A step-by-step detection method for common-phase error in optical sparse aperture based on deep learning

Abstract

The present invention provides a deep learning-based step-by-step detection method for optical sparse aperture common-phase errors. When both piston and tip-tilt errors exist in an optical sparse aperture imaging system, the method can still decouple and detect the piston and tip-tilt errors of the system with high precision. Specifically, a first feature map containing both piston and tip-tilt errors is first used to predict the tip-tilt error of the system based on a T-CNN and calibrate it. Then, a trained P-CNN that only considers the piston error of the system is used to further predict the piston error of the second feature map. The present invention can achieve a detection accuracy of 1λ / 50 for the tip-tilt error and 1λ / 20 for the piston error, ultimately achieving high-precision detection of both piston and tip-tilt errors.

Description

Technical Field

[0001] The present invention belongs to the technical field of common-phase error detection in optical sparse aperture imaging systems, and in particular relates to a step-by-step detection method for common-phase errors in optical sparse aperture imaging systems based on deep learning. Background Art

[0002] The resolution of an optical system is a key parameter. According to the Rayleigh criterion, the larger the aperture of an optical system, the stronger its resolution. However, currently, due to limitations in optical processing, surface detection capabilities, and transportation costs, the practical application of single, large-aperture optical systems is difficult. To address these issues and effectively improve the resolution of optical systems, researchers have proposed optical sparse aperture (OSA) imaging technology. OSA collects light information by arranging multiple subapertures in a specific pattern on the same phase plane. Light diffracts within each subaperture and forms an interference image on the receiving surface, achieving a resolution approaching that of a single, large-aperture system. Due to factors such as spatial perturbations during splicing or operation, the subapertures may be out of phase. When there is a phase error between subapertures, the subwavefront at the exit pupil of the optical system will shift along the optical axis or deflect radially or tangentially, causing the light wavefront at the exit pupil to deviate from its ideal state, ultimately affecting image quality. Therefore, how to detect the piston and tip-tilt errors of each sub-aperture of the optical sparse aperture imaging system and achieve common phase is a key research issue in the field of optical sparse aperture imaging systems.

[0003] Currently, common-phase error detection methods for optical sparse-aperture imaging systems fall into two main categories: pupil-plane common-phase detection techniques that rely on wavefront sensors and focal-plane common-phase detection techniques that do not rely on additional sensors. Pupil-plane common-phase detection techniques typically utilize sensors with specific structures to modulate and analyze the system's pupil wavefront to obtain common-phase error information. Typical pupil-plane common-phase detection techniques include Shack-Hartmann sensing, dispersion fringe sensing, and pyramid sensing. These methods are generally highly efficient and can rapidly analyze wavefront states, but their structures and operations are complex and costly. Focal-plane common-phase detection techniques, on the other hand, do not require additional sensors and simply calculate the wavefront error at the optical system's exit pupil based on images of the focal or through-focus planes captured by the detector. Typical focal-plane common-phase detection techniques include phase diversity, phase retrieval, and stochastic parallel gradient descent. These detection techniques offer simple optical system implementation, low cost, and enhanced practicality, but they also have a relatively narrow detection range and limitations. For example, the PR method is only applicable to point targets, the PD method has a large amount of calculation and takes a long time, and the SPGD method has poor convergence stability.

[0004] In recent years, with the development of deep learning, it has been introduced to common-phase error detection in optical sparse aperture imaging systems. Deep learning possesses powerful feature extraction and nonlinear fitting capabilities. Driven by extensive data, it establishes a relationship between the common-phase error and the system's PSF or characteristic map, achieving high detection accuracy. However, current common-phase error detection often assumes that only one of the errors (piston or tip-tilt) is present and performs separate detection. However, in actual engineering, both errors exist simultaneously. Therefore, it is necessary to optimize existing theories and methods to achieve joint detection of both errors. Summary of the Invention

[0005] To solve the above problems, the present invention provides a step-by-step detection method for optical sparse aperture common-phase errors based on deep learning, which can achieve high-precision detection of piston and tip-tilt errors when two types of common-phase errors exist simultaneously in an optical sparse aperture imaging system.

[0006] A step-by-step detection method for optical sparse aperture common phase error based on deep learning, comprising the following steps:

[0007] Imaging the extended target through an optical sparse aperture imaging system, and obtaining a corresponding first feature map having both piston error and tip-tilt error by the optical sparse aperture imaging system;

[0008] The first feature map is input into the trained T-CNN model, and the T-CNN model outputs the tip-tilt error prediction value;

[0009] Compensating the tip-tilt error of the optical sparse aperture imaging system according to the tip-tilt error prediction value until the optical sparse aperture imaging system meets the set accuracy requirement, and then obtaining a second feature map through the compensated optical sparse aperture imaging system;

[0010] The second feature map is input into the trained P-CNN model, and the P-CNN model outputs the piston error prediction value.

[0011] Furthermore, the training method of the T-CNN model is:

[0012] S1: One of the subapertures in the optical sparse aperture imaging system is selected as the reference subaperture, and the remaining subapertures are apertures that contain common phase errors relative to the reference subaperture;

[0013] S2: Add a tip-tilt error of [-1, 1]λ and a piston error of [-0.5, 0.5]λ to each of the subapertures except the reference subaperture, to obtain first feature maps corresponding to at least 50,000 optical sparse aperture imaging systems with different tip-tilt errors and piston errors, where λ is the wavelength of light incident on the optical sparse aperture imaging system for imaging;

[0014] S3: Each first feature map is used as the input of the T-CNN model, and the T-CNN model outputs the tip-tilt error prediction value corresponding to each first feature map;

[0015] S4: constructing a first loss function according to the tip-tilt error prediction value corresponding to each first feature map and the actual tip-tilt error value introduced by the optical sparse aperture imaging system corresponding to each first feature map;

[0016] S5: Determine whether the first loss function is less than a set value. If so, the T-CNN model corresponding to the current loss function is the final T-CNN model. If not, adjust the network parameters of the T-CNN model, and then re-execute steps S3 to S6 using the T-CNN model after adjusting the network parameters until the first loss function is less than the set value.

[0017] Furthermore, the optical sparse aperture imaging system is a Golay-6 optical sparse aperture imaging system having 6 subapertures, and the number of random subapertures is 5;

[0018] Among them, the tip-tilt error is composed of the tip error caused by the tilt of the subaperture along the x-axis and the tilt error caused by the tilt of the subaperture along the y-axis. The T-CNN model has 10 outputs, and the 10 outputs correspond to the tip error prediction values ​​and tilt error prediction values ​​of 5 random subapertures respectively.

[0019] Furthermore, the training method of the P-CNN model is:

[0020] S6: using the tip-tilt error prediction values ​​corresponding to the first feature maps to respectively perform error compensation on the tip-tilt errors initially added in step S2, to obtain a corrected optical sparse aperture imaging system after error compensation, wherein the corrected optical sparse aperture imaging system still has residual tip-tilt errors;

[0021] S7: In the case of the residual tip-tilt error and the piston error initially added in step S2, the optical sparse aperture imaging system is calibrated and the extended target is re-simulated to obtain a corresponding second feature map;

[0022] S8: Using each second feature map as an input of the P-CNN model, and having the P-CNN model output a piston error prediction value corresponding to each second feature map;

[0023] S9: constructing a second loss function according to the piston error prediction value corresponding to each second feature map and the piston error value actually introduced by the optical sparse aperture imaging system corresponding to each second feature map;

[0024] S10: Determine whether the second loss function is less than a set value. If so, the P-CNN model corresponding to the current loss function is the final P-CNN model. If not, adjust the network parameters of the P-CNN model, and then re-execute steps S7 to S10 using the P-CNN model after adjusting the network parameters until the first loss function is less than the set value.

[0025] Furthermore, the optical sparse aperture imaging system is a Golay-6 optical sparse aperture imaging system having 6 subapertures, and the number of random subapertures is 5;

[0026] The P-CNN model has five outputs, and the five outputs correspond to piston errors caused by translation of five random sub-apertures along the z-axis.

[0027] Furthermore, any optical sparse aperture imaging system images the extended target to obtain the corresponding first feature map M sharpness The method is:

[0028]

[0029] Where G is the Fourier transform of the focal plane image obtained by imaging the extended target with the optical sparse aperture imaging system, G d is the Fourier transform of the defocused surface image obtained by imaging the extended target with the optical sparse aperture imaging system, * is the conjugate, O is the Fourier transform of the extended target, OTF is the optical transfer function of the optical sparse aperture imaging system, OTF is the optical transfer function of the optical sparse aperture imaging system, d is the optical transfer function of the optical sparse aperture imaging system in the defocused state.

[0030] Furthermore, the wavelength band of light generated by the extended target and incident on the optical sparse aperture imaging system is monochromatic light or polychromatic light.

[0031] Furthermore, in addition to the piston error and tip-tilt error, the optical sparse aperture imaging system also has Zernike aberrations of Z4-Z11 orders corresponding to the wavefront root mean square error less than 0.132λ, where λ is the wavelength of light incident to the optical sparse aperture imaging system for imaging.

[0032] Beneficial effects:

[0033] 1. The present invention provides a step-by-step detection method for optical sparse aperture common-phase errors based on deep learning. When piston and tip-tilt errors simultaneously exist in an optical sparse aperture imaging system, the method can still decouple and detect the piston and tip-tilt errors of the system with high precision. Specifically, a first feature map containing both piston and tip-tilt errors is first used to predict the tip-tilt error of the system based on T-CNN and calibrate it. Then, a trained P-CNN that only considers the piston error of the system is used to further predict the piston error of the system on the second feature map. The tip-tilt error of the present invention can achieve a detection accuracy of 1λ / 50, and the piston error can achieve a detection accuracy of 1λ / 20, ultimately achieving high-precision detection of piston and tip-tilt errors.

[0034] 2. The present invention provides a step-by-step detection method for the common-phase error of an optical sparse aperture based on deep learning. First, a Golay-6 optical sparse aperture imaging system is constructed; then, an extended target is imaged and a data set containing a common-phase error feature map is constructed; thereafter, a tip-tilt error detection network is constructed in conjunction with a step-by-step detection theoretical model; then, a first feature map containing both tip-tilt and piston errors is used to train the network, with the first feature map as input and the tip-tilt error as output, to predict and correct the tip-tilt error and obtain a new second feature map containing the piston error; finally, a piston error detection network is constructed and trained and the piston error is predicted from the second feature map; after all the training is completed, the network can adaptively output the predicted high-precision tip-tilt error and piston error in sequence from the input feature map containing the common-phase error.

[0035] 3. The present invention provides a step-by-step detection method for the common-phase error of an optical sparse aperture based on deep learning. When the optical sparse aperture imaging system has other aberrations besides the common-phase error, the characteristic graph will change accordingly, thereby affecting the detection results; however, when the wavefront RMS generated by the remaining aberrations of the system is less than 0.132λ, the method proposed in the present invention is still feasible and has strong robustness. BRIEF DESCRIPTION OF THE DRAWINGS

[0036] Figure 1 A flow chart of step-by-step detection of common phase error in the optical sparse aperture imaging system provided by the present invention;

[0037] Figure 2 The Golay-6 optical sparse aperture imaging system and imaging target provided by the present invention;

[0038] Figure 3 Schematic diagram of piston and tip-tilt errors of the optical sparse aperture imaging system provided by the present invention;

[0039] Figure 4 The imaging and characteristic diagram of the Golay-6 system provided by the present invention without and with common phase error;

[0040] Figure 5 The two-subaperture optical sparse aperture imaging system provided by the present invention;

[0041] Figure 6 The T-CNN network structure diagram provided by the present invention;

[0042] Figure 7 Characteristic images before and after tip-tilt error correction provided by the present invention;

[0043] Figure 8 The P-CNN network structure diagram provided by the present invention;

[0044] Figure 9 The system PSF and focal plane imaging results after common phase error correction provided by the present invention;

[0045] Figure 10 The present invention provides the influence of system aberrations with different coefficients on the characteristic graph. DETAILED DESCRIPTION

[0046] In order to enable those skilled in the art to better understand the solution of the present application, the technical solution in the embodiments of the present application will be clearly and completely described below in conjunction with the drawings in the embodiments of the present application.

[0047] Current research on common-phase error detection in optical sparse aperture imaging systems assumes that only one of the two errors exists, and does not implement the joint detection of piston and tip-tilt, so there are certain limitations in its application.

[0048] In order to solve this problem, the present invention provides a method for detecting piston and tip-tilt errors of an optical sparse aperture imaging system based on deep learning in a step-by-step manner when piston and tip-tilt errors exist simultaneously. Taking the Golay-6 optical sparse aperture imaging system as an example, Figure 1 As shown in the figure, a theoretical model for the step-by-step detection of piston and tip-tilt errors is first derived. Specifically, tip-tilt error detection is performed first, followed by correction, and then piston error detection. Then, for an extended target, a simulation study of the step-by-step detection of common-phase errors is conducted based on the Golay-6 system. The results show that the tip-tilt error detection accuracy (mean absolute error) can reach 1λ / 50, and the piston error detection accuracy reaches 1λ / 20, ultimately achieving high-quality imaging in the Golay-6 system. Finally, the feasibility of the proposed method under polychromatic light and the robustness of the system in the presence of other aberrations are verified.

[0049] Specifically, the present invention is as follows Figure 2 Taking the Golay-6 optical sparse aperture imaging system shown in (a) as an example, a step-by-step detection method for optical sparse aperture common phase error based on deep learning is described in detail. The method specifically includes the following steps:

[0050] Step 1: imaging the extended target through an optical sparse aperture imaging system, and obtaining a corresponding first feature map having both piston and tip-tilt errors through the optical sparse aperture imaging system;

[0051] Step 2: Input the first feature map into the trained T-CNN model, and the T-CNN model outputs the tip-tilt error prediction value;

[0052] Step 3: Compensate the tip-tilt error of the optical sparse aperture imaging system according to the tip-tilt error prediction value until the optical sparse aperture imaging system meets the set accuracy requirement, and then obtain a second feature map through the compensated optical sparse aperture imaging system;

[0053] Step 4: Input the second feature map into the trained P-CNN model, and the P-CNN model outputs the piston error prediction value.

[0054] Furthermore, the training method of the T-CNN model is:

[0055] S1: One of the subapertures in the optical sparse aperture imaging system is selected as the reference subaperture, and the remaining subapertures are apertures that contain common phase errors relative to the reference subaperture;

[0056] S2: Add a tip-tilt error of [-1, 1]λ and a piston error of [-0.5, 0.5]λ to the subapertures except the reference subaperture, and obtain the first feature maps corresponding to at least 50,000 optical sparse aperture imaging systems with different tip-tilt errors and piston errors as a training dataset, where λ is the wavelength of light incident on the optical sparse aperture imaging system for imaging;

[0057] It can be seen from this that the present invention is as follows Figure 2 Taking reference subaperture 0 shown in (a) as the benchmark, a tip-tilt error of [-1, 1]λ and a piston error of [-0.5, 0.5]λ are randomly added to subapertures 1-5 to generate 50,000 training data sets. In addition, 1,000 validation data sets and 100 test sets are also generated.

[0058] S3: Each first feature map is used as the input of the T-CNN model, and the T-CNN model outputs the tip-tilt error prediction value corresponding to each first feature map;

[0059] S4: constructing a first loss function according to the tip-tilt error prediction value corresponding to each first feature map and the actual tip-tilt error value introduced by the optical sparse aperture imaging system corresponding to each first feature map;

[0060] S5: Determine whether the first loss function is less than the set value. If yes, the T-CNN model corresponding to the current loss function is the final T-CNN model. If not, adjust the network parameters of the T-CNN model, and then re-execute steps S3 to S6 using the T-CNN model after adjusting the network parameters until the first loss function is less than the set value. At this time, the tip-tilt error can be predicted with high precision.

[0061] It should be noted that the convolutional neural network (T-CNN) for detecting tip-tilt error is constructed as follows Figure 6 As shown in Figure 2, the network consists of 16 convolutional layers, 5 max pooling layers, 5 batch normalization layers, and 3 fully connected layers. The MSE loss function is used, with a feature map containing both piston and tip-tilt as input and the tip-tilt errors of the five sub-apertures as output. The learning rate is set to 10-5, the batch size is 64, the Adam optimizer is used, and the number of epochs is set to 120. Training is completed on a GeForce RTX 3090.

[0062] The mean absolute error (MAE) is used as the evaluation standard to evaluate the prediction results. MAE is defined as follows:

[0063] MAE=|y prediction -y truth | (12)

[0064] Among them, y pediction is the tip-tilt error of the prediction, y truth is the true tip-tilt error.

[0065] The prediction results of the tip-tilt error are shown in Table 2. As can be seen from Table 2, the MAE error of subaperture 1 is 2.48 nm, the MAE error of subaperture 2 is 2.80 nm, the MAE error of subaperture 3 is 5.69 nm, the MAE error of subaperture 4 is 2.87 nm, and the MAE error of subaperture 5 is 4.63 nm. The average MAE error is 3.69 nm, achieving high-precision tip-tilt error detection.

[0066] Table 2 Tip-tilt error prediction results

[0067]

[0068] According to the prediction results, the tip-tilt error is corrected. The correction formula is:

[0069] y error =y truth -y prediction (13)

[0070] In the residual tip-tilt error y error In the case of the initial piston error, the simulation generates a new feature map, which is used as the input of the next network to predict the piston error. The feature map before and after correcting the tip-tilt error is as follows Figure 7 As shown, (a) is the feature map before correction, and (b) is the feature map after correction.

[0071] It should be noted that the piston error detection network only needs to change the network output based on the original tip-tilt error detection network, from 10 outputs to 5 outputs, corresponding to the piston errors of the five sub-apertures. Figure 8 shown.

[0072] Generate 10,000 sets of feature maps containing only piston errors to train the network, with a network learning rate of 10-4, a batch size of 16, and the Adam optimizer.

[0073] Furthermore, the training method of the P-CNN model is:

[0074] S6: using the tip-tilt error prediction values ​​corresponding to the first feature maps to respectively perform error compensation on the tip-tilt errors initially added in step S2, to obtain a corrected optical sparse aperture imaging system after error compensation, wherein the corrected optical sparse aperture imaging system still has residual tip-tilt errors;

[0075] S7: In the case of the residual tip-tilt error and the piston error initially added in step S2, the optical sparse aperture imaging system is calibrated and the extended target is re-simulated to obtain a corresponding second feature map;

[0076] S8: Using each second feature map as an input of the P-CNN model, and having the P-CNN model output a piston error prediction value corresponding to each second feature map;

[0077] S9: constructing a second loss function according to the piston error prediction value corresponding to each second feature map and the piston error value actually introduced by the optical sparse aperture imaging system corresponding to each second feature map;

[0078] S10: Determine whether the second loss function is less than the set value. If so, the P-CNN model corresponding to the current loss function is the final P-CNN model. If not, adjust the network parameters of the P-CNN model, and then re-execute steps S7 to S10 using the P-CNN model after adjusting the network parameters until the first loss function is less than the set value. At this time, the piston error can be predicted with high precision.

[0079] After the network is trained, the second feature map obtained in the previous step is used as input to predict the piston error. MAE is still used to evaluate the prediction results. The evaluation results are shown in Table 3:

[0080] Table 3 Piston error prediction results

[0081] Aperture number Sub1 Sub2 Sub3 Sub4 Sub5 average MAE / nm 33.55 33.98 9.61 35.90 21.53 26.91

[0082] It can be seen from Table 3 that the MAE error of sub-aperture 1 is 33.55nm, the MAE error of sub-aperture 2 is 33.98nm, the MAE error of sub-aperture 3 is 9.61nm, the MAE error of sub-aperture 4 is 35.90nm, and the MAE error of sub-aperture 5 is 21.53nm. The average MAE error is 26.91nm, achieving high-precision piston error detection.

[0083] After completing the tip-tilt and piston error correction, the PSF and focal plane imaging results of the Golay-6 system are as follows: Figure 9 As shown, (a) is the system PSF and (b) is the focal plane imaging result.

[0084] from Figure 9 In the figure, it can be seen that after correcting the common-phase error, the system PSF is very concentrated, the focal plane image is clear, and the piston and tip-tilt errors of the system are accurately calibrated.

[0085] The imaging principle of the Golay-6 optical sparse aperture imaging system adopted by the present invention is described in detail below.

[0086] Golay-6 optical sparse aperture imaging system such as Figure 2 As shown in (a), 0 is the reference sub-aperture, and the other 5 are sub-apertures with some tilt errors and translation errors randomly added to the reference sub-aperture to make their postures different from the reference sub-aperture.

[0087] The imaging target is a resolution plate such as Figure 2 (b) The parameters of the Golay-6 system are shown in Table 1.

[0088] Table 1 Golay-6 system parameters

[0089]

[0090] Establishing the xoy rectangular coordinate system on the pupil plane, the pupil function of a single sub-aperture can be expressed as:

[0091]

[0092] Where (x0, y0) is the center coordinate of the subaperture, r is the radius of the subaperture, and cir represents the circular function. The pupil function of Golay-6 can be expressed as:

[0093]

[0094] Where i represents the subaperture number, (x i ,y i ) is the center coordinate of the subaperture. δ is the unit impulse function.

[0095] The common phase error of the optical sparse aperture system includes piston error and tip-tilt error, such as Figure 3 shown. Figure 3 In (a), a subaperture is translated along the z-axis relative to the reference subaperture, which is called piston error. Figure 3 (b) The subaperture is tilted along the x-axis relative to the reference subaperture, known as tip error. Similarly, the subaperture is tilted along the y-axis relative to the reference subaperture, known as tilt error. Both piston error and tip-tilt error can cause phase shift in optical sparse-aperture imaging systems, severely degrading image quality.

[0096] When there is a common phase error in the Golay-6 system, the pupil function P error (x,y) is represented as:

[0097]

[0098] Where λ is the wavelength, P(x,y) is the pupil function without common phase error, and p n is the piston error of the nth subaperture relative to the reference subaperture, α n and β n are the tip error along the x-axis and the tip-tilt error along the y-axis of the nth subaperture relative to the reference subaperture, respectively.

[0099] The construction of the feature map requires the introduction of defocus. When the system has defocus, the defocus phase needs to be introduced. d It can be expressed as:

[0100]

[0101] Where k is the wave vector, f is the focal length of the system, and ΔL is the defocus distance. The defocus distance introduced in this study is 1.9720 mm.

[0102] The point spread function (PSF) describes the imaging result of a point light source after passing through a diffraction-limited optical system. According to the principle of Fourier optics, the PSF is the Fourier transform of the pupil function. When there is a common phase error in the system, the PSF of the focal plane and the defocus plane can be expressed as:

[0103]

[0104] Among them, (η,ξ) represents the coordinates on the image plane, represents the Fourier transform.

[0105] The imaging process of the Golay-6 system can be expressed as the convolution of the extended target and the focal plane PSF or the defocused plane PSF in the spatial domain, as shown in formula (7):

[0106] G(η,ξ)=PSF(η,ξ)*O(η,ξ) (7)

[0107] Among them, O(η,ξ) represents the expansion target, PSF(η,ξ) is the PSF focus (η,ξ) or PSF defocus (η,ξ).

[0108] The target-independent feature map of the Golay-6 system is constructed by equation (8), which contains all the common-phase error information of the system. The feature map has a nonlinear relationship with the piston error and the tip-tilt error. Therefore, a convolutional neural network can be used to fit this nonlinear relationship and then solve it.

[0109]

[0110] Among them, M sharpness is the feature map, G is the Fourier transform of the focal plane image obtained by imaging the extended target with the optical sparse aperture imaging system, G d is the Fourier transform of the defocused surface image obtained by imaging the extended target with the optical sparse aperture imaging system, * is the conjugate, O is the Fourier transform of the extended target, OTF is the optical transfer function of the optical sparse aperture imaging system, OTF is the optical transfer function of the optical sparse aperture imaging system, d is the optical transfer function of the optical sparse aperture imaging system in the defocused state.

[0111] In the case of Golay-6 system without common phase error, the focal plane PSF is as follows Figure 4 As shown in (a), the focal plane image is Figure 4 (b), the defocused surface image is shown in 4(c), and the feature map is shown in Figure 4 (d) shows that when piston and tip-tilt errors are present at the same time, the focal plane PSF is as follows: Figure 4As shown in (e), the focal plane image is Figure 4 (f), the defocused surface image is shown in 4(g), and the first feature map is shown in Figure 4 (h) shown.

[0112] The following is a detailed derivation of the basic principle of decoupling the tip-tilt error from the feature map of the mixed piston and tip-tilt errors.

[0113] Take the two-subaperture optical sparse aperture imaging system as an example, Figure 5 The theoretical basis for decoupling the tip-tilt error from the feature map containing both piston and tip-tilt errors is derived.

[0114] Based on the left sub-aperture, the piston and tip-tilt errors are added to the right sub-aperture, where p is the piston error of the sub-aperture along the z-axis, a is the tilt angle of the sub-aperture along the x-axis, and b is the tilt angle of the sub-aperture along the y-axis. The diameters of the two symmetrically distributed sub-apertures are both D, and the coordinates of the circle centers are At this time, the pupil function can be expressed as:

[0115]

[0116] According to the Fourier optics principle, the optical transfer function OTF can be expressed as:

[0117]

[0118] in, OTF sub is the diffraction-limited optical transfer function of a single subaperture, expressed as:

[0119]

[0120] From Equation (10), we can see that the first two terms constitute the main lobe of the OTF, the third and fourth terms are the sidelobes symmetrically distributed on both sides of the main lobe, the second term contains only the tip-tilt error, and the third and fourth terms contain both the piston error and the tip-tilt error. Therefore, the tip-tilt error can be decoupled from the characteristic map of the mixed piston and tip-tilt errors.

[0121] Furthermore, the wavelength band of light incident on the optical sparse aperture imaging system generated by the extended target is monochromatic or polychromatic. Therefore, in the case of 500-600nm polychromatic light, the system introduces a tip-tilt error of [-1, 1]λ (λ = 550nm) and a piston error of [-1, 1]λ. Following the above steps, the system tip-tilt and piston errors are simulated and predicted. The prediction results are shown in Table 4:

[0122] Table 4 Tip-tilt and piston error prediction results under polychromatic light

[0123]

[0124] As can be seen from Table 4, the average prediction accuracy of the tip-tilt error can reach 11.86nm, and the average prediction accuracy of the piston error can reach 21.32nm. High-precision common-phase error detection can still be achieved under polychromatic light.

[0125] Under polychromatic light, the detection range of piston can reach the coherence length, that is, While keeping the tip-tilt error range unchanged, the piston error range is expanded to [-5, 5]λ. The tip-tilt and piston errors are still predicted according to the above steps. The prediction results are shown in Table 5.

[0126] Table 5 Tip-tilt and piston error prediction results under coherence length

[0127]

[0128] As can be seen from Table 5, the average prediction accuracy of the tip-tilt error is 11.68 nm, and the average prediction accuracy of the piston error is 21.53 nm. Under polychromatic light, P-CNN can achieve high-precision prediction of the piston error range up to the coherence length.

[0129] Furthermore, in order to verify the stability of the present invention, in addition to the piston error and tip-tilt error, the optical sparse aperture imaging system also has Z5-Z11 order Zernike aberrations with corresponding wavefront root mean square errors less than 0.132λ, where λ is the wavelength of light incident to the optical sparse aperture imaging system for imaging.

[0130] Specifically, other aberrations of the system are expressed using Zernike polynomials. When the system has other aberrations, the distorted wavefront generated by the aberrations can be expressed as:

[0131]

[0132] Among them, aj represents the coefficient of the jth Zernike mode, Z j represents the j-th Zernike mode.

[0133] Introduce Zernike aberrations of order 5 to 11 with Zernike coefficients of 0.05λ (λ=600), 0.1λ, 0.5λ and 1λ respectively into the Golay-6 system (the coefficients of each order are equal in each case). Taking the characteristic graph of piston error as an example, the influence of different system aberrations on the characteristic graph is studied, such as Figure 10 (a) is the characteristic diagram corresponding to each aberration coefficient of 0.05λ; (b) is the characteristic diagram corresponding to each aberration coefficient of 0.1λ; (c) is the characteristic diagram corresponding to each aberration coefficient of 0.5λ; (d) is the characteristic diagram corresponding to each aberration coefficient of 1λ.

[0134] from Figure 10 It can be seen that when there are 5th-11th order aberrations with coefficients greater than 0.1λ, the characteristic diagram changes significantly, and the system aberrations will overlay the original common phase error, making it difficult to decouple the true piston error. Therefore, other system aberrations cannot be too large.

[0135] We introduced additional aberrations, represented by Zernike polynomials of orders 5-11, into the Golay-6 system, with each Zernike mode coefficient set to 0.05λ (corresponding to a wavefront RMS of 0.132λ). We generated training, validation, and test sets containing these additional aberrations to test the robustness of the network in the presence of these aberrations. Following the above steps, we predicted the tip-tilt and piston errors, respectively. The prediction results are shown in Table 6.

[0136] Table 6 Prediction results of tip-tilt and piston errors when Z5-Z11 aberrations exist

[0137]

[0138] As can be seen from Table 6, in the presence of certain other system aberrations, the average detection accuracy of the tip-tilt error reaches 4.01nm, and the average detection accuracy of the piston error reaches 30.50nm. High-precision tip-tilt and piston error predictions can still be achieved, proving that the network has a certain degree of robustness to other system aberrations.

[0139] In summary, most domestic and international studies on common-phase error detection in optical sparse aperture imaging systems have only considered how to achieve common-phase error detection when only one error, piston error or tip-tilt error, exists. However, in reality, it is impossible for a system to contain only a single error. Therefore, the key is how to detect piston and tip-tilt errors when both types of common-phase errors exist in the system. In addition, researchers rarely consider the impact of other system aberrations on the feature map. In reality, other system aberrations are inevitable, and ensuring the robustness of the proposed method in the presence of other system aberrations is also very important.

[0140] 1. The present invention innovatively proposes a step-by-step detection method for piston and tip-tilt errors in an optical sparse aperture imaging system. Compared with previous research methods, the proposed method can achieve high-precision detection of piston and tip-tilt errors when two types of common-phase errors exist simultaneously in an optical sparse aperture imaging system. The feasibility of first decoupling the tip-tilt error from a feature map containing two types of common-phase errors is theoretically derived; secondly, the tip-tilt error of the system is first predicted using T-CNN, and the system is error-corrected to obtain a new feature map containing only piston errors; then, the P-CNN that has been trained only for piston errors is used to predict the piston error on the new feature map. Ultimately, high-precision detection of two types of common-phase errors is achieved.

[0141] 2. Compared with the current research on common-phase error detection in optical sparse aperture imaging systems, this paper fully studies the impact of other system aberrations on the feature map, and explores the robustness of T-CNN and P-CNN in the presence of other system aberrations, which has certain reference significance for engineering practice.

[0142] 3. Using the same network, only by changing the network input and output and adjusting the hyperparameters, the piston and tip-tilt errors can be detected step by step, realizing the multi-purpose use of one network.

[0143] Of course, the present invention may have many other embodiments. Without departing from the spirit and essence of the present invention, those skilled in the art may of course make various corresponding changes and modifications based on the present invention, but these corresponding changes and modifications should all fall within the scope of protection of the claims attached to the present invention.

Claims

1. A step-by-step detection method for optical sparse aperture common phase error based on deep learning, characterized in that: The following steps are involved: Imaging the extended target through an optical sparse aperture imaging system, and obtaining a corresponding first feature map having both piston error and tip-tilt error by the optical sparse aperture imaging system; The first feature map is input into the trained T-CNN model, and the T-CNN model outputs the tip-tilt error prediction value; Compensating the tip-tilt error of the optical sparse aperture imaging system according to the tip-tilt error prediction value until the optical sparse aperture imaging system meets the set accuracy requirement, and then obtaining a second feature map through the compensated optical sparse aperture imaging system; The second feature map is input into the trained P-CNN model, and the P-CNN model outputs the piston error prediction value.

2. The optical sparse aperture common phase error step-by-step detection method based on deep learning according to claim 1, characterized in that: The training method of the T-CNN model is: S1: One of the subapertures in the optical sparse aperture imaging system is selected as the reference subaperture, and the remaining subapertures are apertures that contain common phase errors relative to the reference subaperture; S2: Add a tip-tilt error of [-1, 1]λ and a piston error of [-0.5, 0.5]λ to each of the subapertures except the reference subaperture, to obtain first feature maps corresponding to at least 50,000 optical sparse aperture imaging systems with different tip-tilt errors and piston errors, where λ is the wavelength of light incident on the optical sparse aperture imaging system for imaging; S3: Each first feature map is used as the input of the T-CNN model, and the T-CNN model outputs the tip-tilt error prediction value corresponding to each first feature map; S4: constructing a first loss function according to the tip-tilt error prediction value corresponding to each first feature map and the actual tip-tilt error value introduced by the optical sparse aperture imaging system corresponding to each first feature map; S5: Determine whether the first loss function is less than a set value. If so, the T-CNN model corresponding to the current loss function is the final T-CNN model. If not, adjust the network parameters of the T-CNN model, and then re-execute steps S3 to S6 using the T-CNN model after adjusting the network parameters until the first loss function is less than the set value.

3. The optical sparse aperture common phase error step-by-step detection method based on deep learning according to claim 2, characterized in that: The optical sparse aperture imaging system is a Golay-6 optical sparse aperture imaging system having 6 subapertures, and the number of random subapertures is 5; Among them, the tip-tilt error is composed of the tip error caused by the tilt of the subaperture along the x-axis and the tilt error caused by the tilt of the subaperture along the y-axis. The T-CNN model has 10 outputs, and the 10 outputs correspond to the tip error prediction values ​​and tilt error prediction values ​​of 5 random subapertures respectively.

4. The optical sparse aperture common phase error step-by-step detection method based on deep learning according to claim 2, characterized in that: The training method of the P-CNN model is: S6: using the tip-tilt error prediction values ​​corresponding to the first feature maps to respectively perform error compensation on the tip-tilt errors initially added in step S2, to obtain a corrected optical sparse aperture imaging system after error compensation, wherein the corrected optical sparse aperture imaging system still has residual tip-tilt errors; S7: In the case of the residual tip-tilt error and the piston error initially added in step S2, the optical sparse aperture imaging system is calibrated and the extended target is re-simulated to obtain a corresponding second feature map; S8: Using each second feature map as an input of the P-CNN model, and having the P-CNN model output a piston error prediction value corresponding to each second feature map; S9: constructing a second loss function according to the piston error prediction value corresponding to each second feature map and the piston error value actually introduced by the optical sparse aperture imaging system corresponding to each second feature map; S10: Determine whether the second loss function is less than a set value. If so, the P-CNN model corresponding to the current loss function is the final P-CNN model. If not, adjust the network parameters of the P-CNN model, and then re-execute steps S7 to S10 using the P-CNN model after adjusting the network parameters until the first loss function is less than the set value.

5. The method for detecting optical sparse aperture common phase error step by step based on deep learning according to claim 4, wherein: The optical sparse aperture imaging system is a Golay-6 optical sparse aperture imaging system having 6 subapertures, and the number of random subapertures is 5; The P-CNN model has five outputs, and the five outputs correspond to piston errors caused by translation of five random sub-apertures along the z-axis.

6. The optical sparse aperture common phase error step-by-step detection method based on deep learning according to claim 2, characterized in that: Any optical sparse aperture imaging system images the extended target and obtains the corresponding first feature map M sharpness The method is: Where G is the Fourier transform of the focal plane image obtained by imaging the extended target with the optical sparse aperture imaging system, G d is the Fourier transform of the defocused surface image obtained by imaging the extended target with the optical sparse aperture imaging system, * is the conjugate, O is the Fourier transform of the extended target, OTF is the optical transfer function of the optical sparse aperture imaging system, OTF is the optical transfer function of the optical sparse aperture imaging system, d is the optical transfer function of the optical sparse aperture imaging system in the defocused state.

7. The optical sparse aperture common phase error step-by-step detection method based on deep learning according to claim 1, characterized in that: The wavelength band of light generated by the extended target and incident on the optical sparse aperture imaging system is monochromatic light or polychromatic light.

8. The optical sparse aperture common phase error step-by-step detection method based on deep learning according to claim 1, characterized in that: In addition to the piston error and tip-tilt error, the optical sparse aperture imaging system also has Zernike aberrations of orders Z4-Z11, with corresponding wavefront root mean square errors less than 0.132λ, where λ is the wavelength of light incident on the optical sparse aperture imaging system for imaging.

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