Method and system for extracting and correcting phase modulation depth and eliminating nonlinear influencing factors in a PGC-Atan demodulation method

Abstract

The present invention relates to a method and system for extracting and correcting the phase modulation depth and eliminating nonlinear influencing factors in a PGC-Atan demodulation method. A light source modulation module generates an interference signal after a high-frequency carrier is modulated by the high-frequency carrier and a signal to be measured, which is processed into an electrical signal and multiplied with a carrier frequency-doubled sine signal, a carrier frequency-doubled cosine signal and a carrier frequency-doubled cosine signal, respectively. An inverse tangent operation is performed on a pair of signals multiplied with the carrier frequency-doubled signal to extract the carrier phase delay; an ellipse fitting is performed on a pair of signals multiplied with the carrier cosine signal. The phase modulation depth is extracted by combining the carrier phase delay and the ellipse fitting parameters, and is fed back to the light source modulation module for closed-loop control. A pair of strictly orthogonal signals are constructed by combining the pair of signals multiplied with the carrier cosine signal and the ellipse fitting parameters, and then an inverse tangent operation is performed and the signal to be measured is accurately obtained by high-pass filtering. The present invention solves the problem of nonlinear distortion and is conducive to improving the accuracy of phase demodulation.

Description

Technical Field

[0001] The present invention relates to a method and system for extracting and correcting phase modulation depth and eliminating nonlinear influencing factors in a PGC-Atan demodulation method. Background Art

[0002] Demodulation is a key technology for achieving high-precision measurements in interferometric fiber optic sensors, such as Fabry-Perot and Michelson sensors. Phase-generated carrier (PGC) is a homodyne demodulation method that introduces a high-frequency carrier outside the signal band to cause the operating point to oscillate, avoiding zero phase offset. This method offers advantages such as high sensitivity, wide dynamic range, and good linearity, and is widely used in the demodulation of interferometric fiber optic sensors.

[0003] In the PGC demodulation method, carrier generation can be achieved through external modulation or internal modulation. External modulation generates a high-frequency carrier using devices such as electro-optical modulators, acousto-optic modulators, and piezoelectric ceramics. This requires the introduction of electrical components into the system, increasing the system size. Internal modulation adjusts the laser wavelength (frequency) by adjusting the laser current. However, current modulation of the optical frequency is accompanied by optical power modulation, resulting in the superposition of a ripple related to the associated amplitude modulation on the originally stable optical power. This generates associated amplitude modulation and introduces nonlinear errors into the demodulation results.

[0004] Classic PGC demodulation methods primarily use the differential-cross-multiplication method (PGC-DCM) or the inverse tangent method (PGC-Atan) to demodulate the phase information of the signal under test. The PGC-Atan demodulation method divides a pair of quadrature components and then performs an inverse tangent operation, thereby minimizing the impact of light source perturbations on the demodulation results. However, in the classic PGC algorithm, perturbations in the phase modulation depth can cause harmonic distortion in the demodulation results. Furthermore, factors such as optical propagation, circuit transmission, and digital-to-analog conversion can also cause carrier phase delays, leading to deviations in the demodulation results.

[0005] Currently, methods that can simultaneously eliminate the effects of nonlinear factors such as carrier phase delay, associated amplitude modulation, and phase modulation depth perturbations primarily involve correcting or reconstructing a pair of orthogonal signals. Patent 201510293444.3 combines PGC demodulation with a fixed phase shift method based on a 3×3 coupler. This method demodulates the measured signal using two elliptical fitting operations, eliminating the effects of associated amplitude modulation and correcting for nonlinear phase shifts. However, this method increases system complexity and reduces demodulation real-time performance. Patent 201910554854.7 iteratively calculates the square vector of the orthogonal signal and further predicts the error and gain matrix to correct the orthogonal signal amplitude, compensating for nonlinear errors caused by modulation depth perturbations and carrier phase delay, but does not address associated amplitude modulation. Patent 202010203943.X eliminates the effects of optical intensity perturbations and phase modulation depth perturbations through differential cross-division and differentiation operations within the interference cancellation module, but does not address the effects of associated amplitude modulation and carrier phase delay. Patent 202010397297.7 uses operations such as differentiation of carrier frequency signals, double frequency signals, and triple frequency signals to extract harmonic amplitudes and calculate the phase modulation depth. It then reconstructs a pair of orthogonal harmonic amplitude signals for demodulation, but does not consider the impact of carrier phase delay. While this patent addresses the effects of some nonlinear factors, once the demodulation system is affected by other nonlinear factors, the accuracy and stability of the demodulation results are reduced, potentially limiting its applicability to modulation methods outside the light source.

[0006] In order to use the PGC-Atan demodulation method to accurately extract the phase of the signal to be measured and achieve interferometric measurement with nanometer or even higher precision, it is necessary to simultaneously address the influence of nonlinear factors such as phase modulation depth disturbance, carrier phase delay, and associated amplitude modulation on the demodulation results, and overcome the deficiency that existing technologies cannot simultaneously address the influence of nonlinear factors. Summary of the Invention

[0007] The purpose of the present invention is to overcome the shortcomings of the prior art and to propose a method and system for extracting and correcting phase modulation depth and eliminating nonlinear factors in the PGC-Atan demodulation method. Through phase extraction, ellipse fitting, and closed-loop feedback, the present invention simultaneously addresses the problem of demodulation distortion caused by nonlinear factors such as phase modulation depth perturbations, carrier phase delay, and associated amplitude modulation. It also achieves extraction and stable control of phase modulation depth, avoids fitting errors caused by real-time perturbations of the phase modulation depth during the ellipse fitting process, and improves phase demodulation accuracy. The method can be used for demodulation of interferometric fiber optic sensors such as Fabry-Perot sensors, Michelson sensors, and Mach-Zehnder sensors.

[0008] The present invention provides a method for extracting and correcting phase modulation depth and eliminating nonlinear influencing factors in a PGC-Atan demodulation method. The technical solution adopted includes the following steps:

[0009] In step S1, the light source modulation module sets the phase modulation depth of the high-frequency carrier to an initial value and modulates the light source. The modulated light output by the light source modulation module is then modulated by the external signal to be measured to obtain the interference light signal I(t). This is then converted into an electrical signal V(t) by the optoelectronic conditioning module. The electrical signal V(t) is expressed as follows:

[0010]

[0011] Where m is the current modulation depth generated by light source modulation, and its value is in the range of [0, 1); ω0 is the carrier frequency; θ is the phase delay; mcos(ω0t+θ) is the associated amplitude modulation term caused by the current modulation depth; A and B are constant terms related to the intensity of the interference light; C is the phase modulation depth; is the phase to be measured at time t.

[0012] Specifically, the initial value of the phase modulation depth is selected as follows: when the current modulation depth m is in the range of [0, 0.5], it satisfies [m(J0(C)-J2(C)) / J1(C)] 2 <<4 and [m(J3(C)-J1(C)) / J2(C)] 2 Any C value << 4 can be used as the initial value; when the current modulation depth m is in the range of (0.5, 1), [m(J0(C)-J2(C)) / J1(C)] is satisfied 2 =[m(J3(C)-J1(C)) / J2(C)] 2 The C value can be used as the initial value. Taking the current modulation depth m ≤ 0.1 as an example, the initial value of C can be selected in the range of [0.92, 3.5] rad. Taking the current modulation depth m = 0.9 as an example, the initial C value can be selected as 2.37 rad.

[0013] Step S2: The electric signal V(t) is multiplied by the carrier frequency-doubled sinusoidal signal Gsinω0t and low-pass filtered to obtain the signal P. sin (t); at the same time, the electrical signal V(t) is multiplied by the carrier frequency-doubled cosine signal Gcosω0t and low-pass filtered to obtain the signal P(t); at the same time, the electrical signal V(t) is multiplied by the carrier frequency-doubled cosine signal Hcos2ω0t and low-pass filtered to obtain the signal Q(t). Three-way signal P sin (t), P(t) and Q(t) are expanded as follows:

[0014]

[0015]

[0016]

[0017] Where G and H are the amplitudes of the carrier frequency-doubled signal and the carrier frequency-doubled signal, respectively, and G and H are equal. J0(C) represents the value of the 0th-order first-kind Bessel function with respect to C; J1(C) represents the value of the 1st-order first-kind Bessel function with respect to C; J2(C) represents the value of the 2nd-order first-kind Bessel function with respect to C; and J3(C) represents the value of the 3rd-order first-kind Bessel function with respect to C.

[0018] Step S3, using signal P sin The phase delay θ is obtained by dividing the signal P(t) by the inverse tangent operation and finding the inverse number. The calculation formula is as follows:

[0019]

[0020] Step S4, use the ellipse fitting algorithm to perform ellipse fitting on the signal P(t) and the signal Q(t) to obtain the ellipse implicit equation P 2 (t)+EP(t)Q(t)+FQ 2 Parameters E, F and L for (t)+LP(t)+MQ(t)+N=0.

[0021] In step S5, the phase delay θ obtained in step S3 and the ellipse fitting parameter F obtained in step S4 are used to calculate the ratio of the first-order Bessel function with respect to C. The calculation formula is simplified as follows:

[0022]

[0023] Specifically, the simplified calculation formula method is to control the phase modulation depth C within the initial value range so that [m(J0(C)-J2(C)) / J1(C)] 2 <<4 and [m(J3(C)-J1(C)) / J2(C)] 2 <<4, or [m(J0(C)-J2(C)) / J1(C)] 2 =[m(J3(C)-J1(C)) / J2(C)] 2 , in order to eliminate the term related to the current modulation index m in the expansion of the ellipse parameter F, so as to extract the phase modulation depth value. The expansion of the ellipse parameter F is as follows:

[0024]

[0025] In step S6, the phase modulation depth C is calculated by inverse calculation using the ratio obtained in step S5. This value is then fed into the light source modulation module for closed-loop feedback control, stabilizing the phase modulation depth at any set value within the initial range. This completes the extraction and correction of the phase modulation depth in the PGC-Atan demodulation method.

[0026] Step S7, using P(t), Q(t) and the E, F and L parameters obtained in step S4 to construct a pair of signals that contain the signal to be measured and are strictly orthogonal, and then performing arc tangent operation and high-pass filtering to extract the signal to be measured The calculation formula is as follows:

[0027]

[0028] Here, HPF[] represents high-pass filtering of the signal. Thus, high-precision demodulation of the PGC-Atan demodulation method is completed.

[0029] The method employs the following system: a light source modulation module generates a high-frequency carrier to modulate the light source. The modulated light is further modulated into interference light by the signal to be measured, and an electrical signal V(t) is output through an optoelectronic conditioning module. The output of the optoelectronic conditioning module is connected to the inputs of a first multiplier, a second multiplier, and a third multiplier, respectively. A carrier frequency-doubled sine signal is connected to the input of the first multiplier, a carrier frequency-doubled cosine signal is connected to the input of the second multiplier, and a carrier frequency-doubled cosine signal is connected to the input of the third multiplier. The output of the first multiplier is connected to the input of a first low-pass filter, the output of the second multiplier is connected to the input of a second low-pass filter, and the output of the third multiplier is connected to the input of a third low-pass filter. The outputs of the first and second low-pass filters are connected to the input of a divider. The output of the divider is connected to the input of a negation operator via a first inverse tangent operator. The outputs of the second and third low-pass filters are connected to the input of an ellipse fitter. The output of the negation operator and the output of the ellipse fitter are connected to a phase modulation depth function operator for computation, and then input to a phase modulation depth solver. The output of the phase modulation depth solver is connected to a light source modulation module. The output of the second low-pass filter, the output of the third low-pass filter, and the output of the ellipse fitter are connected to a tangent function operator for computation, and then input to a second inverse tangent operator. The second inverse tangent operator outputs the phase to be measured through a high-pass filter.

[0030] The light source modulation module at least includes a light source, a carrier generation circuit, and a closed-loop feedback control circuit.

[0031] The photoelectric conditioning module at least includes a photoelectric conversion circuit, and a filtering circuit and an amplifying circuit can be added according to actual scenarios.

[0032] Compared with the existing technology, the technical solution provided by the present invention has the following significant advantages:

[0033] The present invention extracts the phase modulation depth based on the carrier phase delay and the ellipse fitting parameters, and feeds back to the light source modulation module for closed-loop feedback control of the phase modulation depth; a pair of strictly orthogonal signals is constructed based on the mixed signal and the ellipse fitting parameters, and an inverse tangent operation is performed and the measured signal is obtained through high-pass filtering, thereby eliminating the influence of nonlinear factors such as carrier phase delay and associated amplitude modulation on the demodulation result. On the one hand, the present invention realizes the extraction and correction of the phase modulation depth in the PGC-Atan demodulation method, and solves the problem of demodulation result distortion caused by phase modulation depth disturbance; on the other hand, the present invention simultaneously solves the influence of nonlinear factors such as phase modulation depth disturbance, carrier phase delay, and associated amplitude modulation on the demodulation result, which is conducive to improving the phase demodulation accuracy. BRIEF DESCRIPTION OF THE DRAWINGS

[0034] Figure 1 This is a principle block diagram of a method for extracting and correcting phase modulation depth and eliminating nonlinear influencing factors in the PGC-Atan demodulation method.

[0035] In the figure: 1 is the light source modulation module, 2 is the photoelectric conditioning module, 3 is the carrier frequency doubling sine signal, 4 is the first multiplier, 5 is the carrier frequency doubling cosine signal, 6 is the second multiplier, 7 is the carrier frequency doubling cosine signal, 8 is the third multiplier, 9 is the first low-pass filter, 10 is the second low-pass filter, 11 is the third low-pass filter, 12 is the divider, 13 is the first inverse tangent operator, 14 is the negation operator, 15 is the phase modulation depth function operator, 16 is the phase modulation depth solver, 17 is the ellipse fitter, 18 is the tangent function operator, 19 is the second inverse tangent operator, and 20 is the high-pass filter. DETAILED DESCRIPTION

[0036] In order to make the purpose, technical solutions and advantages of the present invention more clearly understood, the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not intended to limit the present invention.

[0037] like Figure 1As shown, a method for extracting and correcting phase modulation depth and eliminating nonlinear influencing factors in a PGC-Atan demodulation method according to the present invention employs the following system: a light source modulation module 1 generates a high-frequency carrier to modulate an internal light source. The modulated light is further modulated into interference light by the signal to be measured, and an electrical signal V(t) is output via an optoelectronic conditioning module 2. The output of the optoelectronic conditioning module 2 is connected to the inputs of a first multiplier 4, a second multiplier 6, and a third multiplier 8, respectively. A carrier-frequency-doubled sine signal 3 is connected to the input of the first multiplier 4, a carrier-frequency-doubled cosine signal 5 is connected to the input of the second multiplier 6, and a carrier-frequency-doubled cosine signal 7 is connected to the input of the third multiplier 8. The output of the first multiplier 4 is connected to the input of a first low-pass filter 9, the output of the second multiplier 6 is connected to the input of a second low-pass filter 10, and the output of the third multiplier 8 is connected to the input of a third low-pass filter 11. The outputs of the first low-pass filter 9 and the second low-pass filter 10 are connected to the input of a divider 12. The output of the divider 12 is connected to the input of the negation operator 14 via the first inverse tangent operator 13. The output of the second low-pass filter 10 and the output of the third low-pass filter 11 are connected to the input of the ellipse fitter 17. The output of the negation operator 14 and the output of the ellipse fitter 17 are connected to the phase modulation depth function operator 15 for calculation and then input to the phase modulation depth solver 16. The output of the phase modulation depth solver 16 is connected to the light source modulation module 1. The output of the second low-pass filter 10, the output of the third low-pass filter 11 and the output of the ellipse fitter 17 are connected to the tangent function operator 18 for calculation and then input to the second inverse tangent operator 19. The second inverse tangent operator 19 outputs the phase to be measured via the high-pass filter 20.

[0038] The implementation example of the present invention, that is, the implementation process, is as follows:

[0039] In step S1, the light source modulation module 1 sets the phase modulation depth of the high-frequency carrier to an initial value and modulates the light source. The modulated light output by the light source modulation module 1 is then modulated by the external signal to be measured to obtain the interference light signal I(t), which is converted into an electrical signal V(t) by the optoelectronic conditioning module 2. The electrical signal V(t) is expressed as follows:

[0040]

[0041] Where m is the current modulation depth generated by light source modulation, and its value is in the range of [0, 1) and usually does not exceed 0.1 in practice; ω0 is the carrier frequency; θ is the phase delay; mcos(ω0t+θ) is the associated amplitude modulation term caused by the current modulation depth; A and B are constant terms related to the intensity of the interference light; C is the phase modulation depth; is the phase to be measured at time t.

[0042] Step S2: The electrical signal V(t) and the carrier frequency-doubled sinusoidal signal Gsinω0t are input to the first multiplier 4 for multiplication and then pass through the first low-pass filter 9 to obtain the signal P. sin (t); At the same time, the electrical signal V(t) and the carrier frequency-doubled cosine signal Gcosω0t are input to the second multiplier 6 for multiplication and then pass through the second low-pass filter 10 to obtain the signal P(t); At the same time, the electrical signal V(t) and the carrier frequency-doubled cosine signal Hcos2ω0t are input to the third multiplier 8 for multiplication and then pass through the third low-pass filter 11 to obtain the signal Q(t). The three-way signal P sin (t), P(t) and Q(t) are expanded as follows:

[0043]

[0044]

[0045]

[0046] Where G and H are the amplitudes of the carrier frequency-doubled signal and the carrier frequency-doubled signal, respectively, and G and H are equal. J0(C) represents the value of the 0th-order first-kind Bessel function with respect to C; J1(C) represents the value of the 1st-order first-kind Bessel function with respect to C; J2(C) represents the value of the 2nd-order first-kind Bessel function with respect to C; and J3(C) represents the value of the 3rd-order first-kind Bessel function with respect to C.

[0047] Step S3: Signal P sin (t) and the signal P(t) are input to the divider 12, and then the carrier phase delay θ is obtained by the first inverse tangent operator 13 and the negation operator 14. The calculation formula is as follows:

[0048]

[0049] Step S4: input the signal P(t) and the signal Q(t) into the ellipse fitter 17 to obtain the ellipse implicit equation P 2 (t)+EP(t)Q(t)+FQ 2 Parameters E, F and L for (t)+LP(t)+MQ(t)+N=0.

[0050] In step S5, the carrier phase delay θ obtained in step S3 and the ellipse fitting parameter F obtained in step S4 are input into the phase modulation depth function operator 15 to calculate the first-order Bessel function ratio of the phase modulation depth C. The calculation formula is simplified as follows:

[0051]

[0052] In step S6, the ratio obtained by the phase modulation depth function operator 15 is input to the phase modulation depth solver 16 for inverse calculation to determine the phase modulation depth C. This ratio is then input to the light source modulation module 1 for closed-loop feedback control, stabilizing the phase modulation depth at any set value within the initial value range. This completes the extraction and correction of the phase modulation depth in the PGC-Atan demodulation method.

[0053] Step S7: Input the signal P(t), signal Q(t) and the E, F and L parameters output by the ellipse fitter 17 into the tangent function operator 18 to construct a pair of signals containing the signal to be measured and strictly orthogonal. Then, the signal to be measured is extracted by the second inverse tangent operator 19 and the high-pass filter 20. The calculation formula is as follows:

[0054]

[0055] Here, HPF[] represents high-pass filtering of the signal. Thus, high-precision demodulation of the PGC-Atan demodulation method is completed.

[0056] Furthermore, the initial value of the phase modulation depth is selected in such a way that when the current modulation depth m is in the range of [0, 0.5], [m(J0(C)-J2(C)) / J1(C)] is satisfied. 2 <<4 and [m(J3(C)-J1(C)) / J2(C)] 2 Any C value << 4 can be used as the initial value; when the current modulation depth m is in the range of (0.5, 1), [m(J0(C)-J2(C)) / J1(C)] is satisfied 2 =[m(J3(C)-J1(C)) / J2(C)] 2 Any C value can be used as the initial value. Taking the current modulation depth m ≤ 0.1 as an example, the initial value of C can be selected in the range of [0.92, 4.64] rad. Taking the current modulation depth m = 0.9 as an example, the initial C value can be selected as 2.37 rad.

[0057] Furthermore, the simplified calculation formula is to control the phase modulation depth C within the initial value range so that [m(J0(C)-J2(C)) / J1(C)] 2 <<4 and [m(J3(C)-J1(C)) / J2(C)] 2 <<4, or [m(J0(C)-J2(C)) / J1(C)] 2 =[m(J3(C)-J1(C)) / J2(C)] 2 , eliminating the term related to the current modulation index m in the expansion of the ellipse parameter F, making it easier to extract the phase modulation depth value.

[0058] Furthermore, the light source modulation module 1 at least includes a light source, a carrier generation circuit, and a closed-loop feedback control circuit.

[0059] Furthermore, the photoelectric conditioning module 2 at least includes a photoelectric conversion circuit, and a filtering circuit and an amplifying circuit can be added according to actual scenarios.

[0060] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions and improvements made within the spirit and principles of the present invention should be included in the scope of protection of the present invention.

Claims

1. A method for extracting and correcting phase modulation depth and eliminating nonlinear influencing factors in a PGC-Atan demodulation method, characterized in that: The following steps are included: Step S1, the light source modulation module sets the phase modulation depth of the high frequency carrier to an initial value and modulates the light source; The modulated light output by the light source modulation module is modulated by the external signal to be measured to obtain the interference light signal I(t), which is then converted into an electrical signal V(t) by the optoelectronic conditioning module. The electrical signal V(t) is expressed as follows: Where m is the current modulation depth generated by light source modulation, and its value is in the range of [0, 1); ω0 is the carrier frequency; θ is the phase delay; mcos(ω0t+θ) is the associated amplitude modulation term caused by the current modulation depth; A and B are constant terms related to the intensity of the interfering light signal; C is the phase modulation depth; is the phase to be measured at time t; Step S2: The electric signal V(t) is multiplied by the carrier frequency-doubled sinusoidal signal Gsinω0t and low-pass filtered to obtain the signal P. sin (t); At the same time, the electrical signal V(t) is multiplied by the carrier frequency-doubled cosine signal Gcosω0t and low-pass filtered to obtain the signal P(t); At the same time, the electrical signal V(t) is multiplied by the carrier frequency-doubled cosine signal Hcos2ω0t and low-pass filtered to obtain the signal Q(t); The three signals P sin (t), P(t) and Q(t) are expanded as follows: Wherein, G and H are the amplitudes of the carrier frequency-doubled signal and the carrier frequency-doubled signal, respectively, and G and H are equal; J0(C) represents the value of the 0th-order first-kind Bessel function with respect to C; J1(C) represents the value of the 1st-order first-kind Bessel function with respect to C; J2(C) represents the value of the 2nd-order first-kind Bessel function with respect to C; J3(C) represents the value of the 3rd-order first-kind Bessel function with respect to C; Step S3, using signal P sin The phase delay θ is obtained by dividing the signal P(t) by the inverse tangent operation and finding the inverse number. The calculation formula is as follows: Step S4, use the ellipse fitting algorithm to perform ellipse fitting on the signal P(t) and the signal Q(t) to obtain the ellipse implicit equation P 2 (t)+EP(t)Q(t)+FQ 2 Parameters E, F and L for (t)+LP(t)+MQ(t)+N=0; In step S5, the phase delay θ obtained in step S3 and the ellipse fitting parameter F obtained in step S4 are used to calculate the ratio of the first-order Bessel function with respect to C. The calculation formula is simplified as follows: Step S6, using the ratio obtained in step S5 to inversely calculate the phase modulation depth C value, and input it to the light source modulation module for closed-loop feedback control, so that the phase modulation depth is stabilized at any set value within the initial value range. At this point, the extraction and correction of the phase modulation depth in the PGC-Atan demodulation method is achieved; Step S7, using P(t), Q(t) and the E, F and L parameters obtained in step S4 to construct a pair of signals that contain the signal to be measured and are strictly orthogonal, and then perform inverse tangent operation and high-pass filtering to extract the phase to be measured The calculation formula is as follows: Among them, HPF[] represents high-pass filtering of the signal; at this point, the high-precision demodulation of the PGC-Atan demodulation method is completed.

2. The method for extracting and correcting phase modulation depth and eliminating nonlinear influencing factors in a PGC-Atan demodulation method according to claim 1, characterized in that: The initial value of the phase modulation depth in step S1 is selected as follows: when the current modulation depth m is in the range of [0, 0.5], it satisfies [m(J0(C)-J2(C)) / J1(C)] 2 <<4 and [m(J3(C)-J1(C)) / J2(C)] 2 The C value of <<4 can be used as the initial value; when the current modulation depth m is in the range of (0.5, 1), [m(J0(C)-J2(C)) / J1(C)] is satisfied 2 =[m(J3(C)-J1(C)) / J2(C)] 2 The C value can be used as the initial value.

3. The method for extracting and correcting phase modulation depth and eliminating nonlinear influencing factors in a PGC-Atan demodulation method according to claim 1, characterized in that: The simplified calculation formula of step S5 is to control the phase modulation depth C within the initial value range so that [m(J0(C)-J2(C)) / J1(C)] 2 <<4 and [m(J3(C)-J1(C)) / J2(C)] 2 <<4, or [m(J0(C)-J2(C)) / J1(C)] 2 =[m(J3(C)-J1(C)) / J2(C)] 2 , in order to eliminate the term related to the current modulation index m in the expansion of the ellipse parameter F, so as to extract the phase modulation depth value; the expansion of the ellipse parameter F is as follows:

4. A system for extracting and correcting phase modulation depth and eliminating nonlinear influencing factors in a PGC-Atan demodulation method, characterized in that: The structure of the system is as follows: the light source modulation module (1) generates a high-frequency carrier to modulate the light source, the modulated light is modulated again into interference light by the signal to be measured, and the electrical signal V(t) is output through the photoelectric conditioning module (2); the output end of the photoelectric conditioning module (2) is respectively connected to the input ends of the first multiplier (4), the second multiplier (6) and the third multiplier (8); the carrier frequency-doubled sine signal (3) is connected to the input end of the first multiplier (4), the carrier frequency-doubled cosine signal (5) is connected to the input end of the second multiplier (6), and the carrier frequency-doubled cosine signal (7) is connected to the input end of the third multiplier (8); the output end of the first multiplier (4) is connected to the input end of the first low-pass filter (9), the output end of the second multiplier (6) is connected to the input end of the second low-pass filter (10), and the output end of the third multiplier (8) is connected to the input end of the third low-pass filter (11); the output end of the first low-pass filter (9) is connected to the input end of the second low-pass filter (11). The output end of the divider (10) is connected to the input end of the divider (12); the output of the divider (12) is connected to the input end of the negation operator (14) via the first inverse tangent operator (13); the output end of the second low-pass filter (10) and the output end of the third low-pass filter (11) are connected to the input end of the ellipse fitter (17); the output end of the negation operator (14) and the output end of the ellipse fitter (17) are connected to the phase modulation depth function operator (15) for operation and then input to the phase modulation depth solver (16); the output end of the phase modulation depth solver (16) is connected to the light source modulation module (1); the output end of the second low-pass filter (10), the output end of the third low-pass filter (11) and the output end of the ellipse fitter (17) are connected to the tangent function operator (18) for operation and then input to the second inverse tangent operator (19); the second inverse tangent operator (19) outputs the phase to be measured via a high-pass filter (20).

5. The system according to claim 4, wherein: The light source modulation module (1) comprises at least a light source, a carrier generation circuit, and a closed-loop feedback control circuit.

6. The system according to claim 4, wherein: The photoelectric conditioning module (2) comprises at least a photoelectric conversion circuit, and a filtering circuit and an amplifying circuit can be added according to actual scenarios.

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