Dual-frequency laser interferometer displacement measurement method based on adaptive nonlinear error compensation

Abstract

The application provides a dual-frequency laser interference displacement measurement method based on adaptive nonlinear error compensation, and belongs to the technical field of laser precision measurement. The method comprises the following steps: collecting a reference beat frequency signal and a measurement beat frequency signal of a dual-frequency laser interferometer, performing quadrature demodulation to obtain a phase difference sequence, and generating an initial displacement sequence; performing motion trend fitting and trend separation on the phase difference sequence according to a sliding measurement window to obtain a phase residual sequence, and extracting a window state parameter; calculating a dynamic update coefficient according to the window state parameter, and updating a nonlinear error model in combination with the phase residual sequence; calculating a nonlinear error compensation amount according to the updated nonlinear error model, compensating the initial displacement sequence, and obtaining a displacement measurement result. The application is helpful to improve the compensation stability and measurement consistency of the dual-frequency laser interference displacement measurement under a dynamic working condition.

Description

Technical Field

[0001] This application belongs to the field of laser precision measurement technology, and in particular relates to a dual-frequency laser interferometric displacement measurement method based on adaptive nonlinear error compensation. Background Technology

[0002] Dual-frequency laser interferometric displacement measurement technology is widely used in semiconductor manufacturing, precision calibration of CNC machine tools, and nano-positioning systems due to its advantages such as high resolution and strong anti-interference capability. This technology typically uses dual-frequency lasers with a fixed frequency difference to generate a reference beat frequency signal and a measurement beat frequency signal, and achieves displacement measurement through phase demodulation.

[0003] However, in practical applications, dual-frequency laser interferometers always suffer from a nonlinear error with a period of λ / 2, the amplitude of which typically ranges from several nanometers to tens of nanometers. This is a major bottleneck restricting precision measurements down to the sub-nanometer and even picometer levels. This error mainly includes frequency / polarization aliasing (Type I error) caused by insufficient extinction ratio of the polarization beam splitter, and ghost reflections / virtual beams generated by multiple reflections at the optical interface (Type II error). More importantly, these nonlinear errors undergo significant dynamic drift with changes in measurement speed, ambient temperature, light intensity fluctuations, optical path disturbances, and long-term system aging, making it difficult for error compensation models with fixed parameters to consistently and accurately describe the actual error characteristics.

[0004] In existing technologies, nonlinear error compensation methods are mainly divided into two categories: hardware suppression and software compensation. While hardware methods can suppress error sources to a certain extent, they suffer from problems such as complex structure, high cost, and difficult debugging. Regarding software compensation, early methods primarily relied on Heydemann elliptic fitting and fixed-coefficient harmonic models, followed by the development of algorithms such as Kalman filtering. However, most of these methods are based on offline calibration or static model parameters, and their compensation effectiveness significantly decreases under dynamic measurement conditions.

[0005] While some adaptive compensation algorithms that have emerged in recent years have attempted online updates to some extent, they still suffer from the following shortcomings: they typically employ fixed-length sliding windows, making it difficult to balance dynamic response speed and statistical stability; they often rely on a single feature parameter to drive model updates, failing to comprehensively reflect error variations under complex dynamic conditions; furthermore, they generally lack effective signal quality gating mechanisms, easily introducing erroneous updates under low signal-to-noise ratio or abnormal conditions, leading to model parameter oscillations or divergence; and moreover, most existing model update strategies lack smoothing constraints, making it difficult to achieve reliable and stable parameter evolution. These deficiencies mean that current technologies still struggle to meet the sub-nanometer long-term stable accuracy requirements of high-end precision equipment in industrial scenarios such as variable speed, variable temperature, and long-term continuous measurement.

[0006] Therefore, there is an urgent need for a dual-frequency laser interferometric displacement measurement method that can adaptively update the nonlinear error model according to the real-time changes in the system state under dynamic measurement conditions, and achieve stable and highly robust error compensation by combining multi-parameter state joint judgment and signal validity gating. Summary of the Invention

[0007] This application provides a dual-frequency laser interferometric displacement measurement method based on adaptive nonlinear error compensation, which solves the problem that existing dual-frequency laser interferometric displacement measurement technology is difficult to adapt to dynamic working conditions.

[0008] This application provides a dual-frequency laser interferometric displacement measurement method based on adaptive nonlinear error compensation, comprising the following steps: S1. Acquire the reference beat frequency signal and the measured beat frequency signal of the dual-frequency laser interferometer, perform orthogonal demodulation on the reference beat frequency signal and the measured beat frequency signal to obtain the phase difference sequence, and generate the initial displacement sequence based on the phase difference sequence; S2. Fit the motion trend of the phase difference sequence according to the sliding measurement window, and perform trend separation based on the fitting result to obtain the phase residual sequence. Extract window state parameters based on the phase difference sequence, the phase residual sequence, the reference beat frequency signal, and the measured beat frequency signal. The window state parameters include the equivalent frequency difference change, the phase residual fluctuation, and the channel amplitude imbalance. S3. Perform weighted calculations based on the window state parameters to obtain dynamic update coefficients. When the current sliding measurement window meets the signal validity condition, update the nonlinear error model based on the dynamic update coefficients and the phase residual sequence. When the current sliding measurement window does not meet the signal validity condition, keep the model parameters of the nonlinear error model unchanged. S4. Calculate the nonlinear error compensation amount of the current sliding measurement window according to the updated nonlinear error model, and use the nonlinear error compensation amount to compensate the initial displacement sequence to obtain the displacement measurement result.

[0009] As an optional approach in this application, in step S1, the reference beat frequency signal and the measured beat frequency signal are orthogonally demodulated to obtain the corresponding in-phase component and quadrature component, respectively, and then the phase difference sequence is obtained according to the following formula: ; in, For the first i Phase difference at each sampling time, I m，i , Q m，i These are the in-phase and quadrature components of the beat frequency signal, respectively. I r，i ,Q r，i These are the in-phase and quadrature components of the reference beat frequency signal, respectively, and unwrap[ ] represents phase expansion processing.

[0010] As an optional embodiment of this application, in step S1, the initial displacement sequence is generated according to the following formula: ; in, L 0,i For the first i The initial displacement value at each sampling time. l The laser wavelength used in the dual-frequency laser interferometer q The optical path multiplication factor corresponding to the measurement optical path configuration. For the first i The phase difference at each sampling time.

[0011] As an optional approach in this application, in step S2, the process of fitting the motion trend of the phase difference sequence according to the sliding measurement window and performing trend separation based on the fitting result is as follows: In the current sliding measurement window W j Within this process, a polynomial motion trend fitting is performed on the phase difference sequence to obtain the motion trend phase fitting term: ; in, W j For the first j A sliding measurement window, For the first i The motion trend phase fitting value corresponding to each sampling time. a p,j For the current sliding measurement window W j The first p Order of fit coefficients, t i For the first i The amount of time between each sampling moment and the start time of the current sliding measurement window. For the first i Each sampling moment corresponds to a time quantity p Second item, K Let be the order of the motion trend fitting, and K It is a positive integer; And based on the motion trend phase fitting term, the phase difference sequence is subjected to trend separation to obtain the phase residual sequence: ; in, For the first iThe phase residual value corresponding to each sampling time. For the first i Phase difference at each sampling time, For the first i The motion trend phase fitting value corresponding to each sampling time.

[0012] As an optional approach in this application, step S2, extracting the window state parameters, includes: a. Determine the current sliding measurement window based on the phase difference sequence. W j Corresponding equivalent frequency difference parameter n j Then, based on the current sliding measurement window W j Corresponding equivalent frequency difference parameter n j And the previous sliding measurement window W j-1 Corresponding equivalent frequency difference parameter n j-1 Determine the equivalent frequency difference change Δ n j ; Current sliding measurement window W j Corresponding equivalent frequency difference parameter n j for: ; in, N j For the current sliding measurement window W j The number of sampling points within, Δt The time interval between adjacent sampling times. For the first i The phase difference corresponding to each sampling time; Current sliding measurement window W j The corresponding equivalent frequency difference change Δ n j for: ; in, n j For the current sliding measurement window W j The corresponding equivalent frequency difference parameter, n j-1 For the previous sliding measurement window W j-1 The corresponding equivalent frequency difference parameter; e The preset stability adjustment parameters, and e>0; b. Determine the current sliding measurement window based on the phase residual sequence. W j The corresponding mean phase residual Then, based on the mean of the phase residuals Determine the current sliding measurement window W j Corresponding phase residual fluctuation s e,j ; Current sliding measurement window W j The corresponding mean phase residual for: ; Current sliding measurement window W j Corresponding phase residual fluctuation s e,j for: ; in, For the first i The phase residual corresponding to each sampling time. For the current sliding measurement window W j The corresponding mean of the phase residuals; N j For the current sliding measurement window W j The number of sampling points within; c. Determine the current sliding measurement window based on the reference beat frequency signal and the measured beat frequency signal. W j Corresponding channel amplitude imbalance d A,j : ; in, A m,j For the current sliding measurement window W j The amplitude statistics of the internally measured beat frequency signal. A r,j For the current sliding measurement window W j Amplitude statistics of the internal reference beat frequency signal. A m,0 To measure the amplitude statistics of the beat frequency signal under calibrated conditions, A r,0 This is a statistical measure of the amplitude of the reference beat frequency signal under calibrated conditions. e The preset stability adjustment parameters, and e >0.

[0013] As an optional approach in this application, in step S3, the dynamic update coefficients are obtained by weighted calculation based on the window state parameters, including: According to the equivalent frequency difference change Δ n j The phase residual fluctuation amount s e,j and the channel amplitude imbalance d A,j Determine the current sliding measurement window W j Corresponding dynamic state factor or j : ; in, E 0 This is the normalized reference value for the phase residual. α , β , c Let be the weighting coefficient, and satisfy: 0≤ α ≤1,0≤ β ≤1,0≤ c ≤1, α + β + c =1; According to the dynamic state factor or j Determine the current sliding measurement window W j Corresponding dynamic update coefficients m j : ; in, m j For the current sliding measurement window W j The corresponding dynamic update coefficients, m max To update the upper limit of the coefficient, m 0 Based on the updated coefficients, This is a dynamic adjustment coefficient. R j The effective factor of the signal; If the current sliding measurement window W j When the signal validity condition is met, R j =1; If the current sliding measurement windowW j When the signal validity condition is not met, R j =0.

[0014] As an optional approach in this application, in step S3, the current sliding measurement window is determined. W j Whether the signal is valid includes: The current sliding measurement window is determined based on the measured beat frequency signal and the reference beat frequency signal, respectively. W j Corresponding measurement channel signal-to-noise ratio S m,j and reference channel signal-to-noise ratio S r,j ; When the signal-to-noise ratio of the measurement channel S m,j Not less than the signal-to-noise ratio threshold of the measurement channel S m,min The reference channel signal-to-noise ratio S r,j Not less than the reference channel signal-to-noise ratio threshold S r,min The channel amplitude imbalance d A,j Not greater than the amplitude imbalance threshold d max And the current sliding measurement window W j The phase residual jump variable corresponding to adjacent sampling times is not greater than the residual jump threshold. E max At that time, determine the current sliding measurement window. W j The signal validity condition is met; Otherwise, determine the current sliding measurement window. W j The signal validity conditions are not met.

[0015] As an optional embodiment of this application, the nonlinear error model is a phase nonlinear error model based on periodic phase mapping. In step S3, updating the nonlinear error model according to the dynamic update coefficients and the phase residual sequence includes: Based on the current sliding measurement window W j The candidate nonlinear error model parameter vector is obtained by fitting the phase residual sequence within the interval. ; Based on the previous sliding measurement window W j-1 Corresponding model parameter vector Pj-1 Current sliding measurement window W j Corresponding candidate nonlinear error model parameter vector and dynamic update coefficients m j Update the current sliding measurement window W j Corresponding model parameter vector P j : ; in, P j For the current sliding measurement window W j The corresponding updated model parameter vector, P j-1 For the previous sliding measurement window W j-1 The corresponding model parameter vector, Based on the current sliding measurement window W j The parameter vector of the candidate nonlinear error model obtained by fitting the inner phase residual sequence. m j For the current sliding measurement window W j The corresponding dynamic update coefficients.

[0016] As an optional embodiment of this application, the phase nonlinear error model based on periodic phase mapping is constructed as follows: Based on phase difference Determine the first i The periodic phase corresponding to each sampling time i i : ; in, i i For the first i The periodic phase corresponding to each sampling time. This indicates the floor function; According to the periodic phase i i Construct a phase nonlinear error model: ; in, For the current sliding measurement window W j The corresponding phase nonlinearity error value, H It is the harmonic order, and H It is a positive integer. hFor harmonic order indexing, c h,j and d h,j These are the current sliding measurement windows. W j Inner h The sine and cosine model parameters corresponding to the first harmonic; The model parameter vector P includes: ; in,[ ] T This indicates the transpose operation.

[0017] As an optional embodiment of this application, step S4, calculating the nonlinear error compensation amount of the current sliding measurement window based on the updated nonlinear error model, and using the nonlinear error compensation amount to compensate the initial displacement sequence, includes: According to the i The periodic phase corresponding to each sampling time i i and the current sliding measurement window W j The corresponding updated model parameter vector P j Determine the first i Phase nonlinear error value at each sampling time ; According to the phase nonlinear error value Determine the first i The nonlinear error compensation amount Δ at each sampling time L i : ; Where, Δ L i For the first i The nonlinear error compensation amount corresponding to each sampling time. l The laser wavelength used in the dual-frequency laser interferometer q The optical path multiplication factor corresponding to the form of the measurement optical path; According to the nonlinear error compensation amount Δ L i For the first i Initial displacement value corresponding to each sampling time L 0,i Error compensation is performed to obtain the first... i Displacement measurement results at each sampling time L i : ; in,L i No. i Displacement measurement results corresponding to each sampling time. L 0,i Let be the initial displacement value corresponding to the i-th sampling time.

[0018] Compared with the prior art, this application has the following beneficial effects: This application provides a dual-frequency laser interferometric displacement measurement method based on adaptive nonlinear error compensation. It uses a sliding measurement window to fit and separate the motion trend of the phase difference sequence, and calculates dynamic update coefficients based on multiple parameters such as equivalent frequency difference change, phase residual fluctuation, and channel amplitude imbalance. This enables real-time adaptive updating of the nonlinear error model. Simultaneously, a signal validity condition judgment mechanism is introduced to maintain model parameters unchanged under low-quality signal conditions, thereby avoiding erroneous updates and improving compensation stability and robustness under dynamic conditions such as variable speed and temperature. Compared with existing technologies, this application can improve the accuracy and long-term reliability of dual-frequency laser interferometric displacement measurement under dynamic conditions such as measurement speed changes and environmental disturbances, making it suitable for the high-stability measurement requirements of high-precision equipment. Attached Figure Description

[0019] To more clearly illustrate the technical solutions in the embodiments of this application or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0020] Figure 1 A flowchart of a dual-frequency laser interferometric displacement measurement method based on adaptive nonlinear error compensation provided in an embodiment of this application. Detailed Implementation

[0021] To make the objectives, technical solutions, and advantages of the embodiments of this application clearer, the technical solutions in the embodiments of this application are described clearly and completely below. Obviously, the described embodiments are only some embodiments of this application, not all embodiments. Based on the embodiments in this application, all other embodiments obtained by those skilled in the art without creative effort are also within the scope of protection of this application.

[0022] This application provides a dual-frequency laser interferometric displacement measurement method based on adaptive nonlinear error compensation, relating to real-time nonlinear error compensation technology for dual-frequency laser heterodyne interferometers, such as... Figure 1 As shown, the dual-frequency laser interferometric displacement measurement method based on adaptive nonlinear error compensation includes the following steps: S1. Acquire the reference beat frequency signal and the measured beat frequency signal of the dual-frequency laser interferometer, perform orthogonal demodulation on the reference beat frequency signal and the measured beat frequency signal to obtain the phase difference sequence, and generate the initial displacement sequence based on the phase difference sequence; S2. Fit the motion trend of the phase difference sequence according to the sliding measurement window, and perform trend separation based on the fitting results to obtain the phase residual sequence. Extract the window state parameters based on the phase difference sequence, the phase residual sequence, the reference beat frequency signal, and the measured beat frequency signal. The window state parameters include the equivalent frequency difference change, the phase residual fluctuation, and the channel amplitude imbalance. S3. Perform weighted calculations based on window state parameters to obtain dynamic update coefficients. When the current sliding measurement window meets the signal validity condition, update the nonlinear error model based on the dynamic update coefficients and phase residual sequence. When the current sliding measurement window does not meet the signal validity condition, keep the model parameters of the nonlinear error model unchanged. S4. Calculate the nonlinear error compensation amount of the current sliding measurement window based on the updated nonlinear error model, and use the nonlinear error compensation amount to compensate the initial displacement sequence to obtain the displacement measurement result.

[0023] The dual-frequency laser interferometric displacement measurement method based on adaptive nonlinear error compensation provided in this embodiment first acquires a reference beat frequency signal and a measured beat frequency signal, and then performs orthogonal demodulation on the two beat frequency signals to obtain the corresponding phase difference sequence. The initial displacement sequence is then generated from the phase difference sequence. Since the nonlinear error in dual-frequency laser interferometric displacement measurement is usually superimposed on the actual phase change process, the initial displacement sequence contains not only the true displacement information of the measured object but also periodic error components caused by optical aliasing, channel imbalance, and local disturbances. If a fixed-parameter model is directly used to correct the initial displacement result, deviations between the model parameters and the actual error state are likely to occur when the measurement speed changes, the environmental state fluctuates, or the signal state changes. Therefore, this embodiment further fits the motion trend of the phase difference sequence according to a sliding measurement window and performs trend separation based on the fitting results to obtain the corresponding phase residual sequence. After this processing, the main phase change caused by the normal motion of the measured object can be distinguished from the local nonlinear error fluctuations to a certain extent. The subsequent model update process no longer directly relies on the original phase difference sequence but combines the analysis with the phase residual sequence, which helps to reduce the influence of the normal motion trend on the error feature extraction process.

[0024] After obtaining the phase residual sequence, this embodiment further extracts window state parameters based on the phase difference sequence, the phase residual sequence, the reference beat frequency signal, and the measured beat frequency signal. These window state parameters are defined as the equivalent frequency difference change, the phase residual fluctuation, and the channel amplitude imbalance. The equivalent frequency difference change reflects the phase change state within the current sliding measurement window; the phase residual fluctuation reflects the degree of fluctuation in the residual phase after trend separation; and the channel amplitude imbalance reflects the amplitude correspondence between the reference channel and the measured channel. These parameters correspond to the dynamic state, residual state, and channel state, respectively, describing the measurement state changes within the current sliding measurement window from different perspectives. This embodiment utilizes these window state parameters to participate in the calculation of the dynamic update coefficients, enabling the model update process to adjust according to changes in the current measurement state. When the measurement state change is small, the model parameter change is relatively small; when the dynamic state or residual state changes significantly, the model update process also adjusts accordingly, thus maintaining a good correspondence between the nonlinear error model and the current measurement state.

[0025] Furthermore, this embodiment does not update the nonlinear error model in all states. Instead, it first determines whether the current sliding measurement window meets the signal validity condition. When the current sliding measurement window meets the signal validity condition, the nonlinear error model is updated by combining the dynamic update coefficients and the phase residual sequence. When the current sliding measurement window does not meet the signal validity condition, the current model parameters remain unchanged. After this processing, abnormal phase changes generated in low signal-to-noise ratio states, local abnormal disturbance states, or abnormal channel amplitude states will not directly participate in the model parameter update process, thereby reducing the impact of abnormal windows on the continuous change of model parameters. After completing the model parameter update, this embodiment calculates the corresponding nonlinear error compensation amount based on the updated nonlinear error model and corrects the initial displacement sequence. Since the compensation process can be adjusted according to the measurement state changes within the current sliding measurement window, a dynamic correspondence can be maintained between the model parameters and the error state under variable speed measurement, environmental fluctuations, or long-term continuous measurement conditions, which helps to improve the compensation stability and measurement consistency in the dual-frequency laser interferometric displacement measurement process.

[0026] Furthermore, in some embodiments, in step S1, the reference beat frequency signal and the measured beat frequency signal are orthogonally demodulated to obtain the corresponding in-phase component and quadrature component, respectively, and then the phase difference sequence is obtained according to the following formula: ; in, For the first i Phase difference at each sampling time, I m，i , Qm，i These are the in-phase and quadrature components of the beat frequency signal, respectively. I r，i , Q r，i These are the in-phase and quadrature components of the reference beat frequency signal, respectively, and unwrap[ ] represents phase expansion processing.

[0027] In this embodiment, the reference beat frequency signal and the measured beat frequency signal are first orthogonally demodulated to obtain the corresponding in-phase and quadrature components. Then, the corresponding phase is calculated using the arctangent function, and the phase difference sequence is obtained through the difference operation between the two phases. In dual-frequency laser interferometric displacement measurement, displacement information is mainly characterized by the phase change between the reference light and the measured light. Therefore, the phase extraction result directly affects the subsequent displacement calculation and error compensation process.

[0028] This embodiment employs both in-phase and quadrature components in the instantaneous phase calculation, ensuring that the phase information is related not only to changes in a single amplitude but also to the phase change state of the signal in the complex plane. Even when the beat frequency signal amplitude fluctuates, it can still stably reflect the phase change, thereby reducing the impact of single amplitude changes on the phase calculation results. Simultaneously, the reference beat frequency signal and the measured beat frequency signal undergo phase calculation separately before differential processing. This weakens some common-mode variation factors in the reference and measurement channels during the phase difference calculation process, helping to improve the correspondence between the phase difference sequence and the actual displacement change.

[0029] After obtaining the phase difference sequence, this embodiment further performs phase unwrapping processing on the phase difference sequence. Since the phase output by the arctangent function is usually located within a fixed period interval, when the measured object moves continuously, the phase value is prone to abrupt changes at the period boundary. If the unwrapped phase sequence is directly processed, the phase jump at the period boundary may be mistaken for a true phase fluctuation, thus affecting the subsequent trend fitting and residual analysis results. In addition, this embodiment uses unwrap phase unwrapping processing to keep the phase difference sequence in a continuously changing state during continuous measurement, making the phase change relationship between different sampling times smoother. After this processing, when generating the initial displacement sequence, the correspondence between phase change and displacement change is more continuous; at the same time, when performing motion trend fitting and phase residual analysis within the sliding measurement window, the influence of period jumps on the window state analysis results can also be reduced.

[0030] In this embodiment, the quadrature demodulation, arctangent phase calculation, and phase expansion processing can all be implemented using digital signal processing methods. During implementation, the corresponding calculation processes can be completed by an FPGA, DSP, industrial control computer, or other digital processing units. Those skilled in the art can set the quadrature demodulation method, the number of sampling points, and the phase expansion processing process according to the beat frequency signal sampling frequency and the system's real-time requirements, thereby generating the corresponding phase difference sequence.

[0031] Furthermore, in some embodiments, in step S1, the initial displacement sequence is generated according to the following formula: ; in, L 0,i For the first i The initial displacement value at each sampling time. l The laser wavelength used in the dual-frequency laser interferometer q The optical path multiplication factor corresponding to the measurement optical path configuration. For the first i The phase difference at each sampling time.

[0032] In the above embodiments, after obtaining the phase difference sequence, an initial displacement sequence is further generated based on the correspondence between the phase difference and the displacement. L 0,i .in, l Corresponding to the laser wavelength used in the dual-frequency laser interferometer, q The optical path multiplication factor corresponds to the optical path configuration used in the measurement. Therefore, the phase change can be converted into a displacement change according to a corresponding proportional relationship. Since there is a correspondence between actual displacement and optical path change in dual-frequency laser interferometry, the optical path multiplication relationship is not the same for different optical path structures. For example, the displacement conversion relationships for single-pass reflection structures, double-pass reflection structures, or multi-pass reflection structures differ. Therefore, this embodiment introduces an optical path multiplication factor into the displacement conversion formula. q This allows the displacement calculation process to correspond to the actual measured optical path form, reducing displacement conversion errors caused by differences in optical path structure.

[0033] In this embodiment, the initial displacement value L 0,i Corresponding to the iThe displacement result calculated directly from the phase difference at each sampling time reflects the original displacement measurement state corresponding to the current sampling time. In practice, after obtaining the phase difference sequence, displacement conversion can be performed point-by-point according to the sampling time, thereby generating an initial displacement sequence corresponding to the phase difference sequence. This process maintains the correspondence between sampling points between the phase difference data and the displacement data. Subsequent error analysis, model updates, and error compensation within the sliding measurement window can be directly based on the displacement data at the corresponding sampling time, helping to reduce the impact of index deviations between different data sequences on subsequent calculations.

[0034] In practical applications l This refers to the laser wavelength used in the dual-frequency laser interferometer. In this embodiment, the dual-frequency laser interferometer uses a He-Ne dual-frequency laser with a nominal wavelength of 632.8 nm. l 632.8 nm was used in the initial displacement calculation; when the dual-frequency laser interferometer used has an actual wavelength obtained through metrological calibration, the actual wavelength obtained through metrological calibration can also be used as... l Substitute into the calculation. Optical path multiplication factor. q The settings can be adjusted according to the optical path configuration. When using the common Michelson two-way reflection measurement structure, q It can be set to 2. This embodiment clarifies... l , q , as well as L 0,i The correspondence between them provides a clear data source and calculation relationship for the displacement conversion process, allowing those skilled in the art to generate the initial displacement sequence based on the corresponding parameters.

[0035] In some embodiments, in step S2, the process of fitting the motion trend of the phase difference sequence according to the sliding measurement window and performing trend separation based on the fitting result is as follows: In the current sliding measurement window W j Within this process, a polynomial motion trend fitting is performed on the phase difference sequence to obtain the motion trend phase fitting term: ; in, W j For the first j A sliding measurement window, For the first i The motion trend phase fitting value corresponding to each sampling time. a p,j For the current sliding measurement window W j The first p Order of fit coefficients, t i For the first i The amount of time between each sampling moment and the start time of the current sliding measurement window. For the first i Each sampling moment corresponds to a time quantity p Second item, K Let be the order of the motion trend fitting, and K It is a positive integer; And based on the motion trend phase fitting term, the phase difference sequence is trend separated to obtain the phase residual sequence: ; in, For the first i The phase residual value corresponding to each sampling time. For the first i Phase difference at each sampling time, For the first i The motion trend phase fitting value corresponding to each sampling time.

[0036] In the above embodiment, the phase difference sequence is not directly used for subsequent nonlinear error analysis, but is first fitted with motion trends according to the sliding measurement window. Because the phase difference sequence in dual-frequency laser interferometric displacement measurement includes both the main phase changes caused by the motion of the measured object and local changes caused by nonlinear errors, local disturbances, and signal fluctuations, if error analysis is performed directly based on the original phase difference sequence, normal motion changes and local error fluctuations can easily overlap, thus affecting the results of subsequent window state analysis. Therefore, in this embodiment, within the current sliding measurement window... W j Within this process, a polynomial motion trend fitting is performed on the phase difference sequence, and the motion trend phase fitting term is used to... The main phase change states within the window are described here. t i Adopting the first i The time value of each sampling moment relative to the start time of the current sliding measurement window enables different sliding measurement windows to complete local trend fitting based on the time benchmark within the corresponding window, facilitating continuous processing window by window.

[0037] After obtaining the motion trend phase fitting term, this embodiment further uses phase difference... Phase fit value with motion trend The difference between them generates a phase residual sequence. The phase residual value corresponds to the phase change portion remaining after deducting the main motion trend within the current window, reflecting the local fluctuation state outside the trend change. This processing allows the low-order change components caused by the normal motion of the measured object in the phase difference sequence to be distinguished to some extent from the local error fluctuation components, thus enabling the subsequent window state parameter extraction process to focus more on the residual changes outside the trend. For measurement conditions involving variable speed motion, short-term dynamic changes, or significant local disturbances, the polynomial trend fitting method is more suitable for describing the phase change state within the window than simple mean processing or adjacent difference processing, helping to reduce the impact of normal motion changes on the phase residual analysis results.

[0038] In practical applications, the data processing unit can sequentially select the current sliding measurement window from the phase difference sequence according to the preset window length and sliding step size. W j The trend fitting calculation is performed based on the phase difference data corresponding to each sampling time within the current window. During implementation, the polynomial fitting coefficients... a p,j The least squares fitting method can be used to obtain the fitting order. K The settings can be adjusted based on the measurement dynamic range, sampling frequency, and computational resources. When the measurement motion changes relatively smoothly, a lower-order fitting method can be used to reduce the impact of local high-order fluctuations on the trend fitting results. After fitting, calculations are performed for each sampling time within the window. The corresponding phase residual value can then be obtained.

[0039] In some embodiments, step S2, extracting window state parameters includes: a. Determine the current sliding measurement window based on the phase difference sequence. W j Corresponding equivalent frequency difference parameter n j Then, based on the current sliding measurement window W j Corresponding equivalent frequency difference parameter n j And the previous sliding measurement window W j-1 Corresponding equivalent frequency difference parameter n j-1 Determine the equivalent frequency difference change Δ n j ; Current sliding measurement window W j Corresponding equivalent frequency difference parameter n j for: ; in, N j For the current sliding measurement window W j The number of sampling points within, Δt The time interval between adjacent sampling times. f i For the first i The phase difference corresponding to each sampling time; Current sliding measurement window W j The corresponding equivalent frequency difference change Δ n j for: ; in, n j For the current sliding measurement window W j The corresponding equivalent frequency difference parameter, n j-1 For the previous sliding measurement window W j-1 The corresponding equivalent frequency difference parameter; e The preset stability adjustment parameters, and e >0; b. Determine the current sliding measurement window based on the phase residual sequence. W j The corresponding mean phase residual Then based on the mean of the phase residuals Determine the current sliding measurement window W j Corresponding phase residual fluctuation s e,j ; Current sliding measurement window W j The corresponding mean phase residual for: ; Current sliding measurement window W j Corresponding phase residual fluctuation s e,j for: ; in, For the first i The phase residual corresponding to each sampling time. For the current sliding measurement window W j The corresponding mean of the phase residuals; N jFor the current sliding measurement window W j The number of sampling points within; c. Determine the current sliding measurement window based on the reference beat frequency signal and the measured beat frequency signal. W j Corresponding channel amplitude imbalance d A,j : ; in, A m,j For the current sliding measurement window W j The amplitude statistics of the internally measured beat frequency signal. A r,j For the current sliding measurement window W j Amplitude statistics of the internal reference beat frequency signal. A m,0 To measure the amplitude statistics of the beat frequency signal under calibrated conditions, A r,0 This is a statistical measure of the amplitude of the reference beat frequency signal under calibrated conditions. e The preset stability adjustment parameters, and e >0.

[0040] In this embodiment, the window state parameters include the equivalent frequency difference change Δ n j Phase residual fluctuation s e,j and channel amplitude imbalance d A,j Among them, the equivalent frequency difference parameter n j Through the current sliding measurement window W j The rate of change of phase difference between adjacent sampling times is calculated, reflecting the overall state of phase change over time within the current window. Since the phase change rate changes accordingly with the motion state of the measured object during dual-frequency laser interferometric displacement measurement, the equivalent frequency difference parameter between different sliding measurement windows will also change.

[0041] This embodiment further considers the current sliding measurement window. W j Corresponding equivalent frequency difference parameter n j and the previous sliding measurement window W j-1 Corresponding equivalent frequency difference parameter n j-1 Calculate the equivalent frequency difference change Δ n j This reflects the dynamic changes in the state between adjacent windows. In implementation, a stability adjustment parameter is introduced into the denominator. e This is used to reduce the impact of local fluctuations on the calculation results when the equivalent frequency difference parameter of the previous window is small, making the dynamic state change analysis between windows more stable.

[0042] After obtaining the equivalent frequency difference change, this embodiment further calculates the phase residual fluctuation based on the phase residual sequence. s e,j During implementation, first adjust the current sliding measurement window. W j The phase residuals within the range are statistically analyzed to obtain the mean value of the phase residuals. The phase residual fluctuation is then determined based on the dispersion of each phase residual relative to the mean. Since the phase residual sequence corresponds to the local phase change state after trend separation, the phase residual fluctuation can reflect the dispersion of the residual phase change within the current window. When the system is in a relatively stable measurement state, the phase residual changes corresponding to each sampling time are relatively concentrated, and the phase residual fluctuation is usually small; when affected by local disturbances, vibration changes, or signal fluctuations, the dispersion of the phase residual will change accordingly, and the phase residual fluctuation will also increase accordingly. By parameterizing the phase residual change state, the subsequent model update process can be adjusted in conjunction with the local fluctuation state within the current window.

[0043] Furthermore, this embodiment also determines the channel amplitude imbalance based on the reference beat frequency signal and the measured beat frequency signal. d A,j In practice, the current sliding measurement window is statistically analyzed separately. W j The amplitude states corresponding to the internal measurement beat frequency signal and the reference beat frequency signal are normalized by combining the amplitude statistics corresponding to the calibration state. Then, the channel amplitude imbalance is determined based on the amplitude difference relationship between the two signals. Here, the amplitude statistics can be obtained by using the average amplitude, root mean square value, or envelope statistics within the window. When the light intensity state, device state, or local optical path state between the reference channel and the measurement channel changes, the amplitude relationship between the two beat frequency signals usually changes accordingly. Therefore, the channel amplitude imbalance can reflect the amplitude correspondence state between the two channels within the current window. In this embodiment, by establishing the equivalent frequency difference change, phase residual fluctuation, and channel amplitude imbalance respectively, the dynamic state, residual state, and channel state within the current sliding measurement window can be described in parameter form. The subsequent dynamic update coefficient can be calculated in combination with the above window state parameters. In some embodiments, in step S3, the dynamic update coefficient is obtained by weighted calculation based on the window state parameters, including: Based on the equivalent frequency difference change Δ n j Phase residual fluctuation s e,j Channel amplitude imbalance d A,j Determine the current sliding measurement window W j Corresponding dynamic state factor or j : ; in, E 0 This is the normalized reference value for the phase residual. α , β , c Let be the weighting coefficient, and satisfy: 0≤ α ≤1,0≤ β ≤1,0≤ c ≤1, α + β + c =1; Based on dynamic state factors or j Determine the current sliding measurement window W j Corresponding dynamic update coefficients m j : ; in, m j For the current sliding measurement window W j The corresponding dynamic update coefficients, m max To update the upper limit of the coefficient, m 0 Based on the updated coefficients, This is a dynamic adjustment coefficient. R j The effective factor of the signal; If the current sliding measurement window W j When the signal validity condition is met, R j =1; If the current sliding measurement window W j When the signal validity condition is not met, R j =0.

[0044] In the above embodiments, the dynamically updated coefficients are not fixed values, but are based on the current sliding measurement window. W j The window state parameters within are weighted and calculated. During implementation, the equivalent frequency difference change Δ is first used as the basis. n j Phase residual fluctuation s e,j and channel amplitude imbalance d A,j Calculate the dynamic state factor corresponding to the current window. or j Among them, the equivalent frequency difference change is used to describe the difference in dynamic change state between adjacent sliding measurement windows; the phase residual fluctuation is used to reflect the dispersion of local residual change within the current window; and the channel amplitude imbalance is used to reflect the amplitude correspondence state between the reference channel and the measurement channel. Since the above parameters correspond to the dynamic change state, residual fluctuation state, and channel state respectively, this embodiment uses weighting coefficients... α , β , c The above parameters are weighted and combined so that the dynamic state factor can comprehensively reflect the changes in measurement state within the current sliding measurement window. In implementation, α + β + c =1, used to constrain the weighting relationship between different state parameters; simultaneously, the phase residual fluctuation is normalized to a reference value. E 0 Normalization is performed to make it similar in dimensions to other parameters, thereby reducing the impact of differences in the numerical range of local parameters on the calculation results.

[0045] After obtaining the dynamic state factor or j Subsequently, this embodiment further determines the dynamic update coefficient based on the dynamic state factor corresponding to the current window. m j Among them, the basic update coefficient m 0 Used to determine the base magnitude of model parameter updates, dynamic adjustment coefficients Upper limit of the update coefficient, used to adjust the degree of influence of dynamic state factors on the update process. m max This is used to limit the rapid changes in model parameters when the dynamically updated coefficients are too large. In implementation, m 0 , , m max It can satisfy: 0 < m 0 < mmax <1. In some embodiments, m 0 A value of 0.01 to 0.10 is acceptable. m max A value of 0.10 to 0.50 is acceptable. The value can be 0.5 to 2.0; in this embodiment, m 0 Take 0.05, m max Take 0.2, We set it to 1.0. With this processing, when the window state changes little, the dynamic update coefficients change relatively little, and the model parameters largely retain the changes corresponding to the previous window. When the window state changes significantly, the dynamic update coefficients will also be adjusted accordingly, thus making the candidate model parameters corresponding to the current window have a more significant impact on the model update process. During implementation, those skilled in the art can adjust the parameters according to the dynamic range, sampling frequency, and measurement stability requirements of the measurement system. m 0 , , m max And the weighting coefficients are set. In this embodiment, the weighting coefficients... α , β , c The values ​​are 0.4, 0.3, and 0.3 respectively. In other embodiments, the values ​​of the three can be adjusted according to the degree of influence of the measurement speed change, phase residual fluctuation, and channel amplitude change on the compensation process, but the sum of the three is 1.

[0046] Furthermore, this embodiment also introduces a signal effectiveness factor during the dynamic update coefficient calculation process. R j During implementation, when the current sliding measurement window meets the signal validity condition, R j If the value is set to 1, the dynamically updated coefficients will participate in the calculation normally according to the corresponding formula; when the current sliding measurement window does not meet the signal validity condition, R j Setting it to 0 corresponds to a zero dynamic update coefficient, meaning the model parameters for the current window do not participate in the update. This process prevents anomalous data generated under conditions of low signal-to-noise ratio, localized disturbances, or abnormal channel states from directly participating in the current model parameter update process, thus reducing the impact of the anomalous window on the continuous changes in model parameters.

[0047] In some embodiments, in step S3, the current sliding measurement window is determined. W j Whether the signal is valid includes: The current sliding measurement window is determined based on the measured beat frequency signal and the reference beat frequency signal, respectively.W j Corresponding measurement channel signal-to-noise ratio S m,j and reference channel signal-to-noise ratio S r,j ; When measuring channel signal-to-noise ratio S m,j Not less than the signal-to-noise ratio threshold of the measurement channel S m,min Reference channel signal-to-noise ratio S r,j Not less than the reference channel signal-to-noise ratio threshold S r,min Channel amplitude imbalance d A,j Not greater than the amplitude imbalance threshold d max And the current sliding measurement window W j The phase residual jump variable corresponding to adjacent sampling times is not greater than the residual jump threshold. E max At that time, determine the current sliding measurement window. W j The signal validity condition is met; Otherwise, determine the current sliding measurement window. W j The signal validity conditions are not met.

[0048] In this embodiment, the current sliding measurement window W j Whether a signal meets the valid conditions is not determined solely by a single parameter, but rather by a combination of the signal-to-noise ratio of the measured channel. S m,j Reference channel signal-to-noise ratio S r,j Channel amplitude imbalance d A,j A comprehensive analysis is performed on the phase residual jump variables. In implementation, the signal-to-noise ratio (SNR) of the measurement channel and the reference channel are calculated first, based on the amplitude statistics and noise statistics of the measured and reference beat frequency signals within the current sliding measurement window. When the channel SNR is low, it indicates a relative increase in noise components in the beat frequency signal within the current window. In this case, the phase demodulation result is more prone to local fluctuations. Therefore, this embodiment uses the SNR parameter to determine the signal quality status within the current window.

[0049] After completing the signal-to-noise ratio analysis, this embodiment further incorporates the channel amplitude imbalance. d A,jThe amplitude state between the reference channel and the measurement channel is analyzed. Since the amplitude relationship between the reference beat frequency signal and the measurement beat frequency signal is affected by factors such as light intensity fluctuations, local optical disturbances, and changes in device state, when the amplitude relationship between the two channels deviates significantly from the calibration state, the channel amplitude imbalance will also change accordingly. Therefore, this embodiment uses the channel amplitude imbalance to assist in judging the channel state within the current sliding measurement window, ensuring that the signal validity condition is related not only to the signal noise state but also to the current channel state changes.

[0050] Furthermore, this embodiment also analyzes the phase residual jump variable corresponding to adjacent sampling times within the current sliding measurement window. When the phase residual change within a local window is relatively stable, the phase residual jump variable is usually small; when affected by external disturbances, local noise fluctuations, or transient abnormal demodulation states, the phase residual jump variable will show corresponding changes. In practice, only when the signal-to-noise ratio of the measurement channel is measured... S m,j Reference channel signal-to-noise ratio S r,j Channel amplitude imbalance d A,j The current sliding measurement window is considered to meet the signal validity condition only when both the phase residual jump variable and the corresponding threshold condition are met; otherwise, it is considered not to meet the signal validity condition. This processing ensures that the model update process considers not only the signal quality state within the current window but also the channel state and residual change state for comprehensive judgment, helping to reduce the impact of abnormal window states on the model parameter update process. Those skilled in the art can further refine the process based on the measurement system's noise level, dynamic range, and sampling conditions. S m,min , S r,min , d max as well as E max Configure the settings to determine the validity conditions of the corresponding signal.

[0051] In some embodiments, the nonlinear error model is a phase nonlinear error model based on periodic phase mapping. In step S3, updating the nonlinear error model according to the dynamic update coefficients and the phase residual sequence includes: Based on the current sliding measurement window W j The candidate nonlinear error model parameter vector is obtained by fitting the phase residual sequence within the interval. ; Based on the previous sliding measurement window W j-1 Corresponding model parameter vector P j-1Current sliding measurement window W j Corresponding candidate nonlinear error model parameter vector and dynamic update coefficients m j Update the current sliding measurement window W j Corresponding model parameter vector P j : ; in, P j For the current sliding measurement window W j The corresponding updated model parameter vector, P j-1 For the previous sliding measurement window W j-1 The corresponding model parameter vector, Based on the current sliding measurement window W j The parameter vector of the candidate nonlinear error model obtained by fitting the inner phase residual sequence. m j For the current sliding measurement window W j The corresponding dynamic update coefficients.

[0052] In this embodiment, the nonlinear error model adopts a phase nonlinear error model based on periodic phase mapping. Firstly, based on the current sliding measurement window... W j The phase residual sequence within the range is fitted to obtain the corresponding candidate nonlinear error model parameter vector. The phase residual sequence corresponds to the local phase change data within the current window after separation from the motion trend, primarily containing residual phase fluctuation information beyond the trend change. Since the periodic nonlinear error in dual-frequency laser interferometry typically changes with the current phase state, this embodiment uses the phase residual data within the current window to fit the nonlinear error model parameters, ensuring that the candidate model parameters reflect the local error change state corresponding to the current window. During implementation, least squares fitting, harmonic parameter estimation, or other conventional parameter fitting methods can be used to complete the candidate model parameter vector. For the calculation, those skilled in the art can select the corresponding fitting method based on the sampling frequency, window length, and error fluctuation. In specific implementation, the current sliding measurement window can be... W j Periodic phase corresponding to each sampling time i i As the independent variable, the corresponding phase residual value As the target value for fitting, a harmonic error function in the form of a combination of sine and cosine terms is constructed to solve for the model parameters corresponding to each harmonic, thereby obtaining the candidate model parameter vector corresponding to the current window. During implementation, the least squares method can be used to estimate the parameters of each harmonic order.

[0053] After obtaining the parameter vector of the candidate nonlinear error model Subsequently, this embodiment does not directly use the fitting result corresponding to the current window as the updated model parameters, but instead combines the previous sliding measurement window. W j-1 Corresponding model parameter vector P j-1 and dynamic update coefficients m j For the model parameter vector corresponding to the current window P j Perform a recursive update. Where (1- m j ) P j-1 Used to retain the model state information corresponding to the previous window. This is used to introduce candidate model parameters corresponding to the current window. After this processing, the model parameters corresponding to the current window are not only related to the error change state within the current window, but also maintain a continuous relationship with the model state of the previous window. When the dynamic update coefficient is small, the updated model parameters retain more of the model state from the previous window; when the dynamic update coefficient increases, the influence of the candidate model parameters corresponding to the current window on the update result also increases accordingly, thus enabling the model parameters to adjust accordingly to changes in the current measurement state.

[0054] Furthermore, this embodiment employs a recursive update method to update the model parameters, rather than directly replacing the original model parameters with the current fitting result within each sliding measurement window. Since the nonlinear error state in dual-frequency laser interferometric displacement measurement typically changes continuously over time, if a local window is affected by noise disturbances, vibration changes, or short-term abnormal states, the candidate model parameters fitted within the current window may exhibit local fluctuations. In implementation, a weighted combination of historical model parameters and current candidate model parameters is used through dynamic update coefficients. This ensures that the model parameter update process maintains a relatively continuous state of change, thereby reducing the impact of local abnormal windows on the model parameter change process. Those skilled in the art can set the dynamic update coefficients and the candidate model parameter fitting method according to the dynamic changes of the measurement system, the window length, and the sampling conditions to complete the update of the corresponding nonlinear error model.

[0055] In some embodiments, the phase nonlinear error model based on periodic phase mapping is constructed as follows: Based on phase difference Determine the first i The periodic phase corresponding to each sampling time i i : ; in, i i For the first i The periodic phase corresponding to each sampling time. This indicates the floor function; According to the periodic phase i i Construct a phase nonlinear error model: ; in, For the current sliding measurement window W j The corresponding phase nonlinearity error value, H It is the harmonic order, and H It is a positive integer. h For harmonic order indexing, c h,j and d h,j These are the current sliding measurement windows. W j Inner h The sine and cosine model parameters corresponding to the first harmonic; The model parameter vector P includes: ; in,[ ] T This indicates the transpose operation.

[0056] In this embodiment, firstly based on the phase difference Determine the corresponding periodic phase i i In practice, through By mapping the continuously changing phase difference to a single-period range, the phase state corresponding to different sampling times can be analyzed within a unified periodic interval. Since the periodic nonlinear error in a dual-frequency laser interferometry system typically repeats with the phase period position, the periodic phase form is more suitable for describing the characteristics of error repeating with the phase period compared to directly using continuous accumulated phase for modeling. Here, a floor operation is used to periodically fold back the phase, which preserves the positional relationship of the current sampling point within a single phase period, without being directly affected by changes in the magnitude of the accumulated displacement. After this processing, even if the measured displacement continues to increase, the corresponding periodic phase will still cyclically change within a fixed periodic interval, and the periodic phase data between subsequent sliding measurement windows can be compared and analyzed within a unified periodic range. Those skilled in the art can calculate the periodic phase point by point based on the phase difference data corresponding to each sampling time.

[0057] After obtaining the periodic phase i i Subsequently, this embodiment further employs a combination of sine and cosine terms to establish a phase nonlinear error model. During implementation, the harmonic order is used... H Establish the corresponding harmonic expansion form, and utilize... c h,j and d h,j These represent the current sliding measurement window. W j Inner h The sine and cosine model parameters corresponding to the first harmonic are used to obtain the phase nonlinearity error value corresponding to the current window. Since the periodic nonlinear error in a dual-frequency laser interferometry system typically exhibits a fluctuating state that repeats with the phase period, a combination of sine and cosine terms can describe the error variation corresponding to different periodic positions. When the harmonic order is low, the model is mainly used to describe relatively smooth periodic fluctuations; as the harmonic order increases, it can further reflect more complex periodic error variations. Those skilled in the art can adjust the harmonic order according to the error fluctuations in the measurement system and the computational complexity requirements. H Configure the settings.

[0058] Furthermore, this embodiment uses model parameter vectors. The model parameters corresponding to the current sliding measurement window are uniformly represented. After this processing, the sine and cosine parameters corresponding to each harmonic can participate in subsequent model updates and error compensation calculations in vector form, facilitating parameter recursion between different windows. During implementation, the corresponding model parameters can be fitted and calculated based on the phase residual data within the current sliding measurement window to obtain the model parameter vector corresponding to the current window. In some embodiments, step S4, calculating the nonlinear error compensation amount for the current sliding measurement window based on the updated nonlinear error model, and using the nonlinear error compensation amount to compensate the initial displacement sequence includes: According to the i The periodic phase corresponding to each sampling time i i and the current sliding measurement window W j The corresponding updated model parameter vector P j Determine the first i Phase nonlinear error value at each sampling time ; Based on the phase nonlinearity error value Determine the first i The nonlinear error compensation amount Δ at each sampling time L i : ; Where, Δ L i For the first i The nonlinear error compensation amount corresponding to each sampling time. l The laser wavelength used in the dual-frequency laser interferometer q The optical path multiplication factor corresponding to the form of the measurement optical path; Based on the nonlinear error compensation amount Δ L i For the first i Initial displacement value corresponding to each sampling time L 0,i Error compensation is performed to obtain the first... i Displacement measurement results at each sampling time L i : ; in, L i No. i Displacement measurement results corresponding to each sampling time. L 0,i For the first i The initial displacement value corresponding to each sampling time.

[0059] In this embodiment, according to the first i The periodic phase corresponding to each sampling time i i and the current sliding measurement window W j The corresponding updated model parameter vector P j Calculate the phase nonlinear error value corresponding to the current sampling time. In practice, the periodic phase corresponding to the current sampling point is substituted into the updated phase nonlinear error model to obtain the periodic error estimation result for that sampling point. Since the aforementioned model parameters have already been updated in conjunction with the phase residual state within the current sliding measurement window, the currently calculated phase nonlinear error value can reflect the local periodic error change within the current window. After this processing, the error compensation results corresponding to different sampling times can be adjusted accordingly with the current periodic phase change, thus maintaining a correspondence between the error compensation process and the current measurement state.

[0060] After obtaining the phase nonlinearity error value Subsequently, this embodiment is further based on:

[0061] The phase nonlinearity error value is converted into the corresponding displacement error compensation value. Among them, l The laser wavelength used in the dual-frequency laser interferometer q To measure the optical path multiplication factor corresponding to the optical path configuration, the phase error and displacement error can be converted according to a proportional relationship. During implementation, the phase nonlinearity error value at each sampling moment can independently calculate the corresponding displacement compensation, thereby generating a sequence of nonlinear error compensation values ​​corresponding to the sampling sequence. Those skilled in the art can calculate the corresponding displacement error compensation based on the laser wavelength parameters and the optical path multiplication factor corresponding to the measured optical path configuration.

[0062] After obtaining the nonlinear error compensation amount Δ L i Subsequently, this embodiment further follows... For the initial displacement value L 0,i Error correction is performed to obtain the corresponding displacement measurement results. L i Among them, Δ L iThis corresponds to the error estimated by the phase nonlinear error model at the current sampling time. Therefore, during the displacement correction process, the periodic nonlinear error is corrected by subtracting the corresponding error compensation from the initial displacement value. In practice, each sampling point can independently complete the compensation calculation based on the corresponding periodic phase and the model parameters corresponding to the current sliding measurement window. Therefore, the error compensation process can be adjusted point by point as the measurement state changes within the sliding measurement window, and it is also easy to correspond with the aforementioned model update process.

[0063] Furthermore, to realize the dual-frequency laser interferometric displacement measurement method based on adaptive nonlinear error compensation in this embodiment, the dual-frequency laser interferometric displacement measurement system used in this embodiment includes a dual-frequency laser, an isolator, a beam splitter, a reference mirror, a measurement mirror, a photodetector, a signal acquisition and analog-to-digital conversion module, a digital quadrature demodulation module, and a data processing module. The dual-frequency laser outputs a dual-frequency laser with a fixed frequency difference. The dual-frequency laser is incident on the beam splitter after passing through the isolator and enters the reference optical path and the measurement optical path respectively. The beam in the reference optical path is reflected back by the reference mirror, and the beam in the measurement optical path is reflected back by the measurement mirror. The two beams are combined by interference to form corresponding interference beat frequency signals, which are then converted into corresponding electrical signals by the photodetector.

[0064] In this embodiment, the reference optical path is mainly used to provide reference phase information. The optical path length in the measurement optical path changes with the position of the measurement mirror, thus the phase state of the corresponding measurement optical path also changes accordingly. The electrical signal output by the photodetector is sampled by the signal acquisition and analog-to-digital conversion module and then input to the digital quadrature demodulation module for digital quadrature demodulation processing to obtain the reference IQ signal corresponding to the reference beat frequency signal and the measurement IQ signal corresponding to the measurement beat frequency signal. Subsequently, the data processing module calculates the corresponding phase difference data based on the reference IQ signal and the measurement IQ signal, and analyzes the phase change using a sliding measurement window to complete the processing steps such as window state parameter extraction, dynamic update coefficient calculation, nonlinear error model update, and error compensation calculation, ultimately outputting the corresponding displacement measurement result.

[0065] During actual measurement, when the measuring mirror shifts with the object being measured, the optical path length of the measuring optical path changes, causing a phase change in the measuring beat frequency signal. The data processing module calculates the displacement based on the phase difference between the reference beat frequency signal and the measured beat frequency signal, and updates the nonlinear error model by combining the dynamic state within the current sliding measurement window, thereby compensating for the periodic nonlinear error in the displacement measurement results.

[0066] To enable those skilled in the art to clearly understand the specific implementation process and parameter selection of each step of the present invention, three specific embodiments are given below. Embodiment 1 is a preferred embodiment, which provides a complete operation flow under typical parameter configuration; Embodiment 2 focuses on the dynamic adjustment of the state parameters of each window and the model update when the speed changes, for variable speed measurement conditions; Embodiment 3 focuses on the model parameter preservation strategy when the signal quality deteriorates, for low signal-to-noise ratio long-term continuous measurement scenarios.

[0067] Example 1 This embodiment uses a typical Michelson-type dual-frequency laser interferometer, with a laser wavelength of... l The optical path multiplication factor is 632.8 nm. q The value is set to 2, and the sampling frequency is 10kHz. In this embodiment, the sliding measurement window length is... N j It can be set to 1024 sampling points, and the order of motion trend fitting. K Take 2, the harmonic order of the nonlinear error model. H Take 3. Weighting coefficient α , β , c In this embodiment, the values ​​are 0.4, 0.3, and 0.3 respectively, which are normalized reference values. E 0 Set to 1 and update the upper limit of the coefficient. m max Set to 0.2, the basic update coefficient. m 0 Set to 0.05, dynamic adjustment coefficient Set to 1.0. Signal-to-noise ratio threshold. S m,min and S r,min All values ​​are set to 20dB, amplitude imbalance threshold. d max Set the threshold to 0.15 for residual jumps. E max Take 0.05 rad.

[0068] During operation, the reference beat frequency signal and the measured beat frequency signal are first orthogonally demodulated to obtain in-phase and quadrature components. Then, the phase difference sequence is calculated and the initial displacement sequence is generated. L 0,i Next, a polynomial trend fitting is performed on the phase difference sequence within the current sliding measurement window to obtain the motion trend phase fitting term. Then, the phase residual sequence is calculated, and the equivalent frequency difference change Δ is extracted sequentially. n j Phase residual fluctuation s e,j Channel amplitude imbalance dA,j Subsequently, the dynamic state factor is calculated based on the three window state parameters mentioned above. or j And determine whether the current window meets the signal validity conditions: if all four conditions are met, then R j Take 1, otherwise R j Set it to 0. Finally, update the coefficients dynamically. m j Complete the model parameter vector P j The update is then based on the model parameter vector of the current window. P j and the periodic phase θ at each sampling time i Calculate the phase nonlinearity error value and generate the compensation amount Δ. L i For the initial displacement value L 0,i After correction, the final displacement measurement result is obtained. L i .

[0069] Example 2 This embodiment is based on the hardware of Embodiment 1, and also uses a typical Michelson-type dual-frequency laser interferometer. The object being measured moves at a speed of 0–50 mm / s. In this embodiment, the length of the sliding measurement window is... N j It can still be set to 1024 sampling points, and the fitting order can be adjusted. K Take 2, harmonic order H Take 3, and keep the other parameters the same as in Example 1.

[0070] During operation, the acquisition and demodulation process of the reference beat frequency signal and the measured beat frequency signal is the same as in Example 1. As the speed of the motion platform changes, the equivalent frequency difference change Δ within each sliding measurement window... n j As changes occur, the trend fitting term adjusts accordingly to the phase change within the window, and the phase residual sequence also changes accordingly. During the model update phase, the coefficients are dynamically updated. m j The model parameters are adjusted according to changes in the window state parameters. When the signal quality meets the update conditions, the model parameters are recursively updated according to the dynamic update coefficients; when the signal quality deteriorates and the update conditions are no longer met, the model parameters retain the values ​​corresponding to the previous window. Subsequently, the error compensation amount corresponding to each sampling time is calculated based on the updated model parameters.

[0071] Example 3

[0072] This embodiment simulates a long-term continuous measurement scenario where ambient light fluctuations are significant, resulting in a low signal-to-noise ratio. In this embodiment, the sliding measurement window length... N j It can still be set to 1024 sampling points. K Take 2, H The value is 3. To adapt to low signal-to-noise ratio conditions, the signal-to-noise ratio threshold is adjusted to 25dB in this embodiment, and the remaining parameters are the same as in Embodiment 1.

[0073] During operation, the acquisition and demodulation process of the reference beat frequency signal and the measured beat frequency signal is the same as in Example 1. Within each sliding measurement window, the phase residual fluctuation... s e,j and channel amplitude imbalance d A,j It will change accordingly with changes in noise conditions. During the model update phase, when any condition (signal-to-noise ratio, amplitude imbalance, or residual jump variable) fails to meet the corresponding threshold condition, R j Set the parameter to 0, and retain the corresponding value from the previous window; only when all conditions are met will the coefficients be dynamically updated. m j For model parameter vectors P j The model is then updated. Subsequently, with the model parameters remaining stable, the error compensation amount corresponding to each sampling time point is calculated.

[0074] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of this application, and are not intended to limit them. Although this application has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some or all of the technical features therein. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of this application.

Claims

1. A dual-frequency laser interferometric displacement measurement method based on adaptive nonlinear error compensation, characterized in that, Includes the following steps: S1. Acquire the reference beat frequency signal and the measured beat frequency signal of the dual-frequency laser interferometer, perform orthogonal demodulation on the reference beat frequency signal and the measured beat frequency signal to obtain the phase difference sequence, and generate the initial displacement sequence based on the phase difference sequence; S2. Fit the motion trend of the phase difference sequence according to the sliding measurement window, and perform trend separation based on the fitting result to obtain the phase residual sequence. Extract window state parameters based on the phase difference sequence, the phase residual sequence, the reference beat frequency signal, and the measured beat frequency signal. The window state parameters include the equivalent frequency difference change, the phase residual fluctuation, and the channel amplitude imbalance. S3. Perform weighted calculations based on the window state parameters to obtain dynamic update coefficients. When the current sliding measurement window meets the signal validity condition, update the nonlinear error model based on the dynamic update coefficients and the phase residual sequence. When the current sliding measurement window does not meet the signal validity condition, keep the model parameters of the nonlinear error model unchanged. S4. Calculate the nonlinear error compensation amount of the current sliding measurement window according to the updated nonlinear error model, and use the nonlinear error compensation amount to compensate the initial displacement sequence to obtain the displacement measurement result; In step S3, the dynamic update coefficients are obtained by weighted calculation based on the window state parameters, including: According to the equivalent frequency difference change Δ ν j The phase residual fluctuation amount σ e,j and the channel amplitude imbalance δ A,j Determine the current sliding measurement window W j Corresponding dynamic state factor η j : ； in, E 0 This is the normalized reference value for the phase residual. α , β , γ Let be the weighting coefficient, and satisfy: 0≤ α ≤1,0≤ β ≤1,0≤ γ ≤1, α + β + γ =1； According to the dynamic state factor η j Determine the current sliding measurement window W j Corresponding dynamic update coefficients μ j : ； in, μ j For the current sliding measurement window W j The corresponding dynamic update coefficients, μ max To update the upper limit of the coefficient, μ 0 Based on the updated coefficients, This is a dynamic adjustment coefficient. R j The effective factor of the signal; If the current sliding measurement window W j When the signal validity condition is met, R j =1; If the current sliding measurement window W j When the signal validity condition is not met, R j =0; The nonlinear error model is a phase nonlinear error model based on periodic phase mapping. In step S3, updating the nonlinear error model according to the dynamic update coefficients and the phase residual sequence includes: Based on the current sliding measurement window W j The candidate nonlinear error model parameter vector is obtained by fitting the phase residual sequence within the interval. ; Based on the previous sliding measurement window W j-1 Corresponding model parameter vector P j-1 Current sliding measurement window W j Corresponding candidate nonlinear error model parameter vector and dynamic update coefficients μ j Update the current sliding measurement window W j Corresponding model parameter vector P j : ； in, P j For the current sliding measurement window W j The corresponding updated model parameter vector, P j-1 For the previous sliding measurement window W j-1 The corresponding model parameter vector, Based on the current sliding measurement window W j The parameter vector of the candidate nonlinear error model obtained by fitting the inner phase residual sequence. μ j For the current sliding measurement window W j The corresponding dynamic update coefficients.

2. The dual-frequency laser interferometric displacement measurement method based on adaptive nonlinear error compensation according to claim 1, characterized in that, In step S1, the reference beat frequency signal and the measured beat frequency signal are orthogonally demodulated to obtain the corresponding in-phase component and quadrature component, respectively. Then, the phase difference sequence is obtained according to the following formula: ； in, For the first i Phase difference at each sampling time, I m，i , Q m，i These are the in-phase and quadrature components of the beat frequency signal, respectively. I r，i , Q r，i These are the in-phase and quadrature components of the reference beat frequency signal, respectively, and unwrap[ ] represents phase expansion processing.

3. The dual-frequency laser interferometric displacement measurement method based on adaptive nonlinear error compensation according to claim 2, characterized in that, In step S1, the initial displacement sequence is generated according to the following formula: ； in, L 0,i For the first i The initial displacement value at each sampling time. λ The laser wavelength used in the dual-frequency laser interferometer q The optical path multiplication factor corresponding to the measurement optical path configuration. For the first i The phase difference at each sampling time.

4. The dual-frequency laser interferometric displacement measurement method based on adaptive nonlinear error compensation according to claim 1, characterized in that, In step S2, the process of fitting the motion trend of the phase difference sequence according to the sliding measurement window and performing trend separation based on the fitting results is as follows: In the current sliding measurement window W j Within this process, a polynomial motion trend fitting is performed on the phase difference sequence to obtain the motion trend phase fitting term: ； in, W j For the first j A sliding measurement window, For the first i The motion trend phase fitting value corresponding to each sampling time. a p,j For the current sliding measurement window W j The first p Order of fit coefficients, τ i For the first i The amount of time between each sampling moment and the start time of the current sliding measurement window. For the first i Each sampling moment corresponds to a time quantity p Second item, K Let be the order of the motion trend fitting, and K It is a positive integer; And based on the motion trend phase fitting term, the phase difference sequence is subjected to trend separation to obtain the phase residual sequence: ； in, For the first i The phase residual value corresponding to each sampling time. For the first i Phase difference at each sampling time, For the first i The motion trend phase fitting value corresponding to each sampling time.

5. The dual-frequency laser interferometric displacement measurement method based on adaptive nonlinear error compensation according to claim 4, characterized in that, In step S2, the extracted window state parameters include: a. Determine the current sliding measurement window based on the phase difference sequence. W j Corresponding equivalent frequency difference parameter ν j Then, based on the current sliding measurement window W j Corresponding equivalent frequency difference parameter ν j And the previous sliding measurement window W j-1 Corresponding equivalent frequency difference parameter ν j-1 Determine the equivalent frequency difference change Δ ν j ; Current sliding measurement window W j Corresponding equivalent frequency difference parameter ν j for: ； in, N j For the current sliding measurement window W j The number of sampling points within, Δt The time interval between adjacent sampling times. For the first i The phase difference corresponding to each sampling time; Current sliding measurement window W j The corresponding equivalent frequency difference change Δ ν j for: ； in, ν j For the current sliding measurement window W j The corresponding equivalent frequency difference parameter, ν j-1 For the previous sliding measurement window W j-1 The corresponding equivalent frequency difference parameter; ε The preset stability adjustment parameters, and ε >0; b. Determine the current sliding measurement window based on the phase residual sequence. W j The corresponding mean phase residual Then, based on the mean of the phase residuals Determine the current sliding measurement window W j Corresponding phase residual fluctuation σ e,j ; Current sliding measurement window W j The corresponding mean phase residual for: ； Current sliding measurement window W j Corresponding phase residual fluctuation σ e,j for: ； in, For the first i The phase residual corresponding to each sampling time. For the current sliding measurement window W j The corresponding mean of the phase residuals; N j For the current sliding measurement window W j The number of sampling points within; c. Determine the current sliding measurement window based on the reference beat frequency signal and the measured beat frequency signal. W j Corresponding channel amplitude imbalance δ A,j : ； in, A m,j For the current sliding measurement window W j The amplitude statistics of the internally measured beat frequency signal. A r,j For the current sliding measurement window W j Amplitude statistics of the internal reference beat frequency signal. A m,0 To measure the amplitude statistics of the beat frequency signal under calibrated conditions, A r,0 This is a statistical measure of the amplitude of the reference beat frequency signal under calibrated conditions. ε The preset stability adjustment parameters, and ε >0.

6. The dual-frequency laser interferometric displacement measurement method based on adaptive nonlinear error compensation according to claim 1, characterized in that, In step S3, determine the current sliding measurement window. W j Whether the signal is valid includes: The current sliding measurement window is determined based on the measured beat frequency signal and the reference beat frequency signal, respectively. W j Corresponding measurement channel signal-to-noise ratio S m,j and reference channel signal-to-noise ratio S r,j ; When the signal-to-noise ratio of the measurement channel S m,j Not less than the signal-to-noise ratio threshold of the measurement channel S m,min The reference channel signal-to-noise ratio S r,j Not less than the reference channel signal-to-noise ratio threshold S r,min The channel amplitude imbalance δ A,j Not greater than the amplitude imbalance threshold δ max And the current sliding measurement window W j The phase residual jump variable corresponding to adjacent sampling times is not greater than the residual jump threshold. E max At that time, determine the current sliding measurement window. W j The signal validity condition is met; Otherwise, determine the current sliding measurement window. W j The signal validity conditions are not met.

7. The dual-frequency laser interferometric displacement measurement method based on adaptive nonlinear error compensation according to claim 1, characterized in that, The phase nonlinear error model based on periodic phase mapping is constructed as follows: Based on phase difference Determine the first i The periodic phase corresponding to each sampling time θ i : ； in, θ i For the first i The periodic phase corresponding to each sampling time. This indicates the floor function; According to the periodic phase θ i Construct a phase nonlinear error model: ； in, For the current sliding measurement window W j The corresponding phase nonlinearity error value, H It is the harmonic order, and H It is a positive integer. h For harmonic order indexing, c h,j and d h,j These are the current sliding measurement windows. W j Inner h The sine and cosine model parameters corresponding to the first harmonic; The model parameter vector P includes: ； in,[ ] T This indicates the transpose operation.

8. The dual-frequency laser interferometric displacement measurement method based on adaptive nonlinear error compensation according to claim 7, characterized in that, In step S4, calculating the nonlinear error compensation amount for the current sliding measurement window based on the updated nonlinear error model, and using the nonlinear error compensation amount to compensate the initial displacement sequence includes: According to the i The periodic phase corresponding to each sampling time θ i and the current sliding measurement window W j The corresponding updated model parameter vector P j Determine the first i Phase nonlinear error value at each sampling time ; According to the phase nonlinear error value Determine the first i The nonlinear error compensation amount Δ at each sampling time L i : ； Where, Δ L i For the first i The nonlinear error compensation amount corresponding to each sampling time. λ The laser wavelength used in the dual-frequency laser interferometer q The optical path multiplication factor corresponding to the form of the measurement optical path; According to the nonlinear error compensation amount Δ L i For the first i Initial displacement value corresponding to each sampling time L 0,i Error compensation is performed to obtain the first... i Displacement measurement results at each sampling time L i : ； in, L i No. i Displacement measurement results corresponding to each sampling time. L 0,i Let be the initial displacement value corresponding to the i-th sampling time.

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