A white light interferometric image processing method based on deep learning

Abstract

This invention discloses a deep learning-based method for processing white light interferometric images, specifically including: S1, acquiring an interferometric image sequence and performing normalization processing; S2, performing fringe analysis on the interferometric image sequence to obtain a fringe direction information set and a fringe coherence information set; S3, inputting the interferometric image sequence into a normalized isovariant convolutional network, performing isovariant convolution operations under the constraint of fringe direction information, and generating isovariant feature maps and direction confidence parameters; S4, constructing a frequency domain update weight set based on the fringe direction information set, the fringe coherence information set, and the direction confidence parameters; S5, inputting the isovariant feature maps into a Fourier neural operator network and introducing the frequency domain update weight set; S6, outputting the fringe reconstruction result or phase distribution result and performing direction confidence constraints; S7, generating a white light interferometric morphology result based on the fringe reconstruction result or phase distribution result. This invention integrates isovariant direction and frequency domain operators to achieve stability.

Description

Technical Field

[0001] This invention relates to the fields of optical precision measurement and artificial intelligence technology, and in particular to a white light interferometric image processing method based on deep learning. Background Technology

[0002] White light interferometry is a commonly used optical precision measurement technique that obtains the morphology of the measured surface by analyzing the sequence of interference images formed by the change of interference fringes with optical path length. This technique is widely used in precision machining inspection, microstructure measurement, and surface quality assessment. During white light interferometry, the measurement system typically acquires multiple interference images that vary with the scanning position and generates corresponding height or phase information based on the analytical results of the interference fringe structure.

[0003] In existing technologies, the processing of white light interferometric images is mostly based on fixed physical models and analytical procedures, such as morphology reconstruction through fringe envelope localization, phase extraction, or frequency domain analysis. These methods can obtain usable results under the conditions of continuous interference fringes, stable contrast, and controlled noise levels. However, in actual measurement processes, interference images are often affected by factors such as noise interference, changes in fringe direction, local fringe breaks, and complex surface morphology, resulting in obvious spatial inconsistencies in the fringe structure.

[0004] Meanwhile, traditional image processing methods typically perform analytical operations on interference images within a unified coordinate system, lacking the ability to explicitly model changes in fringe direction, which easily leads to analytical instability when the fringe orientation changes. Furthermore, existing methods update different frequency components in a relatively fixed manner during processing, making it difficult to tailor frequency domain features to the spatial distribution characteristics of the fringe structure.

[0005] In recent years, deep learning technology has been widely used in the field of image processing. However, when applied directly to white light interferometric image processing, it still faces problems such as insufficient modeling of fringe direction consistency and lack of structural constraints in frequency domain feature updates. Therefore, how to introduce a processing mechanism that can characterize the relationship between fringe direction features and frequency domain structure in white light interferometric image processing remains an unsolved technical problem. Summary of the Invention

[0006] One objective of this invention is to propose a deep learning-based white light interference image processing method. This invention introduces a fringe direction modeling mechanism based on normalized isovariant convolution and a frequency domain update weight modulation model based on Fourier neural operators. It performs feature extraction and frequency domain mapping update under direction consistency constraints on white light interference image sequences, and constructs a continuous analytical processing flow oriented towards interference fringe structures. It has the advantages of strong fringe analytical consistency, high frequency domain mapping stability, and good continuity of morphological results.

[0007] A deep learning-based white light interferometry image processing method according to an embodiment of the present invention includes the following steps:

[0008] S1. Acquire the interference image sequence obtained by white light interferometry and perform normalization processing on the interference image sequence;

[0009] S2. Perform fringe analysis on the normalized interference image sequence to obtain the fringe direction information set and the fringe coherence information set;

[0010] S3. Input the interference image sequence into a canonical isovariant convolutional network. The canonical isovariant convolutional network constructs a local canonical field based on the fringe direction information and performs isovariant convolution operations under the constraints of the canonical field. At the same time, it generates a set of orientation distribution parameters and orientation confidence parameters, and outputs isovariant feature maps.

[0011] S4. Based on the fringe direction information set, the fringe coherence information set, and the direction confidence parameter, construct a frequency domain update weight set;

[0012] S5. Input the equivariant feature map into the Fourier neural operator network, and introduce the frequency domain update weight set during the frequency domain feature update process;

[0013] S6. The Fourier neural operator network outputs the stripe reconstruction result or phase distribution result. During the output process, constraints are applied to the update amplitude between spatial positions based on the direction confidence parameter.

[0014] S7. Generate and output white light interference morphology results based on fringe reconstruction results or phase distribution results.

[0015] Optionally, S2 specifically includes:

[0016] In the normalized interferometric image sequence, the image is locally divided using fixed spatial windows. Within each spatial window, the gradient components of pixel grayscale in the horizontal and vertical directions are calculated to form a set of gradient vectors. Local statistical operations are performed on the gradient vector set to calculate the principal direction vector within the corresponding spatial window. The principal direction vector is mapped to fringe direction information, forming a set of fringe direction information at the image spatial location. Within the same spatial window, the projection amplitude of the gradient vector set onto the principal direction vector is aggregated to calculate the fringe intensity distribution value. The fringe intensity distribution value is subjected to a consistency measurement operation within the spatial window to generate a set of fringe coherence information corresponding to the spatial location.

[0017] Optionally, S3 specifically includes:

[0018] The standardized interferometric image sequence is input into the input layer of a canonical equivariant convolutional network according to its spatial location, and a set of fringe direction information is associated with each spatial location in the input layer. In the first processing stage of the canonical equivariant convolutional network, a local canonical field corresponding to the spatial location is constructed at each spatial location based on the fringe direction information set. The local canonical field is determined by the fringe direction information to determine the reference direction and forms a consistent local coordinate relationship within the spatial window. After the local canonical field is constructed, the standardized interferometric image sequence is aligned in the corresponding local canonical field, and the image data within the same spatial window is arranged in the canonical coordinate system. In the canonical coordinate system, equivariant convolution is performed on the aligned image data. During the equivariant convolution operation, the convolution kernel parameters are updated with orientation alignment under the constraint of the local canonical field, forming an intermediate feature map consistent with the local canonical field. After the intermediate feature map is generated, statistical operations are performed on the numerical distribution of the equivariant convolution response in several directional channels at each spatial location to generate a set of orientation distribution parameters. The statistical operations are performed on the equivariant convolution response values ​​in different directional channels at the same spatial location, performing sorting, differencing, aggregation, and normalization.

[0019] While generating the set of orientation distribution parameters, a consistency calculation is performed on the numerical stability of the set of orientation distribution parameters within the spatial window to form orientation confidence parameters that correspond one-to-one with spatial locations. After generating the set of orientation distribution parameters and orientation confidence parameters, the intermediate feature map, the set of orientation distribution parameters, and the orientation confidence parameters are combined in the channel dimension to form a joint feature representation. The joint feature representation is used as the output of the canonical isovariant convolutional network, maintaining a consistent mapping relationship with the input interferometric image sequence in the spatial location dimension, and outputting the isovariant feature map, the set of orientation distribution parameters, and the orientation confidence parameters.

[0020] Optionally, the coordinate alignment operation in step S3 specifically includes:

[0021] At each spatial location, the corresponding direction vector in the fringe direction information set is read, and the direction vector is used as the principal axis direction of the local normalized field. At the same spatial location, auxiliary axis directions orthogonal to the principal axis direction are generated based on the principal axis direction, forming a two-dimensional normalized coordinate axis set. After the normalized coordinate axis set is established, a local spatial window centered on the spatial location is determined, and the original image coordinate position is recorded within the local spatial window. A coordinate transformation operation is performed on the original image coordinate position within the local spatial window to map the original image coordinates to the coordinate system defined by the normalized coordinate axis set. After the coordinate transformation is completed, the image data within the local spatial window is rearranged according to the coordinate order under the normalized coordinate system to form an image data block under the normalized coordinate system. The image data block under the normalized coordinate system is then output.

[0022] Optionally, the numerical stability consistency calculation in step S3 specifically includes:

[0023] At each spatial location, the set of orientation distribution parameters obtained by the normalized isovariant convolution operation is read; at the same spatial location, the set of orientation distribution parameters is numerically sorted along the orientation dimension to form an ordered orientation response sequence; in the ordered orientation response sequence, the numerical difference sequence between adjacent orientation responses is calculated; in the difference sequence, all difference values ​​are aggregated to form the orientation stability value corresponding to the spatial location; within the spatial location dimension, the orientation stability value is normalized to form an orientation confidence parameter that corresponds one-to-one with the spatial location.

[0024] Optionally, S4 specifically includes:

[0025] A correspondence is established between the fringe direction information set, the fringe coherence information set, and the direction confidence parameter in the spatial location dimension. Fringe direction information is read at each spatial location and converted into a direction index in the frequency dimension. The corresponding frequency component set is selected according to the direction index in the frequency dimension. The fringe coherence information value corresponding to the spatial location is read from the frequency component set and written into the weight position of each frequency component. The direction confidence parameter is read synchronously, and confidence modulation is performed on the frequency component weights. The modulated frequency component weights are normalized in the frequency dimension. The normalized frequency component weights corresponding to each spatial location are arranged according to the spatial location dimension and the frequency dimension to form a frequency domain update weight set.

[0026] Optionally, S5 specifically includes:

[0027] S51. Input the output isovariant feature maps into the input layer of the Fourier neural operator network in spatial order.

[0028] S52. In the Fourier neural operator network, the frequency domain transformation operation is performed on the equivariant feature map in the spatial dimension to convert the spatial domain feature map into the frequency domain feature representation, and a frequency component index corresponding to the frequency domain feature representation is established in the frequency dimension.

[0029] S53. After the frequency domain feature representation is generated, read the frequency domain update weight set and establish the correspondence between the frequency domain update weight set and the frequency domain feature representation according to the spatial location index and the frequency component index.

[0030] S54. For each spatial location and each frequency component, perform a weighted mapping operation on the corresponding frequency domain feature representation and the corresponding frequency domain update weight to form a weighted frequency domain feature representation.

[0031] S55. After completing the frequency domain update weight introduction, the weighted frequency domain feature representation is input into the frequency domain mapping unit of the Fourier neural operator network, and the frequency domain feature mapping operation is performed to generate the updated frequency domain feature representation.

[0032] S56. After the updated frequency domain feature representation is generated, perform an inverse frequency domain transformation operation on the updated frequency domain feature representation to map the updated frequency domain feature representation to the spatial domain, forming a spatial domain updated feature mapping.

[0033] S57. In the case that the Fourier neural operator network contains several processing layers, the spatial domain updated feature map is used as the input feature map of the next processing layer, and the frequency domain transformation, frequency domain updated weight introduction, frequency domain feature map operation and frequency domain inverse transformation operation are repeatedly executed until the operation of all processing layers is completed.

[0034] S58. After completing all processing layer operations of the Fourier neural operator network, output the final spatial domain updated feature map as the output result of the Fourier neural operator network.

[0035] Optionally, S6 specifically includes:

[0036] The system reads the spatial domain update feature map from the Fourier neural operator network and establishes an output index in the spatial location dimension. At each spatial location, the spatial domain update feature map is converted into fringe reconstruction values ​​or phase distribution values ​​to form the initial output result. Simultaneously, the orientation confidence parameter is read, and a correspondence between the orientation confidence parameter and the initial output result is established in the spatial location dimension. The numerical change of the initial output result is calculated between adjacent spatial locations. During the calculation of the numerical change, the orientation confidence parameter of the corresponding spatial location is introduced to perform an amplitude limitation operation on the numerical change, forming a limited change. The limited change is written back to the initial output result of the corresponding spatial location to form a limited output result. After completing the limited output result writing operation for all spatial locations, the fringe reconstruction result or phase distribution result is output.

[0037] Optionally, S7 specifically includes:

[0038] S71. Read the fringe reconstruction results or phase distribution results, and establish a result index in the spatial location dimension;

[0039] S72. Within the spatial location dimension, perform numerical expansion processing on the fringe reconstruction result or phase distribution result, and perform consistency verification on the values ​​of adjacent spatial locations to form a continuous numerical distribution.

[0040] S73. Map the continuous numerical distribution to a height numerical distribution, and form a height mapping result in the spatial location dimension;

[0041] S74. In the height mapping results, the spatial locations are resampled and arranged to form topographic data with a regular grid structure;

[0042] S75. Output the topography data of the regular grid structure as the white light interference topography result.

[0043] The beneficial effects of this invention are:

[0044] (1) In the white light interference image processing, the present invention introduces a standard equivariant feature extraction process based on fringe direction information. By establishing a standard field consistent with the fringe direction in a local spatial location and performing equivariant convolution operation under the constraint of the standard field, the interference image maintains a consistent feature expression under different fringe direction distribution conditions, reducing the problem of inconsistent feature expression caused by fringe direction changes.

[0045] (2) In the frequency domain feature update stage, the present invention introduces a frequency domain update weight set composed of a fringe direction information set, a fringe coherence information set, and a direction confidence parameter, and embeds the frequency domain update weight set into the frequency domain mapping process of the Fourier neural operator, so that the frequency domain feature update process maintains a correspondence with the spatial structure distribution of the interference fringes, thereby forming a frequency domain processing flow with structural constraints.

[0046] (3) In the output stage of the operator network, the present invention introduces a spatial position update amplitude constraint mechanism based on the direction confidence parameter. During the generation of stripe reconstruction results or phase distribution results, the numerical changes between adjacent spatial positions are controlled in a consistent manner, so that the output results maintain continuous distribution characteristics in the spatial dimension, which is conducive to the stable generation of subsequent morphological results.

[0047] (4) The present invention constructs a white light interferometric image processing flow that combines fringe direction modeling, frequency domain weight modulation and operator network mapping, so that the interferometric image processing can still form a continuous and controllable morphological output result when the fringe structure is complex and the direction changes significantly, and has good engineering applicability. Attached Figure Description

[0048] The accompanying drawings are provided to further illustrate the invention and form part of the specification. They are used in conjunction with embodiments of the invention to explain the invention and do not constitute a limitation thereof. In the drawings:

[0049] Figure 1 This is a flowchart of a deep learning-based white light interferometric image processing method proposed in this invention.

[0050] Figure 2 This is a schematic diagram of the canonical isovariant convolutional network and orientation confidence generation of a deep learning-based white light interferometric image processing method proposed in this invention.

[0051] Figure 3 This is a Fourier neural operator graph guided by the frequency domain update weight set of a deep learning-based white light interferometric image processing method proposed in this invention. Detailed Implementation

[0052] The present invention will now be described in further detail with reference to the accompanying drawings. These drawings are simplified schematic diagrams, illustrating only the basic structure of the invention, and therefore only show the components relevant to the invention.

[0053] refer to Figure 1-3 A deep learning-based method for processing white light interference images includes the following steps:

[0054] S1. Acquire the interference image sequence obtained by white light interferometry and perform normalization processing on the interference image sequence;

[0055] S2. Perform fringe analysis on the normalized interference image sequence to obtain the fringe direction information set and the fringe coherence information set;

[0056] S3. Input the interference image sequence into a canonical isovariant convolutional network. The canonical isovariant convolutional network constructs a local canonical field based on the fringe direction information and performs isovariant convolution operations under the constraints of the canonical field. At the same time, it generates a set of orientation distribution parameters and orientation confidence parameters, and outputs isovariant feature maps.

[0057] S4. Based on the fringe direction information set, the fringe coherence information set, and the direction confidence parameter, construct a frequency domain update weight set;

[0058] S5. Input the equivariant feature map into the Fourier neural operator network, and introduce the frequency domain update weight set during the frequency domain feature update process;

[0059] S6. The Fourier neural operator network outputs the stripe reconstruction result or phase distribution result. During the output process, constraints are applied to the update amplitude between spatial positions based on the direction confidence parameter.

[0060] S7. Generate and output white light interference morphology results based on fringe reconstruction results or phase distribution results.

[0061] In this embodiment, S2 specifically includes:

[0062] In the normalized interferometric image sequence, the image is locally divided using fixed spatial windows. Within each spatial window, the gradient components of pixel grayscale in the horizontal and vertical directions are calculated to form a set of gradient vectors. Local statistical operations are performed on the gradient vector set to calculate the principal direction vector within the corresponding spatial window. The principal direction vector is mapped to fringe direction information, forming a set of fringe direction information at the image spatial location. Within the same spatial window, the projection amplitude of the gradient vector set onto the principal direction vector is aggregated to calculate the fringe intensity distribution value. The fringe intensity distribution value is subjected to a consistency measurement operation within the spatial window to generate a set of fringe coherence information corresponding to the spatial location.

[0063] In this embodiment, S3 specifically includes:

[0064] The standardized interferometric image sequence is input into the input layer of a canonical equivariant convolutional network according to its spatial location, and a set of fringe direction information is associated with each spatial location in the input layer. In the first processing stage of the canonical equivariant convolutional network, a local canonical field corresponding to the spatial location is constructed at each spatial location based on the fringe direction information set. The local canonical field is determined by the fringe direction information to determine the reference direction and forms a consistent local coordinate relationship within the spatial window. After the local canonical field is constructed, the standardized interferometric image sequence is aligned in the corresponding local canonical field, and the image data within the same spatial window is arranged in the canonical coordinate system. In the canonical coordinate system, equivariant convolution is performed on the aligned image data. During the equivariant convolution operation, the convolution kernel parameters are updated with orientation alignment under the constraint of the local canonical field, forming an intermediate feature map consistent with the local canonical field. After the intermediate feature map is generated, statistical operations are performed on the numerical distribution of the equivariant convolution response in several directional channels at each spatial location to generate a set of orientation distribution parameters. The statistical operations are performed on the equivariant convolution response values ​​in different directional channels at the same spatial location, performing sorting, differencing, aggregation, and normalization.

[0065] While generating the set of orientation distribution parameters, a consistency calculation is performed on the numerical stability of the set of orientation distribution parameters within the spatial window to form orientation confidence parameters that correspond one-to-one with spatial locations. After generating the set of orientation distribution parameters and orientation confidence parameters, the intermediate feature map, the set of orientation distribution parameters, and the orientation confidence parameters are combined in the channel dimension to form a joint feature representation. The joint feature representation is used as the output of the canonical isovariant convolutional network, maintaining a consistent mapping relationship with the input interferometric image sequence in the spatial location dimension, and outputting the isovariant feature map, the set of orientation distribution parameters, and the orientation confidence parameters.

[0066] In this embodiment, the coordinate alignment operation in step S3 specifically includes:

[0067] At each spatial location, the corresponding direction vector in the fringe direction information set is read, and the direction vector is used as the principal axis direction of the local normalized field. At the same spatial location, auxiliary axis directions orthogonal to the principal axis direction are generated based on the principal axis direction, forming a two-dimensional normalized coordinate axis set. After the normalized coordinate axis set is established, a local spatial window centered on the spatial location is determined, and the original image coordinate position is recorded within the local spatial window. A coordinate transformation operation is performed on the original image coordinate position within the local spatial window to map the original image coordinates to the coordinate system defined by the normalized coordinate axis set. After the coordinate transformation is completed, the image data within the local spatial window is rearranged according to the coordinate order under the normalized coordinate system to form an image data block under the normalized coordinate system. The image data block under the normalized coordinate system is then output.

[0068] In this embodiment, the numerical stability consistency calculation in step S3 specifically includes:

[0069] At each spatial location, the set of orientation distribution parameters obtained by the normalized isovariant convolution operation is read; at the same spatial location, the set of orientation distribution parameters is numerically sorted along the orientation dimension to form an ordered orientation response sequence; in the ordered orientation response sequence, the numerical difference sequence between adjacent orientation responses is calculated; in the difference sequence, all difference values ​​are aggregated to form the orientation stability value corresponding to the spatial location; within the spatial location dimension, the orientation stability value is normalized to form an orientation confidence parameter that corresponds one-to-one with the spatial location.

[0070] In this embodiment, S4 specifically includes:

[0071] A correspondence is established between the fringe direction information set, the fringe coherence information set, and the direction confidence parameter in the spatial location dimension. Fringe direction information is read at each spatial location and converted into a direction index in the frequency dimension. The corresponding frequency component set is selected according to the direction index in the frequency dimension. The fringe coherence information value corresponding to the spatial location is read from the frequency component set and written into the weight position of each frequency component. The direction confidence parameter is read synchronously, and confidence modulation is performed on the frequency component weights. The modulated frequency component weights are normalized in the frequency dimension. The normalized frequency component weights corresponding to each spatial location are arranged according to the spatial location dimension and the frequency dimension to form a frequency domain update weight set.

[0072] In this embodiment, S5 specifically includes:

[0073] S51. Input the output isovariant feature maps into the input layer of the Fourier neural operator network in spatial order.

[0074] S52. In the Fourier neural operator network, the frequency domain transformation operation is performed on the equivariant feature map in the spatial dimension to convert the spatial domain feature map into the frequency domain feature representation, and a frequency component index corresponding to the frequency domain feature representation is established in the frequency dimension.

[0075] S53. After the frequency domain feature representation is generated, read the frequency domain update weight set and establish the correspondence between the frequency domain update weight set and the frequency domain feature representation according to the spatial location index and the frequency component index.

[0076] S54. For each spatial location and each frequency component, perform a weighted mapping operation on the corresponding frequency domain feature representation and the corresponding frequency domain update weight to form a weighted frequency domain feature representation.

[0077] S55. After completing the frequency domain update weight introduction, the weighted frequency domain feature representation is input into the frequency domain mapping unit of the Fourier neural operator network, and the frequency domain feature mapping operation is performed to generate the updated frequency domain feature representation.

[0078] S56. After the updated frequency domain feature representation is generated, perform an inverse frequency domain transformation operation on the updated frequency domain feature representation to map the updated frequency domain feature representation to the spatial domain, forming a spatial domain updated feature mapping.

[0079] S57. In the case that the Fourier neural operator network contains several processing layers, the spatial domain updated feature map is used as the input feature map of the next processing layer, and the frequency domain transformation, frequency domain updated weight introduction, frequency domain feature map operation and frequency domain inverse transformation operation are repeatedly executed until the operation of all processing layers is completed.

[0080] S58. After completing all processing layer operations of the Fourier neural operator network, output the final spatial domain updated feature map as the output result of the Fourier neural operator network.

[0081] In this embodiment, the frequency domain inverse transform operation in step S56 specifically includes:

[0082] The updated frequency domain feature representation is read in the frequency domain dimension, while maintaining the correspondence between frequency component indices and spatial location indices. The updated frequency domain feature representation is stored with frequency components as indices, and each frequency component corresponds to a set of frequency domain feature values ​​in complex or real number form.

[0083] At each spatial location, a reverse frequency domain mapping operation is performed on the updated frequency domain feature representation in the order of frequency component indices. The reverse frequency domain mapping operation uses the frequency component indices as input and maps the frequency domain feature values ​​back to their corresponding spatial domain locations one by one. The mapping process maintains a one-to-one correspondence between the frequency dimension and the spatial dimension, without introducing new frequency components or spatial locations.

[0084] During the reverse mapping process, frequency synthesis is performed on the frequency domain eigenvalues ​​corresponding to each frequency component. The values ​​of different frequency components at the same spatial location are accumulated and reconstructed to form the eigenvalues ​​in the spatial domain. The frequency synthesis operation ends after all frequency components have been processed.

[0085] After completing the frequency synthesis operation, a complete spatial domain feature map is generated within the spatial location dimension. The spatial domain feature map maintains the correspondence with the frequency domain feature representation before the inverse transform in terms of spatial resolution, spatial arrangement order, and number of channels.

[0086] After the spatial domain feature map is generated, the spatial domain feature map is used as the output of the current layer of the Fourier neural operator network.

[0087] In this embodiment, S6 specifically includes:

[0088] The system reads the spatial domain update feature map from the Fourier neural operator network and establishes an output index in the spatial location dimension. At each spatial location, the spatial domain update feature map is converted into fringe reconstruction values ​​or phase distribution values ​​to form the initial output result. Simultaneously, the orientation confidence parameter is read, and a correspondence between the orientation confidence parameter and the initial output result is established in the spatial location dimension. The numerical change of the initial output result is calculated between adjacent spatial locations. During the calculation of the numerical change, the orientation confidence parameter of the corresponding spatial location is introduced to perform an amplitude limitation operation on the numerical change, forming a limited change. The limited change is written back to the initial output result of the corresponding spatial location to form a limited output result. After completing the limited output result writing operation for all spatial locations, the fringe reconstruction result or phase distribution result is output.

[0089] In this embodiment, S7 specifically includes:

[0090] S71. Read the fringe reconstruction results or phase distribution results, and establish a result index in the spatial location dimension;

[0091] S72. Within the spatial location dimension, perform numerical expansion processing on the fringe reconstruction result or phase distribution result, and perform consistency verification on the values ​​of adjacent spatial locations to form a continuous numerical distribution.

[0092] S73. Map the continuous numerical distribution to a height numerical distribution, and form a height mapping result in the spatial location dimension;

[0093] S74. In the height mapping results, the spatial locations are resampled and arranged to form topographic data with a regular grid structure;

[0094] S75. Output the topography data of the regular grid structure as the white light interference topography result.

[0095] Example 1:

[0096] In this embodiment, the method of the present invention is applied to a white light interferometry scenario where there are variations in fringe direction and local fringe discontinuities. In the acquired interferometric image sequence, the fringe orientation varies significantly at different spatial locations, some regions exhibit fringe rotation characteristics, local fringe contrast is reduced, and random noise interference is present. When processing the above interferometric images using traditional analytical methods, phase calculation discontinuities easily occur in regions with varying fringe direction, and the height difference between adjacent pixels exceeds a preset threshold in fringe breakage regions, resulting in significant jumps in the morphological results.

[0097] Under the same interference image sequence conditions, the method of this invention is used for processing. Through the fringe analysis step, the corresponding fringe direction information set and fringe coherence information set are obtained at each spatial location. In the feature extraction stage, a local canonical field is constructed based on the fringe direction information, and isovariant convolution operation is performed under the constraint of the canonical field, so that the fringe features at different spatial locations are processed under a unified directional reference. By performing statistical operations on the numerical distribution of the isovariant convolution response in multiple directional channels, a set of directional distribution parameters is generated, and further, directional confidence parameters corresponding one-to-one with spatial locations are formed.

[0098] In the frequency domain processing stage, a frequency domain update weight set is constructed by combining the fringe direction information set, the fringe coherence information set, and the direction confidence parameter. This weight set is then introduced into the frequency domain mapping process of the Fourier neural operator network. Through this processing flow, the frequency component update process at different spatial locations maintains a correspondence with the fringe structure. In the output stage, constraints are applied to the numerical update amplitude between spatial locations based on the direction confidence parameter, ensuring that the fringe reconstruction result or phase distribution result maintains a continuous distribution characteristic in the spatial dimension. The final generated white light interference morphology result does not exhibit any threshold jumps in the fringe direction change region or the break region.

[0099] Table 1: Numerical Comparison of White Light Interference Image Processing Methods

[0100] Comparison indicators Traditional analytical methods Common deep learning methods Method of the present invention Quantitative judgment criteria Consistent conclusions Stripe direction consistency The standard deviation of the orientation angle is 8.6°. The standard deviation of the orientation angle is 4.2°. The standard deviation of the orientation angle is 1.1°. Standard deviation ≤ 2.0° satisfy High continuity of the fracture region 37 height difference points exceeding the threshold 14 height difference points exceeding the threshold 0 points exceeding the threshold height difference Points=0 satisfy Phase distribution continuity Over-threshold phase difference term 29 Over-threshold phase difference term 11 Over-threshold phase difference term 0 Number of terms = 0 satisfy Topography error under noise conditions Mean square error 0.92 Mean square error 0.48 Mean square error 0.17 Error ≤ 0.20 satisfy analytical stability of complex structures Effective resolution rate: 81% Effective resolution rate: 89% 100% effective resolution rate Ratio = 100% satisfy

[0101] Table 1 presents a numerical comparison of white light interferometric images processed using traditional analytical methods, conventional deep learning methods, and the method of this invention, under the same interferometric image sequence. All comparison indicators in the table are described using quantifiable statistics and consistent with preset threshold conditions to ensure the reproducibility and verifiability of the comparison results.

[0102] In the fringe direction consistency index, the standard deviation of the direction angle is used as a quantitative indicator to statistically analyze the dispersion of the fringe direction distribution at each spatial location. The standard deviation of the direction angle obtained by the traditional analytical method is 8.6°, indicating that the fringe direction has a large discrete distribution within the spatial range; the standard deviation of the direction angle of the ordinary deep learning method is 4.2°, and some spatial locations still exceed the direction consistency judgment range; the standard deviation of the direction angle of the method of this invention is 1.1°, which is less than the preset judgment threshold of 2.0°, thus satisfying the fringe direction consistency condition.

[0103] In the height continuity index of the fracture region, the height continuity is evaluated by counting the number of points where the height difference between adjacent pixels exceeds a preset difference threshold. Traditional analytical methods detected 37 points exceeding the threshold height difference in the fracture region, and ordinary deep learning methods detected 14 points exceeding the threshold. However, the method of this invention did not detect any points exceeding the threshold height difference in the corresponding region, with a threshold value of 0, thus satisfying the height continuity judgment condition.

[0104] In the phase distribution continuity index, the number of phase difference sequences exceeding a preset change threshold is compared. The traditional analytical method has 29 phase difference sequences exceeding the threshold, the common deep learning method has 11, while the method of this invention has 0, indicating that the phase distribution does not exhibit any difference exceeding the change threshold throughout the entire spatial range.

[0105] In the topography error index under noisy conditions, the mean square error (MSE) is used as a quantification statistic to evaluate the error distribution between the topography result and the reference result. The MSE of the traditional analytical method is 0.92, and that of the common deep learning method is 0.48. The MSE of the method in this invention is 0.17, which is lower than the preset error judgment threshold of 0.20, thus meeting the error control conditions.

[0106] In the analytical stability index of complex structures, the proportion of spatial regions that can generate effective morphological results is compared statistically. The effective resolution ratio of traditional analytical methods is 81%, that of ordinary deep learning methods is 89%, and the effective resolution ratio of the method of this invention reaches 100%, that is, effective morphological results are generated in all test regions, thus meeting the analytical stability judgment condition.

[0107] As can be seen from the numerical results shown in Table 1, the method of the present invention meets the preset judgment conditions under multiple evaluation indicators such as fringe direction consistency, height continuity, phase distribution continuity, error control, and analytical stability of complex structures, thus verifying the feasibility of the method in complex white light interferometric image processing scenarios.

[0108] The above description is only a preferred embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any equivalent substitutions or modifications made by those skilled in the art within the scope of the technology disclosed in the present invention, based on the technical solution and inventive concept of the present invention, should be covered within the scope of protection of the present invention.

Claims

1. A deep learning-based white light interferometric image processing method, characterized in that, Includes the following steps: S1. Acquire the interference image sequence obtained by white light interferometry and perform normalization processing on the interference image sequence; S2. Perform fringe analysis on the normalized interference image sequence to obtain the fringe direction information set and the fringe coherence information set; S3. Input the interference image sequence into a canonical isovariant convolutional network. The canonical isovariant convolutional network constructs a local canonical field based on the fringe direction information and performs isovariant convolution operations under the constraints of the canonical field. At the same time, it generates a set of orientation distribution parameters and orientation confidence parameters, and outputs isovariant feature maps. S4. Based on the fringe direction information set, the fringe coherence information set, and the direction confidence parameter, construct a frequency domain update weight set; S5. Input the equivariant feature map into the Fourier neural operator network, and introduce the frequency domain update weight set during the frequency domain feature update process; S6. The Fourier neural operator network outputs the stripe reconstruction result or phase distribution result. During the output process, constraints are applied to the update amplitude between spatial positions based on the direction confidence parameter. S7. Generate and output white light interference morphology results based on fringe reconstruction results or phase distribution results.

2. The deep learning-based white light interferometric image processing method according to claim 1, characterized in that, S2 specifically includes: In the normalized interferometric image sequence, the image is locally divided using fixed spatial windows. Within each spatial window, the gradient components of pixel grayscale in the horizontal and vertical directions are calculated to form a set of gradient vectors. Local statistical operations are performed on the gradient vector set to calculate the principal direction vector within the corresponding spatial window. The principal direction vector is mapped to fringe direction information, forming a set of fringe direction information at the image spatial location. Within the same spatial window, the projection amplitude of the gradient vector set onto the principal direction vector is aggregated to calculate the fringe intensity distribution value. The fringe intensity distribution value is subjected to a consistency measurement operation within the spatial window to generate a set of fringe coherence information corresponding to the spatial location.

3. The deep learning-based white light interferometric image processing method according to claim 1, characterized in that, S3 specifically includes: The standardized interferometric image sequence is input into the input layer of a canonical equivariant convolutional network according to its spatial location, and a set of fringe direction information is associated with each spatial location in the input layer. In the first processing stage of the canonical equivariant convolutional network, a local canonical field corresponding to the spatial location is constructed at each spatial location based on the fringe direction information set. The local canonical field is determined by the fringe direction information to determine the reference direction and forms a consistent local coordinate relationship within the spatial window. After the local canonical field is constructed, the standardized interferometric image sequence is aligned in the corresponding local canonical field, and the image data within the same spatial window is arranged in the canonical coordinate system. In the canonical coordinate system, equivariant convolution is performed on the aligned image data. During the equivariant convolution operation, the convolution kernel parameters are updated with orientation alignment under the constraint of the local canonical field, forming an intermediate feature map consistent with the local canonical field. After the intermediate feature map is generated, statistical operations are performed on the numerical distribution of the equivariant convolution response in several directional channels at each spatial location to generate a set of orientation distribution parameters. The statistical operations are performed on the equivariant convolution response values ​​in different directional channels at the same spatial location, performing sorting, differencing, aggregation, and normalization. While generating the set of orientation distribution parameters, a consistency calculation is performed on the numerical stability of the set of orientation distribution parameters within the spatial window to form orientation confidence parameters that correspond one-to-one with spatial locations. After generating the set of orientation distribution parameters and orientation confidence parameters, the intermediate feature map, the set of orientation distribution parameters, and the orientation confidence parameters are combined in the channel dimension to form a joint feature representation. The joint feature representation is used as the output of the canonical isovariant convolutional network, maintaining a consistent mapping relationship with the input interferometric image sequence in the spatial location dimension, and outputting the isovariant feature map, the set of orientation distribution parameters, and the orientation confidence parameters.

4. The deep learning-based white light interferometric image processing method according to claim 1, characterized in that, The coordinate alignment operation in step S3 specifically includes: At each spatial location, the corresponding direction vector in the fringe direction information set is read, and the direction vector is used as the principal axis direction of the local normalized field. At the same spatial location, auxiliary axis directions orthogonal to the principal axis direction are generated based on the principal axis direction, forming a two-dimensional normalized coordinate axis set. After the normalized coordinate axis set is established, a local spatial window centered on the spatial location is determined, and the original image coordinate position is recorded within the local spatial window. A coordinate transformation operation is performed on the original image coordinate position within the local spatial window to map the original image coordinates to the coordinate system defined by the normalized coordinate axis set. After the coordinate transformation is completed, the image data within the local spatial window is rearranged according to the coordinate order under the normalized coordinate system to form an image data block under the normalized coordinate system. The image data block under the normalized coordinate system is then output.

5. The deep learning-based white light interferometric image processing method according to claim 1, characterized in that, The numerical stability consistency calculation in step S3 specifically includes: At each spatial location, the set of orientation distribution parameters obtained by the normalized isovariant convolution operation is read; at the same spatial location, the set of orientation distribution parameters is numerically sorted along the orientation dimension to form an ordered orientation response sequence; in the ordered orientation response sequence, the numerical difference sequence between adjacent orientation responses is calculated; in the difference sequence, all difference values ​​are aggregated to form the orientation stability value corresponding to the spatial location; within the spatial location dimension, the orientation stability value is normalized to form an orientation confidence parameter that corresponds one-to-one with the spatial location.

6. The white light interferometric image processing method based on deep learning according to claim 1, characterized in that, S4 specifically includes: A correspondence is established between the fringe direction information set, the fringe coherence information set, and the direction confidence parameter in the spatial location dimension. Fringe direction information is read at each spatial location and converted into a direction index in the frequency dimension. The corresponding frequency component set is selected according to the direction index in the frequency dimension. The fringe coherence information value corresponding to the spatial location is read from the frequency component set and written into the weight position of each frequency component. The direction confidence parameter is read synchronously, and confidence modulation is performed on the frequency component weights. The modulated frequency component weights are normalized in the frequency dimension. The normalized frequency component weights corresponding to each spatial location are arranged according to the spatial location dimension and the frequency dimension to form a frequency domain update weight set.

7. The deep learning-based white light interferometric image processing method according to claim 1, characterized in that, S5 specifically includes: S51. Input the output isovariant feature maps into the input layer of the Fourier neural operator network in spatial order. S52. In the Fourier neural operator network, the frequency domain transformation operation is performed on the equivariant feature map in the spatial dimension to convert the spatial domain feature map into the frequency domain feature representation, and a frequency component index corresponding to the frequency domain feature representation is established in the frequency dimension. S53. After the frequency domain feature representation is generated, read the frequency domain update weight set and establish the correspondence between the frequency domain update weight set and the frequency domain feature representation according to the spatial location index and the frequency component index. S54. For each spatial location and each frequency component, perform a weighted mapping operation on the corresponding frequency domain feature representation and the corresponding frequency domain update weight to form a weighted frequency domain feature representation. S55. After completing the frequency domain update weight introduction, the weighted frequency domain feature representation is input into the frequency domain mapping unit of the Fourier neural operator network, and the frequency domain feature mapping operation is performed to generate the updated frequency domain feature representation. S56. After the updated frequency domain feature representation is generated, perform an inverse frequency domain transformation operation on the updated frequency domain feature representation to map the updated frequency domain feature representation to the spatial domain, forming a spatial domain updated feature mapping. S57. In the case that the Fourier neural operator network contains several processing layers, the spatial domain updated feature map is used as the input feature map of the next processing layer, and the frequency domain transformation, frequency domain updated weight introduction, frequency domain feature map operation and frequency domain inverse transformation operation are repeatedly executed until the operation of all processing layers is completed. S58. After completing all processing layer operations of the Fourier neural operator network, output the final spatial domain updated feature map as the output result of the Fourier neural operator network.

8. The deep learning-based white light interferometric image processing method according to claim 1, characterized in that, S6 specifically includes: The system reads the spatial domain update feature map from the Fourier neural operator network and establishes an output index in the spatial location dimension. At each spatial location, the spatial domain update feature map is converted into fringe reconstruction values ​​or phase distribution values ​​to form the initial output result. Simultaneously, the orientation confidence parameter is read, and a correspondence between the orientation confidence parameter and the initial output result is established in the spatial location dimension. The numerical change of the initial output result is calculated between adjacent spatial locations. During the calculation of the numerical change, the orientation confidence parameter of the corresponding spatial location is introduced to perform an amplitude limitation operation on the numerical change, forming a limited change. The limited change is written back to the initial output result of the corresponding spatial location to form a limited output result. After completing the limited output result writing operation for all spatial locations, the fringe reconstruction result or phase distribution result is output.

9. The white light interferometric image processing method based on deep learning according to claim 1, characterized in that, Specifically, S7 includes: S71. Read the fringe reconstruction results or phase distribution results, and establish a result index in the spatial location dimension; S72. Within the spatial location dimension, perform numerical expansion processing on the fringe reconstruction result or phase distribution result, and perform consistency verification on the values ​​of adjacent spatial locations to form a continuous numerical distribution. S73. Map the continuous numerical distribution to a height numerical distribution, and form a height mapping result in the spatial location dimension; S74. In the height mapping results, the spatial locations are resampled and arranged to form topographic data with a regular grid structure; S75. Output the topography data of the regular grid structure as the white light interference topography result.

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