Method and system for eliminating the influence of carrier phase delay and phase modulation depth perturbation in phase generation carrier-arc tangent demodulation method

Abstract

The present application relates to a kind of phase generation carrier-phase modulation method in arctangent demodulation method carrier phase delay and phase modulation depth disturbance influence elimination method and system. High-frequency carrier is generated using light source external modulation module to modulate the light output by light source, and after receiving the signal to be measured, it is converted into an electrical signal by an optoelectronic conditioning module, and is multiplied with carrier one frequency sine signal, carrier one frequency cosine signal and carrier two frequency cosine signal respectively. The signal multiplied with carrier one frequency cosine signal is divided by the other two multiplied signals. The result of the division operation on the carrier one frequency multiplied signal is subjected to arctangent operation to extract the carrier phase delay, and the inverse multiplication coefficient is calculated. The result of the division operation is multiplied with the inverse multiplication coefficient, and then subjected to arctangent operation and high-pass filtering to obtain the signal to be measured. The present application eliminates the influence of carrier phase delay and phase modulation depth disturbance, which is beneficial to improve the stability and accuracy of phase demodulation.

Description

Technical Field

[0001] This invention relates to a method and system for eliminating the effects of carrier phase delay and phase modulation depth disturbances in the phase generation carrier-argument demodulation method. Background Technology

[0002] Phase-generated carrier wave method has advantages such as high sensitivity, large dynamic range and good linearity, and is widely used in demodulation of interferometric fiber optic sensors such as Fabry-Perot sensors and Michelson sensors.

[0003] Phase-generated carrier demodulation uses an interference signal modulated by a high-frequency carrier and the signal under test. This interference signal is then multiplied and filtered with the carrier's first and second harmonic signals to construct a pair of orthogonal signals. The high-frequency carrier can be generated through external modulation or internal modulation. Internal modulation adjusts the laser wavelength (frequency) by regulating the laser current. However, current modulation of the optical frequency is accompanied by modulation of the optical power, resulting in a ripple of magnitude related to the accompanying amplitude modulation superimposed on the originally stable optical power, thus introducing nonlinear errors into the demodulation result. External modulation uses devices such as electro-optic modulators, acousto-optic modulators, and piezoelectric ceramics to generate high-frequency carrier-modulated light from the source. Although this increases the system size, it does not introduce accompanying amplitude modulation. Regardless of the carrier modulation method, perturbations in the phase modulation depth will cause distortion in the demodulation result. The classic methods for demodulating this pair of orthogonal signals are the differential cross-multiplication method and the arctangent method. Among them, the demodulation result of the phase-generated carrier-differential cross-multiplication method is easily affected by light source disturbances, while the phase-generated carrier-arctangent method can eliminate the influence of light source disturbances through division operations. However, factors such as optical path propagation, circuit transmission, and digital-to-analog conversion in the demodulation system will inevitably cause carrier phase delay, resulting in nonlinear distortion of the demodulation result.

[0004] Currently, improvements to the phase generation carrier-argument algorithm focus on simultaneously eliminating the influence of nonlinear factors such as phase modulation depth perturbation and carrier phase delay. Patent 201811358943.6 uses six carrier frequency-doubled signals for multiplication and harmonic amplitude extraction to construct a phase delay correction coefficient, and extracts the measured phase through four-quadrant arctangent operation, but it does not solve the phase modulation depth perturbation problem. Patent 201911031845.6 compensates for the solved carrier phase delay in the carrier frequency-doubled signal and extracts nonlinear characteristic parameters to eliminate residual initial phase delay and associated amplitude modulation effects, but it fails to solve the most critical phase modulation depth perturbation problem. Patent 202110872720.7 extracts the harmonic amplitude and harmonic differential components of a pair of orthogonal signals multiplied by the interference signal and carrier frequency-doubled signal, performs mutual operations, and extracts the phase modulation depth value using the Bessel function recursive formula, compensating it into the calculation result, thus eliminating the influence of light intensity perturbation and Bessel function terms, but it does not solve the carrier phase delay problem. Patent 202111683651.1 constructs a reference signal to characterize the accompanying amplitude modulation by adding a noise-free digital carrier signal and comparing the signals, thereby eliminating the influence of the accompanying amplitude modulation, but it does not solve the influence of other nonlinear factors.

[0005] The aforementioned patents lack attention to the impact of phase modulation depth perturbations or carrier phase delays. Some introduce multiple carrier frequency-doubling signals, increasing system complexity, while others rely on specific phase modulation depth values ​​to eliminate Bessel function terms, limiting the nonlinear influencing factors they can eliminate. To accurately and rapidly extract the phase of the signal under test and achieve real-time interferometric measurements with nanometer-level or even higher precision, it is essential to eliminate the influence of nonlinear factors such as phase modulation depth perturbations and carrier phase delays in real time, overcoming the shortcomings of existing technologies that cannot simultaneously address the influence of nonlinear factors or have high algorithm complexity. Summary of the Invention

[0006] The purpose of this invention is to overcome the shortcomings of existing technologies and propose a method for eliminating the effects of carrier phase delay and phase modulation depth perturbation in the phase generation carrier-argumentation demodulation method. This invention solves the problem of demodulation result distortion caused by carrier phase delay and phase modulation depth perturbation simultaneously by constructing inverse multiplication coefficients. The algorithm is simple, which helps improve phase demodulation accuracy and can be used for accurate demodulation of interferometric fiber optic sensors such as Fabry-Perot sensors, Michelson sensors, and Mach-Zehnder sensors under external light source modulation conditions.

[0007] This invention provides a method for eliminating the effects of carrier phase delay and phase modulation depth disturbances in the phase generation carrier-arctangent demodulation method. The technical solution includes the following steps:

[0008] Step S1: The light output from the light source is modulated by a high-frequency carrier generated by the external modulation module, and then modulated by an external signal to be measured to obtain an interference light signal I(t). This signal is then converted into an electrical signal V(t) by the photoelectric conditioning module. The electrical signal V(t) is represented as follows:

[0009]

[0010] Where ω0 is the frequency of the high-frequency carrier; θ is the carrier phase delay; A and B are constant terms related to the intensity of the interferometric light; and C is the phase modulation depth. The phase to be measured.

[0011] In step S2, the electrical signal V(t) is multiplied by the carrier first-harmonic sine signal Gsinω0t, the carrier first-harmonic cosine signal Gcosω0t, and the carrier second-harmonic cosine signal Hcos2ω0t, respectively, and then low-pass filtered to obtain the signal P. sin (t), P(t), Q(t). Mixed signal P sin P(t), Q(t), and P(t) are expanded as follows:

[0012]

[0013]

[0014]

[0015] Where G and H are the amplitudes of the first harmonic and second harmonic signals of the carrier, respectively, and G = H. J1(C) represents the first-order Bessel function of the first kind with respect to C; J2(C) represents the value of the second-order Bessel function of the first kind with respect to C.

[0016] Step S3: Perform a division operation between signal P(t) and signal Q(t), using the following formula:

[0017]

[0018] Step S4, using signal P sin The carrier phase delay θ is obtained by dividing P(t) by P(t), then performing an arctangent operation and taking the inverse. The calculation formula is as follows:

[0019]

[0020] Step S5: Construct the first type of Bessel function ratio using the phase modulation depth C fed back by the external modulation module of the light source, and construct the inverse multiplication coefficient E with the carrier phase delay θ obtained in step S4. The calculation formula is as follows:

[0021]

[0022] Step S6: Multiply the division result obtained in step S3 with the inverse multiplication coefficient E obtained in step S5, then perform arctangent operation and high-pass filtering to obtain the phase to be measured. The calculation formula is as follows:

[0023]

[0024] Here, HPF|| represents high-pass filtering of the signal. This completes the high-precision demodulation using the phase-generated carrier-arctangent demodulation method.

[0025] The method employs the following system: light output from the light source is input to an external modulation module, modulated by a high-frequency carrier generated by the external modulation module, and output from the output terminal. This light is then modulated by the signal under test into an interference light signal I(t) and input to an opto-conditioning module to obtain an electrical signal V(t). The output terminal of the opto-conditioning module is connected to the input terminals of a first multiplier, a second multiplier, and a third multiplier, respectively, via a carrier first-harmonic sine signal, a carrier first-harmonic cosine signal, and a carrier second-harmonic cosine signal. The output terminals of the first, second, and third multipliers are connected to the input terminals of a first low-pass filter, a second low-pass filter, and a third low-pass filter, respectively. The output terminals of the second and third low-pass filters are connected to the input terminal of a second divider. The output terminals of the first and second low-pass filters are connected to the input terminal of the first divider. The output of the first divider is connected to the input terminal of an inverting operator via a first arctangent operator. The output terminal of the inverting operator and another output terminal of the external modulation module are connected to the input terminal of an inverse multiplication coefficient solver. The output of the second divider and the output of the inverse multiplication coefficient solver are connected to the fourth multiplier for calculation, and then input to the second arctangent calculator. The second arctangent calculator outputs the phase to be measured after passing through a high-pass filter.

[0026] Compared with existing technologies, the technical solution provided by this invention has the following significant advantages:

[0027] This invention, based on the signal characteristics affected by carrier phase delay, introduces a carrier first-harmonic signal into the classic phase generation carrier-arctangent algorithm. The carrier phase delay is extracted through division and arctangent operations. Inverse multiplication coefficients are constructed using the phase modulation depth output from the external modulation module. These coefficients are then used to cancel out the coefficients of the division result obtained after multiplying, filtering, and dividing the carrier first-harmonic cosine signal and the carrier second-harmonic cosine signal. This invention eliminates the influence of carrier phase delay and phase modulation depth disturbances in the phase generation carrier-arctangent demodulation method through simple calculations, which is beneficial for improving the stability and accuracy of phase demodulation, without requiring complex calculations such as iteration and fitting. Attached Figure Description

[0028] Figure 1 This is a block diagram illustrating the principle of a method for eliminating the effects of carrier phase delay and phase modulation depth disturbances in a phase generation carrier-arctenosing demodulation method.

[0029] In the diagram: 1 is the light source, 2 is the external modulation module for the light source, 2-1 is the first output terminal of the external modulation module for the light source, 2-2 is the second output terminal of the external modulation module for the light source, 3 is the photoelectric conditioning module, 4 is the carrier frequency-doubled sine signal, 5 is the first multiplier, 6 is the carrier frequency-doubled cosine signal, 7 is the second multiplier, 8 is the carrier frequency-doubled cosine signal, 9 is the third multiplier, 10 is the first low-pass filter, 11 is the second low-pass filter, 12 is the third low-pass filter, 13 is the first divider, 14 is the second divider, 15 is the first arctangent operator, 16 is the inverting operator, 17 is the inverse multiplication coefficient solver, 18 is the fourth multiplier, 19 is the second arctangent operator, and 20 is the high-pass filter.

[0030] Figure 2 This is a simulation experiment data graph for the present invention. Detailed Implementation

[0031] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention.

[0032] like Figure 1 As shown, the method for eliminating the influence of carrier phase delay and phase modulation depth disturbance in the phase generation carrier-arctangent demodulation method of the present invention adopts the following system, including a light source 1, a light source external modulation module 2, a first output terminal 2-1 of the light source external modulation module, a second output terminal 2-2 of the light source external modulation module, an optoelectronic conditioning module 3, a carrier first-harmonic sinusoidal signal 4, a first multiplier 5, a carrier first-harmonic cosine signal 6, a second multiplier 7, a carrier second-harmonic cosine signal 8, a third multiplier 9, a first low-pass filter 10, a second low-pass filter 11, a third low-pass filter 12, a first divider 13, a second divider 14, a first arctangent operator 15, an inversion operator 16, an inverse multiplication coefficient solver 17, a fourth multiplier 18, a second arctangent operator 19, and a high-pass filter 20.

[0033] The light output from light source 1 is input to external modulation module 2. After being modulated by the high-frequency carrier generated by external modulation module 2, the light is output from the second output terminal 2-2 and modulated into an interference light signal I(t) by the signal to be measured. This signal is then input to photoelectric conditioning module 3 to obtain an electrical signal V(t). The output terminal of photoelectric conditioning module 3 is connected to the input terminals of the first multiplier 5, the second multiplier 7, and the third multiplier 9, respectively, via a carrier first harmonic sine signal 4, a carrier first harmonic cosine signal 6, and a carrier second harmonic cosine signal 8. The output terminals of the first multiplier 5, the second multiplier 7, and the third multiplier 9 are connected to the input terminals of the first low-pass filter 10, the second low-pass filter 11, and the third low-pass filter 12, respectively. The output terminals of the second low-pass filter 11 and the third low-pass filter 12 are connected to the input terminal of the first divider 13. The output terminals of the first low-pass filter 10 and the second low-pass filter 11 are connected to the input terminal of the second divider 14. The output of the second divider 14 is connected to the input of the inverter 16 via the first arctangent operator 15. The output of the inverter 16 and the first output 2-1 of the external modulation module 2 are connected to the input of the inverse multiplication coefficient solver 17. The output of the first divider 13 and the output of the inverse multiplication coefficient solver 17 are connected to the fourth multiplier 18 for calculation and then input to the second arctangent operator 19. The second arctangent operator 19 outputs the phase to be measured via the high-pass filter 20.

[0034] The implementation process of this invention is as follows:

[0035] Step S1: The light output from light source 1 is modulated by a high-frequency carrier generated by the external modulation module 2, and then modulated by an external signal to be measured to obtain an interference light signal I(t). This signal is then converted into an electrical signal V(t) by the photoelectric conditioning module 3. The electrical signal V(t) is represented as follows:

[0036]

[0037] Where ω0 is the frequency of the high-frequency carrier; θ is the carrier phase delay; A and B are constant terms related to the intensity of the interferometric light; and C is the phase modulation depth. The phase to be measured.

[0038] In step S2, the electrical signal V(t) is multiplied by the carrier first harmonic sine signal 4, the carrier first harmonic cosine signal 6, and the carrier second harmonic cosine signal 8 respectively through the first multiplier 5, the second multiplier 7, and the third multiplier 9, and then passed through the first low-pass filter 10, the second low-pass filter 11, and the third low-pass filter 12 respectively to obtain the signal P. sin (t), P(t), Q(t). Three signals P sin P(t), Q(t), and P(t) are expanded as follows:

[0039]

[0040]

[0041]

[0042] Where G is the amplitude of the carrier-first harmonic sine signal 4 and the carrier-first harmonic cosine signal 6, H is the amplitude of the carrier-second harmonic cosine signal 8, and G = H. J1(C) represents the first-order Bessel function of the first kind with respect to C; J2(C) represents the value of the second-order Bessel function of the first kind with respect to C.

[0043] Step S3: Pass signals P(t) and Q(t) through the first divider 13, and calculate the results as follows:

[0044]

[0045] Step S4, send signal P sin The carrier phase delay θ is obtained by passing the signal P(t) and the signal P(t) through the second divider 14, then through the first arctangent operator 15 and the inverting operator 16, and the calculation formula is as follows:

[0046]

[0047] Step S5: Input the phase modulation depth C fed back by the external modulation module 2 and the carrier phase delay θ obtained in step S4 into the inverse multiplication coefficient solver 17 to construct the inverse multiplication coefficient E. The calculation formula is as follows:

[0048]

[0049] Step S6: The result of the first divider 13 and the inverse multiplication coefficient E obtained in step S5 are input to the fourth multiplier 18 for multiplication. Then, the result is passed through the second arctangent operator 19 and the high-pass filter 20 to obtain the phase to be measured. The calculation formula is as follows:

[0050]

[0051] Here, HPF|| represents high-pass filtering of the signal. This completes the high-precision demodulation using the phase-generated carrier-arctangent demodulation method.

[0052] In the actual simulation, the same simulated composite electrical signal V(t) was generated in LabVIEW according to the formula for the electrical signal V(t). The amplitude of the phase to be measured was 1 rad, the phase modulation depth was set to fluctuate within the range of 2.63 ± 0.2 rad, and the carrier phase delay was successively set to 5°, 10°, 15°, 20°, 25°, 30°, 35°, 40°, 50°, 60°, 70°, and 80°. The phase to be measured was demodulated using the phase generation carrier-argument demodulation method proposed in this invention, which eliminates the influence of carrier phase delay and phase modulation depth disturbances, and the classic PGC-Atan demodulation method. The final result is as follows: Figure 2 The data shown. Figure 2 In the data shown, the solid line with solid circles represents the demodulation amplitude of the method of the present invention, which is stable at 0.99 rad; the dashed line with hollow circles represents the signal-to-speech ratio of the demodulation result of the method of the present invention, which is stable at 54.45 dB. The solid line with solid triangles and the dashed line with hollow triangles represent the demodulation amplitude and signal-to-speech ratio of the classical PGC-Atan demodulation method, respectively, which are unstable and have large distortion. This data shows that the carrier phase delay and phase modulation depth disturbance elimination method proposed in this invention can effectively eliminate the influence of carrier phase delay and phase modulation depth disturbance, and achieve high-precision phase demodulation.

[0053] Those skilled in the art will readily understand that the above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for eliminating the effects of carrier phase delay and phase modulation depth disturbances in a phase generation carrier-argument demodulation method, characterized in that, Includes the following steps: In step S1, the light output from the light source is sequentially modulated by the external modulation module and the external signal to be measured to obtain an interference light signal I(t), which is then converted into an electrical signal V(t) by the photoelectric conditioning module; the electrical signal V(t) is represented as follows: Where ω0 is the frequency of the high-frequency carrier; θ is the carrier phase delay; A and B are constants related to the intensity of the interferometric light; and C is the phase modulation depth. The phase to be measured; In step S2, the electrical signal V(t) is multiplied by the carrier first-harmonic sine signal Gsinω0t, the carrier first-harmonic cosine signal Gcosω0t, and the carrier second-harmonic cosine signal Hcos2ω0t, respectively, and then low-pass filtered to obtain the signal P. sin (t), P(t), Q(t); mixed signal P sin P(t), Q(t), and P(t) are expanded as follows: Where G and H are the amplitudes of the carrier first harmonic signal and the carrier second harmonic signal, respectively, and G = H is given; J1(C) is the first-order Bessel function of the first kind with respect to C; J2(C) is the second-order Bessel function of the first kind with respect to C; Step S3: Perform a division operation between signal P(t) and signal Q(t), using the following formula: Step S4, signal P sin After dividing P(t) by P(t), the carrier phase delay θ is obtained by arctangent operation and inversion operation, as shown in the following formula: Step S5: Construct the first type of Bessel function ratio using the phase modulation depth C fed back by the external modulation module of the light source, and construct the inverse multiplication coefficient E with the carrier phase delay θ obtained in step S4. The calculation formula is as follows: Step S6: Multiply the division result obtained in step S3 with the inverse multiplication coefficient E obtained in step S5, then perform arctangent operation and high-pass filtering to obtain the phase to be measured. The calculation formula is as follows: Here, HPF|| represents high-pass filtering of the signal. Thus, the high-precision demodulation of the phase-generated carrier-arctangent demodulation method is completed.

2. A system used in a phase generation carrier-argument demodulation method for eliminating the effects of carrier phase delay and phase modulation depth disturbances, characterized in that, The system structure is as follows: the light output from the light source (1) is input to the external modulation module (2), modulated by the high-frequency carrier generated by the external modulation module (2), and output from the second output terminal (2-2). After being modulated by the signal to be measured, it becomes an interference light signal I(t) and is input to the photoelectric conditioning module (3) to obtain an electrical signal V(t). The output terminal of the photoelectric conditioning module (3) is connected to the input terminal of the first multiplier (5) with the carrier first harmonic sine signal (4), the input terminal of the second multiplier (7) with the carrier first harmonic cosine signal (6), and the input terminal of the third multiplier (9) with the carrier second harmonic cosine signal (8). The output terminals of the first multiplier (5), the second multiplier (7), and the third multiplier (9) are respectively connected to the first low-pass filter (10), the second low-pass filter (11), and the third low-pass filter (12). At the input end, the output ends of the second low-pass filter (11) and the third low-pass filter (12) are connected to the input end of the first divider (13). The output ends of the first low-pass filter (10) and the second low-pass filter (11) are connected to the input end of the second divider (14). The output of the second divider (14) is connected to the input end of the inverting operator (16) via the first arctangent operator (15). The output end of the inverting operator (16) and the first output end (2-1) of the external modulation module (2) are connected to the input end of the inverse multiplication coefficient solver (17). The output end of the first divider (13) and the output end of the inverse multiplication coefficient solver (17) are connected to the fourth multiplier (18) for operation and then input to the second arctangent operator (19). The second arctangent operator (19) outputs the phase to be measured via the high-pass filter (20).

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