of the invention is used to demodulate the vibration of the target object.

[0149] To verify the feasibility of the detection scheme proposed in this embodiment of the invention, a piece of white paper (e.g., ...) was placed near the focal point of the optical antenna. Figure 6 Using Target A as the detection target, an audio signal from a loudspeaker was emitted to drive the paper to vibrate at the same frequency, thus conducting a paper vibration detection experiment. The effective detection aperture of the optical antenna was designed to be 0.048. After turning on the light source, without focusing on the detection target, the parasitic backlight intensity measured at port 3 of the circulator was approximately 0.227 μW, and the proportion of parasitic light intensity was calculated based on this. The internal modulation voltage Vpp was set to 2 mV, and the external modulation voltage Vpp was set to 2.5 V (corresponding to a modulation depth of approximately 2.2 rad). To drive the paper to vibrate, a loudspeaker was placed approximately 200 mm away from the paper, and a 600 Hz single-tone sound wave was generated by driving the loudspeaker through a power amplifier. The paper vibrated weakly at 600 Hz under the excitation of the sound wave.

[0150] To test the demodulation performance under different parasitic light intensity ratios, this experiment changed the effective detected return light intensity by adjusting the angle of the test paper relative to the optical antenna axis, and used the detected interference signal to verify the effectiveness of the proposed Ref-PGC-CTC-Arctan scheme. Figure 7 The figure shown is a Lissajous figure of the quadrature signal pairs before and after zero-point drift correction for detecting quadrature signal amplitude and zero-point drift (blue is before correction, orange is after correction). Figure 7 As the proportion of parasitic light intensity increases in (a, c and e), the centrifugal distortion of the Lissajous figure of the detection signal becomes more and more severe. This is consistent with the results of theoretical analysis and numerical simulation, proving the accuracy of the analysis of parasitic light effect and the mathematical model of the detection signal in the embodiments of the present invention. Figure 7 In (b, dand f), it can be observed that when the proportion of parasitic light intensity is less than 50%, the correction method described in this embodiment of the invention can still correct the severely distorted Lissajous figure into a closed circle, that is, it can realize the correction of amplitude and zero-point drift of the probe orthogonal signal. This proves the feasibility of the first and second parts of the Ref-PGC-CTC-Arctan scheme.

[0151] The 600Hz paper vibration detection signal was demodulated using two methods: the commonly used Ref-PGC-EFA-Arctan method and the Ref-PGC-CTC-Arctan method proposed in this embodiment. The time-domain and frequency-domain distributions of the demodulation results of the two methods are shown below. Figure 8 As shown (red represents the Ref-PGC-EFA-Arctan method, blue represents the Ref-PGC-CTC-Arctan method). The total harmonic distortion (SINAD) and signal-to-susceptibility distortion (THD) ratios of the demodulation results for both methods were calculated. When the parasitic light intensity ratio was 23.8%, the Ref-PGC-CTC-Arctan method proposed in this embodiment improved SINAD by 13.58 dB and reduced THD by 4.88 percentage points compared to the conventional Ref-PGC-EFA-Arctan method. When the parasitic light intensity ratio was 37.1%, the Ref-PGC-EFA-Arctan method became ineffective, while the Ref-PGC-CTC-Arctan method proposed in this embodiment could still achieve effective demodulation, with a demodulation result of SINAD of 17.80 dB and THD of 0.14%. When the parasitic light intensity accounts for 45.7%, the SINAD of the demodulation result of the Ref-PGC-CTC-Arctan method proposed in this embodiment of the invention is 17.59 dB, and the THD is 0.24%. The above experimental results show that the method and system proposed in this embodiment of the invention are feasible, and fully demonstrate that the proposed Ref-PGC-CTC-Arctan demodulation scheme can achieve effective demodulation of the measured vibration under interference from large parasitic light intensity.

[0152] To test the performance of the detection system and demodulation scheme proposed in this embodiment of the invention, while keeping the effective detection aperture of the optical antenna constant, a piezoelectric displacement stage (e.g., ...) is placed near the focal point of the optical antenna. Figure 6 Target B). The piezoelectric displacement stage is driven to generate uniform linear motion. A detection system is used to detect this uniform linear motion, and the demodulation results and deviations are as follows: Figure 9 As shown. From Figure 9 It can be seen that within the displacement range of 2μm to 7μm, the displacement measurement value exhibits a linear relationship with time, consistent with the displacement stage setup, indicating that the text detection system possesses good linearity. The deviation curve shows that the maximum absolute value of the deviation is approximately 20nm. This is because single-mode optical fibers are highly sensitive to environmental disturbances, causing low-frequency drift in the displacement measurement results due to factors such as ambient temperature and vibration. For vibration displacement detection, this slow drift can be distinguished by the frequency spectrum, and a high-pass filter can accurately extract the measured vibration. The nanometer displacement measurement experiment demonstrates the accuracy of the displacement detection by the system and method of this invention.

[0153] To verify the insensitivity of the proposed method to external modulation depth, vibration measurement experiments were conducted at different external modulation depths. In the experiments, the voltage Vpp of the piezoelectric displacement stage controller was set to 15mV, causing the displacement stage to generate small-amplitude vibrations at a frequency of 200 Hz. The external modulation depth was controlled by adjusting the external modulation voltage, and the aforementioned system was used to detect weak vibration displacements. The measured vibrations were demodulated using traditional PGC-Arctan, PGC-EFA-Arctan, Ref-PGC-EFA-Arctan, and the Ref-PGC-CFC-Arctan demodulation scheme proposed in this embodiment (internal modulation was disabled when using the conventional PGC-Arctan and PGC-EFA-Arctan schemes). The PGC-Arctan algorithm directly performs division on the detected orthogonal signal pairs before performing arctangent and phase unwrapping operations. The PGC-EFA-Arctan algorithm uses the Lissajous ellipse formed by the probe orthogonal signal pairs. After fitting the ellipse, parameters such as the major and minor axes and tilt angle are obtained. These parameters are then used to normalize the amplitude of the orthogonal signal pairs, followed by arctangent and phase unwrapping operations, effectively correcting the orthogonal signal pairs (this has certain requirements on the displacement of the measured target; generally, the Lissajous ellipse should not be less than 1 / 4 of a circle). The Ref-PGC-EFA-Arctan algorithm, on the other hand, uses the Lissajous ellipse fitting result of the reference orthogonal interference signal to correct the probe orthogonal signals, achieving normalization of the probe orthogonal signal pairs, before performing arctangent and phase unwrapping operations.

[0154] In the experiment, the effective detection aperture of the optical antenna was approximately 0.048. The 200Hz vibration displacement detection signal was demodulated using the aforementioned four demodulation schemes, and the results are as follows: Figure 10 and Figure 11 As shown in the figure, the Ref-PGC-CFT-Arctan demodulation scheme proposed in this embodiment of the invention exhibits the best and most stable THD (both 1% lower) and SINAD (both better than 20dB). Vibration measurement results verify that the proposed method and system are insensitive to external modulation depth.

[0155] To further investigate the detection performance of the method in this embodiment and verify its superiority, vibration measurement experiments at different frequencies were conducted. In the experiments, the driving voltage Vpp of the piezoelectric controller was set to 20mV, and the driving signal frequency range was 80Hz~300Hz. Phase demodulation of the detection signal was performed using four methods: the conventional PGC-Arctan, two commonly used improved algorithms PGC-EFA-Arctan and Ref-PGC-EFA-Arctan, and the Ref-PGC-CTC-Arctan algorithm proposed in this embodiment. The demodulation performance of these methods was compared in terms of THD and SINAD. The external modulation voltage for each demodulation scheme in the experiment was 2.5V. The SINAD and THD of the vibration detection results at different frequencies are shown below. Figure 12 and 13 As shown in the figures, the proposed demodulation scheme exhibits the best demodulation performance. The SINAD of the Ref-PGC-CFT-Arctan demodulation scheme is on average approximately 16.85 dB higher than the conventional PGC-Arctan scheme, approximately 16.63 dB higher than the PGC-EFA-Arctan scheme, and approximately 14.95 dB higher than the Ref-PGC-EFA-Arctan scheme. Regarding THD, the proposed method reduces the THD by an average of approximately 6.77, 11.76, and 3.06 percentage points compared to the conventional PGC-Arctan, PGC-EFA-Arctan, and Ref-PGC-EFA-Arctan schemes, respectively. These results validate the superior demodulation performance of the proposed method.

[0156] To investigate the background noise level of the experimental system and verify the performance of the proposed solution in suppressing laser noise, a static target detection experiment was conducted. The power supply to the piezoelectric controller was turned off during the experiment. Static target detection signals were obtained using the aforementioned experimental system and demodulated using the traditional PGC-Arctan, Ref-PGC-EFA-Arctan, and the Ref-PGC-CTC-Arctan demodulation scheme of this invention (internal modulation was disabled when applying the traditional PGC-Arctan algorithm). The frequency domain distribution of the demodulation results for the three methods is shown below. Figure 14 As shown, the noise floor of the three methods is -77.03 dB re rad√Hz, -76.35 dB re rad√Hz, and -89.03 dB re rad√Hz, respectively. It is evident that the embodiments of the present invention are significantly effective in reducing system noise and substantially improve the sensitivity of the detection system.

[0157] To demonstrate the application potential of the text system and demodulation scheme, this section presents a speech signal detection experiment. The system of this embodiment detects the vibration displacement of paper excited by audio, and the demodulation result is compared with the signal acquired by the microphone. In the experiment, the paper and microphone are positioned approximately 200 mm from the speaker, and the optical antenna is approximately 1000 mm from the paper (effective detection aperture approximately 0.012). The parasitic light intensity ratio is measured to be 20.3%. A speech signal containing the phrase "I love you." is played through the speaker.

[0158] The system of this embodiment of the invention synchronously detects the aforementioned speech signal with a microphone, wherein the microphone performs direct detection, while the system of this embodiment detects the paper. The final detection results of the two methods are as follows: Figure 15 As shown. The normalized time-domain and frequency-domain distributions of the demodulated signal and pickup signal of the experimental device in this embodiment of the invention are as follows. Figure 15 As shown in (a) and (b), the calculated cosine similarity is 83.2%. When the demodulated signal from this experimental setup is played back through a speaker, the human ear can clearly recognize the speech content. Therefore, the system and demodulation scheme of this invention can better restore the audio signal and further help to extract semantic information.

[0159] The beneficial effects of the technical solutions provided in the embodiments of the present invention include at least the following:

[0160] (1) In this invention, a reference interferometer is introduced and internal modulation is applied to the light source, which serves as an indicator of laser jitter noise. Since the internal modulation depth is proportional to the optical path difference of the interferometer, the magnitude of laser noise in the probe signal can be accurately estimated by obtaining the ratio of the internal modulation depth in the reference interference signal to that in the probe interference signal. Furthermore, the noise component is subtracted from the probe phase using the reference phase, thereby effectively suppressing the influence of light source noise on the measurement results and significantly improving the signal-to-noise ratio and sensitivity of the detection system.

[0161] (2) In this invention, to address the problem of zero-point drift caused by parasitic light interference in the detection of orthogonal signal pairs, a method based on Lissajous figure center trajectory fitting and correction is proposed. This method first uses a reference interference signal to correct for non-ideal modulation factors, and then performs polynomial fitting on the center drift trajectory of the orthogonal components of the detection signals based on the reference phase. By subtracting the fitted center trajectory function from the detection orthogonal signals, the zero-point drift introduced by parasitic interference is effectively eliminated, and a pure orthogonal signal pair is recovered. This ensures the accuracy and robustness of the arctangent phase demodulation, significantly improving the measurement stability of the system under strong parasitic light interference.

[0162] (3) In this invention, a complete high-robustness signal demodulation scheme is constructed through the coordinated design of internal and external dual-frequency modulation and the introduction of a reference interferometer. This scheme not only solves the two core problems that restrict the detection performance of non-cooperative targets—laser noise and parasitic light interference—but also ensures the high dynamic range of the system through external modulation. Ultimately, it achieves accurate and stable demodulation of target vibration under weak echo signal conditions, providing a feasible technical approach for vibration measurement of long-distance, low-reflectivity targets and practical applications such as voice signal interception.

[0163] The above are merely specific embodiments of the present invention, but the scope of protection of the present invention is not limited thereto. The scope of protection of the present invention should be determined by the scope of the claims.

Claims

1. A method of demodulating a fiber interferometer measuring vibration with reference interferometer dual frequency phase modulation, characterized in that, include: S1: Acquire a reference interference signal and a probe interference signal, wherein both the reference interference signal and the probe interference signal contain an external modulation phase carrier and an internal modulation phase term; S2: Perform phase generation carrier demodulation on the reference interference signal to obtain a reference orthogonal signal pair, and perform amplitude correction on the reference orthogonal signal pair based on the ellipse fitting algorithm; S3: Obtain the reference phase based on the demodulation of the corrected reference quadrature signal pair; S4: Perform phase generation carrier demodulation on the probe interference signal to obtain probe orthogonal signal pairs; S5: The amplitude correction parameters of the reference quadrature signal pair are used to perform amplitude correction on the probe quadrature signal pair to obtain the corrected probe quadrature signal pair; S6: Based on the reference phase, perform polynomial fitting on the Lissajous figure center trajectory of the corrected probe orthogonal signal pair to eliminate the zero-point drift introduced by parasitic interference and obtain the probe orthogonal signal pair after secondary correction. S7: Perform arctangent and unwrapping operations on the second-corrected detection orthogonal signal pair to obtain an initial detection phase containing the target vibration phase, laser noise phase, and internal modulation phase; S8: Based on the ratio of the reference phase to the internal modulation depth in the initial detection phase, the laser noise phase and the internal modulation phase are eliminated from the initial detection phase to obtain the target vibration phase.

2. The fiber optic interferometric vibration demodulation method based on dual-frequency phase modulation of a reference interferometer according to claim 1, characterized in that, In step S1, the reference interference signal and the probe interference signal are represented by the following formula: in, For the reference interference signal amplitude, To detect the amplitude of the interference signal, For the depth of external modulation, The externally modulated angular frequency, The internal modulation angular frequency, The depth of the internal modulation in the reference signal. To detect the depth of internal modulation in the signal, The phase noise is caused by laser frequency jitter in the reference signal. To detect phase noise caused by laser frequency jitter in the signal, The phase to be demodulated is generated by the target vibration.

3. The method of claim 1, wherein the reference interferometer dual-frequency phase- modulated fiber interferometric vibration-sensing demodulation method is characterized by, Step S2, which involves elliptic fitting and amplitude correction of the reference orthogonal signal pair, further includes the following sub-steps: S201: The following elliptic equation is used to apply to the reference orthogonal signal pair. and Perform fitting: wherein is a quadrature component of a reference quadrature signal pair, is an in-phase component of a reference quadrature signal pair, and are elliptic equation parameters; S202: Calculate the ellipse parameters according to the least square principle using the following formula and : wherein is a reference in-phase signal pair in-phase component value for the i-th sample point, is a reference in-phase signal pair in-phase component value for the i-th sample point, denotes a summation over all sample points; S203: Amplitude correction is performed on the reference quadrature signal pair by using the elliptical parameters according to the following formula, to obtain a corrected reference quadrature signal pair and to demodulate a reference phase : in, As a reference phase, For phase unwrapping operation For arctangent operation, For the reference orthogonal components of the orthogonal signal pair, For the reference quadrature signal pair in-phase component, and These are the parameters of the ellipse equation.

4. The method of claim 3, wherein the reference interferometer is a dual frequency phase modulated fiber optic interferometer. The step S5, which involves using the amplitude correction parameters of the reference quadrature signal pair to perform amplitude correction on the probe quadrature signal pair, includes: S501: Using the ellipse parameters obtained in S203 and The following formula is used to detect orthogonal signal pairs. and Perform amplitude correction: in, To detect the orthogonal components of orthogonal signal pairs, To detect the in-phase components of quadrature signal pairs, and These are the parameters of the ellipse equation. and These are the corrected detection orthogonal signal pairs.

5. The method of claim 1, wherein the reference interferometer dual-frequency phase- modulated fiber interferometric vibration sensing demodulation method is characterized by, Step S6, which involves polynomial fitting of the Lissajous figure center trajectory of the corrected probe orthogonal signal pairs, further includes the following sub-steps: S601: Establish a model of the detected quadrature signal pair containing the parasitic interference influence, denoted as reference phase which is expressed by the following formula: in, For the corrected detection orthogonal signal pairs of orthogonal components, For the corrected detection quadrature signal pairs in-phase components, To detect the amplitude of the in-phase component of a quadrature signal pair, To detect the amplitude of the quadrature components of quadrature signal pairs, The amplitude of the in-phase component of the parasitic interference quadrature signal pair. The amplitudes of the orthogonal components of the parasitic interference orthogonal signal pair are given. As a scaling factor, It is the ratio of the modulation depth within the parasitic interference to the modulation depth within the reference signal. To detect the depth of internal modulation in the signal, The depth of the internal modulation in the reference signal. The depth of internal modulation in the parasitic interference signal. As a reference phase, The target vibration phase; S602: Represent the probed quadrature signal pair as about the reference phase The function, and denoted as , The function of the circle's center trajectory is expressed by the following formula. and : Where x represents the quadrature component of the corrected probe quadrature signal pair, and y represents the in-phase component of the corrected probe quadrature signal pair. For reference phase The orthogonal component center locus function, For reference phase The in-phase component's circular center trajectory function, where E is a constant; S603: Using a second-order polynomial function to calculate the trajectory of the circle's center. and The following formula is used for fitting: wherein are polynomial coefficients of the in-quadrature component circle centered locus function, are polynomial coefficients of the in-phase component circle centered locus function, z is a reference phase; S604: Calculate the coefficients of the polynomial according to the least squares principle.

6. The reference interferometer dual frequency phase modulated fiber interferometric vibration sensing demodulation method according to claim 5, wherein, The elimination of zero-point drift introduced by parasitic interference in step S6 further includes: S605: Zero-point correction of the probed orthogonal signal pairs is performed using the following formula based on the fitted circle center trajectory function: in, For the corrected detection orthogonal signal pairs of orthogonal components, For the corrected detection quadrature signal pairs in-phase components, The function is the locus of the center of the orthogonal components. Let z be the trajectory function of the center of the in-phase component, and z be the reference phase. and These are the orthogonal detection signal pairs after secondary correction.

7. The fiber optic interferometric vibration demodulation method based on dual-frequency phase modulation of a reference interferometer according to claim 1, characterized in that, Step S8, which involves eliminating laser noise and internal modulation phase based on the ratio of the internal modulation depth in the reference phase to the initial probe phase, further includes the following sub-steps: S801: Reference Phase Perform a Fast Fourier Transform to extract the internal modulation frequency. The amplitude at that point, i.e., the modulation depth of the internal modulation, is determined using the following formula: wherein is the reference phase, is the fast Fourier transform, is the angular frequency of the inner modulation, is the depth corresponding to the inner modulation frequency in the reference phase; S802: Perform a Fast Fourier Transform on the initial probe phase extract the amplitude at the inner modulation frequency extract the amplitude at the inner modulation frequency wherein is an initial detection phase, is a fast Fourier transform, is an angular frequency of the internal modulation, is a depth corresponding to the internal modulation frequency in the initial detection phase; S803: Calculate the proportionality coefficient using the following formula: in, The depth corresponding to the internal modulation frequency in the initial probe phase. The depth corresponding to the internal modulation frequency in the reference phase, where 'a' is the scaling factor; S804: Laser noise and internal modulation phase are eliminated from the initial probe phase using the following formula: in, The initial detection phase is denoted by 'a', where 'a' is the scaling factor. As a reference phase, The target vibration phase.

8. The method of claim 1, wherein the reference interferometer dual-frequency phase- modulated fiber interferometric vibration-sensing demodulation method further comprises: The external modulation is achieved by an electro-optic phase modulator or a fiber PZT modulator, with a modulation frequency higher than the target vibration frequency; the internal modulation is achieved by periodically changing the injection current of the DFB semiconductor laser, with a modulation frequency lower than the external modulation frequency.

9. The method of claim 1, wherein the reference interferometer dual-frequency phase- modulated fiber interferometric vibration-sensing demodulation method further comprises: The reference interference signal and the probe interference signal are obtained by a Mach-Zehnder interferometer optical path with a shared reference arm. The reference arm is externally modulated, and the probe interference signal contains parasitic light interference generated by reflection from the end face of the optical device.

10. The method of claim 1, wherein the reference interferometer dual-frequency phase- modulated fiber interferometric vibration sensing demodulation method further comprises: The method further comprises a step S9 of converting the demodulated target vibration phase in combination with the laser operating wavelength into a vibration displacement using the following formula: wherein, is the laser operating wavelength, is the target vibration phase, is the vibration displacement.

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