A Deep Learning-Based Method and System for Fitting Aspheric Removal Functions

Abstract

This invention provides a method and system for fitting aspherical removal functions based on deep learning, relating to the field of optical technology. The method includes: obtaining at least two true removal functions for spherical workpieces with different radii of curvature, and multiple true removal functions for a continuously curvatured aspherical calibration workpiece at corresponding continuously changing curvature positions on its surface; discretizing each removal function in polar coordinates to obtain several data samples; constructing a deep learning network; obtaining a preset composite loss function; using several data samples, iteratively optimizing the network parameters of the deep learning network with the goal of minimizing the composite loss function, to obtain a trained deep learning network; inputting the polar radius, polar angle, and radius of curvature of any point D on the aspherical surface to be processed into the trained deep learning network to obtain the height distribution of the removal function at point D; this invention can significantly improve the processing accuracy and surface quality of aspherical optical elements.

Description

Technical Field

[0001] This invention relates to the field of optical technology, and in particular to a method and system for fitting aspheric removal functions based on deep learning. Background Technology

[0002] In existing deterministic polishing processes for optical components, removal functions are typically calibrated using planar or spherical workpieces with a single radius of curvature. However, for aspherical optical components with continuously varying curvature, the local curvature differences at different locations on the surface are significant. This causes the removal function calibrated under a planar or single curvature to fail to accurately reflect the material removal characteristics during actual processing, resulting in curvature mismatch. Consequently, low-frequency surface shape errors are not thoroughly corrected, and mid-frequency errors are easily introduced during processing. Furthermore, traditional removal function calibration methods require re-experimentation for each new curvature, which is not only inefficient but also unable to adapt to the continuously varying curvature characteristics of aspherical surfaces. Summary of the Invention

[0003] To address the aforementioned technical problems, the technical solution adopted by this invention is as follows:

[0004] According to a first aspect of this application, a deep learning-based method for fitting aspheric removal functions is provided, the method comprising the following steps:

[0005] S100, obtain at least two real removal functions for spherical workpieces with different radii of curvature, and multiple real removal functions for an aspherical calibration workpiece with continuously varying curvature at the corresponding continuously varying curvature positions on the surface;

[0006] S200 discretizes each removal function in polar coordinates to obtain several data samples; each data sample contains the polar radius ρ, polar angle θ, radius of curvature R, and the corresponding removal function height value.

[0007] S300, construct a deep learning network with polar radius ρ, polar angle θ, and radius of curvature R as inputs and the height value of the removal function as output;

[0008] S400, Obtain the preset composite loss function; the composite loss function includes: a data fitting loss term, used to measure the difference between the network's predicted removal function and the actual removal function; a rotational symmetry constraint term, used to penalize the asymmetry of the network output in the polar angle θ direction; and a volume continuity constraint term, used to constrain the smoothness of the removal function volume change with curvature under adjacent curvature radii.

[0009] S500: Using several data samples, with the goal of minimizing the composite loss function, iteratively optimize the network parameters of the deep learning network to obtain a trained deep learning network.

[0010] S600 inputs the polar radius, polar angle, and radius of curvature of any point D on the aspherical surface to be processed into the trained deep learning network to obtain the height distribution of the removal function at point D.

[0011] According to another aspect of this application, a deep learning-based aspherical removal function fitting system is also provided, the system comprising:

[0012] The data acquisition module is used to acquire the real removal functions of at least two spherical workpieces with different radii of curvature, and multiple real removal functions of an aspherical calibration workpiece with continuously varying curvature at the corresponding continuously varying curvature positions on the surface.

[0013] The data sample generation module is used to discretize each removal function in polar coordinates to obtain several data samples; each data sample contains the polar radius ρ, polar angle θ, radius of curvature R, and the corresponding removal function height value.

[0014] The network building module is used to build a deep learning network that takes the polar radius ρ, polar angle θ, and radius of curvature R as inputs and the height value of the removal function as output.

[0015] The loss function configuration module is used to obtain a preset composite loss function. The composite loss function includes: a data fitting loss term, which measures the difference between the network's predicted removal function and the actual removal function; a rotational symmetry constraint term, which penalizes the asymmetry of the network output in the polar angle θ direction; and a volume continuity constraint term, which constrains the smoothness of the removal function volume as the curvature changes under adjacent radii of curvature.

[0016] The training module is used to iteratively optimize the network parameters of the deep learning network using several data samples, with the goal of minimizing the composite loss function, to obtain a trained deep learning network.

[0017] The fitting application module is used to input the polar radius, polar angle, and radius of curvature of any point D on the aspherical surface to be processed into the trained deep learning network to obtain the height distribution of the removal function at point D.

[0018] The present invention has at least the following beneficial effects:

[0019] The aspherical removal function fitting method based on deep learning of the present invention obtains at least two real removal functions of spherical workpieces with different radii of curvature and multiple real removal functions of an aspherical calibration workpiece with continuously varying curvature at corresponding positions of continuously varying curvature on the surface. This constructs a training dataset covering discrete and continuous curvature intervals. Then, a deep learning network is trained with the polar radius, polar angle, and radius of curvature as inputs and the height value of the removal function as output. During the training process, a composite loss function including a data fitting loss term, a rotational symmetry constraint term, and a volume continuity constraint term is used, enabling the network to accurately learn the nonlinear mapping relationship between curvature and the shape of the removal function. Therefore, when this network is applied to the aspherical workpiece to be processed, it can dynamically output a removal function that matches the local curvature at any position on the surface, fundamentally solving the curvature mismatch problem caused by planar or single curvature calibration in the prior art. It also overcomes the technical defect of poor adaptability of removal function under continuous change of aspherical curvature. Since the accuracy and curvature adaptability of the removal function are significantly improved, the residence time distribution calculated based on it is more accurate, which can efficiently correct low-frequency surface shape errors and effectively suppress the introduction of mid-frequency errors, ultimately greatly improving the processing accuracy and surface quality of aspherical optical elements. Attached Figure Description

[0020] To more clearly illustrate the technical solutions in the embodiments of the present invention, the accompanying drawings used in the description of the embodiments will be briefly introduced below. Obviously, the accompanying drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0021] Figure 1 A flowchart of a deep learning-based aspheric removal function fitting method provided in an embodiment of the present invention. Detailed Implementation

[0022] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0023] It should be noted that, based on this disclosure, those skilled in the art will understand that one aspect described herein can be implemented independently of any other aspect, and two or more of these aspects can be combined in various ways. For example, any number of aspects set forth herein can be used to implement the device and / or practice the method. Furthermore, this device and / or practice the method can be implemented using other structures and / or functionalities besides one or more of the aspects set forth herein.

[0024] The following will refer to Figure 1 The flowchart shown is for a deep learning-based aspheric removal function fitting method, which introduces such a method.

[0025] The deep learning-based method for fitting aspheric removal functions may include the following steps:

[0026] S100, obtain at least two true removal functions for spherical workpieces with different radii of curvature, and multiple true removal functions for an aspherical calibration workpiece with continuously varying curvature at corresponding positions on the surface.

[0027] In this embodiment, it is assumed that the radius of curvature needs to be obtained. and The true removal function for two spherical workpieces.

[0028] High-quality optical glass (such as fused silica or silicon carbide) can be used to make spherical lenses or mirrors, whose radius of curvature is precisely measured (e.g., using a laser interferometer or sphere gauge). The workpiece surface needs to be pre-polished to a certain smoothness, and the initial surface height is known (recorded as...). x represents the coordinate value of the workpiece surface in the horizontal direction (usually transverse), and the unit is generally millimeters (mm). y represents the coordinate value of the workpiece surface in the vertical direction (usually longitudinal), and the unit is also millimeters (mm).

[0029] Using the same polishing process parameters (polishing wheel speed) Polishing pressure Immersion depth Polishing time The robotic polishing equipment performs point-to-point polishing on localized areas of each spherical workpiece. The surface shape before and after polishing is measured using an interferometer, and the difference in surface shape is calculated and divided by the polishing time to obtain the true removal function for the two spherical workpieces. and .

[0030] In this embodiment, the reason for obtaining the true removal functions of the spherical workpiece under at least two different radii of curvature is that the removal function for a single curvature cannot reflect the impact of curvature changes; data from at least two different curvatures can preliminarily reveal trends (such as how the size or peak value of the removal function changes as the curvature increases / decreases). Furthermore, deep learning models require diverse input-output pairs to learn meaningful mappings. Using two or more discrete curvatures as supervision signals, combined with subsequent continuous curvature data, is sufficient to allow the network to interpolate removal functions for arbitrary intermediate curvatures.

[0031] Furthermore, the multiple true removal functions of the aspherical calibration workpiece with continuously varying curvature at the corresponding positions of continuously varying curvature on the surface are obtained through the following steps:

[0032] S110 provides an aspherical calibration workpiece with a surface curvature radius that varies continuously in the radial direction, and pre-measures the initial surface shape distribution of the aspherical calibration workpiece.

[0033] In this embodiment, a non-spherical calibration workpiece with a surface curvature radius that continuously varies radially is machined. For example, a quadratic surface equation is used:

[0034] ;

[0035] in, Radial coordinates, For vertex curvature, This is the conic coefficient. By selecting an appropriate... and This can make the radius of curvature Monotonically changing along the radial direction, for example from the vertex Gradually increase to the edge .

[0036] Using a high-precision laser interferometer or coordinate measuring machine, the surface shape distribution of the workpiece before processing is measured to obtain the initial surface height matrix. The spacing between measurement points is typically 0.1mm to 1mm, resulting in hundreds to thousands of data points throughout the entire workpiece diameter.

[0037] Based on the workpiece's design equations, each radial position can be analytically calculated. radius of curvature at:

[0038] ;

[0039] Discretize the function to obtain the coordinates corresponding to each point. The value serves as a known condition for subsequent solutions.

[0040] In this embodiment, the aperture can be used. Silicon carbide aspherical calibration workpiece, vertex radius of curvature Edge curvature radius The curvature changes approximately linearly along the radial direction. The initial surface shape PV value is better than 0.1λ (λ=632.8nm).

[0041] S120, using the same polishing process parameters as the spherical workpiece, perform a standard polishing process on the surface of the non-spherical calibration workpiece, measure the surface shape distribution after processing, calculate the surface shape difference before and after processing, and obtain the removal depth distribution of the entire workpiece surface.

[0042] The same process parameters as those used for the spherical workpiece in step S100 are employed: polishing wheel speed. Polishing pressure Immersion depth Polishing time The polishing solution is a cerium oxide suspension (concentration). ).

[0043] The goal of this process is to obtain material removal information at different curvature locations across the entire workpiece surface; therefore, the polishing tool must cover the entire workpiece surface. A spiral path or a raster scan path can be used, with the tool's dwell time at each point remaining constant (e.g., uniform scanning). In this way, the removal depth distribution is primarily influenced by the shape of the local removal function, and is independent of the dwell time distribution.

[0044] After polishing, the surface shape of the workpiece was measured again using the same interferometer to obtain... .

[0045] Calculate the depth distribution to be removed:

[0046] ;

[0047] Because the polishing time is short The values ​​are typically between tens of nanometers and a few micrometers. This distribution reflects the total amount of material removed per unit time at each location on the workpiece surface (but is affected by convolution and is not directly equal to the removal function).

[0048] S130, based on the known radius of curvature distribution function of the aspherical calibration workpiece. Based on the aforementioned removal depth distribution, the removal function shapes corresponding to different curvature radii are calculated using a deconvolution algorithm or a region decomposition algorithm, resulting in several real removal function samples covering continuous curvature intervals; among which, The coordinates are the radial coordinates of the workpiece surface.

[0049] The measured removal depth distribution is due to the polishing path covering the entire workpiece. This is the result of a two-dimensional convolution between the removal function and the polishing time distribution. Given the polishing tool's trajectory and dwell time distribution, the shape of the removal function for each local region can be solved through inverse operations, as follows:

[0050] Based on the radius of curvature distribution function The workpiece surface is divided radially into Each annular region has a radius of curvature that varies no more than a preset threshold (e.g., ±5mm).

[0051] Within each annular region, since the curvature is approximately constant, the removal function can be considered spatially invariant. At this point, the measured removal depth distribution... Within this region, it is approximately equal to the convolution of the removal function and the tool dwell time distribution.

[0052] Since the dwell time distribution is known (uniform scanning, dwell time is inversely proportional to scanning speed), a system of linear equations can be established, and the removal function of the region can be solved by the least squares method.

[0053] Sort the removal functions obtained from each region according to their radius of curvature to obtain the results. A sample of real removal functions, covering from... arrive The continuous curvature interval.

[0054] Example: In this embodiment, the radial direction is divided into 10 equally wide annular zones, with a curvature variation of approximately 60 mm within each zone. Removal depth data along the centerline of each zone is selected, and using the known dwell time (calculated from the scan velocity distribution), a least-squares fit is obtained. The pixel removal function matrix (each pixel corresponds to a polar coordinate grid point). A total of 10 removal functions are obtained, with curvature radii of 630, 690, 750, ..., 1170 mm.

[0055] The calculated removal function may contain noise, which can be smoothed using Gaussian filtering or singular value decomposition (SVD). To ensure consistency with the spherical calibration data, the calculated result can be compared and calibrated with two real removal functions obtained from the spherical calibration. For example, the magnitude of the removal function can be adjusted by linear scaling to make the two consistent at the overlapping curvature.

[0056] S200 discretizes each removal function in polar coordinates to obtain several data samples; each data sample contains the polar radius ρ, polar angle θ, radius of curvature R, and the corresponding removal function height value.

[0057] Furthermore, the polar coordinate system established in step S200 is as follows:

[0058] With the center point of the distribution of the removal function as the pole, and any ray as the polar axis, the polar radius... The range of values ​​for is [0, ρ max ],in To remove the effective radius of action of the function; polar angle The range of values ​​is During discretization, the polar radius directions are taken at equal intervals. Each sampling point is taken at an equal angle in the polar direction. There are 10 sampling points, and each sampling point corresponds to a data sample.

[0059] In this embodiment, the center point of the removal function distribution (i.e., the center of the contact area between the polishing tool and the workpiece) is taken as the pole, and any ray (such as the horizontal rightward direction) is taken as the polar axis. Polar radius The range of values ​​for is [0, ρ max ],in, To determine the effective radius of the removal function, the removal height is typically reduced to its peak value. or Radius values ​​within, for example: Polar angle The range of values ​​is During discretization, the polar radius directions are taken at equal intervals. A number of sampling points, for example: Polar angle direction is taken as equal angle. A number of sampling points, for example: (corresponding to each) (One sampling point). Each sampling point corresponds to a data sample, whose radius of curvature is equal to the radius of curvature of the workpiece to which the removal function belongs. The height of the removal function is the experimentally measured removal depth value divided by the polishing time. In this example, a total of [data points] are obtained. One data sample.

[0060] S300 constructs a deep learning network that takes the polar radius ρ, polar angle θ, and radius of curvature R as inputs and the height of the removal function as output.

[0061] Furthermore, the deep learning network is a neural network consisting of six fully connected layers connected sequentially; the input layer receives a three-dimensional vector (ρ, θ, R), the first fully connected layer has 128 neurons, the second fully connected layer has 256, the third fully connected layer has 256, the fourth fully connected layer has 128, the fifth fully connected layer has 64, and the output layer has 1 neuron; except for the output layer, all other layers use the ReLU activation function, and the output layer does not use an activation function.

[0062] In this embodiment, the deep learning network employs a fully connected (dense) feedforward neural network, consisting of six fully connected layers connected sequentially. The input layer receives a three-dimensional vector. , where the polar diameter and polar angle Discretized from polar coordinates, radius of curvature The curvature distribution originates from the calibrated or workpiece to be processed. The network structure is as follows:

[0063] 1. Input normalization:

[0064] To improve training convergence, the three features are normalized separately before being input into the network:

[0065] Divide by the maximum radius (like ), transform to the [0,1] interval.

[0066] Divide by Transform to the [0,1] interval.

[0067] : Use min-max normalization, ,in and Take the minimum and maximum values ​​of the radius of curvature in the training data, respectively.

[0068] 2. Network layer configuration:

[0069] First fully connected layer (FC1): Input dimension 3, output dimension 128. Weight matrix size. The bias vector length is 128.

[0070] Second fully connected layer (FC2): Input dimension 128, output dimension 256. Weights , bias 256.

[0071] The third fully connected layer (FC3): input dimension 256, output dimension 256. Weights , bias 256.

[0072] Fourth fully connected layer (FC4): Input dimension 256, output dimension 128. Weights , bias 128.

[0073] Fifth fully connected layer (FC5): Input dimension 128, output dimension 64. Weights , bias 64.

[0074] The sixth fully connected layer (output layer, FC6): input dimension 64, output dimension 1. Weights , bias 1.

[0075] 3. Activation function:

[0076] Except for the output layer, FC1 through FC5 all use the ReLU activation function (Rectified Linear Unit). ReLU can effectively alleviate the vanishing gradient problem and accelerate training.

[0077] The output layer does not use an activation function; it directly outputs a linear value, which is the predicted height of the removal function (units consistent with the training data, e.g., ...). ).

[0078] The network has approximately 128,000 parameters, making it a lightweight network that can be trained in minutes on a mainstream GPU.

[0079] S400, Obtain the preset composite loss function; the composite loss function includes: a data fitting loss term, used to measure the difference between the network's predicted removal function and the actual removal function; a rotational symmetry constraint term, used to penalize the asymmetry of the network output in the polar angle θ direction; and a volume continuity constraint term, used to constrain the smoothness of the removal function volume change with curvature under adjacent curvature radii.

[0080] Furthermore, the composite loss function The following relationship must be satisfied:

[0081] ;

[0082] in, The loss term for data fitting is expressed in the form of mean squared error:

[0083] ;

[0084] The total number of data samples, For deep learning networks targeting the first The height value of the removal function predicted for each data sample. This corresponds to the actual height value of the removal function.

[0085] During the training loop, a small batch is read from the data loader, forward propagation is performed to obtain the predicted values, and then the MSE is calculated. This loss is a standard regression loss, ensuring that the network has a basic ability to fit the training data.

[0086] Physical significance: It forces the removal function output by the network to be as close as possible to the experimental measurement at every point in space, which is the basis for training convergence.

[0087] For rotational symmetry constraints, ;

[0088] is the number of polar radius sampling points, j is the index number of the polar radius sampling point, and k is the index number of the polar angle sampling point; Indicates that at the polar radius is Polar angle is At the position, the removal function height value predicted by the deep learning network; Indicates the same polar radius Next, take the predicted height values ​​corresponding to all different polar angles and calculate the corresponding variance.

[0089] In practical polishing, for spherical or axisymmetric aspherical local regions, the removal function usually has rotational symmetry (i.e., it only changes with the extreme radius). Related to polar angle (Irrelevant). To constrain the network output to conform to this property, define... .

[0090] During training, for the same radius of curvature All polar coordinate grid points are grouped by polar radius, and the variance of the predicted height value is calculated for each group. Then, the variances of all polar radii are averaged. Typically, this loss term is accumulated over all samples in the batch and averaged.

[0091] Physical meaning: When the network output is perfectly rotationally symmetric, each polar radius... The angular variance is zero. If asymmetry exists, the loss increases, thus penalizing the asymmetry of the network output. This avoids the non-physical "warping" removal function caused by data noise or network overfitting.

[0092] For volume continuity constraints, ;

[0093] This represents the number of different radii of curvature in the data sample, where m is the index of the radius of curvature. For the m-th radius of curvature value, the volume function , representing the radius of curvature The total volume of the corresponding removal function within its supporting region; and These are the preset weighting coefficients.

[0094] The volume of the polishing removal function (i.e. the total amount of material removed) should maintain physical continuity as the workpiece radius of curvature changes—when the radius of curvature changes slowly, the volume of the removal function should also change slowly, without abrupt changes.

[0095] During training, for each radius of curvature First, calculate all predicted height values ​​under this curvature, then substitute them into the numerical integral to obtain the volume. Then sum the squares of the volume differences between adjacent radii of curvature. To prevent numerical instability, the volume can be normalized first (e.g., divided by the maximum volume).

[0096] Physical meaning: The volume of the removal function learned by the constraint network exhibits a smooth and monotonic trend with curvature (e.g., as the radius of curvature increases, the contact area decreases, and the volume usually decreases). If the network experiences abrupt changes (e.g., ... The volume was very large at that time. When the volume suddenly becomes very small, this loss will increase significantly, forcing the network to learn more reasonable physical relationships.

[0097] α controls the strength of the rotational symmetry constraint. Recommended value range: If the training data itself has good symmetry, a smaller value can be set (such as 0.01); if the data noise causes the network output to be asymmetrical, it can be appropriately increased to 0.1.

[0098] β controls the strength of the volume continuity constraint. Recommended value range: Since the volume is typically large, to avoid affecting the dominant role of data fitting, it can be set to... Compare A smaller order of magnitude, for example .

[0099] Through the aforementioned composite loss function, the deep learning network not only learns the mapping between curvature and the height of the removal function, but also inherently satisfies the prior knowledge of rotational symmetry and volume continuity of optical polishing, thereby improving the model's generalization ability and physical credibility.

[0100] S500: Using several data samples, with the goal of minimizing the composite loss function, iteratively optimize the network parameters of the deep learning network to obtain a trained deep learning network.

[0101] Furthermore, in step S500, the Adam optimizer is used for iterative optimization, with the initial learning rate set to 0.001. When the composite loss function... The value dropped to The decrease in the following 10 consecutive iterations is less than Training should be stopped at this time.

[0102] In this embodiment, the data sample obtained in step S200 is used to minimize the composite loss function. To achieve this, the deep learning network constructed in step S300 is trained. The specific training strategy is as follows:

[0103] Optimizer: The Adam optimizer is used, with an initial learning rate set to... First-order moment attenuation coefficient Second-order moment attenuation coefficient .

[0104] Batch size: Set to 256 to balance training speed and stability.

[0105] Iteration termination condition: When the composite loss function The value dropped to Below, and the decrease within 10 consecutive epochs is less than Training should be stopped when the time comes.

[0106] Training process: In each epoch, the training samples are randomly shuffled and input into the network in batches. Forward propagation is used to calculate the predicted height, and then the composite loss (including data fitting loss, rotational symmetry constraint, and volume continuity constraint) is calculated. Finally, backpropagation is used to update the network weights. After each epoch, the loss change is monitored on the validation set.

[0107] Model saving: After the stopping condition is met, the network structure and weight parameters are saved for subsequent fitting applications in step S600.

[0108] S600 inputs the polar radius, polar angle, and radius of curvature of any point D on the aspherical surface to be processed into the trained deep learning network to obtain the height distribution of the removal function at point D.

[0109] In this embodiment, after the deep learning network is trained, the polar coordinate parameters and radius of curvature of each point on the surface of the aspherical workpiece to be processed are input into the trained deep learning network to obtain the spatial distribution of the removal function at that point.

[0110] Furthermore, the method for obtaining the radius of curvature of any point D on the aspherical surface to be processed in step S600 is as follows:

[0111] Based on the surface shape equation of the aspherical surface to be processed Calculate the principal radius of curvature or the mean radius of curvature at point D, and use it as the radius of curvature of D. .

[0112] Based on the surface shape equation of the aspherical surface to be processed Calculate any point on the surface The principal radius of curvature. The mean radius of curvature is usually used. ,in, These are the radii of curvature in the two principal directions. Alternatively, the radius of curvature in the meridional direction can be used directly. [The point is...] polar diameter Polar angle (with the center of the polishing tool as the origin) and the calculated radius of curvature The normalized values ​​are then input into the network.

[0113] Furthermore, obtaining the removal function height distribution at point D in step S600 includes:

[0114] The polar radius of point D Polar angle and radius of curvature After inputting the trained deep learning network, the deep learning network outputs a two-dimensional array, which represents the removal height value on the polar coordinate grid in the local region centered at D, thus forming the spatial distribution of the removal function at point D.

[0115] The deep learning network outputs a two-dimensional array of size . (Number of polar radius sampling points × Number of polar angle sampling points), corresponding to the height values ​​removed on the polar coordinate grid. For example, Then output a The matrix, representing the matrix with... This represents the material removal depth distribution per unit time within a local region centered on the matrix. Transforming this matrix (e.g., interpolating to a Cartesian grid) yields the removal function shape at that point. Repeating this process for all machining locations on the workpiece surface allows us to obtain the removal function for each location.

[0116] Furthermore, after step S600, the method further includes the following steps:

[0117] S700: Using the height distribution of the removal function at each point on the aspherical surface to be processed obtained in step S600, convolve the result with the preset target removal amount distribution to calculate the residence time distribution of the polishing tool at each point on the aspherical surface to be processed.

[0118] Using the removal functions obtained in step S600 and the known target removal amount distribution (initial surface error minus ideal surface shape), the dwell time distribution is solved through convolution. Since the removal function varies with curvature (spatial variation), an iterative deconvolution algorithm (such as the Richardson-Lucy or conjugate gradient method) can be used to calculate the dwell time of the polishing tool at each point on the workpiece surface. .

[0119] It should be noted that those skilled in the art can use existing iterative deconvolution algorithms (such as the Richardson-Lucy or conjugate gradient method) to calculate the dwell time of the polishing tool at various points on the workpiece surface, according to actual needs. This will not be elaborated upon here.

[0120] S710 controls the polishing equipment to perform polishing processes based on the residence time distribution.

[0121] The calculated residence time distribution is converted into CNC code to control the polishing equipment (such as a robotic polishing system) to move along the planned path, and the residence time at each point is calculated accordingly. The shape is directly proportional to the surface shape, thus achieving deterministic removal. After processing, the surface shape can be measured again; if it does not meet the standard, the above process is repeated.

[0122] Furthermore, although the steps of the method in this disclosure are described in a specific order in the accompanying drawings, this does not require or imply that the steps must be performed in that specific order, or that all the steps shown must be performed to achieve the desired result. Additional or alternative steps may be omitted, multiple steps may be combined into one step, and / or a step may be broken down into multiple steps.

[0123] Embodiments of the present invention also provide a deep learning-based aspherical removal function fitting system, the system comprising:

[0124] The data acquisition module is used to acquire the actual removal functions of at least two spherical workpieces with different radii of curvature, and multiple actual removal functions of an aspherical calibration workpiece with continuously varying curvature at the corresponding continuously varying curvature positions on the surface.

[0125] The data sample generation module is used to discretize each removal function in polar coordinates to obtain several data samples; each data sample contains the polar radius ρ, polar angle θ, radius of curvature R, and the corresponding removal function height value.

[0126] The network building module is used to construct a deep learning network that takes the polar radius ρ, polar angle θ, and radius of curvature R as inputs and the height value of the removal function as output.

[0127] The loss function configuration module is used to obtain a preset composite loss function. The composite loss function includes: a data fitting loss term, which measures the difference between the network's predicted removal function and the actual removal function; a rotational symmetry constraint term, which penalizes the asymmetry of the network output in the polar angle θ direction; and a volume continuity constraint term, which constrains the smoothness of the removal function volume change with curvature under adjacent curvature radii.

[0128] The training module is used to iteratively optimize the network parameters of the deep learning network using several data samples, with the goal of minimizing the composite loss function, to obtain a trained deep learning network.

[0129] The fitting application module is used to input the polar radius, polar angle, and radius of curvature of any point D on the aspherical surface to be processed into the trained deep learning network to obtain the height distribution of the removal function at point D.

[0130] While specific embodiments of the invention have been described in detail by way of examples, those skilled in the art should understand that the examples are for illustrative purposes only and are not intended to limit the scope of the invention. Those skilled in the art should also understand that various modifications can be made to the embodiments without departing from the scope and spirit of the invention.

Claims

1. A method for fitting an aspherical removal function based on deep learning, characterized in that, The method includes the following steps: S100, obtain at least two real removal functions for spherical workpieces with different radii of curvature, and multiple real removal functions for an aspherical calibration workpiece with continuously varying curvature at the corresponding continuously varying curvature positions on the surface; S200 discretizes each removal function in polar coordinates to obtain several data samples; each data sample contains the polar radius ρ, polar angle θ, radius of curvature R, and the corresponding removal function height value. S300 constructs a deep learning network that takes the polar radius ρ, polar angle θ, and radius of curvature R as inputs and the height value of the removal function as output; S400, Obtain the preset composite loss function; the composite loss function includes: a data fitting loss term, used to measure the difference between the network's predicted removal function and the actual removal function; a rotational symmetry constraint term, used to penalize the asymmetry of the network output in the polar angle θ direction; and a volume continuity constraint term, used to constrain the smoothness of the removal function volume change with curvature under adjacent curvature radii. S500: Using several data samples, with the goal of minimizing the composite loss function, iteratively optimize the network parameters of the deep learning network to obtain a trained deep learning network. S600 inputs the polar radius, polar angle, and radius of curvature of any point D on the aspherical surface to be processed into the trained deep learning network to obtain the height distribution of the removal function at point D.

2. The aspheric removal function fitting method based on deep learning according to claim 1, characterized in that, The multiple real removal functions for the aspherical calibration workpiece with continuously varying curvature at the corresponding positions of continuously varying surface curvature are obtained through the following steps: S110 provides an aspherical calibration workpiece with a continuously varying radial surface curvature radius, and pre-measures the initial surface shape distribution of the aspherical calibration workpiece; S120, using the same polishing process parameters as the spherical workpiece, perform a standard polishing process on the surface of the aspherical calibration workpiece, measure the surface shape distribution after processing, calculate the surface shape difference before and after processing, and obtain the removal depth distribution of the entire workpiece surface. S130, based on the known radius of curvature distribution function of the aspherical calibration workpiece. Based on the aforementioned removal depth distribution, the removal function shapes corresponding to different curvature radii are calculated using a deconvolution algorithm or a region decomposition algorithm, resulting in several real removal function samples covering continuous curvature intervals; among which, The coordinates are the radial coordinates of the workpiece surface.

3. The aspheric removal function fitting method based on deep learning according to claim 1, characterized in that, The composite loss function The following relationship must be satisfied: ； in, The loss term for data fitting is expressed in the form of mean squared error: ； The total number of data samples, For deep learning networks targeting the first The height value of the removal function predicted for each data sample. This corresponds to the actual height value of the removal function; For rotational symmetry constraints, ; is the number of polar radius sampling points, j is the index number of the polar radius sampling point, and k is the index number of the polar angle sampling point; Indicates that at the polar radius is Polar angle is At the position, the removal function height value predicted by the deep learning network; Indicates the same polar radius Next, take the predicted height values ​​corresponding to all different polar angles and calculate the corresponding variance; For volume continuity constraints, ; This represents the number of different radii of curvature in the data sample, where m is the index of the radius of curvature. For the m-th radius of curvature value, the volume function , representing the radius of curvature The total volume of the corresponding removal function within its supporting region; and These are the preset weighting coefficients.

4. The aspheric removal function fitting method based on deep learning according to claim 1, characterized in that, The deep learning network is a neural network consisting of six fully connected layers connected sequentially. The input layer receives a three-dimensional vector (ρ, θ, R). The first fully connected layer has 128 neurons, the second fully connected layer has 256 neurons, the third fully connected layer has 256 neurons, the fourth fully connected layer has 128 neurons, the fifth fully connected layer has 64 neurons, and the output layer has 1 neuron. Except for the output layer, all other layers use the ReLU activation function, while the output layer does not use an activation function.

5. The aspheric removal function fitting method based on deep learning according to claim 1, characterized in that, In step S500, the Adam optimizer is used for iterative optimization, with the initial learning rate set to 0.

001. When the composite loss function... The value dropped to The decrease in the following 10 consecutive iterations is less than Training should be stopped at this time.

6. The aspheric removal function fitting method based on deep learning according to claim 1, characterized in that, The polar coordinate system established in step S200 is as follows: With the center point of the distribution of the removal function as the pole, and any ray as the polar axis, the polar radius... The range of values ​​for is [0, ρ max ],in To remove the effective radius of action of the function; polar angle The range of values ​​is During discretization, the polar radius directions are taken at equal intervals. Each sampling point is taken at an equal angle in the polar direction. There are 10 sampling points, and each sampling point corresponds to a data sample.

7. The aspheric removal function fitting method based on deep learning according to claim 1, characterized in that, The method for obtaining the radius of curvature of any point D on the aspherical surface to be processed in step S600 is as follows: Based on the surface shape equation of the aspherical surface to be processed Calculate the principal radius of curvature or the mean radius of curvature at point D, and use it as the radius of curvature of D. .

8. The aspheric removal function fitting method based on deep learning according to claim 1, characterized in that, The step S600 of obtaining the removal function height distribution at point D includes: The polar radius of point D Polar angle and radius of curvature After inputting the trained deep learning network, the deep learning network outputs a two-dimensional array, which represents the removal height value on the polar coordinate grid in the local region centered at D, thus forming the spatial distribution of the removal function at point D.

9. The aspheric removal function fitting method based on deep learning according to claim 1, characterized in that, Following step S600, the method further includes the following steps: S700: Using the height distribution of the removal function at each point on the aspherical surface to be processed obtained in step S600, convolution operation is performed with the preset target removal amount distribution to calculate the residence time distribution of the polishing tool at each point on the aspherical surface to be processed. S710 controls the polishing equipment to perform polishing processes based on the residence time distribution.

10. A deep learning-based aspherical removal function fitting system, characterized in that, The system includes: The data acquisition module is used to acquire the real removal functions of at least two spherical workpieces with different radii of curvature, and multiple real removal functions of an aspherical calibration workpiece with continuously varying curvature at the corresponding continuously varying curvature positions on the surface. The data sample generation module is used to discretize each removal function in polar coordinates to obtain several data samples; each data sample contains the polar radius ρ, polar angle θ, radius of curvature R, and the corresponding removal function height value. The network building module is used to build a deep learning network that takes the polar radius ρ, polar angle θ, and radius of curvature R as inputs and the height value of the removal function as output. The loss function configuration module is used to obtain a preset composite loss function. The composite loss function includes: a data fitting loss term, which measures the difference between the network's predicted removal function and the actual removal function; a rotational symmetry constraint term, which penalizes the asymmetry of the network output in the polar angle θ direction; and a volume continuity constraint term, which constrains the smoothness of the removal function volume as the curvature changes under adjacent radii of curvature. The training module is used to iteratively optimize the network parameters of the deep learning network using several data samples, with the goal of minimizing the composite loss function, to obtain a trained deep learning network. The fitting application module is used to input the polar radius, polar angle, and radius of curvature of any point D on the aspherical surface to be processed into the trained deep learning network to obtain the height distribution of the removal function at point D.

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