Laser self-mixing interference feedback factor estimation and displacement reconstruction method and system

Abstract

The invention discloses a laser self-mixing interference feedback factor estimation and displacement reconstruction method and system, and the method comprises the following steps: obtaining a laser self-mixing interference time domain signal, recognizing peak and valley points in the time domain signal based on a dual-threshold screening mechanism, and dividing a fringe interval; calculating the average energy difference between two adjacent stripe intervals to judge the inclination direction of the stripe; calculating the average value of the original signal values of all the sampling points as an energy characteristic quantity in the stripe interval determined to be in the specific inclination direction; calling a mapping relation between the energy characteristic quantity and a feedback factor, substituting the energy characteristic quantity into the mapping relation, and interpolating and estimating a current optical feedback factor; and introducing the estimated optical feedback factor into a phase unwrapping algorithm, correcting and unwrapping the phase, and reconstructing to obtain a displacement signal of the target object. The method has the advantages of being low in overall processing flow calculation amount, high in operation speed and high in anti-noise performance.

Description

Technical Field

[0001] This invention belongs to the field of optical measurement technology, and specifically relates to a method and system for estimating laser self-mixing interferometry feedback factors and reconstructing displacement. Background Technology

[0002] Self-Mixing Interferometry (SMI) utilizes the coherent superposition of reflected or scattered light from the target surface with the cavity field to obtain an intensity-modulated signal related to the measured motion in a single-channel structure. Compared to traditional interferometry systems, SMI requires no external reference arm or beam splitter, and features compact structure, low cost, self-alignment, and easy integration, thus gaining attention in scenarios such as micro-displacement, vibration, velocity, and angle measurement.

[0003] In the classical self-mixing model, the optical feedback factor C and the linewidth broadening factor α affect morphological characteristics such as fringe symmetry, phase jump, and amplitude distribution. In practical applications, if C cannot be accurately obtained or is approximated as a constant, it can easily lead to phase unwrapping failure and amplification of proportionality error, thus affecting the accuracy and robustness of displacement reconstruction. Existing displacement reconstruction methods mainly include fringe counting, phase unwrapping methods, and orthogonal phase demodulation methods. These methods have their own advantages and disadvantages in different applications, but in practical applications, they all generally rely on the accurate estimation of the optical feedback factor C. The accuracy of C is crucial to the accuracy and robustness of displacement reconstruction, but existing methods often cannot obtain this parameter efficiently and accurately in complex or low signal-to-noise ratio environments.

[0004] Regarding the estimation of C, Chinese invention patent application CN108760236A discloses a method for measuring the linewidth broadening factor α of a laser and the feedback factor C in a laser feedback system, which is based on the three-mirror cavity theory and L... Based on the K-rate equation theory, a self-mixing system containing feedback is established for measurement. The self-mixing system includes a laser, an optical attenuator, a vibrating target, a beam splitter, a photodetector, and an oscilloscope. The laser emitted from the laser is incident on the vibrating surface of the vibrating target through the optical attenuator. After being reflected by the vibrating target, it is fed back into the laser resonant cavity along the original path, forming a self-mixing signal. The beam splitter splits the self-mixing signal onto the photodetector, which converts the self-mixing signal into an electrical signal and outputs it to the oscilloscope. By analyzing the self-mixing signal, the correspondence between the parameters SR,F and the laser linewidth broadening factor α and the feedback factor C is obtained. Based on this correspondence, the measurement of the laser linewidth broadening factor α and the feedback factor C in the laser feedback system is realized.

[0005] Chinese invention patent application CN118089532A discloses a method for real-time calculation of the optical feedback intensity factor of a laser self-mixing interferometry system. The method involves extracting the time-frequency ridge line from the self-mixing interferometry signal under arbitrary feedback intensity and locating the peak value of the time-frequency ridge line; determining the time node ti when the phase of the interference without optical feedback is equal to 0 based on the peak value; performing phase deconvolution on the signal to obtain the optical feedback interferometry phase; locating the phase value at time node ti based on the optical feedback interferometry phase; and solving for the optical feedback intensity factor based on the phase value.

[0006] The aforementioned solutions suffer from complex hardware structures, high alignment and calibration costs, and are not conducive to miniaturization and single-channel integration; or they are sensitive to ridge lines and positioning quality under low signal-to-noise ratio, speckle ripple, or strong non-stationary conditions, while also incurring heavy time-frequency computational burdens. Achieving rapid and robust estimation of C using only a single SMI signal under medium-strong feedback and non-stationary interference conditions, without introducing complex optical paths, and linking this with phase unwrapping and orientation determination to complete high-precision displacement reconstruction, remains an urgent need in engineering applications. Summary of the Invention

[0007] This invention provides a method and system for estimating the feedback factor and reconstructing displacement in laser self-mixing interferometry. It replaces single-point features with energy statistics, robustly identifies fringes and flip regions using a dual-threshold approach of amplitude and spacing, and achieves online estimation of C using an offline-calibrated energy-C polynomial mapping. Finally, displacement reconstruction is completed within a feedback-corrected PUM framework. This invention aims to address the problems of complex hardware structures, high costs, and heavy computational burdens inherent in existing technologies.

[0008] To address the aforementioned technical problems, in a first aspect, this invention proposes a method for estimating the laser self-mixing interferometry feedback factor and reconstructing displacement, comprising the following steps: The time-domain signal of laser self-mixing interference is acquired, and the peak and valley points in the time-domain signal are identified based on a dual threshold screening mechanism consisting of amplitude threshold and spacing threshold, forming a fringe sequence and dividing the fringe intervals. Calculate the average energy difference between two adjacent stripe intervals, and determine the tilt direction of the stripes based on the average energy difference; Within the stripe interval determined to be in a specific tilt direction, the average value of the original signal values ​​of all sampling points within the corresponding stripe interval is calculated as the energy feature quantity. The mapping relationship between energy characteristics and feedback factors, which was pre-constructed through offline calibration, is invoked. The energy characteristics are substituted into the mapping relationship, and the current optical feedback factor is estimated by interpolation. The estimated optical feedback factor is introduced into the phase unwrapping algorithm to correct and unwrap the phase, and the displacement signal of the target object is reconstructed.

[0009] Preferably, the method for identifying peaks and valleys in the time-domain signal is as follows: The amplitude difference between candidate peaks and valleys in the statistical time-domain signal is calculated, and the mean or moving average of the amplitude difference is calculated. An amplitude threshold is set based on the mean or moving average of the amplitude difference. The distance between valid peaks and valleys of the same type in the statistical time-domain signal is calculated, and the mean or moving average of the distance is calculated. A distance threshold is set based on the mean or moving average of the distance. Candidate peak and valley points are filtered using the amplitude threshold. When the amplitude difference between a candidate peak / valley value and its adjacent points is greater than the amplitude threshold, the point is determined to be a true peak / valley point. The identified real peaks and valleys are divided using the spacing threshold. When the spacing between adjacent real peaks and valleys of the same type exceeds the spacing threshold, it is determined that the two points form a flipped interval, and the stripes between two adjacent flipped intervals are taken as stripe intervals.

[0010] Preferably, the method for determining the tilt direction of the stripes is as follows: Calculate the difference between the average energy of the next fringe interval and the average energy of the previous fringe interval; If the average energy difference is greater than zero, the next stripe interval is determined to be a right-leaning stripe; if the average energy difference is less than zero, the next stripe interval is determined to be a left-leaning stripe.

[0011] Preferably, the method for calculating the energy characteristic quantity is as follows:

[0012] In the formula, Represents energy characteristic quantity, Let N be the signal amplitude at the i-th sampling point within the right-sloping stripe region, and N be the number of sampling points in the corresponding stripe region.

[0013] Preferably, the mapping relationship is constructed using polynomial fitting; the method for estimating the optical feedback factor is as follows: input the energy characteristic quantity into a preset third-order polynomial equation, and calculate the corresponding optical feedback factor value.

[0014] Preferably, the method for constructing the mapping relationship is as follows: Set the range of optical feedback factor variation, and generate multiple self-mixing interference sample signal sets corresponding to different optical feedback factors within the range of variation; The sample signal set is processed by a dual threshold screening mechanism to identify the real peak and valley points and divide the stripe intervals. Calculate the average energy difference between two adjacent stripe intervals, and identify and extract the right-sloping stripe intervals in the sample signal set based on the average energy difference; Calculate the energy characteristics of the right-sloping fringe interval and establish a sample library consisting of multiple energy characteristic-light feedback factor data pairs; The data in the sample library are fitted with a third-order polynomial to obtain the coefficients of the third-order polynomial equation, and the mapping relationship between energy characteristics and feedback factors is established.

[0015] Preferably, the displacement signal is calculated as follows:

[0016] In the formula, Indicates the displacement of the target object. The wavelength of the laser. The phase signal after unwrapping is given, and C is the optical feedback factor. This is the linewidth broadening factor.

[0017] Secondly, the present invention also proposes a laser self-mixing interferometry feedback factor estimation and displacement reconstruction system, said system being used to implement the feedback factor estimation and displacement reconstruction method as described in the first aspect of the present invention, comprising: The signal acquisition module is used to acquire the time-domain signal of the laser self-mixing interference. The stripe recognition module is used to construct a dual-threshold screening mechanism consisting of an amplitude threshold and a spacing threshold, and to identify peak and valley points in the time-domain signal based on the dual-threshold screening mechanism, forming a stripe sequence and dividing the stripe intervals. The energy analysis module is used to calculate the average energy difference between two adjacent stripe intervals, determine the tilt direction of the stripes based on the average energy difference, and calculate the average value of the original signal values ​​of all sampling points in the stripe interval determined to be in a specific tilt direction as the energy feature quantity. The feedback estimation module is used to store the mapping relationship between energy characteristics and feedback factors that has been pre-constructed through offline calibration, and to substitute the energy characteristics output by the energy analysis module into the mapping relationship to interpolate and estimate the current optical feedback factor. The phase reconstruction module receives the estimated optical feedback factor and introduces a phase unwrapping algorithm to correct and unwrap the phase, thereby reconstructing the displacement signal of the target object.

[0018] Thirdly, the present invention provides an electronic device comprising: One or more processors; Memory, used to store one or more computer programs; One or more computer programs stored in the memory are executed by the one or more processors, causing the one or more processors to implement the feedback factor estimation and displacement reconstruction method as described in the first aspect of the invention.

[0019] Fourthly, the present invention provides a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the feedback factor estimation and displacement reconstruction method as described in the first aspect of the present invention.

[0020] Compared with the prior art, the present invention has the following technical effects: 1. The feedback factor estimation and displacement reconstruction method proposed in this invention, without introducing complex optical paths, utilizes only a single-channel SMI signal. Under medium-strong feedback and non-stationary interference conditions, it can accurately determine the fringe tilt direction by calculating the energy difference between adjacent fringe intervals, thereby determining the object's motion direction. Compared to traditional frequency-shifting or orthogonal demodulation methods, it requires no additional optical auxiliary components, maintaining the core advantages of a self-mixing interferometer system—compact structure, low cost, and self-alignment—while achieving rapid estimation of the feedback factor and high-precision displacement reconstruction.

[0021] 2. The feedback factor estimation and displacement reconstruction method proposed in this invention is based on the estimation method of fringe energy characteristics. By calculating the average signal value within the fringe interval in a specific tilt direction as the characteristic value, the statistical characteristics of interval averaging are utilized to effectively offset the influence of random interference such as Gaussian white noise. Combined with a dual-threshold screening mechanism, it can accurately identify the real peaks and valleys and divide the fringes under non-stationary interference and low signal-to-noise ratio environments, significantly improving the robustness and accuracy of feedback factor C estimation under moderate and strong feedback conditions.

[0022] 3. The feedback factor estimation and displacement reconstruction method proposed in this invention adopts an offline calibration and online interpolation strategy. By constructing the mapping relationship between energy characteristics and feedback factors offline and fitting it as a low-order polynomial, the calculation in the online measurement stage only involves simple addition and multiplication operations, without the need for complex time-frequency transformations (such as wavelet transform, EEMD) or solving transcendental equations. This constant-level computational complexity greatly reduces the requirements for hardware computing power, and the fast operation speed makes it very suitable for real-time measurement on embedded microprocessors such as FPGAs and DSPs. Attached Figure Description

[0023] Figure 1 This is a schematic flowchart of the feedback factor estimation and displacement reconstruction method described in this invention; Figure 2 This is a simulation result diagram of the displacement reconstruction of simple harmonic motion according to an embodiment of the present invention; Figure 3 This is a diagram showing the experimental results of simple harmonic motion displacement reconstruction according to an embodiment of the present invention; Figure 4 This is an experimental result diagram of displacement reconstruction for non-simple harmonic motion according to an embodiment of the present invention. Detailed Implementation

[0024] To make the objectives, technical solutions, and advantages of the present invention clearer, the technical solutions of the present invention will be clearly and completely described below in conjunction with specific embodiments of the present application and with reference to the accompanying drawings.

[0025] Example 1 This embodiment presents a method for estimating the feedback factor and reconstructing the displacement of a laser self-mixing interferometry system. Figure 1 As shown, it includes the following steps one through five: Step 1: Obtain the time-domain signal of laser self-mixing interference, identify the peak and valley points in the time-domain signal based on the dual threshold screening mechanism composed of amplitude threshold and spacing threshold, form a fringe sequence and divide the fringe intervals.

[0026] The implementation process of this step includes four stages: signal acquisition, basic model analysis, dual threshold construction, and signal screening and segmentation.

[0027] In the signal acquisition stage, a semiconductor laser is used to emit laser light onto the surface of the target. A photodetector receives the self-mixed interference optical signal carrying the target's motion information and converts it into an electrical signal. After amplification, filtering, and analog-to-digital conversion, a discrete self-mixed interference time-domain signal is obtained.

[0028] The physical model of the self-mixing interferometer system follows the Lang-Kobayashi theory. The power of the time-domain signal... With phase The relationship satisfies:

[0029]

[0030] in, is the output power without feedback, and m is the modulation coefficient; For the phase when there is optical feedback, For a non-feedback phase that is linearly related to the object's motion, C is the optical feedback factor. The linewidth broadening factor is denoted as C. When the optical feedback factor C > 1, the system is in the medium-strong feedback region, and the phase equation exhibits multiple solutions, resulting in an asymmetric shape of the time-domain interference fringes (i.e., sawtooth-shaped, steep on one side and smooth on the other) accompanied by hysteresis jumps. This embodiment utilizes this morphological feature to achieve fringe counting and segmentation by identifying peak and valley values.

[0031] In the dual-threshold construction stage, since actual measurement signals often contain noise, directly searching for extreme points can lead to a large number of misjudgments. This embodiment constructs a dual-threshold screening mechanism consisting of an amplitude threshold and a spacing threshold.

[0032] Amplitude threshold Setting: The amplitude difference between candidate peaks and valleys in the statistical time-domain signal is calculated, the mean or moving average of the amplitude difference is calculated, and the amplitude threshold is set according to the mean or moving average of the amplitude difference. First, all candidate peaks and valleys in the signal are extracted by finding local extrema. The longitudinal amplitude difference (i.e., peak-valley amplitude difference) between adjacent candidate peaks and valleys is calculated. These amplitude differences are statistically analyzed, and their mean or moving average is calculated and denoted as... Set amplitude threshold for:

[0033] in, The first empirical coefficient (e.g., can be taken as) (This is used to eliminate small-amplitude noise disturbances.)

[0034] Spacing threshold Setting: The spacing between valid peaks and valleys of the same type in the statistical time domain signal is calculated, the mean or moving average of the spacing is calculated, and the spacing threshold is set according to the mean or moving average of the spacing. In statistical signals, the time axis interval or difference in the number of sampling points between adjacent valid peaks and troughs of the same type (i.e., between peaks or between troughs) is calculated. The mean or moving average of these valid peak intervals is denoted as... Set the spacing threshold. for:

[0035] in, For the second empirical coefficient (e.g., can be taken as) (This is used to determine the integrity of the stripe period.)

[0036] In the signal screening and segmentation stage, the amplitude threshold is used to screen candidate peak and valley points. When the amplitude difference between a candidate peak and valley value and its adjacent points is greater than the amplitude threshold, the point is determined to be a real peak and valley point. All real peak and valley points are spliced ​​together in time sequence to form a stripe sequence. The identified real peaks and valleys are divided using the aforementioned spacing threshold. When the spacing between adjacent real peaks and valleys of the same type exceeds the spacing threshold, it is determined that the two points constitute a flipped interval, and the stripes between two adjacent flipped intervals are taken as stripe intervals. To explain the stripe intervals described in this embodiment, take a stripe sequence {1,1,1.2,3,1.4,1,1.5,3.2,1.1,1,1} as an example. Each element in the sequence represents the spacing between adjacent real peaks and valleys of the same type. If the spacing threshold is set to 2.5, then the spacings 3 and 3.2 in the sequence exceed the threshold. Therefore, the two points with a spacing of 3 are flipped intervals, and the two points with a spacing of 3.2 are also flipped intervals. Therefore, after removing the spacings that exceed the spacing threshold, the remaining continuous spacing sequence can be divided into three segments: {1,1,1.2}, {1.4,1,1.5}, and {1.1,1,1}. Each of these continuous spacing segments corresponds to a stripe interval.

[0037] Specifically, this stage involves a comprehensive screening of the aforementioned dual-threshold signals, including the identification of true peaks and valleys, and the formation and division of stripe sequences and inversion regions.

[0038] True peak and valley point identification: For each candidate peak and valley point, calculate the amplitude difference between it and the adjacent reverse extreme point. ,like If the candidate point is true, it is determined to be a true peak / valley point; otherwise, it is considered noise and discarded.

[0039] Stripe sequence formation and flip region division: The selected true peaks and valleys are arranged in chronological order to form a stripe sequence. The spacing between adjacent peaks and valleys of the same type (such as two adjacent peaks) is checked. If the distance between two adjacent points Less than or equal to the spacing threshold (i.e. ≤ This indicates that the signal phase change within this interval is continuous and periodic, determining that the region between these two points belongs to a complete fringe region, with each fringe corresponding to a displacement of half a wavelength of the object. Since the flipped interval only represents a change in the direction of motion and does not itself have fringes, the distance between two adjacent points... Greater than the spacing threshold (i.e.) This indicates that the object's motion within the region has reversed direction, and no complete interference fringes have been generated. Therefore, the area between these two points is determined to be a flip region. As an example, the spacing threshold in this embodiment... It can be set to a certain multiple of the average spacing.

[0040] In other embodiments of the present invention, the derivative thresholding method is used to obtain the fringe sequence and divide the fringe intervals. Based on this, the peak-to-valley spacing is also used to distinguish between complete fringe regions and flipped regions. The complete fringe region contains continuous interference fringes, while the flipped region corresponds to the fringe-free transition state at the moment the object's motion direction changes.

[0041] Step 2: Calculate the average energy difference between two adjacent stripe intervals, and determine the tilt direction of the stripes based on the average energy difference.

[0042] After dividing the complete fringe intervals in step one, it is necessary to further determine the tilt direction (leftward or rightward) of these fringes. The tilt direction of the fringes directly corresponds to the direction of motion of the target object relative to the laser (moving away or approaching). In this embodiment, a fast determination method based on the average energy difference between adjacent intervals is adopted, and the specific steps are as follows: S21-S22: S21: Calculation of the average energy of the stripe interval. Calculate the difference between the average energy of the next stripe interval and the average energy of the previous stripe interval.

[0043] Specifically, select two adjacent complete stripe intervals and denote them as the previous interval (the first interval). Each has an average energy of [number] units. ) and the next interval (the first) Each has an average energy of [number] units. ). Calculate the average energy difference between the two. :

[0044] This index reflects the changing trend of the average amplitude of the fringes in the self-mixed interferometric signal over time.

[0045] In this embodiment, the average energy value refers to the arithmetic mean of the original signal amplitudes of all sampling points within the corresponding interval. For each complete fringe interval (denoted as the i-th interval) divided in step one, the average energy value of the signal within that interval is calculated. .

[0046] S22: If the average energy difference is greater than zero, the next stripe interval is determined to be a right-leaning stripe; if the average energy difference is less than zero, the next stripe interval is determined to be a left-leaning stripe.

[0047] Specifically, based on the energy / amplitude variation characteristics of laser self-mixing interference signals under different motion directions, the following judgment logic is established: Right-leaning stripe determination ( When the average energy of the later fringe interval is greater than the average energy of the earlier fringe interval, i.e. When the fringe pattern of the next fringe interval is determined to be right-tilted, in a typical self-mixing interferometry model setting, right-tilted fringes usually correspond to the motion of the target object along a specific direction (e.g., away from the laser).

[0048] Left-leaning stripe determination ( When the average energy of the later fringe interval is less than the average energy of the earlier fringe interval, i.e. When the fringe pattern of the next fringe interval is determined to be left-leaning, this usually corresponds to the target object moving in the opposite direction (e.g., towards the laser).

[0049] In this embodiment, when the average energy difference between adjacent fringe intervals is exactly zero, the fringe tilt direction is uncertain. In this case, a preset default value, Hilbert transform, or differential-based discrimination method can be used for determination. Although this embodiment uses the energy difference method for direction determination, in other embodiments of the invention, the geometric characteristics of the time-domain signal can be combined or used for auxiliary determination. For example, the slopes of the rising and falling edges of the fringe can be directly calculated. If the absolute value of the rising edge slope is greater than the absolute value of the falling edge slope, it is determined to be a certain tilt direction.

[0050] It should be noted that the core objective of step S2 of this invention is to determine the tilt state of the stripes, and thus determine the direction of motion. The specific correspondence between the direction and the object's motion may be affected by the optical path structure or definitional conventions, but as long as a determination method is selected, the correspondence is determined.

[0051] Step 3: Within the stripe interval determined to be in a specific tilt direction, calculate the average value of the original signal values ​​of all sampling points within the corresponding stripe interval as the energy feature quantity.

[0052] After determining the fringe tilt direction in step two, this step aims to extract statistical features that are strongly correlated with the optical feedback factor C. Studies have shown that under a specific fringe tilt direction, the average energy of the fringes exhibits a stable monotonic relationship with the feedback factor C. In this embodiment, the right-tilted fringe region is selected as the specific interval for feature extraction, and the specific implementation process is as follows: Traverse the stripe sequences processed in steps one and two, and based on the judgment result of step two, filter out all complete stripe intervals marked as right-leaning.

[0053] It should be noted that the right-leaning direction was chosen because the left-leaning section will produce abrupt changes due to its stripe characteristics. This embodiment will use the right-leaning stripes as an example for explanation.

[0054] For each selected right-sloping fringe interval, calculate the average energy characteristic of the signal within that interval. The calculation method involves averaging the signal amplitudes of all original sampling points within the interval. Specifically, the energy characteristic is calculated as follows:

[0055] In the formula Let N be the signal amplitude at the i-th sampling point within the right-sloping stripe region, and N be the number of sampling points in the corresponding stripe region.

[0056] The reason for using the above averaging process instead of single-point values ​​as feature quantities is as follows: Mixed interference signals are often accompanied by Gaussian white noise and other interference. By averaging over the entire interval, the zero-mean random noise can be effectively canceled out, making the calculated characteristic quantities more accurate. More stable and reliable; This characteristic quantity comprehensively reflects the overall morphological changes of the stripes. Compared with the local ridge peaks, which are highly susceptible to speckle noise, the average energy can more accurately characterize the modulation effect of the feedback intensity C on the overall thickness or tilt of the waveform.

[0057] Step four: Invoke the mapping relationship between energy characteristics and feedback factors that was pre-constructed through offline calibration, substitute the energy characteristics into the mapping relationship, and interpolate to estimate the current optical feedback factor.

[0058] This step is the core of achieving rapid estimation of the feedback factor. To address the computational complexity caused by the need to solve for the feedback factor C in traditional methods, this embodiment employs an offline calibration and online table lookup / interpolation strategy. The specific implementation includes two stages: offline mapping relationship construction and online estimation.

[0059] In this embodiment, the method for constructing offline mapping relationships includes the following steps S41 to S45.

[0060] S41: Set the range of change of the optical feedback factor, and generate a set of self-mixing interference sample signals corresponding to multiple different optical feedback factors within the range of change.

[0061] Specifically, before actual measurement, a large number of self-mixing interferometric sample signals can be generated through computer simulation to establish a mathematical model of energy characteristics and feedback factors. Based on the theoretical model of self-mixing interferometrics, the range of parameter variation is set. The traversal range of the optical feedback factor C is set as follows: It covers typical application ranges from moderate to strong feedback. Within this range, a series of discrete parameter combinations are generated, producing corresponding time-domain simulation signals.

[0062] S42: The sample signal set is processed through a dual threshold screening mechanism to identify the real peak and valley points and divide the stripe intervals.

[0063] S43: Calculate the average energy difference between two adjacent stripe intervals, and identify and extract the right-sloping stripe intervals in the sample signal set based on the average energy difference.

[0064] S44: Calculate the energy characteristic of the right-sloping fringe interval. A sample library consisting of multiple energy feature quantity-light feedback factor data pairs was established. All samples were collected. Data pair. Linewidth broadening factor. This is related to the material of the laser and is a fixed constant, given in advance in this embodiment. Therefore, all data points can be projected onto... Fitting is performed on a plane.

[0065] S45: Perform third-order polynomial fitting on the data in the sample library to obtain the coefficients of the third-order polynomial equation and establish the mapping relationship between energy characteristics and feedback factors.

[0066] The mapping relationship is constructed using polynomial fitting; the estimation method for the optical feedback factor is as follows: the energy characteristic quantity is input into a preset third-order polynomial equation, and the corresponding optical feedback factor value is calculated. In this embodiment, a third-order polynomial is preferably used to fit the data, establishing the following mapping relationship:

[0067] in, These are the coefficients of a fixed polynomial obtained by fitting using the least squares method. These coefficients are pre-stored in the memory of the measurement system.

[0068] During real-time measurement, the system does not require complex iterative calculations; it only needs to call the offline calibration results mentioned above: the system reads the current right-tilted fringe region energy characteristic obtained in real-time calculation in step three. ; This real-time Substitute the values ​​into the pre-stored third-order polynomial equation above:

[0069] The current estimated value of the optical feedback factor can be directly calculated using simple addition and multiplication operations. .

[0070] Although this embodiment preferably uses a third-order polynomial for fitting, in other embodiments, polynomials of other orders (such as second-order or fourth-order) can be selected according to accuracy requirements and computational resource limitations, or piecewise linear interpolation, lookup table methods, etc. can be used to characterize the mapping relationship between energy characteristics and feedback factors.

[0071] Through this step, the system can provide strong feedback and pre-determine the linewidth expansion factor. Under these conditions, it consumes very little computation time (constant complexity) to quickly and robustly obtain the accurate optical feedback factor C, providing key parameters for subsequent high-precision displacement reconstruction.

[0072] Step 5: The estimated optical feedback factor is introduced into the Phase Unwrapping Method (PUM) to correct and unwrap the phase, and the displacement signal of the target object is reconstructed.

[0073] The parameter preparation for this step includes: The optical feedback factor C is obtained by calling the real-time value estimated through polynomial interpolation in step four. value; Linewidth broadening factor The laser material is specified in advance. laser wavelength The known system parameters.

[0074] The phase unwrapping algorithm is used to process time-domain signals. First, the normalized time-domain interferometric signal is subjected to inverse cosine transform and transition point detection using the PUM algorithm to obtain a preliminary unwrapped phase including feedback modulation. In this process, this embodiment employs a feedback correction strategy, using the estimated C value to perform weighted smoothing on the noise near the phase transition point. Due to the accurate estimation of the C value, the algorithm can more accurately identify the height of the fringe transition, thereby effectively suppressing speckle noise and circuit noise common in self-mixed signals and preventing cumulative errors during the unpacking process.

[0075] Based on the Lang-Kobayashi physical model, the following formula is used to convert the phase containing feedback. Restored to a feedback-free phase representing actual motion And eventually converted into displacement. :

[0076] In the formula, Indicates the displacement of the target object. The wavelength of the laser. The phase signal after unwrapping is given, and C is the optical feedback factor. This is the linewidth broadening factor.

[0077] After the above processing, the system finally outputs the displacement curve of the target object. Experimental verification shows that the method described in this embodiment is applicable not only to regular harmonic motion but also to complex non-harmonic motion. As long as identifiable interference fringe features exist in the signal, this method can achieve high-precision displacement reconstruction.

[0078] To verify the effectiveness of the method provided in this embodiment, some specific examples are provided below.

[0079] Case 1 The simple harmonic vibration signal was simulated using MATLAB, and the parameter settings are shown in Table 1.

[0080] Table 1 Parameter Setting Table

[0081] The simulated harmonic self-mixing interference signal with 10dB noise, after the first threshold screening, yields the correct fringe sequence as shown below. Figure 2 As shown in (a); after the second threshold screening, the stripe region is divided as follows. Figure 2 As shown in (b). The direction is determined based on the energy difference between adjacent intervals, as shown in [the diagram]. Figure 2 As shown in (c); the right-leaning energy exhibits a monotonic characteristic as C changes, from Figure 2 (d) Interpolation estimation feedback factor The value is 1.51. Initial unpacking. Phase Figure 2 As shown in (e), the estimated With fixed The displacement reconstruction curve of the external vibrating object is obtained by correcting the feedback-free phase and calculating it. Figure 2 (f).

[0082] The displacement curve is reconstructed based on the PUM algorithm, as shown below. Figure 2 (g), where the root mean square error (green line) is 19.81 nm. Figure 2 (h) is the residual distribution plot, which illustrates the reliability of the root mean square error results.

[0083] The results show that the present invention measured The method has high accuracy, and it also exhibits high reconstruction accuracy after PUM displacement reconstruction.

[0084] Case 2 To verify the effectiveness of the proposed laser self-mixing interference feedback factor estimation and displacement reconstruction method based on fringe energy and dual threshold screening under different signal-to-noise ratios, the optical feedback factor C value was estimated and the displacement was reconstructed under different signal-to-noise ratios.

[0085] Estimated optical feedback factor The values ​​and the root mean square error of reconstruction are shown in Table 2.

[0086] Table 2 Optical feedback factors under different feedback intensities at different signal-to-noise ratios. Comparison table of root mean square errors of estimation and reconstruction

[0087] The results show that the laser self-mixing interferometry feedback factor estimation and displacement reconstruction method based on fringe energy and dual threshold screening proposed in this embodiment has high accuracy in estimating the optical feedback factor and small root mean square error in displacement reconstruction under different signal-to-noise ratios and different feedback intensities. The method has strong robustness in estimating the optical feedback factor C.

[0088] Case 3 To verify the effectiveness of the laser self-mixing interference feedback factor estimation and displacement reconstruction method based on fringe energy and dual threshold screening described in this embodiment for simple harmonic vibration in the experiment, the laser self-mixing interference signal obtained in the experiment was processed experimentally.

[0089] and Figure 2 Consistent, among which Figure 3 (a) shows the correct stripe sequence obtained after the first threshold screening. Figure 3 (b) shows the stripe region division after the second threshold screening. Figure 3 (c) To determine the direction based on the energy difference between adjacent intervals, Figure 3 (d) illustrates the monotonic characteristic of right-leaning energy as a function of C. Here, the interpolation estimation feedback factor C is 1.96. Figure 3 (e) Initial unpacking Phase, Figure 3 (f) To introduce the estimated C and a fixed The feedback-free phase is corrected, and the displacement reconstruction curve of the external vibrating object is calculated. The absolute error of the reconstruction is obtained as follows: Figure 3 As shown in (g), the root mean square error is 31.19 nm. Figure 3 (h) is the residual distribution plot, which illustrates the reliability of the root mean square error results.

[0090] Case 4 To verify the effectiveness of the laser self-mixing interference feedback factor estimation and displacement reconstruction method based on fringe energy and dual threshold screening described in this embodiment for nonharmonic vibration in the experiment, the laser self-mixing interference signal obtained in the experiment was processed experimentally.

[0091] and Figure 2 Consistent, among which Figure 4 (a) shows the correct stripe sequence obtained after the first threshold screening. Figure 4 (b) shows the stripe region division after the second threshold screening. Figure 4 (c) To determine the direction based on the energy difference between adjacent intervals, Figure 4 (d) illustrates the monotonic characteristic of right-leaning energy as a function of C. Here, the interpolation estimation feedback factor C is 1.34. Figure 4 (e) Initial unpacking Phase, Figure 4 (f) To introduce the estimated C and a fixed The feedback-free phase is corrected, and the displacement reconstruction curve of the external vibrating object is calculated. The absolute error of the reconstruction is obtained as follows: Figure 4 As shown in (g), the root mean square error is 32.26 nm. Figure 4 (h) is the residual distribution plot, which illustrates the reliability of the root mean square error results.

[0092] The results show that the laser self-mixing interference feedback factor estimation and displacement reconstruction method based on fringe energy and dual threshold screening proposed in this embodiment can effectively process experimental signals.

[0093] Example 2 This embodiment is a laser self-mixing interferometry feedback factor estimation and displacement reconstruction system. The system is used to implement the feedback factor estimation and displacement reconstruction method as described in Embodiment 1, including: The signal acquisition module is used to acquire the time-domain signal of the laser self-mixing interference. The stripe recognition module is used to construct a dual-threshold screening mechanism consisting of an amplitude threshold and a spacing threshold, and to identify peak and valley points in the time-domain signal based on the dual-threshold screening mechanism, forming a stripe sequence and dividing the stripe intervals. The energy analysis module is used to calculate the average energy difference between two adjacent stripe intervals, determine the tilt direction of the stripes based on the average energy difference, and calculate the average value of the original signal values ​​of all sampling points in the stripe interval determined to be in a specific tilt direction as the energy feature quantity. The feedback estimation module is used to store the mapping relationship between energy characteristics and feedback factors that has been pre-constructed through offline calibration, and to substitute the energy characteristics output by the energy analysis module into the mapping relationship to interpolate and estimate the current optical feedback factor. The phase reconstruction module receives the estimated optical feedback factor and introduces a phase unwrapping algorithm to correct and unwrap the phase, thereby reconstructing the displacement signal of the target object.

[0094] Example 3 This embodiment is an electronic device, including: One or more processors; Memory, used to store one or more computer programs; One or more computer programs stored in the memory are executed by the one or more processors, causing the one or more processors to implement the feedback factor estimation and displacement reconstruction method as described in Embodiment 1.

[0095] Example 4 This embodiment is a computer-readable storage medium storing a computer program that, when executed by a processor, implements the feedback factor estimation and displacement reconstruction method as described in Embodiment 1.

[0096] The above description is only a preferred embodiment of the present invention. It should be noted that those skilled in the art can make several modifications and improvements without departing from the inventive concept of the present invention, and these all fall within the protection scope of the present invention.

Claims

1. A method for estimating the feedback factor and reconstructing the displacement of a laser self-mixing interferometry, characterized in that, Includes the following steps: The time-domain signal of laser self-mixing interference is acquired, and the peak and valley points in the time-domain signal are identified based on a dual threshold screening mechanism consisting of amplitude threshold and spacing threshold, forming a fringe sequence and dividing the fringe intervals. Calculate the average energy difference between two adjacent stripe intervals, and determine the tilt direction of the stripes based on the average energy difference; Within the stripe interval determined to be in a specific tilt direction, the average value of the original signal values ​​of all sampling points within the corresponding stripe interval is calculated as the energy feature quantity. The mapping relationship between energy characteristics and feedback factors, which was pre-constructed through offline calibration, is invoked. The energy characteristics are substituted into the mapping relationship, and the current optical feedback factor is estimated by interpolation. The estimated optical feedback factor is introduced into the phase unwrapping algorithm to correct and unwrap the phase, and the displacement signal of the target object is reconstructed.

2. The method according to claim 1, characterized in that, The method for identifying peaks and valleys in the time-domain signal, forming a stripe sequence, and dividing stripe intervals is as follows: The amplitude difference between candidate peaks and valleys in the statistical time-domain signal is calculated, and the mean or moving average of the amplitude difference is calculated. An amplitude threshold is set based on the mean or moving average of the amplitude difference. The distance between valid peaks and valleys of the same type in the statistical time-domain signal is calculated, and the mean or moving average of the distance is calculated. A distance threshold is set based on the mean or moving average of the distance. Candidate peak and valley points are filtered using the amplitude threshold. When the amplitude difference between a candidate peak / valley value and its adjacent points is greater than the amplitude threshold, the point is determined to be a true peak / valley point. The identified real peaks and valleys are divided using the spacing threshold. When the spacing between adjacent real peaks and valleys of the same type exceeds the spacing threshold, it is determined that the two points form a flipped interval, and the stripes between two adjacent flipped intervals are taken as stripe intervals.

3. The method according to claim 1, characterized in that, The method for determining the tilt direction of the stripes is as follows: Calculate the difference between the average energy of the next fringe interval and the average energy of the previous fringe interval; If the average energy difference is greater than zero, then the next fringe interval is determined to be a right-sloping fringe; If the average energy difference is less than zero, then the next stripe interval is determined to be a left-leaning stripe.

4. The method according to claim 1, characterized in that, The method for calculating the energy characteristic quantity is as follows: In the formula, Represents energy characteristic quantity, Let N be the signal amplitude at the i-th sampling point within the right-sloping stripe region, and N be the number of sampling points in the corresponding stripe region.

5. The method according to claim 1, characterized in that, The mapping relationship is constructed using polynomial fitting; the method for estimating the optical feedback factor is as follows: input the energy characteristic quantity into a preset third-order polynomial equation, and calculate the corresponding optical feedback factor value.

6. The method according to claim 5, characterized in that, The method for constructing the mapping relationship is as follows: Set the range of optical feedback factor variation, and generate multiple self-mixing interference sample signal sets corresponding to different optical feedback factors within the range of variation; The sample signal set is processed by a dual threshold screening mechanism to identify the real peak and valley points and divide the stripe intervals. Calculate the average energy difference between two adjacent stripe intervals, and identify and extract the right-sloping stripe intervals in the sample signal set based on the average energy difference; Calculate the energy characteristics of the right-sloping fringe interval and establish a sample library consisting of multiple energy characteristic-light feedback factor data pairs; The data in the sample library are fitted with a third-order polynomial to obtain the coefficients of the third-order polynomial equation and establish the mapping relationship between energy characteristics and feedback factors.

7. The method according to claim 1, characterized in that, The method for calculating the displacement signal is as follows: In the formula, Indicates the displacement of the target object. The wavelength of the laser. The phase signal after unwrapping is given, and C is the optical feedback factor. This is the linewidth broadening factor.

8. A laser self-mixing interferometry feedback factor estimation and displacement reconstruction system, characterized in that, The system is used to implement the feedback factor estimation and displacement reconstruction method as described in any one of claims 1-7, including: The signal acquisition module is used to acquire the time-domain signal of the laser self-mixing interference. The stripe recognition module is used to construct a dual-threshold screening mechanism consisting of an amplitude threshold and a spacing threshold, and to identify peak and valley points in the time-domain signal based on the dual-threshold screening mechanism, forming a stripe sequence and dividing the stripe intervals. The energy analysis module is used to calculate the average energy difference between two adjacent stripe intervals, determine the tilt direction of the stripes based on the average energy difference, and calculate the average value of the original signal values ​​of all sampling points in the stripe interval determined to be in a specific tilt direction as the energy feature quantity. The feedback estimation module is used to store the mapping relationship between energy characteristics and feedback factors that has been pre-constructed through offline calibration, and to substitute the energy characteristics output by the energy analysis module into the mapping relationship to interpolate and estimate the current optical feedback factor. The phase reconstruction module receives the estimated optical feedback factor and introduces a phase unwrapping algorithm to correct and unwrap the phase, thereby reconstructing the displacement signal of the target object.

9. An electronic device, comprising: One or more processors; Memory, used to store one or more computer programs; The feature is that one or more computer programs stored in the memory are executed by the one or more processors, causing the one or more processors to implement the feedback factor estimation and displacement reconstruction method as described in any one of claims 1-7.

10. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the program is executed by the processor, it implements the feedback factor estimation and displacement reconstruction method as described in any one of claims 1-7.

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