A large-aperture optical element surface shape measurement method based on sub-aperture deduction

Abstract

The application discloses a large-aperture optical element surface shape measurement method based on sub-aperture deduction, and belongs to the field of precise optical detection. The method is proposed in view of the problems of low efficiency and dependence on large-aperture interferometer in traditional large-aperture optical element full-aperture surface shape interference measurement. A data set is constructed by using large-aperture surface shape characteristics randomly generated according to statistical rules of actually measured full-aperture surface shape and two small sub-aperture surface shape characteristics, and is used for neural network training and evaluation. In actual measurement, only two small sub-aperture surface shape characteristics of a measured element are collected, are input into the trained neural network, and full-aperture surface shape characteristics are output, and then the full-aperture surface shape is reconstructed. The method does not need a large-aperture interferometer, significantly reduces the measurement times of a small-aperture interferometer, effectively solves the problem of low efficiency in large-aperture optical element surface shape measurement, and has important application value in the field of precise optical detection.

Description

Technical Field

[0001] This invention relates to the field of optical detection technology for measuring the surface shape of large-aperture optical elements, and specifically to a method for measuring the surface shape of large-aperture optical elements based on sub-aperture derivation. Background Technology

[0002] In the field of optical inspection technology, full-aperture surface shape measurement of large-aperture optical elements is a key step in achieving high-precision optical system performance. This type of measurement typically faces two main technical approaches: direct measurement using large-aperture interferometers and stitched measurement based on small-aperture interferometers. Direct measurement using large-aperture interferometers imposes stringent requirements on the measurement environment, necessitating its implementation in a specialized optical measurement workshop. Stitched measurement using small-aperture interferometers suffers from significant efficiency bottlenecks, and the assembly and adjustment errors introduced during the stitching process, accumulated errors from environmental disturbances, and errors in the data fusion algorithm significantly reduce the accuracy of the final surface shape data.

[0003] Patent document CN117705005A discloses a method and apparatus for detecting the full-aperture surface shape of a convex freeform surface mirror. This method sequentially aligns an interferometer, a phase-calculation holographic element, a quadric surface mirror, and the mirror under test. Interferometry is used to obtain the normal deviation of each detection point relative to the theoretical surface shape. Finally, data processing is used to analyze and determine the actual full-aperture surface shape of the mirror under test. However, this method cannot obtain the full-aperture surface shape of a large-aperture optical element solely through sub-aperture measurement. Patent document CN110243306A discloses a robot-based planar surface shape sub-aperture stitching interferometry device and method. While it uses a small-aperture measurement, it still requires detecting all sub-apertures of the large-aperture optical element, resulting in low efficiency. Patent document CN105318847A discloses a system-modeled aspherical non-zero-position annular sub-aperture stitching method that eliminates the need for specialized morphological stitching operations and overlapping areas, reducing the number of possible sub-apertures and increasing stitching accuracy. However, it can only be applied to annular wavefront sub-apertures, and the number of sub-apertures is still relatively large.

[0004] Therefore, in order to address the problem of low efficiency in the full-aperture surface interferometry of large-aperture optical elements, there is an urgent need for a technical solution that can directly generate the full-aperture surface of large-aperture optical elements through a small number of local small-aperture surface interferometry measurements, so as to achieve high-efficiency, high-precision, and full-parameter full-aperture surface detection of large-aperture optical elements. Summary of the Invention

[0005] The purpose of this invention is to overcome the shortcomings of the prior art and address the problems of low efficiency, strong equipment dependence, and accumulation of splicing errors in the full-aperture surface shape measurement of large-aperture optical elements. This invention provides a method for measuring the surface shape of large-aperture optical elements based on sub-aperture deduction. This method can deduce the full-aperture surface shape by combining two local sub-aperture measurements of the optical element with a neural network model, thereby achieving high-efficiency, high-precision, and low-cost surface shape detection of large-aperture optical elements.

[0006] The technical solution of the present invention is as follows:

[0007] A method for measuring the surface shape of large-aperture optical elements based on sub-aperture derivation, characterized by the following steps:

[0008] Dataset construction steps: Based on the statistical regularity of the measured full-aperture surface shape of optical elements, multiple simulated full-aperture surface shapes are generated; from each of the simulated full-aperture surface shapes, a first simulated sub-aperture surface shape located in a first preset measurement area and a second simulated sub-aperture surface shape located in a second preset measurement area are extracted respectively; the first simulated sub-aperture surface shape and the second simulated sub-aperture surface shape are fitted respectively to obtain the first simulated feature parameters and the second simulated feature parameters; the first simulated feature parameters and the second simulated feature parameters are used as input samples, and the feature parameters of the simulated full-aperture surface shape are used as output samples to construct a training dataset;

[0009] Model training steps: Using the training dataset, train a preset neural network model to obtain a deduction model. The deduction model is used to establish the mapping relationship from the feature parameters of two local sub-apertures to the feature parameters of the full aperture surface.

[0010] Measurement and deduction steps: Measure the first measured sub-aperture surface shape of the optical element under test in the first preset measurement area and the second measured sub-aperture surface shape in the second preset measurement area; fit the first measured sub-aperture surface shape and the second measured sub-aperture surface shape to obtain the first measured feature parameter and the second measured feature parameter; input the first measured feature parameter and the second measured feature parameter into the deduction model to obtain the predicted full-aperture feature parameters; based on the predicted full-aperture feature parameters, reconstruct the full-aperture surface shape of the optical element under test.

[0011] Furthermore, the characteristic parameter is the Zernike coefficient.

[0012] Furthermore, in the dataset construction step, generating multiple simulated full-aperture surface shapes based on the statistical regularities of the measured full-aperture surface shape of optical elements specifically includes:

[0013] Zernike polynomial fitting was performed on the full aperture surface shape of several measured large-aperture optical elements to obtain multiple sets of measured Zernike coefficients;

[0014] Statistical analysis was performed on the multiple sets of measured Zernike coefficients to obtain the mean and standard deviation of each Zernike coefficient.

[0015] Based on the mean and standard deviation, multiple sets of simulated Zernike coefficients are generated through random sampling;

[0016] Based on the multiple sets of simulated Zernike coefficients, multiple simulated full-aperture surface shapes are reconstructed and generated.

[0017] Furthermore, the first preset measurement area is the central area of ​​the optical element, specifically a circular area with a diameter of 150mm whose center is located within the coordinate range (0±5mm, 0±5mm) in the Cartesian coordinate system with the geometric center of the optical element as the origin;

[0018] The second preset measurement area is the corner area of ​​the optical element, specifically a circular area with a diameter of 150mm whose center is located within the coordinate range (-200±5mm, -75±5mm) in the Cartesian coordinate system with the geometric center of the optical element as the origin.

[0019] Furthermore, the Zernike polynomial has 36 terms, such that: the first simulation feature parameter and the second simulation feature parameter each have 36 Zernike coefficients; the input sample is a 72-dimensional vector concatenated from the first simulation feature parameter and the second simulation feature parameter; and the output sample has 36 Zernike coefficients.

[0020] Furthermore, after the dataset construction step, the method also includes a step of standardizing the input and output samples and saving the corresponding standardization parameters.

[0021] Furthermore, the preset neural network model is a fully connected neural network, and its structure is as follows: input layer, first hidden layer, second hidden layer, third hidden layer, fourth hidden layer and output layer; the number of neurons in the input layer is 72, the number of neurons in the first to fourth hidden layers are 128, 256, 512 and 128 respectively, and the number of neurons in the output layer is 36; the first to fourth hidden layers all use the ReLU activation function.

[0022] Furthermore, in the model training step, when training the preset neural network model, the loss function used is the mean squared error loss function, and an early stopping mechanism and gradient pruning strategy are adopted.

[0023] Furthermore, the stopping condition for the model training step is: the mean squared error loss value of the preset neural network model on the test set is less than a preset threshold, or the early stopping mechanism is triggered.

[0024] Furthermore, in the measurement and deduction steps, a small-aperture interferometer with a measurement aperture of 150mm is used to measure the surface shape of the first measured sub-aperture and the surface shape of the second measured sub-aperture.

[0025] Furthermore, in the measurement and deduction steps, before inputting the first measured feature parameter and the second measured feature parameter into the deduction model, the method further includes a step of standardizing the first measured feature parameter and the second measured feature parameter using the standardization parameter; after obtaining the predicted full-caliber feature parameter, the method further includes a step of de-standardizing the predicted full-caliber feature parameter using the standardization parameter.

[0026] Compared with the prior art, the technical effects of the present invention are as follows:

[0027] 1) The traditional measurement process that requires full-aperture scanning or multiple stitching is transformed into a method that only requires two local sub-aperture measurements to deduce the full-aperture surface shape, breaking through the efficiency bottleneck of the traditional measurement mode.

[0028] 2) Based on the statistical laws of the measured surface shape of optical elements, a large-scale simulation dataset is constructed. The intrinsic mapping relationship between the surface shape features of sub-aperture and full-aperture is learned through neural networks, enabling the model to deduce global information from local information, thus avoiding complex physical modeling and error compensation algorithms.

[0029] 3) Using Zernike coefficients as surface feature representation, the high-dimensional surface data is reduced to a low-dimensional feature space. At the same time, the Zernike coefficients of the two sub-apertures of the central region and the corner region are concatenated to achieve effective fusion of local surface information, providing high-quality input features for the neural network.

[0030] 4) Through neural network architecture and training strategies, high-precision mapping from sub-aperture features to full-aperture features was achieved. The error between the reconstructed full-aperture surface shape and the true surface shape can be controlled within 1×10⁻⁶. -4 The error is on the order of magnitude (Zernike coefficient error) or two orders of magnitude lower than the surface height value (surface error), meeting the requirements for high-precision optical inspection.

[0031] 5) It can directly generate the full aperture surface shape of an optical element by only two interferometric measurements of the local surface shape of the large aperture optical element, which greatly improves the detection efficiency of large aperture optical elements. Attached Figure Description

[0032] Figure 1 This is a schematic diagram of the method for measuring the surface shape of large-aperture optical elements based on sub-aperture derivation according to the present invention;

[0033] Figure 2 This is a flowchart of the method for measuring the surface shape of large-aperture optical elements based on sub-aperture derivation according to the present invention;

[0034] Figure 3 This is a schematic diagram of the neural network designed by the large-aperture optical element surface shape measurement method based on sub-aperture derivation of the present invention.

[0035] Figure 4 This is a schematic diagram illustrating the effect of the large-aperture optical element surface shape measurement method based on sub-aperture derivation of the present invention. In this diagram, (a) is the full-aperture surface shape of the large-aperture optical element generated by 36 Zernike terms, (b) is the sub-aperture surface shape corresponding to the central region of the large-aperture optical element in (a), (c) is the sub-aperture surface shape corresponding to the corner region of the large-aperture optical element in (a), (d) is the full-aperture surface shape generated by a neural network based on (b) and (c), (e) is the error obtained by subtracting (a) from (d), and (f) is the Zernike coefficient error between (d) and (a). Detailed Implementation

[0036] The present invention will be further described below with reference to the accompanying drawings in the embodiments. This embodiment is implemented based on the technical solution of the present invention, and provides detailed implementation methods and specific operating procedures; however, the scope of protection of the present invention is not limited to the following embodiments.

[0037] A method for measuring the surface shape of a large-aperture optical element based on sub-aperture derivation includes: a neural network model design, parameter training, and model evaluation stage for generating the full-aperture surface shape based on local surface shape measurements; and a stage for generating the full-aperture surface shape based on local surface shape measurements using the trained neural network.

[0038] The neural network model design, parameter training, and model evaluation stage for generating the full-aperture surface shape based on local surface shape measurements specifically includes the following steps:

[0039] S1. Randomly generate 50,000 sets of 36 Zernike coefficients according to certain statistical laws of the measured full-aperture surface shape of optical elements, and then use these 50,000 sets of Zernike coefficients to construct 50,000 full-aperture surface shapes of large-aperture optical elements of a certain size.

[0040] S2. From the 50,000 large-aperture optical element surface shapes constructed in step S1, a circular sub-aperture surface shape in the central region is extracted to simulate the measurement of the sub-aperture of the central region of the optical element in local measurement.

[0041] S3. Extract the circular sub-aperture surface of the corner region from the 50,000 large-aperture optical element surface shapes constructed in step S1, simulate the measurement of the sub-aperture of the corner region of the optical element in the local measurement, and complete the preparation of the optical element surface shape dataset.

[0042] S4. Fit the circular sub-aperture surface of the central region and the circular sub-aperture surface of the corner region intercepted in steps S2 and S3 respectively using Zernike polynomials to obtain 36 Zernike coefficients respectively.

[0043] S5. Take the 72 Zernike coefficients of the two sub-aperture surfaces fitted in step S4 as input and the 36 Zernike coefficients of the full aperture surface randomly generated in step S1 as output to complete the feature extraction of the optical element surface shape.

[0044] S6. Divide the feature dataset obtained in step S5 into a training set and a test set, design the neural network architecture, set the learning parameters, and set the evaluation function.

[0045] S7. Start the training loop of the neural network model. In each iteration of training, test the neural network on the test set. Stop training when the evaluation function requirements are met, and export the neural network. This completes the design of the neural network architecture, the training loop, and the model evaluation.

[0046] The stage of generating the full-aperture surface shape based on local surface shape measurements using a trained neural network specifically includes the following steps:

[0047] S8. Use a small-aperture interferometer to measure the central region of a large-aperture optical element to obtain the surface shape data of the central region of the optical element.

[0048] S9. Fit the surface shape data of the central region of the optical element obtained in step S8 with 36 Zernike polynomials to obtain the 36 Zernike coefficients of the surface shape data of the central region of the optical element.

[0049] S10. Use a small-aperture interferometer to measure the corner region of a large-aperture optical element to obtain the surface shape data of the corner region of the optical element.

[0050] S11. Fit the surface shape data of the optical element corner region obtained in step S10 with 36 Zernike polynomials to obtain the 36 Zernike coefficients of the surface shape data of the optical element corner region.

[0051] S12. The 36 Zernike coefficients of the surface shape data of the central region of the optical element obtained in step S9 and the 36 Zernike coefficients of the surface shape data of the corner region of the optical element obtained in step S10 are input into the neural network trained in step S6. The neural network outputs 36 Zernike coefficients after calculation.

[0052] S13. Using the 36 Zernike coefficients output in step S12, construct the full-aperture surface of the large-aperture optical element with the same size as in step S7. That is, the full-aperture surface of the large-aperture optical element is obtained through two local measurements.

[0053] Furthermore, the certain statistical regularity mentioned in step S1 includes, but is not limited to, the mean, standard deviation, variance, median, quantile, etc. of the 36 Zernike coefficients of the measured full-aperture surface shape of the optical element;

[0054] Furthermore, the certain size mentioned in step S1 includes, but is not limited to, a rectangular optical element with a length of 810 mm and a width of 460 mm;

[0055] Furthermore, the center of the circular sub-aperture in the central region described in step S2 is located within the coordinate range (0±5mm, 0±5mm) of the Cartesian coordinate system with the geometric center of the optical element as the origin, and the diameter is 150mm.

[0056] Furthermore, the center of the circular sub-aperture in the corner region described in step S3 is located within the coordinate range (-200±5mm, -75±5mm) of the Cartesian coordinate system with the geometric center of the optical element as the origin, and the diameter is 150mm.

[0057] Furthermore, the ratio of the training set to the test set in step S6 is 4:1;

[0058] Furthermore, the neural network architecture described in step S6 includes, but is not limited to, fully connected neural networks, long short-term memory networks, convolutional neural networks, and fully connected neural networks.

[0059] Furthermore, the evaluation function described in step S6 includes, but is not limited to, mean squared error loss and smoothing L1 loss;

[0060] Furthermore, the evaluation function described in step S7 requires that the evaluation function value of the test set is less than 1×10⁵;

[0061] Furthermore, the measuring aperture of the small-aperture interferometer described in steps S8 and S10 is 150 mm;

[0062] Furthermore, the size of the large-aperture optical element described in steps S8 and S10 is the same as that of the large-aperture optical element in step S1.

[0063] Furthermore, the center of the central region described in step S8 is located within the coordinate range (0±5mm, 0±5mm) of a Cartesian coordinate system with the geometric center of the optical element as the origin, and has a diameter of 150mm.

[0064] Furthermore, the center of the corner region described in step S10 is located within the coordinate range (-200±5mm, -75±5mm) of the Cartesian coordinate system with the geometric center of the optical element as the origin, and the diameter is 150mm.

[0065] Please see Figure 1 , Figure 1 This is a schematic diagram of the method for measuring the surface shape of a large-aperture optical element based on sub-aperture derivation according to the present invention. As shown in the figure, in the present invention, the known information is the two sub-aperture surface shapes of the central region and corner region of the large-aperture optical element measured by a small-aperture interferometer; the unknown information is the full-aperture surface shape of the large-aperture optical element.

[0066] The large-aperture optical element is a rectangular optical element of 810mm × 460mm. The measuring aperture of the small-aperture interferometer is 150mm. The center of the sub-aperture in the central region is located within the coordinates (0±5mm, 0±5mm) of the Cartesian coordinate system with the geometric center of the optical element as the origin. The center of the sub-aperture in the corner region is located within the coordinates (-200±5mm, -75±5mm) of the Cartesian coordinate system with the geometric center of the optical element as the origin. The purpose of giving the range is to account for the relative position error between the interferometer and the optical element in actual interferometric measurement.

[0067] Figure 2 The flowchart of the method for measuring the surface shape of large-aperture optical elements based on sub-aperture derivation of the present invention is shown in the figure. Before training the neural network model, it is necessary to measure the full-aperture surface shape of several large-aperture optical elements and use Zernike polynomials to fit the measured surface shape to obtain several sets of 36 Zernike polynomial coefficients.

[0068] Statistical analysis was performed on the 36 Zernike polynomial coefficients of the full aperture surface shape of several sets of measured large-aperture optical elements to obtain the mean and standard deviation of each coefficient. These coefficients were then used to randomly generate 50,000 sets of 36 Zernike coefficients. Each set of coefficients was used to construct a 36-dimensional vector, which is the output feature of the neural network.

[0069] 50,000 large-aperture surfaces of the same size as those measured in reality were constructed using Zernike polynomials from 50,000 randomly generated sets of Zernike coefficients. Figure 1 The optical element is represented by 50,000 cut-out surfaces, each with a diameter of 150 mm, from the central and corner regions.

[0070] The Zernike polynomial is used to fit the surface shape of the central and corner regions of the optical element, obtaining 50,000 sets of 36 Zernike coefficients for each region. The 36 Zernike coefficients for the central and corner regions of the same optical element are then concatenated into a 72-dimensional vector, which is the input feature of the neural network.

[0071] The neural network uses 50,000 sets of input and output features as its dataset, which are then divided into training and test sets in a 4:1 ratio.

[0072] Build as Figure 3 The fully connected neural network shown adopts a stacked structure of an input layer, four hidden layers, and an output layer. The network's dimensionality mapping follows the path 72→128→256→512→128→36. All hidden layers in the network are equipped with the ReLU activation function, introducing non-linear characteristics to the model.

[0073] The model uses the AdamW optimizer, whose built-in weight decay function achieves L2 regularization. During training, the initial learning rate is set to 0.001, the weight decay coefficient is 1e-4, and a cosine annealing scheduler is used to dynamically adjust the learning rate. The scheduler's decay period is set to 100, and the minimum learning rate is 1e-6. The learning rate is updated after each training round.

[0074] Mean squared error loss was chosen as the training objective, and the batch size was set to 100 to fully utilize the parallel computing efficiency of the GPU. The training data was split into batches, and the data shuffling function was enabled to prevent the model from learning the data sequence pattern and causing overfitting.

[0075] During the data preprocessing stage, the mean and standard deviation of the training set are calculated independently for feature standardization, while the statistics of the training set are reused for the test set to avoid data leakage.

[0076] To prevent gradient explosion during deep network training, a gradient pruning strategy is adopted after backpropagation to calculate the gradient, limiting the gradient norm of all parameters to within 0.2. If the gradient norm exceeds the threshold, it is scaled proportionally to ensure the stability of the parameter update process.

[0077] An early stopping mechanism is introduced to prevent model overfitting and avoid invalid training. The training continues by monitoring the test set loss. The patience value is set to 30,000 and the minimum improvement threshold is 1e-10. When the test set loss does not exceed the threshold improvement for 30,000 consecutive rounds, the training is terminated immediately.

[0078] The complete training process for a single round is as follows: First, the model is switched to training mode. Then, the batch data in the DataLoader is traversed. For each batch, forward propagation is performed to calculate the predicted value, the batch loss is calculated, backpropagation is performed to solve the gradient, gradient pruning is performed, the optimizer parameters are updated, and the gradient cache is cleared. Finally, the loss values ​​of all batches are accumulated. After each training round, the learning rate is updated, the average training loss of this round is calculated, and the test set loss is evaluated. Then, based on the test loss, it is determined whether to update the optimal model or trigger early stopping. The termination condition for the entire training process is reaching the maximum number of training rounds of 2100 or triggering the early stopping mechanism.

[0079] During the model evaluation phase, the model is switched to evaluation mode and gradient calculation is disabled. The optimal model is then used to perform forward propagation on the entire test set, with mean squared error loss used as the evaluation metric to measure model performance. After training, the optimal model is exported in ONNX format, and dynamic axes are set to support input and output of different batch sizes, facilitating cross-platform deployment. Simultaneously, the mean and standard deviation of the training set are saved as CSV files for standardization of new data during the deployment phase.

[0080] The sub-aperture surface shape of the central and corner regions of a large-aperture optical element was measured using a 150mm aperture interferometer. The positions of the central and corner regions followed... Figure 1 Location expression.

[0081] The surface shapes of the central and corner regions of the optical element were fitted using Zernike polynomials to obtain 36 Zernike coefficients for each region. These coefficients were then concatenated into a 72-dimensional vector, which was used as input features to train the neural network and output 36 Zernike coefficients.

[0082] The 36 output Zernike coefficients are used to generate a surface shape of the same size as the measured large-aperture optical element through Zernike polynomials, thus completing the global generation of the large-aperture optical surface shape based on local measurements.

[0083] Figure 4 This is a schematic diagram illustrating the effect of the large-aperture optical element surface shape measurement method based on sub-aperture derivation of the present invention. Figure 4 (a) is one of the full-aperture surfaces of a large-aperture optical element generated by fitting the mean and standard deviation of 36 Zernike coefficients based on the measured surface shape of the optical element. The positions of the sub-apertures of the central and corner regions that need to be truncated are marked with white dashed lines in the figure.

[0084] Figure 4 (b) corresponds to Figure 4 (a) Sub-aperture profile of the central region of a large-aperture optical element. Figure 4(c) is the sub-aperture shape of the corner region corresponding to the large-aperture optical element in (a).

[0085] Figure 4 (d) is based on a neural network Figure 4 (b) and Figure 4 (c) The full-aperture surface shape generated by each of the 36 fitted Zernike coefficients, which is compared with... Figure 4 (a) Extremely high similarity.

[0086] Figure 4 (e) is Figure 4 (d) and Figure 4 (a) The prediction error obtained by subtraction is two orders of magnitude lower than the surface height value, in wavelength.

[0087] Figure 4 (f) is Figure 4 (d) and Figure 4 (a) Zernike coefficient error, with an error value in the range of 1×10⁻⁶. -4 Magnitude.

Claims

1. A large aperture optical element surface shape measurement method based on sub-aperture extrapolation, characterized in that, Includes the following steps: Dataset construction steps: Based on the statistical regularity of the measured full-aperture surface shape of optical elements, multiple simulated full-aperture surface shapes are generated; from each of the simulated full-aperture surface shapes, a first simulated sub-aperture surface shape located in a first preset measurement area and a second simulated sub-aperture surface shape located in a second preset measurement area are extracted respectively; the first simulated sub-aperture surface shape and the second simulated sub-aperture surface shape are fitted respectively to obtain the first simulated feature parameters and the second simulated feature parameters; the first simulated feature parameters and the second simulated feature parameters are used as input samples, and the feature parameters of the simulated full-aperture surface shape are used as output samples to construct a training dataset; Model training steps: Using the training dataset, train a preset neural network model to obtain a deduction model. The deduction model is used to establish the mapping relationship from the feature parameters of two local sub-apertures to the feature parameters of the full aperture surface. Measurement and deduction steps: Measure the first measured sub-aperture surface shape of the optical element under test in the first preset measurement area and the second measured sub-aperture surface shape in the second preset measurement area; fit the first measured sub-aperture surface shape and the second measured sub-aperture surface shape to obtain the corresponding first measured feature parameter and second measured feature parameter; input the first measured feature parameter and the second measured feature parameter into the deduction model to obtain the predicted full-aperture feature parameter; based on the predicted full-aperture feature parameter, reconstruct the full-aperture surface shape of the optical element under test; The first preset measurement area is the central area of ​​the optical element, specifically a circular area with a diameter of 150mm whose center is located within the coordinates (0±5mm, 0±5mm) in the Cartesian coordinate system with the geometric center of the optical element as the origin. The second preset measurement area is the corner area of ​​the optical element, specifically a circular area with a diameter of 150mm whose center is located within the coordinate range (-200±5mm, -75±5mm) in the Cartesian coordinate system with the geometric center of the optical element as the origin.

2. The method for measuring the surface shape of large-aperture optical elements based on sub-aperture derivation according to claim 1, characterized in that, The characteristic parameter is the Zernike coefficient.

3. The method for measuring the surface shape of large-aperture optical elements based on sub-aperture derivation according to claim 1, characterized in that, In the dataset construction step, generating multiple simulated full-aperture surface shapes based on the statistical regularities of the measured full-aperture surface shape of optical elements specifically includes: Zernike polynomial fitting was performed on the full aperture surface shape of several measured large-aperture optical elements to obtain multiple sets of measured Zernike coefficients; Statistical analysis was performed on the multiple sets of measured Zernike coefficients to obtain the mean and standard deviation of each Zernike coefficient. Based on the mean and standard deviation, multiple sets of simulated Zernike coefficients are generated through random sampling; Based on the multiple sets of simulated Zernike coefficients, multiple simulated full-aperture surface shapes are reconstructed and generated.

4. The method for measuring the surface shape of large-aperture optical elements based on sub-aperture derivation according to claim 3, characterized in that, The Zernike polynomial has 36 terms, such that: the first simulation feature parameter and the second simulation feature parameter each have 36 Zernike coefficients; the input sample is a 72-dimensional vector formed by concatenating the first simulation feature parameter and the second simulation feature parameter; and the output sample has 36 Zernike coefficients.

5. The method for measuring the surface shape of large-aperture optical elements based on sub-aperture derivation according to claim 1, characterized in that, Following the dataset construction step, the method further includes a step of standardizing the input and output samples and saving the corresponding standardization parameters.

6. The method for measuring the surface shape of large-aperture optical elements based on sub-aperture derivation according to claim 1, characterized in that, The preset neural network model is a fully connected neural network, and its structure is as follows: input layer, first hidden layer, second hidden layer, third hidden layer, fourth hidden layer and output layer; the number of neurons in the input layer is 72, the number of neurons in the first to fourth hidden layers are 128, 256, 512 and 128 respectively, and the number of neurons in the output layer is 36; the first to fourth hidden layers all use the ReLU activation function.

7. The method for measuring the surface shape of large-aperture optical elements based on sub-aperture derivation according to claim 1, characterized in that, In the model training step, when training the preset neural network model, the loss function used is the mean squared error loss function, and an early stopping mechanism and gradient pruning strategy are adopted.

8. The method for measuring the surface shape of large-aperture optical elements based on sub-aperture derivation according to claim 7, characterized in that, The stopping condition for the model training step is: the mean squared error loss value of the preset neural network model on the test set is less than a preset threshold, or the early stopping mechanism is triggered.

9. The method for measuring the surface shape of large-aperture optical elements based on sub-aperture derivation according to claim 1, characterized in that, In the measurement and deduction steps, a small-aperture interferometer with a measurement aperture of 150mm is used to measure the surface shape of the first measured sub-aperture and the surface shape of the second measured sub-aperture.

10. The method for measuring the surface shape of large-aperture optical elements based on sub-aperture derivation according to claim 1, characterized in that, In the measurement and deduction steps, before inputting the first measured feature parameter and the second measured feature parameter into the deduction model, the method further includes a step of standardizing the first measured feature parameter and the second measured feature parameter using standardization parameters; after obtaining the predicted full-caliber feature parameter, the method further includes a step of de-standardizing the predicted full-caliber feature parameter using standardization parameters.

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