阅读说明：本技术 一种补偿载波相位延迟非线性误差的pgc相位解调方法 (PGC phase demodulation method for compensating carrier phase delay nonlinear error ) 是由 严利平 陈本永 张倚得 谢建东 于 2020-05-12 设计创作，主要内容包括：本发明公开了一种补偿载波相位延迟非线性误差的PGC相位解调方法。采用高频正弦和低频正弦扫描复合的调制方法,对采样得到的复合正弦调制数字干涉信号进行一阶、二阶正交下混频,获得两对正交幅值信号,运用一阶正交幅值信号及一阶正交微分信号准确提取出相位延迟并对相位延迟进行补偿,根据相位延迟大小对一阶、二阶正交幅值信号进行优选获得两路不受相位延迟影响的新幅值信号,再通过反正切与相位解包裹运算求得复合相位,最后通过滑动平均计算获得待测相位。本发明解决了PGC相位解调技术中相位延迟难以准确测量及相位延迟引起的非线性误差难以实时补偿的问题,提高了相位测量精度,能广泛应用于正弦相位调制干涉技术领域。(The invention discloses a PGC phase demodulation method for compensating nonlinear errors of carrier phase delay. The method comprises the steps of performing first-order and second-order quadrature down-mixing on a sampled composite sinusoidal modulation digital interference signal by adopting a modulation method of high-frequency sine scanning and low-frequency sine scanning compounding to obtain two pairs of quadrature amplitude signals, accurately extracting phase delay by using the first-order quadrature amplitude signals and the first-order quadrature differential signals, compensating the phase delay, optimally selecting the first-order and second-order quadrature amplitude signals according to the phase delay to obtain two paths of new amplitude signals which are not influenced by the phase delay, obtaining a composite phase through arctangent and phase unwrapping operation, and finally obtaining the phase to be detected through sliding average calculation. The invention solves the problems that the phase delay is difficult to accurately measure and the nonlinear error caused by the phase delay is difficult to compensate in real time in the PGC phase demodulation technology, improves the phase measurement precision, and can be widely applied to the technical field of sinusoidal phase modulation interference.)

1. A PGC phase demodulation method for compensating carrier phase delay nonlinear errors is characterized in that:

(1) applying a composite modulation signal containing a high-frequency sinusoidal modulation signal and a low-frequency sinusoidal scanning signal to an electro-optic phase modulator in a sinusoidal phase modulation interferometer to realize composite modulation on the phase of an interference signal;

(2) filtering out direct current components and high-frequency noise in a composite phase modulation interference signal output by a sinusoidal phase modulation interferometer through a band-pass filter, and then performing analog-to-digital sampling on the composite phase modulation interference signal to obtain a sinusoidal phase modulation digital interference signal S (t), wherein the expression is as follows:

wherein A is amplitude of sinusoidal phase modulation digital interference signal, m is phase modulation depth, J₀(m) is a zero-order Bessel function of the first kind, J_2n(m) and J_2n-1(m) are first-class Bessel functions of even order and odd order, respectively, n represents the order, ω_cIs the angular frequency of the high frequency sinusoidal modulated signal, theta is the carrier phase delay, t represents time,representing a composite phase of a sinusoidal phase modulated digital interference signal;

phase positionThe phase position to be measured and the scanning phase position in the t-time sinusoidal phase modulation interferometer are contained, and the formula is as follows:

wherein the content of the first and second substances,for the low-frequency sinusoidal scanning phase,for the phase to be measured, B is the amplitude of the scanning phase, omega_sAngular frequency which is the scanning phase;

(3) a first order reference signal (cos omega) generated by a digital frequency synthesizer (1, 18)_ct，sinω_ct) and a second order reference signal (cos2 ω)_ct，sin 2ω_ct) are multiplied by the sinusoidal phase modulation digital interference signal S (t) respectively and low-pass filtered to obtain a first-order quadrature amplitude signal (P)₁，Q₁) And a second order quadrature amplitude signal (P)₂，Q₂) The formula is as follows:

wherein, LPF [ alpha ], []Represents a low pass filtering operation; sin (omega)_ct)、cos(ω_ct) represents the sine and cosine components of the first-order reference signal, sin (2 ω) respectively_ct)、cos(2ω_ct) represent the sine and cosine components of a second-order reference signal, respectively, P₁,Q₁Respectively representing the cosine and sine amplitude components, P, of a first-order quadrature amplitude signal₂,Q₂Respectively representing a cosine amplitude component and a sine amplitude component of a second-order quadrature amplitude signal;

then a first order quadrature amplitude signal (P)₁，Q₁) Obtaining a first-order orthogonal differential signal (D) after differential operation_P，D_Q)：

Wherein the content of the first and second substances,to compound phasePartial differential over time t, D_PAnd D_QA cosine differential component and a sine differential component respectively representing a first-order quadrature differential signal;

(4) using a first order quadrature amplitude signal (P)₁，Q₁) A first order quadrature differential signal (D)_P，D_Q) Calculating to obtain carrier phase delay theta_cThe calculation formula is as follows:

wherein sign () represents a sign function, and has a value of 1 when the value in the parentheses is equal to or greater than zero and a value of-1 when the value in the parentheses is less than zero;

(5) applying the carrier phase delay theta calculated in the step (4)_cFirst order quadrature amplitude signal (P)₁，Q₁) And a second order quadrature amplitude signal (P)₂，Q₂) Reconstructing a pair of new amplitude signals (R) whose amplitudes are not affected by the phase delay of the carrier₁，R₂) The calculation formula is as follows:

wherein R is₁And R₂Respectively representing a sine amplitude component and a cosine amplitude component of the new amplitude signal;

(6) for new amplitude signal (R)₁，R₂) Performing four-quadrant arc tangent operation to obtain wrapped phaseThe calculation formula is as follows:

(7) to wrapping phaseThe phase unwrapping is carried out to obtain a continuously changing composite phaseStoring composite phases using a queue of length MPerforming summation operation on the stored M data, dividing the result of the summation operation by M to complete the moving average operation, eliminating the scanning phase in the composite phase, and finally obtaining the phase to be detectedThe formula is as follows:

wherein U [ ] represents the phase unwrapping operation and Σ [ ] represents the summation operation of M data.

2. The phase demodulation method of PGC for compensating for nonlinear error in carrier phase delay according to claim 1, wherein: the method adopts the following PGC phase demodulation system, wherein the input ends of a first multiplier (2), a second multiplier (3), a third multiplier (19) and a fourth multiplier (20) are connected with a digital interference signal S (t); the output end of the first digital frequency synthesizer (1) is respectively connected to the input ends of a first multiplier (2) and a second multiplier (3), the output end of the first multiplier (2) is connected to the input end of a first low-pass filter (4), and the output end of the second multiplier (3) is connected to the input end of a second low-pass filter (5); the output end of the first low-pass filter (4) is respectively connected to the input end of the second square arithmetic unit (9), the input end of the first symbol extractor (26), the input end of the first differential arithmetic unit (6) and the input end of the phase delay compensation module (17), and the output end of the first differential arithmetic unit (6) is connected to the input end of the first square arithmetic unit (8); the output end of the second low-pass filter (5) is connected to the input end of the third square arithmetic unit (10), the input end of the second symbol extractor (27), the input end of the second differential arithmetic unit (7) and the input end of the phase delay compensation module (17), and the output end of the second differential arithmetic unit (7) is connected to the input end of the fourth square arithmetic unit (11); the output end of the first square operator (8) and the output end of the second square operator (9) are connected to the input end of a first adder (12), the output end of a third square operator (10) and the output end of a fourth square operator (11) are connected to the input end of a second adder (13), the output end of the first adder (12) is connected to the input end of a fifth multiplier (28) together with the output end of a first symbol extractor (26) after passing through a first open operator (14), the output end of the second adder (13) is connected to the input end of the fifth multiplier (28) together with the output end of a second symbol extractor (27) after passing through a second open operator (15), and the output end of the fifth multiplier (28) and the output end of a sixth multiplier (29) are connected to the input end of a first arctangent operator (16); the output end of the second digital frequency synthesizer (18) is connected to the input ends of a third multiplier (19) and a fourth multiplier (20), the output ends of the third multiplier (19) and the fourth multiplier (20) are respectively connected to the input end of a phase delay compensation module (17) through a third low-pass filter (21) and a fourth low-pass filter (22), the output end of a first arctangent operator (16) is connected to the input end of the phase delay compensation module (17), two output ends of the phase delay compensation module (17) are both connected to the input end of a second arctangent operator (23), the output end of the second arctangent operator (23) is connected to the input end of a phase unwrapping processor (24), the output end of the phase unwrapping processor (24) is connected to the input end of a sliding average processor (25), and the output end of the sliding average processor (25) outputs the phase to be measured.

3. The phase demodulation method of PGC for compensating for nonlinear error in carrier phase delay according to claim 2, wherein: the phase delay compensation module specifically comprises: the output end of the first arc tangent arithmetic unit (16) is respectively connected with the input end of a first-order new amplitude signal selector (1708), the input end of a second-order new amplitude signal selector (1709) and the input end of a first sine/cosine arithmetic unit (1702), two output ends of the first sine/cosine arithmetic unit (1702) are respectively connected with the input end of a first divider (1704) and the input end of a second divider (1705), meanwhile, the output end of the first arc tangent arithmetic unit (16) is connected with the input end of a second sine/cosine arithmetic unit (1703) through a multiplier (1701), two output ends of the second sine/cosine arithmetic unit (1703) are respectively connected with the input end of a third divider (1706) and the input end of a fourth divider (1707), the output end of a first low pass filter (4) and the output end of a second low pass filter (5) are respectively connected with the input end of the first divider (1704) and the input end of the second divider (1705), the output end of the third low-pass filter (21) and the output end of the fourth low-pass filter (22) are respectively connected to the input end of a third divider (1706) and the input end of a fourth divider (1707), the output end of the first divider (1704) and the output end of the second divider (1705) are both connected to the input end of a first-order new amplitude signal selector (1708), and the output end of the third divider (1706) and the output end of the fourth divider (1707) are both connected to the input end of a second-order new amplitude signal selector (1709).

Technical Field

The invention belongs to the technical field of laser interferometry, and particularly relates to a PGC phase demodulation method for compensating nonlinear errors of carrier phase delay.

Background

The Phase Generated Carrier (PGC) demodulation technology is widely used in interferometric fiber sensors and sinusoidal phase modulation interferometers due to its advantages of low frequency interference resistance, high sensitivity, large dynamic range, etc. The PGC demodulation techniques mainly include a differential cross multiplication algorithm (PGC-DCM) and an Arctan algorithm (PGC-Arctan). The PGC-DCM method obtains the phase to be measured by carrying out operations such as differential cross multiplication and integration on the orthogonal signal, and is easily influenced by laser intensity fluctuation, carrier phase delay and phase modulation depth. The PGC-Arctan method directly obtains the phase to be measured by dividing the orthogonal component and performing arc tangent operation, eliminates the influence caused by light intensity fluctuation, but is still influenced by carrier phase delay and modulation depth. In order to compensate for the effect of carrier phase delay, a quadrature demodulation method is usually used to obtain a carrier phase delay value, and a phase compensator is added to a reference carrier signal to keep the carrier term of an interference signal in phase with the reference carrier signal. The quadrature demodulation method cannot obtain the carrier phase delay when the phase to be measured is a specific value. In addition, in practice, the phase delay drifts with environmental changes, and the existing method is difficult to realize accurate and rapid compensation on the phase delay, so that nonlinear errors are generated, and the improvement of phase measurement precision is limited. Therefore, accurately extracting the phase delay in the PGC phase demodulation algorithm and compensating the drift of the phase delay are key technical problems to be solved for improving the accuracy of the sinusoidal modulation interferometry.

Disclosure of Invention

In order to overcome the defects in the prior art, the invention discloses a PGC phase demodulation method for compensating nonlinear errors of carrier phase delay, which solves the influence caused by phase delay in PGC demodulation, solves the problems that the phase delay is difficult to accurately measure and the nonlinear errors caused by the phase delay are difficult to compensate in real time in the PGC phase demodulation technology, improves the phase measurement precision, and can be widely applied to the technical field of sinusoidal phase modulation interference.

The technical scheme adopted by the invention comprises the following steps:

applying a composite modulation signal containing a high-frequency sinusoidal modulation signal and a low-frequency sinusoidal scanning signal to an electro-optic phase modulator in a sinusoidal phase modulation interferometer to realize composite modulation on the phase of an interference signal;

filtering out direct current components and high-frequency noise in a composite phase modulation interference signal output by a sinusoidal phase modulation interferometer through a band-pass filter, and then performing analog-to-digital sampling on the composite phase modulation interference signal to obtain a sinusoidal phase modulation digital interference signal S (t), wherein the expression is as follows:

wherein A is amplitude of sinusoidal phase modulation digital interference signal, m is phase modulation depth, J₀(m) is a zero-order Bessel function of the first kind, J_2n(m) and J_2n-1(m) are first-class Bessel functions of even order and odd order, respectively, n represents the order, ω_cIs the angular frequency of the high frequency sinusoidal modulated signal, theta is the carrier phase delay, t represents time,representing a composite phase of a sinusoidal phase modulated digital interference signal;

phase positionThe phase position to be measured and the scanning phase position in the t-time sinusoidal phase modulation interferometer are contained, and the formula is as follows:

wherein the content of the first and second substances,for the low-frequency sinusoidal scanning phase,for the phase to be measured, B is the amplitude of the scanning phase, omega_sFor sweeping the angle of the phaseFrequency;

the phase to be measured is an offset phase caused by displacement of an object to be measured in the sinusoidal phase modulation interferometer. The scanning phase is the phase applied when scanning with a low frequency sinusoidal scanning signal in a sinusoidal phase modulation interferometer.

A first order reference signal (cos omega) generated by a digital frequency synthesizer (1, 18)_ct，sinω_ct) and a second-order reference signal (cos2 ω)_ct，sin2ω_ct) are multiplied by the sinusoidal phase modulation digital interference signal S (t) respectively and low-pass filtered to obtain a first-order quadrature amplitude signal (P)₁，Q₁) And a second order quadrature amplitude signal (P)₂，Q₂) The formula is as follows:

wherein, LPF [ alpha ], []Represents a low pass filtering operation; sin (omega)_ct)、cos(ω_ct) represents the sine and cosine components of the first-order reference signal, sin (2 ω) respectively_ct)、cos(2ω_ct) represent the sine and cosine components of a second-order reference signal, respectively, P₁,Q₁Respectively representing the cosine and sine amplitude components, P, of a first-order quadrature amplitude signal₂,Q₂Respectively representing a cosine amplitude component and a sine amplitude component of a second-order quadrature amplitude signal;

then a first order quadrature amplitude signal (P)₁，Q₁) Obtaining a first-order orthogonal differential signal (D) after differential operation_P，D_Q)：

Wherein the content of the first and second substances,to compound phasePartial differential over time t, D_PAnd D_QA cosine differential component and a sine differential component respectively representing a first-order quadrature differential signal;

using a first order quadrature amplitude signal (P)₁，Q₁) A first order quadrature differential signal (D)_P，D_Q) Calculating to obtain carrier phase delay theta_cThe calculation formula is as follows:

wherein sign () represents a sign function, and has a value of 1 when the value in the parentheses is equal to or greater than zero and a value of-1 when the value in the parentheses is less than zero;

calculated carrier phase delay theta_cThe value of (a) ranges from-pi/2 to pi/2.

Using the carrier phase delay theta calculated in the step_cFirst order quadrature amplitude signal (P)₁，Q₁) And a second order quadrature amplitude signal (P)₂，Q₂) Reconstructing a pair of new amplitude signals (R) whose amplitudes are not affected by the phase delay of the carrier₁，R₂) The calculation formula is as follows:

wherein R is₁And R₂Respectively representing a sine amplitude component and a cosine amplitude component of the new amplitude signal;

for new amplitude signal (R)₁，R₂) Performing four-quadrant arc tangent operation to obtain wrapped phaseThe calculation formula is as follows:

wrapped phase calculated in formulaWrapped between-pi and + pi.

Drawings

FIG. 1 is a schematic block diagram of the method and apparatus of the present invention.

Fig. 2 is a functional block diagram of a phase delay compensation module.

FIG. 3 is a graph of the results of simulation experimental data of the present invention.

In the figure: 1. a first digital frequency synthesizer, 2, a first multiplier, 3, a second multiplier, 4, a first low-pass filter, 5, a second low-pass filter, 6, a first differential operator, 7, a second differential operator, 8, a first square operator, 9, a second square operator, 10, a third square operator, 11, a fourth square operator, 12, a first adder, 13, a second adder, 14, a first squarer, 15, a second squarer, 16, a first arctangent operator, 17, a phase delay compensation module, 18, a second digital frequency synthesizer, 19, a third multiplier, 20, a fourth multiplier, 21, a third low-pass filter, 22, a fourth low-pass filter, 23, a second arctangent operator, 24, a phase unwrapping processor, 25, a sliding average processor, 26, a first symbol extractor, 27, a second symbol extractor, A second symbol extractor 28, a fifth multiplier 29, a sixth multiplier 1701, a multiplier 1702, a first sine/cosine operator 1703, a second sine/cosine operator 1704, a first divider 1705, a second divider 1706, a third divider 1707, a fourth divider 1708, a first-order new amplitude signal selector 1709 and a second-order new amplitude signal selector.

In a specific implementation, assume that the modulation depth m is 2.63, J₁(m)＝J₂(m)。

To wrapping phaseThe phase unwrapping is carried out to obtain a continuously changing composite phaseAccording to the scanning phase within the period of a low-frequency sinusoidal scanning signalThe property that the mean value is zero, M data are totally stored in the period of a low-frequency sine scanning signal, and the queue with the length of M is adopted to store the composite phasePerforming summation operation on the stored M data, dividing the result of the summation operation by M to complete the moving average operation, eliminating the scanning phase in the composite phase, and finally obtaining the phase to be detectedThe formula is as follows:

wherein U [ ] represents the phase unwrapping operation and Σ [ ] represents the summation operation of M data.

The method adopts the following PGC phase demodulation system, wherein the input ends of a first multiplier, a second multiplier, a third multiplier and a fourth multiplier are all connected with a digital interference signal S (t); the output end of the first digital frequency synthesizer is respectively connected to the input ends of a first multiplier and a second multiplier, the output end of the first multiplier is connected to the input end of the first low-pass filter, and the output end of the second multiplier is connected to the input end of the second low-pass filter; the output end of the first low-pass filter is respectively connected to the input end of the second square arithmetic unit, the input end of the first symbol extractor, the input end of the first differential arithmetic unit and the input end of the phase delay compensation module, and the output end of the first differential arithmetic unit is connected to the input end of the first square arithmetic unit; the output end of the second low-pass filter is connected to the input end of the third square arithmetic unit, the input end of the second symbol extractor, the input end of the second differential arithmetic unit and the input end of the phase delay compensation module, and the output end of the second differential arithmetic unit is connected to the input end of the fourth square arithmetic unit; the output end of the first square arithmetic unit and the output end of the second square arithmetic unit are both connected to the input end of the first adder, the output end of the third square arithmetic unit and the output end of the fourth square arithmetic unit are both connected to the input end of the second adder, the output end of the first adder is connected to the input end of the fifth multiplier together with the output end of the first symbol extractor after passing through the first squaring arithmetic unit, the output end of the second adder is connected to the input end of the fifth multiplier together with the output end of the second symbol extractor after passing through the second squaring arithmetic unit, and the output end of the fifth multiplier and the output end of the sixth multiplier are both connected to the input end of the first arctangent arithmetic unit; the output end of the second digital frequency synthesizer is connected to the input ends of a third multiplier and a fourth multiplier, the output ends of the third multiplier and the fourth multiplier are connected to the input end of a phase delay compensation module through a third low-pass filter and a fourth low-pass filter respectively, the output end of the first arc tangent arithmetic unit is connected to the input end of the phase delay compensation module, two output ends of the phase delay compensation module are connected to the input end of a second arc tangent arithmetic unit, the output end of the second arc tangent arithmetic unit is connected to the input end of a phase unwrapping processor, the output end of the phase unwrapping processor is connected to the input end of a sliding average processor, and the output end of the sliding average processor outputs a phase to be measured.

The phase delay compensation module specifically comprises: the output end of the first arc tangent arithmetic unit is respectively connected with the input end of the first-order new amplitude signal selector, the input end of the second-order new amplitude signal selector and the input end of the first sine/cosine arithmetic unit, two output ends of the first sine/cosine arithmetic unit are respectively connected with the input end of the first divider and the input end of the second divider, the output end of the first arc tangent arithmetic unit is connected with the input end of the second sine/cosine arithmetic unit through the multiplier, two output ends of the second sine/cosine arithmetic unit are respectively connected with the input end of the third divider and the input end of the fourth divider, the output end of the first low-pass filter and the output end of the second low-pass filter are respectively connected with the input end of the first divider and the input end of the second divider, the output end of the third low-pass filter and the output end of the fourth low-pass filter are respectively connected with the input end of the third divider, the output end of the first divider and the output end of the second divider are both connected to the input end of the first-order new amplitude signal selector, and the output end of the third divider and the output end of the fourth divider are both connected to the input end of the second-order new amplitude signal selector.

Compared with the background art, the invention has the beneficial effects that:

(1) the method of the invention uses the first-order orthogonal amplitude signal and the first-order orthogonal differential signal to accurately extract the carrier phase delay, the extracted phase delay is not affected by the phase to be detected, and the real-time extraction and compensation of the phase delay can be realized;

(2) the method realizes composite phase modulation by adding low-frequency sinusoidal scanning voltage to high-frequency sinusoidal voltage, so that the composite phase of the object to be measured is still continuously changed when the object to be measured is static, and the problem that phase delay is difficult to solve and compensate when the phase to be measured is a specific value is solved;

(3) the invention eliminates the nonlinear error caused by the phase delay by calculating and compensating the phase delay, improves the precision of PGC phase demodulation, and can be widely applied to the technical field of sinusoidal phase modulation interference.