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

Abstract

The invention discloses a deep learning wavefront restoration method based on a single-frame focal plane light intensity image. Since two sets of wavefronts in an adaptive optical system that are in a complex conjugate relationship rotated by 180° have the same far-field light spot distribution, This leads to the problem of multiple solutions when inverting the near-field wavefront from a single far-field spot. The wavefront restoration method based on the phase modulation of the walsh function can ensure that the far-field spot distribution corresponds to a unique near-field wavefront, but the calculation speed is still limited by the number of iterations and the calculation time of a single-step iteration. The deep learning algorithm can self-extract the deep feature information of the image, so the mapping relationship between the far-field light intensity image and the near-field wavefront can be learned based on the phase modulation of the walsh function, which is an end-to-end calculation from the far-field image to the near-field wavefront. , which can avoid the iterative calculation process of traditional wavefront restoration methods. Based on this, the present invention uses a deep learning algorithm to avoid the iterative calculation process of the traditional wavefront restoration method, improves calculation efficiency, and realizes fast wavefront restoration of a single frame of focal plane light intensity image.

Description

A 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 technique

In adaptive optics systems, Zernike polynomials are often used to characterize the wavefront in the circular domain, and different random wavefront aberrations can be generated by selecting different groups of Zernike coefficients. However, when the two sets of wavefronts have a complex conjugate relationship that is rotated 180° to each other, they will produce the same far-field spot distribution. In this case, the traditional wavefront restoration algorithm is used to invert the near-field wavefront phase from a single far-field spot. , the corresponding wavefronts generated are not unique, which will lead to wrong solutions or even failure to converge in the restoration calculation. The wavefront restoration algorithm based on the phase modulation of the walsh function can break the spatial symmetry of the near-field wavefront with fewer iterations than the traditional wavefront restoration algorithm, so that the far-field spot distribution corresponds to a unique near-field wavefront , that is, corresponding to a unique set of Zernike coefficients (see Kong Qingfeng. Research on wavefront phase inversion method based on single-frame focal plane image [D]. University of Electronic Science and Technology of China, 2019). The wavefront restoration method based on walsh function modulation has many advantages. It uses the asymmetry of the function to solve the multi-solution problem caused by the 180° complex conjugate relationship of the near-field wavefront rotation, and at the same time reduces the number of iterations compared with the traditional algorithm. , reducing the running time of the algorithm.

However, the effectiveness of the far-field modulation of the walsh function phase plate on the wavefront restoration result depends not only on whether the correct shape of the walsh function with non-180° rotational flip symmetry is selected, but also on the relationship between the walsh function of different orders and the phase step depth of the photo. The selection also affects the accuracy of the wavefront restoration. And the improved algorithm still continues the iterative solution of the traditional phase inversion method. Although the number of iterations is relatively reduced, there is still a lack of speed. Therefore, how to improve the computational efficiency while ensuring that the far-field spot distribution corresponds to a unique near-field wavefront is a problem that needs to be solved.

SUMMARY OF THE INVENTION

The technical problem to be solved by the present invention is to further improve the operation speed on the basis of ensuring the uniqueness of the near-field wavefront phase solution and the restoration accuracy of the far-field spot inversion.

The technical scheme adopted by the present invention to solve the above problems is: a deep learning wavefront restoration method based on a single frame focal plane light intensity image, selecting a diverse sample data set to learn the mapping relationship between the far-field spot distribution and the near-field wavefront , after the network training converges, input the far-field spot image to obtain its unique corresponding wavefront aberration. This mapping solution process no longer uses iterative operations and reduces the solution time. The specific implementation steps are as follows:

Step 1: Design a wavefront sensor based on walsh function phase modulation;

Step 2: Verify whether the sensor designed in Step 1 can ensure that the far-field spot distribution corresponds to only one wavefront information, that is, the solution is unique;

Step 3: If the solution is unique, obtain the one-to-one correspondence of far-field spot and near-field wavefront data according to the design in Step 1. As a data set, if the solution is not unique, repeat Step 1 to design the sensor again until the solution is unique;

Step 4: Configure the deep learning environment and build a learning network;

Step 5: Use 90% of the data set as the training set, so that the network can learn the correspondence between the far-field spot and the near-field wavefront, and the remaining 10% of the samples are used as the verification set to adjust and verify the correctness of the network.

Among them, the selection of the shape of the walsh function should satisfy that its modulation phase is non-180° rotational flip symmetry.

Among them, the theoretical basis for judging whether the only corresponding far-field spot distribution can be obtained after phase modulation of the near-field wavefront based on the walsh function is:

与

其相位满足：For a set of wavefronts that are 180° rotationally flip symmetrical to each other

and

Its phase satisfies:

That is, the far fields corresponding to the two wavefronts, in the case of ignoring the coefficients, their complex amplitudes can be expressed as:

where (x, y) and (x ₀ , y ₀ ) are the Cartesian space two-dimensional coordinates of the near field and far field, respectively, and (u, v) are the frequency domain coordinates; it can be seen that U _far (x ₀ , y ₀ ) and U′ _far (x ₀ , y ₀ ) have the same real part and opposite sign of the imaginary part, then the corresponding light intensity distribution:

|U′ _far (x ₀ , y ₀ )| ² = |U _far (x ₀ , y ₀ )| ² (4)

与

对应相同的远场光强分布；This shows that the wavefront

and

Corresponding to the same far-field light intensity distribution;

且，In the walsh function, there is a non-180° rotation-flip symmetry shape. Using this characteristic to modulate the wavefront, it is assumed that the additional discrete aberration of the phase plate is

and,

but,

to ensure that,

|U′ _far (x ₀ , y ₀ )| ² ≠ |U _far (x ₀ , y ₀ )| ² (7)

That is, the one-to-one correspondence between the far-field spot and the near-field wavefront is guaranteed, that is, the uniqueness of the far-field inversion wavefront solution is guaranteed;

Therefore, to judge whether the solution is unique, it is only necessary to compare the corresponding light intensity distributions |U' _far (x ₀ , y ₀ )| ² and |U _far (x ₀ , y ₀ ) of the near-field wavefronts that are 180° rotationally flip symmetrical to each other | ² is the same, the same is not unique, and the different is unique.

Among them, the number of data sets should be more than 10,000 groups to ensure sufficient data samples and meet the diversity of data.

Among them, the learning network may be a convolutional neural network (CNN) or other suitable neural networks.

The advantages of the present invention compared with the prior art are:

(1) Compared with the traditional wavefront sensor technology, the wavefront sensor of the present invention has a simple structure, high utilization rate of light energy, and can overcome the multi-solution problem of the traditional single-frame light intensity phase inversion algorithm;

(2) Compared with the wavefront restoration method improved by the walsh function phase modulation, the wavefront phase is directly restored by using the mapping relationship between the far-field spot distribution and the near-field wavefront, which can avoid the iterative process and improve the computational efficiency.

Description of drawings

1 is a flowchart of a deep learning wavefront restoration method based on a single-frame focal plane light intensity image of the present invention;

Figure 2 is a schematic diagram of a wavefront sensor based on W3 (third-order walsh function) phase plate modulation;

Figure 3 is a positive defocus wavefront diagram without modulation by the W3 phase plate and the corresponding far-field spot diagram;

Figure 4 is a negative defocus wavefront diagram and a corresponding far-field spot diagram without modulation by the W3 phase plate;

5 is a far-field speckle diagram of a positive defocus wavefront and a far-field speckle diagram of a negative defocus wavefront modulated by the W3 phase plate;

FIG. 6 is a schematic diagram of the Xception convolutional neural network learning wavefront restoration principle adopted in the present invention.

Detailed ways

In order to make the objectives, technical solutions and advantages of the present invention clearer, the present invention will be further described in detail below with reference to specific embodiments and accompanying drawings.

Figure 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:

Step 1: Design the wavefront sensor based on the phase modulation of the walsh function. After the comparison of the simulation results, the W3 function is selected as the phase plate. As shown in Figure 2, the principle diagram of the wavefront sensor based on the modulation of the W3 phase plate is shown;

Step 2: Use the positive and negative defocus wavefronts represented by Zernike polynomials to verify whether the sensor designed in Step 1 can ensure that the far-field spot distribution corresponds to only one wavefront information, that is, the solution is unique. Figure 3 and Figure 4 are respectively without W3 The positive and negative defocus wavefront diagrams modulated by the phase plate and the corresponding far-field speckle diagram. Figure 5 is the far-field speckle diagram of the positive and negative defocus wavefronts modulated by the W3 phase plate. The phase step of the phase plate is

Step 3: In this experimental design, the far-field spot distributions corresponding to the positive and negative defocus wavefronts before W3 modulation in Figure 3 and Figure 4 are the same, and from the comparison of the two far-field images in Figure 5, it can be seen that after W3 The far-field spot distributions corresponding to the positive and negative defocusing wavefronts modulated by the phase plate are no longer the same, indicating that the wavefront sensor designed in step 1 conforms to the unique characteristics of the solution. Therefore, 10,000 sets of near-field wavefronts are collected from the simulation and correspond to them. The far-field spot data of , as a dataset;

Step 4: Configure the deep learning environment and build the Xception convolutional neural network;

Step 5: Take 9000 groups of samples in the data set as the training set, so that the network can learn the correspondence between the far-field spot and the near-field wavefront, and 1000 groups of samples are used as the verification set to adjust and verify the correctness of the network.

After the network training has converged, it is only necessary to input the far-field spot distribution map to the network, and then the near-field wavefront information corresponding to the far-field spot can be output. As shown in Figure 6, the Xception convolutional neural network used in the present invention learns the wavefront restoration principle. picture. This process no longer involves iterative operations, which greatly improves the calculation speed. Currently, the calculation time of this process is expected to be in the millisecond level.

The above is only a specific embodiment of the present invention, but the protection scope of the present invention is not limited to this, any person familiar with the technology can understand the transformation or replacement that comes to mind within the technical scope disclosed by the present invention, All should be included within 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

And

the phase thereof satisfies:

i.e., the far fields corresponding to the two wavefronts, the complex amplitudes of which, ignoring coefficients, can be expressed as:

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

And

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

And:

then the process of the first step is carried out,

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.

Images