White light interference three-dimensional reconstruction algorithm for dual filtering of modal decomposition and wavelet transform

Abstract

The invention relates to the technical field of three-dimensional reconstruction, and discloses a white light interference three-dimensional reconstruction algorithm based on modal decomposition and wavelet transform dual filtering, comprising the following steps: S1, collecting an original interference signal; s2, performing CEEMDAN mode decomposition on the interference signal to obtain a plurality of I MF components; s3, I MF components with high correlation with the original signals are screened out; s4, carrying out wavelet transform filtering processing on the I MF component after screening; s5, extracting an effective area of the interference signal; s6, obtaining a modulation degree based on a seven-step phase shift algorithm, and performing fitting processing on the modulation degree to extract an envelope curve; s7, extracting a coherent peak position according to the fitting envelope and resolving an initial phase; and S8, reconstructing the three-dimensional height of the object to be measured according to the inter-frame displacement information. According to the method, through dual filtering of modal decomposition and wavelet transformation and adaptive parameter adjustment, effective suppression of noise, reservation of signal details and improvement of three-dimensional reconstruction precision are realized.

Description

Technical Field

[0001] The present invention relates to the technical field of three-dimensional reconstruction, and in particular to a white light interferometric three-dimensional reconstruction algorithm of modal decomposition and wavelet transform dual filtering. Background Art

[0002] In today's rapidly advancing science and technology, miniaturization has become an inevitable trend in high-end manufacturing, particularly in the fields of mechanics, electronics, semiconductors, and modern optics. The surface micromorphology of micro-precision components in these industries has a significant impact on their performance, reliability, and lifespan, placing higher demands on surface machining accuracy and corresponding inspection technologies. Semiconductor wafers are key components of integrated circuits, containing hundreds of millions of tiny electronic components. Due to the inherent complexity of the wafer fabrication process, high demands are placed on machining accuracy and surface quality. Surface flatness and roughness can significantly impact chip performance and yield. Micro-electro-mechanical systems (MEMS) are widely used in various fields, particularly in automotive electronics, aerospace, medical devices, and consumer electronics. Their sizes typically range from micrometers to nanometers. Any submicron-level defects, such as abnormal surface roughness or microcracks, on MEMS surfaces can reduce their mechanical strength, thermal stability, or electrical performance. In modern optics, nanometer-level deviations in the surface topography of precision optical components such as Fresnel lenses and microlens arrays can cause optical path deviations and image distortion. The above cases demonstrate that accurate measurement of microscopic surface topography is a crucial factor influencing the performance of high-end devices. However, due to the large diameter and low resolution of conventional measurement techniques, these measurements of surface microtopography are insufficient. Therefore, the development of 3D microtopography measurement technology with micron- to nanometer-level resolution is of great significance.

[0003] In the existing microscopic surface topography measurement technology landscape, contact and non-contact methods exhibit significant differences in their technical characteristics due to differences in their physical mechanisms. Contact measurement acquires topography information through direct contact between the probe and the surface. Its technical advantage lies in its adaptability to surfaces with high reflectivity, transparency, or complex optical properties. However, the mechanical interaction between the probe and the sample inevitably introduces the risk of surface damage. This is particularly true when measuring soft materials or micro-nano cantilever structures, where plastic deformation or structural fracture caused by the probe's contact force has become a fatal flaw that restricts its application. Non-contact technologies achieve morphological characterization through the non-destructive interaction of photons, electrons, or near-field physical fields with surfaces. While scanning probe microscopy (STM, AFM) can achieve atomic-level resolution, its stringent requirements for sample conductivity, surface flatness, or environmental stability significantly limit its industrial applicability. Optical microscopy, while promising rapid full-field measurement, is constrained by inherent bottlenecks in physical principles. The point-by-point scanning modes of confocal microscopy and defocus detection struggle to meet high-throughput detection requirements. Structured light projection technology cannot resolve submicron features due to the optical diffraction limit, and laser interferometry is limited to continuous surface morphology measurements due to phase ambiguity. Against this backdrop, white-light interferometry, with its unique wide-spectrum interference characteristics and computational reconstruction capabilities, has become one of the few technical approaches capable of achieving both micro- and nanoscale resolution, millimeter-level range, and non-destructive testing. This technology can theoretically avoid phase ambiguity and achieve cross-scale morphology reconstruction through envelope analysis of the interference signal of a short-coherent light source. However, in practical applications, factors such as noise interference and system errors will seriously affect the reconstruction accuracy. Therefore, how to improve the noise resistance and accuracy of the white-light interferometric 3D reconstruction algorithm has become a hot topic in current research. Summary of the Invention

[0004] In response to the shortcomings of the existing technology, the present invention provides a white light interferometric 3D reconstruction algorithm with dual filtering of modal decomposition and wavelet transform, which solves the problems in the existing technology such as the difficulty in effectively separating signal noise and effective information, insufficient reconstruction accuracy and detail retention, and lack of adaptive adjustment capabilities.

[0005] To achieve the above objectives, the present invention is implemented through the following technical solutions: a white light interferometry 3D reconstruction algorithm with dual filtering of modal decomposition and wavelet transform, comprising the following steps:

[0006] S1, collecting the original interference signal;

[0007] S2. Perform CEEMDAN modal decomposition on the interference signal to obtain several IMF components;

[0008] S3, filter out the IMF components that have high correlation with the original signal;

[0009] S4, performing wavelet transform filtering on the filtered IMF components;

[0010] S5, extracting the effective area of ​​the interference signal;

[0011] S6. Obtaining the modulation index based on a seven-step phase shift algorithm, and performing fitting processing on the modulation index to extract an envelope curve;

[0012] S7, extracting the coherence peak position according to the fitted envelope and solving the initial phase;

[0013] S8. Reconstruct the three-dimensional height of the object to be measured based on the inter-frame displacement information.

[0014] Preferably, when performing CEEMDAN decomposition on the interference signal in S2, an adaptive noise perturbation method is used to decompose the interference signal to obtain multiple intrinsic mode function (IMF) components, and the components are screened based on the correlation between the components and the original signal.

[0015] Preferably, the Pearson correlation coefficient is used as a screening criterion when screening the IMF components in S3, and the components with a Pearson correlation coefficient greater than a set threshold are retained as valid signals.

[0016] Preferably, the wavelet transform filtering in S4 uses the db3 wavelet basis in the Daubechies wavelet family for decomposition, with 5 decomposition layers, and uses a soft threshold function to process the wavelet coefficients to achieve noise reduction.

[0017] Preferably, the soft threshold function linearly reduces the wavelet coefficient when its absolute value is greater than a set threshold, and sets it to zero when its absolute value is less than or equal to the set threshold.

[0018] Preferably, the specific method of extracting the effective area of ​​the interference signal in S5 includes: removing the DC component of the signal, calculating the absolute value of the first-order difference, finding the local maximum point as the center point, and extracting a fixed number of discrete signals from this point forward and backward as the effective area signal.

[0019] Preferably, when fitting the modulation index in S6, a Gaussian function is used for nonlinear fitting, and characteristic parameters of the Gaussian function are obtained by least square method and used to construct a smooth envelope curve of the modulation index.

[0020] Preferably, the coherence peak position in S7 corresponds to the maximum point of the fitting function in the modulation index curve, and this point is used as the central frame when calculating the initial phase.

[0021] Preferably, in said S8, the calculation of the three-dimensional height is converted based on the multiplication and division relationship of the central wavelength, the initial phase, the moving step and the number of frames of the zero-point coherence peak position, and the final height reconstruction result is output.

[0022] The present invention provides a white light interferometric 3D reconstruction algorithm using dual filtering of modal decomposition and wavelet transform. It has the following beneficial effects:

[0023] 1. This invention utilizes a dual filtering approach combining modal decomposition and wavelet transform to effectively remove noise while preserving signal detail. Compared to existing 3D reconstruction methods that rely on a single filtering approach, this invention more accurately processes interference signals, avoids oversmoothing and loss of detail, and improves the model's sophistication and accuracy.

[0024] 2. This paper introduces a multi-scale decomposition method based on CEEMDAN, which can adaptively decompose the individual frequency components of complex signals. Compared with traditional decomposition methods in the prior art, CEEMDAN can more accurately extract effective information from interference signals, avoid the mixing of low-frequency signals and high-frequency noise, and significantly improve reconstruction quality. BRIEF DESCRIPTION OF THE DRAWINGS

[0025] Figure 1 A diagram showing the steps of the method of the present invention. DETAILED DESCRIPTION

[0026] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the drawings in the present specification. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative efforts are within the scope of protection of the present invention.

[0027] Please see the attached Figure 1 The embodiment of the present invention provides a white light interferometry 3D reconstruction algorithm using dual filtering of modal decomposition and wavelet transform, comprising the following steps:

[0028] S1, collecting the original interference signal;

[0029] In one embodiment of the present invention, a sampling signal acquisition model for white light interferometric 3D reconstruction is first established. The model relies on an optical interferometric measurement system, including a light source unit, an interferometer lens assembly, an objective lens assembly, an image acquisition device, and a displacement control module.

[0030] The light source unit uses a broadband low-coherence white light source to achieve short-coherence interferometric imaging. The interferometer group is used to split the light and combine the interference signal. The objective lens assembly is used to focus the interference light onto the surface of the object being measured and transmit the reflected signal back to the image acquisition device.

[0031] The image acquisition device includes a CCD or CMOS sensor connected to a processing terminal, which can acquire interference patterns of consecutive frames with micrometer or nanometer precision.

[0032] The displacement control module is connected to the stage or piezoelectric ceramic (PZT) adjustment mechanism to control the object or reference mirror to move along the axial direction with a fixed step length to achieve scanning and recording of the interference pattern.

[0033] During the interference process, under the condition of ensuring optical path matching, the reflected light beam interferes to form an interference signal f(t), the intensity of which changes nonlinearly with the displacement t.

[0034] The interference signal model is defined as follows:

[0035]

[0036] Where: f(t) is the sampling signal of the tth frame; I b is the background intensity, representing the DC component; I m is the amplitude of the interference modulation, which determines the fringe contrast; λ0 is the central wavelength of the white light source; h(t) is the relative displacement or height corresponding to the current frame; φ(t) is the initial phase; η(t) is the system noise or measurement error, which is approximately zero-mean Gaussian white noise.

[0037] After the above model is established, the reference arm or sample is moved through the displacement control module to collect a continuous N-frame interference image sequence to form an interference signal set {f(1), f(2), ..., f(N)}.

[0038] The displacement step between sample frames is controlled by the piezoelectric ceramic module, preferably within the range of tens of nanometers to ensure the spatial sampling density that meets the interference conditions.

[0039] During the image acquisition process, the system needs to maintain a stable optical path to avoid coherence state instability due to environmental vibration or thermal drift, which would affect the integrity of the interference signal structure.

[0040] To achieve subsequent modal decomposition and reconstruction processing, the collected signal must meet the following technical requirements:

[0041] The frame sequence is continuous, and the number of sampling frames is not less than 7 frames;

[0042] The dynamic range of the light intensity signal matches the change of the interference fringes to ensure clear modulation;

[0043] The sampled signal contains complete interference peak information and covers at least one coherent envelope peak.

[0044] The sampling signal is finally transmitted to the processing terminal in the form of a time series vector and stored in the form of a two-dimensional image sequence, providing basic data for subsequent CEEMDAN decomposition and wavelet filtering.

[0045] Through the above acquisition scheme, this embodiment can achieve the interference signal acquisition effect with multi-frame continuity and strong anti-interference ability, ensuring the effectiveness and accuracy of the subsequent signal analysis link.

[0046] S2. Perform CEEMDAN modal decomposition on the interference signal to obtain several IMF components;

[0047] First, a time series model of the original interference signal is established, which is recorded as the input sequence f(t), where t represents the frame sequence or the number of equally spaced sampling points.

[0048] The CEEMDAN algorithm is an enhanced implementation of the empirical mode decomposition method for decomposing functional signals, featuring complete set properties and adaptive noise control mechanisms. The algorithm decomposes the multiscale interference signal f(t) into multiple intrinsic mode functions (IMFs) with local eigenfrequencies and a residual trend term.

[0049] The decomposition form is as follows:

[0050]

[0051] Where: f(t) is the original interference signal; IMF k (t) is the kth IMF component; K is the number of IMFs obtained by decomposition; r(t) is the residual trend term, which represents the part that cannot be decomposed any further.

[0052] To enhance the decomposition stability, CEEMDAN introduces Gaussian white noise and adopts an ensemble averaging strategy. In this embodiment, the decomposition process is performed using the following steps.

[0053] First, the signal is copied into multiple instances, and Gaussian white noise ∈ with different amplitude and phase is superimposed in each instance. i (t), construct the disturbance signal set {f(t)+∈ i (t)}, where i = 1, 2, ..., M, represents the i-th member in the set, and M is the size of the set.

[0054] Then, each disturbance signal is subjected to classical EMD decomposition to extract the first eigenmode function. Compute the first component by ensemble averaging:

[0055]

[0056] This component is then subtracted from the original signal to obtain the residual:

[0057] r1(t)=f(t)-IMF1(t);

[0058] Repeat the above process with the residual r1(t) as the new input signal, and continue to perform EMD decomposition after adding noise to generate the second IMF component IMF2(t), and so on until the residual term r k (t) Until the termination conditions are met or there is no significant fluctuation.

[0059] The final output is:

[0060] Several intrinsic mode function sequences IMF1(t),IMF2(t),…,IMFK(t);

[0061] A trend term r(t) that cannot be decomposed any further.

[0062] The above calculation process has the following mathematical logic structure:

[0063] r k+1 (t) = r k (t)-IMF k+1 (t), k=1,2,...,K-1;

[0064] The modal decomposition algorithm is embedded in the CEEMDAN core module, which includes three parts: a noise superposition algorithm, an EMD processing algorithm, and an averaging algorithm. The noise superposition algorithm is used to construct multiple perturbations, the EMD processing algorithm is used to extract components, and the averaging algorithm is used for ensemble averaging.

[0065] The CEEMDAN method relies on setting the following parameters in actual operation:

[0066] The noise amplitude coefficient σ is taken as a percentage of the original signal amplitude;

[0067] The number of samples in the set, M, is usually 10 to 50;

[0068] The IMF extraction termination criterion is set based on the number of local extreme values ​​and the envelope mean convergence index.

[0069] Furthermore, to avoid the influence of boundary effects on the decomposition quality, before executing each round of EMD, mirror extension processing is performed on both ends of the signal.

[0070] Through the above processing, the original white-light interference signal is restored to a series of IMF components with ordered frequency components and independent fluctuation patterns. These components not only maintain the temporal locality in the original structure but also have frequency analysis functions, making them suitable as the input data source for subsequent correlation screening and wavelet filtering.

[0071] Through this decomposition method, the noise, background drift and main part of the interference signal in the interference signal can be mapped to different IMF channels respectively, thereby providing independent processing dimensions for noise suppression and structure preservation.

[0072] S3, filter out the IMF components that have high correlation with the original signal;

[0073] In signal reconstruction after CEEMDAN decomposition, screening high-information IMF components is a key step. Since noisy IMF components usually have low correlation with the original signal, this patent proposes an adaptive screening method based on the Pearson correlation coefficient. By calculating the Pearson correlation coefficient r between each IMF component and the original signal, and setting a threshold to retain IMF components with high correlation. The Pearson correlation coefficient formula is as follows:

[0074]

[0075] in is the kth IMF, is its average value; f is the original signal, is its average value.

[0076] Through the above-mentioned IMF screening, the system can remove errors introduced by noise, background interference or low-quality modes, retain useful components, and thus improve the accuracy and stability of subsequent wavelet filtering and three-dimensional reconstruction.

[0077] After the screening is completed, the retained IMF signal is reconstructed and then proceeds to the next processing stage, namely wavelet transform filtering, to further optimize the signal quality and provide more accurate input data for the reconstruction process.

[0078] S4, performing wavelet transform filtering on the filtered IMF components;

[0079] First, the reconstructed signal in step S3 is passed as input data to the wavelet transform module. The core task of this module is to filter the reconstructed signal through wavelet transform, thereby further suppressing high-frequency noise and retaining the useful components in the signal.

[0080] Wavelet transform uses discrete wavelet transform (DWT) to decompose the signal. To reconstruct the signal, it is first converted into a set of coefficients at different frequency scales through multi-scale wavelet decomposition. The specific formula is as follows:

[0081]

[0082] Where: f′(t) is the reconstructed signal; c j is the coefficient on the jth wavelet scale; ψ j (t) is the wavelet basis function of the jth scale; J is the maximum scale of wavelet decomposition.

[0083] Wavelet basis function ψ j(t) is achieved by selecting a suitable family of wavelet functions (such as Haar wavelet, Daubechies wavelet, etc.). The specific choice of wavelet basis function is optimized according to the characteristics of the signal in order to better adapt to the local structure of the interference signal.

[0084] Although CEEMDAN initially reduces noise by filtering highly correlated IMF components, minimizing their impact on the signal to a certain extent, the components retained by CEEMDAN are also contaminated with noise, resulting in a low signal-to-noise ratio (SNR) in the CEEMDAN reconstruction. Therefore, wavelet transform filtering is used for secondary noise reduction. A five-level multiscale decomposition is performed on the components retained by CEEMDAN using the Daubechies family db3 wavelet basis. This decomposition parameter was chosen based on the spectral characteristics of white-light interferometric signals. The low-order properties of db3 provide a good balance between detail and noise in the signal, while the five-level decomposition covers the full spectrum of high-frequency transient fluctuations and low-frequency components, preventing the decomposition from being too lengthy. After layer-by-layer wavelet filtering, noise and valid components are separated in the time and frequency domains for each IMF component of the signal. This approach reduces noise and improves the signal-to-noise ratio while preserving the phase and amplitude characteristics of the interference signal.

[0085] In the process of wavelet domain denoising, quantizing wavelet coefficients through threshold function is the core link of noise suppression. Commonly used functions include hard threshold function and soft threshold function.

[0086] (1) The expression of the hard threshold function is as shown in the formula:

[0087]

[0088] Where: T thr is the threshold, W j is the wavelet coefficient, W j ' is the wavelet coefficient after processing;

[0089] (2) The expression of the soft threshold function is as shown in the formula:

[0090]

[0091] Where: T thr is the threshold, W j is the wavelet coefficient, sign() is the sign function (retains the positive and negative coefficients), W j ' is the wavelet coefficient after processing

[0092] Through the thresholding process, low-amplitude coefficients (i.e., noise components) are removed, while high-amplitude coefficients (i.e., the main features of the signal) are retained. This operation can effectively remove noise while preserving the essential features of the signal.

[0093] In the implementation process, attention should be paid to selecting appropriate wavelet basis functions and thresholds to optimize the denoising effect. The threshold of the wavelet coefficients should be adjusted according to the noise characteristics of the signal to achieve the best noise suppression effect.

[0094] Through wavelet transform filtering, the system can effectively remove high-frequency noise while retaining effective low-frequency information in the signal, thereby improving signal quality and providing more accurate input data for subsequent three-dimensional reconstruction.

[0095] This step can effectively improve the reconstruction accuracy by removing unnecessary high-frequency noise, making the 3D reconstruction more stable and accurate.

[0096] S5, extracting the effective area of ​​the interference signal;

[0097] Remove the DC component of the collected white light interference signal and obtain its AC component I ac (m):

[0098]

[0099] Where: I(m) is the light intensity value of the mth collection point; I ac (m) is the net light intensity value of the mth collection point; M is the total number of collection points.

[0100] Will I ac (m) takes the first-order derivative and takes the absolute value. The interval between discrete data points is small enough, so the first-order difference approximate derivative is used to calculate ΔI(n):

[0101] ΔI(n)=|I ac (m+1)-I ac (m)|;

[0102] Where: I ac (m) is the net light intensity value of the mth collection point; I ac (m+1) is the net light intensity value of the m+1th collection point; ΔI(n) is the difference between the two.

[0103] Set the threshold N (N∈M) as the length of the effective signal and calculate the average value within the threshold to obtain

[0104]

[0105] Where: N is the length of the effective signal; ΔI(n) is the difference in net light intensity between adjacent acquisition points; is the mean of N ΔI(n), and M is the total number of sampling points.

[0106] Pick Maximum position o max ;

[0107]

[0108] A fixed number of discrete signals are extracted from this point forward and backward as the effective area signal

[0109] S6. Obtaining the modulation index based on a seven-step phase shift algorithm, and performing fitting processing on the modulation index to extract an envelope curve;

[0110]

[0111] Where: b max is the peak value of the Gaussian curve; m max is the coordinate of the curve peak; s is the half-width of the curve. Taking the natural logarithm of both sides of equation (2-8) yields:

[0112]

[0113] Where: b max is the peak value of the Gaussian curve; m max is the coordinate of the curve peak; s is the half-width information of the curve; b i is the net light intensity value corresponding to the i-th; m i is the coordinate of the i-th collection point.

[0114] set up:

[0115]

[0116] Where: z i ,a0,a1,a2 are all intermediate variables and have no practical significance; b max is the peak value of the Gaussian curve; m max is the coordinate of the curve peak; s is the half-width information of the curve; b i is the net light intensity value corresponding to the i-th; m i is the coordinate of the i-th collection point.

[0117] Then we get Substituting all modulation points into it, we get:

[0118]

[0119] Where: z i ,a0,a1,a2 are all intermediate variables and have no practical significance; m i is the coordinate of the i-th collection point.

[0120] The least squares method is used to solve the problem, which can be expressed in matrix form as follows:

[0121]

[0122] Where: zi ,a0,a1,a2 are all intermediate variables and have no practical significance; m i is the coordinate of the i-th collection point; N is the total number of collection points.

[0123] Can be simplified to:

[0124] Z = MA;

[0125] Where: Z=[z1 z2 … z N ] T ; A=[a0 a1 a2];N is the total number of sampling points. Finally, the solution is:

[0126] A=(M T M) -1 M T Z;

[0127] Where: Z=[z1 z2 … z N ] T ; A=[a0 a1 a2]; N is the total number of collection points.

[0128] Then, the characteristic parameters of the Gaussian function are calculated based on the value of A, and the envelope curve of the modulation degree is extracted.

[0129] S7, extracting the coherence peak position according to the fitted envelope and solving the initial phase;

[0130] First, the position of the interference signal zero-point coherence peak is preliminarily located according to the signal envelope generated in step S6, and then the corresponding initial phase is solved according to the seven-step phase shift method.

[0131] The seven-step phase shift algorithm formula is as follows:

[0132]

[0133] Where: I i is the light intensity value of the i-th collection point

[0134] S8, reconstructing the three-dimensional height of the object to be measured based on the inter-frame displacement information;

[0135] Substitute the position with the maximum modulation obtained in step S6 and the phase value obtained in step S7 into the formula to obtain the height value. The formula is:

[0136]

[0137] Where: h is the height value obtained, Δz is the step length, m max This is the position with the largest modulation index.

[0138] This method calculates the modulation index based on the light intensity value to obtain the maximum value, and also analyzes the phase information to obtain the position of the zero-point coherence peak.

[0139] While embodiments of the present invention have been shown and described, it will be appreciated by those skilled in the art that various changes, modifications, substitutions, and variations may be made to these embodiments without departing from the principles and spirit of the invention, and that the scope of the invention is defined by the appended claims and their equivalents.

Claims

1. A white light interferometry 3D reconstruction algorithm based on dual filtering of modal decomposition and wavelet transform, characterized by: include: The steps include: S1, collecting the original interference signal; S2. Perform CEEMDAN modal decomposition on the interference signal to obtain several IMF components; S3, filter out the IMF components that have high correlation with the original signal; S4, performing wavelet transform filtering on the filtered IMF components; S5, extracting the effective area of ​​the interference signal; S6. Obtaining the modulation index based on a seven-step phase shift algorithm, and performing fitting processing on the modulation index to extract an envelope curve; S7, extracting the coherence peak position according to the fitted envelope and solving the initial phase; S8. Reconstruct the three-dimensional height of the object to be measured based on the inter-frame displacement information.

2. The white light interferometry 3D reconstruction algorithm of dual filtering of modal decomposition and wavelet transform according to claim 1 is characterized in that: When performing CEEMDAN decomposition on the interference signal in S2, an adaptive noise perturbation method is used to decompose the interference signal to obtain multiple intrinsic mode function (IMF) components, and the components are screened based on the correlation between the components and the original signal.

3. The white light interferometry 3D reconstruction algorithm of dual filtering of modal decomposition and wavelet transform according to claim 1 is characterized in that: When screening IMF components in S3, the Pearson correlation coefficient is used as a screening criterion, and components with a Pearson correlation coefficient greater than a set threshold are retained as valid signals.

4. The white light interferometry 3D reconstruction algorithm of dual filtering of modal decomposition and wavelet transform according to claim 1 is characterized in that: The wavelet transform filter in S4 is decomposed using the db3 wavelet basis in the Daubechies wavelet family, with 5 decomposition layers, and a soft threshold function is used to process the wavelet coefficients to achieve noise reduction.

5. The white light interferometry 3D reconstruction algorithm of dual filtering of modal decomposition and wavelet transform according to claim 4 is characterized in that: The soft threshold function linearly reduces the wavelet coefficient when its absolute value is greater than a set threshold, and sets it to zero when its absolute value is less than or equal to the set threshold.

6. The white light interferometry 3D reconstruction algorithm of dual filtering of modal decomposition and wavelet transform according to claim 1 is characterized in that: The specific method of extracting the effective area of ​​the interference signal in S5 includes: removing the DC component of the signal, calculating the absolute value of the first-order difference, finding the local maximum point as the center point, and extracting a fixed number of discrete signals from the point forward and backward as the effective area signal.

7. The white light interferometry 3D reconstruction algorithm of dual filtering of modal decomposition and wavelet transform according to claim 1 is characterized in that: When fitting the modulation index in S6, a Gaussian function is used for nonlinear fitting. The characteristic parameters of the Gaussian function are obtained by least square method and are used to construct a smooth envelope curve of the modulation index.

8. The white light interferometry 3D reconstruction algorithm of dual filtering of modal decomposition and wavelet transform according to claim 1 is characterized in that: The coherence peak position in S7 corresponds to the maximum value point of the fitting function in the modulation index curve, and this point is used as the central frame when calculating the initial phase.

9. The white light interferometry 3D reconstruction algorithm of dual filtering of modal decomposition and wavelet transform according to claim 1 is characterized in that: In the above-mentioned S8, the calculation of the three-dimensional height is converted based on the multiplication and division relationship of the central wavelength, the initial phase, the moving step and the number of frames of the zero-point coherence peak position, and the final height reconstruction result is output.

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