CN117760571B - Unsupervised learning wavefront detection method based on Hartmann detector - Google Patents
Unsupervised learning wavefront detection method based on Hartmann detector Download PDFInfo
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Abstract
The invention discloses an unsupervised learning wavefront detection method based on a Hartmann detector, which comprises the following steps: generating a first Hartmann image; inputting a self-encoding neural network comprising an encoder and a decoder to generate a second Hartmann image; optimizing parameters of the encoder with the improved negative pearson correlation coefficient as a loss function; repeating the foregoing steps to train the encoder in an unsupervised learning manner; and inputting the Hartmann image to be detected to the encoder, wherein the output of the encoder is the phase distortion of the wavefront to be detected. According to the invention, the self-coding neural network is formed by the encoder of the neural network and the decoder of the optical analysis model, so that massive data labeling in the traditional neural network model training is avoided, the training efficiency is improved, the model training can be directly carried out by collecting the real data of the atmosphere, and the model detection precision is improved.
Description
The application is a divisional application provided according to the embodiment of the description of the Hartmann detector-based wavefront detection method, and the application date of the original application is: 2022, 7 months and 18 days, application number: 202210844505.0.
Technical Field
The invention relates to the field of adaptive optics, in particular to an unsupervised learning wavefront detection method based on a Hartmann detector.
Background
The Hartmann detector is widely applied to the self-adaptive optical wavefront detection technology in the fields of laser atmosphere transmission and astronomy due to simple structure and strong robustness.
As shown in fig. 1, the hartmann detector includes a microlens array 1 and a photodetector 2 disposed at a focal plane of the microlens array 1. The working principle of detecting the wave front phase distribution of an incident light beam is as follows: when the light beam is incident, each micro lens forms a sub-aperture, the diameter of the sub-aperture of the traditional Hartmann detector is smaller than the atmospheric coherence length, so that the light in the sub-aperture area can be approximately plane light, and a small light spot can be formed on the photoelectric detector 2 by focusing, therefore, when the incident light beam is incident on the traditional Hartmann detector, a corresponding light spot array can be formed on the photoelectric detector 2. During measurement, the light spot array of the normal incidence plane light beam is taken as a reference standard, and the wave front distortion of the incident light beam relative to the normal incidence plane light in a certain sub-aperture area causes the position deviation of the corresponding light spot. The wave-front phase distribution of the incident light beam can be obtained by calculating the offset of each light spot of the whole light spot array.
Because the Hartmann detector utilizes the micro lens array 1 to divide the wave surface of the incident beam, when the energy of the incident beam is low, the signal to noise ratio and the measurement accuracy of the Hartmann detector are both reduced, and when the energy of the incident beam is severe, the detector cannot work.
Disclosure of Invention
In order to overcome the defects, the technical scheme of the invention provides a wavefront detection method with high signal-to-noise ratio and high measurement accuracy by increasing the diameter of the sub-aperture of the traditional Hartmann detector and combining a deep learning technology, and solves the problem that the traditional Hartmann detector is difficult to measure when the beacon energy is low.
In order to achieve the above purpose, the present invention adopts the following technical scheme:
an unsupervised learning wavefront detection method based on a Hartmann detector, which is characterized by comprising the following steps:
SP1, generating a first Hartmann image;
SP2, inputting the first Hartmann image into a self-coding neural network to generate a second Hartmann image; the self-encoding neural network comprises an encoder and a decoder, wherein the encoder is used for converting the first Hartmann image into wave front phase distortion output; the decoder is used for converting the wave front phase distortion into a second Hartmann image output; the image vector dimensions of the first Hartmann image and the second Hartmann image are the same;
SP3, using negative pearson correlation coefficients (Negative Pearson Correlation Coefficient, NPCC) as a loss function of the self-encoding neural network, training the encoder by constraining the second hartmann image to be equal to the first hartmann image, optimizing model parameters of the encoder;
And SP4, generating a Hartmann image to be detected, inputting the Hartmann image to be detected to the encoder, and outputting the encoder to obtain the wave front phase distortion corresponding to the Hartmann image to be detected.
Further, the first Hartmann image and/or the Hartmann image to be detected are/is generated by atmospheric environment real data.
Further, the network model of the encoder is a convolutional network model ResNet.
Preferably, the decoder performs the following calculation from the wavefront phase distortion to the second hartmann image:
Where φ (x 1,y1) denotes the wavefront phase distortion, t (x 1,y1) denotes the phase screen function of the microlens array, P (x 1,y1) denotes the pupil function, assuming that the light intensity within the pupil is uniform, (x 1,y1) denotes the two-dimensional coordinates of the first Hartmann image, (x 2,y2) denotes the two-dimensional coordinates of the second Hartmann image, f denotes the microlens focal length, λ denotes the wavelength of light, e ikz/iλz denotes the constant exponential factor.
Preferably, the loss function is calculated using a modified NPCC, specifically:
SS1, threshold filtering is carried out on the first Hartmann image;
SS2, normalizing the pixel values of the first and second hartmann images;
SS3 square root division of the first and second hartmann images, respectively;
SS4 computing the square root of the second Hartmann image And the square root of the first Hartmann imageIs a negative pearson correlation coefficient of (c):
Wherein I and I ′ represent the first and second hartmann images, respectively, of the self-encoding network.
Further, the method further comprises preprocessing the first Hartmann image and the Hartmann image to be detected, wherein the preprocessing comprises background light removal and/or threshold filtering.
The invention also provides a self-adaptive optical wavefront detection system based on the Hartmann detector, which at least comprises the Hartmann detector, wherein the Hartmann detector comprises a micro lens array and a photoelectric detector, and the diameter of the sub-aperture of the micro lens array is not more than 3 times of the coherence length of the atmosphere; the photoelectric detector is arranged on the focal plane of the microlens array and is used for generating the first Hartmann image or the Hartmann image to be detected.
Preferably, the adaptive wavefront detection system further includes a light source for generating a collimated light beam, where the collimated light beam is received by the hartmann detector after being irradiated to the atmosphere, and the first hartmann image or the hartmann image to be measured is generated.
From the above, the technical scheme provided by the invention has the following beneficial effects:
1) The self-coding neural network model is utilized to construct an unsupervised learning wavefront detection method based on the Hartmann detector, and the training process of the network model is realized under the condition of no labeling, so that the training speed is improved, and the detection precision of the Hartmann detector is improved through direct acquisition of real atmospheric data for training;
2) The signal to noise ratio of the Hartmann image is improved by preprocessing the Hartmann image and improving the loss function of the self-coding neural network, and the calculation speed and the wave front detection precision of the system are further improved.
Drawings
FIG. 1 is a schematic diagram of a Hartmann detector;
FIG. 2 is a flow chart of a method of wavefront sensing based on a Hartmann detector;
FIG. 3 is a schematic diagram of an adaptive optical wavefront sensing system according to an embodiment of the present invention;
FIG. 4 is a schematic diagram of a neural network model according to an embodiment of the present invention;
FIG. 5 is a graph showing comparison of test results of a wavefront sensing method and a conventional mode method according to an embodiment of the present invention;
FIG. 6 is a diagram illustrating a network configuration of a decoder according to an embodiment of the present invention;
FIG. 7 is a graph showing the comparison of the wavefront restoration results of the loss function before and after correction according to the embodiment of the present invention;
FIG. 8 is a diagram of an adaptive closed-loop correction process for a self-encoding neural network according to a third embodiment of the present invention;
The reference numerals in the drawings respectively indicate:
1. A microlens array; 2. a photodetector; 3. a laser light source; 4. a wavefront corrector; 5. hartmann detector; 6. a beam adapter; 7. hartmann image; 8. zernike coefficient vectors; 200. correcting the front flare map; 201. correcting the light spot diagram by a traditional mode method; 202. correcting the light spot diagram by a wavefront detection method; 301. correcting the residual image by a traditional mode method; 302. and correcting the residual image by a wavefront detection method.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the following detailed description of the present invention will be made with reference to examples. It should be understood that the examples described herein are for illustrative purposes only and are not intended to limit the scope of the present invention.
Example 1
Referring to fig. 2 and fig. 3, fig. 2 is a flowchart of a wavefront detection method based on a hartmann detector according to an embodiment of the present invention, and fig. 3 is a schematic structural diagram of an adaptive optical wavefront detection system according to an embodiment of the present invention. The wavefront detection method of the embodiment of the present invention detects wavefront distortion based on an adaptive optical wavefront detection system, the adaptive optical wavefront detection system including a laser light source 3, a wavefront corrector 4 and a Hartmann detector 5, as can be seen from the figure, the method includes:
S1, generating a distortion phase screen, and loading the distortion phase screen into a wavefront corrector 4 so as to generate wavefront distortion for a collimated light beam; acquiring a training Hartmann image by using a Hartmann detector 5, and constructing a group of training data; in the embodiment of the invention, the generation mode of the distortion phase screen is specifically as follows: firstly, generating a distortion vector, and correspondingly generating a distortion phase screen according to the distortion vector. The distortion vector is a Zernike coefficient vector 8, and the distortion phase screen is the phase difference space distribution of the distorted wavefront and the ideal wavefront of the plane light caused by the distortion vector. In particular, the calculation of the distorted phase screen generated using Zernike polynomial fitting in this embodiment is as follows:
Assuming that a linear combination of the top N term Zernike polynomials is used to generate a distorted phase screen, the distorted phase screen W z (ρ, θ) can be expressed as:
a n represents the coefficients of the nth order Zernike polynomials, then [ a 1,a2,...,aN ] is a set of Zernike coefficient vectors 8, i.e., distortion vectors.
In other embodiments of the present invention, the distortion phase screen may also be obtained by inversion using spectral characteristics, and taking the atmospheric turbulence phase screen as an example, several common frequency spectrum distribution forms include a Kolmogorov spectrum, a von Karman spectrum and an improved von Karman spectrum, whose function forms are respectively:
Where r 0 represents the atmospheric coherence length, f represents the spatial frequency, and f m and f 0 are parameters calculated from the atmospheric internal and external dimensions, respectively. The specific process of calculating the distorted phase screen through the frequency spectrum function is as follows:
Wherein F represents the Fourier transform, A complex vector representing a random phase of unit amplitude. After obtaining the distorted phase screen, the Zernike coefficient vector 8 can be fitted by least square method calculation.
In the embodiment of the invention, a training Hartmann image is used as data, and a corresponding distortion vector is used as a label to construct a group of training data. In other embodiments, a set of training data may also be constructed by training the hartmann image as data and the corresponding distorted phase screen as a tag.
In addition, the training Hartmann image can be preprocessed, and then a group of training data can be constructed by taking the preprocessed training Hartmann image as data, taking the corresponding distortion vector as a label or taking the corresponding distortion phase screen as a label. Wherein the preprocessing includes removing background light and/or performing threshold filtering.
S2, repeating the step S1 to construct a training data set; the training data set comprises M groups of training data, and the value of M is not less than 50000.
And S3, training the neural network model to obtain the trained neural network. The method comprises the following steps: selecting a convolutional neural network ResNet as a neural network model, stacking a training Hartmann image into a three-digit group to serve as the input of the neural network model, enabling the input of the neural network model to be matched with the training Hartmann image dimension, and enabling the output of the neural network model to be matched with the distortion vector dimension;
And (3) training the neural network model by using the training data set constructed in the step (S2) in a supervised learning mode, and optimizing each parameter of the model. In particular, in the embodiment of the present invention, the parameter is optimized by using a back propagation algorithm, and the loss function in the optimization process is the root mean square error (root mean squre, RMS) of the wavefront residual, and the expression is
The meaning of the loss function corresponds to setting an optimization objective to minimize the RMS value of the wavefront residual, which is consistent with the objective of the actual adaptive optics control system. In addition, the embodiment of the invention selects the self-adaptive moment estimation algorithm as an optimizer in the gradient descent algorithm, can adaptively adjust the learning rate of each parameter in the optimization process, and carries out gradient estimation correction through exponential average gradient, thereby improving the optimization speed. To obtain better training and to suppress possible overfitting, the pixel values of all Hartmann images 7 are normalized to between (0, 1) to eliminate the effects of light energy fluctuations. In particular, the training process introduces a Dropout mechanism with a Dropout probability of 0.2. In the embodiment of the invention, other super-parameter settings used in the optimization process are as follows: batch sample size50, initial learning rate 0.0001, training cycle number 10. The embodiment is completed on a cloud server (Intel Xeon Gold 6278C CPU,NVIDIA Tesla T2 GPU) using a deep learning toolbox version Matlab2020 a.
Referring to fig. 4, a schematic structure of the neural network model in this embodiment is shown. In the embodiment of the invention, a Hartmann image 7 with a resolution of 320×320 is subjected to feature extraction through a plurality of residual blocks to obtain feature images with a size of 5×5×2048, wherein the number of the residual blocks is [3, 3], the feature images are subjected to global average pooling to obtain a group of 2048-dimensional feature vectors, the feature vectors are gradually reduced in dimension through 3 full-connection layers to obtain 63-dimensional outputs, and the outputs respectively represent Zernike polynomial coefficients (with pistons and inclination terms removed) of the first 66 terms to form a Zernike coefficient vector 8.
S4, zeroing the wavefront corrector 4, enabling the beam to be detected to enter the wavefront corrector 4, acquiring a Hartmann image to be detected by using the Hartmann detector 5, inputting the Hartmann image to be detected into a trained neural network, and outputting the trained neural network to be the Zernike coefficient vector 8 of the beam to be detected. In the embodiment of the invention, the Hartmann image to be detected is directly input into the trained neural network, and in other embodiments of the invention, if the data of the training data set is the preprocessed trained Hartmann image, the Hartmann image to be detected needs to be preprocessed in the detection process and then is input into the trained neural network.
The embodiment of the invention also provides a self-adaptive optical wavefront detection system based on the Hartmann detector, the wavefront detection system adopts the wavefront detection method, and as can be seen from the figure 3, the wavefront detection system comprises a laser light source 3 for generating a collimated light beam. A wavefront corrector 4 for generating a wavefront aberration for the collimated beam to meet the atmospheric turbulence phase statistics; the Hartmann detector 5 includes a microlens array 1 and a photodetector 2, the photodetector 2 being disposed on a focal plane of the microlens array 1 for generating a Hartmann image 7. The sub-aperture diameter of the microlens array 1 is not more than 3 times of the atmospheric coherence length, and the Hartmann image 7 includes a training Hartmann image and a Hartmann image to be measured. The parameters of the micro lens of the embodiment of the invention are as follows: the aperture of the micro lens is 500 mu m; the arrangement mode is rectangular arrangement; focal length, 30mm; substrate dimensions of 10mm by 10mm; materials: quartz glass. The photodetector 2 adopts MVI-D312I-160-CL series CMOS cameras.
In the embodiment of the present invention, the wavefront sensing system further includes a beam adapter 6 for adjusting the aperture of the incident beam to match the sensing aperture of the Hartmann sensor 5.
Referring to fig. 5, fig. 5 is a graph showing comparison of test results of a wavefront sensing method according to an embodiment of the present invention and a wavefront sensing method according to a conventional mode. In the figure, 200 is a spot diagram before correction, 201 is a spot diagram after correction by a conventional mode method, 202 is a spot diagram after correction by a wavefront detection method, 301 is a residual diagram after correction by a conventional mode method, and 302 is a residual diagram after correction by a wavefront detection method. The conventional mode wavefront sensing method herein refers to a method of acquiring wavefront distortion by calculating centroid displacement using the Hartmann sensor 5 having a sub-aperture diameter smaller than the atmospheric coherence length of the microlens array 1. As can be seen from the graph, the average wavefront residuals RMS of the conventional mode method and the wavefront sensing method according to the embodiment of the invention are 0.0605 and 0.0372, respectively, and the SR values of the corrected far-field light intensities are 0.492 and 0.542, respectively. Therefore, compared with the traditional mode method, the wavefront detection method based on the Hartmann detector provided by the invention can obtain higher wavefront detection precision in the aspects of the RMS of the wavefront residual error and the SR result of the corrected far-field light spot.
In addition, in the embodiment of the invention, the number of the sub-apertures of the Hartmann detector 5 is only 6 multiplied by 6, compared with a phase difference method for acquiring focal plane image characteristics, the technical scheme provided by the invention adopts the sparse sub-aperture Hartmann detector 5 to carry out wave surface segmentation on an incident light beam, so that the light spot shape and image characteristic extraction are simplified, the characteristics are not required to be directly extracted from the complex light spot shape of a focal plane, the neural network structure is simplified, and the calculation speed of deep learning is obviously increased.
Particularly, when the wavefront detection method provided by the invention is applied to wavefront detection caused by atmospheric turbulence, the sub-aperture size is preferably set within 3 times of the atmospheric coherence wavelength, so that the signal-to-noise ratio of the Hartmann image 7 can be improved, and high-precision wavefront detection can be obtained.
Example two
On the basis of the neural network structure of the first embodiment of the invention, a decoder is combined to form a new self-coding neural network structure, the structure performs unsupervised learning, and the neural network automatically solves the mapping relation between the first Hartmann image and the wave front phase distortion by modeling the physical process in a deep learning framework without marking data.
Fig. 6 is a schematic diagram of a network structure of a decoder according to an embodiment of the present invention. In an embodiment of the invention the decoder functions to implement Fresnel diffraction integration in physical optics, taking the wavefront distortion profile as input, to calculate the physical course from phase to the second hartmann image. Therefore, the decoder of the embodiment of the invention has no learnable parameters. The wavefront phase distortion is denoted by phi (x 1,y1), the phase screen function of the microlens array is denoted by t (x 1,y1), the pupil function is denoted by P (x 1,y1), assuming that the intensity of light within the pupil is uniform, a specific physical optical calculation process is as follows:
Wherein (x 1,y1) represents the two-dimensional coordinates of the first Hartmann image, (x 2,y2) represents the two-dimensional coordinates of the second Hartmann image, f represents the focal length of the microlens, λ represents the wavelength of light, and e ikz/iλz represents a constant exponential factor. Forward and backward propagation of the decoder is achieved using the custom DEEP LEARNING LAYER functions in the matlab 2020a deep learning toolbox. At the end of the decoder, the second Hartmann image is normalized to scale the pixel values of the image to between 0-1.
The self-encoding network of the embodiments of the present invention selects the similarity function of the image as a loss function, specifically a negative pearson correlation coefficient (Negative Pearson Correlation Coefficient, NPCC). The loss function treats the image as a vector, and evaluates the similarity between the images by calculating the included angle between the two vectors, which is essentially the cosine included angle of the two images after subtracting the mean value. In the embodiment of the invention, the specific calculation form of the NPCC is as follows:
Wherein X i is the normalized component of the first Hartmann image vector, Is the average value of each component X i, Y i is the normalized component of the second Hartmann image vector,/>Is the average of the components Y i.
The self-decoding neural network takes the first Hartmann image as input, the output form is an array with the same dimension as the first Hartmann image, namely the second Hartmann image, the model parameters can be optimized in an unsupervised mode without additional labels through constraint output equal to the input. After model training is finished, the decoder part is removed, and the output of the encoder is the wave front distortion phase distribution corresponding to the first Hartmann image. It is also noted that the encoder section is actually the neural network in the first embodiment of the invention, and that the decoder network is without trainable parameters.
Example III
Since the vast majority of the pixels in the image obtained by the Hartmann detector are zero or noisy pixels, the pixel values for a small fraction of the pixels (e.g., the pixel locations where the sub-aperture spots are located) are high. Pixels with high pixel values contribute more during the calculation of the correlation coefficient, while pixels with lower pixel values contribute less. Since the phase distribution of wavefront distortion is mainly related to the overall distribution form of optical energy, pixel points with small pixel values may have an important influence on the phase distribution, and thus the recovery accuracy of the correlation coefficient calculated using the NPCC loss function in the second embodiment is limited. In order to further improve the detection accuracy, the embodiment of the invention provides an improved NPCC loss function. Specifically, the threshold filtering is performed on an input image (first Hartmann image) firstly, then pixel values of the input image (first Hartmann image) and an output image (second Hartmann image) are normalized between 0 and 1, the square root of the image is calculated, and then the negative Pelson correlation coefficient of the square root of the image is calculated. Therefore, the pixel value can be effectively amplified under the condition of keeping the image value range unchanged, and the contribution degree of the pixel value in the correlation coefficient calculation is improved.
The modified loss function may be expressed as
Where I and I ′ represent the input image (first hartmann image) and the output image (second hartmann image) from the encoding network, respectively.
The modified loss function is used for calculation, and the wavefront restoration result comparison graph of the loss function before modification and after modification is shown in fig. 7 in the embodiment of the invention. Wherein, graph (a) is the wavefront residual RMS profile of the loss function before correction, graph (b) is the wavefront residual RMS profile of the loss function after correction, graph (c) is the far-field spot map before correction, graph (d) is the far-field spot map after correction obtained using the loss function before correction, and graph (e) is the far-field spot map after correction obtained using the loss function after correction. From the figure, the modified loss function provides a further improvement in wavefront measurement accuracy than the loss function before modification. The average RMS of the wavefront residual was further reduced from 0.152 lambda from the previous training to 0.0743 lambda, and the average SR of the corrected far-field spot was also increased from 0.3678 to 0.5013 (correction Zernike front 66 term).
According to the unsupervised learning neural network model, the diffraction transmission process in the fluctuation optics is realized for the first time, so that the training of the neural network model can discard labels and separate from a laboratory environment, and especially, the real data set in the atmosphere environment can be directly acquired in an external atmosphere self-adaptive optical system to train the neural network model. The characteristics of the training data set and the actual atmospheric turbulence are identical, so that the optimized neural network can further improve the wave front detection precision. As shown in fig. 8, fig. 8 is a diagram of an adaptive closed-loop correction process of a self-encoding neural network according to the third embodiment. To achieve closed loop control, a turbulent phase screen is first generated, then wavefront restoration is performed with a self-encoding neural network model, and proportional integral control is applied to correct the wavefront, wherein the proportional integral factor is 0.3. The closed loop control process can be expressed as:
U(t)＝U(t-1)+bGzcf(I)
Wherein U represents a deformable mirror control voltage, b represents an integral coefficient, G zc represents an interaction matrix, f represents a feedforward calculation process of the neural network, and I represents a first Hartmann image. As can be seen from fig. 8, as the closed loop control process proceeds, the far-field light energy distribution gradually concentrates, the wavefront residual at the end of correction is 0.1249 λ, and the far-field light energy SR is 0.5701.
In addition, in the third embodiment of the invention, 500 groups of turbulence phase screens are generated in total, and proportional-integral self-adaptive closed-loop correction based on deep learning is performed respectively. In the 500 correction results, the wavefront average residual was 0.138 λ, and the corrected far field average SR was 0.5055. The above closed-loop control result verifies the self-adaptive correction force of the technical scheme of the embodiment of the invention under the non-supervision learning condition, and proves that the self-coding neural network trained by the embodiment of the invention has stronger generalization capability, and the self-adaptive correction can be realized by gradually controlling the wavefront corrector 4 through measuring the wavefront residual.
Finally, it should be noted that the above-mentioned embodiments are only for illustrating the technical solution of the present invention, and not for limiting the same, and although the present invention has been described in detail with reference to the preferred embodiments, it should be understood by those skilled in the art that modifications and equivalents may be made to the technical solution of the present invention without departing from the spirit and scope of the technical solution of the present invention, and all such modifications and equivalents are intended to be encompassed in the scope of the claims of the present invention.
Claims (8)
1. An unsupervised learning wavefront detection method based on a Hartmann detector, which is characterized by comprising the following steps:
SP1, generating a first Hartmann image;
SP2, inputting the first Hartmann image into a self-coding neural network to generate a second Hartmann image; the self-encoding neural network comprises an encoder and a decoder, wherein the encoder is used for converting the first Hartmann image into wave front phase distortion output; the decoder is used for converting the wave front phase distortion into a second Hartmann image output; the image vector dimensions of the first Hartmann image and the second Hartmann image are the same;
SP3, using negative pearson correlation coefficients (Negative Pearson Correlation Coefficient, NPCC) as a loss function of the self-encoding neural network, training the encoder by constraining the second hartmann image to be equal to the first hartmann image, optimizing model parameters of the encoder;
And SP4, generating a Hartmann image to be detected, inputting the Hartmann image to be detected to the encoder, and outputting the encoder to obtain the wave front phase distortion corresponding to the Hartmann image to be detected.
2. The wavefront sensing method of claim 1, wherein the first hartmann image and/or the hartmann image under test is generated from atmospheric environment real data.
3. The method of claim 1, wherein the network model of the encoder is a convolutional network model ResNet.
4. The wavefront sensing method of claim 1 wherein the decoder performs the following calculation from the wavefront phase distortion to the second hartmann image:
Where φ (x 1,y1) denotes the wavefront phase distortion, t (x 1,y1) denotes the phase screen function of the microlens array, P (x 1,y1) denotes the pupil function, assuming that the light intensity within the pupil is uniform, (x 1,y1) denotes the two-dimensional coordinates of the first Hartmann image, (x 2,y2) denotes the two-dimensional coordinates of the second Hartmann image, f denotes the microlens focal length, λ denotes the wavelength of light, e ikz/iλz denotes the constant exponential factor.
5. The wavefront sensing method of claim 1, wherein the loss function is calculated using a modified NPCC, in particular:
SS1, threshold filtering is carried out on the first Hartmann image;
SS2, normalizing the pixel values of the first and second hartmann images;
SS3 square root division of the first and second hartmann images, respectively;
SS4 computing the square root of the second Hartmann image And the square root of the first Hartmann imageIs a negative pearson correlation coefficient of (c):
Wherein I and I ′ represent the first and second hartmann images, respectively, of the self-encoding network.
6. The method of claim 1, further comprising preprocessing the first hartmann image and the hartmann image to be detected, the preprocessing including removing background light and/or threshold filtering.
7. An adaptive optical wavefront detection system based on a hartmann detector, the wavefront detection system employing the wavefront detection method according to any one of claims 1 to 6, wherein the adaptive optical wavefront detection system includes at least a hartmann detector, the hartmann detector including a microlens array and a photodetector, the sub-aperture diameter of the microlens array being no more than 3 times the atmospheric coherence length; the photoelectric detector is arranged on the focal plane of the microlens array and is used for generating the first Hartmann image or the Hartmann image to be detected.
8. The adaptive optical wavefront sensing system of claim 7, further comprising a light source for producing a collimated light beam for receipt by the hartmann detector after irradiation of an atmospheric environment to produce the first hartmann image or the hartmann image to be measured.
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