A method for demodulating low frequency signals by an improved phase generation carrier algorithm

Abstract

The application belongs to the field of optical fiber interference measurement and phase generated carrier demodulation technology, and particularly relates to a method for improving a phase generated carrier algorithm to demodulate a low-frequency signal, which is based on three times frequency phase generated carrier mixing, uses an inverse tangent algorithm to demodulate a low-frequency signal, and is combined with an ellipse fitting algorithm to correct non-orthogonal signals and compensate linear errors in real time. In the process of demodulating a low-frequency signal, the application is not affected by carrier modulation depth and light intensity disturbance, avoids the direct current drift problem existing in traditional PGC-DCM in low-frequency signal demodulation, improves the accuracy of demodulation results, and reduces the interference of error factors.

Description

Technical Field

[0001] This invention belongs to the fields of fiber optic interferometry and phase generation carrier demodulation technology, and is used for signal demodulation in interferometric fiber optic sensing systems. Specifically, it relates to an improved method for demodulating low-frequency signals using a phase generation carrier algorithm. Background Technology

[0002] For interferometric fiber optic sensing systems, the light intensity signal is usually obtained directly. By demodulating the phase signal in the light intensity, the phase measurement change is inverted to achieve indirect measurement of the physical quantity to be measured. Therefore, the phase demodulation method is particularly important. Currently, commonly used demodulation techniques can be divided into active homodyne, closed-loop operating point control, 3×3 coupler multiphase detection, and phase generation carrier (PGC) demodulation.

[0003] Active zero-difference detection is a closed-loop testing scheme. This scheme introduces strong low-frequency noise during the process of applying a compensation signal to the modulator. Closed-loop operating point control is a pseudo-zero-difference method. When the system is applied in the low-frequency band, the detection signal is in the same frequency band as the external interference, so it is not suitable for low-frequency signal detection. The demodulation method of 3×3 coupler multiphase detection has the advantages of simplicity, large dynamic range and suitability for low-frequency signals. However, under low-frequency conditions, due to the lack of modulation process to process and protect the signal, the system is more susceptible to external low-frequency interference and influence.

[0004] Phase Generated Carrier (PGC) demodulation is an active passive homodyne demodulation algorithm used to demodulate signals from interferometric fiber optic sensors. This demodulation algorithm converts changes in interference light intensity into changes in phase amplitude. It is suitable for low-frequency signal detection and has advantages such as strong anti-interference capability, high modulation efficiency, and good signal quality. PGC demodulation applies a high-frequency carrier modulation signal, transforming the measured field signal into a sideband of the carrier signal. Then, through low-pass filtering, mixing, and high-pass filtering, noise interference is removed, extracting the intensity and phase information of the weak low-frequency signal from the carrier signal. In demodulation, the Differential Cross-Multiplication (PGC-DCM) algorithm and the Arctangent (PGC-Arctan) algorithm are among the most commonly used algorithms.

[0005] Analysis of the demodulation results shows that the PGC-DCM algorithm is affected by factors such as interferometric visibility, light intensity, and modulation depth. Furthermore, the presence of an integrator during demodulation inevitably introduces a DC term. Since the measured field signal is a low-frequency signal, it cannot be filtered out using a high-pass filter, resulting in DC drift in the demodulation results. While the PGC-Arctan algorithm is not affected by light source instability, it can only demodulate low-frequency signals without distortion when the modulation depth is 2.63 rad. Summary of the Invention

[0006] The purpose of this invention is to address the impact of factors such as interference visibility, light intensity, and modulation depth on the GC-DCM algorithm, and to propose an improved method for demodulating low-frequency signals using a phase-generated carrier algorithm.

[0007] To achieve the above-mentioned objectives, the present invention adopts the following technical solution:

[0008] An improved phase-generated carrier algorithm for demodulating low-frequency signals involves applying a high-frequency carrier modulation signal to transform the field signal under test into a sideband of that carrier signal, and then converting the first-harmonic carrier signal Gcosω... c Second harmonic carrier signal Hcos2ω c Third harmonic carrier signal Dcos3ω c The signals are multiplied by the interference output signal respectively, and the results are low-pass filtered to obtain I1, I2 and I3. The result of subtracting the I1 signal from the I3 signal and the I2 signal is used to estimate and correct the modulation depth through elliptic fitting. The corrected orthogonal signals are divided and the arctangent is calculated to obtain the low-frequency signal to be measured.

[0009] The interference output signal is:

[0010]

[0011] A represents DC bias, and B represents AC amplitude. Let C be the phase of the signal to be measured, and C be the modulation depth of the phase modulator, cosω c t is the phase carrier signal; the first-harmonic carrier signal Gcosω c Second harmonic carrier signal Hcos2ω c Third harmonic carrier signal Dcos3ω c The signal is mixed with the interferometer output signal I, and then passed through a low-pass filter with a cutoff frequency between the frequency of the signal under test and the carrier frequency.

[0012]

[0013]

[0014]

[0015] Wherein, J1(C) is a first-order Bessel function of the first kind, J2(C) is a second-order Bessel function of the first kind, and J3(C) is a third-order Bessel function of the first kind.

[0016] Subtracting I3(t) from I1(t), we get:

[0017]

[0018] Let L2(t) = I2(t), then divide L1(t) by L2(t) to get

[0019]

[0020] In practical applications, factors such as carrier phase delay, light intensity disturbance, modulation depth fluctuations, and non-ideal performance of low-pass filters, as well as electronic noise, can cause dynamic changes in the DC offset and AC amplitude of orthogonal signals. The general expressions for L1(t) and L2(t) can be rewritten as:

[0021] L1(t) = a(t) + b(t)cosθ(t)

[0022] L2(t)=c(t)+d(t)cos[θ(t)+δ]

[0023] In the formula, a(t) and c(t) are DC offsets, b(t) and d(t) are AC amplitudes, and θ(t) is the signal to be measured. δ represents the phase difference between the two signals, and L1(t) and L2(t) are fitted to an ellipse x 2 +A1xy+A2y 2 +A3x+A4y+A5=0, and the values ​​of A1-A5 are obtained based on the fitting results.

[0024]

[0025]

[0026]

[0027]

[0028]

[0029] calculate Feedback is provided on the final demodulation amplitude to improve demodulation accuracy.

[0030] The L1(t) and L2(t) signals are corrected as follows:

[0031] cosθ(t)=[L1(t)-a] / b

[0032]

[0033] Finally, the low-frequency signal to be measured is obtained by dividing the two orthogonal signals and calculating their arctangents.

[0034] The output signal of the fiber optic interferometric sensing system is converted from an optical signal to an electrical signal by a photodetector. The signal is then acquired by a data acquisition card and input to an FPGA high-speed data processing platform for demodulation using a phase generation carrier algorithm. The signal measurement device of the fiber optic interferometric sensing system includes a laser, fiber optic coupler, sensing fiber, reference fiber, phase modulator, Faraday rotator, photodetector, data acquisition card, and FPGA high-speed data processing platform.

[0035] The laser's output port is connected to a 2×2 fiber coupler 2. The 2×2 fiber coupler splits the optical signal into two paths. The first path is reflected back to the 2×2 fiber coupler 2 by a Faraday rotator at the end of the sensing fiber. The second path is phase-modulated by a phase modulator along the reference fiber and reflected by a Faraday rotator at the end of the reference fiber, ultimately interfering with the first path at the 2×2 fiber coupler 2. When an external low-frequency signal acts on the sensing fiber, the optical phase in the sensing fiber is modulated, and the corresponding phase difference between the optical signals in the sensing fiber and the reference fiber also changes. This change is ultimately reflected in the light intensity change detected by the photodetector. The signal is acquired by a data acquisition card and input to the FPGA high-speed data processing platform for demodulation using an improved phase-generating carrier algorithm.

[0036] The FPGA high-speed data processing platform includes: a DDS sine wave generator, a mixer, a multiplier, a low-pass filter, a subtractor, an ellipse fitting module, a divider, and an arctangent module.

[0037] Improved phase generation carrier demodulation includes the following steps:

[0038] (1) Obtain the carrier-modulated interference light intensity signal;

[0039] (2) The DDS sinusoidal signal generator generates a fundamental frequency carrier signal, a second harmonic carrier signal, and a third harmonic carrier signal; the fundamental frequency carrier signal, the second harmonic carrier signal, and the third harmonic carrier signal are mixed with the interference signal respectively;

[0040] (3) The mixed signal is passed through a low-pass filter with a cutoff frequency between the frequency of the signal under test and the carrier frequency.

[0041] (4) Process the low-pass filter output signal according to the Bessel function recursion principle, and demodulate the phase modulation depth in real time by elliptic fitting, and generate two orthogonal signals.

[0042] (5) Finally, the two orthogonal signals are divided and the arctangent is calculated to obtain the low-frequency signal to be measured.

[0043] The beneficial effects of this invention are:

[0044] This invention discloses an improved method for demodulating low-frequency signals using a phase-generated carrier algorithm. By combining third-harmonic mixing with an elliptic fitting algorithm, this method is unaffected by modulation depth and light intensity disturbances in the demodulation results. Furthermore, it avoids the DC offset problem in low-frequency signal demodulation by eliminating the integrator module required in the PGC-DCM demodulation algorithm. The elliptic fitting algorithm module corrects non-orthogonal signals and compensates for amplitude linearity errors, thereby achieving accurate demodulation of low-frequency signals. In the low-frequency band (20Hz–1kHz), this invention achieves a total harmonic distortion of 0.04%, a signal-to-noise ratio of 65.77dB, and a root mean square error of 0.002rad. Attached Figure Description

[0045] Figure 1 A signal measurement device for a fiber optic Michelson interferometric sensing system

[0046] Figure 2 A method for demodulating low-frequency signals using an improved phase-generated carrier algorithm.

[0047] Figure 3 The sum and spectrum of the interferometric signal output by the interferometric sensing system

[0048] Figure 4 Spectrum diagram for signal demodulation Detailed Implementation

[0049] The technical solutions of the present invention will be clearly and completely described below in the embodiments. Obviously, the embodiments described herein represent only a part of the present invention, and not all embodiments. Based on the present invention, those skilled in the art can obtain all other embodiments without creative work, and these embodiments are also protected by the present invention.

[0050] The present invention will be further described below with reference to the accompanying drawings and examples.

[0051] Example 1:

[0052] The output signal of the fiber optic interferometric sensing system is converted into an electrical signal by a photodetector. The signal is then acquired by a data acquisition card and input to the FPGA high-speed data processing platform for demodulation using a phase generation carrier algorithm. The phase generation carrier demodulation module includes a DDS sine wave generator, a mixer, a multiplier, a low-pass filter, an ellipse fitting module, a divider, and an arctangent module.

[0053] The fiber optic interferometric sensing system mainly includes a laser, fiber optic coupler, phase modulator, sensing fiber, reference fiber, Faraday rotator, photodetector, data acquisition card, and FPGA high-speed data processing platform.

[0054] The laser's output port is connected to a 2×2 coupler. The 2×2 fiber coupler splits the optical signal into two paths: one path travels along the sensing fiber, is reflected back to the 2×2 fiber coupler by a Faraday rotator at the end of the sensing fiber, and the other path travels along the reference fiber, is phase-modulated by a phase modulator, is reflected by a Faraday rotator at the end of the reference fiber, and finally interferes at the 2×2 coupler, forming a Michelson interferometer; the interference signal reaches the detector via the fiber coupler. The intensity of the optical interference signal is related to the phase difference between the two beams. When a weak low-frequency signal acts on the sensing fiber, the phase of the light in the sensing fiber is modulated, and the corresponding phase difference between the optical signals in the sensing fiber and the reference fiber also changes.

[0055] The phase modulator is a PZT piezoelectric ceramic. By winding a single-mode optical fiber in the interferometer arm, a high-frequency carrier signal generated by a function generator is applied to the PZT piezoelectric ceramic, thereby modulating the phase of the interferometric output signal.

[0056] Specifically, the interference output signal I is compared with the frequency harmonic carrier signal Gcosω. c Second harmonic carrier signal Hcos2ω c Third harmonic carrier signal Dcos3ω c The results are multiplied and then low-pass filtered to obtain I1, I2, and I3. The result of subtracting the I3 signal from the I1 signal and the I2 signal are used to estimate and correct the modulation depth through the ellipse fitting module. The corrected orthogonal signals are divided and the arctangent module is used to calculate the low-frequency signal to be tested.

[0057] Specifically, the output signal of the interferometer is:

[0058]

[0059] A represents DC bias, and B represents AC amplitude. Let C be the phase of the signal to be measured, and C be the modulation depth of the phase modulator, cosω c t is the phase carrier signal. The phase can be calculated by demodulating the phase using a phase-generated carrier algorithm. The first-harmonic carrier signal Gcosω c Second harmonic carrier signal Hcos2ω c Third harmonic carrier signal Dcos3ω c The signal is mixed with the interferometer output signal I, and then passed through a low-pass filter with a cutoff frequency between the frequency of the signal under test and the carrier frequency.

[0060]

[0061]

[0062]

[0063] Where J1(C) is a first-order Bessel function of the first kind, J2(C) is a second-order Bessel function of the first kind, and J3(C) is a third-order Bessel function of the first kind, according to the recurrence relation of Bessel functions: Subtracting I3(t) from I1(t), we get:

[0064]

[0065] Let L2(t) = I2(t), then dividing L1(t) by L2(t) gives:

[0066]

[0067] In practical applications, factors such as non-ideal performance and electronic noise can cause dynamic changes in the DC offset and AC amplitude of orthogonal signals. Therefore, the general expressions for L1(t) and L2(t) can be rewritten as:

[0068] L1(t) = a(t) + b(t)cosθ(t)

[0069] L2(t)=c(t)+d(t)cos[θ(t)+δ]

[0070] In the formula, a(t) and c(t) are DC offsets, b(t) and d(t) are AC amplitudes, and θ(t) is the signal to be measured. δ represents the phase difference between the two signals. Therefore, L1(t) and L2(t) can be fitted to an ellipse, and expressed as:

[0071] x 2 +A1xy+A2y 2 +A3x+A4y+A5=0

[0072] a(t), b(t), c(t), and d(t) can be calculated:

[0073]

[0074]

[0075]

[0076]

[0077]

[0078] The purpose of ellipse fitting here is:

[0079] (1) Calculation Feedback is provided on the final demodulation amplitude to improve demodulation accuracy.

[0080] (2) Correct the L1(t) and L2(t) signals to:

[0081] cosθ(t)=[L1(t)-a] / b

[0082]

[0083] Finally, the low-frequency signal to be measured is obtained by dividing the two orthogonal signals and calculating their arctangents.

[0084] Example 2:

[0085] refer to Figure 1 A signal measurement device for a fiber optic Michelson interferometer sensing system is provided, comprising a laser 1, a fiber coupler 2, a sensing fiber 3, a reference fiber 5, a phase modulator 6, Faraday rotating mirrors 4 and 7, a photodetector 8, a data acquisition card 9, and an FPGA high-speed data processing platform 10.

[0086] In this embodiment, the output port of laser 1 is connected to port 21 of 2×2 fiber coupler 2. 2×2 fiber coupler 2 splits the optical signal into two paths: one path follows the sensing fiber 3, is reflected back to 2×2 fiber coupler 2 by Faraday rotator 4 at the end of sensing fiber 3, and the other path follows the reference fiber 5, is phase-modulated by phase modulator 6, is reflected by Faraday rotator 4 at the end of reference fiber 5, and finally interferes at 2×2 fiber coupler 2. The intensity of the optical interference signal is related to the phase difference between the two beams. When an external low-frequency signal acts on sensing fiber 3, the phase of the light in sensing fiber 3 is modulated, and the corresponding phase difference between the optical signals in sensing fiber 3 and reference fiber 5 also changes, ultimately reflected as a change in light intensity detected by photodetector 8. The signal is acquired by data acquisition card 9 and input to FPGA high-speed data processing platform 10 for demodulation using the improved phase generation carrier algorithm of this invention.

[0087] In this embodiment, the phase modulator 6 is a PZT piezoelectric ceramic. By winding a single-mode optical fiber on the PZT piezoelectric ceramic, a high-frequency carrier signal generated by a function generator is applied to the PZT piezoelectric ceramic, thereby modulating the phase of the interference output signal.

[0088] In this embodiment, the interference signal output by the photodetector 8 is acquired by the 16-bit data acquisition card 9 with a sampling frequency of 1M / s and a storage depth of 64M.

[0089] The system output interference light intensity acquired by data acquisition card 9 is:

[0090]

[0091] A is the DC bias, B is the AC amplitude, ω is the phase of the signal under test, C is the modulation depth of the phase modulator, and cosω is the phase angle. c t is the phase carrier signal.

[0092] like Figure 2 As shown, an improved phase generation carrier algorithm demodulates low-frequency signals. The FPGA high-speed data processing platform 10 includes a baseband carrier signal 10-1, a second harmonic carrier signal 10-2, a third harmonic carrier signal 10-3, multipliers 10-4, 10-5, and 10-6, low-pass filters 10-7, 10-8, and 10-9, a subtractor 10-10, an ellipse fitting module 10-11, a divider 10-12, and an arctangent module 10-13.

[0093] In this embodiment, a DDS sine wave generator is used to generate a fundamental frequency carrier signal, a second harmonic carrier signal, and a third harmonic carrier signal. These signals are then mixed with an interference signal, and the resulting signals are passed through a low-pass filter with a cutoff frequency between the frequency of the signal under test and the carrier frequency.

[0094]

[0095]

[0096]

[0097] Where J1(C) is a first-order Bessel function of the first kind, J2(C) is a second-order Bessel function of the first kind, and J3(C) is a third-order Bessel function of the first kind, according to the recurrence relation of Bessel functions: Subtracting I3(t) from I1(t), we get:

[0098]

[0099] Let L2(t) = I2(t), then dividing L1(t) by L2(t) gives:

[0100]

[0101] In practical applications, factors such as non-ideal performance and electronic noise can cause dynamic changes in the DC offset and AC amplitude of orthogonal signals. Therefore, the general expressions for L1(t) and L2(t) can be rewritten as:

[0102] L1(t) = a(t) + b(t)cosθ(t)

[0103] L2(t)=c(t)+d(t)cos[θ(t)+δ]

[0104] In the formula, a(t) and c(t) are DC offsets, b(t) and d(t) are AC amplitudes, and θ(t) is the signal to be measured. δ represents the phase difference between the two signals. Therefore, L1(t) and L2(t) can be fitted to an ellipse, and expressed as:

[0105] x 2 +A1xy+A2y 2 +A3x+A4y+A5=0

[0106] Therefore, a(t), b(t), c(t), and d(t) can be calculated:

[0107]

[0108]

[0109]

[0110]

[0111]

[0112] The purpose of ellipse fitting here is:

[0113] (1) Calculation Feedback is provided on the final demodulation amplitude to improve demodulation accuracy.

[0114] (2) Correct the L1(t) and L2(t) signals to:

[0115] cosθ(t)=[L1(t)-a] / b

[0116]

[0117] Finally, the low-frequency signal to be measured is obtained by dividing the two orthogonal signals and calculating their arctangents.

[0118] The device selection and parameters for the PGC algorithm demodulation low-frequency signal test device are as follows:

[0119] (1) Laser 1: A narrow linewidth laser with a center wavelength of 1550nm, an output power of 12m, and a linewidth of approximately 0.0179nm;

[0120] (2) Fiber optic coupler 2: operating wavelength 1550nm, splitting ratio 50%:50%, insertion loss ≤3.7dB;

[0121] (3) Sensing fiber 3: 10m magnetorefractive doped fiber;

[0122] (4) Faraday Rotation Mirror 4: 1550nm fiber Faraday Rotation Mirror, single-pass rotation angle 45°, maximum insertion loss 0.6dB (at 25℃).

[0123] (5) Phase modulator 6: PZT piezoelectric ceramic phase modulator, the optical phase modulation constant is 6 rad / V at the resonant frequency (27~32kHz) and 0.3 rad / V at the non-resonant frequency;

[0124] (6) Photodetector 8: Type is InGaAs / PIN photodetector, connection mode is

[0125] FC / APC type, operating wavelength between 1200 and 1700 nm, total output voltage noise <9mV RMS ;

[0126] (7) Data acquisition card 9: sampling rate 1MS / s, 4-channel synchronous 16-bit analog input, input voltage amplitude ±10V, sampling clock is the internal clock of the acquisition card, memory depth 64M, input impedance 10MΩ;

[0127] use Figure 1 An experiment was conducted using a fiber optic Michelson interferometric sensing system signal measurement device. A 1kHz high-frequency carrier wave was applied to the PZT piezoelectric ceramic via one path, while a 20Hz sensing signal was applied to the other sensing fiber 3. The spectrum of the acquired interferometric signal is shown below. Figure 3 As shown, the 20Hz signal is buried in the low-frequency band, and a spectrum analyzer cannot extract the low-frequency signal.

[0128] Therefore, the algorithm of this invention is used to demodulate the signal, and the demodulation result is as follows. Figure 4 As shown, the 20Hz sensor signal was effectively extracted.

[0129] The embodiments described above are merely preferred embodiments of the present invention and are not intended to limit the invention. Those skilled in the art can make various changes and modifications without departing from the spirit and scope of the invention. Therefore, all technical solutions obtained through equivalent substitution or transformation fall within the protection scope of the present invention.

Claims

1. A method for demodulating low-frequency signals using an improved phase-generating carrier algorithm, characterized in that: By applying a high-frequency carrier modulation signal, the field signal under test is transformed into a sideband of that carrier signal, and the first-harmonic carrier signal is transformed into a second-harmonic carrier signal. Second harmonic carrier signal Third harmonic carrier signal The signals are multiplied by the interference output signal, and the results are low-pass filtered to obtain I1, I2, and I3. The result of subtracting I1 from I3 and I2 is then used for modulation depth estimation and correction through elliptic fitting. The corrected orthogonal signals are divided and their arctangents are calculated to obtain the low-frequency signal to be measured. The interference output signal is: A represents DC bias, and B represents AC amplitude. Let C be the phase of the signal to be measured, and C be the modulation depth of the phase modulator. For phase carrier signals; use a frequency-doubled carrier signal Second harmonic carrier signal Third harmonic carrier signal The signal is mixed with the interferometer output signal I, and then passed through a low-pass filter with a cutoff frequency between the frequency of the signal under test and the carrier frequency. Where J1(C) is a first-order Bessel function of the first kind, J2(C) is a second-order Bessel function of the first kind, and J3(C) is a third-order Bessel function of the first kind. Will ,have to: make ,Will remove get: ； and The general expression is rewritten as: In the formula, a(t) and c(t) are the DC offset, and b(t) and d(t) are the AC amplitude. The signal to be measured, = , The phase difference between the two signals and Fit to an ellipse , ； calculate The final demodulated amplitude is fed back to improve demodulation accuracy. Will and Signal correction is as follows: Finally, the low-frequency signal to be measured is obtained by dividing the two orthogonal signals and calculating their arctangents. .

2. The method for demodulating low-frequency signals using the improved phase generation carrier algorithm according to claim 1, characterized in that: The output signal of the fiber optic interferometric sensing system is converted into an electrical signal by a photodetector. The signal is then acquired by a data acquisition card and input to the FPGA high-speed data processing platform for demodulation using a phase generation carrier algorithm.

3. The method for demodulating low-frequency signals using the improved phase generation carrier algorithm according to claim 2, characterized in that: The signal measurement device of the fiber optic interferometric sensing system includes a laser, fiber optic coupler, sensing fiber, reference fiber, phase modulator, Faraday rotator, photodetector, data acquisition card, and FPGA high-speed data processing platform.

4. The method for demodulating low-frequency signals using the improved phase generation carrier algorithm according to claim 3, characterized in that: The laser's output port is connected to a 2×2 fiber coupler 2. The 2×2 fiber coupler splits the optical signal into two paths. The first path is reflected back to the 2×2 fiber coupler 2 by a Faraday rotator at the end of the sensing fiber. The second path is phase-modulated by a phase modulator along the reference fiber and reflected by a Faraday rotator at the end of the reference fiber, ultimately interfering with the first path at the 2×2 fiber coupler 2. When an external low-frequency signal acts on the sensing fiber, the optical phase in the sensing fiber is modulated, and the corresponding phase difference between the optical signals in the sensing fiber and the reference fiber also changes. This change is ultimately reflected in the light intensity change detected by the photodetector. The signal is acquired by a data acquisition card and input to the FPGA high-speed data processing platform for demodulation using an improved phase-generating carrier algorithm.

5. The method for demodulating low-frequency signals using an improved phase-generating carrier algorithm according to claim 4, characterized in that... The FPGA high-speed data processing platform includes: a DDS sine wave generator, a mixer, a multiplier, a low-pass filter, a subtractor, an ellipse fitting module, a divider, and an arctangent module.

6. The method for demodulating low-frequency signals using an improved phase-generating carrier algorithm according to claim 5, characterized in that, The improved phase generation carrier demodulation includes the following steps: (1) Obtain the interference light intensity signal after carrier modulation; (2) The DDS sine wave generator generates a fundamental frequency carrier signal, a second harmonic carrier signal, and a third harmonic carrier signal; the fundamental frequency carrier signal, the second harmonic carrier signal, and the third harmonic carrier signal are mixed with the interference signal respectively; (3) The mixed signal passes through a low-pass filter with a cutoff frequency between the frequency of the signal under test and the carrier frequency; (4) Process the low-pass filter output signal according to the Bessel function recursion principle, and demodulate the phase modulation depth in real time by elliptic fitting, and generate two orthogonal signals. (5) Finally, the two orthogonal signals are divided and the arctangent is calculated to obtain the low-frequency signal to be measured.

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