Mode decomposition and phase regression-based Michelson interference micro-displacement measurement method and device

Abstract

The invention discloses a Michelson interference micro-displacement measurement method and device based on modal decomposition and phase regression, and belongs to the technical field of nanoscale displacement measurement. The device is composed of an optical system and an electronic system, wherein the optical system is used for generating an interference light field carrying displacement information, and the electronic system is responsible for collecting, preprocessing and digitizing interference signals. According to the method, self-adaptive decomposition is carried out on interference signals through a band-limited dynamic noise addition CEEMDAN algorithm, noise is effectively separated, phase trend information is extracted, high-precision phase reconstruction is achieved in combination with prior linear least square regression, and finally the nanoscale displacement is obtained through calculation. According to the invention, excellent measurement precision and robustness can still be maintained under complex conditions of incomplete signal period, undersampling, low signal-to-noise ratio and the like, and the system is simple in structure and easy to implement, and can be widely applied to the fields of precision processing, optical detection, micro-nano sensing, semiconductor manufacturing and the like.

Description

Technical Field

[0001] This invention belongs to the field of nanoscale displacement measurement technology, specifically a micro-displacement measurement system based on interference signal trend extraction and fitting demodulation. Background Technology

[0002] Interferometric displacement measurement is a high-precision, non-contact measurement method based on the principle of optical interference. Its core idea is to convert the minute displacement of the measured object into a change in optical path difference, thereby causing a change in the phase of the interference signal. Due to the extremely short wavelength of the light source, sub-nanometer to picometer-level resolution can be achieved using optical interference, making this technology irreplaceable in high-end manufacturing and scientific research. Compared with traditional contact displacement measurement methods, interferometric displacement measurement has significant advantages such as non-contact measurement, no introduction of mechanical load, high sensitivity, fast dynamic response, and high spatial resolution, making it ideal for online detection and dynamic monitoring of precision components, fragile structures, and micro / nano devices. This technology has been widely applied in many cutting-edge fields, including photolithography and alignment in semiconductor manufacturing processes, nanofabrication and detection, assembly and calibration of precision optical systems, biosensing in life sciences, and dynamic response characterization of microelectromechanical systems (MEMS) structures.

[0003] Among numerous interferometric structures, the Michelson interferometer is one of the most common interferometric architectures in the field of micro-displacement measurement due to its symmetrical optical path design, simple structure, high stability, and ease of integration and miniaturization. Its working principle involves splitting the incident laser into two beams using a beam splitter: one beam is directed towards a reference mirror, and the other towards a measuring mirror. After reflection, the beams recombine to form an interference signal on the detector. The changes in the interference spot contain crucial information about the measured displacement and serve as the direct physical basis for displacement measurement. Therefore, effectively extracting phase information from the interference signal and achieving high-resolution displacement demodulation under complex conditions has become a key issue in the design and application of interferometric measurement systems.

[0004] However, in applications involving nanometer displacement measurement, the actual acquired interference signals often exhibit significant non-ideal characteristics. When the measured displacement amplitude is too small, the obtained interference signal has insufficient period, a limited number of fringes, and an unclear signal variation trend, leading to a significant increase in demodulation difficulty. When the acquisition time window is limited, the signal spectral resolution is insufficient, and frequency-domain-based methods cannot operate stably. Simultaneously, the actual measurement environment and system hardware introduce various interference factors, such as background noise, light intensity fluctuations, detector nonlinear drift, and thermal effects of optical devices, further reducing the signal-to-noise ratio and stability. These factors cause the actual interference signal to deviate significantly from ideal conditions, making it difficult for traditional methods to maintain the expected measurement accuracy in engineering applications.

[0005] Common interferometric signal demodulation methods currently include fringe counting, envelope detection, Fourier transform, phase generation carrier (PGC), lock-in amplification, Hilbert transform, and more recently proposed methods such as wavelet transform, adaptive filtering, and machine learning-based intelligent demodulation. Fringe counting determines displacement by the change in the number of interference fringes, making it suitable for large-scale measurements, but it relies on complete fringes and cannot accurately handle minute displacements less than one period, exhibiting significant limitations in sub-period or nanometer-scale displacement detection. Envelope detection reflects displacement trends by extracting the envelope of the interference signal, offering a simple structure, but it is highly sensitive to noise, and the filtering stage easily introduces errors, leading to poor stability. Fourier transform extracts phase information through frequency domain analysis, suitable for periodically stable signals with low noise levels, but its spectral resolution is insufficient when the acquisition time window is limited or the signal period is insufficient, resulting in a significant decrease in demodulation accuracy. Phase generation carrier (PGC) achieves demodulation through high-frequency modulation and demodulation. High-resolution phase measurement offers strong noise immunity, but requires additional high-frequency modulation sources and complex circuits, resulting in high system costs and stringent requirements for modulation depth and stability. Locked-in amplification (LIA) utilizes phase-sensitive detection to extract signal amplitude and phase, exhibiting good anti-interference capabilities, but it relies on external reference signals, has complex circuit implementation, and demands high system synchronization. Hilbert transform extracts instantaneous phase by constructing an analytic signal, adapting to aperiodic signals to some extent, but it is highly sensitive to background noise and low-frequency drift, and has high computational complexity. Wavelet transform and adaptive filtering methods offer advantages in processing non-stationary and short-time signals, but their algorithms are highly dependent on parameter selection and lack robustness. Existing interferometric signal demodulation methods, while each possessing unique characteristics, generally suffer from limited applicability, high requirements for signal integrity and stability, insufficient noise and drift immunity, strong hardware dependence, or excessive computational complexity. In complex real-world environments, these shortcomings can lead to unstable measurement results or decreased accuracy, making it difficult to simultaneously meet the comprehensive requirements of high resolution, strong robustness, and real-time performance. Summary of the Invention

[0006] To address the aforementioned issues, this invention provides a Michelson interferometric micro-displacement measurement method and apparatus based on mode decomposition and phase regression. This method can accurately extract the low-frequency variation trend of the interference signal under conditions of incomplete signal period, undersampling, and low signal-to-noise ratio, and achieve high-fidelity demodulation of nanometer-level displacement information.

[0007] To achieve the above objectives, the present invention provides the following technical solution: a Michelson interferometric micro-displacement measurement device based on mode decomposition and phase regression, comprising an optical system and an electronic system.

[0008] The optical system is responsible for displacement sensing and interference signal generation. Its main structure includes a laser, a beam-splitting prism, a beam-contracting lens, a reflecting mirror, and a photoelectric detection module. The laser emits a monochromatic laser with a stable wavelength, which is then incident on the beam-splitting prism after passing through the beam-contracting lens. After being split by the beam-splitting prism, one beam is used as a reference beam to illuminate a reference mirror, while the other beam is used as a measurement beam to illuminate a measuring mirror rigidly connected to the object being measured. The two reflected beams are then combined by the beam-splitting prism to form an interference pattern that changes with displacement. The photoelectric detection module collects the local optical power at the center of the interference pattern, and the output interference electrical signal changes periodically with increasing displacement.

[0009] The electronic system is used for the acquisition, trend extraction, phase estimation, and displacement calculation of interference signals. Its structure includes a dual positive and negative DC power supply module, a transimpedance amplifier, a fifth-order active Butterworth low-pass filter module, an analog-to-digital converter module, a microcontroller, and a host computer. The dual positive and negative DC power supply module provides stable voltage to the fifth-order active Butterworth low-pass filter module and the transimpedance amplifier. The input and output terminals of the transimpedance amplifier are connected to the output of the photodetector module and the input of the fifth-order active Butterworth low-pass filter module, respectively, amplifying the electrical signal while suppressing power supply ripple. The input and output terminals of the analog-to-digital converter module are connected to the output of the fifth-order active Butterworth low-pass filter module and the microcontroller, respectively, converting the interference electrical signal into a digital signal. The microcontroller communicates with the host computer via a serial port to process the digital interference signal and perform phase inversion.

[0010] The main flow of the measurement method designed in this invention is as follows: S1: Construct an optical system based on the Michelson interferometer structure to form an interference spot that changes with displacement; S2: The measuring mirror is rigidly connected to the displaced object, and the displacement is measured. Converted into the change in optical path difference between the two arms Displacement As the interference spot continues to increase, the local spot at the center of the interference spot will exhibit a regular alternation of brightness and darkness; S3: Adjust the optical path so that the local light spot at the center of the interference spot falls on the photosensitive surface of the photoelectric detection module, and collect the local optical power at the center of the interference spot through the photoelectric detection module. , to increase optical power Converted into photocurrent carrying displacement information ; In the formula The output power of the laser. This refers to the responsivity of the photoelectric detection module.

[0011] S4: A weak current signal is amplified using a transimpedance amplifier and converted into a voltage signal that varies sinusoidally with the increase of displacement. ; in The amplitude of the interference signal; For bias; The noise is superimposed, including high-frequency power supply ripple, mechanical micro-vibration interference, etc. S5: Suppresses voltage signals using a fifth-order active Butterworth low-pass filter module. The high-frequency power supply ripple superimposed in the middle improves the signal-to-noise ratio; S6: Original interference voltage signal The analog-to-digital converter converts the signal into a digital value and sends it to the microcontroller. The sampling frequency is... After preprocessing the digital signal, the microcontroller sends a data frame containing a frame header, a data length field, and a CRC check field to the host computer via a serial port. S7: The CEEMDAN algorithm based on band-limited dynamic noise is used in the host computer to process the digital signal and obtain the denoised trend signal. The process of obtaining the trend of the interference signal using the band-limited dynamic noise-adding CEEMDAN algorithm proposed in this invention is as follows: Band-limited noise generated by the algorithm: Generate white noise with a mean of zero and a standard deviation of 1. Bandpass filtering is applied to limit the frequency range.

[0012] In the formula As a bandpass filter, it can adaptively adjust according to signal characteristics to ensure that the noise energy is mainly injected into the high-frequency band, which helps to strip away high-frequency interference without disrupting the low-frequency trend.

[0013] In the formula This is the lower limit of band-limited noise; This represents the upper limit of the band-limited noise. To keep the added noise energy away from the low-frequency region where the trend signal is located, the lower limit of the band-limited noise is taken. for: In the formula The upper limit of noise in the main frequency band of the interference fringes Subject to system sampling rate and Nyquist sampling rate limit: The formula for adjusting the dynamic noise amplitude is as follows: Calculate the standard deviation of the current residuals: Calculate the energy percentage of the residual in the noise-added frequency band and assess the relative intensity of the residual noise: in For residuals Fourier transform, The system sampling rate is set. A dynamic noise factor is defined to ensure that the noise level is increased when the residual noise energy percentage is low. in The base noise addition ratio, with a value ranging from 0.1 to 0.3; This is an adjustment coefficient, defaulting to 0.3~0.7, and needs to be selected based on the signal SNR, residual amplitude scale, and iterative stability. Therefore, the noise addition amplitude value is: For voltage signals Add noise to the k-th layer: EMD is performed to obtain the IMF. The k-th layer IMF is the average of multiple noisy decompositions. The number of noisy decompositions is 300, which can be increased as needed to improve stability, but also to increase the computational cost. The residuals are then updated as follows: Set the number of iterations to 40, and repeat the iteration until the termination condition is met. ), ultimately obtained: Finally, the high-frequency noise is stripped down to the first few layers of the IMF, and the last layer of the IMF becomes the final residual signal. The pure low-frequency trend is preserved, and the trend signal is: = S8: Sliding window detects the trend change of the interference signal, locates and extracts the signal data segment carrying displacement information; S9: After denoising and trend extraction using the band-limited dynamic noise-adding CEEMDAN algorithm, a pure sinusoidal trend signal with a high signal-to-noise ratio can be obtained. The denoised trend signal is fitted using the linear least squares method, and the interferometric signal model is reconstructed based on the signal features as follows: S10: Order , , Given sample value Construct the matrix: S11: Fit the interference signal of the displacement data segment using the prior linear least squares method, and solve for the fitting parameters: S12: Calculate the phase distribution of the interference signal using the fitting results. and displacement change .

[0014] Compared with the prior art, the beneficial effects of the present invention are as follows: The measurement method of this invention has a simple structure and is easy to integrate. It acquires the interference signal through a photoelectric detection module, eliminating the need for modulation devices and resulting in low system construction costs. By introducing mode decomposition and sinusoidal phase regression algorithms, it is possible to achieve stable and reliable phase extraction and micro-displacement measurement even under conditions of incomplete interference signal period, undersampling, and low signal-to-noise ratio. Attached Figure Description

[0015] Figure 1 This is a schematic diagram of the structure of the present invention; Figure 2 This is a physical hardware diagram of the present invention; Figure 3 This is a circuit connection diagram of the electronic system of the present invention; Figure 4 This is a flowchart of the signal processing during the displacement measurement process of the present invention; Figure 5 The IMF obtained after processing the interferometric electrical signal using the band-limited dynamic noise-adding CEEMDAN algorithm; Figure 6 The interference pattern varies with displacement; Figure 7 The voltage signal carrying displacement information is collected by the measuring device.

[0016] In the diagram: 1. Laser; 2. Convex lens; 3. Mirror 1; 4. Beam splitter prism; 5. Mirror 2; 6. Photodetector module; 7. Transimpedance amplifier module; 8. Fifth-order active Butterworth low-pass filter module; 9. Analog-to-digital converter module; 10. Microcontroller; 11. Positive and negative dual DC power supply module; 12. Switching power supply; 13. Host computer. Detailed Implementation

[0017] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0018] like Figure 1 As shown, a Michelson interferometric micro-displacement measurement method and apparatus based on mode decomposition and phase regression includes a laser 1, a convex lens 2, a first reflector 3, a beam splitter prism 4, a second reflector 5, a photoelectric detection module 6, a transimpedance amplifier 7, a fifth-order active Butterworth low-pass filter module 8, an analog-to-digital converter module 9, a microcontroller 10, a positive and negative dual DC power supply module 11, a switching power supply 12, and a host computer 13. The first reflector 3 is fixed to the object being measured to return the laser beam along its original path; the second reflector 5 is fixed in place; displacement is provided by a piezoelectric displacement stage; the beam splitter prism has a splitting ratio of 50:50. The physical hardware of this invention is as follows Figure 2 As shown, its working principle is based on the Michelson interference effect, achieving displacement detection at the nanometer to micrometer scale through changes in the phase and intensity of optical interference fringes. Specifically, laser 1 outputs a stable laser beam, which is collimated and focused by convex lens 2 and then incident on beam splitter prism 4. Beam splitter prism 4 splits the incident beam into two paths, one as the measurement beam, which returns to beam splitter prism 4 after reflection by mirror 3; the other as the reference beam, which also returns to beam splitter prism 4 after reflection by mirror 5. The two beams recombine and interfere within beam splitter prism 4, forming an interference spot. When the object being measured undergoes a small displacement, the optical path of the measurement beam changes accordingly, causing a phase shift and change in the intensity distribution of the interference spot fringes. By precisely adjusting the optical path, the local spot at the center of the interference spot is stably positioned on the photosensitive surface of photodetector module 6. The local optical power change caused by the displacement is recorded in real time and converted into a photocurrent signal proportional to the optical power by photodetector module 6, thus realizing the electrical conversion of optical displacement information. Figure 3As shown, this invention designs a complete signal acquisition and processing chain in the electronic system to ensure high-precision detection of weak interference signals. The photocurrent signal output by the photodetector module 6 first enters the transimpedance amplifier 7, which performs current-to-voltage conversion and amplifies the weak photocurrent signal into a detectable voltage signal through high-gain amplification. The transimpedance amplifier design ensures a wide bandwidth and low noise characteristics, thereby effectively suppressing external interference while maintaining signal fidelity. Subsequently, the voltage signal is filtered by the fifth-order active Butterworth low-pass filter module 8. This filter module is designed with a cutoff frequency based on signal characteristics, which can effectively suppress high-frequency noise and ripple from the power supply and environment, significantly improving the signal-to-noise ratio and creating favorable conditions for subsequent high-precision analog-to-digital conversion. The filtered voltage signal, carrying displacement information, enters the 16-bit high-precision analog-to-digital converter (ADC) module 9 to realize the conversion from analog signal to digital signal. The converted digital signal is transmitted to the microcontroller 10, which preprocesses the acquired data, including preliminary noise suppression and data buffering. Subsequently, the preprocessed digital signal is transmitted to the host computer 13 via serial port. The positive and negative dual DC power supply modules provide stable, low-noise bipolar voltages for the transimpedance amplifier 7 and the fifth-order active Butterworth low-pass filter module 8, and configure independent decoupling capacitors for each unit circuit, ensuring the linear operating characteristics of the operational amplifiers across the entire dynamic range. This also effectively reduces the impact of power supply ripple on the signal, thereby improving the overall measurement accuracy and stability of the system. In the host computer signal processing stage, this invention proposes and implements a signal processing method based on a combination of band-limited dynamic noise-adding CEEMDAN and prior-constrained linear least-squares sine fitting to achieve high-precision phase extraction and micro-displacement calculation. First, addressing the background noise and mode aliasing problems in the interferometric signal, the host computer runs the band-limited dynamic noise-adding CEEMDAN algorithm to decompose the original interferometric signal into several intrinsic mode functions (IMFs) and residual trend terms. Unlike the traditional CEEMDAN method, this approach strictly constrains the noise spectrum range during noise injection using a band-limited filter to prevent noise interference with low-frequency trend components. Simultaneously, it adaptively adjusts the noise amplitude in each iteration based on the residual standard deviation and frequency band energy distribution, achieving dynamic matching between noise intensity and signal characteristics. This not only ensures the stability and robustness of the decomposition but also effectively extracts the low-frequency trend signal representing displacement information. After obtaining the trend components, a priori-based linear least squares sine fitting algorithm is used to model the signal. Since the interference signal can be represented as a frequency-estimated sine function, and its phase change is linearly related to the measured displacement, introducing prior constraints such as the light source wavelength and sampling frequency to construct the fitting equation can significantly improve the fitting accuracy and convergence speed.Ultimately, the fitted sinusoidal model can accurately reflect the true trend of the interference signal. Based on this, the system extracts the phase change and realizes the analysis of micro-displacement through the physical conversion relationship between phase and displacement.

[0019] like Figure 4 As shown, the present invention relates to a Michelson interferometric micro-displacement measurement method and apparatus based on mode decomposition and phase regression. The signal processing flow during displacement measurement is as follows: S1: Construct an optical system based on the Michelson interferometer structure, with the measuring mirror rigidly connected to the displaced object, to measure the displacement. Converted into the change in optical path difference between the two arms Displacement As the interference spot continues to increase, the local spot at the center of the interference spot will exhibit a regular alternation of brightness and darkness; S2: Adjust the optical path so that the local light spot at the center of the interference spot falls on the photosensitive surface of the photoelectric detection module, and collect the local optical power at the center of the interference spot through the photoelectric detection module. , to increase optical power Converted into photocurrent carrying displacement information ; In the formula The output power of the laser. This refers to the responsivity of the photoelectric detection module.

[0020] S3: The weak current signal is amplified by the transimpedance amplifier 7 and converted into a voltage signal that varies sinusoidally with the increase of displacement. ; in The amplitude of the interference signal; For bias; The noise is superimposed, including high-frequency power supply ripple, mechanical micro-vibration interference, etc. S4: Suppress voltage signals using a fifth-order active Butterworth low-pass filter module 8. The high-frequency power supply ripple superimposed in the middle improves the signal-to-noise ratio; S5: Original interference voltage signal The analog-to-digital converter module 9 converts the signal into a digital value and sends it to the microcontroller. The sampling frequency is... kSPS. After preprocessing the digital signal, the microcontroller 10 sends a data frame containing a frame header, a data length field, and a CRC check field to the host computer 13 via a serial port; S6: The CEEMDAN algorithm based on band-limited dynamic noise is used in the host computer to process the digital signal and obtain the denoised trend signal. The process of obtaining the trend of the interference signal using the band-limited dynamic noise-adding CEEMDAN algorithm proposed in this invention is as follows: First, band-limited noise is generated: white noise with a mean of zero and a standard deviation of 1. Bandpass filtering is applied to limit the frequency range; In the formula As a bandpass filter, it can adaptively adjust according to signal characteristics to ensure that the noise energy is mainly injected into the high-frequency band, which helps to strip away high-frequency interference without disrupting the low-frequency trend.

[0021] In the formula This is the lower limit of band-limited noise; This represents the upper limit of the band-limited noise. To keep the added noise energy away from the low-frequency region where the trend signal is located, the lower limit of the band-limited noise is taken. for: In the formula The upper limit of noise in the main frequency band of the interference fringes Subject to system sampling rate and Nyquist sampling rate limit: The formula for adjusting the dynamic noise amplitude is as follows: Calculate the standard deviation of the current residuals: Calculate the energy percentage of the residual in the noise-added frequency band and assess the relative intensity of the residual noise: in For residuals Fourier transform, The system sampling rate is set. A dynamic noise factor is defined to ensure that the noise level is increased when the residual noise energy percentage is low. in The base noise addition ratio typically ranges from 0.1 to 0.3. This is an adjustment coefficient, defaulting to 0.3~0.7, and needs to be selected based on the signal SNR, residual amplitude scale, and iterative stability. Therefore, the noise addition amplitude value is: For voltage signals Add noise to the k-th layer: Perform EMD to obtain the IMF. The k-th layer IMF is the average of multiple noisy decompositions. The number of noisy decompositions is 300, which can be increased as needed to improve stability, but the computational cost will also increase. Then update the residual as follows: The iteration count is set to 40, and the iterations are repeated until the termination condition is met, ultimately yielding: Finally, the high-frequency noise is stripped down to the first few layers of the IMF, and the last layer of the IMF becomes the final residual signal. The pure low-frequency trend is preserved, and the trend signal is: S7: Sliding window detects the trend change of the interference signal, locates and extracts the signal data segment carrying displacement information; S8: After denoising and trend extraction using the band-limited dynamic noise-adding CEEMDAN algorithm, a pure sinusoidal trend signal with a high signal-to-noise ratio can be obtained. The denoised trend signal is fitted using the linear least squares method, and the interferometric signal model is reconstructed based on the signal features as follows: S9: Order , , Given sample values Construct the matrix: S10: The interference signal of the displacement data segment is fitted using the prior linear least squares method, and the fitting parameters are solved: S11: Calculate the phase distribution of the interference signal using the fitting results. and displacement change .

[0022] Example 1: This example is an experimental case. At the beginning of the experiment, the Michelson interference optical path must be precisely constructed. The laser (1) emits a helium-neon laser with a wavelength of 632.8 nm, which is collimated by the convex lens (2) and then incident on the beam splitter prism (4). The beam splitter prism splits the beam into two paths: one path is directed towards the fixed reference mirror (5), and the other path is directed towards the measuring mirror (3) mounted on the piezoelectric displacement stage. The optical path is adjusted to ensure that the two beams are strictly coaxial and form clear interference fringes on the target surface of the photodetector (6). To achieve high-sensitivity measurement, the optical path needs to be finely adjusted so that the center of the interference spot falls on the center of the sensitive area of ​​the photodetector, such as Figure 6 As shown in the dashed box, this area has the highest stripe contrast and is most sensitive to displacement changes.

[0023] The measured displacement was 300 nm, and the laser wavelength was... =632.8 nm, the specific measurement process is as follows: Building such Figure 1 In the measurement system shown, mirror 3 is fixed on a high-precision displacement stage. As the stage moves 300 nm along the optical axis, the optical path difference changes by 600 nm due to the two-way effect in the Michelson interference structure. The phase of the interference field changes accordingly, causing a periodic change in the light intensity at the center of the interference spot. The photodetector converts the light intensity signal into a photocurrent. This current is converted into a voltage signal by a transimpedance amplifier (gain of 10000 V / A), and then suppressed for high-frequency noise by a fifth-order Butterworth low-pass filter (cutoff frequency of 3.6 kHz). The analog-to-digital converter digitizes the signal at a sampling rate of 200 kSPS and uploads it to the host computer via a microcontroller.

[0024] The change in optical path difference causes significant modulation of the interference signal, resulting in a periodic fringe evolution in the interference spot. Particularly in the central region of the interference spot, the local interference fringes exhibit clear alternations of bright and dark areas, as shown in the diagram. Figure 6 As shown within the dashed box, the periodic change in phase due to displacement is accurately reflected. During signal detection, the photoelectric detection module 6 collects the local optical power at the center of the interference spot in real time and converts it into photocurrent. The photocurrent signal undergoes current-to-voltage conversion and amplification by the transimpedance amplifier 7 to obtain the interference voltage signal carrying displacement information. As the displacement stage moves, the output voltage signal exhibits an approximately sinusoidal trend, such as... Figure 7As shown, the phase and amplitude of the voltage waveform both carry precise information corresponding to the target displacement. The voltage signal is processed by a fifth-order active Butterworth low-pass filter module 8, then sampled and digitized by a 16-bit ADC module 9 at a sampling rate of 200 kSPS. The digital signal is then uploaded to a host computer in real time via a microcontroller. In the host computer, the digital signal is processed using the band-limited dynamic noise-adding CEEMDAN algorithm to extract the signal trend of the displacement data. First, the original interference voltage signal after sampling and digitization... The input algorithm framework involves superimposing limited-band Gaussian white noise onto the signal during the decomposition process. The noise disturbance signal is obtained: The noise frequency band is taken from the dominant frequency of the interference signal. 90% to 110% of the noise energy is injected into the high-frequency band, thus ensuring that the decomposition process occurs within the frequency band corresponding to the displacement signal. Secondly, for each noise disturbance signal... EMD decomposition yields a series of intrinsic mode functions (IMFs): in For the i-th order IMF, This represents the residual. To avoid excessive noise introduction or insufficient decomposition, the noise addition amplitude is adaptively adjusted based on the residual signal energy during the iteration process. The algorithm is set to a maximum of 40 iterations, with a base noise level of [missing information]. Dynamic adjustment coefficient We set the set size to 1.5 and the number of decomposition iterations (i.e., the number of noisy decomposition iterations) to 300 to ensure decomposition stability and statistical significance. Through the aforementioned adaptive adjustment mechanism, the noise intensity is matched with the high-frequency noise energy in the current residual, effectively suppressing mode mixing while avoiding interference with low-frequency trend components, significantly improving decomposition robustness and trend extraction accuracy. After decomposition, high-frequency noise is stripped to the first few IMF layers, resulting in the final residual signal. Retaining the pure low-frequency trend, the resulting trend signal is: like Figure 5 The figure shows the IMF obtained after processing the interferometric electrical signal using the band-limited dynamic noise-adding CEEMDAN algorithm. IMF0~IMF10 represent the high-frequency noise doped into the signal, and IMF11 represents the desired clean low-frequency trend. By detecting trend signals through a sliding window and locating displacement data segments, the interference signal model is reconstructed based on the signal characteristics as follows: Then, the displacement data is fitted based on the prior linear least squares method to analyze the phase distribution of the displacement data. Finally, the relationship between the phase change and the displacement of the Michelson interferometer structure is used. The calculated displacement was 297.61 nm, with an error of only 2.39 nm, which verifies the high accuracy of the method in nanoscale measurement, and the error is within a reasonable range.

[0025] Example 2: In this example, the calibration method of the measurement method designed in this invention will be explained and elaborated in detail.

[0026] like Figure 6 As shown, during the displacement process, the local spot at the center of the interference spot will exhibit obvious periodic changes in brightness. This change originates from the interference phase fluctuation caused by the change in optical path difference. When the local spot changes from bright to dark or from dark to bright, it means that the phase of the interference signal has changed. The transition. According to the Michelson interference structure, the corresponding change in optical path difference is... The actual displacement of the object is... Therefore, each local bright-dark reversal can serve as a precise displacement reference unit. By accurately identifying the peaks and valleys of the interference electrical signal, the [missing information] can be calibrated. The displacement reference element.

[0027] In actual interferometric signal acquisition, this phenomenon manifests as peak-valley transitions in the interferometric signal: when the light spot changes from bright to dark, the acquired signal transitions from a peak value to a valley value; conversely, when the light spot changes from dark to bright, the signal transitions from a valley value to a peak value. By identifying and extracting the signal segment between adjacent peaks and valleys, a peak value can be accurately calibrated. The displacement. Based on this, the system can accumulate and track multiple displacements one by one during the displacement process. The proposed method utilizes the inherent periodicity of interference fringes as a natural scale, and significantly improves anti-interference capability and resolution through peak-valley identification, ensuring that the measurement system maintains stable and reliable displacement calibration performance even in complex environments.

[0028] To improve calibration accuracy, the signal needs to be denoised using the band-limited dynamic noise-adding CEEMDAN algorithm to accurately extract the location of extreme points. Furthermore, the system utilizes linear least squares fitting to model the trend signal, further reducing the error in extreme point identification caused by noise.

[0029] This method is particularly suitable for long-term displacement monitoring or large-scale displacement measurement because it utilizes the inherent periodicity of interference fringes as a scale, eliminating the need for external references and avoiding accumulated errors. In precision machining and semiconductor manufacturing, it can be used to continuously track multiple... The displacement unit enables high-precision calibration of micrometer-level displacement. Furthermore, this method exhibits robustness to light source fluctuations and environmental vibrations because the calibration is based on relative phase changes rather than absolute light intensity.

[0030] Example 3: Micro-displacement measurement in a high-noise environment The robustness and measurement accuracy of the method and apparatus described in this invention under strong noise interference conditions were verified. The experimental environment simulated a precision machining workshop, where significant mechanical vibration and electromagnetic interference were present.

[0031] (1) Experimental conditions Displacement: 500 nm; Laser wavelength: λ = 632.8 nm; Noise environment: An additional 1 kHz sinusoidal wave with an amplitude of approximately 30% of the signal amplitude was introduced to simulate mechanical vibration interference, and broadband white noise was superimposed, reducing the original signal-to-noise ratio (SNR) to approximately 5 dB.

[0032] The optical structure of the measurement system is the same as that in Example 1.

[0033] (2) Measurement process and signal processing The measuring mirror is fixed to a controlled vibration table, and the target displacement and simulated vibration disturbance are applied simultaneously. The interferometric electrical signal output by the photoelectric detection module will contain strong background noise.

[0034] As attached Figure 6 As shown, despite strong interference, a faint trend of brightness variation can still be observed in the local spot at the center of the interference spot. After preliminary preprocessing by transimpedance amplification and fifth-order active Butterworth low-pass filtering (cutoff frequency 3.6kHz, stopband attenuation ≥60dB), the signal is sampled by the ADC module and uploaded to the host computer.

[0035] (3) Application of core algorithms In the host computer, the band-limited dynamic noise-adding CEEMDAN algorithm is used to decompose the strong noise signal. The algorithm parameters are adaptively adjusted for this strong noise scenario. Band-limited noise band is based on the dominant frequency of the interferometric signal and system sampling rate Adaptive adjustment ensures that the noise-injected signal is only injected into the interfering frequency band.

[0036] Base noise ratio Set to 0.2, adjustment coefficient Set to 0.5 to enhance decomposition performance under high noise conditions.

[0037] The number of set iterations was increased to 400 to improve statistical stability.

[0038] After the algorithm is executed, high-frequency noise and specific interference are effectively separated into the first few layers of IMF (such as IMF0~IMF10).

[0039] As attached Figure 5 As shown in IMF11, the final residual Trend signals It clearly presents the sinusoidal variation trend extracted by the algorithm.

[0040] (4) Phase regression and displacement calculation For the extracted trend signals A priori-based linear least squares method was used for fitting. The constructed fitting model and solution process are the same as described in the patent text. The phase change was calculated by back-calculating the fitting parameters. And finally according to the formula Calculate the displacement.

[0041] (5) Results and Analysis The final displacement, calculated by the measurement system, was 498.3 nm, with a relative error of 0.34% compared to the set value of 500 nm. This embodiment demonstrates that even under harsh conditions of strong noise and low signal-to-noise ratio, this invention effectively removes noise through the band-limited dynamic noise-adding CEEMDAN algorithm and combines it with a robust phase regression algorithm, still achieving nanometer-level precision micro-displacement measurement, exhibiting excellent anti-interference capability and environmental adaptability.

[0042] Example 4: Precise calibration and measurement of sub-nanometer micro-displacements It demonstrates calibration methods and precise measurement capabilities for measuring extremely small displacements (sub-nanometer scale), suitable for scenarios requiring extremely high displacement resolution, such as semiconductor device characterization or material surface morphology measurement.

[0043] (1) Experimental conditions Displacement: 0.8 nm (sub-nanometer level) Laser wavelength: = 532 nm (using a green laser to achieve higher optical resolution) System calibration: Internal calibration is performed using the inherent periodicity of interference fringes. The specific method is as described in the patent document (corresponding to claim 8 and embodiment two of the specification): by identifying the signal segment between adjacent peaks and valleys of the interference electrical signal, corresponding... Displacement reference (for) = 532 nm, with a reference displacement of 133 nm). The system first applies a known, greater than The displacement (e.g., 300 nm) is recorded, and the complete peak-valley-peak change cycle is recorded, thereby accurately calibrating the phase change gradient corresponding to each sampling point, laying the foundation for accurate inversion of sub-nanometer displacement.

[0044] (2) Measurement process After calibration, a target displacement of 0.8 nm is applied. Since the displacement is much smaller than one interference fringe period ( (2 = 266 nm), the collected interference signal is only a very short and weakly changing segment on the complete sine curve, and the traditional fringe counting method or simple threshold method is completely ineffective.

[0045] (3) Signal processing and trend extraction The voltage signal obtained from the ADC sampling exhibits extremely weak changes. The host computer uses the band-limited dynamic noise-adding CEEMDAN algorithm for processing. In this case, the algorithm parameter settings focus on the precise extraction of subtle trends: The band-limited noise bandwidth is narrow and concentrated at the main signal frequency. To achieve 95% to 105%, avoid introducing unnecessary frequency band interference.

[0046] Base noise ratio Set to 0.15, adjustment coefficient Setting it to 0.35 employs a gentler noise-adding strategy to avoid masking subtle trends.

[0047] Through adaptive decomposition using an algorithm, baseline drift and extremely low-frequency noise in the signal are separated, extracting a pure trend signal that reflects the minute phase change caused by a 0.8 nm displacement. .

[0048] (4) High-precision phase fitting and displacement calculation For the extracted minute trend segments, linear least squares sine fitting is used. Due to the extremely small displacement, the frequencies of the cosine and sine basis functions required for fitting are... This can be considered known (determined during the system calibration phase), making the fitting process very stable. The initial phase corresponding to this small data segment is calculated by solving for the fitting parameters a, b, and c. and termination phase Its phase difference Although small, it can be calculated precisely. Final displacement. .

[0049] (5) Results and Advantages The calculated displacement was 0.82 nm. This embodiment demonstrates that the method of the present invention is not only applicable to displacement measurements of hundreds of nanometers, but also, through precise internal calibration and advanced signal processing techniques, can effectively resolve sub-nanometer level micro-displacements. Its advantages are: Using inherent periodic calibration: No external high-precision calibration equipment is required, reducing system complexity and cost.

[0050] Processing non-complete periodic signals: Overcomes the dependence of traditional methods on complete signal periods.

[0051] High resolution: Sub-nanometer resolution is achieved by combining the trend extraction of CEEMDAN with the mathematical precision of least squares fitting.

[0052] In summary, the supplementary embodiments three and four further enrich the content of this patent from the two dimensions of anti-interference capability and extremely high resolution measurement, respectively, and verify the effectiveness, robustness and high precision of the method and device in different application scenarios.

[0053] The specific embodiments described above further illustrate the purpose, technical solution, and beneficial effects of the present invention. It should be understood that the above description is only a specific embodiment of the present invention and is not intended to limit the scope of protection of the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A Michelson interferometric micro-displacement measurement method based on mode decomposition and phase regression, characterized in that, include: The optical system, including a laser, a beam-shrinking lens, a beam-splitting prism, a measuring mirror, and a reference mirror, is used to convert the measured displacement into a change in the interference spot. Electronic systems, including: The photoelectric detection module converts the local intensity changes of the interference spot into an interference electrical signal carrying displacement information; A transimpedance amplifier, whose input is connected to the output of a photodetector module, converts the photocurrent signal into a voltage signal; A fifth-order active Butterworth low-pass filter module, whose input is connected to the output of the transimpedance amplifier, is used to suppress high-frequency noise; A dual positive and negative DC power supply module powers the transimpedance amplifier and the fifth-order active Butterworth low-pass filter module; The analog-to-digital conversion module, specifically the ADC module, has its input connected to the output of the low-pass filter module, converting the voltage signal into a digital signal. The microcontroller reads the digital signal output by the analog-to-digital converter module and sends the preprocessed digital signal to the host computer via the serial port. The host computer is used to receive digital signals and execute adaptive mode decomposition and sinusoidal phase regression algorithms based on band-limited dynamic noise addition to extract signal trends and calculate displacement.

2. A Michelson interferometric micro-displacement measurement method based on mode decomposition and phase regression, characterized in that, Includes the following steps: S1: Construct a Michelson interference structure to convert displacement into changes in the interference spot; S2: Detect the local optical power at the center of the light spot using a photoelectric detection module. It is then converted into a photocurrent that varies sinusoidally. ; S3: Convert and amplify the photocurrent via a transimpedance amplifier. voltage signal ; S4: Use a fifth-order active Butterworth low-pass filter module to suppress high-frequency noise, convert the filtered voltage signal from analog to digital to a digital signal, and transmit it to the host computer after preprocessing by a microcontroller. S5: Execute the CEEMDAN trend extraction algorithm with band-limited dynamic noise addition in the host computer to obtain the trend of the interference signal; S6: Fit the trend signal based on the linear least squares method, analyze the phase distribution and calculate the displacement.

3. The Michelson interferometric micro-displacement measurement method based on mode decomposition and phase regression as described in claim 1, characterized in that, The transimpedance amplifier employs a low-noise operational amplifier. The inverting input is connected to the output of the photodetector module via an input resistor, while the non-inverting input is grounded. A feedback resistor and a feedback capacitor are connected in parallel between the inverting input and the output to form a transimpedance amplification network. The output is directly connected to the input of a fifth-order active Butterworth low-pass filter module via a RC buffer network consisting of a series current-limiting resistor and a parallel decoupling capacitor. The transimpedance gain is 10000V / A, and the noise voltage density is less than 20nV / √Hz.

4. The Michelson interferometric micro-displacement measurement method based on mode decomposition and phase regression as described in claim 1, characterized in that, The fifth-order active Butterworth low-pass filter module consists of a first-order third-order active filter circuit and a first-order second-order active filter circuit connected in series. The input of the first stage is connected to the RC buffer network at the output of the transimpedance amplifier module, and the output of the second stage is connected to the analog input of the analog-to-digital converter module. The two filter modules are equipped with local decoupling capacitors and share a common regulated power supply. The overall cutoff frequency is 3.6kHz, and the stopband attenuation is not less than 60dB.

5. The Michelson interferometric micro-displacement measurement method based on mode decomposition and phase regression as described in claim 1, characterized in that, The analog-to-digital conversion module has a resolution of 16 bits and a sampling rate of 200kSPS. Its analog input terminal is connected in parallel with an anti-aliasing capacitor, and its digital interface is connected to the microcontroller module via an SPI bus.

6. The Michelson interferometric micro-displacement measurement method based on mode decomposition and phase regression as described in claim 1, characterized in that, The microcontroller is a microcontroller with a hardware SPI interface and a USB OTG interface. Its SPI interface is connected to the digital interface of the analog-to-digital converter module, and its USB OTG interface is connected to the host computer communication module. It sends data frames containing a frame header, a data length field, and a CRC check field to the host computer via a serial port. The microcontroller's external clock signal is used as the sampling clock input for the analog-to-digital converter module to achieve synchronous sampling and real-time processing. The microcontroller and the analog-to-digital converter module share a low-noise regulated power supply and decoupling capacitors are configured at each power supply pin.

7. The Michelson interferometric micro-displacement measurement method based on mode decomposition and phase regression as described in claim 2, characterized in that, Step two involves acquiring the local optical power of the interference spot using a photodetector. The optical power Converted into photocurrent The photocurrent The voltage signal, which varies sinusoidally with increasing displacement, is obtained after transimpedance amplification and low-pass filtering. in The amplitude of the interference signal; For bias; This is superimposed noise, including high-frequency power supply ripple, mechanical micro-vibration interference, etc.

8. The Michelson interferometric micro-displacement measurement method based on mode decomposition and phase regression as described in claim 2, characterized in that, Step six involves signal processing of the trend signal to identify signal segments with adjacent peaks and troughs, and the corresponding phase change of the interference signal. Combined with laser wavelength calculate The displacement reference value is used for system calibration.

9. The Michelson interferometric micro-displacement measurement method based on mode decomposition and phase regression as described in claim 2, characterized in that, The band-limited dynamic noise-adding CEEMDAN algorithm replaces the original white noise with band-limited noise whose amplitude can be dynamically adjusted in the traditional CEEMDAN noise-adding step, so as to adapt to the energy characteristics of the signal at different decomposition stages.

10. The Michelson interferometric micro-displacement measurement method based on mode decomposition and phase regression as described in claim 2, characterized in that, The band-limited noise generated by the CEEMDAN algorithm described above is: in This is the lower limit of band-limited noise; This represents the upper limit of the band-limited noise. To keep the added noise energy away from the low-frequency region where the trend signal is located, the lower limit of the band-limited noise is taken. for: in The upper limit of noise in the main frequency band of the interference fringes Subject to system sampling rate and Nyquist sampling rate limit: in As a bandpass filter, it can adaptively adjust according to signal characteristics to ensure that noise energy is injected only into the high-frequency band, which helps to strip high-frequency noise without disrupting the low-frequency trend.

11. The Michelson interferometric micro-displacement measurement method based on mode decomposition and phase regression as described in claim 2, characterized in that, The band-limited dynamic noise addition algorithm described herein dynamically adjusts the noise amplitude based on the standard deviation of the residuals and the energy proportion. The steps for calculating the noise addition amplitude are as follows: S1: Calculate the standard deviation of the current residual: S2: Calculate the energy proportion of the residual in the noise band: in For residuals Fourier transform; For system sampling rate S3: Set the dynamic noise factor: in The base noise addition ratio; This is the adjustment coefficient. Therefore, the noise amplitude value is: 。 12. The Michelson interferometric micro-displacement measurement method based on mode decomposition and phase regression as described in claim 2, characterized in that, The band-limited dynamic noise-adding CEEMDAN algorithm decomposes the signal, selecting low-frequency components as the trend signal and the remaining components as noise suppression targets. The noise decomposition process of the band-limited dynamic noise-adding CEEMDAN algorithm is as follows: S1: Add noise to the k-th layer: S2: Perform EMD to obtain the IMF. The IMF of the k-th layer is the average of multiple noisy decompositions. Then update the residuals: S3: Repeat the iteration until the termination condition is met. ), ultimately obtained: S4: Finally, the high-frequency noise is stripped to the first few layers of IMF, and the residual signal... The pure low-frequency trend is preserved, and the trend signal is: 。 13. The Michelson interferometric micro-displacement measurement method based on mode decomposition and phase regression as described in claim 2, characterized in that, The phase regression algorithm uses a priori-based linear least squares method to analyze the denoised trend signal. Perform fitting to construct trend signals The model is: make , , Given sample values Construct the matrix: The interference signal of the displacement data segment is fitted using the prior linear least squares method, and the fitting parameters are solved: 。

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