A method, system and device for correcting phase measurement errors in a laser frequency modulated interferometer

Abstract

The application discloses a laser frequency modulation interferometer phase measurement error correction method, system and device, relates to the field of photoelectric precise measurement technology, and comprises the following steps: acquiring a laser frequency modulation interferometer quadrature phase measurement signal, and expressing the quadrature phase measurement signal by using a standard ellipse equation; defining variables in Kalman filtering, discretizing and normalizing the equation; acquiring a time update equation of a Kalman filter, and measurement noise covariance and process noise covariance according to the normalized standard ellipse equation; acquiring a phase measurement update equation; introducing four points in the vicinity of four axes of the ellipse to perform iterative fitting; initializing iteration by rotating the ellipse through scanning laser temperature; and correcting the quadrature phase measurement signal by using posterior estimation. According to the conversion relationship between the quadrature signal characteristics and the ellipse parameters, the unequal amplitude and the bias of the quadrature signal are corrected in real time, so that the correction of the nonlinear error of the phase measurement is finally realized.

Description

Technical Field

[0001] This invention relates to the field of optoelectronic precision measurement technology, and in particular to a method, system and device for correcting phase measurement errors of a laser frequency modulated interferometer. Background Technology

[0002] Laser frequency-modulated interferometric displacement measurement technology has wide applications in industrial manufacturing, precision measurement, and scientific research. This technology utilizes the principle of laser frequency modulation and interferometric measurement techniques to achieve displacement measurement with nanometer-level precision.

[0003] However, this technology also has some bottlenecks. System stability and environmental interference have a significant impact on measurement accuracy, requiring effective measures to suppress them. Secondly, the complex data processing algorithms and phase nonlinear demodulation techniques need further optimization to improve the system's real-time performance and measurement accuracy.

[0004] Fiber optic sinusoidal frequency modulated interferometers (SFMIs), based on phase generated carrier (PGC) technology, offer high sensitivity and excellent accuracy. However, SFMIs are subject to nonlinear error factors such as carrier phase delay (CPD), associated intensity modulation (AOIM), and variations in phase modulation depth (PMD). Variations in phase modulation depth are the most significant nonlinear error in large-range displacement measurements, causing amplitude changes in the signal's Lissajous figure and resulting in phase measurement errors. This is the biggest obstacle to improving the range and accuracy of SFMI displacement measurements. Summary of the Invention

[0005] The purpose of this invention is to address the shortcomings of the prior art by providing a method, system, and device for correcting phase measurement errors in a laser frequency modulated interferometer. This addresses the problem that changes in phase modulation depth are the most significant nonlinear error in large-range displacement measurements, causing amplitude changes in the signal Lissajous pattern and resulting in phase measurement errors. This is the biggest obstacle to improving the range and accuracy of SFMI displacement measurements.

[0006] This invention specifically provides the following technical solution: a method for correcting phase measurement errors in a laser frequency modulated interferometer, comprising the following steps:

[0007] Acquire the orthogonal phase measurement signal of the laser frequency modulated interferometer, and represent the acquired orthogonal phase measurement signal using the standard elliptic equation;

[0008] The standard elliptic equation is discretized using a Kalman filter, and the discretized state vector is defined.

[0009] The state vector is input into a Kalman filter to obtain the prior estimate of the state vector and the posterior estimate of the state vector at the previous time step, and to obtain the time update equation relating the prior estimate and the posterior estimate.

[0010] Obtain the posterior estimated covariance, determine the Kalman gain based on the posterior estimated covariance with zero partial derivative, and obtain the phase measurement update equation at the current time through the Kalman gain and the time update equation.

[0011] Four discrete points are introduced in the region near the four axes of the Lisajous ellipse for iterative fitting. The Lisajous ellipse is rotated by scanning the laser temperature for initial iteration to obtain an orthogonal phase measurement signal containing the four discrete points. The orthogonal phase measurement signal containing the four discrete points is corrected using the phase measurement update equation.

[0012] Preferably, the steps of acquiring the orthogonal phase measurement signal of the laser frequency-modulated interferometer and representing the acquired orthogonal phase measurement signal using the standard elliptic equation include the following:

[0013] The expression for the orthogonal phase measurement signal of the laser frequency modulated interferometer is:

[0014]

[0015] Among them, I′ x (t) and I′ y (t) represent the orthogonal phase measurement signals in the x and y directions, respectively, a x =BJ1(C) and a y =BJ2(C) represents the amplitudes of the orthogonal signals in the x and y directions, respectively, where B is the amplitude of the AC component of the laser interference signal, J1 and J2 are the first-order and second-order Bessel functions, respectively, C is the phase modulation depth, and x0 and y0 are the offsets. The phase angle is t, and the time variable is t.

[0016] The orthogonal phase measurement signal is represented using the standard elliptic equation as follows:

[0017] aI x ′(t) 2 +cI y ′(t) 2 +2dI x ′(t)+2eI y ′(t)+f=0

[0018] a+c>0

[0019] Where a, c, d, e, and f are the coefficients of the standard elliptic equation, and the relationship between the amplitude and offset of the orthogonal signal and the coefficients of the standard elliptic equation is as follows:

[0020]

[0021] Preferably, after discretizing the standard elliptic equation using the Kalman filter, the standard elliptic equation is normalized using f = -1, specifically as follows:

[0022] a k I' x (k) 2 +c k I' y (k) 2 +2d k I' x (k)+2e k I' y (k)=1,

[0023] a k +c k >0)

[0024] Among them, a k c k d k and e k For different parameters of the discretized elliptic equation, I′ x (k) and I′ y (k) represents the discrete orthogonal phase measurement signals in the x and y directions, respectively.

[0025] Preferably, when defining the discretized state vector, the state vector is defined as follows, using k = 1, 2…N-1 as the numbering of the cache sequence:

[0026] X k =(a k ,c k ,d k ,e k ) T

[0027] Observation matrix for:

[0028]

[0029] The approximate value that can be obtained as the truth value is:

[0030] H k =[I x ′0(k) 2 ,I′ y0 (k) 2 ,2I x ′0(k),2I′ y0 (k)]

[0031] The measurement results are as follows:

[0032] Z k =Hk X k =1

[0033] Among them, Z k For the measurement results, H k An approximation of the true value can be obtained, X k Let I′ be the state vector. x0 (k) and I′ y0 (k) are the orthogonal measurement discrete signals offset in the x and y directions, respectively.

[0034] Preferably, the time update equation for obtaining the relationship between the prior estimate and the posterior estimate includes the following steps:

[0035] The time update equation is obtained, and its specific expression is:

[0036]

[0037] in, and Let be the prior estimate of the state vector at time k and the prior estimate of the error. and Let w be the posterior estimate of the state vector at time k-1 and the posterior estimate of the error covariance, respectively. k With Q k =E[w k w k T ] represents process noise and covariance, where, and The initial values ​​are as follows:

[0038]

[0039] in, and They are respectively and The initial value.

[0040] Preferably, the process of obtaining the time update equation further includes the following steps:

[0041] The measurement noise covariance and process noise covariance are obtained using the following expressions:

[0042]

[0043] Among them, R k To measure the noise covariance, σ 2 For variance, and These are the prior estimates of the state vector, Q. k Let E be the process noise covariance, and w be the process noise covariance. k wk T The expectation is that the noise of the two demodulation channels is independent and has equal variance, and the specific expression is:

[0044] I x ′~N(I x ′0,σ 2 )

[0045] I' y ~N(I′) y0 ,σ 2 )

[0046] Among them, I x ′~N(·) represents the noise of the demodulation channel in the x-direction, I′ y ~N(·) represents the noise of the demodulation channel in the y direction, I x ′0 is the orthogonal phase signal after offset in the x-direction, I′ y0 It is the orthogonal phase signal after offset in the y direction.

[0047] Preferably, the step of determining the Kalman gain based on the posterior estimated covariance with zero partial derivatives, and obtaining the phase measurement update equation at the current time through the Kalman gain and the time update equation, includes the following steps:

[0048] The Kalman gain is determined based on the fact that the partial derivative of the posterior estimated covariance is zero. The specific expression is as follows:

[0049]

[0050] Among them, P k =E[e k e k T [K] is the posterior estimate of the covariance. k Kalman gain;

[0051] The specific expression for the phase measurement update equation is as follows:

[0052]

[0053] in, Let k be the error covariance. Observation matrix The transpose of the matrix, For X k The posterior estimate, Z k For the measurement result, I is a constant value.

[0054] Preferably, the orthogonal phase measurement signal containing four discrete points is corrected using the phase measurement update equation, specifically expressed as follows:

[0055]

[0056] Among them, I″ x (k) and I″ y (k) represents the discrete orthogonal phase measurement signals in the x and y directions after correction, respectively, where x0(k) and y0(k) are the offsets in the x and y directions at time k, respectively. x (k) and a y (k) represents the amplitude of the orthogonal signal in the x and y directions at time k, respectively. For precise interference phase.

[0057] The present invention also provides a phase measurement error correction system for a laser frequency modulated interferometer, comprising:

[0058] The acquisition module is used to acquire the orthogonal phase measurement signal of the laser frequency modulated interferometer, and to represent the acquired orthogonal phase measurement signal using the standard elliptic equation.

[0059] The preprocessing module is used to discretize the standard elliptic equation using a Kalman filter and define the discretized state vector.

[0060] The data processing module is used to input the state vector into the Kalman filter, obtain the prior estimate of the state vector and the posterior estimate of the state vector at the previous time step, and obtain the time update equation of the relationship between the prior estimate and the posterior estimate.

[0061] The update module is used to obtain the posterior estimated covariance, determine the Kalman gain based on the posterior estimated covariance with zero partial derivative, and obtain the phase measurement update equation at the current time through the Kalman gain and the time update equation.

[0062] The correction module is used to introduce four discrete points in the region near the four axes of the Lissajous ellipse for iterative fitting, and to perform initial iteration by rotating the Lissajous ellipse by scanning the laser temperature to obtain an orthogonal phase measurement signal containing the four discrete points. The orthogonal phase measurement signal containing the four discrete points is then corrected using the phase measurement update equation.

[0063] The present invention also provides a computer device, including a memory and a processor, wherein the memory stores a program, and when the program is executed by the processor, the processor performs the steps of the laser frequency modulated interferometer phase measurement error correction method.

[0064] Compared with the prior art, the present invention has the following significant advantages:

[0065] This invention acquires orthogonal phase measurement signals and a standard elliptic equation representation, discretizes the standard elliptic equation, and generates a state vector. Based on the state vector, it obtains a time update equation relating the prior estimate of the state vector to the posterior estimate of the state vector at the previous moment. This time update equation is then used to correct the orthogonal phase measurement signals at discrete points. In other words, it corrects the phase and other information of the orthogonal signals in real time based on the transformation relationship between the characteristics of the orthogonal signals and the elliptic parameters, avoiding the influence of phase measurement errors on the measurement results. Ultimately, this achieves the correction of nonlinear errors in phase measurement, improving the measurement accuracy under large displacement ranges. Attached Figure Description

[0066] Figure 1 This is a flowchart of the nonlinear error correction method for phase measurement of a laser frequency modulated interferometer based on Kalman filtering, according to an embodiment of the present invention.

[0067] Figure 2 This is a schematic diagram of Lissajous ellipse iterative fitting according to an embodiment of the present invention. Detailed Implementation

[0068] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of the present invention. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort should fall within the scope of protection of the present invention.

[0069] Embodiments of the present invention provide a method for correcting phase measurement errors in a laser frequency-modulated interferometer. This method corrects the unequal amplitudes and biases of orthogonal signals in real time based on the conversion relationship between the characteristics of orthogonal signals and elliptic parameters, thereby ultimately correcting the nonlinear errors in phase measurement. Figures 1-2 As shown, it includes the following steps:

[0070] Step S1: Obtain the orthogonal phase measurement signal from the laser frequency modulated interferometer, and represent the orthogonal phase measurement signal using the standard elliptic equation.

[0071] Specifically, the steps include the following:

[0072] The expression for the orthogonal phase measurement signal of a laser frequency modulated interferometer is:

[0073]

[0074] Among them, I′ x (t) and I′ y (t) represent the orthogonal phase measurement signals in the x and y directions, respectively, a x =BJ1(C) and a y=BJ2(C) represents the amplitudes of the orthogonal signals in the x and y directions, respectively, where B is the amplitude of the AC component of the laser interference signal, J1 and J2 are the first-order and second-order Bessel functions, respectively, C is the phase modulation depth value, and x0 and y0 are offsets. Let t be the phase angle and t be the time variable.

[0075] After discretizing the standard elliptic equation using a Kalman filter, and normalizing the standard elliptic equation using f = -1, the orthogonal phase measurement signal can be represented using the standard elliptic equation as follows:

[0076] aI x ′(t) 2 +cI y ′(t) 2 +2dI x ′(t)+2eI y ′(t)+f=0

[0077] a+c>0

[0078] Where a, c, d, e, and f are the coefficients of the standard elliptic equation, and the relationship between the amplitude and offset of the orthogonal signal and the standard elliptic coefficients is as follows:

[0079]

[0080] Step S2: Discretize the standard elliptic equation using a Kalman filter and define the discretized state vector.

[0081] This step specifically includes:

[0082] Define the variables in the Kalman filter, discretize the equation, and normalize the standard elliptic equation using f = -1. The specific expression is as follows:

[0083] a k I' x (k) 2 +c k I y ′(k) 2 +2d k I' x (k)+2e k I y ′(k)=1,

[0084] a k +c k >0)

[0085] Among them, a k c k d k and e k For different parameters of the discretized elliptic equation, I′x (k) and I′ y (k) represents the discrete orthogonal phase measurement signals in the x and y directions, respectively.

[0086] When defining the discretized state vector, k = 1, 2, ..., N-1 is used as the numbering of the buffer sequence. Based on this discretization equation, the state vector is defined as follows:

[0087] X k =(a k ,c k ,d k ,e k ) T

[0088] Observation matrix:

[0089]

[0090] Approximate values ​​that can be obtained as the truth value:

[0091] H k =[I x ′0(k) 2 ,I′ y0 (k) 2 ,2I x ′0(k),2I′ y0 (k)]

[0092] The measurement results are as follows:

[0093] Z k =H k X k =1

[0094] Among them, Z k For the measurement results, H k An approximation of the true value can be obtained, X k Let I′ be the state vector. x0 (k) and I′ y0 (k) are the orthogonal measurement discrete signals offset in the x and y directions, respectively.

[0095] Step S3: Input the state vector into the Kalman filter to obtain the prior estimate of the state vector and the posterior estimate of the state vector at the previous time step, and obtain the time update equation relating the prior estimate and the posterior estimate.

[0096] Specifically, the steps include the following:

[0097] The time update equation is obtained, and its specific expression is:

[0098]

[0099] in, and Let be the prior estimate of the state vector at time k and the prior estimate of the error. and Let w be the posterior estimate of the state vector at time k-1 and the posterior estimate of the error covariance, respectively. k With Q k =E[w k w k T [W represents process noise and covariance.] k F represents k Approximate error to I, initial value and Set as:

[0100]

[0101] When obtaining the time update equation, it is necessary to obtain the measurement noise covariance and the process noise covariance, the specific expressions of which are as follows:

[0102]

[0103] Among them, R k To measure the noise covariance, σ 2 For variance, and These are the prior estimates of the state vector, Q. k Let E be the process noise covariance, and w be the process noise covariance. k w k T The expectation is that the noise of the two demodulation channels is independent and has equal variance, and the specific expression is:

[0104] I x ′~N(I x ′0,σ 2 )

[0105] I y ′~N(I y ′0,σ 2 )

[0106] Among them, I x ′~N(·) represents the noise of the demodulation channel in the x-direction, I′ y ~N(·) represents the noise of the demodulation channel in the y direction, I x ′0 is the orthogonal phase signal after offset in the x-direction, I′ y0 This is the orthogonal phase signal after offset in the y-direction. x and a y The estimation biases are independently distributed, with variances of (ξa) and (ξa) respectively. x ) 2 With (ξa)y ) 2 Where ξ is a proportionality constant, and to compensate for the amplitude uncertainty caused by factors such as probe coupling efficiency, ξ is set to 2×10⁻⁵. The observation covariance Q is obtained under the condition that d and e are sufficiently small relative to a and c. K .

[0107] Step S4: Obtain the posterior estimated covariance, determine the Kalman gain based on the posterior estimated covariance with zero partial derivative, and obtain the phase measurement update equation at the current time through the Kalman gain and the time update equation.

[0108] Specifically, the steps include the following:

[0109] The Kalman gain is determined based on the fact that the partial derivative of the posterior estimated covariance is zero. The specific expression is as follows:

[0110]

[0111] Among them, P k =E[e k e k T [K] is the posterior estimate of the covariance. k For Kalman gain.

[0112] The specific expression for the phase measurement update equation is as follows:

[0113]

[0114] in, Let k be the error covariance. Observation matrix The transpose of the matrix, For X k The posterior estimate, Z k For the measurement result, I is a constant value.

[0115] Step S5: Introduce four discrete points near the four axes of the Lissajous ellipse for iterative fitting, setting a displacement interval of 1 / n (n=8) wavelength between two iterations. Initialize the iteration by rotating the Lissajous ellipse using scanning laser temperature to obtain orthogonal phase measurement signals containing the four discrete points. Correct these signals using the phase measurement update equation. To ensure the dynamic fitting capability of the variable Lissajous ellipse, the proportionality constant ξ is usually assigned a large value.

[0116] The orthogonal phase measurement signal is corrected using posterior estimation, and the specific expression is as follows:

[0117]

[0118] Among them, I″ x (k) and I″ y (k) represents the discrete orthogonal phase measurement signals in the x and y directions after correction, respectively, where x0(k) and y0(k) are the offsets in the x and y directions at time k, respectively. x (k) and a y (k) represents the amplitude of the orthogonal signal in the x and y directions at time k, respectively. For precise interference phase.

[0119] Based on the above methods and statements, the present invention provides a laser frequency modulated interferometer phase measurement error correction system, including an acquisition module, a preprocessing module, an update module and a correction module.

[0120] The system comprises the following modules: an acquisition module for acquiring the orthogonal phase measurement signal from a laser frequency-modulated interferometer and representing it using the standard elliptic equation; a preprocessing module for discretizing the standard elliptic equation using variables in a Kalman filter and defining the discretized state vector; a data processing module for inputting the state vector into the Kalman filter, acquiring the prior estimate of the state vector and the posterior estimate of the state vector at the previous time step, and obtaining the time update equation relating the prior and posterior estimates; an update module for acquiring the posterior estimate covariance, determining the Kalman gain based on the posterior estimate covariance with zero partial derivatives, and obtaining the phase measurement update equation for the current time step using the Kalman gain and the time update equation; and a correction module for introducing four discrete points in the vicinity of the four axes of the Lissajous ellipse for iterative fitting, initializing the iteration by rotating the Lissajous ellipse by scanning the laser temperature, obtaining the orthogonal phase measurement signal containing the four discrete points, and correcting the orthogonal phase measurement signal containing the four discrete points using the phase measurement update equation.

[0121] The present invention also provides a computer device, including a memory and a processor. The memory stores a program, and when the program is executed by the processor, the processor performs the steps of a laser frequency modulated interferometer phase measurement error correction method.

[0122] According to the disclosed embodiments, the computer device can communicate with one or more external devices (e.g., keyboard, pointing device, Bluetooth communication, etc.) or with any device that enables the computing device to communicate with one or more other computing devices (e.g., router, demodulator, etc.).

[0123] The above description, in conjunction with specific preferred embodiments, provides a more detailed explanation of the present invention. For those skilled in the art, various simple deductions or substitutions can be made without departing from the concept of the present invention, and all such deductions or substitutions should be considered to fall within the scope of protection of the present invention.

Claims

1. A method of correcting phase measurement errors in a laser frequency-modulation interferometer, characterized by, The method comprises the following steps: obtaining a laser frequency modulation interferometer quadrature phase measurement signal, and representing the obtained quadrature phase measurement signal by using a standard ellipse equation; discretizing the standard ellipse equation by using a Kalman filter, and defining a discretized state vector; inputting the state vector into the Kalman filter, obtaining a priori estimation of the state vector and a posteriori estimation of the state vector at a previous time, and obtaining a time update equation of the relationship between the priori estimation and the posteriori estimation; obtaining a posteriori estimation covariance, determining a Kalman gain according to the posteriori estimation covariance being zero, and obtaining a phase measurement update equation at a current time by using the Kalman gain and the time update equation; introducing four discrete points near four axes of a Lissajous ellipse for iterative fitting, setting a two-time iterative displacement interval of 1 / 8 wavelength, rotating the Lissajous ellipse by scanning a laser temperature to perform initialization iteration, obtaining a quadrature phase measurement signal containing the four discrete points, and correcting the quadrature phase measurement signal containing the four discrete points by using the phase measurement update equation; the time update equation of the relationship between the priori estimation and the posteriori estimation comprises the following steps: the time update equation is obtained, and a specific expression is as follows: ； ； wherein with is the prior estimate of the state vector at time k and the prior estimate of the error, with are the posterior estimate of the state vector at time k-1 and the posterior estimate of the error covariance, respectively, and w k with is the process noise and the covariance, wherein with the initial values of are, respectively, ； ； wherein and are respectively and the initial value of when the time update equation is obtained, the following steps are further included: obtaining a measurement noise covariance and a process noise covariance, and a specific expression is as follows: ； ； Among them, R k To measure the noise covariance, σ 2 For variance, , , and These are the prior estimates of the state vector, Q. k Let E be the process noise covariance. The expectation is that the noise of the two demodulation channels is independent and has equal variance, and the specific expression is: ； ； where is the noise of the x-direction demodulation channel, is the noise of the y-direction demodulation channel, is the x-direction offset quadrature phase signal, is the y-direction offset quadrature phase signal; a x and a y are the amplitudes of the quadrature signals in the x-direction and y-direction, respectively, where a x and a y are the estimation biases, which are independently distributed with variances and where is a proportionality constant, and is set to 2 x 10 -5 .

2. A method of correcting phase measurement errors in a laser frequency modulated interferometer as claimed in claim 1, characterized in that, the method for obtaining the laser frequency modulation interferometer quadrature phase measurement signal and representing the obtained quadrature phase measurement signal by using the standard ellipse equation comprises the following steps: a specific expression of the laser frequency modulation interferometer quadrature phase measurement signal is as follows: ； ； wherein, and are orthogonal phase measurement signals in x and y directions, respectively, and are amplitudes of the orthogonal signals in x and y directions, respectively, wherein B is an amplitude of an AC component of the laser interference signal, J1 and J2 are first and second order Bessel functions, respectively, C is a phase modulation depth value, and x0 and y0 are offsets, is a phase angle, and t is a time variable; the quadrature phase measurement signal is represented by using the standard ellipse equation, and a specific expression is as follows: ； ； wherein a, c, d, e and f are standard ellipse equation coefficients, and a relationship between an amplitude, an offset and the standard ellipse equation coefficients of the quadrature signal is as follows: ； ； ； 。 3. A method of correcting phase measurement errors in a laser frequency modulated interferometer as claimed in claim 2, wherein, after the standard ellipse equation is discretized by using the Kalman filter, the standard ellipse equation is normalized by using f=-1, and a specific expression is as follows: ； ； where a k , c k , d k , and e k are the discretized different parameters of the ellipse equation, respectively, and are the discretized orthogonal phase measurement signals in x and y directions, respectively.

4. A method of correcting phase measurement errors in a laser frequency modulated interferometer as claimed in claim 3, wherein, when the discretized state vector is defined, k=1, 2…N-1 is taken as a buffer sequence number, and the state vector is defined as follows: ； Observation matrix is: ； an available approximate value as a true value is as follows: ； a measurement result is as follows: ； where Z k is the measurement result, H k is the true value of the approximated value, X k is the state vector, and are the offset orthogonal measurement discrete signals in the x direction and y direction, respectively.

5. A method of correcting phase measurement errors in a laser frequency modulated interferometer as recited in claim 1, wherein, the method for determining the Kalman gain according to the posteriori estimation covariance being zero and obtaining the phase measurement update equation at the current time by using the Kalman gain and the time update equation comprises the following steps: the Kalman gain is determined according to the derivative of the posteriori estimation covariance being zero, and a specific expression is as follows: ； wherein, is the posterior covariance estimate, K k is the Kalman gain; a specific expression of the phase measurement update equation is as follows: ； ； ； wherein, is the error covariance at time k, is the observation matrix is the transpose matrix of is the posterior estimate of Z k is the measurement, and I is a constant value.

6. A method of correcting phase measurement errors in a laser frequency modulated interferometer as recited in claim 1, wherein, the quadrature phase measurement signal containing the four discrete points is corrected by using the phase measurement update equation, and a specific expression is as follows: ； ； ； wherein and are the corrected discrete quadrature phase measurement signals in the x- and y-direction, respectively, and are the offsets in the x- and y-direction at time k, respectively, and are the amplitudes of the quadrature signals in the x- and y-direction at time k, respectively, is the exact interference phase.

7. A laser frequency-modulation interferometer phase measurement error correction system characterized by, the method comprises the following steps: an obtaining module is configured to obtain a laser frequency modulation interferometer quadrature phase measurement signal, and represent the obtained quadrature phase measurement signal by using a standard ellipse equation; a preprocessing module is configured to discretize the standard ellipse equation by using a Kalman filter, and define a discretized state vector; The data processing module is configured to input the state vector into a Kalman filter, obtain a priori estimation of the state vector and a posteriori estimation of the state vector at a previous time, and obtain a time update equation of the relationship between the priori estimation and the posteriori estimation. The updating module is configured to obtain a posteriori estimation covariance, determine a Kalman gain according to the posteriori estimation covariance being zero, and obtain a phase measurement update equation at a current time by the Kalman gain and the time update equation. The correction module is configured to introduce four discrete points in a vicinity of four axes of a Lissajous ellipse for iterative fitting, set a two-time iterative displacement interval of 1 / 8 wavelength, initialize iteration by rotating the Lissajous ellipse by scanning laser temperature, obtain quadrature phase measurement signals containing the four discrete points, and correct the quadrature phase measurement signals containing the four discrete points by using the phase measurement update equation. The time update equation of the relationship between the priori estimation and the posteriori estimation comprises the following steps: The time update equation is obtained, and a specific expression is as follows: ； ； wherein with is the prior estimate of the state vector at time k and the prior estimate of the error, with are the posterior estimate of the state vector at time k-1 and the posterior estimate of the error covariance, respectively, and w k with is the process noise and the covariance, wherein with the initial values of and are, respectively, ； ； wherein and are respectively and the initial value of When the time update equation is obtained, the following steps are further included: The measurement noise covariance and the process noise covariance are obtained, and specific expressions are as follows: ； ； Among them, R k To measure the noise covariance, σ 2 For variance, , , and These are the prior estimates of the state vector, Q. k Let E be the process noise covariance. The expectation is that the noise of the two demodulation channels is independent and has equal variance, and the specific expression is: ； ； where is the noise of the x-direction demodulation channel, is the noise of the y-direction demodulation channel, is the x-direction offset quadrature phase signal, is the y-direction offset quadrature phase signal; a x and a y are the amplitudes of the quadrature signals in the x-direction and y-direction, respectively, where a x and a y are the estimation errors of a and where is a proportionality constant, and is set to 2 x 10 -5 .

8. A computer device, comprising: The laser frequency modulation interferometer phase measurement error correction method comprises a memory and a processor, the memory stores a program, and the program is executed by the processor to enable the processor to execute the steps of the laser frequency modulation interferometer phase measurement error correction method according to any one of claims 1 to 6.

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