Frequency shift PGC demodulation method and system based on frequency domain extraction

Abstract

This invention provides a frequency-shifted PGC demodulation method and system based on frequency domain extraction, belonging to the field of fiber optic sensing. It performs FFT on the interference signal to obtain the amplitudes of , , , , and , calculates the carrier phase delay, and constructs , , , , ; calculates the modulus considering symbol effects, and calculates the modulation depth; it compensates for and ; and divides the result of the first mixed signal divided by and the result of the second mixed signal divided by ; thus solving the problem of not being able to simultaneously correct and accurately invert and .

Description

Technical Field

[0001] This invention relates to the field of interferometric fiber optic sensing technology, and in particular to a frequency-shift PGC demodulation method and system based on frequency domain extraction. Background Technology

[0002] Phase Generation Carrier (PGC) technology, with its high sensitivity, large dynamic range, excellent linearity, and unique advantages of shifting the signal spectrum to higher frequencies to suppress low-frequency noise, is widely used in interferometric fiber optic sensors. The basic process of traditional PGC demodulation involves first mixing and low-pass filtering the signal, then extracting the target signal using either the arctangent algorithm (PGC-Arctan) or the differential cross-multiplication algorithm (PGC-DCM). However, traditional PGC demodulation methods are highly sensitive to modulation depth drift, carrier phase delay, and optical intensity disturbances. When the system deviates from the ideal values ​​of these influencing factors, nonlinear errors are introduced, significantly affecting the demodulation results.

[0003] To eliminate the interference of modulation depth drift, carrier phase delay, and light intensity disturbance on the demodulation results, existing technologies have proposed a variety of improved PGC demodulation algorithms, but various methods still have obvious limitations: (1) Improved algorithms for modulation depth drift can offset the influence of modulation depth fluctuations through mathematical operations, but the division operation in the algorithm is prone to distortion points (for example, the denominator approaches 0), which in turn causes new nonlinear distortions; (2) Real-time calibration methods represented by ellipse fitting (including two implementation methods based on least squares and Kalman filtering) generally have problems of large computational load and complex hardware implementation, and the calibration process has a delay, making it difficult to adapt to high-speed measurement scenarios; (3) Existing reference signal construction algorithms have high reliability (their core logic is to first calculate the modulation depth C value and carrier phase delay). The specific values ​​are then used to construct an appropriate mixing signal based on the calculation results. However, most of these methods can only correct for a single interference factor and cannot simultaneously solve the combined effects of modulation depth drift and carrier phase delay.

[0004] In the prior art, Chinese invention patent application CN120890486A, entitled "A Phase Generation Carrier Demodulation Method Based on Dual-Parameter Estimation," first estimates the C value by extracting the amplitude ratio of the carrier frequency harmonic component in the spectrum of the interference signal output by the fiber optic interferometer and combining it with the characteristics of the Bessel function; then, it extracts the carrier phase delay using first and second harmonic signal processing. Finally, dynamic phase compensation is used to eliminate its influence. After plotting the Bessel function ratio change curve, this method extracts the amplitude of each order signal and calculates the ratio to correspond with the curve value. This method is similar to a lookup table, which is complex to use and has limited accuracy. When calculating the carrier phase delay, a series of steps such as mixing filtering, differentiation, sum of squares, and sign determination are used. The calculation process is complex and phase jumps are prone to occur at the boundaries.

[0005] Further analysis reveals that even attempts to improve the system to address multiple interference factors face key technical bottlenecks: at the time domain level, when calculating the modulation depth using multiple harmonics, not only are the calculation results susceptible to fluctuations due to noise, but they also fluctuate at the operating point. Sometimes, computational singularities occur, causing demodulation interruptions. At the frequency domain level, the modulation depth and carrier phase delay can be calculated numerically using the modulation frequency and multiple harmonics, but the problem of computational singularities also exists—when the operating point takes special values. Sometimes, only the first and third harmonics, or only the second and fourth harmonics, may exist, making it impossible to accurately invert the C value using harmonic values. For example, in the paper "Phase Modulation Depth Evaluation and Correction Technique for the PGC Demodulation Scheme in Fiber-Optic Interferometric Sensors" (Anton V. Volkov et al., IEEE SENSORSJOURNAL, VOL.17, NO.13, JULY 1, 2017), when the interferometric operating point is close to... In such cases, traditional methods for calculating and compensating for modulation depth and carrier phase delay based on time or frequency domain will result in computational singularities due to the disappearance of 1st or 3rd order or 2nd or 4th order signals.

[0006] In summary, there is an urgent need to optimize the demodulation algorithm for constructing reference signals, so that it can not only estimate and correct the modulation depth and carrier phase delay in real time and accurately, but also accurately solve for the modulation depth C and carrier phase delay at singular points. These two nonlinear influencing factors allow us to overcome the limitations of existing technologies in application. Summary of the Invention

[0007] The technical problem to be solved by this invention is: how to solve the problem that traditional PGC demodulation methods cannot simultaneously correct modulation depth and carrier phase delay, and cannot accurately invert modulation depth and carrier phase delay at singular points.

[0008] This invention solves the above-mentioned technical problems through the following technical solution: a frequency-shift PGC demodulation method based on frequency domain extraction, comprising:

[0009] The sensing light is coupled with the reference light after AOM frequency shifting to obtain an interference light signal. The interference light signal is then converted into an initial digital interference signal after photoelectric conversion and analog-to-digital conversion. The frequency is obtained by performing an FFT on the initial digital interference signal. , , , , amplitude at , , , , According to amplitude , Calculate the carrier phase delay and construct complex numbers , , , , The angular frequency of the AOM modulated signal. The carrier angular frequency; According to amplitude , and complex numbers Calculate the complex number , Calculate complex numbers The magnitude of the sign effect Based on the modulus considering the influence of sign Calculate the modulation depth Based on modulation depth Calculate the parameters ,parameter ; Based on carrier phase delay For reference signal , Compensation is performed to obtain a reference signal. , The initial digital interference signal is compared with the reference signal. , After multiplication and low-pass filtering, the first and second mixed signals are obtained. First mixed signal divided by parameter The result is divided by the parameter of the second mixed signal. Divide the result to obtain the signal to be processed. Perform arctangent operation and phase unwrapping on the signal to be processed to obtain the signal to be measured.

[0010] This invention calculates and compensates for modulation depth and carrier phase delay by extracting the frequency domain signal after performing an FFT on the interference signal and obtaining the frequency domain amplitude (complex number) of carrier signals of different orders. A new complex number is constructed by dividing adjacent order (1st to 4th order) complex amplitudes, and the argument of the new complex number is calculated, which represents the carrier phase delay. θ .

[0011] According to the recursive formula of the Bessel function, the modulation depth can be calculated and compensated from the amplitudes of complex signals of orders 1 to 4. However, as the modulation depth continues to increase, the sign of the Bessel function changes, requiring the addition of an appropriate sign before the complex signal amplitude to achieve accurate calculation. To solve this problem, the method adopted in this invention is as follows: extract the 0th-order carrier signal (the nth-order carrier frequency is...). The frequency domain amplitude (complex number) of ) will n Frequency domain amplitude of the first carrier signal divided by n The angle constructed in the previous step is θ The new complex number is then divided by the 0th-order carrier signal (to eliminate the influence of the initial phase), rotating the complex signal amplitude onto the coordinate axes. This amplitude is then compared to the positions of the 1st to 4th-order complex signals (positive y-axis, negative x-axis, negative y-axis, positive x-axis) when both the phase angle and initial phase are 0. If the amplitude differs from this state, a sign is added before the amplitude. This method enables sign determination, allowing for accurate calculation of the modulation depth over a wider range.

[0012] Preferably, the initial digital interference signal The expression is:

[0013] in, For signal amplitude, , , The signals to be measured are respectively amplitude, angular frequency This is a noise signal. For time, This is the initial phase.

[0014] Preferably, based on amplitude , Calculate the carrier phase delay The method is as follows: According to amplitude , Constructing complex numbers : ,in, Represents the imaginary unit; complex number Dividing the imaginary part by the real part and then taking the arctangent yields the carrier phase delay. By dividing the complex signals of adjacent orders by... This yields an argument equal to the carrier phase delay. The complex number is used to calculate the carrier phase delay by calculating its argument.

[0015] Preferably, based on amplitude , and complex numbers Calculate the complex number The method is as follows: .

[0016] By rotating the complex number, the influence of the operating point and carrier phase delay is eliminated, and the first four orders of signals are rotated onto the coordinate axis. The sign of the signal is determined by judging whether it is located on the positive or negative half axis.

[0017] Preferred, complex The magnitude of the sign effect for:

[0018] in, , This represents the function for finding the modulus of a complex number. , , , , , These represent finding the imaginary and real parts of a complex number, respectively. For a sign function, when the sign is positive, When the value is 1 and the sign is negative, It is -1.

[0019] Preferably, based on the modulus considering the influence of sign. Calculate the modulation depth The method is as follows:

[0020] in, , , , These are the modulus lengths considering the influence of sign. exist The values ​​are 1, 2, 3, and 4.

[0021] The present invention does not require the modulation depth to be controlled at 2.63, and the calculated modulation depth is a fixed value rather than having small fluctuations over time.

[0022] This invention also provides a frequency-shift PGC demodulation system based on frequency domain extraction, comprising: The signal processing module is used to couple the sensing light with the reference light after AOM frequency shifting to obtain an interference light signal. The interference light signal is then converted into an initial digital interference signal after photoelectric conversion and analog-to-digital conversion. The carrier phase delay calculation module is used to obtain the frequency after performing an FFT on the initial digital interferometric signal. , , , , amplitude at , , , , According to amplitude , Calculate the carrier phase delay and construct complex numbers , , , , The angular frequency of the AOM modulated signal. The carrier angular frequency; Modulation depth calculation module, used to calculate based on amplitude , and complex numbers Calculate the complex number , Calculate complex numbers The magnitude of the sign effect Based on the modulus considering the influence of sign Calculate the modulation depth Based on modulation depth Calculate the parameters ,parameter ; Demodulation module, used for carrier phase delay-based... For reference signal , Compensation is performed to obtain a reference signal. , The initial digital interference signal is compared with the reference signal. , After multiplication and low-pass filtering, a first mixed signal and a second mixed signal are obtained; the first mixed signal is divided by the parameter. The result is divided by the parameter of the second mixed signal. Divide the result to obtain the signal to be processed. Perform arctangent operation and phase unwrapping on the signal to be processed to obtain the signal to be measured.

[0023] Preferably, based on amplitude , Calculate the carrier phase delay The method is as follows: According to amplitude , Constructing complex numbers : ,in, Represents the imaginary unit; complex number Dividing the imaginary part by the real part and then taking the arctangent yields the carrier phase delay. .

[0024] Preferably, based on amplitude , and complex numbers Calculate the complex number The method is as follows: .

[0025] Preferred, complex The magnitude of the sign effect for:

[0026] in, , This represents the function for finding the modulus of a complex number. , , , , , These represent finding the imaginary and real parts of a complex number, respectively. For a sign function, when the sign is positive, When the value is 1 and the sign is negative, -1 The advantages provided by this invention are: 1. Traditional PGC demodulation improvement methods are effective when the operating point (initial phase) is close to a specific value ( , When the frequency is a positive integer, only first- and third-order carrier signals or second- and fourth-order carrier signals exist in the frequency domain. Whether calculating modulation depth, carrier phase delay, or signal demodulation, the calculated results will significantly deviate from the actual values. This invention introduces AOM to change the light intensity formula, ensuring that the first four harmonics exist under various operating point conditions, thus enabling successful demodulation.

[0027] 2. Traditional PGC demodulation improvement methods require differentiation and division calculations when calculating carrier phase delay in the time domain. This process easily introduces nonlinearity, and problems can arise when the denominator is zero. This invention calculates carrier phase delay in the frequency domain using complex phase angles, enabling calculations across the entire phase range.

[0028] 3. This invention extracts five complex amplitudes corresponding to the 0th to 4th order carriers after performing FFT on the interference signal. Based on these, the modulation depth and carrier phase delay can be calculated. The calculation method is simple and has a large calculation range. Attached Figure Description

[0029] The accompanying drawings, which are incorporated in and form part of this specification, illustrate embodiments consistent with this application and, together with the description, serve to explain the principles of this application.

[0030] Figure 1 A schematic diagram of a Mach-Zehnder interferometer sensing system in the prior art; Figure 2 This is a schematic diagram of the frequency-shift PGC demodulation method based on frequency domain extraction provided in Embodiment 1 of the present invention; Figure 3(a) shows the complex domain representation of the first four orders of signals when the carrier phase delay and the initial phase are both 0 in the frequency shift PGC demodulation method based on frequency domain extraction provided in Embodiment 1 of the present invention; Figure 3(b) shows the complex domain representation of the first four signals when only the initial phase exists in the frequency shift PGC demodulation method based on frequency domain extraction provided in Embodiment 1 of the present invention; Figure 3(c) shows the complex domain representation of the first four orders of signals in the frequency-shift PGC demodulation method based on frequency domain extraction provided in Embodiment 1 of the present invention when only carrier phase delay exists; Figure 3(d) shows the complex domain representation of the first four signals in the frequency-shift PGC demodulation method based on frequency domain extraction provided in Embodiment 1 of the present invention when both carrier phase delay and initial phase exist; Figure 4 The demodulation results of the signal under test at different modulation depths in the frequency-shift PGC demodulation method based on frequency domain extraction provided in Embodiment 1 of the present invention; Figure 5 This refers to the demodulation results of the signal under test under different carrier phase delays in the frequency-shift PGC demodulation method based on frequency domain extraction provided in Embodiment 1 of the present invention. Figure 6 The demodulation results of the signal under test at different operating points in the frequency-shift PGC demodulation method based on frequency domain extraction provided in Embodiment 1 of the present invention; Figure 7 This is a schematic diagram of a frequency-shift PGC demodulation system based on frequency domain extraction provided in Embodiment 2 of the present invention.

[0031] The accompanying drawings illustrate specific embodiments of this application, which will be described in more detail below. These drawings and descriptions are not intended to limit the scope of the concept in any way, but rather to illustrate the concept of this application to those skilled in the art through reference to particular embodiments. Detailed Implementation

[0032] To make the objectives, technical solutions, and advantages of this invention clearer, the technical solutions of this invention will be clearly and completely described below in conjunction with specific embodiments and with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of this invention. All other embodiments obtained by those skilled in the art based on the embodiments of this invention without creative effort are within the scope of protection of this invention.

[0033] Example 1 like Figure 2 As shown, this embodiment provides a frequency-shift PGC demodulation method based on frequency domain extraction, including the following steps: Step 1, set up as follows Figure 1 The Mach-Zehnder interferometer sensing system shown in the diagram uses a laser (representing a laser beam to provide highly coherent continuous light), a coupler (OC), a circulator (Cir), a polarization controller (PC) to adjust the polarization state of the reference light, an acousto-optic modulator (AOM), an electrical signal amplifier (AMP), a signal generator (SG), a balanced photodetector (BPD), an oscilloscope (OSC), a piezoelectric transducer (PZT), and a sensor (used to convert the measured signal into an optical phase signal). Specifically, the coupler OC1 splits an incident light beam into two paths. One path enters port 1 of the circulator and exits from port 2 to the sensing arm. The piezoelectric transducer PZT modulates the light in the sensing arm with a high-frequency carrier, providing the necessary carrier signal for subsequent phase generation carrier (PGC) demodulation. The sensing arm is exposed to the environment under test. The signal under test causes strain in the sensor, which in turn changes the phase of the light wave (containing the signal under test). The light reflected from the sensing arm enters through port 2, exits through port 3 of the circulator, and enters coupler OC2. Another beam of light enters the reference arm as a reference beam. The acousto-optic modulator AOM applies a fixed frequency shift to the reference beam, shifting the spectrum of the interference signal to a higher frequency band. Coupler OC2 recombines the two beams, causing interference.

[0034] The sensing light is coupled with the reference light after AOM frequency shifting to obtain an interference light signal. The interference light signal is then converted into an initial digital interference signal after photoelectric conversion and analog-to-digital conversion. Initial digital interference signal The expression is: (1) in, For signal amplitude, , , The signals to be measured are respectively amplitude, angular frequency This is a noise signal. For time, This is the initial phase.

[0035] Step 2: Obtain the frequency by performing a Fast Fourier Transform (FFT) on the initial digital interference signal. , , , , amplitude at , , , , For amplitude The modulus is defined as Argument is , According to amplitude , Calculate the carrier phase delay and construct complex numbers , , , , The angular frequency of the AOM modulated signal. This is the carrier angular frequency.

[0036] use Expanding the trigonometric form of formula (1) into the complex exponential form of formula (2), and considering only the positive frequency part, i.e., deleting the expanded terms. ,get: (2) Applying the Jacobi-Anger Expansion formula (2) ,get: (3) Substituting formula (3) into formula (2) yields: (4) This can be further expanded. The factors affecting the magnitude and amplitude of the nth-order carrier signal in the expansion are those not present in the expansion. i item By analyzing formula (4), we can obtain the complex signal. Length of the module Argument for:

[0037]

[0038] Define function exist When the value is greater than or equal to 0, the value is 0. When less than 0, the value is taken as The representation of the complex amplitude in the complex domain is shown in Figure 3. Figure 3 illustrates the effects of carrier phase delay and initial phase on the complex signal. Figure 3(a) shows the first four orders of the signal when there is no phase delay and the initial phase is 0. , , , Figure 3(b) shows the effect of the initial phase on the signal, Figure 3(c) shows the effect of the carrier phase delay on the signal, and Figure 3(d) shows the effect of the simultaneous presence of the initial phase and the carrier phase delay on the signal.

[0039] According to formula (4), we can obtain: The modulus length is Argument is . The modulus length is , The modulus length is , The modulus length is , The modulus length is .

[0040] According to amplitude , Calculate the carrier phase delay The method is as follows: According to amplitude , Constructing complex numbers : ,in, Represents the imaginary unit; complex number Dividing the imaginary part by the real part and then taking the arctangent yields the carrier phase delay. By dividing the complex signals of adjacent orders by... This yields an argument equal to the carrier phase delay. The complex number is used to calculate the carrier phase delay by calculating its argument.

[0041] In the complex field, it is equivalent to Rotated clockwise The argument of is expressed in the formula as:

[0042] The calculation results contain only:

[0043] formula Divide by the imaginary unit It was later eliminated. ,and The calculation results are only 0 All three results, regardless of which one, affect the modulation depth. The calculations are unaffected. At this point, it can be considered that an argument of [value] has been obtained. To find the argument of a complex number, we can calculate the argument of that complex number. .

[0044] Step 3: Based on amplitude , and complex numbers Calculate the complex number , Calculate complex numbers The magnitude of the sign effect Based on the modulus considering the influence of sign Calculate the modulation depth Modulation depth Substitute into MATLAB software to obtain parameters ,parameter .

[0045] According to amplitude , and complex numbers Calculate the complex number The method is as follows:

[0046] in, ,plural The argument is or ,when When the result is positive, the complex number The argument is ,when When the result is negative, the complex number The argument is . The argument is the initial phase. The argument is the carrier phase delay, expressed by the formula. Calculate the complex number Then, by determining whether its argument lies on the positive or negative half-axis of the y-axis, we can determine whether the first-order Bessel function is positive or negative.

[0047] Similarly, we can obtain the nth order signal divided by and New signals after ,plural The argument is or : ,when When the result is positive, the complex number The argument is ,when When the result is negative, the complex number The argument is .

[0048] ,when When the result is positive, the complex number The argument is ,when When the result is negative, the complex number The argument is .

[0049] ,when When the result is positive, the complex number The argument is ,when When the result is negative, the complex number The argument is .

[0050] Therefore, when , , , When all results are positive, complex numbers The argument is ,plural The argument is ,plural The argument is ,plural The argument is The first four levels of signals , , , The symbols are positive, negative, negative, positive in sequence.

[0051] By rotating the complex number, the influence of the operating point and carrier phase delay is eliminated, and the first four orders of signals are rotated onto the coordinate axis. The sign of the signal is determined by judging whether it is located on the positive or negative half axis.

[0052] Compare the actual calculation results with the signals of the first four orders. , , , By considering the similarities and differences in the symbols, we can obtain the modulus that takes into account the influence of the symbols. The sign of the value, combined with the magnitude considering the effect of the sign. The modulation depth can be calculated using the recursive formula. C Size.

[0053] plural The magnitude of the sign effect for:

[0054] in, , This represents the function for finding the modulus of a complex number. , , , , , These represent finding the imaginary and real parts of a complex number, respectively. For a sign function, when the sign is positive, When the value is 1 and the sign is negative, It is -1.

[0055] thus, , , ,

[0056] Based on the modulus considering the influence of sign Calculate the modulation depth The method is as follows:

[0057] in, , , , These are the modulus lengths considering the influence of sign. exist The values ​​are 1, 2, 3, and 4.

[0058] By processing the initial digital interference signal The modulation depth and carrier phase delay are obtained from the spectrum calculation.

[0059] Step 4: Based on carrier phase delay For reference signal , Compensation is performed to obtain a reference signal. , The initial digital interferometric signal, after being bandpass filtered, is compared with the reference signal. , After multiplication and low-pass filtering, the first and second mixed signals are obtained. First mixed signal divided by parameter The result is divided by the parameter of the second mixed signal. Divide the result to obtain the signal to be processed. Perform arctangent operation and phase unwrapping on the signal to be processed to obtain the signal to be measured.

[0060] Traditional PGC demodulation improvement methods approach a specific value at the operating point (initial phase). , When the value is a positive integer, only first- and third-order carrier signals or second- and fourth-order carrier signals exist in the frequency domain. Whether calculating modulation depth, carrier phase delay, or signal demodulation, the calculated results will significantly deviate from the actual values. This invention introduces AOM to change the light intensity formula, ensuring that the first four harmonics exist under various operating point conditions, thus achieving smooth demodulation (see results). Figure 6 ).

[0061] Traditional PGC demodulation improvement methods require differentiation and division calculations when calculating carrier phase delay in the time domain, which can easily introduce nonlinearity and cause problems when the denominator is zero. This invention calculates carrier phase delay in the frequency domain using complex phase angles, enabling calculations across the entire phase range. This complex-domain-based modulation depth symbol determination method solves the operating point and carrier phase delay calculation singularity problems existing in PGC demodulation algorithms.

[0062] This invention calculates and compensates for modulation depth and carrier phase delay by extracting the frequency domain signal after performing an FFT on the interference signal and obtaining the frequency domain amplitude (complex number) of carrier signals of different orders. A new complex number is constructed by dividing adjacent order (1st to 4th order) complex amplitudes, and the argument of the new complex number is calculated, which represents the carrier phase delay. θ .

[0063] According to the recursive formula of the Bessel function, the modulation depth can be calculated and compensated from the amplitudes of complex signals of orders 1 to 4. However, as the modulation depth continues to increase, the sign of the Bessel function changes, requiring the addition of an appropriate sign before the complex signal amplitude to achieve accurate calculation. To solve this problem, the method adopted in this invention is as follows: extract the 0th-order carrier signal (the nth-order carrier frequency is...). The frequency domain amplitude (complex number) of ) will n Frequency domain amplitude of the first carrier signal divided by n The angle constructed in the previous step is θ The new complex number is then divided by the 0th-order carrier signal (to eliminate the influence of the initial phase), rotating the complex signal amplitude onto the coordinate axes. This amplitude is then compared to the positions of the 1st to 4th-order complex signals (positive y-axis, negative x-axis, negative y-axis, positive x-axis) when both the phase angle and initial phase are 0. If the amplitude differs from this state, a sign is added before the amplitude. This method enables sign determination, allowing for accurate calculation of the modulation depth over a wider range.

[0064] This invention extracts five complex amplitudes corresponding to the 0th to 4th order carriers after performing an FFT on the interference signal. Based on these, the modulation depth and carrier phase delay can be calculated. The calculation method is simple and has a large calculation range. This invention does not require controlling the modulation depth to 2.63, and the calculated modulation depth is a fixed value rather than subject to small fluctuations over time.

[0065] When the interference working point is close to k At π / 2, traditional methods for calculating and compensating for modulation depth and carrier phase delay based on time or frequency domains will result in computational singularities due to the disappearance of 1st and 3rd order or 2nd and 4th order signals. The first 4 order signals of this invention are always present at the computational singularities corresponding to the traditional methods and can still accurately calculate key parameters, thus eliminating computational singularities.

[0066] Set the parameters of the simulation signal as follows: the amplitude of the signal under test is 0.5 rad, the frequency is 300 Hz, the carrier signal frequency is 40 kHz, the AOM modulation frequency is 82.5 MHz, the sampling frequency is 10 MHz, and the amplitude of the interference signal is 1. Figure 4 , 5 Figure 6 shows the demodulation results for the simulated signal under different modulation depths, carrier phase delays, and operating points. The method is insensitive to changes in modulation depth, carrier phase delay, and operating point, and can achieve correct demodulation of the signal under test. This proves that the algorithm successfully eliminates the influence of nonlinear factors in the demodulation results, and the demodulation method has high stability in actual demodulation.

[0067] Example 2 See Figure 7 This embodiment provides a frequency-shift PGC demodulation system based on frequency domain extraction, including: The signal processing module couples the sensing light with a reference light that has undergone AOM frequency shifting to obtain an interference light signal. This interference light signal is then converted from light to light by photoelectric conversion and analog to digital conversion to obtain an initial digital interference signal. The expression is:

[0068] in, For signal amplitude, , , The signals to be measured are respectively amplitude, angular frequency This is a noise signal. For time, This is the initial phase.

[0069] The carrier phase delay calculation module is used to obtain the frequency after performing an FFT on the initial digital interferometric signal. , , , , amplitude at , , , , According to amplitude , Calculate the carrier phase delay and construct complex numbers , , , , The angular frequency of the AOM modulated signal. The carrier angular frequency; based on the amplitude , Calculate the carrier phase delay The method is as follows: According to amplitude , Constructing complex numbers : ,in, Represents the imaginary unit; complex number Dividing the imaginary part by the real part and then taking the arctangent yields the carrier phase delay. .

[0070] Modulation depth calculation module, used to calculate based on amplitude , and complex numbers Calculate the complex number , Calculate complex numbers The magnitude of the sign effect Based on the modulus considering the influence of sign Calculate the modulation depth Modulation depth Substitute into MATLAB software to obtain parameters ,parameter According to amplitude , and complex numbers Calculate the complex number The method is as follows:

[0071] plural The magnitude of the sign effect for:

[0072] in, , This represents the function for finding the modulus of a complex number. , , , , , These represent finding the imaginary and real parts of a complex number, respectively. For a sign function, when the sign is positive, When the value is 1 and the sign is negative, It is -1.

[0073] Based on the complex modulus considering the influence of sign Calculate the modulation depth The method is as follows:

[0074] in, , , , These are the modulus lengths considering the influence of sign. exist The values ​​are 1, 2, 3, and 4.

[0075] Demodulation module, used for carrier phase delay-based... For reference signal , Compensation is performed to obtain a reference signal. , The initial digital interference signal is compared with the reference signal. , After multiplication and low-pass filtering, a first mixed signal and a second mixed signal are obtained; the first mixed signal is divided by the parameter. The result is divided by the parameter of the second mixed signal. Divide the result to obtain the signal to be processed. Perform arctangent operation and phase unwrapping on the signal to be processed to obtain the signal to be measured.

[0076] The above embodiments are only used to illustrate the technical solutions of the present invention, and are not intended to limit it. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A frequency-shift PGC demodulation method based on frequency domain extraction, characterized in that: include: The sensing light is coupled with the reference light after AOM frequency shifting to obtain an interference light signal. The interference light signal is then converted into an initial digital interference signal after photoelectric conversion and analog-to-digital conversion. The frequency is obtained by performing an FFT on the initial digital interference signal. , , , , amplitude at , , , , According to amplitude , Calculate the carrier phase delay and construct complex numbers , , , , The angular frequency of the AOM modulated signal. The carrier angular frequency; According to amplitude , and complex numbers Calculate the complex number , Calculate complex numbers The magnitude of the sign effect Based on the modulus considering the influence of sign Calculate the modulation depth Based on modulation depth Calculate the parameters ,parameter ; Based on carrier phase delay For reference signal , Compensation is performed to obtain a reference signal. , The initial digital interference signal is compared with the reference signal. , After multiplication and low-pass filtering, the first and second mixed signals are obtained. First mixed signal divided by parameter The result is divided by the parameter of the second mixed signal. Divide the result to obtain the signal to be processed. Perform arctangent operation and phase unwrapping on the signal to be processed to obtain the signal to be measured.

2. The frequency-shift PGC demodulation method based on frequency domain extraction according to claim 1, characterized in that: Initial digital interference signal The expression is: in, For signal amplitude, , , The signals to be measured are respectively amplitude, angular frequency This is a noise signal. For time, This is the initial phase.

3. The frequency-shift PGC demodulation method based on frequency domain extraction according to claim 1, characterized in that: According to amplitude , Calculate the carrier phase delay The method is as follows: According to amplitude , Constructing complex numbers : ,in, Represents the imaginary unit; complex number Dividing the imaginary part by the real part and then taking the arctangent yields the carrier phase delay. .

4. The frequency-shift PGC demodulation method based on frequency domain extraction according to claim 1, characterized in that: According to amplitude , and complex numbers Calculate the complex number The method is as follows: 。 5. The frequency-shift PGC demodulation method based on frequency domain extraction according to claim 1, characterized in that: plural The magnitude of the sign effect for: in, , This represents the function for finding the modulus of a complex number. , , , , , These represent finding the imaginary and real parts of a complex number, respectively. For a sign function, when the sign is positive, When the value is 1 and the sign is negative, It is -1.

6. The frequency-shift PGC demodulation method based on frequency domain extraction according to claim 1, characterized in that: Based on the modulus considering the influence of sign Calculate the modulation depth The method is as follows: in, , , , These are the modulus lengths considering the influence of sign. exist The values ​​are 1, 2, 3, and 4.

7. A frequency-shift PGC demodulation system based on frequency domain extraction, characterized in that: include: The signal processing module is used to couple the sensing light with the reference light after AOM frequency shifting to obtain an interference light signal. The interference light signal is then converted into an initial digital interference signal after photoelectric conversion and analog-to-digital conversion. The carrier phase delay calculation module is used to obtain the frequency after performing an FFT on the initial digital interferometric signal. , , , , amplitude at , , , , According to amplitude , Calculate the carrier phase delay and construct complex numbers , , , , The angular frequency of the AOM modulated signal. The carrier angular frequency; Modulation depth calculation module, used to calculate based on amplitude , and complex numbers Calculate the complex number , Calculate complex numbers The magnitude of the sign effect Based on the modulus considering the influence of sign Calculate the modulation depth Based on modulation depth Calculate the parameters ,parameter ; Demodulation module, used for carrier phase delay-based... For reference signal , Compensation is performed to obtain a reference signal. , The initial digital interference signal is compared with the reference signal. , After multiplication and low-pass filtering, a first mixed signal and a second mixed signal are obtained; the first mixed signal is divided by the parameter. The result is divided by the parameter of the second mixed signal. Divide the result to obtain the signal to be processed. Perform arctangent operation and phase unwrapping on the signal to be processed to obtain the signal to be measured.

8. The frequency-shift PGC demodulation system based on frequency domain extraction according to claim 7, characterized in that: According to amplitude , Calculate the carrier phase delay The method is as follows: According to amplitude , Constructing complex numbers : ,in, Represents the imaginary unit; complex number Dividing the imaginary part by the real part and then taking the arctangent yields the carrier phase delay. .

9. The frequency-shift PGC demodulation system based on frequency domain extraction according to claim 7, characterized in that: According to amplitude , and complex numbers Calculate the complex number The method is as follows: 。 10. The frequency-shift PGC demodulation system based on frequency domain extraction according to claim 7, characterized in that: plural The magnitude of the sign effect for: in, , This represents the function for finding the modulus of a complex number. , , , , , These represent finding the imaginary and real parts of a complex number, respectively. For a sign function, when the sign is positive, When the value is 1 and the sign is negative, It is -1.

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