CN111854981B - Deep learning wavefront restoration method based on single-frame focal plane light intensity image - Google Patents

Deep learning wavefront restoration method based on single-frame focal plane light intensity image Download PDF

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CN111854981B
CN111854981B CN202010660807.3A CN202010660807A CN111854981B CN 111854981 B CN111854981 B CN 111854981B CN 202010660807 A CN202010660807 A CN 202010660807A CN 111854981 B CN111854981 B CN 111854981B
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孔令曦
程涛
邱学晶
杨超
王帅
杨平
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Abstract

The invention discloses a deep learning wavefront restoration method based on a single-frame focal plane light intensity image, wherein the problem of multiple solutions exists when a single far-field light spot inverts a near-field wavefront because two groups of wavefronts which are in a complex conjugate relation of rotating 180 degrees mutually in a self-adaptive optical system have the same far-field light spot distribution. The wave front restoration method based on the walsh function phase modulation can ensure that the far-field light spot distribution corresponds to the unique near-field wave front, but the calculation speed is still limited by the iteration times and the single step iteration calculation time. The deep learning algorithm can self-extract deep characteristic information of the image, so that the mapping relation from the far-field light intensity image to the near-field wavefront can be learned on the basis of the walsh function to the phase modulation, the calculation from the far-field image to the near-field wavefront is end-to-end, and the iterative calculation process of the traditional wavefront restoration method can be avoided. Based on the method, the iterative computation process of the traditional wavefront restoration method is avoided by utilizing a deep learning algorithm, the computation efficiency is improved, and the rapid wavefront restoration of the single-frame focal plane light intensity image is realized.

Description

Deep learning wavefront restoration method based on single-frame focal plane light intensity image
Technical Field
The invention relates to a wavefront restoration method, in particular to a deep learning wavefront restoration method based on a single-frame focal plane light intensity image.
Background
In the adaptive optical system, a Zernike polynomial is commonly used for characterizing the wavefront in a circular domain, and different groups of Zernike coefficients are selected to generate different random wavefront aberrations. However, when two groups of wavefronts have a complex conjugate relationship of 180 degrees of rotation, they will generate the same far-field light spot distribution, in this case, the conventional wavefront reconstruction algorithm is adopted to invert the near-field wavefront phase from a single far-field light spot, and the generated corresponding wavefront is not unique, which will cause that the reconstruction calculation is misconverged or even cannot be converged. The wave front restoration algorithm based on the walsh function phase modulation can break the space symmetry of the near field wave front under the condition that the iteration times of the wave front restoration algorithm are less compared with that of the traditional wave front restoration algorithm, so that far field light spots are distributed to correspond to a unique near field wave front, namely, a unique group of Zernike coefficients (seen in Kongqing peaks, research [ D ] of electronic technology university, 2019) of a wave front phase inversion method based on a single-frame focal plane image. The wave front restoration method based on the walsh function modulation has many advantages, solves the problem of multi-solution caused by the complex conjugate relation of the near field wave front rotation of 180 degrees by utilizing the asymmetry of the function, and simultaneously reduces the iteration times and the operation time of the algorithm compared with the traditional algorithm.
However, the effectiveness of the wave front restoration result of the wave front phase plate modulation far field depends on whether the correct wave front function shape with non-180 ° rotation inversion symmetry is selected, and the accuracy of the wave front restoration is also affected by the selection of the wave front functions of different orders and the phase step depth of the photo. The improved algorithm still continues the iterative solution of the traditional phase inversion method, and although the iteration times are relatively reduced, the speed is still deficient. Therefore, how to improve the calculation efficiency while ensuring that the far-field light spot distribution corresponds to the unique near-field wavefront is a problem to be solved.
Disclosure of Invention
The technical problem to be solved by the invention is as follows: on the basis of ensuring the uniqueness and the recovery accuracy of the far-field light spot inversion near-field wave front phase solution, the operation speed is further improved.
The technical scheme adopted by the invention for solving the problems is as follows: a deep learning wavefront restoration method based on a single-frame focal plane light intensity image selects a sample data set with diversity to learn a mapping relation between far-field light spot distribution and near-field wavefront, and after network training convergence, a far-field light spot image is input to obtain a unique corresponding wavefront aberration thereof, wherein iterative operation is not used in the mapping solving process, so that the solving time is reduced, and the method specifically comprises the following steps:
step 1: designing a wave front sensor based on walsh function phase modulation;
step 2: verifying whether the sensor designed in the step 1 can ensure that the far-field light spot distribution only corresponds to one wave front information, namely, the solution is unique;
and 3, step 3: if the solution is unique, obtaining far-field light spots and near-field wavefront data which correspond to each other one by one according to the design in the step 1 and using the far-field light spots and the near-field wavefront data as a data set, and if the solution is not unique, repeatedly executing the step 1 to design the sensor again until the solution is unique;
and 4, step 4: configuring a deep learning environment and building a learning network;
and 5: and taking 90% of the data set quantity as a training set, enabling the network to learn the corresponding relation between the far-field light spots and the near-field wave fronts, taking the remaining 10% of samples as a verification set, and adjusting and verifying the correctness of the network.
The shape of the walsh function is selected to satisfy that the modulation phase is not 180-degree rotation and inversion symmetry.
The theoretical basis for judging whether the unique corresponding far-field light spot distribution is obtained after the near-field wavefront phase is modulated based on the walsh function is as follows:
for a set of wavefront wavefronts that are rotationally flipped 180 ° from each other
Figure BDA0002578494180000021
And
Figure BDA0002578494180000022
the phase thereof satisfies:
Figure BDA0002578494180000023
i.e. the corresponding far fields of the two wavefronts, whose complex amplitudes can be expressed as:
Figure BDA0002578494180000024
Figure BDA0002578494180000025
wherein (x, y) and (x) 0 ，y 0 ) Cartesian space two-dimensional coordinates of a near field and a far field, respectively, (u, v) are frequency domain coordinates; can see U far (x 0 ，y 0 ) And U' far (x 0 ，y 0 ) The real parts are equal and the imaginary parts are opposite in sign, and then the corresponding light intensity distribution is as follows:
|U′ far (x 0 ，y 0 )| 2 ＝|U far (x 0 ，y 0 )| 2 (4)
this illustrates the wave front
Figure BDA0002578494180000026
And with
Figure BDA0002578494180000027
Corresponding to the same far field light intensity distribution;
the walsh function has a non-180 deg. rotationally flipped symmetrical shape, and uses this characteristic to modulate the wavefront, assuming that the phase plate adds discrete aberrations of
Figure BDA0002578494180000028
And the number of the first and second electrodes,
Figure BDA0002578494180000029
then the user can use the device to make a visual display,
Figure BDA00025784941800000210
thereby ensuring that the temperature of the molten steel is ensured,
|U′ far (x 0 ，y 0 )| 2 ≠|U far (x 0 ，y 0 )| 2 (7)
the one-to-one correspondence between far-field light spots and near-field wavefronts is ensured, namely, the uniqueness of a far-field inversion wavefront solution is ensured;
therefore, whether the solution is unique is judged by only comparing the light intensity distribution | U 'corresponding to the near-field wave fronts which are in rotational flip symmetry with each other by 180 degrees' far (x 0 ，y 0 )| 2 And | U far (x 0 ，y 0 )| 2 Whether the two are the same or not is not unique if the two are the same, and is unique if the two are not the same.
The number of the data sets is more than ten thousand, so that the data samples are sufficient and the diversity of the data is met.
The learning network may be a Convolutional Neural Network (CNN), or may be another applicable neural network.
Compared with the prior art, the invention has the advantages that:
(1) compared with the traditional wave front sensor technology, the wave front sensor has simple structure and high light energy utilization rate, and can overcome the multi-solution problem of the traditional single-frame light intensity phase inversion algorithm;
(2) compared with a wave front restoration method improved by walsh function phase modulation, the wave front phase is restored by directly utilizing the mapping relation between far-field light spot distribution and near-field wave front, so that the iterative process can be avoided, and the calculation efficiency is improved.
Drawings
FIG. 1 is a flow chart of a deep learning wavefront reconstruction method based on a single-frame focal plane light intensity image according to the present invention;
FIG. 2 is a schematic diagram of a wavefront sensor based on W3 (third order walsh function) phase plate modulation;
FIG. 3 is a diagram of a positive defocus wavefront without W3 phase plate modulation and a corresponding far-field speckle pattern;
FIG. 4 is a diagram of a negative defocus wavefront without W3 phase plate modulation and a corresponding far field speckle pattern;
FIG. 5 is a far-field speckle pattern of a positive defocused wavefront and a far-field speckle pattern of a negative defocused wavefront modulated by a W3 phase plate;
FIG. 6 is a schematic diagram of the concept of wavefront restoration by Xception convolutional neural network learning.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is described in further detail below with reference to specific embodiments and the accompanying drawings.
Fig. 1 is a flowchart of a deep learning wavefront restoration method based on a single-frame focal plane light intensity image, and the specific implementation process is as follows:
step 1: designing a wave-front sensor based on walsh function phase modulation, comparing simulation results, and selecting a W3 function as a phase plate, which is a wave-front sensor schematic diagram based on W3 phase plate modulation as shown in fig. 2;
step 2: verifying whether the sensor designed in the step 1 can ensure that the far-field light spot distribution only corresponds to one piece of wavefront information through positive and negative defocused wavefront characterized by Zernike polynomial, namely, the solution is unique, fig. 3 and fig. 4 respectively show a positive and negative defocused wavefront map without W3 phase plate modulation and a corresponding far-field light spot map, fig. 5 shows a far-field light spot map with positive and negative defocused wavefronts modulated by W3 phase plate, and the phase step of the phase plate is a far-field light spot map
Figure BDA0002578494180000041
And step 3: in the experimental design, the far-field light spots corresponding to the positive and negative defocused wavefronts before modulation by W3 in fig. 3 and 4 are the same in distribution, and as can be seen from the comparison of the two far-field patterns in fig. 5, the far-field light spots corresponding to the positive and negative defocused wavefronts after modulation by the W3 phase plate are no longer the same in distribution, which indicates that the wavefront sensor designed in step 1 conforms to the unique characteristic of the solution, so 10000 groups of near-field wavefronts and the far-field light spot data corresponding to the near-field wavefronts are collected from the simulation and serve as the data set;
and 4, step 4: configuring a deep learning environment and building an Xception convolution neural network;
and 5: 9000 groups of samples in the data set are used as a training set, so that the network learns the corresponding relation between the far-field light spots and the near-field wave fronts, and 1000 groups of samples are used as a verification set, and the correctness of the network is adjusted and verified.
After the network training is converged, only the far-field light spot distribution diagram needs to be input to the network, and the near-field wavefront information corresponding to the far-field light spot can be output, and as shown in fig. 6, the diagram is the wave-front restoration principle diagram for the Xception convolutional neural network learning adopted by the invention. Iterative operation is not involved in the process, the calculation speed is greatly improved, and the calculation time in the process is estimated to be millisecond level at present.
The above description is only an embodiment of the present invention, but the scope of the present invention is not limited thereto, and any person skilled in the art can understand that the modifications or substitutions within the technical scope of the present invention are included in the scope of the present invention.

Claims (1)

1. A deep learning wavefront restoration method based on a single-frame focal plane light intensity image is characterized by comprising the following steps:
step 1: designing a wave front sensor based on walsh function phase modulation;
and 2, step: verifying whether the wavefront sensor designed in the step 1 can ensure that the far-field light spot distribution only corresponds to one wavefront information, namely, the solution is unique;
and step 3: if the solution is unique, obtaining far-field light spots and near-field wavefront data which correspond to each other one by one according to the design in the step 1 and using the far-field light spots and the near-field wavefront data as a data set, and if the solution is not unique, repeatedly executing the step 1 to design the sensor again until the solution is unique;
and 4, step 4: configuring a deep learning environment and building a learning network;
and 5: taking 90% of the data sets as a training set, enabling the network to learn the corresponding relation between the far-field light spots and the near-field wave fronts, taking the remaining 10% of samples as a verification set, and adjusting and verifying the correctness of the network;
wherein, the shape of the walsh function in the step 1 is selected to satisfy that the modulation phase is not 180 degrees rotationally and symmetrically overturned;
the theoretical basis for judging whether the unique corresponding far-field light spot distribution is obtained after the near-field wavefront phase is modulated based on the walsh function in the step 2 is as follows:
for a set of wavefront wavefronts that are rotationally flipped 180 ° from each other
Figure FDA0003696331450000011
And
Figure FDA0003696331450000012
the phase thereof satisfies:
Figure FDA0003696331450000013
i.e., the far fields corresponding to the two wavefronts, the complex amplitudes of which, ignoring coefficients, can be expressed as:
Figure FDA0003696331450000014
Figure FDA0003696331450000015
wherein (x, y) and (x) 0 ,y 0 ) Cartesian space two-dimensional coordinates of a near field and a far field, respectively, (u, v) are frequency domain coordinates; can see U far (x 0 ,y 0 ) And U' far (x 0 ,y 0 ) The real parts are equal and the imaginary parts are opposite in sign, and then the corresponding light intensity distribution is as follows:
|U′ far (x 0 ,y 0 )| 2 ＝|U far (x 0 ,y 0 )| 2 (4)
this illustrates the wave front
Figure FDA0003696331450000016
And
Figure FDA0003696331450000017
corresponding to the same far field light intensity distribution;
the walsh function has a non-180 deg. rotationally flipped symmetrical shape, and uses this characteristic to modulate the wavefront, assuming that the phase plate adds discrete aberrations of
Figure FDA0003696331450000021
And:
Figure FDA0003696331450000022
then the process of the first step is carried out,
Figure FDA0003696331450000023
thereby ensuring that the temperature of the molten steel is ensured,
|U′ far (x 0 ,y 0 )| 2 ≠|U far (x 0 ,y 0 )| 2 (7)
the one-to-one correspondence between far-field light spots and near-field wavefronts is ensured, namely, the uniqueness of a far-field inversion wavefront solution is ensured;
therefore, whether the solution is unique is judged by only comparing the light intensity distribution | U 'corresponding to the near-field wave fronts which are in rotational flip symmetry with each other by 180 degrees' far (x 0 ,y 0 )| 2 And | U far (x 0 ,y 0 )| 2 Whether the two are the same or not, if the two are the same, the two are not unique, and if the two are not the same, the two are unique;
the number of the data sets in the step 3 is more than ten thousand, so that the data diversity is met while sufficient data samples are ensured;
the learning network in the step 4 is a convolutional neural network CNN.
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