Nanoscale displacement real-time compensation measurement method and system based on dual-frequency laser interference

Abstract

The invention discloses a nano-scale displacement real-time compensation measurement method and system based on double-frequency laser interference, and belongs to the technical field of precision measurement. In order to solve the problems that three error sources of environmental drift, periodic nonlinear error and dynamic vibration are mutually coupled and have high real-time requirements in dual-frequency laser interference measurement, a multi-source error unified state space model including measured displacement, an air refractive index parameter, a nonlinear error parameter and a vibration disturbance quantity is constructed. A high-dimensional state vector is divided into a displacement-refractive index group and a nonlinear parameter group by adopting an extended Kalman filter of a grouping updating strategy, the displacement-refractive index group and the nonlinear parameter group are alternately updated in an assembly line parallel mode, nonlinear parameters are identified in real time in combination with an online recursive least square algorithm, and the state of the filter is corrected through a state coupling injection mechanism. Real-time compensation with the end-to-end delay smaller than 80 microseconds is achieved, the displacement measurement residual error is controlled within + / -0.3 nm under the composite disturbance condition, and the method is suitable for precise assembly of intelligent glasses optical assemblies.

Description

Technical Field

[0001] This invention relates to the field of precision measurement technology, and in particular to a method and system for real-time compensation measurement of nanoscale displacement based on dual-frequency laser interferometry for precision assembly of optical components in smart glasses. Background Technology

[0002] Dual-frequency laser interferometry, with its high resolution and large range, has become the mainstream solution for nanometer-level precision displacement measurement, and is widely used in semiconductor lithography, precision machining, and optical component assembly. Especially in the manufacturing process of smart glasses, the assembly precision requirements for diffractive waveguides, microdisplay arrays, and freeform optical lenses have reached sub-micron or even nanometer levels, placing extremely high demands on the real-time performance and environmental adaptability of displacement measurement systems.

[0003] However, in real-world nanoscale assembly environments, dual-frequency laser interferometry faces interference from multiple sources of errors: wavelength drift caused by fluctuations in air refractive index with temperature, humidity, and air pressure; frequency drift and non-orthogonality errors in the dual-frequency signals output by the laser; periodic nonlinear errors introduced by the non-ideal polarization of optical components; and high-frequency mechanical vibrations in the environment. Existing technologies typically employ independent compensation schemes for these errors, such as using the Edlén formula for low-frequency offline correction of environmental parameters, or using an offline calibration lookup table method to correct nonlinear errors.

[0004] However, the aforementioned existing technologies mainly suffer from the following problems: First, algorithms such as environmental drift compensation, nonlinear error correction, and dynamic vibration suppression are usually executed independently and sequentially, resulting in an overall compensation delay that often exceeds 1ms, which cannot meet the stringent requirement of less than 100μs for the control loop response time in the precision bonding process of diffractive waveguides for smart glasses; Second, serial compensation ignores the coupling effect between various error sources, and in complex working conditions where multiple error sources coexist, the compensation residuals accumulate, making it difficult to achieve sub-nanometer measurement accuracy; Finally, nonlinear error compensation based on offline calibration lacks adaptive capability, and once the optical path conditions change due to the switching of optical components, the original calibration parameters become invalid, leading to production interruption. Summary of the Invention

[0005] To achieve the above objectives, this invention provides a real-time nanoscale displacement compensation measurement method based on dual-frequency laser interferometry, which includes the following steps:

[0006] The dual-frequency laser interferometric optical unit acquires the measurement beat frequency signal carrying the displacement information and the reference beat frequency signal as the phase reference, and the orthogonal signal detection unit converts the measurement beat frequency signal into two orthogonal electrical signals; at the same time, the environmental parameter sensing unit collects the temperature, air pressure and humidity data of the interferometric optical path environment in real time.

[0007] A unified state-space model for multi-source errors is established, defining a high-dimensional state vector that includes the measured actual displacement, displacement velocity, air refractive index deviation, air refractive index deviation change rate, periodic nonlinear error harmonic parameters, and external mechanical vibration disturbance. A state transition equation describing the evolution of the state vector over time and an observation equation describing the nonlinear mapping relationship between the phase observation value and the state vector are also established.

[0008] The high-dimensional state vector is estimated in real time using a group-updated extended Kalman filter. In each sampling period, all state components are first predicted uniformly according to the state transition equation. Then, the state vector is divided into a first state group and a second state group. The first state group and the second state group are updated in turn using phase observations.

[0009] Extract the measured true displacement component from the updated state vector and output it as the compensated displacement value.

[0010] As a preferred technical solution of the present invention, the high-dimensional state vector specifically includes 9 state components: the measured actual displacement, displacement velocity, air refractive index deviation, air refractive index deviation change rate, cosine amplitude of the first-order periodic nonlinear error, sine amplitude of the first-order periodic nonlinear error, cosine amplitude of the second-order periodic nonlinear error, sine amplitude of the second-order periodic nonlinear error, and external mechanical vibration disturbance.

[0011] As a preferred embodiment of the present invention, the specific process of dividing the state vector into a first state group and a second state group, and updating the first state group and the second state group sequentially using phase observation values ​​is as follows:

[0012] The first state group is defined to include the measured actual displacement, displacement velocity, air refractive index deviation, air refractive index deviation change rate, and external mechanical vibration disturbance; the second state group is defined to include the cosine amplitude and sine amplitude of the first-order and second-order periodic nonlinear errors.

[0013] Calculate the Jacobian submatrix corresponding to the first state group, calculate the first Kalman gain using the phase observations and the current predictions, update the state estimates and covariance matrix of the first state group, and simultaneously update the cross-covariance matrix between the first and second state groups.

[0014] Calculate the Jacobian submatrix corresponding to the second state group, calculate the observation residuals using the phase observations, the updated estimates of the first state group, and the predicted values ​​of the second state group, calculate the second Kalman gain, and update the state estimates and covariance matrix of the second state group.

[0015] As a preferred embodiment of the present invention, the method further includes a state coupling injection step:

[0016] The online recursive least squares parameter identification algorithm is run in parallel, and the periodic nonlinear error parameters are identified in real time using the Lissajous ellipse fitting residuals of the two orthogonal electrical signals.

[0017] Determine whether the difference between the parameter identification value output by the recursive least squares algorithm and the current estimated value of the second state group in the grouped updated extended Kalman filter exceeds a preset threshold.

[0018] When the difference exceeds a preset threshold, the parameter identification value is injected into the state estimate of the second state group in a weighted manner, and the covariance matrix value of the second state group is increased accordingly.

[0019] As a preferred embodiment of the present invention, the online recursive least squares parameter identification algorithm adopts a recursive mechanism with a forgetting factor. The forgetting factor ranges from 0.98 to 0.995, which enables it to quickly converge to new nonlinear error parameters when the optical path conditions change.

[0020] As a preferred embodiment of the present invention, the method further includes an environmental observation-assisted update step:

[0021] Based on the temperature, air pressure, and humidity data, the observed values ​​of air refractive index deviation are calculated using the modified Edlén formula;

[0022] The air refractive index deviation and its rate of change component in the high-dimensional state vector are independently updated and corrected using the air refractive index deviation observations.

[0023] As a preferred technical solution of the present invention, the nonlinear mapping relationship between the phase observation value and the state vector in the observation equation is specifically expressed as follows: the phase observation value is equal to the true displacement phase including the refractive index deviation correction plus the additional phase offset introduced by the nonlinear error; wherein, the true displacement phase term reflects the product coupling relationship between the refractive index deviation and the total displacement including the vibration disturbance.

[0024] As a preferred embodiment of the present invention, the method operates on a heterogeneous computing platform of FPGA and ARM:

[0025] The FPGA is responsible for performing digital phase demodulation, unified state prediction, and group update operations of the first and second state groups. Each step is executed in parallel using a pipelined approach.

[0026] The ARM is responsible for performing the Edlén formula calculation of environmental parameters, the online recursive least squares parameter identification algorithm, and the state coupling injection logic judgment.

[0027] As a preferred embodiment of the present invention, the method is applied to a precision assembly production line for smart glasses diffractive waveguides or micro-display arrays, and the compensated displacement value is used for closed-loop position feedback control of a nano-positioning stage.

[0028] This invention also provides a real-time nanoscale displacement compensation measurement system based on dual-frequency laser interferometry, comprising:

[0029] The dual-frequency laser interference optical unit is used to generate dual-frequency lasers and form an interference optical path, outputting a measurement beat frequency signal and a reference beat frequency signal, and outputting orthogonal electrical signals after orthogonal detection;

[0030] The environmental parameter sensing unit is used to collect temperature, air pressure, and humidity data of the optical path environment.

[0031] A signal processing and computing platform, including an FPGA coprocessor and an ARM processor, is configured to execute the nanoscale displacement real-time compensation measurement method based on dual-frequency laser interferometry as described in any of the above preferred technical solutions.

[0032] Beneficial effects of the present invention

[0033] 1. This invention reconstructs three types of algorithms—environmental drift compensation, nonlinear error correction, and dynamic vibration suppression—into a unified multi-source error parallel fusion compensation architecture. By utilizing a group update strategy, the computational complexity of a single filtering cycle is significantly reduced, enabling pipelined parallel execution. This reduces the overall compensation delay from over 1ms in existing technologies to less than 80μs, effectively meeting the high real-time requirements of the control loop in the precision bonding process of optical waveguides for smart glasses.

[0034] 2. This invention constructs a unified multi-source error state space model, which incorporates the three types of error sources that were originally processed independently into the same extended Kalman filter for joint estimation. This eliminates the problems of mutual interference and residual accumulation among error terms in serial compensation, and significantly improves the compensation accuracy of displacement measurement under the combined disturbance conditions of temperature, air pressure fluctuations and mechanical vibration.

[0035] 3. This invention identifies periodic nonlinear error parameters in real time using the online recursive least squares method and corrects the state of the Kalman filter through a state coupling injection mechanism, replacing the traditional offline calibration method. This allows the system to be recalibrated without stopping when optical path conditions change, and provides rapid adaptive capability in different optical component switching scenarios. Attached Figure Description

[0036] Figure 1 A schematic diagram of the overall architecture of the nanoscale displacement real-time compensation measurement system based on dual-frequency laser interferometry provided in an embodiment of the present invention;

[0037] Figure 2 This is a flowchart illustrating the multi-source error parallel fusion compensation method in an embodiment of the present invention;

[0038] Figure 3 This is a schematic diagram illustrating the collaborative working logic of the group-updated extended Kalman filter and the online recursive least squares parameter identification module in an embodiment of the present invention.

[0039] Figure reference numerals: 100, Dual-frequency laser interference optical unit; 101, Dual-frequency laser source; 102, Polarization beam splitting and interference optical path; 103, Orthogonal signal detection unit; 200, Environmental parameter sensing unit; 201, Temperature sensing array; 202, Barometric pressure sensor; 300, Signal processing and computing platform; 301, FPGA coprocessor; 302, ARM processor; 400, Digital phase demodulation module; 500, Multi-source error unified state space modeling module; 600, Environmental parameter Edlén formula correction module; 700, Grouped update extended Kalman parallel fusion estimation module; 800, Online recursive least squares nonlinear parameter identification module; 900, Compensated displacement output module. Detailed Implementation

[0040] The technical solution of the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the following embodiments are only for illustrative purposes and do not constitute a limitation on the scope of protection of the present invention. All equivalent transformations and improvements based on the technical concept of the present invention in this field should be covered within the scope of protection of the present invention.

[0041] This invention provides a method and system for real-time nanoscale displacement compensation measurement based on dual-frequency laser interferometry. The technical concept lies in unifying three error sources—environmental drift, periodic nonlinear error, and dynamic vibration—that objectively exist during dual-frequency laser interferometry measurement into a single state-space framework for joint modeling. Furthermore, leveraging the collaborative working mechanism between an extended Kalman filter with a group update strategy and an online recursive least squares parameter identification algorithm, an end-to-end latency of less than [a certain value] is achieved on a heterogeneous computing platform of FPGA and ARM. This solution achieves real-time parallel fusion compensation of multi-source errors. It overcomes the latency accumulation and accuracy degradation problems caused by the independent and sequential execution of various error compensation algorithms in existing technologies, and can address issues related to temperature fluctuations. air pressure fluctuations Vibration amplitude Under the combined disturbance conditions, the residual error of displacement measurement is controlled within... ( ) within.

[0042] like Figure 1-3As shown, the system of this invention is divided into two layers in its overall architecture: a hardware layer and a software layer. The hardware layer is responsible for the generation and acquisition of optical interference signals and the sensing of environmental parameters, while the software layer carries all the algorithm logic for parallel fusion compensation of multi-source errors. The two layers are tightly coupled through a high-speed digital interface, together forming a complete real-time compensation measurement closed loop. The following describes each component in detail.

[0043] The dual-frequency laser interference optical unit 100 constitutes the core of the system's optical signal acquisition, and its internal components include three sub-modules: a dual-frequency laser source 101, a polarization beam splitting and interference optical path 102, and an orthogonal signal detection unit 103.

[0044] The dual-frequency laser source 101 uses a He-Ne laser based on Zeeman effect splitting as its light source. Under the influence of an axial magnetic field, this laser outputs two beams of laser light with slightly different frequencies and orthogonal polarization directions, denoted as _frequency_1_2_3_4_5_6_6_7_6_8_1_6_8_9_6_1_6_8_9_1_6 ... and The frequency difference between the two In to Within the range, operating wavelength The selection of this frequency difference range is based on the following considerations: if the frequency difference is too small, the signal-to-noise ratio of the beat frequency signal will be insufficient to support high-precision phase demodulation; if the frequency difference is too large, it will place excessive demands on the bandwidth of the photodetector and the rate of the subsequent digital sampling system. A photodetector is integrated inside the laser cavity to directly pick up the reference beat frequency signal formed by the superposition of two orthogonally polarized beams. The signal is not modulated by an external optical path, thus preserving the frequency and phase information of the dual-frequency laser itself, and is used as a phase-locked reference in subsequent digital phase demodulation.

[0045] The polarization beam splitting and interference optical path 102 includes a polarization beam splitter prism (PBS), a quarter-wave plate (QWP), a reference mirror, and a measurement mirror. The combined beam emitted from the dual-frequency laser source 101 is incident on the PBS. The P-polarized component of light is transmitted into the reference arm and reflected by the reference mirror before returning along the same path. The S-polarization component of the light is reflected by the PBS and enters the measuring arm. A measuring mirror is mounted at the end of the measuring arm, fixed to the nano-positioning stage of the smart glasses assembly platform, and moves synchronously with the object being measured. A quarter-wave plate is placed in the optical path of both the reference arm and the measuring arm, causing the light beam to pass through the quarter-wave plate twice after reflection by the mirror, rotating its polarization direction by 90°. This ensures that the beam is correctly guided in the outgoing direction upon returning to the PBS and does not return to the light source, while also preventing the backlight from interfering with the laser's stability. When the measuring mirror shifts... At that time, the change in optical path of the measuring arm is 2d (the round-trip path of light), making Light carries an additional Doppler phase change. ,in This represents the actual refractive index of air in the optical path. After the two reflected beams recombine at the PBS, the analyzer generates a measured beat frequency signal.

[0046]

[0047] The orthogonal signal detection unit 103 is located downstream of the beam combiner optical path and is used to convert the interference phase information into orthogonal electrical signals that are easy to digitally process. This unit places two polarizers after the beam combiner optical path, with their polarization transmission axes at a 45° angle to each other. Each is connected to a high-speed photodetector, thus forming an orthogonal detection pair, which outputs I-channel and Q-channel signals respectively. The I-channel signal represents the cosine component of the interference phase, and the Q-channel signal represents the sine component, specifically expressed as follows:

[0048]

[0049]

[0050] In the formula, The periodic nonlinear phase error is introduced by a combination of factors, including the non-ideal extinction ratio of polarization beam splitters, residual birefringence on the surface of optical elements, and the imperfect orthogonality of the dual-frequency beams of the laser. and These are the DC offset components in the two signals, originating from factors such as dark current in the photodetector, electronic zero drift, and stray light. Using orthogonal detection allows for the simultaneous acquisition of the amplitude and direction information of the interference phase, providing the necessary raw data foundation for subsequent high-precision phase demodulation and nonlinear error identification.

[0051] The environmental parameter sensing unit 200 is responsible for real-time acquisition of key environmental physical quantities that affect the air refractive index. It includes a temperature sensing array 201, a barometric pressure sensor 202, a humidity sensor 203, and a signal conditioning and ADC board 204.

[0052] Temperature sensing array 201 arranges 3 to 5 platinum resistance temperature sensors (Pt1000) at equal intervals along the interference optical path, achieving a measurement accuracy of [missing information]. Sampling rate Used to obtain the air temperature distribution along the optical path. The reason for using a multi-point arrangement instead of single-point measurement is that, under nanometer-level measurement accuracy requirements, the influence of temperature gradients at different locations along the interference optical path on the equivalent optical path is not negligible. Multi-point acquisition allows for more accurate acquisition of the equivalent optical path temperature through weighted averaging or spatial interpolation. The barometric pressure sensor 202 is a high-precision MEMS barometric pressure sensor with a measurement accuracy of [insert accuracy here]. Sampling rate Output the current atmospheric pressure value The humidity sensor 203 uses a capacitive humidity sensor, with high measurement accuracy. Sampling rate Output relative humidity value The analog output signals of the above three types of sensors are uniformly connected to the signal conditioning and ADC board 204, which performs the necessary signal amplification and anti-aliasing filtering, and then... A high-resolution analog-to-digital converter performs digitization, and the digitized environmental parameter data is transmitted to the ARM processor 302 in the signal processing and computing platform 300 via the SPI bus. In an alternative implementation, the temperature sensing array 201 can also be replaced with other temperature sensor types with equal or higher accuracy, such as thermistors (NTCs) or fiber Bragg grating temperature sensors, as long as their measurement accuracy and response speed meet the system's input requirements for refractive index correction.

[0053] The signal processing and computing platform 300 is the core hardware carrier for real-time compensation calculation in this invention, employing a heterogeneous collaborative architecture of FPGA and ARM. The FPGA coprocessor 301 uses a Xilinx Kintex-7 series device with a main frequency of... It undertakes the real-time tasks most sensitive to computational latency, including receiving the I / Q signals output by the orthogonal signal detection unit 103 and the reference beat frequency signal output by the dual-frequency laser source 101. This system enables high-speed digital phase demodulation and performs matrix prediction and update operations involved in the grouped update extended Kalman filter. The FPGA's internal computation logic is organized using a four-stage pipeline, allowing key steps such as state prediction, A-group state update, and B-group state update to be executed consecutively in an overlapping pipeline manner, significantly reducing the equivalent computational latency within a single filtering cycle. The ARM processor 302 uses an ARM Cortex-A53 quad-core processor with a clock speed of [missing information - likely a specific frequency]. It runs a Linux real-time operating system (e.g., real-time Linux with PREEMPT-RT kernel patch), and is responsible for handling tasks with relatively low computational density but complex logical branches. Specifically, this includes executing recursive least squares parameter identification algorithms, calculating Edlén formula corrections for environment parameters, judging and executing state-coupled injection logic, and managing communication with the host computer system. The ARM processor 302 and the FPGA coprocessor 301 exchange data via the AXI4 bus using DMA, with single data transfer latency controlled within [specific parameters]. Within this range, it is ensured that data collaboration between the two processing units does not become a bottleneck in the overall latency compensation link. In another equivalent implementation, the FPGA coprocessor 301 can also be an Intel (Altera) Cyclone V SoC or a similar SoC FPGA device with an integrated ARM hard core, integrating the ARM processor 302 and the FPGA coprocessor 301 on the same chip, and further reducing data exchange latency through on-chip AXI interconnect.

[0054] At the software level, the digital phase demodulation module 400 runs on the FPGA coprocessor 301 and consists of three functional units: a digital phase-locked loop 401, an I / Q quadrature signal digitization and DC offset cancellation module 402, and a coarse phase calculation module 403.

[0055] Digital phase-locked loop 401 with reference beat frequency signal To lock the reference, it internally incorporates a numerically controlled oscillator (NCO) to generate the beat frequency. The local oscillator signal is tracked synchronously, and the local oscillator signal is compared with the measured beat frequency signal. After digital mixing, the phase difference between the two components is extracted using a low-pass filter. The loop bandwidth of the digital phase-locked loop is set to... In frequency difference for to Stable locking can be maintained within the specified range. The selection of loop bandwidth needs to strike a balance between tracking speed and noise suppression: if the bandwidth is too narrow, it will be unable to track the Doppler frequency shift caused by rapid changes in the measured displacement; if the bandwidth is too wide, too much high-frequency noise will be introduced into the phase extraction results. The settings can cover the Doppler frequency shift range corresponding to the typical movement speed of the nano-positioning stage during the assembly of smart glasses, while maintaining sufficient attenuation of out-of-band noise.

[0056] The I / Q quadrature signal digitization and DC offset cancellation module 402 processes the I-channel and Q-channel analog signals output by the quadrature signal detection unit 103. The sampling rate is used for analog-to-digital conversion to obtain discretized data. and The sampling rate is selected based on the Nyquist criterion and must be at least the highest frequency of the beat frequency signal. More than twice as much, While meeting this condition, sufficient oversampling margin is maintained, which is beneficial for the subsequent transition band design of the digital filter. This is to eliminate the DC offset component. and This module uses a sliding window mean method, calculating and subtracting the current DC offset estimate in real time using a window of 256 sampling points, and outputting a normalized value. and Signal. 256-point window at Approximately at sampling rate The time window can cover several complete oscillation cycles of the beat frequency signal, thus obtaining a stable and reliable DC estimate; at the same time, the window length will not be too long, so as to avoid the lag effect of the DC estimate interfering with the signal normalization when the measured displacement changes rapidly.

[0057] The coarse phase calculation module 403 uses the CORDIC (coordinate rotation digital calculation) algorithm to process the normalized phase. and Performing the arctangent operation yields the coarse phase value: The CORDIC algorithm is naturally suited to the shift-add hardware architecture of FPGAs, enabling efficient trigonometric function operations without consuming dedicated multiplier resources. The angular resolution of this coarse phase is... The displacement resolution is approximately This coarse phase value As one of the main observation inputs for subsequent multi-source error parallel fusion estimation, the entire operation of the aforementioned digital phase-locked loop 401, DC offset cancellation module 402, and coarse phase calculation module 403 is implemented on the FPGA using pipelined hardware logic, with the total delay from the original signal input to the coarse phase output not exceeding [a certain value]. .

[0058] The multi-source error unified state-space modeling module 500 is the key component of this invention, which integrates all error sources into the same framework for joint description at the mathematical level. The modeling results of this module are used collaboratively by the FPGA coprocessor 301 and the ARM processor 302: the FPGA uses the established state-space model to perform high-speed filtering operations, and the ARM uses the structural information of the model to perform parameter identification and injection logic.

[0059] The core of this module lies in defining a 9-dimensional state vector. The characteristic parameters of the measured physical quantity and various error sources are uniformly incorporated:

[0060]

[0061] The physical meaning of each component is as follows. The measured displacement is in nm, representing the actual positional change of the positioning stage for the optical components of the smart glasses in the measurement direction. The displacement velocity, in nm / s, is introduced as a first-order dynamic extension of the displacement state, giving the filter the ability to predict and track uniform and slowly varying velocity motions. The deviation of the air refractive index is dimensionless and is defined as the actual refractive index. Compared to the standard state ( , , (lower refractive index) The deviation value, i.e. . The rate of change of refractive index deviation is dimensionless ( / s), and is used as a measure of the rate of change of refractive index deviation. The first-order dynamic extension is used to track the refractive index drift trend caused by slow changes in temperature and pressure. and Let be the cosine and sine amplitude parameters of the first-order periodic nonlinear error, respectively, in rad. The phase of this first-order nonlinear error is thus expressed as: . and Let be the cosine and sine amplitude parameters of the second-order periodic nonlinear error, respectively, in rad, and let be the corresponding phase of the second-order nonlinear error. . The high-frequency displacement disturbance caused by external mechanical vibration, in nm, is modeled as the output of a band-limited white noise-driven decay process. The reason for including both first-order and second-order nonlinear error parameters in the state vector is that, in actual dual-frequency laser interferometers, the periodic nonlinear errors caused by polarization leakage and mixing errors are mainly first- and second-order harmonic components. The amplitudes of higher-order components are usually more than an order of magnitude smaller than the first two, and can be disregarded under nanometer-level precision requirements. However, for cases where higher-order components cannot be ignored under specific optical path configurations, the state vector can be extended to a higher-dimensional form containing third- or higher-order harmonic parameters, with the modeling method being completely consistent with that of the first and second-order components.

[0062] The state transition equation describes the evolution of the system state between adjacent sampling times:

[0063]

[0064] Wherein, the state transition matrix for A matrix in which the vast majority of elements are zero. The non-zero elements are defined as follows: , ( The sampling period is , (Sampling frequency), this line illustrates the recursive relationship between displacement and velocity under the assumption of uniform motion. ; This corresponds to the constant velocity assumption under the condition of no external force. , This line describes the gradual recursion of refractive index deviation over time. ; ,in The value is 0.995, which is the first-order decay coefficient of the refractive index change rate. It reflects the physical characteristics that the change of environmental parameters has a slow trend rather than a rapid random jump. The decay coefficient is close to 1, which means that the trend of refractive index change has a strong time correlation. The harmonic parameters of the nonlinear error are modeled as slow variables, approximately constant between adjacent sampling periods, and their actual changes are mediated by process noise. The corresponding components are used to express uncertainty; ,in The value is 0.90, which is the damping coefficient for vibration disturbance. This value is significantly smaller than the refractive index damping coefficient. This reflects the physical fact that mechanical vibrations have a rapid decay characteristic—external vibrations will quickly decay to zero in the absence of continuous excitation.

[0065] This item is an external control input; when the nano-positioning platform executes an active displacement command, For the instruction displacement increment, for The column vector has only the first element as 1 and the rest as 0, indicating that the control input directly affects the displacement state. Let be the process noise vector, assumed to be zero-mean Gaussian white noise, and its covariance matrix be... This is a diagonal matrix, and the values ​​of each diagonal element are set according to the dynamic characteristics and uncertainty level of the corresponding physical quantity. In this embodiment, The diagonal elements take values ​​of The displacement and velocity components correspond to larger process noise to accommodate the uncertainty of the nano-positioning stage motion, the refractive index-related components correspond to extremely small process noise to reflect the gradual change characteristics of environmental changes, the process noise of the nonlinear parameters is between the two to adapt to possible gradual changes in optical path conditions, and the vibration component corresponds to larger process noise to reflect the random strong excitation characteristics of vibration.

[0066] The observation equation describes the functional relationship between the system's available measurement information and its state vector:

[0067]

[0068] This system has two observation inputs. The first input is a phase observation. The CORDIC output from the coarse phase calculation module 403 has the following nonlinear relationship with the state vector:

[0069]

[0070] in This is the predicted phase based on the nominal refractive index and the current displacement estimate. The physical meaning of this observation equation is: the coarse phase observation equals the true displacement phase including the refractive index deviation correction plus the additional phase shift introduced by nonlinear errors. In the observation equation... One study demonstrates the coupling effect between refractive index deviation and vibration disturbance displacement—when both exist simultaneously, their influence on the phase is not simply superimposed but rather involves a product cross term. This is precisely why it is necessary to incorporate all error sources into a unified state space for joint estimation.

[0071] The second observation is the environmental parameter refractive index correction value. The air refractive index deviation is calculated by the Edlén formula correction module 600 based on temperature, air pressure, and humidity sensor data. Its observation equation is: That is, directly observing the refractive index deviation state component. To observe the noise vector, assume it is zero-mean Gaussian white noise, its covariance matrix is... The settings are based on the phase demodulation accuracy and the accuracy of the environmental sensors; specifically, the phase observation noise variance... The quantization accuracy corresponding to the CORDIC algorithm, and the variance of environmental refractive index observation noise. This reflects the uncertainty in refractive index calculation under given sensor accuracy conditions, as described by the modified Edlén formula.

[0072] The Edlén formula correction module 600 for environmental parameters runs on the ARM processor 302 and receives temperature data from the environmental parameter sensing unit 200. air pressure and humidity The air refractive index under current environmental conditions was calculated using the modified Edlén formula. The specific form of this modified formula is:

[0073]

[0074] In the formula The refractive index of standard dry air under standard temperature and pressure conditions. For Vacuum wavenumber in units For the sake of temperature and relative humidity The calculated partial pressure of water vapor. In practical applications, this formula is relevant to temperature. The weighted average value is taken from each measuring point in the temperature sensing array 201. The weights can be allocated based on the distance of each measuring point from the optical axis or its contribution to the optical path; air pressure. and humidity The current readings are taken from the barometric pressure sensor 202 and the humidity sensor 203, respectively. The calculated refractive index deviation is as follows:

[0075]

[0076] This module is Frequency output The value is used as the second observation input of the Kalman filter. . The update rate is the lowest among environmental parameter sensors (barometric pressure and humidity sensors). (This is a match for the refractive index variation above this frequency, which will be determined by the state-space model.) and The dynamic prediction capability is used to compensate.

[0077] The group-update extended Kalman parallel fusion estimation module 700 is the core algorithm module of this invention, which is executed collaboratively by the FPGA coprocessor 301 and the ARM processor 302. Based on the model established by the multi-source error unified state space modeling module 500, this module decomposes the high-dimensional matrix operation of extended Kalman filtering into several low-dimensional sub-matrix operations through a group update strategy, thereby significantly reducing the computational complexity while maintaining the joint estimation accuracy.

[0078] The grouping strategy divides the 9-dimensional state vector into group A and group B. Group A is the displacement-refractive index group, which includes... There are five state components in total. These components share the common characteristic of exhibiting strong nonlinear coupling with the interference phase and changing rapidly. Group B is the nonlinear parameter group, containing... There are four state components, characterized by being introduced into the observation equations as slowly varying parameters via trigonometric functions. The physical basis for this grouping method lies in the different mechanisms by which group A and group B influence the observations—group A states are introduced into the equations via slowly varying parameters via trigonometric functions. The product relationship affects the principal phase term, and the state of group B affects the additional periodic offset term through coupling with the trigonometric function of the interferometric phase. The two groups are processed sequentially in the filtering update, with group A updated before group B. This allows the update of group B to utilize the latest estimate from group A to calculate a more accurate observation residual, thereby improving the convergence and accuracy of the overall estimation.

[0079] In each filtering cycle (In this embodiment, the sampling frequency is taken) ,Right now Module 700 performs the following five steps.

[0080] Step S1 is the unified state prediction, executed on the FPGA coprocessor 301, taking approximately [time missing]. This step performs a one-step prior prediction on the complete 9-dimensional state vector:

[0081]

[0082]

[0083] This step is implemented on the FPGA using a hardware matrix multiplier. Due to the state transition matrix... Highly sparsity ( (If there are no more than 11 non-zero elements in the array), the FPGA's hardware logic only performs multiplication and addition operations on the non-zero elements, skipping all operations on zero elements, thus... The computational cost of matrix multiplication is reduced to just over ten multiplication-addition operations, significantly saving computation time and hardware resources.

[0084] Step S2 is the state update for group A, which involves correcting the state of group A using phase observations. This is executed on the FPGA coprocessor 301 and takes approximately [time missing]. The processing procedure for this step is as follows: using the first phase observation value... Construct the Jacobian submatrix of group A This is The row vector, in the current predicted value Linearization calculations are performed at the point, specifically in the form of:

[0085]

[0086] In the formula and These are the displacement and refractive index deviation estimates obtained from the current step. In this Jacobian matrix, the first and fifth elements are equal, reflecting the displacement... and vibration disturbance The influence coefficients on the observed phase are the same (both are multiplied by ). Mapped to the phase domain), the 3rd element Reflects refractive index deviation By comparing with the current displacement The product relationship affects the phase. The second and fourth elements are zero, meaning the velocity... and rate of change of refractive index They do not appear directly in the observation equations; they only indirectly affect the current time-to-time estimate through the state prediction equations. Based on this, the Kalman gain and state update for group A are calculated:

[0087]

[0088]

[0089]

[0090] At the same time, the cross-covariance matrix between group A and group B also needs to be updated:

[0091]

[0092] The update of the cross-covariance ensures that subsequent updates to group B accurately reflect the impact of updated information from group A on the uncertainty of group B's estimation. All the above calculations only involve... submatrices and Vector operations have a lower computational cost compared to complete vector operations. Matrix operations are significantly reduced and are performed by the second stage of the FPGA pipeline.

[0093] Step S3 is the group B state update, which involves correcting the group B state using the residuals from phase observations. This is executed on the FPGA coprocessor 301 and takes approximately [time missing]. Construct the Jacobian submatrix of group B. ,for Row vectors:

[0094]

[0095] The Kalman gain calculation for Group B needs to consider the updated cross-covariance information from Group A and the re-evaluated residual variance. :

[0096]

[0097] The status of Group B has been updated as follows:

[0098]

[0099] A key design element here is the observation equation. The calculation uses the updated values ​​of group A. and the current forecast value of Group B Instead of using all predicted values, the B group updates A first, then B. This sequential dependency ensures that the B group update utilizes the latest estimation information from the A group under the current observations, improving the accuracy of the nonlinear parameter update. This is especially important when rapid displacement changes cause significant shifts in the phase principal term. If the B group still calculates the residuals based on the old predicted values ​​from the A group, it will lead to biases in the nonlinear parameter estimation. The B group covariance update is as follows:

[0100]

[0101] This step only involves The submatrix operations are executed by the third stage of the FPGA pipeline. Through the grouping processing in steps S2 and S3, the matrix operation scale of a single filtering cycle is reduced from... The complete matrix is ​​reduced to and The computational complexity of sequentially operating on the two submatrices decreases from... Reduce to The magnitude is approximately the original. This reduction is for meeting Total delay constraints are crucial.

[0102] Step S4 is an environmental observation-assisted update, executed on the ARM processor 302, taking approximately [time missing]. This step is performed in parallel with steps S2 and S3 in time. The Edlén formula correction module 600 outputs a new environmental parameter. Triggered when value (frequency is) That is, each Execute once), using the second-path observation Refractive index deviation state and rate of change Auxiliary corrections are made. Due to the second-path observation equation... For linear updates involving only a single component of the state vector, the update process degenerates into a scalar Kalman update, which only involves... Submatrix operations of this scale can be efficiently performed on the ARM using double-precision floating-point operations. The update results are injected into the corresponding components of the state vector via the AXI4 bus before the start of the next FPGA filtering cycle. Environmentally assisted updates, although less frequent ( However, its role is indispensable: it provides an external constraint on the refractive index deviation state, independent of the interference phase, preventing... The estimated values ​​drift over long periods due to the accumulation of process noise. The change in refractive index deviation during the interval between two environmental observations depends on the state-space model. and Extrapolate the dynamic predictions. The introduction of states enables the system to track trend changes in refractive index even between environmental parameter sensor update intervals.

[0103] Step S5 is state coupling injection, executed on the ARM processor 302, and is a conditionally triggered mechanism. The function of this step is to inject the identification results of the online recursive least squares nonlinear parameter identification module 800 into the B group states of the Kalman filter in a controlled manner. The specific criteria and injection operation are as follows: when the nonlinear parameter estimate output by the RLS module... Current estimates of Kalman filter group B The Euclidean distance between them exceeds a preset threshold. At that time, perform the following injection operation:

[0104]

[0105]

[0106] In the formula This is the injection gain coefficient, and its value range is... , Estimate the covariance matrix for the parameters of the RLS algorithm. Injection gain. The design of the value reflects a compromise: If the value is too large, the statistical optimality of the Kalman filter will be greatly compromised, and the filter may oscillate or diverge. If the value is too small, the fast identification information of RLS cannot be effectively passed to the filter, thus losing the purpose of introducing external identification. Within the range of 0.3 to 0.5, this injection mechanism introduces the fast parameter tracking capability of RLS into the filter in a "soft injection" manner, while simultaneously increasing the covariance matrix accordingly. This informs the filter group B that the uncertainty of its state has increased due to the injection operation, enabling the filter to adaptively adjust its gain in subsequent updates, thereby maintaining the stability and convergence of the overall estimate. Threshold The introduction of this avoids unnecessary injection interference when the estimates of the two sets of algorithms are already consistent.

[0107] The online recursive least squares nonlinear parameter identification module 800 runs on the ARM processor 302. Independent of the Kalman filter, it performs real-time identification of nonlinear error parameters at a higher execution frequency (once per sampling period), providing input data for the state coupling injection in step S5.

[0108] The algorithm principle of this module is based on the Lissajous graphical analysis of I / Q orthogonal signals. Under ideal conditions without nonlinear errors, the normalized I' and Q' signals satisfy... The Lissajous plot is drawn as a standard circular trajectory on the IQ plane. However, when periodic nonlinear errors are present, polarization leakage and mixing effects cause the Lissajous plot to deform from a standard circle into an ellipse, and the tilt direction and ellipticity of the ellipse change with the error parameters. Based on this, the Lissajous ellipse fitting model is defined as follows:

[0109]

[0110]

[0111] The above nonlinear model is linearized at the current parameter estimates through a first-order Taylor expansion, defining the parameter vector to be identified. Construct the regression matrix Regression matrix for A matrix whose elements are determined by the current phase value. and signal amplitude The trigonometric function combination reflects the partial derivative relationship of each nonlinear parameter with respect to the I-channel and Q-channel signals. Based on this, a forgetting factor is used... The recursive least squares algorithm is used for parameter recursive updates:

[0112]

[0113]

[0114]

[0115] In the formula The residual vector is the fit to the ellipse. The initial value is taken as the covariance matrix for parameter estimation in the RLS algorithm. ( A larger initial covariance scalar allows the algorithm to have a faster learning rate during the startup phase. Forgetting factor. The value ranges from 0.98 to 0.995; in this embodiment, it is taken as... The introduction of the forgetting factor allows the algorithm to assign exponentially decreasing weights to historical data, enabling it to quickly "forget" old parameter values ​​when optical path conditions change (e.g., when different models of optical components are replaced in a smart glasses assembly line, causing changes in polarization leakage characteristics). This process takes approximately 5 interference cycles (corresponding to approximately...) The convergence of the new parameters is completed within the displacement. If the displacement is... If the value is too close to 1, the algorithm responds more slowly to new data, and the time required for parameter convergence is prolonged; if the value is too small, the variance of the steady-state estimate of the algorithm increases, and the parameter values ​​will fluctuate significantly after convergence. The value of 0.99 achieves a good balance between convergence speed and steady-state accuracy.

[0116] The collaborative mechanism between the RLS identification module 800 and the Kalman filter module 700 deserves further explanation. The two modules are not simply connected in series or parallel, but rather form a two-layer architecture of "outer layer identification - inner layer filtering" through the state coupling injection mechanism in step S5. The RLS algorithm directly uses the original I / Q orthogonal signals as input for parameter identification, without relying on the output of the Kalman filter. Therefore, it is not affected by filter inertia when parameters change abruptly, resulting in faster parameter tracking. The Kalman filter, on the other hand, uses a unified state-space model to jointly estimate nonlinear parameters with other states such as displacement, refractive index, and vibration, exhibiting globally optimal statistical characteristics. The state coupling injection mechanism combines the advantages of both: when the optical path conditions are stable, the RLS estimate and the Kalman filter B group estimate tend to be consistent, without triggering the injection operation, and the filter continues to operate autonomously; when the optical path conditions suddenly change, the RLS is the first to detect the parameter change and generate a deviation, triggering the injection operation to quickly transmit the new parameter information to the filter, accelerating the convergence of the filter B group state to the true value.

[0117] The compensation displacement output module 900 directly extracts the first component from the updated state vector of the group-updated extended Kalman filter. This is the final compensated displacement output value. This output value has already intrinsically subtracted the air refractive index drift (via...) during the joint estimation process of the Kalman filter. State estimation), first-order and second-order periodic nonlinear errors (through... State estimation) and external mechanical vibration disturbances (through The influence of state estimation is eliminated, eliminating the need for additional post-processing subtraction compensation after the filter output. The compensated displacement value is... floating-point format The update rate is transmitted to the downstream motion controller via a high-speed serial interface. For the specific interface selection, deterministic communication can be achieved using the EtherCAT industrial Ethernet protocol, or a fiber optic serial interface or other low-latency communication protocols can be selected based on the existing architecture of the production line. This compensated displacement signal is directly used for closed-loop position feedback control of the nano-positioning stage in the smart glasses assembly line.

[0118] The following is a complete description of the system's signal processing flow to clarify the data flow and timing coordination between the modules.

[0119] The dual-frequency laser source 101 has an output frequency of [frequency value missing]. and The orthogonally polarized beam. After the beam enters the polarization beam splitting and interference optical path 102, The component is transmitted through the PBS into the reference arm, and returns after being reflected by the reference mirror. The component light is reflected by the PBS into the measuring arm, and then reflected back by the measuring mirror mounted on the nano-positioning stage. The two reflected beams recombine at the PBS and are converted into I-channel and Q-channel electrical signals by the two orthogonal polarization photodetectors of the orthogonal signal detection unit 103, respectively. Simultaneously, the photodetector inside the dual-frequency laser source 101 outputs a reference beat frequency signal. .

[0120] The aforementioned I(t), Q(t), and R(t) signals enter the digital phase demodulation module 400. The I / Q quadrature signal digitization and DC offset cancellation module 402 then... The digital phase-locked loop 401 completes sampling digitization and DC offset cancellation at a high rate. For reference, lock the beat frequency. The phase difference of the measured signal is extracted, and the coarse phase calculation module 403 calculates the coarse phase using the CORDIC algorithm. All the above steps are implemented using pipelined hardware logic on the FPGA coprocessor 301, with a latency of less than [specified value]. .

[0121] In parallel with digital phase demodulation, the temperature sensor array 201, barometric pressure sensor 202, and humidity sensor 203 in the environmental parameter sensing unit 200 continuously acquire environmental parameters at their respective sampling rates. The signal conditioning and ADC board 204 digitizes the sensor signals and transmits them to the ARM processor 302 via the SPI bus. The environmental parameter Edlén formula correction module 600, on the ARM processor 302, uses... Frequency will affect temperature air pressure and humidity Converted to air refractive index deviation , which serves as the second observation input for the Kalman filter.

[0122] Building upon this foundation, the system enters the core stage of parallel fusion estimation of multi-source errors. The extended Kalman filter is updated in groups for each... During the sampling period, the FPGA coprocessor 301 sequentially executes the unified state prediction of step S1 (approximately...). Step S2, Group A status update (approximately) ) and the status update of group B in step S3 (approximately This forms a three-stage pipeline structure, with data transfer between stages via the FPGA's on-chip block random access memory (BRAM). Parallel to the execution of S1 through S3 by the FPGA, the ARM processor 302 executes step S4 (environment-assisted update) upon receiving a new Edlén refractive index value, and performs step S5 (state coupling injection) based on the identification result of the online recursive least squares nonlinear parameter identification module 800. The computations of the FPGA and ARM form an overlapping pipeline in time: when the FPGA executes step S1... During steps S1 to S3 of the cycle, the ARM executes the... In steps S4 and S5 of the cycle, the update result of ARM is in the... Before step S1 of the cycle begins, the status register of the FPGA is injected via the AXI4 bus. This heterogeneous collaborative pipeline scheduling ensures that the computational latency on the ARM side does not occur on the critical path, and the overall latency depends only on the cumulative latency of the three-stage pipeline on the FPGA side.

[0123] The online recursive least squares nonlinear parameter identification module 800 performs an RLS recursion once per sampling period on an ARM processor 302. This module obtains normalized parameters from the FPGA. and The signal is used to calculate the Lissajous ellipse fitting residuals and recursively update the nonlinear parameters. When optical path conditions change—for example, when a smart glasses assembly line changes to a different specification of diffractive waveguide substrate, causing a change in polarization leakage characteristics—the forgetting factor... This allows the parameters to reconverge to a new steady-state value within approximately 5 interference cycles. The identification results are then soft-injected into the B-group states of the Kalman filter via a state-coupled injection mechanism, increasing the injection gain. Values ​​are taken in the range of 0.3 to 0.5 to ensure that the two algorithms converge together.

[0124] After all the above processing steps, the compensation displacement output module 900 extracts the first component from the updated state vector of the Kalman filter. This is the final compensated actual displacement output. This displacement value is... floating-point format The update rate is transmitted to the motion controller of the smart glasses assembly line via an EtherCAT interface or fiber optic serial interface for closed-loop position feedback control of the nano-positioning stage. The end-to-end delay from interference signal acquisition to compensated displacement output is less than [value missing]. The phase demodulation delay is less than Step S1 predicts approximately Step S2, Group A update approx. Step S3, Group B update approx. Output communication app Each step is executed in a pipelined manner, and the actual end-to-end delay is taken as the complete throughput time of the pipeline.

[0125] The following is a complete implementation description of the core algorithm of this invention.

[0126] The initialization phase of the grouped update extended Kalman filter main loop algorithm sets the initial values ​​of the 9-dimensional state vector. Initial covariance matrix Process noise covariance Phase observation noise variance Environmental refractive index observation noise variance The values ​​of the diagonal elements of the initial covariance reflect the initial uncertainty perception of each state component at system startup: the initial variances of displacement and vibration components are relatively large (100 and 50 respectively) because the actual position of the worktable and the current vibration level are completely unknown when the system is powered on; the initial variances of refractive index deviation and its rate of change are very small ( and This is because the refractive index deviation under standard conditions is usually on the order of a tiny number; the initial variance of the nonlinear parameter is between the two, corresponding to the empirical prior range of the nonlinear error parameter of a typical dual-frequency laser interferometer.

[0127] The main loop operates on a per sampling period. The process is triggered, sequentially completing steps S1 to S5 and outputting the compensated displacement. In step S1, the FPGA performs a one-step prediction of the state vector. and predicted covariance Simultaneously, the current observation value of the coarse phase calculation module 403 is obtained. And calculate the predicted phase In step S2, extract group A of the predicted covariance. submatrix Calculate the Jacobian matrix for group A. New information Kalman gain In addition to the observed residuals, update the state and covariance of group A, and simultaneously update the cross covariance. In step S3, the Jacobian matrix of group B is calculated. Based on the updated values ​​of group A and the predicted values ​​of group B, calculate the observed residuals of group B, and complete the status and determination of group B. Covariance update. Step S4 performs scalar Kalman update correction when environmental observations are available. Status. Step S5 performs a soft injection update when the difference between the RLS estimate and the EKF B group estimate exceeds a threshold. Extraction at the end of the loop. As compensation displacement output.

[0128] Initialization phase of the RLS nonlinear parameter identification algorithm with forgetting factor: setting the parameter vector Covariance matrix and forgetting factor In each sampling period, the algorithm obtains normalized data from the DC offset cancellation module 402. and Calculate the current phase ,structure Regression Matrix (Its elements are composed of) , , , , (combination of elements), calculate the ellipse fitting residual. Execute the RLS recursive formula to update the parameters. Covariance The updated parameters are then output to the group update extended Kalman parallel fusion estimation module 700 for use in state coupling injection.

[0129] The measurement method and system of this invention are primarily aimed at the precision manufacturing of optical components for smart glasses. The assembly accuracy of core optical components in smart glasses, such as diffractive waveguides, Micro-LED or Micro-OLED microdisplays, and freeform optical lenses, directly affects image quality. Taking the bonding process of diffractive waveguides as an example, the relative positional deviation between the grating coupling area and the coupling area needs to be controlled within a certain range. Only by ensuring diffraction efficiency and eyebox uniformity can the present invention provide this. The residual error is less than The measurement capability that compensates for delay provides ample accuracy and speed margins for the closed-loop control of this process. Besides the field of smart glasses, the technical solution of this invention can also be applied to semiconductor lithography alignment systems, displacement compensation of precision machine tools, online inspection of MEMS devices, and other precision manufacturing and metrology scenarios requiring real-time nanometer-level displacement measurement. In these applications, the measurement mirror in the system hardware layer is mounted on the corresponding measured motion platform, the environmental parameter sensing unit 200 is configured and adjusted according to the actual environmental conditions, and the algorithm architecture and parameter settings in the software layer can be adaptively adjusted based on the above embodiments according to specific error characteristics and real-time requirements.

[0130] It should be noted that the above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A method for real-time compensation measurement of nanoscale displacement based on dual-frequency laser interferometry, characterized in that, Includes the following steps: The dual-frequency laser interferometric optical unit acquires the measurement beat frequency signal carrying the displacement information and the reference beat frequency signal as the phase reference, and the orthogonal signal detection unit converts the measurement beat frequency signal into two orthogonal electrical signals; at the same time, the environmental parameter sensing unit collects the temperature, air pressure and humidity data of the interferometric optical path environment in real time. A unified state-space model for multi-source errors is established, defining a high-dimensional state vector that includes the measured actual displacement, displacement velocity, air refractive index deviation, air refractive index deviation change rate, periodic nonlinear error harmonic parameters, and external mechanical vibration disturbance. A state transition equation describing the evolution of the state vector over time and an observation equation describing the nonlinear mapping relationship between the phase observation value and the state vector are also established. The high-dimensional state vector is estimated in real time using a group-updated extended Kalman filter. In each sampling period, all state components are first predicted uniformly according to the state transition equation. Then, the state vector is divided into a first state group and a second state group. The first state group and the second state group are updated in turn using phase observations. The measured real displacement component is extracted from the updated state vector and output as the compensated displacement value.

2. The method for real-time compensation measurement of nanoscale displacement based on dual-frequency laser interferometry according to claim 1, characterized in that, The high-dimensional state vector specifically includes nine state components: the measured actual displacement, displacement velocity, air refractive index deviation, air refractive index deviation change rate, cosine amplitude of the first-order periodic nonlinear error, sine amplitude of the first-order periodic nonlinear error, cosine amplitude of the second-order periodic nonlinear error, sine amplitude of the second-order periodic nonlinear error, and external mechanical vibration disturbance.

3. The method for real-time compensation measurement of nanoscale displacement based on dual-frequency laser interferometry according to claim 2, characterized in that, The specific process of dividing the state vector into a first state group and a second state group, and updating the first and second state groups sequentially using phase observations, is as follows: The first state group is defined to include the measured actual displacement, displacement velocity, air refractive index deviation, air refractive index deviation change rate, and external mechanical vibration disturbance. The second state group is defined to include the cosine and sine amplitudes of first-order and second-order periodic nonlinear errors. The Jacobian submatrix corresponding to the first state group is calculated, and the first Kalman gain is calculated using the phase observations and current predictions. The state estimate and covariance matrix of the first state group are updated, and the cross-covariance matrix between the first and second state groups is updated simultaneously. The Jacobian submatrix corresponding to the second state group is calculated, and the observation residual is calculated using the phase observations, the updated first state group estimate, and the second state group prediction. The second Kalman gain is calculated, and the state estimate and covariance matrix of the second state group are updated.

4. The method for real-time compensation measurement of nanoscale displacement based on dual-frequency laser interferometry according to claim 3, characterized in that, The method also includes a state coupling injection step: running an online recursive least squares parameter identification algorithm in parallel, using the Lissajous ellipse fitting residual of the two orthogonal electrical signals to identify periodic nonlinear error parameters in real time; and determining whether the difference between the parameter identification value output by the recursive least squares algorithm and the current estimated value of the second state group in the grouped updated extended Kalman filter exceeds a preset threshold. When the difference exceeds a preset threshold, the parameter identification value is injected into the state estimate of the second state group in a weighted manner, and the covariance matrix value of the second state group is increased accordingly.

5. The method for real-time compensation measurement of nanoscale displacement based on dual-frequency laser interferometry according to claim 4, characterized in that, The online recursive least squares parameter identification algorithm employs a recursive mechanism with a forgetting factor, the forgetting factor ranging from 0.98 to 0.995, which enables it to quickly converge to new nonlinear error parameters when optical path conditions change.

6. The method for real-time compensation measurement of nanoscale displacement based on dual-frequency laser interferometry according to claim 2, characterized in that, The method also includes an environmental observation-assisted update step: calculating the observed air refractive index deviation using the modified Edlén formula based on the temperature, air pressure, and humidity data; and using the observed air refractive index deviation to perform independent Kalman update correction on the air refractive index deviation and its rate of change component in the high-dimensional state vector.

7. The method for real-time compensation measurement of nanoscale displacement based on dual-frequency laser interferometry according to claim 2, characterized in that, The nonlinear mapping relationship between the phase observation value and the state vector in the observation equation is specifically expressed as follows: the phase observation value is equal to the true displacement phase including the refractive index deviation correction plus the additional phase offset introduced by the nonlinear error; where the true displacement phase term reflects the product coupling relationship between the refractive index deviation and the total displacement including the vibration disturbance.

8. The method for real-time compensation measurement of nanoscale displacement based on dual-frequency laser interferometry according to claim 4, characterized in that, The method runs on a heterogeneous computing platform of FPGA and ARM: the FPGA is responsible for performing digital phase demodulation, unified state prediction, and group update operations of the first state group and the second state group, and each step is executed in parallel in a pipeline manner; the ARM is responsible for performing environmental parameter Edlén formula calculation, online recursive least squares parameter identification algorithm, and state coupling injection logic judgment.

9. The method for real-time compensation measurement of nanoscale displacement based on dual-frequency laser interferometry according to claim 1, characterized in that, The method is applied to the precision assembly production line of smart glasses diffractive waveguides or micro-display arrays, and the compensated displacement value is used for closed-loop position feedback control of the nano-positioning stage.

10. A real-time nanoscale displacement compensation measurement system based on dual-frequency laser interferometry, characterized in that, include: The dual-frequency laser interference optical unit is used to generate dual-frequency lasers and form an interference optical path, outputting a measurement beat frequency signal and a reference beat frequency signal, and outputting orthogonal electrical signals after orthogonal detection; An environmental parameter sensing unit is used to collect temperature, air pressure, and humidity data of the optical path environment; a signal processing and computing platform includes an FPGA coprocessor and an ARM processor, wherein the signal processing and computing platform is configured to execute the nanoscale displacement real-time compensation measurement method based on dual-frequency laser interferometry as described in any one of claims 1 to 9.

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