A white light interference three-dimensional reconstruction method and device based on lightweight preliminary positioning

Abstract

The application provides a white light interference three-dimensional reconstruction method and device based on a lightweight initial positioning, and the method comprises the following steps: extracting a one-dimensional interference signal along the scanning direction of a pixel based on a white light interference image; performing preprocessing on the one-dimensional interference signal to obtain a weak positioning feature; determining an initial positioning index according to the weak positioning feature; determining an initial absolute height according to a physical scanning step and the initial positioning index; performing local phase calculation on the one-dimensional interference signal to obtain a height correction amount; constructing a plurality of cycle candidate absolute heights according to the initial absolute height, the height correction amount, a white light center wavelength and the periodicity of a phase; and performing discrimination scoring on the plurality of cycle candidate absolute heights to obtain a final absolute height corresponding to the pixel. The initial positioning method has a small amount of calculation, and the dependence on the initial positioning accuracy of the white light interference is significantly reduced.

Description

Technical Field

[0001] This invention relates to a method and apparatus for three-dimensional reconstruction by white light interferometry based on lightweight initial positioning. Background Technology

[0002] White light interferometry is a high-precision three-dimensional measurement method widely used in precision manufacturing, semiconductor inspection, optical component measurement, micro / nano device characterization, and material surface analysis. This method utilizes a low-coherence broadband light source to generate interference signals. By scanning the sample along the vertical direction, it acquires the interference intensity sequence of each pixel at different scanning positions, and then reconstructs the absolute height information of the sample surface based on this sequence.

[0003] In vertical scanning white light interferometry, each pixel acquires a one-dimensional interference signal along the scanning direction. This interference signal can typically be represented as the product of an envelope function and a cosine carrier wave, exhibiting a significant envelope peak near zero optical path difference, accompanied by rapid phase oscillations. Existing 3D reconstruction methods can generally be categorized into envelope methods, phase-shifting methods, and combinations of both.

[0004] Among them, the envelope method has strong absolute positioning capability, but its accuracy is often insufficient due to the limitation of discrete sampling step size; the phase shift method has high subsampling accuracy, but the phase result has a 2π periodicity, which leads to half-wavelength periodicity ambiguity in the absolute height. In order to balance absolute positioning capability and phase accuracy, existing 3D reconstruction technologies generally need to introduce an initial positioning stage.

[0005] Initial positioning refers to the process of roughly locating the envelope peak (i.e., the zero optical path difference position) in the one-dimensional interference signal sequence acquired by the camera using an algorithm. Initial positioning is crucial for three main reasons: First, it resolves 2π phase ambiguity (period ambiguity), providing an "absolute coordinate" reference to lock the true physical height within a specific half-wavelength period range. Second, it provides a computational anchor point for "local phase refinement," as the algorithm only needs to extract a very limited number of frames of data near the initial positioning anchor point to calculate the envelope phase using the local phase shift formula, significantly saving computational resources. Third, it prevents misjudgment of half-wavelength jumps; if the initial positioning deviates too much from the true height, subsequent phase calculations will "misidentify the fringes," leading to severe jump errors in height that are integer multiples of half a wavelength.

[0006] Because initial positioning has a decisive impact on avoiding periodic misjudgments, existing technologies typically employ a "strong initial positioning" strategy. This involves improving initial positioning accuracy through complex envelope filtering, multi-level frequency domain analysis, or fitting, followed by fine positioning using phase-shifting methods near zero optical path difference. For example, patent CN108759709B provides a white light interferometric 3D reconstruction method suitable for surface topography detection, which uses low-pass filtering and quadratic function fitting for initial positioning. However, quadratic function fitting can only produce a symmetrical parabolic shape, and the dispersion of white light interferometry causes the envelope shape to deviate from a symmetrical Gaussian shape, resulting in distortion and peak error. Another example is the master's thesis "Research on High-Precision Topography Restoration Technology Based on White Light Interferometry" (Qing Lekang), which proposes using Fourier transform to extract the envelope and employing non-uniform cubic spline interpolation technology to forcibly improve the coarse positioning accuracy to decimal frames. However, this strategy of simply pursuing ultimate mathematical precision involves a large number of floating-point divisions and matrix inversion operations, which are extremely resource-intensive. Furthermore, it only refines the envelope center at the algorithmic level, but cannot fundamentally eliminate the physical envelope distortion caused by optical diffraction at the step edges. It is evident that existing technologies generally suffer from an over-reliance on high-precision initial positioning. To avoid phase calculations falling into erroneous periods, complex enhancements and precise positioning of the envelope peaks are often required, leading to an overly complex algorithm structure, numerous parameters, and high computational complexity, which is detrimental to real-time applications in high-resolution, large-field-of-view, or online measurement scenarios. Summary of the Invention

[0007] This invention provides a method and apparatus for three-dimensional reconstruction of white light interferometry based on lightweight initial localization, which effectively reduces the computational load of three-dimensional reconstruction of white light interferometry.

[0008] A white-light interferometric 3D reconstruction method based on lightweight initial localization includes: One-dimensional interference signals are extracted along the scanning direction of pixels based on white light interference images; The one-dimensional interference signal is preprocessed to obtain weak localization features; The initial positioning index is determined based on the weak positioning characteristics; Determine the initial absolute height based on the physical scan step size and the initial positioning index; Local phase calculations are performed on the one-dimensional interference signal to obtain the height correction amount; Based on the initial absolute height, height correction amount, white light center wavelength, and phase periodicity, multiple periodic candidate absolute heights are constructed. Multiple candidate absolute heights for each period are evaluated and scored, and the final absolute height corresponding to each pixel is calculated based on the scoring results.

[0009] Furthermore, the one-dimensional interference signal is preprocessed to obtain weak localization features, including: Calculate the average intensity of the one-dimensional interference signal of each pixel along the scanning direction; The one-dimensional interference signal of each pixel is subjected to mean-reduction processing based on the average intensity value to obtain the absolute value signal; The absolute value signal is locally averaged using a first sliding window to obtain weak localization features.

[0010] Furthermore, the one-dimensional interference signal is preprocessed to obtain weak localization features, including: A second sliding window is set up, and the sum of squares of the one-dimensional interference signal intensity of each pixel is calculated along the scanning direction within the second sliding window. The sum of squares is used as the weak localization feature.

[0011] Further, determining the initial location index based on the weak location features includes: The frame containing the pixel with the largest weak localization feature value is located in the scanning direction, and the corresponding frame index is used as the initial localization index.

[0012] Furthermore, the initial absolute height is the product of the physical scan step size and the initial positioning index; The physical scanning step size is one-eighth of the center wavelength of white light.

[0013] Furthermore, local phase calculation is performed on the one-dimensional interference signal to obtain a height correction, including: Based on the initial positioning index, select adjacent sampling point signals from the one-dimensional interference signal; Based on the sampling point signals, extract the sinusoidal correlation component and the cosine correlation component; Using the arctangent function, the local wrapping phase within the preset principal value interval is calculated based on the sinusoidal and cosine correlation components; The height correction amount is calculated based on the local wrapping phase and the center wavelength of the white light.

[0014] Furthermore, based on the initial absolute height, height correction, white light center wavelength, and phase periodicity, multiple periodic candidate absolute heights are constructed, including: Based on the periodicity of the phase, set the range of candidate period parameters; Different candidate period parameters are selected, and the candidate absolute height of the period is calculated based on the initial absolute height, height correction amount, and white light center wavelength. The candidate absolute height of the period is the sum of the product of the candidate period parameter and half the center wavelength of the white light, the initial absolute height, and the height correction amount.

[0015] Furthermore, multiple periodic candidate heights are discriminated and scored, and the final absolute height corresponding to the pixel is calculated based on the scoring results, including: Calculate the deviation between the candidate absolute height of each cycle and the initial absolute height to obtain the initial positioning consistency score of the candidate absolute height of each cycle; The absolute height of the periodic candidate is converted back to the discrete frame index, a preset local window is set, and the local consistency score of each periodic candidate absolute height is calculated based on the one-dimensional interference signal intensity within the local window. Set an empirical threshold scale and calculate the envelope consistency score of each period's candidate absolute height based on the discrete frame index and the initial positioning index; Based on the corresponding current pixel coordinates, find the pixels in the neighborhood and form an effective neighborhood set. Calculate the reference average height in the effective neighborhood set. Calculate the spatial continuity score based on the reference average height and the corresponding periodic candidate absolute height. The initial positioning consistency score, local consistency score, envelope consistency score, and spatial continuity score are weighted and summed to obtain a comprehensive score. The frame with the highest overall score is selected as the optimal candidate frame, and the final absolute height is calculated based on the optimal candidate frame.

[0016] Furthermore, the initial positioning consistency score is the ratio of the negative absolute value of the difference between the periodic candidate absolute height and the initial absolute height to half the center wavelength of white light. The local consistency score is the ratio of the sum of the absolute values ​​of the differences in one-dimensional interference signal intensities between the two frames on either side of the discrete frame index within the preset local window, to the sum of the absolute values ​​of the one-dimensional interference signal intensities on both sides. The envelope consistency score is the ratio of the absolute value of the difference between the discrete frame index and the initial positioning index to the empirical threshold scale. The spatial continuity score is the ratio of the negative absolute value of the difference between the reference average height and the candidate height to half the center wavelength of white light. The final absolute height is the sum of half the center wavelength of white light multiplied by the optimal candidate frame number, the initial absolute height, and the height correction amount.

[0017] A lightweight initial localization-based white light interferometric 3D reconstruction device includes: The signal extraction module extracts one-dimensional interference signals along the scanning direction of pixels based on white light interference images; The preprocessing module is used to preprocess the one-dimensional interference signal to obtain weak localization features; The initial positioning module is used to determine the initial positioning index based on the weak positioning features; The initial height determination module is used to determine the initial absolute height based on the physical scan step size and the initial positioning index; The correction module is used to perform local phase calculation on the one-dimensional interference signal to obtain a high degree of correction. The candidate module is used to construct multiple periodic candidate absolute heights based on the initial absolute height, height correction amount, white light center wavelength, and phase periodicity. The final height determination module is used to discriminate and score multiple periodic candidate absolute heights, and calculate the final absolute height corresponding to the pixel based on the scoring results.

[0018] Furthermore, the preprocessing module preprocesses the one-dimensional interference signal to obtain weak localization features, including: Calculate the average intensity of the one-dimensional interference signal of each pixel along the scanning direction; The one-dimensional interference signal of each pixel is subjected to mean-reduction processing based on the average intensity value to obtain the absolute value signal; The absolute value signal is locally averaged using a first sliding window to obtain weak localization features.

[0019] Furthermore, the preprocessing module preprocesses the one-dimensional interference signal to obtain weak localization features, including: A second sliding window is set up, and the sum of squares of the one-dimensional interference signal intensity of each pixel is calculated along the scanning direction within the second sliding window. The sum of squares is used as the weak localization feature.

[0020] Further, the initial positioning module determines the initial positioning index based on the weak positioning features, including: The frame containing the pixel with the largest weak localization feature value is located in the scanning direction, and the corresponding frame index is used as the initial localization index.

[0021] Furthermore, the initial absolute height is the product of the physical scan step size and the initial positioning index; The physical scanning step size is one-eighth of the center wavelength of white light.

[0022] Furthermore, the correction module performs local phase calculations on the one-dimensional interference signal to obtain a high-level correction, including: Based on the initial positioning index, select adjacent sampling point signals from the one-dimensional interference signal; Based on the sampling point signals, extract the sinusoidal correlation component and the cosine correlation component; Using the arctangent function, the local wrapping phase within the preset principal value interval is calculated based on the sinusoidal and cosine correlation components; The height correction amount is calculated based on the local wrapping phase and the center wavelength of the white light.

[0023] Furthermore, the candidate module constructs multiple periodic candidate absolute heights based on the initial absolute height, height correction amount, white light center wavelength, and phase periodicity, including: Based on the periodicity of the phase, set the range of candidate period parameters; Different candidate period parameters are selected, and the candidate absolute height of the period is calculated based on the initial absolute height, height correction amount, and white light center wavelength. The candidate absolute height of the period is the sum of the product of the candidate period parameter and half the center wavelength of the white light, the initial absolute height, and the height correction amount.

[0024] Furthermore, the final height determination module discriminates and scores multiple periodic candidate heights, and calculates the final absolute height corresponding to the pixel based on the scoring results, including: Calculate the deviation between the candidate absolute height of each cycle and the initial absolute height to obtain the initial positioning consistency score of the candidate absolute height of each cycle; The absolute height of the periodic candidate is converted back to the discrete frame index, a preset local window is set, and the local consistency score of each periodic candidate absolute height is calculated based on the one-dimensional interference signal intensity within the local window. Set an empirical threshold scale and calculate the envelope consistency score of each period's candidate absolute height based on the discrete frame index and the initial positioning index; Based on the corresponding current pixel coordinates, find the pixels in the neighborhood and form an effective neighborhood set. Calculate the reference average height in the effective neighborhood set. Calculate the spatial continuity score based on the reference average height and the corresponding periodic candidate absolute height. The initial positioning consistency score, local consistency score, envelope consistency score, and spatial continuity score are weighted and summed to obtain a comprehensive score. The frame with the highest overall score is selected as the optimal candidate frame, and the final absolute height is calculated based on the optimal candidate frame.

[0025] Furthermore, the initial positioning consistency score is the ratio of the negative absolute value of the difference between the periodic candidate absolute height and the initial absolute height to half the center wavelength of white light. The local consistency score is the ratio of the sum of the absolute values ​​of the differences in one-dimensional interference signal intensities between the two frames on either side of the discrete frame index within the preset local window, to the sum of the absolute values ​​of the one-dimensional interference signal intensities on both sides. The envelope consistency score is the ratio of the absolute value of the difference between the discrete frame index and the initial positioning index to the empirical threshold scale. The spatial continuity score is the ratio of the negative absolute value of the difference between the reference average height and the candidate height to half the center wavelength of white light. The final absolute height is the sum of half the center wavelength of white light multiplied by the optimal candidate frame number, the initial absolute height, and the height correction amount.

[0026] The white light interferometric 3D reconstruction method and apparatus based on lightweight initial localization provided by this invention have at least the following beneficial effects: (1) The initial positioning method with less computation is adopted, which significantly reduces the dependence on the initial positioning accuracy of white light interferometry and eliminates the need for high-complexity precise extraction of the envelope peak; subsequent discrimination is carried out by combining height correction and periodic candidates to ensure the accuracy of height calculation. (2) It retains the subsampling accuracy advantage of the phase method and achieves high-precision three-dimensional reconstruction with low computational complexity; (3) By constructing and judging periodic candidate heights, and taking into account the consistency of initial positioning, local consistency, envelope consistency and spatial continuity, the accuracy of the final absolute height calculation is guaranteed; (4) The algorithm structure is lightweight and suitable for high-resolution, large field of view and online real-time measurement scenarios; (5) The candidate scoring mechanism can be flexibly configured according to the scenario and has strong scalability and engineering adaptability. Attached Figure Description

[0027] Figure 1 This is a flowchart of an embodiment of the white light interferometry 3D reconstruction method based on lightweight initial localization provided by the present invention.

[0028] Figure 2 This is a schematic diagram of an embodiment of the one-dimensional interference signal in the white light interferometry three-dimensional reconstruction method based on lightweight initial positioning provided by the present invention.

[0029] Figure 3 This is a schematic diagram of an embodiment of the local phase calculation in the white light interferometry three-dimensional reconstruction method based on lightweight initial positioning provided by the present invention.

[0030] Figure 4 This is a flowchart of one embodiment of the white light interferometry 3D reconstruction device based on lightweight initial positioning provided by the present invention. Detailed Implementation

[0031] To better understand the above technical solutions, the following will provide a detailed explanation of the technical solutions in conjunction with the accompanying drawings and specific implementation methods.

[0032] refer to Figure 1 In some embodiments, a white light interferometry 3D reconstruction method based on lightweight initial localization is provided, including: S1. Based on the white light interference image, extract the one-dimensional interference signal along the scanning direction of the pixel; S2. Preprocess the one-dimensional interference signal to obtain weak localization features; S3. Determine the initial positioning index based on the weak positioning features; S4. Determine the initial absolute height based on the physical scan step size and the initial positioning index; S5. Perform local phase calculation on the one-dimensional interference signal to obtain the height correction amount; S6. Based on the initial absolute height, height correction amount, white light center wavelength, and phase periodicity, construct multiple periodic candidate absolute heights; S7. Discriminate and score multiple candidate absolute heights for each period, and calculate the final absolute height corresponding to each pixel based on the scoring results.

[0033] Specifically, in step S1, assume there are K frames of white light interference images, where (x,y) represents the pixel coordinates, k represents the scan frame number, and the value of k ranges from [0, K-1]; the physical scan step size of adjacent scan frames is Δz; the center wavelength of the white light is λ0; and the size of the white light interference image is m rows and n columns. For any pixel (x,y), its one-dimensional interference signal intensity along the scanning direction is [I(x,y,0), I(x,y,1)...I(x,y,K-1)], as shown below. Figure 2 As shown, then reconstruct its absolute height using the following steps.

[0034] Further, in step S2, the one-dimensional interference signal is preprocessed to obtain weak localization features, including: S21. Calculate the average intensity of the one-dimensional interference signal of each pixel along the scanning direction; S22. The one-dimensional interference signal of each pixel is subjected to mean-reduction processing based on the average intensity value to obtain the absolute value signal; S23. The absolute value signal is locally averaged using a first sliding window to obtain weak positioning features.

[0035] Specifically, in step S21, the original one-dimensional optical interference signal is superimposed on a strong ambient background light. To accurately extract the energy of the interference fringes, it is first necessary to calculate the average intensity of the one-dimensional interference signal of each pixel along the scanning direction: (1) Among them, I mean (x,y) represents the average intensity of pixel (x,y).

[0036] In step S22, after obtaining the average intensity value, it is subtracted from the original one-dimensional interference signal so that the interference fringes can oscillate perfectly around the zero mark. The absolute value of the signal after the mean is removed is taken to flip all the negative troughs into positive ones, in preparation for envelope extraction.

[0037] The absolute value signal is calculated using the following formula: I abs(x,y,k)=|I(x,y,k)-I mean (x,y)|;(2) Among them, I abs (x,y) represents an absolute value signal.

[0038] Further, in step S23, a first sliding window with a width of W is set, and the absolute value signal is locally averaged along the vertical direction within this window, as shown in the following formula: (3) Where A(x,y,k) is a localization feature.

[0039] This step flattens out the dense, spike-like absolute value stripes and merges them into a gentle, hill-like curve, resulting in the weak localization feature A(x, y, k) of pixel (x, y).

[0040] In step S2, the one-dimensional interference signal is preprocessed to obtain weak localization features, including: A second sliding window is set up, and the sum of squares of the one-dimensional interference signal intensity of each pixel is calculated along the scanning direction within the second sliding window. The sum of squares is used as the weak localization feature.

[0041] Set a second sliding window of size [-r, r], and construct a local energy function E(k) for the one-dimensional interference signal I(x, y,k) along the vertical direction. This function is used to calculate the sum of squares of the one-dimensional interference signal intensity within the second sliding window. (4) The goal of solving for the value of the local energy function E(k) is to find the index of its peak and use it as the initial localization index. Although the values ​​of A(k) and E(k) obtained by the two methods are not the same, the index of the peak is located near the peak of the interference envelope.

[0042] Further, in step S3, determining the initial positioning index based on the weak positioning features includes: The frame containing the pixel with the largest weak localization feature value is located in the scanning direction, and the corresponding frame index is used as the initial localization index.

[0043] Specifically, for the weak localization features A(k) or E(k) extracted in the previous step, the frame index k0 of the point with the largest value in the vertical scanning direction is found and used as the initial localization index. The specific formula is as follows: k0=argmax k∈[0,K-1] {A(x,y,k)};(5) or, k0=argmaxk∈[0,K-1] {E(x,y,k)};(6) The frame index k0 represents the approximate location where the interference energy of the pixel (x, y) is strongest.

[0044] Furthermore, in step S4, the initial absolute height is the product of the physical scan step size and the initial positioning index.

[0045] Specifically, multiplying the initial positioning index k0 by the hardware-preset physical scan step size Δz converts it into the initial absolute height H in physical space. H=k0*△z;(7) The initial absolute height H is not required to reach the final accuracy; it is only required that the actual height is within a finite number of half-wavelength periods in its vicinity.

[0046] Through the above steps, the algorithm defines a rough physical height range for each pixel in the entire image with extremely low computational cost (mainly using low-complexity operations such as addition, subtraction, absolute value, shifting, accumulation, or square accumulation), laying the foundation for subsequent calculations.

[0047] In some embodiments, the physical scan step size is one-eighth of the center wavelength of white light.

[0048] Further, in step S5, local phase calculation is performed on the one-dimensional interference signal to obtain a height correction amount, including: S51. Select adjacent sampling point signals from the one-dimensional interference signal according to the initial positioning index; S52. Extract the sine correlation component and cosine correlation component based on the sampling point signal; S53. Using the arctangent function, calculate the local wrapping phase within the preset principal value interval based on the sinusoidal correlation component and the cosine correlation component; S54. Calculate the height correction amount based on the local wrapping phase and the center wavelength of the white light.

[0049] Specifically, although weak initial localization finds the approximate peak value of the interference envelope of pixel (x, y) (initial localization index k0), this position has a large quantization error due to the limitations of the hardware's discrete scanning step size. Therefore, multiple sampling points are selected around the initial localization index k0 for local phase calculation of the one-dimensional interference signal [I(x,y,0), I(x,y,1)...I(x,y,K-1)]. In this embodiment, a five-step phase shift is used to calculate the local envelope phase and determine the height correction. The specific implementation method is as follows.

[0050] First, it is determined whether the initial positioning index k0 is too close to the beginning or end boundaries of the scan sequence frames. If the initial positioning index k0 is insufficient to support a 5th-order window (i.e., missing the first 2 frames or the last 2 frames), the algorithm will safely exit and mark the pixel as invalid to avoid out-of-bounds crashes.

[0051] Otherwise, in step S51, with the initial positioning index k0 as the absolute center, five adjacent sampling point signals are selected consecutively from the one-dimensional interference signal intensity [I(x,y,0), I(x,y,1)...I(x,y,K-1)], that is, let: I -2 =I(x,y,k0-2); (8) I -1 =I(x,y,k0-1); (9) I0=I(x,y,k0);(10) I1=I(x,y,k0+1);(11) I2=I(x,y,k0+2);(12) Among them, I -2 I -1 I0, I1, and I2 are five sampling point signals, representing the k-th sampling point and the k-th sampling point, respectively. -2 Frame, kth -1 The one-dimensional interference signal intensity of frame k, frame k0, frame k1, and frame k2.

[0052] The physical scan step size Δz of adjacent scan frames is set to one-eighth of the center wavelength λ0 of the white light. In this way, the signals of the 5 sampling points have a precise 90° physical phase shift.

[0053] Further, in step S52, such as Figure 3 As shown, using the phase quadrature demodulation logic of the Hariharan five-step phase shift algorithm, the sinusoidal correlation component A and cosine correlation component B of the extracted pixel (x, y) are calculated: A=2 (I -1 -I1); (13) B=2I0-I -2 -I2; (14) In the above formula, all coefficients involve only addition, subtraction, and multiplication by 2. In low-level digital circuit (RTL) design, the multiplication by 2 operation is directly mapped to an arithmetic left shift by one bit (<<1) hardwired operation with no logic delay or resource consumption, thus eliminating the need for a high-consumption hardware multiplier.

[0054] In step S53, the arctangent function (usually instantiated as a lookup table (LUT) or CORDIC algorithm pipeline in hardware) is used to calculate the local wrapping phase in the preset principal value interval [-π, π]. : (15) Finally, in step S54, the local wrapping phase is converted into the specific physical height correction amount Δh of the pixel (x, y). w : (16) like Figure 3 As shown, the purpose of this step is to extract a high-precision local wrap-around phase near the initial positioning index k0 using the classic 5-step phase shift algorithm, and convert it into a height correction amount, thereby compensating for the error caused by discrete sampling.

[0055] Further, in step S6, based on the initial absolute height, height correction amount, white light center wavelength, and phase periodicity, multiple periodic candidate absolute heights are constructed, including: S61. Set the candidate period parameter range according to the periodicity of the phase; S62. Take different candidate period parameters and calculate the candidate absolute height of the period based on the initial absolute height, height correction amount, and white light center wavelength. The candidate absolute height of the period is the sum of the product of the candidate period parameter and half the center wavelength of the white light, the initial absolute height, and the height correction amount.

[0056] Specifically, in step S61, based on the periodicity of the phase, multiple periodic candidate absolute heights of the pixel (x, y) are constructed: (17) Where p is the candidate period parameter, which is an integer, and the range of the candidate period parameter is set to [-P, P], which can be set by the user. hp is the absolute height of the candidate period when the candidate period parameter is p.

[0057] Assuming the candidate period parameter range is set to [-2, 2], then the following 5 possible candidate absolute heights for the period are listed: (18) (19) (20) ;(twenty one) ;(twenty two) Assuming the candidate period parameter range is set to [-3, 3], then 7 possible candidate absolute heights are listed: ;(twenty three) ;(twenty four) (25) (26) (27) (28) (29) And so on.

[0058] Further, in step S7, multiple candidate absolute heights for each period are discriminated and scored to obtain the final absolute height corresponding to the pixel, including: S71. Calculate the deviation between the candidate absolute height of each cycle and the initial absolute height to obtain the initial positioning consistency score of the candidate absolute height of each cycle. S72. Convert the absolute height of the periodic candidate back to the discrete frame index, set a preset local window, and calculate the local consistency score of each periodic candidate absolute height based on the one-dimensional interference signal intensity within the local window. S73. Set an empirical threshold scale and calculate the envelope consistency score of each period's candidate absolute height based on the discrete frame index and the initial positioning index. S74. Based on the corresponding current pixel coordinates, find the pixels in the neighborhood and form an effective neighborhood set. Calculate the reference average height in the effective neighborhood set. Calculate the spatial continuity score based on the reference average height and the corresponding periodic candidate absolute height. S75. The initial positioning consistency score, local consistency score, envelope consistency score, and spatial continuity score are weighted and summed to obtain a comprehensive score. S76. Select the frame with the highest comprehensive score as the optimal candidate frame, and calculate the final absolute height based on the optimal candidate frame.

[0059] Further, in step S71, the initial positioning consistency score is the ratio of the negative absolute value of the difference between the periodic candidate absolute height and the initial absolute height to half the center wavelength of white light, calculated using the following formula: (30) Among them, J init (p) represents the absolute height h of the periodic candidate. p The corresponding initial positioning consistency score.

[0060] The physical meaning of the initial alignment score is: in the absence of stronger evidence, candidates that are closer to the initial absolute height H have higher priority.

[0061] In step S72, the absolute height of the periodic candidate is converted back to the discrete frame index and a preset local window is set. Within the preset local window, the ratio of the sum of the absolute values ​​of the difference between the one-dimensional interference signal intensities on both sides of the discrete frame index and the sum of the absolute values ​​of the one-dimensional interference signal intensities on both sides is calculated, and the ratio is used as the local consistency score.

[0062] Specifically, the absolute height of the periodic candidate is first converted back to the discrete frame index: (31) Where, k p The absolute height h of the periodic candidate p The corresponding discrete frame index.

[0063] The formula for calculating the local consistency score is as follows: (32) Among them, J signal (p) indicates that the discrete frame index is k. p The local consistency score of the absolute height of the periodic candidate, where L represents the preset local window size and ε represents the minimum value.

[0064] The numerator represents the sum of the absolute values ​​of the differences between the one-dimensional interference signal intensities on both sides of the discrete frame index, and the denominator represents the sum of the absolute values ​​of the one-dimensional interference signal intensities on both sides of the discrete frame index.

[0065] The local signal consistency score characterizes the degree of matching between the absolute height of the periodic candidate and the intensity of the original local one-dimensional interference signal. This score utilizes the symmetry of the signal near the main peak within a preset local window; the more symmetrical the signal, the higher the score. For hardware implementation, a smaller value for L can be chosen to reduce the number of multiplications and additions.

[0066] Further, in step S73, an empirical threshold scale is set, the absolute height of the periodic candidate is converted back to the discrete frame index, and the negative of the ratio of the absolute value of the difference between the discrete frame index and the initial positioning index to the empirical threshold scale is used as the envelope consistency score. The specific calculation formula is as follows: (33) Among them, J env (p) represents the envelope consistency score, W env The empirical threshold scale is expressed by the following formula: (34) The envelope consistency score is used to characterize the degree of matching between the absolute height of the periodic candidate and the empirical threshold scale. If the absolute height of the periodic candidate deviates too much from the empirical threshold scale, the envelope consistency score will decrease.

[0067] Further, in step S74, for the currently processed pixel coordinate (x,y), corresponding pixel points are searched within its neighborhood range to form a neighborhood set. For example, the left point (x, y-1), the upper-left point (x-1, y-1), the directly upper point (x-1, y) and the upper-right point (x-1, y+1) can be selected, and the neighborhood set can be expressed as: S ideal ={(x,y-1),(x-1,y-1),(x-1,y),(x-1,y+1)}; (35) At the actual image boundary, out-of-bounds invalid coordinates must be eliminated, and the effective neighborhood set Nc after boundary truncation is defined as: Nc={(u,v)∈S ideal |0<u<m and 0<v<n}; (36) wherein u and v represent pixel coordinates in the effective neighborhood set Nc.

[0068] Let |Nc| be the number of effective neighborhood points in the effective neighborhood set, obtain the pre-calculated final absolute heights of each pixel point in the effective neighborhood set, calculate a reference average height according to the final absolute heights, take the negative value of the absolute value of the difference between the reference average height and the candidate height, and use the ratio of said negative value to half of the central wavelength of white light as the spatial continuity score.

[0069] According to the traversal order, the left point (x, y-1), the upper-left point (x-1, y-1), the directly upper point (x-1, y) and the upper-right point (x-1, y+1) have all been pre-calculated.

[0070] The spatial continuity score functions to use the surface continuity constraint of the reconstructed neighborhood to suppress erroneous period jumps.

[0071] The reference average absolute height is calculated by the following formula: ; (37) wherein HN represents the reference average absolute height.

[0072] The calculation formula of the spatial continuity score is: ; (38) wherein J spatial (p) represents the spatial continuity score.

[0073] For continuous smooth surfaces, the spatial continuity score can effectively suppress isolated erroneous periods. For step edges, steep slopes or groove regions, this term can be weakened or turned off according to a local gradient threshold to avoid excessive smoothing.

[0074] Further, in step S75, the overall score J(p) is calculated using the following formula: J(p) = w1 * J signal (p)+w2*J init (p)+w3*J env (p)+w4*J spatial (p); (39) Among them, w1, w2, w3, and w4 are non-negative weights, and preferably satisfy w1 + w2 + w3 + w4 = 1. When the sample surface has weak continuity or many edges, w4 can be decreased; when the initial localization features are relatively stable, w2 or w3 can be appropriately increased. Finally, the frame number p* corresponding to the largest comprehensive score J(p) is taken as the optimal candidate frame, that is: p*=argmaxJ(p); (40) Reconstruct the final absolute height of this point: (41) in, This represents the final absolute height of the pixel (x, y) in the optimal candidate frame.

[0075] refer to Figure 4 In some embodiments, a white light interferometry 3D reconstruction device based on lightweight initial localization is provided, comprising: A lightweight initial localization-based white light interferometric 3D reconstruction device includes: The signal extraction module 201 extracts a one-dimensional interference signal along the scanning direction of the pixels based on the white light interference image; Preprocessing module 202 is used to preprocess the one-dimensional interference signal to obtain weak localization features; Initial positioning module 203 is used to determine an initial positioning index based on the weak positioning features; The initial height determination module 204 is used to determine the initial absolute height based on the physical scan step size and the initial positioning index; Correction module 205 is used to perform local phase calculation on the one-dimensional interference signal to obtain a height correction amount; Candidate module 206 is used to construct multiple periodic candidate absolute heights based on the initial absolute height, height correction amount, white light center wavelength, and phase periodicity. The final height determination module 207 is used to discriminate and score multiple periodic candidate absolute heights, and calculate the final absolute height corresponding to the pixel based on the scoring results.

[0076] Furthermore, the preprocessing module 202 preprocesses the one-dimensional interference signal to obtain weak localization features, including: Calculate the average intensity of the one-dimensional interference signal of each pixel along the scanning direction; The one-dimensional interference signal of each pixel is subjected to mean-reduction processing based on the average intensity value to obtain the absolute value signal; The absolute value signal is locally averaged using a first sliding window to obtain weak localization features.

[0077] Furthermore, the preprocessing module 202 preprocesses the one-dimensional interference signal to obtain weak localization features, including: A second sliding window is set up, and the sum of squares of the one-dimensional interference signal intensity of each pixel is calculated along the scanning direction within the second sliding window. The sum of squares is used as the weak localization feature.

[0078] Further, the initial positioning module 203 determines the initial positioning index based on the weak positioning features, including: The frame containing the pixel with the largest weak localization feature value is located in the scanning direction, and the corresponding frame index is used as the initial localization index.

[0079] Furthermore, the initial absolute height is the product of the physical scan step size and the initial positioning index; The physical scanning step size is one-eighth of the center wavelength of white light.

[0080] Furthermore, the correction module 205 performs local phase calculations on the one-dimensional interference signal to obtain a high-level correction amount, including: Based on the initial positioning index, select adjacent sampling point signals from the one-dimensional interference signal; Based on the sampling point signals, extract the sinusoidal correlation component and the cosine correlation component; Using the arctangent function, the local wrapping phase within the preset principal value interval is calculated based on the sinusoidal and cosine correlation components; The height correction amount is calculated based on the local wrapping phase and the center wavelength of the white light.

[0081] Furthermore, candidate module 206 constructs multiple periodic candidate absolute heights based on the initial absolute height, height correction amount, white light center wavelength, and phase periodicity, including: Based on the periodicity of the phase, set the range of candidate period parameters; Different candidate period parameters are selected, and the candidate absolute height of the period is calculated based on the initial absolute height, height correction amount, and white light center wavelength. The candidate absolute height of the period is the sum of the product of the candidate period parameter and half the center wavelength of the white light, the initial absolute height, and the height correction amount.

[0082] Furthermore, the final height determination module 207 discriminates and scores multiple periodic candidate heights, and calculates the final absolute height corresponding to the pixel based on the scoring results, including: Calculate the deviation between the candidate absolute height of each cycle and the initial absolute height to obtain the initial positioning consistency score of the candidate absolute height of each cycle; The absolute height of the periodic candidate is converted back to the discrete frame index, a preset local window is set, and the local consistency score of each periodic candidate absolute height is calculated based on the one-dimensional interference signal intensity within the local window. Set an empirical threshold scale and calculate the envelope consistency score of each period's candidate absolute height based on the discrete frame index and the initial positioning index; Based on the corresponding current pixel coordinates, find the pixels in the neighborhood and form an effective neighborhood set. Calculate the reference average height in the effective neighborhood set. Calculate the spatial continuity score based on the reference average height and the corresponding periodic candidate absolute height. The initial positioning consistency score, local consistency score, envelope consistency score, and spatial continuity score are weighted and summed to obtain a comprehensive score. The frame with the highest overall score is selected as the optimal candidate frame, and the final absolute height is calculated based on the optimal candidate frame.

[0083] Furthermore, the initial positioning consistency score is the ratio of the negative absolute value of the difference between the periodic candidate absolute height and the initial absolute height to half the center wavelength of white light. The local consistency score is the ratio of the sum of the absolute values ​​of the differences in one-dimensional interference signal intensities between the two frames on either side of the discrete frame index within the preset local window, to the sum of the absolute values ​​of the one-dimensional interference signal intensities on both sides. The envelope consistency score is the ratio of the absolute value of the difference between the discrete frame index and the initial positioning index to the empirical threshold scale. The spatial continuity score is the ratio of the negative absolute value of the difference between the reference average height and the candidate height to half the center wavelength of white light. The final absolute height is the sum of half the center wavelength of white light multiplied by the optimal candidate frame number, the initial absolute height, and the height correction amount.

[0084] To evaluate the trade-off between accuracy and computational cost of different white light interferometry 3D reconstruction strategies, this embodiment selects four representative reconstruction algorithms and conducts comparative experiments on a dataset, including the reference method-temporal approximation version, the reference method-true FFT version, the candidate method provided by this invention, and the interpolation FFT method mentioned in the master's thesis in the background technology. The main process and characteristics of each method are shown in Table 1.

[0085] Table 1

[0086] The "candidate method" provided by this invention demonstrates how to achieve high-precision and high-efficiency 3D reconstruction through subsequent correction mechanisms, while allowing for weak initial localization. The values ​​w1=0.40, w2=0.25, w3=0.20, and w4=0.15 were used. The effective root mean square error (RMSE), mean absolute error (MAE), correlation coefficient, and end-to-end processing time of each algorithm were statistically analyzed on the dataset. The results of the comparative experiments are shown in Table 2.

[0087] Table 2

[0088] On the dataset, the candidate method provided by this invention achieves an effective pixel RMSE of 8.982549 and a correlation coefficient of 0.858737, with absolute accuracy superior to the reference method (true FFT version, RMSE 9.058293) and the interpolation FFT method mentioned in the background master's thesis (RMSE 9.064921). Simultaneously, its processing time is only 14.74 s, significantly lower than the true FFT version's 134.36 s and the interpolation FFT method's 160.89 s. This demonstrates that the method provided in this embodiment achieves the optimal trade-off between accuracy and efficiency without relying on complex, high-precision initial localization.

[0089] The white light interferometric 3D reconstruction method and apparatus based on lightweight initial localization provided in the above embodiments have at least the following beneficial effects: (1) The initial positioning method with less computation is adopted, which significantly reduces the dependence on the initial positioning accuracy of white light interferometry and eliminates the need for high-complexity precise extraction of the envelope peak; subsequent discrimination is carried out by combining height correction and periodic candidates to ensure the accuracy of height calculation. (2) It retains the subsampling accuracy advantage of the phase method and achieves high-precision three-dimensional reconstruction with low computational complexity; (3) By constructing and judging periodic candidate heights, and taking into account the consistency of initial positioning, local consistency, envelope consistency and spatial continuity, the accuracy of the final absolute height calculation is guaranteed; (4) The algorithm structure is lightweight and suitable for high-resolution, large field of view and online real-time measurement scenarios; (5) The candidate scoring mechanism can be flexibly configured according to the scenario and has strong scalability and engineering adaptability.

[0090] Although preferred embodiments of the invention have been described, those skilled in the art, upon learning the basic inventive concept, can make other changes and modifications to these embodiments. Therefore, the appended claims are intended to be interpreted as including both the preferred embodiments and all changes and modifications falling within the scope of the invention. Clearly, those skilled in the art can make various alterations and modifications to the invention without departing from its spirit and scope. Thus, if these modifications and modifications of the invention fall within the scope of the claims and their equivalents, the invention is also intended to include these modifications and modifications.

Claims

1. A method for white light interferometric three-dimensional reconstruction based on lightweight initial positioning, characterized in that, include: One-dimensional interference signals are extracted along the scanning direction of pixels based on white light interference images; The one-dimensional interference signal is preprocessed to obtain weak localization features; The initial positioning index is determined based on the weak positioning characteristics; Determine the initial absolute height based on the physical scan step size and the initial positioning index; Local phase calculations are performed on the one-dimensional interference signal to obtain the height correction amount; Based on the initial absolute height, height correction amount, white light center wavelength, and phase periodicity, multiple periodic candidate absolute heights are constructed. The process involves: scoring multiple candidate absolute heights for each period; calculating the final absolute height corresponding to each pixel based on the scoring results; calculating the deviation of each candidate absolute height from the initial absolute height to obtain an initial positioning consistency score for each candidate absolute height; converting the candidate absolute heights back to discrete frame indices; setting a preset local window; calculating the local consistency score for each candidate absolute height within the local window based on the intensity of a one-dimensional interference signal; setting an empirical threshold scale; calculating the envelope consistency score for each candidate absolute height based on the discrete frame index and the initial positioning index; finding neighboring pixels based on the corresponding current pixel coordinates and forming an effective neighborhood set; calculating the reference average height within the effective neighborhood set; and calculating the spatial continuity score based on the reference average height and the corresponding candidate absolute height. The initial positioning consistency score, local consistency score, envelope consistency score, and spatial continuity score are weighted and summed to obtain a comprehensive score. The frame with the highest comprehensive score is selected as the optimal candidate frame, and the final absolute height is calculated based on the optimal candidate frame.

2. The method of claim 1, wherein, The one-dimensional interference signal is preprocessed to obtain weak localization features, including: Calculate the average intensity of the one-dimensional interference signal of each pixel along the scanning direction; The one-dimensional interference signal of each pixel is subjected to mean-reduction processing based on the average intensity value to obtain the absolute value signal; The absolute value signal is locally averaged using a first sliding window to obtain weak localization features.

3. The method of claim 1, wherein, The one-dimensional interference signal is preprocessed to obtain weak localization features, including: A second sliding window is set up, and the sum of squares of the one-dimensional interference signal intensity of each pixel is calculated along the scanning direction within the second sliding window. The sum of squares is used as the weak localization feature.

4. The method of claim 1, wherein, Determining the initial localization index based on the weak localization features includes: The frame containing the pixel with the largest weak localization feature value is located in the scanning direction, and the corresponding frame index is used as the initial localization index.

5. The method according to claim 1 or 4, characterized in that, The initial absolute height is the product of the physical scan step size and the initial positioning index; The physical scanning step size is one-eighth of the center wavelength of white light.

6. The method of claim 1, wherein, Local phase calculation is performed on the one-dimensional interference signal to obtain a height correction, including: Based on the initial positioning index, select adjacent sampling point signals from the one-dimensional interference signal; Based on the sampling point signals, extract the sinusoidal correlation component and the cosine correlation component; Using the arctangent function, the local wrapping phase within the preset principal value interval is calculated based on the sinusoidal and cosine correlation components; The height correction amount is calculated based on the local wrapping phase and the center wavelength of the white light.

7. The method of claim 1, wherein, Based on the initial absolute height, height correction, white light center wavelength, and phase periodicity, multiple periodic candidate absolute heights are constructed, including: Based on the periodicity of the phase, set the range of candidate period parameters; Different candidate period parameters are selected, and the candidate absolute height of the period is calculated based on the initial absolute height, height correction amount, and white light center wavelength. The candidate absolute height of the period is the sum of the product of the candidate period parameter and half the center wavelength of the white light, the initial absolute height, and the height correction amount.

8. The method of claim 1, wherein, The initial positioning consistency score is the ratio of the negative absolute value of the difference between the periodic candidate absolute height and the initial absolute height to half the center wavelength of white light. The local consistency score is the ratio of the sum of the absolute values ​​of the differences in one-dimensional interference signal intensities between the two frames on either side of the discrete frame index within the preset local window, to the sum of the absolute values ​​of the one-dimensional interference signal intensities on both sides. The envelope consistency score is the ratio of the absolute value of the difference between the discrete frame index and the initial positioning index to the empirical threshold scale. The spatial continuity score is the ratio of the negative absolute value of the difference between the reference average height and the candidate height to half the center wavelength of white light. The final absolute height is the sum of half the center wavelength of white light multiplied by the optimal candidate frame number, the initial absolute height, and the height correction amount.

9. A white-light interferometric 3D reconstruction device based on lightweight initial positioning, applicable to the method described in any one of claims 1-8, characterized in that, include: The signal extraction module extracts one-dimensional interference signals along the scanning direction of pixels based on white light interference images; The preprocessing module is used to preprocess the one-dimensional interference signal to obtain weak localization features; The initial positioning module is used to determine the initial positioning index based on the weak positioning features; The initial height determination module is used to determine the initial absolute height based on the physical scan step size and the initial positioning index; The correction module is used to perform local phase calculation on the one-dimensional interference signal to obtain a high degree of correction. The candidate module is used to construct multiple periodic candidate absolute heights based on the initial absolute height, height correction amount, white light center wavelength, and phase periodicity. The final height determination module is used to discriminate and score multiple periodic candidate absolute heights, and calculate the final absolute height corresponding to the pixel based on the scoring results.

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