Multi-scale continuation method for inhibiting optical polishing edge effect

Abstract

The invention discloses a multi-scale continuation method for inhibiting an optical polishing edge effect, relates to the technical field of optical manufacturing and precision polishing processing, and solves the problems that the structural consistency of a continuation area and the reconstruction precision of medium-high frequency surface shape components cannot be considered in the conventional method, connection mutation is easy to occur at a boundary, smooth transition between the continuation area and an original surface shape cannot be realized, and the edge effect is influenced. The calculation precision of the residence time is influenced, and the final processing quality is reduced. According to the method, low-frequency information and high-frequency information of original surface shape data of an optical element are acquired; performing modeling and continuation on the low-frequency information and the high-frequency information respectively to obtain a continued low-frequency image and predict and output high-frequency sub-band prediction images in three directions; and carrying out inverse wavelet transform fusion reconstruction on the low-frequency image and the high-frequency sub-band prediction images in the three directions to obtain a complete surface shape after continuation, and the like. According to the method, the global contour and local details in the surface shape can be effectively extracted, and high-fidelity continuation of complex surface shape information is realized.

Description

Technical Field

[0001] This invention relates to the field of intelligent manufacturing and precision polishing technology, specifically to a multi-scale extension method for suppressing edge effects in optical polishing. Background Technology

[0002] In the ultra-precision machining of high-end optical components, surface accuracy directly determines the imaging quality and optical performance of the system. Modern deterministic machining methods, such as magnetorheological polishing and small tool polishing, generally use a "dwell time-removal function" control model to regulate the process path. The core of this model is to deduce the dwell time distribution based on the target surface shape, thereby achieving precise control over the amount of material removed.

[0003] However, in actual processing, the dwell time calculation model often adopts a two-dimensional convolution form of surface shape and removal function. Since the actual processing area of ​​optical components often cannot undergo a complete convolution removal cycle at the edges, the boundary region cannot form a mathematically closed convolution domain. This results in discontinuities and instabilities in the dwell time distribution, leading to "edge effects" such as insufficient material removal at the edges and accumulation of surface shape errors. This problem is particularly prominent in processes involving nonlinear paths and non-uniform force fields, such as multi-axis polishing of small tools, and has become one of the key obstacles restricting the improvement of overall surface shape accuracy. Traditional edge processing methods often use simplified means such as edge truncation, edge duplication, or mirror extension, but these cannot simultaneously ensure the structural consistency of the extended region and the reconstruction accuracy of high-frequency surface shape components. Abrupt connections easily occur at the boundaries, making it impossible for the extended region to smoothly transition from the original surface shape, thus affecting the accuracy of dwell time calculation and reducing the final processing quality.

[0004] Therefore, constructing a surface extension method with structural fidelity and detail consistency to improve the stability and continuity of the residence time distribution in the edge region is a key step in achieving edge effect suppression and ensuring the quality of ultra-precision machining. Summary of the Invention

[0005] To address the problems of existing methods failing to balance structural consistency of the extended region with reconstruction accuracy of high-frequency surface components, and the tendency for abrupt connection changes at boundaries that prevent a smooth transition between the extended region and the original surface shape, thereby affecting the accuracy of dwell time calculation and reducing final processing quality, this invention provides a multi-scale extension method for suppressing polishing edge effects.

[0006] A multi-scale extension method for suppressing polishing edge effects, the method is implemented by the following steps:

[0007] Step 1: Obtain the original surface shape data of the optical element, and perform two-dimensional discrete wavelet decomposition on the original surface shape data to obtain low-frequency and high-frequency information;

[0008] Step 2: Model and extend the low-frequency information obtained in Step 1 to obtain the extended low-frequency image;

[0009] Step 3: Use a high-frequency feature prediction network to model and extend the high-frequency information obtained in Step 1, and predict the high-frequency sub-band prediction images in three directions.

[0010] Step 4: Transfer the low-frequency image obtained in Step 2 to... And the high-frequency subband prediction images in three directions obtained in step three. The extended complete surface shape is obtained by fusing and reconstructing using inverse wavelet transform.

[0011] The beneficial effects of this invention are:

[0012] 1. In the method described in this invention, the frequency separation of the surface shape information of the component is performed by utilizing the multi-scale analysis capability of discrete wavelet transform, which can effectively extract the global contour and local details in the surface shape and achieve high-fidelity extension of complex surface shape information.

[0013] 2. In the method described in this invention, an orthogonal polynomial fitting model is constructed from the low-frequency information of wavelets to achieve global extension of the edge missing measurement area, effectively preserving large-scale contour information and improving the continuity and authenticity of the extended area.

[0014] 3. In the method described in this invention, a local feature extraction and prediction network is introduced into the high-frequency information. High-frequency detail features are modeled and completed and predicted through deep learning, thereby enhancing the edge accuracy and detail consistency of the extension results. Attached Figure Description

[0015] Figure 1 This is a flowchart of a multi-scale extension method for suppressing edge effects in optical polishing, as described in this invention.

[0016] Figure 2 This is a surface diagram of an optical element;

[0017] Figure 3 The flowchart for multi-scale wavelet decomposition is shown below.

[0018] Figure 4 A flowchart for fitting and extending low-frequency information using a polynomial;

[0019] Figure 5 The result of extending the low-frequency information of the surface shape is shown in the figure.

[0020] Figure 6 A flowchart for extending high-frequency information of surface shape;

[0021] Figure 7 The result of extending the high-frequency information of the surface shape is shown in the figure.

[0022] Figure 8 This is a schematic diagram of the convolution operation after surface extension. Detailed Implementation

[0023] Combination Figures 1 to 8 This embodiment describes a multi-scale extension method for suppressing edge effects in optical polishing. This method uses the original surface shape data of optical elements acquired by a detection device, performs Discrete Wavelet Transform (DWT) on it, and divides the surface shape information into high-frequency and low-frequency information. The low-frequency information represents the overall contour information and is modeled and extended using orthogonal polynomial fitting to ensure continuity and smoothness at the boundaries. The high-frequency information reflects surface details; using the high-frequency sub-bands obtained from wavelet decomposition as input, a local feature extraction network constructed with small convolutional kernels and residual structures learns and predicts the high-frequency features of the edge region, supplementing the detailed information outside the boundaries.

[0024] The extended high and low frequency information is then reconstructed into complete surface data using inverse wavelet transform (IDWT). By expanding the surface data information, the final residence time distribution grid can be larger than the original surface data grid. When solving for residence time, the distribution area of ​​the original surface is consistent with the original surface data region, which means that the material in the edge region cannot obtain a complete material removal cycle, i.e., the convolution process. However, in the edge region of the optical element, since there is no data outside the original surface data, the corresponding residence time cannot be calculated, thus preventing the polishing head from polishing beyond the original surface range. This results in the polishing head always failing to fully contact the material to be removed in the edge region. After surface extension using this method, the residence time can also be calculated within the extended region, allowing the polishing head to completely perform the convolution process on the edge of the original element, ensuring the integrity of material removal in the edge region. This allows the convolution process to be mathematically closed in the edge region, restoring the integrity and continuity of the residence time field, thereby effectively suppressing the edge effect. Ultimately, this method significantly improves the stability of dwell time calculation in edge regions and the overall surface accuracy of the optical processing.

[0025] The specific steps of the multi-scale extension method described in this embodiment are as follows:

[0026] Step 1: Obtain the original surface shape data of the optical element and decompose it into high-frequency information and low-frequency information by multi-scale discrete wavelet transform (DWT).

[0027] like Figure 2 As shown, the original surface shape data of the optical element is obtained through a surface shape detection device and represented as a two-dimensional surface shape function:

[0028]

[0029] Choose the wavelet basis and the number of decomposition layers. The number of decomposition layers is selected based on the complexity and size of the surface, and is commonly 2-4 layers, with 3 layers usually chosen.

[0030] In this embodiment, the input surface data S(x,y) is decomposed layer by layer using two-dimensional discrete wavelet transform (2D-DWT). The structural information in the surface is decomposed by two-dimensional discrete wavelet transform to obtain four sub-bands, which are expressed by the following formula:

[0031]

[0032] In the formula, S LL This refers to the low-frequency sub-band, encompassing the overall conceptual trend and structural patterns of the surface shape; S LH ,S HL ,S HH These are high-frequency sub-bands in the vertical, horizontal, and diagonal directions, respectively, to supplement the display capabilities in terms of detail. As shown in Table 1, Table 1 contains the type information of the four sub-bands;

[0033] Table 1

[0034] Subband type name describe LL Low frequency - low frequency Global contour information (main structure) LH Low frequency - high frequency Vertical edge / detail HL High frequency - low frequency Horizontal edge / detail HH High frequency - high frequency Diagonal texture / detail

[0035] like Figure 3 As shown, in this embodiment, the surface shape is decomposed into structural and small-batch features, which form the basis for subsequent component refinement processing in the extension operation. The input surface shape data S(x,y) is decomposed layer by layer using two-dimensional discrete wavelet transform. The specific steps are as follows:

[0036] Step 11: Input surface data S(x,y) and perform three-level wavelet decomposition;

[0037] Step 12, First-level decomposition:

[0038] Filtering and downsampling are performed along the vertical direction of the surface data S(x,y); that is: low-pass filter: preserves contour information; high-pass filter H: extracts details (such as scratches, local undulations); finally, the low-frequency subband S is obtained. LL (x,y) and the first-level high-frequency subband S H1 (x,y);

[0039] Step 13, Second-level decomposition:

[0040] For the first-level high-frequency subband S H1 (x,y) is then filtered and downsampled along the horizontal direction to obtain the high-frequency subband S representing the vertical direction. LH (x,y) and the second-level high-frequency subband S H2 (x,y);

[0041] Step 14, Third-level decomposition:

[0042] For the second-level high sub-band S H2 (x,y) is then filtered and downsampled along the diagonal to obtain the high-frequency subband S in the horizontal direction. HL (x,y) and the high-frequency subband S in the diagonal direction HH (x,y);

[0043] The high-frequency subband S in the vertical direction LH (x,y), the high-frequency subband S in the horizontal direction HL (x,y) and the high-frequency subband S in the diagonal direction HH (x,y) is used as high-frequency information;

[0044] Step 2: The low-frequency subband S obtained from multi-scale wavelet decomposition... LL Modeling and extending (x,y), such as Figure 4 As shown, the specific process is as follows:

[0045] Step 21, S LL The coordinates (i,j) of each pixel in (x,y) are mapped to standard normalized grid coordinates (u). j ,v i The values ​​are then converted to polar coordinates (ρ, θ); the specific process is as follows:

[0046]

[0047] Where i∈{0,1,...,M′-1}, j∈{0,1,...,N′-1}; M′ and N′ are the number of rows and columns of the low-frequency subband after wavelet decomposition, respectively, in pixels; u j This represents the horizontally normalized coordinates of the j-th pixel, with a normalization range of [-1, 1]. i This represents the vertically normalized coordinates of the pixel in column i, with a normalization range of [-1, 1].

[0048] Then normalize the coordinates (x, y) = (u j ,v i Convert to polar coordinates:

[0049]

[0050] Retain all that satisfy ρ ij Points ≤ 1 constitute the effective fitted sample region within the unit circle.

[0051] Step 22: Select Zernike polynomial basis functions of order K. For S in the aforementioned unit circle region LL Least squares fitting is performed on (x,y) to establish the following function approximation model:

[0052]

[0053] Among them, a k The coefficients of the polynomial to be solved are determined through the following optimization problem:

[0054]

[0055] Step 23: Obtain the optimal coefficient 'a' using the least squares method. k This allows for the construction of a low-frequency fitting model f(ρ,θ) that can be analytically expressed, enabling surface shape estimation for new coordinates within any unit circle domain.

[0056] Step 24: Construct a set of polar coordinate points (ρ) for the region to be extended. m ,θ n ), where ρ m ∈(ρ0,1],θ n ∈(0,2π], and substitute it into the fitting model f(ρ,θ) to obtain the low-frequency predicted values ​​of the extended region:

[0057]

[0058] Step 25: Calculate the low-frequency prediction values ​​of the extended region. Transform back to coordinates (i,j) and compare with the low-frequency subband S. LL (x,y) are stitched together to synthesize and extend the complete low-frequency image. This image will be used for subsequent inverse wavelet transform to recover the complete surface shape after extension.

[0059] like Figure 5 As shown, the left figure illustrates the original surface shape before low-frequency information extrapolation. The yellow circle marks the boundary of the original surface shape, and the green area outside it is the region to be extrapolated. After low-frequency extrapolation processing, the extrapolation result shown in the right figure is obtained. The extrapolated surface shape can be smoothly extrapolated according to the distribution of the original surface shape data, avoiding abrupt changes or sudden shifts at the edges, thus ensuring that the material distribution in the extrapolated region maintains a general continuity and consistency with the original surface shape.

[0060] Step 3: Process the three-level high-frequency information {S} obtained from multi-scale wavelet decomposition. LH ,S HL ,S HH Modeling and extension are performed for the three-level high-frequency information {S}. LH ,S HL ,S HH These three are essentially high-frequency responses in different directions at the same scale, possessing complementary structural information. Therefore, during processing, they are input into the network as tensors of the three channels, forming a high-frequency feature tensor:

[0061] Step 31, as Figure 6 As shown. In this embodiment, in order to extract effective third-level high-frequency information {S} from multi-scale wavelet decomposition. LH ,S HL ,S HH By performing joint modeling and extension, a three-stage high-frequency feature prediction network was constructed. The high-frequency feature prediction network consists of three functional modules: a multi-scale convolutional feature extraction module, a residual enhancement and nonlinear modeling module, and a high-frequency prediction output module.

[0062] Step 32: Using the high-frequency feature tensor S H As input, the spatial distribution characteristics and local texture patterns are learned through a deep neural network to achieve fine-grained completion of missing edge regions. The specific implementation process is as follows:

[0063] Step 33: The multi-scale convolutional feature extraction module employs three sets of parallel convolutional branches. The three sets of parallel convolutional kernels are 3×3, 5×5, and 7×7, respectively, for the input high-frequency feature tensor S. H Feature extraction is performed, and all branches share the high-frequency feature tensor S. H The input is processed through convolutions in each branch, followed by BN layers and FReLU activation functions. Finally, the input is concatenated through channels to form a preliminary feature map F. (1) ;

[0064] Set input as The output of each branch is as follows:

[0065]

[0066] Where, σ i (·) represents the FReLU activation function; C represents the number of output channels in each convolutional branch, and all branches have the same output size;

[0067] The merging method is channel splicing or weighted summation to obtain a preliminary feature map;

[0068]

[0069] By integrating information from three directions (horizontal, vertical, and diagonal), a unified detailed response map is formed.

[0070] Step 34: The residual enhancement and nonlinear modeling module introduces a multi-layer residual structure to enhance the expressive power of complex high-frequency structures. Each layer contains 3×3 convolution, BN, and FReLU activation functions, and the output is the feature-enhanced tensor F. (2) ;

[0071] In this embodiment, multiple residual blocks are constructed, each residual block including two 3×3 convolutions. Each convolution is followed by Batch Normalization (BN) and FreLU. The feature map F output by the multi-scale convolutional feature extraction module is... (1) After passing through a set of residual blocks, the enhanced tensor F is output. (2) The tensor F (2) As an intermediate high-dimensional feature map, it is expressed by the following formula:

[0072] F1 (2) =σ(BN(Conv) 3×3 (F (1) )));

[0073]

[0074]

[0075] Among them, F1 (1) , This is the intermediate output of the first and second layers in the residual block; by stacking two residual blocks, it serves as the deep structure learning part.

[0076] Step 35: After the high-frequency prediction output module completes multi-scale information fusion and deep feature extraction, the network further extracts high-order detail features through two layers of 3×3 convolutions and introduces a spatial attention mechanism to obtain the enhanced feature map.

[0077] In this embodiment, the high-frequency prediction output module is the final link in the entire high-frequency feature prediction network. Its core task is to extract and fuse the intermediate high-dimensional feature maps from the first two layers. Transformed into high-frequency information prediction results with physical meaning

[0078] First, the intermediate high-dimensional feature map F (2) A two-layer cascaded 3×3 convolution (each layer equipped with BatchNormalization (BN) and ReLU activation) is used to preserve the original feature information through residual connections, while introducing deeper nonlinear mapping capabilities. This part of the structure can be represented as:

[0079] F (3) =ReLU(BN(Conv) 3×3 (F (2) )))

[0080] Since optical surface data often exhibits structural discontinuities, texture occlusion, or high-frequency missing features in edge regions, direct completion often leads to unnatural edge transitions or structural drift. Therefore, this module introduces a spatial attention mechanism to dynamically adjust the network's response intensity in the spatial domain. This attention module combines average pooling and max pooling channel information from the input features and generates a spatial weight map through 1×1 convolution and sigmoid activation.

[0081]

[0082] The final enhanced feature map is represented as follows:

[0083]

[0084] Step 36: After feature enhancement, the network finally performs channel compression and projection using a 1×1 convolution, mapping the multi-channel deep features into high-frequency subband prediction results in three directions. Right now:

[0085]

[0086] The three channels in the output tensor correspond to S respectively. LH ,S HL ,S HH The high-frequency subbands of wavelets in three directions, and the high-frequency information prediction results are as follows: Figure 7 As shown.

[0087] Step 4: The extended low-frequency information and the predicted high-frequency information are fused and reconstructed through inverse wavelet transform (IDWT) to obtain the complete extended surface shape.

[0088] The four sub-bands after extension are input into the inverse wavelet transform function to recover the extended image at the full scale;

[0089]

[0090] In this embodiment, the extended surface shape includes information about the virtual extended region missing in the original surface shape, which can numerically complete the edge material distribution, ensuring that the edge region participates in the complete material removal cycle and improving the sufficiency of boundary processing. This characteristic is particularly critical in numerically sensitive algorithms such as Fourier transforms—boundary omissions will cause strong oscillations and decoupling effects, further amplifying edge errors. Therefore, the core value of surface extension lies in: by expanding the surface definition domain in the process-aided software, realizing the mathematical closure of the convolution operation in the edge region, thereby restoring the continuity and integrity of the dwell time distribution, effectively suppressing edge effects, and improving the processing stability and optimization calculation accuracy of the entire system.

[0091] like Figure 8As shown, the left side of the figure presents two-dimensional and three-dimensional views of the original surface shape, displaying its height distribution. The right side is a numerical grid, where each number represents the height information of the surface shape data at the corresponding location. On this grid, the process of the polishing head (which can be understood as a convolution kernel) performing convolution calculations in the extended region can be seen. By extending the surface shape, data that was not present outside the original edge region is obtained, allowing the polishing head to perform complete convolution operations in these regions as well. This ensures the integrity and continuity of the residence time field at the edge of the component, guarantees the amount of material removed at the edge, and effectively suppresses edge effects in optical processing.

[0092] It should be noted that the low-frequency extension method (such as low-frequency information fitting based on Zernike polynomials) and the deep network design for high-frequency regions used in the above embodiments are both feasible implementations of this invention. For low-frequency modeling, it can also be replaced by two-dimensional Legendre polynomial fitting, Chebyshev basis fitting, or custom function family modeling based on Gram-Schmidt orthogonalization; for the completion strategy in high-frequency regions, the specific structure of the local feature prediction network also has a certain degree of flexibility. For example, edge response capabilities can be enhanced by introducing attention mechanisms, multi-scale fusion, graph convolution, or transformer structures.

[0093] The technical features of the above embodiments can be combined in any way. For the sake of brevity, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0094] The embodiments described above are merely illustrative of several implementations of the present invention, and while the descriptions are relatively specific and detailed, they should not be construed as limiting the scope of the invention patent. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of the present invention, and these all fall within the protection scope of the present invention. Therefore, the protection scope of this invention patent should be determined by the appended claims.

Claims

1. A multi-scale extension method for suppressing edge effects in optical polishing, characterized by: This method is implemented by the following steps: Step 1: Obtain the original surface shape data of the optical element, and perform two-dimensional discrete wavelet decomposition on the original surface shape data to obtain low-frequency and high-frequency information; Step 2: Model and extend the low-frequency information obtained in Step 1 to obtain the extended low-frequency image; Step 3: Use a high-frequency feature prediction network to model and extend the high-frequency information obtained in Step 1, and predict the high-frequency sub-band prediction images in three directions. Step 4: Transfer the low-frequency image obtained in Step 2 to... And the high-frequency subband prediction images in three directions obtained in step three. The extended complete surface shape is obtained by fusing and reconstructing using inverse wavelet transform.

2. The multi-scale extension method for suppressing edge effects in optical polishing according to claim 1, characterized in that: In step one, the specific process of obtaining low-frequency and high-frequency information using two-dimensional discrete wavelet decomposition is as follows: Step 1: Input the original surface shape data; Steps 1 and 2: Filtering and downsampling along the vertical direction of the original surface data; obtaining the low-frequency subband S. LL (x,y) and the first-level high-frequency subband S H1 (x,y); Step 13: For the first-level high-frequency subband S H1 (x,y) is then filtered and downsampled along the horizontal direction to obtain the high-frequency subband S representing the vertical direction. LH (x,y) and the second-level high-frequency subband S H2 (x,y); Step 1.4: For the second-level high-frequency subband S H2 (x,y) is then filtered and downsampled along the diagonal to obtain the high-frequency subband S in the horizontal direction. HL (x,y) and the high-frequency subband S in the diagonal direction HH (x,y); The low-frequency subband S LL (x,y) is used as low-frequency information, and the high-frequency subbands S in the vertical, horizontal, and diagonal directions are... LH (x,y),S HL (x,y) and S HH (x,y) is used as high-frequency information.

3. The multi-scale extension method for suppressing edge effects in optical polishing according to claim 2, characterized in that: The specific process of step two is as follows: Step 21: Transfer the low-frequency subband S LL The coordinates of each pixel in (x,y) are mapped to standard normalized grid coordinates, and the grid coordinates are converted to polar coordinates; Step 22: Construct polynomial basis functions within the unit circle domain, fit the known region using the least squares method, and solve for the optimal coefficients; Steps 2 and 3: Construct a low-frequency fitting model based on the optimal coefficients. Step 24: Construct polar coordinate points in the region to be extended and substitute them into the low-frequency fitting model to perform extension, thereby obtaining the low-frequency predicted value of the extended region. Step 25: Convert the low-frequency prediction values ​​of the extended region back to the pixel coordinate form of Step 21, and correlate them with the low-frequency sub-band S. LL (x,y) are stitched together to synthesize a complete low-frequency image after extension.

4. The multi-scale extension method for suppressing edge effects in optical polishing according to claim 1, characterized in that: The specific process of step three is as follows: Step 3: Construct a high-frequency feature prediction network, which consists of a multi-scale convolutional feature extraction module, a residual enhancement and nonlinear modeling module, and a high-frequency prediction output module. Step 3.2: Input the high-frequency information into the high-frequency feature prediction network to form a high-frequency feature tensor S. H ; Step 3: The multi-scale convolutional feature extraction module extracts high-frequency feature tensors S. H Feature extraction is performed to form a preliminary feature map F. (1) ; Steps three and four: The residual enhancement and nonlinear modeling module introduces a multi-layer residual structure, and the initial feature map F... (1) After passing through the residual block, the enhanced tensor F is output. (2) ; Step 3.5: The high-frequency prediction output module processes the enhanced tensor F. (2) Convolution and nonlinear mapping are performed, and a spatial attention mechanism is introduced to finally obtain the enhanced feature map. Step 36: Process the enhanced feature map Channel compression and projection are performed using a 1×1 convolution to map the deep features of multiple channels into high-frequency subband prediction results in three directions.

5. A multi-scale extension method for suppressing edge effects in optical polishing according to claim 4, characterized in that: In step three, five: First, the enhanced tensor F... (2) As the intermediate high-dimensional feature map F (2) Two concatenated 3×3 convolutional layers are used, and feature F is obtained through residual connections and nonlinear mapping. (3) ; Spatial attention mechanism is used for the feature F (3) Perform average pooling and max pooling operations, and generate a spatial weight map through 1×1 convolution and sigmoid activation: The final enhanced feature map is represented as follows:

Images