Synthetic aperture piston error detection method based on optical transfer function decoupling

Abstract

The present application relates to the field of telescope error correction technology, and more particularly to a synthetic aperture piston error detection method based on optical transfer function decoupling. Including: setting a non-redundant mask on the telescope exit pupil plane, dividing the diaphragm into N sub-apertures, making the optical transfer function side lobe corresponding to the measured sub-aperture and the reference sub-aperture independent; extracting a feature vector representing the piston error from the optical transfer function side lobe; constructing a dataset and building a convolutional neural network for piston error detection; training to obtain a piston error detection model; in the actual observation process, real-time image acquisition, extraction of the side lobe feature vector corresponding to the measured sub-aperture and the reference sub-aperture, input into the piston error detection model, and output of the real-time piston error value of each measured sub-aperture relative to the reference sub-aperture. The advantage is that the piston error is decoupled with the help of the non-redundant mask, and the relationship between the feature vector and the piston error is accurately established by combining the feature extraction and nonlinear mapping capabilities of the convolutional neural network.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of telescope error correction technology, and particularly relates to a synthetic aperture piston error detection method based on optical transfer function decoupling. BACKGROUND

[0002] The resolution of a traditional optical imaging system is limited by the diffraction limit. In order to obtain extremely high resolution, the size of a main mirror of a telescope will become extremely large, and manufacturing, launching and deployment will become extremely difficult. A synthetic aperture system uses the way of interference imaging between multiple sub-apertures to achieve the imaging effect of a large aperture. Due to the influence of synthetic aperture deployment, gravity effect and truss vibration, each sub-aperture deviates from the ideal position, introduces a piston error, and causes the imaging quality to decrease. In order to obtain the best imaging performance, the piston error between the sub-apertures must be controlled within the range of a fraction of a wavelength.

[0003] The co-phasing errors between each sub-aperture mainly include piston error and tilt error. The tilt error can be detected by a traditional wavefront detector, while the piston error needs to be detected by other detection techniques or special sensors. Therefore, the detection technique of piston error is one of the most critical core technologies of sparse aperture imaging system. In the past decades, researchers have developed various piston error detection methods. G. Chanan et al. reported in “Phasing the mirror segments of the Keck telescopes II: the narrow-band phasing algorithm” (Applied Optics, 2000, 39(25): 4706-4714) that the edge sensor is used to capture the far-field spot, and then the non-continuous wavefront is obtained by template matching. However, this method has the limitation of template calibration. D. S. Acton et al. reported in “End-to-end commissioning demonstration of the James Webb Space Telescope” (Proceedings of SPIE - The International Society for Optical Engineering, 2007, 6687: 66870601-66870610) that the special dispersive element and microlens are used to generate a dispersive fringe pattern, and the large-scale piston information can be directly extracted. However, the precision is not high. R. E. Carlisle et al. reported in “Demonstration of extended capture range for James Webb Space Telescope phase retrieval” (Applied Optics, 2015, 54(21): 6454-6460) that the phase recovery algorithm is used to realize accurate reconstruction of piston error. However, the real-time performance is poor. With the rapid development of artificial intelligence technology, some new piston detection methods based on neural network have emerged, which can effectively balance the capture range and measurement accuracy. However, when the number of sub-apertures increases or the system exit pupil is a central symmetric structure, the mapping relationship between the feature vector and the piston error is too complex, which affects the performance of piston detection. SUMMARY

[0004] The present application provides a synthetic aperture piston error detection method based on optical transfer function decoupling to solve the above problems.

[0005] The present application provides a synthetic aperture piston error detection method based on optical transfer function decoupling, which specifically comprises the following steps:

[0006] S1. Set a non-redundant mask on the exit pupil of the telescope to divide the aperture into N sub-apertures, one of which is a reference sub-aperture and the rest are sub-apertures to be tested, so that the side lobes of the optical transfer function corresponding to each sub-aperture to be tested are independent of the reference sub-aperture; N≥3;

[0007] S2. Extract the feature vector that can uniquely characterize the piston error from the sidelobe of the optical transfer function; use the feature vector as input and the corresponding piston error as label to construct a dataset for neural network training and testing;

[0008] S3. Construct a convolutional neural network for piston error detection; train the model using training data to obtain the piston error detection model;

[0009] S4. During the actual observation process of the telescope, the system acquires interferometric images or target images in real time, extracts the side lobe feature vectors corresponding to the sub-aperture to be measured and the reference sub-aperture, inputs the feature vectors into the piston error detection model, and outputs the real-time piston error value of each sub-aperture to be measured relative to the reference sub-aperture.

[0010] Preferably, the telescope is a synthetic aperture telescope composed of N sub-mirrors; the sub-aperture is a telescope with a diameter of D The circular sub-apertures, each corresponding to a sub-mirror. D ≥1mm.

[0011] The preferred method for designing a non-redundant mask specifically includes: designing the aperture layout of the non-redundant mask according to the requirements of the optical system; determining the position of the center of each circular sub-aperture, i.e., the optimization variable, through an optimization algorithm; minimizing the objective function under the premise that the optimization variable satisfies the boundary conditions, and calculating the optimal position of the center of each circular sub-aperture after iteration, so as to ensure the independence of the side lobes of each sub-aperture to be tested and the reference sub-aperture OTF.

[0012] Preferably, the objective function is the negative of the minimum value of the distance between the OTF sidelobe center formed between the sub-aperture to be tested and the reference sub-aperture and the distance between the OTF sidelobe centers formed between any two sub-apertures; the boundary condition is that each circular sub-aperture is located inside the corresponding sub-mirror.

[0013] Preferably, step S2 specifically includes the following sub-steps:

[0014] S21. Select one sub-aperture from N sub-apertures as the reference sub-aperture, and use the remaining (N-1) sub-apertures as the sub-apertures to be measured;

[0015] S22. Based on the geometric position of the sub-aperture to be tested relative to the reference sub-aperture, accurately calculate the center position and boundary of the corresponding side lobe;

[0016] Assuming the reference sub-aperture center coordinates are (x0, y0), the center coordinates of a certain target sub-aperture are (x, y), the system's operating center wavelength is λ0, and the telescope focal length is... , D Let be the sub-aperture diameter; then the frequency domain center position of the OTF sidelobe corresponding to the sub-aperture to be measured and the reference sub-aperture is (x0-x, y0-y) / (λ0). The frequency domain boundary radius of the sidelobe is D / (λ0 );

[0017] S23. Divide the circular region of the side lobe into two along a specific direction, take the left half of the real part data and the right half of the imaginary part data; concatenate the extracted data left and right to form a one-dimensional feature vector;

[0018] S24. Following the method in step S23, generate (N-1) corresponding feature vectors for each of the (N-1) sub-apertures to be tested; pair each feature vector with the corresponding piston error value to generate data samples; randomly divide the generated data samples into training datasets and test datasets.

[0019] Preferably, the convolutional neural network includes convolutional blocks and fully connected blocks in series; the convolutional block sequentially includes a convolutional layer, a max pooling layer, and ten convolutional residual network modules; the fully connected block includes three convolutional fully connected layers.

[0020] Preferably, both the convolutional layer and the fully connected layer are followed by a ReLU activation function.

[0021] Preferably, step S3 specifically includes:

[0022] S31. Using deep learning methods, a convolutional neural network for piston error detection was built based on the PyTorch framework;

[0023] S32. Initialize parameters, select optimizer and loss function;

[0024] S33. Optimize the network parameters using the training dataset to obtain the piston error detection model;

[0025] S34. Evaluate the piston error detection model on the test dataset to verify whether the model can accurately predict the corresponding piston error value based on the input OTF sidelobe feature vector.

[0026] Preferably, the optimizer is the Adam optimizer; the loss function is the root mean square error; and the metric evaluated in step S34 is the root mean square error.

[0027] Compared with the prior art, the present invention can achieve the following beneficial effects:

[0028] This invention provides a synthetic aperture telescope piston error detection method based on optical transfer function decoupling. By utilizing a non-redundant mask to decouple the piston error and combining it with the powerful feature extraction and nonlinear mapping capabilities of convolutional neural networks, the relationship between feature vectors and piston errors can be accurately established. Test results show that the sensing deviation of the five sub-apertures under test can be controlled within 30 nm, the probability of residual root mean square error of the test samples being less than 20 nm exceeds 95%, and the training and testing results are highly consistent, exhibiting high precision and robustness. This provides an effective technical means for the accurate detection of piston errors in synthetic aperture telescopes, contributing to the telescope's ability to achieve high-resolution imaging. Attached Figure Description

[0029] Figure 1 This is a schematic diagram of a synthetic aperture system model containing six regular hexagonal sub-mirrors according to an embodiment of the present invention.

[0030] Figure 2 This is a schematic diagram showing the optimized positions of each circular sub-aperture according to an embodiment of the present invention.

[0031] Figure 3 This describes the distribution of the optical transfer function (OTF) side lobes between the reference sub-aperture and the sub-aperture to be measured, according to an embodiment of the present invention.

[0032] Figure 4 This is a feature vector distribution diagram corresponding to the five test sub-aperture pistons with zero error according to an embodiment of the present invention.

[0033] Figure 5 This is a diagram of a convolutional neural network structure provided according to an embodiment of the present invention.

[0034] Figure 6 The root mean square error (RMSE) distribution between the predicted piston value and the true value in the test sample corresponding to the sub-aperture to be tested, provided by an embodiment of the present invention.

[0035] Figure 7 It is the residual root mean square error (RMSE) distribution of the training and test samples of the sub-aperture to be tested according to the embodiments of the present invention. Detailed Implementation

[0036] In the following description, embodiments of the invention will be described with reference to the accompanying drawings. In the description below, the same modules are denoted by the same reference numerals. Where the same reference numerals are used, their names and functions are also the same. Therefore, their detailed description will not be repeated.

[0037] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and specific embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and do not constitute a limitation thereof.

[0038] This invention provides a method for detecting synthetic aperture piston errors based on optical transfer function decoupling, specifically including the following steps:

[0039] S1. Set up a non-redundant mask: Set up a non-redundant mask on the exit pupil of the telescope to divide the aperture into N sub-apertures. The optical transfer function (OTF) side lobes of each sub-aperture (each sub-aperture to be measured and the reference sub-aperture in the imaging system) are independent so that the feature vector can be accurately extracted in the future.

[0040] Specifically, the telescope is a synthetic aperture telescope composed of N sub-mirrors, where N ≥ 3; the sub-aperture is a telescope with a diameter of... D The circular sub-apertures, each corresponding to a sub-mirror. D ≥1mm;

[0041] The design methods for non-redundant masks specifically include:

[0042] Design the aperture layout of the non-redundant mask according to the requirements of the optical system;

[0043] The location of the center of each circular sub-aperture is determined by an optimization algorithm, i.e., the optimization variable;

[0044] Under the premise that the optimization variables satisfy the boundary conditions, the objective function is minimized, and the optimal position of the center of each circular sub-aperture is calculated after multiple iterations to ensure the independence of the side lobes of each sub-aperture to be tested and the reference sub-aperture OTF.

[0045] Based on the optimization results, a non-redundant mask is fabricated; the non-redundant mask is then installed into the optical system and tested and calibrated to ensure that its performance meets the design requirements.

[0046] The objective function is the negative of the minimum value of the distance between the OTF sidelobe center formed between the sub-aperture to be tested and the reference sub-aperture and the OTF sidelobe center formed between any two sub-apertures;

[0047] Let the center coordinates of the nth sub-aperture be ( x n , y n ), n from 1 to N Let the first sub-aperture be the reference sub-aperture, with coordinates ( x 1, y 1) The relative coordinates between the reference sub-aperture and the i-th non-reference sub-aperture are: P1i =( x 1, y 1)-( x i , y i );

[0048] No. j Individual aperture and the first k The relative coordinates between the individual apertures are: P jk =( x j , y j )-( x k , y k );

[0049] The objective function is: ;

[0050] In the formula: i =2,3,… N ; j =1,2,… N ; k =1,2,… N ; jk ≠1 i ;

[0051] The boundary condition is that each circular sub-aperture is located inside the corresponding sub-mirror.

[0052] S2. Extract feature vectors that uniquely characterize piston errors from the sidelobes of the optical transfer function (OTF). Use these feature vectors as input and the corresponding piston errors as labels to construct a dataset for neural network training and testing. This includes the following sub-steps:

[0053] S21. Determine the reference and test sub-apertures: From the N sub-apertures, arbitrarily select one sub-aperture as the reference sub-aperture, and the remaining (N-1) sub-apertures as the test sub-apertures;

[0054] S22. Identify and locate OTF side lobes: For each sub-aperture to be tested, a corresponding side lobe will be generated on the OTF image between it and the reference sub-aperture; due to the use of a non-redundant mask, (N-1) side lobes are separated from each other and do not overlap in the frequency domain plane of the OTF image; based on the geometric position of the sub-aperture, the center position and boundary of each side lobe are accurately calculated.

[0055] Assuming the reference sub-aperture center coordinates are (x0, y0), the center coordinates of a certain target sub-aperture are (x, y), the system's operating center wavelength is λ0, and the telescope focal length is... , D Let be the sub-aperture diameter; then the frequency domain center position of the OTF sidelobe corresponding to the sub-aperture to be measured and the reference sub-aperture is (x0-x, y0-y) / (λ0). The frequency domain boundary radius of the sidelobe is D / (λ0 );

[0056] S23. Constructing Sidelobe Feature Vectors: To effectively decouple and extract piston error information, each located OTF sidelobe is processed as follows to generate its corresponding feature vector:

[0057] Segmenting the side lobe: Dividing the circular domain of the side lobe in two along a specific direction (e.g., along the u-axis in the frequency domain);

[0058] Extract components: Take the left half of the data of the real part of the side lobe and the right half of the data of the imaginary part of the side lobe;

[0059] Combined vector: The two extracted data parts are concatenated left and right to form a one-dimensional feature vector. The dimension of this vector is determined by the number of sampling points contained in the sidelobe region.

[0060] The above construction method can effectively utilize the phase information of the OTF sidelobes, thereby achieving a one-to-one mapping with the piston error;

[0061] S24. Generate Dataset: Following the method in step S23, generate (N-1) corresponding feature vectors for each of the (N-1) sub-apertures to be tested; obtain the true piston error value (unit: wavelength or radians) of each sub-aperture to be tested relative to the reference sub-aperture through precise phase measurement or simulation calculation; pair each feature vector with its corresponding piston error value to form a data sample (feature vector, piston error); repeat the above process by changing the piston error state of the system (e.g., setting different error values ​​in the simulation, or introducing known errors using devices such as piezoelectric actuators in the experiment) to generate a large number of data samples; randomly divide the generated data samples into two parts to form a training dataset and a test dataset respectively; most of the samples (70~80%) are used for training, and the remaining samples are used for testing.

[0062] Preferably, the piston error range is ±4μm; in a specific embodiment, the piston error range is ±3.6μm.

[0063] S3. Using deep learning methods, a convolutional neural network (CNN) for piston error detection was built based on the PyTorch framework; parameters were initialized, optimizer and loss function were selected, and network parameters were optimized using the training dataset to obtain the piston error detection model; the piston error detection model was evaluated on the test dataset to verify whether the model can accurately predict the corresponding piston error value based on the input OTF sidelobe feature vector.

[0064] Convolutional neural networks consist of convolutional blocks and fully-connected blocks.

[0065] Specifically, the convolutional block contains, in sequence: a convolutional layer (followed by a ReLU activation function), a max pooling layer, and ten cascaded ResNet modules; this structure is used to automatically extract deep, abstract features that are highly correlated with piston error from the input feature vector;

[0066] The fully connected block contains three cascaded fully connected layers (each fully connected layer is followed by a ReLU activation function); this structure is used to non-linearly combine and map the features extracted by the convolutional block, and finally output the predicted value of the piston error;

[0067] First, a convolutional layer with ReLU activation function is used to extract features from the input data and introduce non-linearity. Next, a max-pooling layer is used to downsample, reduce the number of parameters, and retain key features. Then, multiple ResNet modules are connected in series, using residual connections to alleviate the gradient vanishing problem during deep network training and more effectively extract complex features. Finally, several fully connected layers integrate the extracted features, ultimately outputting a prediction result related to piston error. The overall structure achieves accurate detection of piston error through the collaborative work of different functional layers.

[0068] The Adam optimizer is selected as the optimizer; the root mean square error is used as the loss function.

[0069] Step S3 specifically includes the following sub-steps:

[0070] S31. Construct a convolutional neural network;

[0071] S32. Training parameter configuration: Randomly initialize all weights and biases of the network; select Adam optimizer (Adaptive Moment Estimation) as the optimization algorithm for model parameters to achieve efficient adaptive learning rate adjustment; use root mean square error (RMSE) as the loss function to measure the difference between the piston error value predicted by the network and the actual piston error value, and guide the network backpropagation for parameter updates;

[0072] S33. Model Training and Optimization: Input the training dataset constructed in step S2 into the built network to calculate the predicted value, calculate the loss value using the loss function, and update all parameters of the network; repeat the above process until the loss value of the network on the training dataset converges to a stable small value;

[0073] S34. Model Performance Evaluation: Using the test dataset constructed in step S2, evaluate the performance of the trained network model; the evaluation metric is still the root mean square error (RMSE); the detection accuracy of the model is quantified by calculating the RMSE between the predicted piston error and the actual piston error for all test samples.

[0074] S4. During the actual observation process of the telescope, the system acquires interferometric images or target images in real time, calculates the OTF, and extracts the sidelobe feature vectors corresponding to the sub-aperture to be tested; the feature vectors extracted in real time are input into the piston error detection model, and the real-time piston error value of each sub-aperture to be tested relative to the reference sub-aperture is output.

[0075] Example 1

[0076] like Figure 1 As shown, a synthetic aperture system model containing six regular hexagonal sub-mirrors is constructed to verify the feasibility of the proposed technology. The diagonal length of the regular hexagonal sub-mirrors is 60 mm, the center of the six sub-mirrors is located on a circle with a radius of 55 mm, the distance from the exit pupil to the image plane is 2 m, the pixel spacing of the image plane is 4 μm, broadband point light source illumination of 550~650 nm is used, the capture range corresponding to the coherence length is ±3.6 μm, and the broadband imaging effect is simulated by accumulating 21 monochromatic point spread functions with a sampling interval of 5 nm and equal weights.

[0077] A synthetic aperture piston error detection method based on optical transfer function decoupling specifically includes the following steps:

[0078] S1. Set a non-redundant mask at the exit pupil, with a circular sub-aperture diameter of [diameter value missing]. D=10mm, the center positions of each circular sub-aperture on the mask are determined through optimization. The circular sub-aperture on sub-mirror 1 is taken as the reference sub-aperture, with center coordinates (x0, y0). The remaining circular sub-apertures are the sub-apertures to be measured, with the center coordinates of the i-th sub-aperture to be measured being (x0, y0). i ,y i ) i=1,2,3,4,5 The coordinates of the OTF sidelobe center formed between the reference sub-aperture and the sub-aperture to be measured are ±(x0-x). i ,y0-y i ) i=1,2,3,4,5 / (λ0 The coordinates of the OTF sidelobe center formed between any two sub-apertures are:

[0079] ;

[0080] in, The center wavelength of the point light source =2m is the distance from the exit pupil to the image plane. The objective function is the minimum distance between the center of the OTF sidelobe formed between the reference sub-aperture and the sub-aperture to be tested, and the center of the OTF sidelobe formed between any two sub-apertures (excluding the OTF sidelobe formed between the reference sub-aperture and the sub-aperture to be tested). For ease of calculation, the boundary condition is set to the fact that each circular sub-aperture is located inside the inscribed circle of its corresponding regular hexagonal sub-mirror. Then, the objective function is minimized. After multiple iterations, the optimal position of the center of each circular sub-aperture is obtained. The optimized positions of each circular sub-aperture are shown below. Figure 2 As shown.

[0081] OTF mold Figure 3 As shown in the figure, after adding the non-redundant mask, the OTF sidelobes formed between the reference sub-aperture and the sub-aperture to be tested are independent. At this time, the piston error of each sub-aperture to be tested is effectively decoupled. In the figure, 6-1, 5-1, 4-1, 3-1, and 2-1 represent the OTF sidelobe identifiers corresponding to the piston error of different sub-apertures to be tested relative to the reference sub-aperture, which can be easily mapped to the feature vector related to the piston error of the specific sub-aperture to be tested relative to the reference sub-aperture.

[0082] S2. After setting a non-redundant mask at the system exit pupil, the five pairs of OTF sidelobes formed between the reference sub-aperture and the sub-aperture to be measured are independent and correspond one-to-one with the five piston errors. Using coordinates (x0-x...) i ,y0-y i ) i=1,2,3,4,5 / λ0 Centered on, with radius as D / (λ0 Using the circular region as the boundary, the OTF sidelobe is divided into two parts. The left half of its real part is combined with the right half of its imaginary part to form a feature vector. Following this method, five feature vectors can be obtained. Each feature vector corresponds to a piston error, thus a nonlinear mapping relationship between the feature vector and the piston error can be established using a convolutional neural network. Training the convolutional neural network first requires generating a dataset. The piston error of the reference sub-aperture is set to zero. For each of the five sub-apertures to be tested, 4000 sets of piston errors in the range of -3.6μm to 3.6μm are introduced, and the corresponding OTF sidelobes are collected. For each sub-aperture to be tested, 4000 feature vectors are generated using its corresponding OTF sidelobe relative to the reference sub-aperture. Figure 4 Figures (a)-(e) sequentially show the feature vectors corresponding to the piston errors of the sub-apertures numbered 2 to 6 when they are 0. A dataset was constructed using the feature vectors corresponding to each sub-aperture as input and the corresponding piston errors as labels. The dataset consisted of 3600 training datasets and 400 test datasets, for a total of five datasets.

[0083] S3. After preparing the training dataset, build a convolutional neural network based on the PyTorch framework. After building the convolutional neural network, initialize the parameters, select the Adam optimizer, and use the root mean square error as the loss function. For each dataset, optimize the network parameters using the training dataset, optimizing a total of five sets of network parameters. Then, evaluate the network on various test datasets. The specific steps include the following:

[0084] S31. Construct a convolutional neural network; a convolutional neural network consists of two parts: convolutional blocks and fully connected blocks. The specific structure is as follows: Figure 5 As shown, the convolutional block contains one convolutional layer (with ReLU activation function), one max pooling layer, and ten ResNet layers, while the fully connected block contains three fully connected layers (with ReLU activation function).

[0085] S32. Training parameter configuration: Randomly initialize all weights and bias parameters of the network; select the Adam optimizer as the optimization algorithm for model parameters to achieve efficient adaptive learning rate adjustment; use root mean square error (RMSE) as the loss function to measure the difference between the piston error value predicted by the network and the actual piston error value, and guide the network backpropagation for parameter updates; the initial learning rate of the Adam optimizer is 1e-3.

[0086] S33. Model Training and Optimization: Input the training dataset constructed in step S2 into the built network to calculate the predicted value, calculate the loss value using the loss function, and update all parameters of the network; repeat the above process until the loss value of the network on the training dataset converges to a stable small value; the hyperparameter epoch is 150, the batch-size is 15, and the learning rate is 0.00005.

[0087] S34. Model Performance Evaluation: Using the test dataset constructed in step S2, evaluate the performance of the trained network model; the evaluation metric is still the root mean square error (RMSE); the detection accuracy of the model is quantified by calculating the RMSE between the predicted piston error and the actual piston error for all test samples.

[0088] Figure 6 (a)-(e) show the RMSE distribution between the predicted piston value and the true value in 400 test samples corresponding to the sub-apertures numbered 2 to 6. It can be seen that the sensing deviation of the five sub-apertures is basically controlled within 30nm.

[0089] To more intuitively demonstrate the sensing performance, Figure 7 Figures (a)-(e) depict the residual RMSE distributions of the training and test samples for sub-apertures numbered 2 to 6, respectively. It is evident that the training and test results are highly consistent, and the probability that the residual RMSE of the test samples for all five sub-apertures is less than 20 nm exceeds 95%. The test results demonstrate that the proposed technique can be used for the accurate detection of piston errors.

[0090] The test results above demonstrate that this method can achieve high-precision detection of piston errors. For the five sub-apertures numbered 2 to 6, the RMSE can be controlled within 30 nm; the probability of the residual RMSE of the test samples being less than 20 nm exceeds 95%, and the results of the training set and the test set show a high degree of consistency, verifying the effectiveness and good generalization ability of the model.

[0091] S4. During the actual observation process of the telescope, the system acquires interferometric images or target images in real time, calculates the OTF, and extracts the sidelobe feature vectors corresponding to the sub-aperture to be tested; the feature vectors extracted in real time are input into the piston error detection model, and the real-time piston error value of each sub-aperture to be tested relative to the reference sub-aperture is output.

[0092] The key technical points of this invention are as follows: First, a non-redundant mask is set at the exit pupil of the system to make the optical transfer function (OTF) sidelobes formed between the reference sub-aperture and the sub-aperture to be tested independent, thereby effectively decoupling the piston errors of each sub-aperture to be tested; then, with a specific coordinate as the center and a circular region of a specific radius as the boundary, the left half of the real part and the right half of the imaginary part of the OTF sidelobes are combined to extract the feature vectors of the corresponding piston errors; a convolutional neural network containing convolutional blocks and fully connected blocks is built based on the PyTorch framework, and the network parameters are optimized using the training dataset, with Adam as the optimizer and root mean square error as the loss function; then, the network is evaluated using the test dataset to achieve accurate detection of piston errors. The advantages are as follows: by decoupling piston errors with a non-redundant mask, combined with the powerful feature extraction and nonlinear mapping capabilities of the convolutional neural network, the relationship between the feature vectors and piston errors can be accurately established. Test results show that the sensing deviation of the five sub-apertures under test can be controlled within 30nm, the probability of the residual root mean square error of the test sample being less than 20nm exceeds 95%, and the training and test results are highly consistent, demonstrating high precision and robustness. This provides an effective technical means for the accurate detection of piston error in synthetic aperture telescopes, helping the telescope achieve high-resolution imaging.

[0093] It should be understood that the various forms of processes shown above can be used to reorder, add, or delete steps. For example, the steps described in this invention disclosure can be executed in parallel, sequentially, or in different orders, as long as the desired result of the technical solution disclosed in this invention can be achieved, and this is not limited herein.

[0094] The specific embodiments described above do not constitute a limitation on the scope of protection of this invention. Those skilled in the art should understand that various modifications, combinations, sub-combinations, and substitutions can be made according to design requirements and other factors. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of this invention should be included within the scope of protection of this invention.

Claims

1. A method for detecting synthetic aperture piston errors based on optical transfer function decoupling, characterized in that: Specifically, the steps include the following: S1. Set a non-redundant mask on the exit pupil surface of the telescope to divide the aperture into N sub-apertures, one of which is a reference sub-aperture and the rest are sub-apertures to be tested, so that the side lobes of the optical transfer function corresponding to each sub-aperture to be tested are independent from those of the reference sub-aperture. N≥3； The design method for the non-redundant mask specifically includes: designing the aperture layout of the non-redundant mask according to the requirements of the optical system; determining the position of the center of each circular sub-aperture, i.e., the optimization variable, through an optimization algorithm; minimizing the objective function under the premise that the optimization variable satisfies the boundary conditions, and calculating the optimal position of the center of each circular sub-aperture after iteration, so as to ensure the independence of the side lobes of each sub-aperture to be tested and the reference sub-aperture OTF. S2. Extract the feature vector that can uniquely characterize the piston error from the sidelobe of the optical transfer function; use the feature vector as input and the corresponding piston error as label to construct a dataset for neural network training and testing; S3. Construct a convolutional neural network for piston error detection; train the model using training data to obtain the piston error detection model; S4. During the actual observation process of the telescope, the system acquires interferometric images or target images in real time, extracts the side lobe feature vectors corresponding to the sub-aperture to be measured and the reference sub-aperture, inputs the feature vectors into the piston error detection model, and outputs the real-time piston error value of each sub-aperture to be measured relative to the reference sub-aperture.

2. The synthetic aperture piston error detection method based on optical transfer function decoupling according to claim 1, characterized in that: The telescope is a synthetic aperture telescope composed of N sub-mirrors; the sub-aperture has a diameter of [missing information]. D The circular sub-apertures, each corresponding to a sub-mirror. D ≥1mm.

3. The synthetic aperture piston error detection method based on optical transfer function decoupling according to claim 2, characterized in that: The objective function is the negative of the minimum distance between the OTF sidelobe center formed between the sub-aperture to be tested and the reference sub-aperture and the OTF sidelobe center formed between any two sub-apertures; the boundary condition is that each circular sub-aperture is located inside the corresponding sub-mirror.

4. The synthetic aperture piston error detection method based on optical transfer function decoupling according to claim 1, characterized in that: Step S2 specifically includes the following sub-steps: S21. Select one sub-aperture from N sub-apertures as the reference sub-aperture, and use the remaining (N-1) sub-apertures as the sub-apertures to be measured; S22. Based on the geometric position of the sub-aperture to be tested relative to the reference sub-aperture, accurately calculate the center position and boundary of the corresponding side lobe; Assuming the reference sub-aperture center coordinates are (x0, y0), the center coordinates of a certain target sub-aperture are (x, y), the system's operating center wavelength is λ0, and the telescope focal length is... , D Let be the sub-aperture diameter; then the frequency domain center position of the OTF sidelobe corresponding to the sub-aperture to be measured and the reference sub-aperture is (x0-x, y0-y) / (λ0). The frequency domain boundary radius of the sidelobe is D / (λ0 ); S23. Divide the circular region of the side lobe in two along a specific direction, take the left half of the real part and the right half of the imaginary part; concatenate the extracted data left and right to form a two-dimensional feature vector; S24. Following the method in step S23, generate (N-1) corresponding feature vectors for each of the (N-1) sub-apertures to be tested; pair each feature vector with the corresponding piston error value to generate data samples; randomly divide the generated data samples into training datasets and test datasets.

5. The synthetic aperture piston error detection method based on optical transfer function decoupling according to claim 1, characterized in that: The convolutional neural network includes convolutional blocks and fully connected blocks in series; the convolutional block contains convolutional layers, max pooling layers, and ten residual network modules in series; the fully connected block contains three fully connected layers in series.

6. The synthetic aperture piston error detection method based on optical transfer function decoupling according to claim 5, characterized in that: Both the convolutional layer and the fully connected layer are followed by a ReLU activation function.

7. The synthetic aperture piston error detection method based on optical transfer function decoupling according to claim 1, characterized in that: Step S3 specifically includes: S31. Using deep learning methods, a convolutional neural network for piston error detection was built based on the PyTorch framework; S32. Initialize parameters, select optimizer and loss function; S33. Optimize the network parameters using the training dataset to obtain the piston error detection model; S34. Evaluate the piston error detection model on the test dataset to verify whether the model can accurately predict the corresponding piston error value based on the input OTF sidelobe feature vector.

8. The synthetic aperture piston error detection method based on optical transfer function decoupling according to claim 7, characterized in that: The optimizer selected is the Adam optimizer; the loss function is the root mean square error; the metric evaluated in step S34 is the root mean square error.

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