A method and system for undersampling fly-scanning 3D surface reconstruction based on white light interferometry

Abstract

This invention discloses a method and system for undersampling fly-scan 3D surface reconstruction based on white light interferometry. The method includes: firstly, acquiring continuous fly-scan undersampling signals; secondly, preprocessing the signals and constructing an effective pixel sample set; and finally, using a position-guided undersampling interferometric reconstruction model to perform height reconstruction, thereby generating a complete 3D surface height map. This invention significantly improves reconstruction accuracy and adaptability to complex surfaces, and can be widely applied in fields such as semiconductor testing, precision optical measurement, and 3D reconstruction of industrial microstructures, especially suitable for complex application scenarios requiring rapid measurement of large-depth samples.

Description

Technical Field

[0001] This invention belongs to the field of optical precision measurement and three-dimensional surface topography reconstruction, specifically involving an undersampling fly-scan three-dimensional surface reconstruction method and system based on white light interferometry. Background Technology

[0002] Existing white-light interferometry systems mostly employ piezoelectric ceramic actuators (PZTs) and perform uniform sampling in a step-by-step manner. During the sampling process, each step requires waiting for the mechanical vibration to decay before exposure. While this method ensures the uniformity of sampling, it severely limits the sampling speed; moreover, the stroke of the PZT is typically limited to tens to hundreds of micrometers, making it difficult to meet the complete measurement requirements of samples with large height differences or large areas. Although the continuous fly-scan mode driven by a linear motor can overcome the travel and speed bottlenecks of the piezoelectric ceramic actuator sampling scheme, the linear motor is affected by servo errors and vibrations during actual movement, resulting in non-uniform sampling and introducing significant height reconstruction errors.

[0003] To address the height reconstruction error introduced by non-uniform sampling, existing non-uniform sampling processing algorithms are all designed based on dense sampling. However, in the undersampling scenario of continuous fly-scanning, the number of effective sampling points per pixel is greatly reduced, and signal redundancy is significantly insufficient. Existing methods show a significant degradation in their ability to estimate and compensate for non-uniform position errors, and lack an effective processing mechanism for the simultaneous existence of undersampling and non-uniformity.

[0004] Existing deep learning-based white light interferometry demodulation methods are primarily designed for uniformly sampled white light interferometry data and cannot be directly applied to white light interferometry data that simultaneously exhibits undersampling and non-uniformity.

[0005] Furthermore, white light interference signals are susceptible to environmental vibrations, fluctuations in light source intensity, and surface scattering noise. Rough surfaces, high-reflectivity areas, and defocused areas all generate low-quality interference signals, which significantly reduce the reconstruction quality of 3D surfaces. Existing methods cannot effectively solve the 3D surface reconstruction problem under complex surface scenarios with varying roughness and structural depth. Summary of the Invention

[0006] To address the problems and needs existing in the background technology, this invention proposes a method and system for three-dimensional surface reconstruction based on white light interferometry undersampling fly-scanning. Addressing the non-uniform sampling data caused by manual undersampling settings and driving methods during continuous white light interferometry fly-scanning, this invention reconstructs a complete three-dimensional surface height map by extracting effective pixels and reconstructing the surface height of each effective pixel. The proposed method is adaptable to the requirements of non-uniform undersampling signal processing and compatible with complex surface scenarios with varying roughness and structural depth. It can be widely applied in fields such as semiconductor inspection, precision optical measurement, and three-dimensional reconstruction of industrial microstructures, and is particularly suitable for complex application scenarios requiring rapid measurement of large-depth samples, thus meeting the practical application needs of optical precision manufacturing and semiconductor inspection.

[0007] The technical solution of the present invention is as follows:

[0008] In a first aspect, the present invention proposes an undersampling fly-scan three-dimensional surface reconstruction method based on white light interferometry, the method comprising the following steps:

[0009] S1: Obtain the original white light interferogram sequence and the corresponding axial position sequence of the sample to be tested;

[0010] S2: After preprocessing the original white light interferogram sequence of the sample under test, the local interference signal segments corresponding to each effective pixel are obtained; then, combined with the axial position sequence of the sample under test, an effective pixel sample set is constructed.

[0011] S3: Based on the effective pixel sample set, the pre-trained position-guided undersampling interferometric reconstruction model is used to reconstruct the height of each effective pixel to obtain the surface height value corresponding to each effective pixel.

[0012] S4: Generate a complete three-dimensional surface height map of the sample under test based on the surface height values ​​corresponding to all valid pixels.

[0013] Furthermore, the original white light interferogram sequence is a non-uniformly undersampled white light interferogram signal sequence.

[0014] Further, in step S2, after preprocessing the original white light interferogram sequence of the sample to be tested, local interference signal segments corresponding to each effective pixel are obtained, including:

[0015] The original white light interference signal sequence of each pixel in the original white light interferogram is quality-discriminated, and the pixels are divided into valid pixels and invalid pixels. Then, local window extraction is performed on the original white light interference signal sequence corresponding to each valid pixel to obtain the local interference signal segment containing the main interference fringes corresponding to each valid pixel.

[0016] Further, in step S2, an effective pixel sample set is constructed by combining the axial position sequence of the sample to be tested, including:

[0017] The axial position sequence corresponding to the local interference signal segment of each effective pixel is extracted from the axial position sequence of the sample to be tested. Each effective pixel sample is composed of the local interference signal segment and the axial position sequence corresponding to the local interference signal segment. After traversing and processing all effective pixels, all effective pixel samples are obtained, thus obtaining the effective pixel sample set.

[0018] Furthermore, the location-guided undersampling interferometric reconstruction model includes:

[0019] The first feature extraction module is used to extract features from local interference signal segments;

[0020] The position preprocessing module is used to encode the axial position sequence and align the position feature dimensions.

[0021] The first fusion module is used to perform feature fusion on the outputs of the first feature extraction module and the location preprocessing module;

[0022] A multi-stage residual shrinkage module is used to extract features from the output of the first fusion module;

[0023] The regression module is used to generate single-pixel surface height values ​​based on the features output by the multi-stage residual shrinkage module.

[0024] Furthermore, the multi-stage residual shrinkage module includes multiple residual shrinkage modules connected in sequence, each residual shrinkage module including:

[0025] The second feature extraction module is used to extract the convolutional features input to each residual shrinking module;

[0026] The global information aggregation module is used to aggregate the multi-channel convolutional features extracted by the second feature extraction module to obtain channel statistics.

[0027] The threshold shrinkage module is used to generate channel adaptive thresholds based on channel statistics, expand the channel adaptive thresholds by channel to match the dimensions of the multi-channel convolutional features, and then perform soft threshold shrinkage on the multi-channel convolutional features based on the expanded channel adaptive thresholds to obtain the soft threshold shrunk features for each channel.

[0028] The shortcut mapping module is used to map the input features of the residual shrinking module to shortcut features with the same dimension as the features after multi-channel soft threshold shrinking.

[0029] The second fusion module is used to perform residual fusion of the soft-threshold shrunk features corresponding to each channel with the shortcut features to obtain the output of the residual shrunk module.

[0030] Secondly, this invention proposes an undersampling fly-scan three-dimensional surface reconstruction system based on white light interferometry, the system comprising:

[0031] The data acquisition module is used to acquire the original white light interferogram sequence and the corresponding axial position sequence of the sample under test;

[0032] The effective pixel sample set construction module is used to generate an effective pixel sample set based on the acquired original white light interferogram sequence and the corresponding axial position sequence.

[0033] The pixel surface height reconstruction module is used to reconstruct the height of each effective pixel based on the effective pixel sample set and using a pre-trained position-guided undersampling interferometric reconstruction model to obtain the surface height value corresponding to each effective pixel.

[0034] The results output module is used to generate a complete three-dimensional surface height map of the sample under test based on the surface height values ​​corresponding to all valid pixels.

[0035] Thirdly, the present invention provides a computer device including a memory and a processor, wherein the memory stores a computer program, and the processor executes the computer program to implement the steps of the method described in the first aspect above.

[0036] Fourthly, the present invention provides a computer-readable storage medium having a computer program stored thereon, wherein the computer program, when executed by a processor, implements the steps of the method described in the first aspect above.

[0037] Fifthly, the present invention provides a computer program product comprising a computer program / instructions which, when executed by a processor, implement the steps of the method described in the first aspect above.

[0038] The present invention has the following beneficial effects:

[0039] Hardware-level support for long-stroke high-speed flying sweep and non-uniform sampling error: The continuous flying sweep of the linear motor and the real-time position recording mechanism of the linear grating ruler are adapted to general surface measurement scenarios with long stroke and high-speed continuous scanning. The axial scanning stroke can reach the millimeter to centimeter level, and the measurement speed is significantly improved, which is better than the traditional piezoelectric ceramic driver (PZT) stepping scanning scheme. At the same time, the high-precision relative position label provided by the linear grating ruler provides a hardware foundation for subsequent algorithms to eliminate non-uniform sampling position errors introduced by continuous motion, ensuring reconstruction accuracy and system stability from the hardware level.

[0040] High-precision surface height robust demodulation of non-uniformly sampled interferometric sequences: The position-guided undersampled interferometric reconstruction model uses local interferometric signal segments and corresponding axial position sequences as dual-branch raw inputs. Noise adaptive suppression is achieved through the threshold shrinkage module in the multi-stage residual shrinkage module. The second branch applies Fourier position coding to the axial position sequence, explicitly embedding high-precision relative displacement information between adjacent frames into high-dimensional position features before participating in joint modeling. This achieves high-precision surface height demodulation of any non-uniformly sampled interferometric sequence, avoiding the accumulation of peak position estimation bias and reconstruction height systematic errors caused by the assumption of uniform and equal-interval sampling in traditional methods.

[0041] Pixel-by-pixel confidence quantification and multi-type surface quality assessment: The signal quality discrimination method based on modulation degree outputs pixel-by-pixel continuous modulation degree values ​​and effective / ineffective pixel binary masks, supporting automatic classification and quality assessment of rough surfaces, high reflectivity areas and defocused areas, providing quantitative basis for reliability evaluation of reconstruction results and subsequent detection decisions;

[0042] Key parameter settings and large-area parallel high-efficiency processing: Key parameters such as half-window length and modulation threshold are adaptively calculated or preset based on the light source coherence length, axial step size setting value and surface characteristics, adapting to diverse general surface scenarios with different light sources, different roughness and structural depth. The pixel-by-pixel parallel processing architecture significantly improves the reconstruction processing efficiency of large-area samples.

[0043] Cross-domain universal adaptability and potential for expansion into industrial precision inspection applications: This invention can be extended to fields such as three-dimensional morphology inspection of semiconductor wafers, surface shape measurement of precision optical components, and three-dimensional reconstruction of industrial microstructures and microelectronic packaging structures. It has universal adaptability to surfaces with different roughness, structural depth, and material reflectivity, and has significant engineering value in potential application areas such as quality control in optical precision manufacturing. Attached Figure Description

[0044] Figure 1 This is a flowchart of the method of the present invention.

[0045] Figure 2 This is a schematic diagram of the framework of a continuous aerial scanning data acquisition and processing system.

[0046] Figure 3 This is a schematic diagram of the location-guided undersampling interferometric reconstruction model.

[0047] Figure 4 The results are the reconstruction results of the Hilbert method under the reference working condition; where (a) is the three-dimensional reconstruction result of the step topography of the Hilbert method under the reference working condition, and (b) is the point-by-point error distribution map of the Hilbert method under the reference working condition.

[0048] Figure 5 The images show the reconstruction results of the Wavelet method under the baseline conditions; where (a) is the three-dimensional reconstruction result of the step topography of the Wavelet method under the baseline conditions, and (b) is the point-by-point error distribution diagram of the Wavelet method under the baseline conditions.

[0049] Figure 6 The results are as follows: (a) is the three-dimensional reconstruction result of the step topography of the benchmark undersampled interferometric reconstruction model under the benchmark working condition; (b) is the point-by-point error distribution diagram of the benchmark undersampled interferometric reconstruction model under the benchmark working condition.

[0050] Figure 7 The image shows the reconstruction results of the position-guided undersampling interferometric reconstruction model of the present invention under the reference working condition; where (a) is the three-dimensional reconstruction result of the step topography of the position-guided undersampling interferometric reconstruction model of the present invention under the reference working condition, and (b) is the point-by-point error distribution diagram of the position-guided undersampling interferometric reconstruction model of the present invention under the reference working condition.

[0051] Figure 8 The results show the sensitivity analysis comparison between the present invention and three other methods; where (a) is the curve of the absolute reconstruction deviation of the present invention and the other three methods as a function of SNR, and (b) is the curve of the absolute reconstruction deviation of the present invention and the other three methods as a function of the non-uniformity ratio.

[0052] Figure 9 This is a statistical graph showing the probability density of the actual step size error during continuous fly-sweeping.

[0053] Figure 10 This is a schematic diagram illustrating the evolution of the actual cumulative error trajectory during continuous aerial sweeping.

[0054] Figure 11 The results are the reconstruction results of the Hilbert method under real continuous aerial sweeping conditions; (a) is the three-dimensional reconstruction result of the step topography of the Hilbert method under real continuous aerial sweeping conditions, and (b) is the point-by-point error distribution map of the Hilbert method under real continuous aerial sweeping conditions.

[0055] Figure 12 The images show the reconstruction results of the Wavelet method under real continuous aerial sweeping conditions; where (a) is the three-dimensional reconstruction result of the step topography of the Wavelet method under real continuous aerial sweeping conditions, and (b) is the point-by-point error distribution map of the Wavelet method under real continuous aerial sweeping conditions.

[0056] Figure 13The results are as follows: (a) is the three-dimensional reconstruction result of the step topography of the benchmark undersampled interferometric reconstruction model under real continuous air-scanning conditions, and (b) is the point-by-point error distribution map of the benchmark undersampled interferometric reconstruction model under real continuous air-scanning conditions.

[0057] Figure 14 The images show the reconstruction results of the position-guided undersampling interferometric reconstruction model of the present invention under real continuous air-scanning conditions; where (a) is the three-dimensional reconstruction result of the step morphology of the position-guided undersampling interferometric reconstruction model of the present invention under real continuous air-scanning conditions, and (b) is the point-by-point error distribution map of the position-guided undersampling interferometric reconstruction model of the present invention under real continuous air-scanning conditions.

[0058] In the diagram: 1. Light source, 2. Camera, 3. Mirau objective lens, 4. Linear motor, 5. Linear grating ruler, 6. Sample to be tested, 7. Computer. Detailed Implementation

[0059] The present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments. It should be understood that the specific embodiments described herein are for illustration and explanation only and are not intended to limit the present invention.

[0060] like Figure 1 As shown, the undersampling fly-scan three-dimensional surface reconstruction method based on white light interferometry proposed in this invention includes the following steps:

[0061] S1: Obtain the original white light interferogram sequence and the corresponding axial position sequence of the sample to be tested;

[0062] In one feasible implementation, the original white light interferogram sequence is a non-uniformly undersampled white light interferogram signal sequence.

[0063] The non-uniform undersampled white light interferometric signal sequence was acquired using a linear motor-based measurement platform. For example... Figure 2As shown, the measurement platform includes a linear motor assembly, a linear grating ruler, and a white light interferometer optical assembly. The linear motor assembly replaces the traditional piezoelectric ceramic actuator (PZT) and serves as the axial drive unit of the measurement platform. The linear motor assembly contains a linear motor 4, which drives the linear grating ruler 5 and the white light interferometer optical assembly to move continuously and uniformly along the optical axis. The camera in the white light interferometer optical assembly acquires the original white light interferogram sequence of the sample 6 under sampled at a fixed frame rate. This sequence is the non-uniformly undersampled white light interferometric signal sequence. Simultaneously, the linear grating ruler synchronously records the axial position corresponding to each sampling frame, obtaining the corresponding axial position sequence. The original white light interferogram sequence and the axial position sequence are sent together to the computer 7. The absolute accuracy of the axial position recorded by the linear grating ruler is affected by the zero-point calibration error, but the relative displacement accuracy between adjacent frames is high, meeting the accuracy requirements of relative displacement for surface topography demodulation.

[0064] In this invention, the non-uniformity of the white light interference signal sequence is not artificially set, but is caused by factors such as servo errors and vibrations in the actual movement of the linear motor. The undersampling mode of the white light interference signal sequence is artificially set, and the undersampling mode depends on the axial step size of the measurement platform. The axial step size is adjusted specifically by adjusting the movement speed of the linear motor and the acquisition frame rate of the camera. Specifically, the axial scanning stroke of the linear motor is not less than 1 mm, the axial step size of the measurement platform is set within the range of λ0 / 3 to λ0, where λ0 is the center wavelength of the light source, and the resolution of the linear grating ruler is less than 1 / 10 of the axial step size setting value of the measurement platform.

[0065] The parameters of the measurement platform (such as the movement speed of the linear motor 4, the exposure time and frame rate of the camera 2, etc.) are adjustable, which can adapt to the needs of large stroke scanning from millimeters to centimeters, nanometer-level relative displacement resolution and continuous fly-scan acquisition driven by high-speed camera frame rate.

[0066] This invention sets up a hardware-level synchronization binding mechanism between the camera frame trigger signal and the linear grating ruler, enabling the manual setting of an undersampling acquisition mode under large stroke (millimeters to centimeters) conditions, and synchronously acquiring non-uniform undersampling interference data caused by linear motor servo errors and vibrations, thus breaking through the dual limitations of traditional PZT stroke and stepping scanning speed.

[0067] In one feasible implementation, the optical components of the white light interferometer include a light source 1, a beam splitter prism, a lens, a Mirau objective lens 3, and a camera 2. White light emitted from the light source passes through a first lens and then enters the beam splitter prism. The reflected light from the beam splitter prism passes through the Mirau objective lens and then enters the surface of the sample to be tested. The reflected light from the surface of the sample to be tested passes through the Mirau objective lens and then enters the beam splitter prism. The transmitted light from the beam splitter prism passes through a second lens and then enters the camera. The camera acquires the white light interference signal, thereby outputting a sequence of white light interferograms.

[0068] S2: After preprocessing the original white light interferogram sequence of the sample under test, the local interference signal segments corresponding to each effective pixel are obtained; then, combined with the axial position sequence of the sample under test, an effective pixel sample set is constructed.

[0069] In one feasible implementation, after preprocessing the original white light interferogram sequence of the sample to be tested, local interference signal segments corresponding to each effective pixel are obtained, including:

[0070] The original white light interference signal sequence of each pixel in the original white light interferogram is quality-discriminated, and the pixels are divided into valid pixels and invalid pixels. Then, local window extraction is performed on the original white light interference signal sequence corresponding to each valid pixel to obtain the local interference signal segment containing the main interference fringes corresponding to each valid pixel.

[0071] In one feasible implementation, the original white light interference signal sequence of each pixel in the white light interferogram is quality-discriminated, and the pixels are divided into valid pixels and invalid pixels, including:

[0072] The original white light interference signal sequence of each pixel in the original white light interferogram is subjected to detrending processing to remove low-frequency components of the white light interference background variation. Detrending processing includes, but is not limited to, polynomial fitting and moving average methods.

[0073] Next, for each pixel's detrended white light interference signal sequence, the envelope of the sequence is extracted using the Hilbert transform. Based on the extracted envelope and the original white light interference signal sequence of that pixel, the modulation degree of each pixel is calculated. The formula for calculating the modulation degree mod is as follows:

[0074] mod = max(env) / raw_mean

[0075] Where env is the envelope extracted using the Hilbert transform, and raw_mean is the mean of the original white light interference signal sequence.

[0076] If the modulation degree of a pixel is greater than or equal to a preset threshold, then the pixel is a valid pixel; otherwise, it is an invalid pixel, thus generating a validity mask.

[0077] This invention employs a mechanism that combines envelope extraction using Hilbert transform with modulation threshold determination to dynamically balance the full preservation of effective signals with the complete removal of low-quality signals. This avoids two types of risks: contamination by false height values ​​from rough surfaces, high-reflectivity areas, or out-of-focus areas, and excessive removal leading to too many holes in the height map. The output effective mask provides spatial positioning information for subsequent invalid pixel filling, while the continuous modulation values ​​can serve as a pixel-by-pixel confidence reference for the reconstruction results.

[0078] In one feasible implementation, local window extraction is performed on the original white light interference signal sequence corresponding to each effective pixel to obtain a local interference signal segment containing the main interference fringes corresponding to each effective pixel, including:

[0079] Based on the envelope of each valid pixel, the position of the envelope peak is first located using the centroid method.

[0080] The specific formula for the center-of-mass method is:

[0081]

[0082] in, This represents the location of the envelope peak (i.e., the centroid location). These are discrete position points in the axial position sequence. For position The envelope value, where N is the number of sampling points within the local window. It represents the square of the modulus.

[0083] Next, a symmetrical fixed window is constructed with the envelope peak position as the center. The original white light interference signal sequence of each effective pixel is extracted using this fixed window, thereby obtaining the local interference signal segment containing the main interference fringes corresponding to the effective pixel.

[0084] Fixed window half width The calculation formula is as follows:

[0085]

[0086] in, This is a rounding up operation. Let be the coherence length of the light source. This sets the axial step size. The scaling factor of 0.75 is used to appropriately narrow the number of sampling points corresponding to the theoretical coherence length, so as to completely capture the effective region containing the main interference fringes, while avoiding the introduction of low signal-to-noise ratio regions at both ends of the window to interfere with subsequent processing.

[0087] This window strategy applies globally to all pixels, without adaptively changing the length pixel by pixel, ensuring consistent processing and guaranteeing network input quality from the source.

[0088] Therefore, the local interference signal segment extraction method proposed in this invention can provide a standardized signal sequence with uniform length for subsequent position-guided undersampled interferometric reconstruction models, and is applicable to scenarios with different combinations of light source coherence length and axial step size parameters.

[0089] In one feasible implementation, an effective pixel sample set is constructed by combining the axial position sequence of the sample to be tested, including:

[0090] The axial position sequence corresponding to the local interference signal segment of each effective pixel is extracted from the axial position sequence of the sample to be tested. Each effective pixel sample is composed of the local interference signal segment and the axial position sequence corresponding to the local interference signal segment. After traversing and processing all effective pixels, all effective pixel samples are obtained, thus obtaining the effective pixel sample set.

[0091] S3: Based on the effective pixel sample set, the pre-trained position-guided undersampling interferometric reconstruction model is used to reconstruct the height of each effective pixel to obtain the surface height value corresponding to each effective pixel.

[0092] One feasible implementation method is, for example Figure 3 As shown, the location-guided undersampling interferometric reconstruction model includes:

[0093] The first feature extraction module is used to extract features from local interference signal segments;

[0094] The position preprocessing module is used to encode the axial position sequence and align the position encoding with position feature dimensions.

[0095] The first fusion module is used to perform feature fusion on the outputs of the first feature extraction module and the location preprocessing module, and to explicitly embed the spatial geometric prior of non-uniform sampling into the feature representation.

[0096] A multi-stage residual shrinkage module is used to extract features from the output of the first fusion module;

[0097] The regression module is used to generate single-pixel surface height values ​​based on the features output by the multi-stage residual shrinkage module.

[0098] In one feasible implementation, the first feature extraction module consists of a one-dimensional convolutional layer, a batch normalization layer, and a ReLU activation layer cascaded sequentially.

[0099] In one feasible implementation, the position preprocessing module performs Fourier position encoding on the axial position sequence.

[0100] In one feasible implementation, the first fusion module first sums the features element-wise between the output of the feature extraction module and the output of the location preprocessing module, then performs convolution processing on the summed result, and uses the convolution result as the output of the fusion module.

[0101] In one feasible implementation, the multi-stage residual shrinkage module includes multiple residual shrinkage modules connected in sequence, each residual shrinkage module including:

[0102] The second feature extraction module is used to extract the multi-channel convolutional features input from each residual shrinkage module;

[0103] The global information aggregation module is used to aggregate the multi-channel convolutional features extracted by the second feature extraction module to obtain channel statistics.

[0104] The threshold shrinkage module is used to generate channel adaptive thresholds based on channel statistics, expand the channel adaptive thresholds by channel to match the dimensions of the multi-channel convolutional features, and then perform soft threshold shrinkage on the multi-channel convolutional features based on the expanded channel adaptive thresholds to obtain the soft threshold shrunk features for each channel.

[0105] The shortcut mapping module is used to map the input features of the residual shrinking module to shortcut features with the same dimension as the features after multi-channel soft threshold shrinking.

[0106] The second fusion module is used to perform residual fusion of the soft-threshold shrunk features corresponding to each channel with the shortcut features to obtain the output of the residual shrunk module.

[0107] In one feasible implementation, the regression module includes a connected average pooling layer and a fully connected layer. The average pooling layer is connected to each residual shrinking module in the multi-stage residual shrinking module. The average pooling layer is used to perform global feature aggregation. The fully connected layer is used to regress the single-pixel surface height value based on the result of global feature aggregation.

[0108] The position-guided undersampling interferometric reconstruction model proposed in this invention adopts a dual-branch input fusion architecture. It uses local interferometric signal segments and their corresponding axial position sequences as two raw inputs. Through end-to-end learning, it establishes a mapping relationship between the joint feature representation of these two inputs and the pixel-by-pixel surface height value. Combined with a threshold shrinkage module in a multi-stage residual shrinkage module, it adaptively suppresses noise components and optimizes the height regression output. The second branch applies Fourier position encoding to the axial position sequence, transforming it into a high-dimensional position feature vector before participating in joint modeling. Since the absolute position accuracy of the recorded axial position sequence is affected by zero-point calibration errors, but the relative displacement accuracy between adjacent frames is high, and the essence of surface topography height demodulation relies on this relative displacement information, meaning that the accuracy error in absolute position does not affect the demodulation accuracy. Therefore, the position-guided undersampling interferometric reconstruction model proposed in this invention does not rely on the assumption of uniform and equidistant sampling, and can achieve accurate height demodulation of any non-uniform sampling sequence. This fundamentally breaks through the dependence of traditional methods on uniform sampling structures, ultimately achieving high-precision surface height demodulation of the non-uniform undersampling white light interferometric signal of each pixel.

[0109] S4: Generate a complete three-dimensional surface height map of the sample under test based on the surface height values ​​corresponding to all valid pixels.

[0110] Specifically, for each invalid pixel, the median of the surface height values ​​of the valid pixels within its preset neighborhood is taken and used as the surface height value of the invalid pixel. This median is then combined with the surface height values ​​of all valid pixels to generate a spatially continuous and complete three-dimensional surface height map.

[0111] This invention fully utilizes the spatial correlation of the surface height field, enabling the automated generation of a spatially continuous and complete 3D surface height map without the need for global interpolation model assumptions or manual intervention. Compared to traditional direct zeroing or linear interpolation strategies, the median filling scheme is naturally robust to local isolated noise points and can effectively preserve surface edge and step structure features. It is compatible with standard point cloud and height map file formats and supports direct interface with downstream semiconductor testing, precision optical measurement, and industrial microstructure 3D reconstruction systems.

[0112] The present invention proposes an undersampling fly-scan 3D surface reconstruction system based on white light interferometry, comprising:

[0113] The data acquisition module is used to acquire the original white light interferogram sequence and the corresponding axial position sequence of the sample under test;

[0114] The effective pixel sample set construction module is used to generate an effective pixel sample set based on the acquired original white light interferogram sequence and the corresponding axial position sequence.

[0115] The pixel surface height reconstruction module is used to reconstruct the height of each effective pixel based on the effective pixel sample set and using a pre-trained position-guided undersampling interferometric reconstruction model to obtain the surface height value corresponding to each effective pixel.

[0116] The results output module is used to generate a complete three-dimensional surface height map of the sample under test based on the surface height values ​​corresponding to all valid pixels. It can be directly connected to downstream application systems such as semiconductor testing, precision optical measurement, and three-dimensional reconstruction of industrial microstructures.

[0117] The system of this invention can be equipped with a GPU-accelerated computing platform and a general-purpose deep learning inference runtime environment, supporting multi-pixel parallel batch processing to meet the high-speed reconstruction requirements of large-area samples. The system integrates an effective pixel sample set construction module, a pixel surface height reconstruction module, and a result output module, specifically including three methods: a modulation-based signal quality discrimination method, an envelope square centroid peak location method, and a position-guided undersampling interferometric reconstruction model inference engine. The system can dynamically and automatically calculate the symmetrical fixed window half-window length based on the input configuration of the light source coherence length and axial step size settings, and dynamically allocate effective pixel processing resources according to the pixel-by-pixel modulation determination results, adapting to surface measurement scenarios with different roughness and structural depths without manual parameter adjustment.

[0118] To eliminate the interference of complex errors that are difficult to decouple in physical experiments, this invention constructs a controlled white light interferometry non-uniform sampling simulation environment to quantitatively evaluate the robustness boundary of the model under specific physical perturbations.

[0119] In the simulation test platform, an interference signal generation model was established based on the nominal properties of the physical instrument. The benchmark test parameters were configured as follows: the center wavelength of the light source was set to 570 nm (corresponding to the near-Gaussian spectral distribution range of 520–620 nm), the nominal axial sampling step size was 300 nm, and the step height was 1.5. To simulate the dynamic disturbance during fly-scan measurement, non-ideal physical constraints were injected into the benchmark conditions: a 5% step size non-uniformity error was introduced, and Gaussian white noise was superimposed to set the signal-to-noise ratio (SNR) to 40 dB.

[0120] Under the aforementioned benchmark conditions, the position-guided undersampling interferometric reconstruction model provided by this invention is compared and tested with the traditional Hilbert method, the Wavelet method, and the benchmark undersampling interferometric reconstruction model.

[0121] The Hilbert method and the Wavelet method are classic algorithms in this field. They strictly rely on the assumption of equal interval sampling. The specific implementation scheme in this embodiment is as follows: First, the white light interferogram sequence with non-uniform error and the axial position sequence are resampled to a uniform grid with a nominal step size (300 nm) by linear interpolation. Then, the Hilbert transform and wavelet transform are performed respectively to extract the signal envelope. The centroid method is then used to extract the envelope peak value, and the height is calculated.

[0122] The baseline undersampled interferometric reconstruction model is formed by removing the explicit position-guided branch from the position-guided undersampled interferometric reconstruction model; that is, it uses only the white light interferogram sequence as a single input, while maintaining the same structure in other aspects. It also uses the same training data as the position-guided undersampled interferometric reconstruction model.

[0123] The reconstruction results of the above methods are as follows: Figure 4 (a) and Figure 4 (b) Figure 5 (a) and Figure 5 (b) Figure 6 (a) and Figure 6 (b) Figure 7 (a) and Figure 7 As shown in (b), the comparative data are shown in Table 1.

[0124] Table 1. Test results of the method of the present invention and other methods under simulated baseline conditions.

[0125]

[0126] Test results show that the root mean square error (RMSE) of the step reconstruction of the position-guided undersampling interferometric reconstruction model is 14.4 nm, and the roughness of the platform region is Sa = 3.6 nm and Sq = 4.5 nm, which is significantly better than the traditional Hilbert method (RMSE 117.2 nm), the Wavelet method (RMSE 95.0 nm), and the benchmark undersampling interferometric reconstruction model (RMSE 18.9 nm). This verifies that under the simulation conditions of undersampling and step size perturbation coupling, the position-guided undersampling interferometric reconstruction model can effectively constrain aliasing error, providing a feasible basis and theoretical accuracy reference for generalization to real-world scenarios.

[0127] To further investigate the robustness of the method of this invention under extreme working conditions, this embodiment performs univariate independent scans on signal-to-noise ratio and step size non-uniformity, respectively. The comparison results of each method are as follows: Figure 8 (a) and Figure 8 As shown in (b). It can be seen from the figure that:

[0128] Non-uniform sampling error suppression capability: When the step size non-uniformity increases from 5% to 10%, the performance of the baseline undersampled interferometric reconstruction model without a position channel degrades significantly, with its absolute reconstruction deviation doubling from 18.9 nm to 37.8 nm; while the absolute reconstruction deviation of the position-guided undersampled interferometric reconstruction model of this invention only slightly increases to 21.0 nm. This proves that the Fourier position encoding mechanism can effectively alleviate the error accumulation problem caused by spatial sampling irregularities.

[0129] Improved robustness under high-noise conditions: When the signal-to-noise ratio (SNR) drops to a harsh 20dB, although the reconstruction error of all methods inevitably increases, the position-guided undersampling interferometric reconstruction model of this invention maintains the most controllable performance degradation rate. This indicates that prior information on the sampling position can effectively constrain the solution space under high-noise conditions, ensuring reconstruction reliability under harsh conditions.

[0130] The above controlled sensitivity analysis based on independent physical variables demonstrates that the dual-branch architecture adopted in this invention, by Fourier encoding the actual physical displacement information and explicitly embedding it into the model representation layer, completely breaks the data dependence of traditional networks on equidistant step-size sampling sequences. This invention fundamentally decouples and eliminates phase demodulation errors caused by dynamic mechanical disturbances, possessing extremely high theoretical upper limits and generalization capabilities, and can provide underlying algorithmic support for the high-tolerance operation of subsequent real-world physical fly-scan systems.

[0131] The present invention also performs white light interference non-uniform sampling and three-dimensional reconstruction on actual samples under fly-scan measurement.

[0132] A white light interferometer equipped with a continuous flying sweep platform with a linear motor and a linear grating ruler was used. The key configuration parameters are shown in Table 2.

[0133] Table 2 Key Configuration Parameters of the Acquisition Hardware

[0134]

[0135] The specific steps are as follows:

[0136] First, the camera frame trigger and linear grating ruler hardware synchronization interface of the hardware acquisition module is invoked. Linear motor motion commands and camera exposure parameters are input, and the frame trigger delay compensation and linear grating ruler zero-position calibration value are set. During the continuous movement of the linear motor, the linear grating ruler records the actual axial position of each frame in real time and writes it to a text file. Figure 9 The measured single-step error distribution ranges from -7% to +8%. Figure 10 The cumulative error shows a quasi-periodic fluctuation as the number of scan steps increases; the output frame-by-frame interferometric image sequence (e.g., .tiff format) and the corresponding measured position file complete synchronous binding dataset are used to obtain the non-uniform undersampled white light interferometric signal sequence and the corresponding complete axial position sequence.

[0137] Read in all frames of interferometric images, construct a three-dimensional interferometric intensity matrix of height × width × number of frames, and perform Hilbert transform envelope extraction and modulation index calculation. Based on the surface material and roughness of the measured surface, a preset modulation index judgment threshold mod_threshold is set, and the validity is judged pixel by pixel. The valid / invalid pixel binary mask valid_mask and the pixel-by-pixel continuous modulation index value matrix mod_map are output. Invalid pixels with low modulation index (such as local surface occlusion, strong reflection saturation and severely out-of-focus areas) and their corresponding axial position sequences do not participate in subsequent height demodulation. They are only replaced by the median of the height values ​​of valid pixels within a preset neighborhood in the final reconstruction step.

[0138] For special scenarios where the bat wing effect is obvious or the overall local modulation is low in the step edge area, a multi-frame averaging noise reduction preprocessing step can be adopted. By performing sliding mean filtering on the interferometric images of adjacent frames, the signal-to-noise ratio in the edge area can be improved, and the bat wing amplitude and the proportion of invalid pixels can be further reduced.

[0139] Then, the centroid method is used to locate the envelope peak for all valid pixels. A symmetrical fixed window of 2×half_win+1 frame length is extracted with the nearest integer frame corresponding to the centroid position as the center. This yields the local interference signal segment containing the main interference fringes and the corresponding local axial position sequence, which are used as the standardized dual-branch explicit input for position-guided undersampled interferometric reconstruction model inference.

[0140] Then, the position-guided undersampling interferometric reconstruction model inference engine is run again, outputting the single-pixel surface height values ​​of all valid pixels, which are then converged into an initial surface height prediction matrix; the batch size is automatically allocated according to the GPU memory, supporting multi-pixel parallel inference.

[0141] Finally, based on the validity mask, all invalid pixel positions are located, and automatic replacement is performed by filling with the median height value of the valid pixels within the preset neighborhood range to generate a spatially continuous complete 3D surface height map; the 3D surface height map, modulation map and binary validity mask are exported and stored as a whole; if it is necessary to connect to the downstream analysis system, it can be exported to .mat, .csv or .tiff formats via the standard format conversion interface;

[0142] The training dataset for the location-guided undersampling interferometric reconstruction model is constructed using densely sampled uniform signals that have undergone downsampling. The preparation process for the training dataset is as follows:

[0143] A PZT stepping method was used to perform dense, uniform axial scanning on a standard stepped sample, covering a step height range of 50 nm to 5000 nm, acquiring pixel-by-pixel white light interference signal sequences. Wavelet transform envelope extraction was performed on the dense, uniform sampling sequences, and the axial coordinates corresponding to the envelope peaks were used as the true height labels. Finally, displacement perturbations conforming to the measured step size error distribution of a linear motor were introduced into the dense sampling sequences to perform downsampling, simulating the non-uniform sampling state under continuous fly-scan conditions. The dense sampling sequences with added displacement perturbations, together with the true height label sequences, formed the training dataset.

[0144] The training dataset is divided into training and validation sets in an 8:2 ratio, with a batch size of 32, a maximum number of iterations of 20, and a learning rate of 0.0008. To enhance the model's generalization ability and prevent overfitting, weight decay (L2 regularization) and an early stopping mechanism are introduced. Standard mean squared error (MSE) is used as the loss function. The model is pre-trained using the training set for location-guided undersampling interferometric reconstruction, and the trained model weights are directly loaded and used during the inference phase.

[0145] In the continuous fly-scan 3D reconstruction test scenario of the coated step sample (measured height 0.5012 μm by white light interferometer), the reconstruction results of each scheme are as follows: Figure 11 (a) and Figure 11 (b) Figure 12 (a) and Figure 12 (b) Figure 13 (a) and Figure 13 (b) Figure 14 (a) and Figure 14 As shown in (b), the comparative data are shown in Table 3.

[0146] Table 3 Test results of the method of the present invention and other methods on actual coating steps

[0147]

[0148] As can be seen from the graphs and tables:

[0149] Accuracy: The absolute deviation of the step reconstruction method of this invention is only 6.7nm, and the roughness of the plateau region is Sa=6.5nm and Sq=9.2nm, which is significantly better than the traditional Hilbert (deviation 114.1nm), Wavelet (deviation 122.0nm) and the benchmark undersampling interferometric reconstruction model (deviation 14.9nm) methods. This verifies that the robustness of the system comes from the structural design of the physical anchoring mechanism rather than data memory-based fitting, and achieves reconstruction accuracy at the level of dense step scanning while maintaining the high-speed advantage of fly-scanning.

[0150] Time efficiency: Compared with the traditional PZT step-dense sampling scheme, this invention improves the overall measurement and reconstruction efficiency by more than an order of magnitude through a triple-synergistic acceleration of undersampling strategy (axial step size increased by 6-10 times), continuous sweeping by linear motor (eliminating the 20-50ms mechanical stabilization wait per step) and fixed window local inference, which can effectively support the online rapid detection needs of large batches of samples.

[0151] Stability: Batch validation on multiple fly-scan test datasets covering different step heights, scanning speeds, and positional error distributions shows that the reconstruction results of the present invention are consistently superior to the comparative methods. The simulation and experimental results of the present invention are in high agreement, demonstrating the strong generalization ability and high stability of the present invention in dealing with variable testing environments and different types of errors.

[0152] Measurable depth range: Due to the deformation of piezoelectric ceramics, the axial scanning stroke of traditional PZT drive solutions is typically only a few hundred degrees. This invention uses a linear motor drive, and the axial travel can be extended to the order of several millimeters to tens of millimeters, increasing the scanning range by about one to two orders of magnitude. This enables the system to have the ability to measure the complete morphology of complex surface structures such as deep trenches, micropores and large elevation differences, breaking through the fundamental travel bottleneck of traditional white light interferometers in the detection of deep samples.

[0153] Surface type adaptability: This invention effectively adapts to various surface types with significant differences in reflectivity through an adjustable modulation threshold and a median filling mechanism for invalid pixel neighborhoods, including coated smooth surfaces, engineered rough surfaces, and locally occluded areas. After automatic filling of invalid pixel areas, the 3D reconstruction results maintain spatial continuity without requiring modification of the core algorithm process for different surface types.

[0154] Output availability: The complete 3D surface height map output by this invention clearly shows the height uniformity and edge sharpness of the upper and lower platform areas of the step. Simultaneously, the modulation map and effective pixel mask are output as auxiliary information for reconstruction confidence, providing highly reliable 3D morphological data support for step height calibration, surface quality evaluation and process monitoring.

[0155] In summary, the method and system proposed in this invention can be extended to scenarios such as online detection of the three-dimensional morphology of semiconductor wafer microstructures and large-scale surface shape measurement of precision optical components. Only the linear motor speed, camera frame rate, light source center wavelength, and modulation determination threshold need to be adjusted, without changing the core processing flow. This provides high-speed, high-precision, long-stroke, and multi-type surface compatible general three-dimensional reconstruction technology support for the fields of optical precision manufacturing quality control and online detection of advanced semiconductor packaging.

Claims

1. A method for undersampling fly-scanning three-dimensional surface reconstruction based on white light interferometry, characterized in that, Includes the following steps: S1: Obtain the original white light interferogram sequence and the corresponding axial position sequence of the sample to be tested; S2: After preprocessing the original white light interferogram sequence of the sample under test, the local interference signal segments corresponding to each effective pixel are obtained; then, combined with the axial position sequence of the sample under test, an effective pixel sample set is constructed. S3: Based on the effective pixel sample set, the pre-trained position-guided undersampling interferometric reconstruction model is used to reconstruct the height of each effective pixel to obtain the surface height value corresponding to each effective pixel. S4: Generate a complete three-dimensional surface height map of the sample under test based on the surface height values ​​corresponding to all valid pixels.

2. The undersampling fly-scan three-dimensional surface reconstruction method based on white light interferometry according to claim 1, characterized in that, The original white light interferogram sequence is a non-uniformly undersampled white light interferogram signal sequence.

3. The undersampling fly-scan three-dimensional surface reconstruction method based on white light interferometry according to claim 1, characterized in that, In step S2, after preprocessing the original white light interferogram sequence of the sample under test, local interference signal segments corresponding to each effective pixel are obtained, including: The original white light interference signal sequence of each pixel in the original white light interferogram is quality-discriminated, and the pixels are divided into valid pixels and invalid pixels. Then, local window extraction is performed on the original white light interference signal sequence corresponding to each valid pixel to obtain the local interference signal segment containing the main interference fringes corresponding to each valid pixel.

4. The undersampling fly-scan three-dimensional surface reconstruction method based on white light interferometry according to claim 1, characterized in that, In step S2, an effective pixel sample set is constructed by combining the axial position sequence of the sample to be tested, including: The axial position sequence corresponding to the local interference signal segment of each effective pixel is extracted from the axial position sequence of the sample to be tested. Each effective pixel sample is composed of the local interference signal segment and the axial position sequence corresponding to the local interference signal segment. After traversing and processing all effective pixels, all effective pixel samples are obtained, thus obtaining the effective pixel sample set.

5. The undersampling fly-scan three-dimensional surface reconstruction method based on white light interferometry according to claim 1, characterized in that, The location-guided undersampling interferometric reconstruction model includes: The first feature extraction module is used to extract features from local interference signal segments; The position preprocessing module is used to encode the axial position sequence and align the position feature dimensions. The first fusion module is used to perform feature fusion on the outputs of the first feature extraction module and the location preprocessing module; A multi-stage residual shrinkage module is used to extract features from the output of the first fusion module; The regression module is used to generate single-pixel surface height values ​​based on the features output by the multi-stage residual shrinkage module.

6. The undersampling fly-scan three-dimensional surface reconstruction method based on white light interferometry according to claim 5, characterized in that, The multi-stage residual shrinkage module includes multiple residual shrinkage modules connected in sequence, and each residual shrinkage module includes: The second feature extraction module is used to extract the convolutional features input to each residual shrinking module; The global information aggregation module is used to aggregate the multi-channel convolutional features extracted by the second feature extraction module to obtain channel statistics. The threshold shrinkage module is used to generate channel adaptive thresholds based on channel statistics, expand the channel adaptive thresholds by channel to match the dimensions of the multi-channel convolutional features, and then perform soft threshold shrinkage on the multi-channel convolutional features based on the expanded channel adaptive thresholds to obtain the soft threshold shrunk features for each channel. The shortcut mapping module is used to map the input features of the residual shrinking module to shortcut features with the same dimension as the features after multi-channel soft threshold shrinking. The second fusion module is used to perform residual fusion of the soft-threshold shrunk features corresponding to each channel with the shortcut features to obtain the output of the residual shrunk module.

7. A three-dimensional surface reconstruction system based on white light interferometry and undersampling, characterized in that, include: The data acquisition module is used to acquire the original white light interferogram sequence and the corresponding axial position sequence of the sample under test; The effective pixel sample set construction module is used to generate an effective pixel sample set based on the acquired original white light interferogram sequence and the corresponding axial position sequence. The pixel surface height reconstruction module is used to reconstruct the height of each effective pixel based on the effective pixel sample set and using a pre-trained position-guided undersampling interferometric reconstruction model to obtain the surface height value corresponding to each effective pixel. The results output module is used to generate a complete three-dimensional surface height map of the sample under test based on the surface height values ​​corresponding to all valid pixels.

8. A computer device comprising a memory and a processor, wherein the memory stores a computer program, characterized in that, When the processor executes the computer program, it implements the steps of the undersampling fly-scan three-dimensional surface reconstruction method based on white light interferometry as described in any one of claims 1 to 6.

9. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by the processor, it implements the steps of the undersampling fly-scan three-dimensional surface reconstruction method based on white light interferometry as described in any one of claims 1 to 6.

10. A computer program product comprising a computer program / instructions, characterized in that, When the computer program / instruction is executed by the processor, it implements the steps of the undersampling fly-scan three-dimensional surface reconstruction method based on white light interferometry as described in any one of claims 1 to 6.

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