CN114880953B - Rapid wavefront restoration method of four-step phase type Fresnel zone plate - Google Patents
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Abstract
The invention discloses a rapid wavefront restoration method of a four-step phase type Fresnel zone plate. The invention designs a wavefront restoration sensor based on a Fresnel zone plate, which has simple operation, simple structure, good instantaneity and high restoration precision, can break the multi-resolution problem of a single-frame far-field image in the traditional wavefront-free sensing technology under the condition that 1-quadrant focal length and 3-quadrant focal length are different from 2-quadrant focal length and 4-quadrant focal length, and utilizes a neural network to construct the nonlinear relation between the far-field image imaged by the four-step phase Fresnel zone plate with mixed focal length and the Zernike mode coefficient, thereby avoiding the phase ambiguity problem of the traditional wavefront-free sensing technology, overcoming the multi-resolution problem by utilizing a plurality of far-field images, combining the neural network with stronger instantaneity, and realizing the rapid phase inversion of the single-frame focal-plane light intensity image without the time-consuming iterative optimization process.
Description
Technical Field
The invention relates to the technical field of single-frame image wave front restoration without a wave front sensor, in particular to a rapid wave front restoration method of a four-step phase type Fresnel zone plate.
Background
The phase inversion method is a detection method for resolving wavefront by utilizing focal plane light intensity distribution, has a simple structure, can realize high-order continuous aberration detection, can perform phase recovery on an extended target, can perform online detection, has high energy concentration, and is suitable for weak light detection. However, the main problems are that the inversion accuracy is not high, a multi-solution problem exists, and stagnation is easy to occur in the iteration process. This iterative stagnation results from the fact that the actual near-field complex amplitude f (x, y) and its rotated 180 degree conjugate complex amplitude have the same light intensity distribution over the far field. Thus, the GS algorithm easily converges to either a local minimum pseudo-solution or one of two global minimum fuzzy solutions.
The wavefront inversion method of the single-frame focal plane image realizes wavefront restoration through one far-field image, and the method has simple light path, but the application range is limited due to the existence of the multi-solution phenomenon. The linear algorithm between the lower order aberration and the spot distribution is obtained by adding an angle of astigmatism to the original aberration by Serge meicon et al, france, but the linear region of this approach is limited and is only effective for lower order aberration detection (see C.Plantet, S.Meimon, J.M.Conan, et al, experimental al validation of LIFT for estimation of low-order modes in low-flux wavefront sensing [ J ] Optics Express,2013,21 (14): 16337-16352). Dong Bing et al in 2015 proposed a hybrid phase inversion algorithm that used a combination of linear phase inversion and GS algorithm. The result of the linear inversion is used as the initial wavefront phase of the GS algorithm. By this method, the higher order aberrations are substantially recovered, but the problem of multiple solutions remains unsolved (see B.Dong, G.Jia, R.Wang.Hybrid phase retrieval from a single defocused image [ C ]. Proc. SPIE,2015, 9622:962205).
The wavefront phase inversion method based on the single-frame focal plane image has the advantages of simple structure, low environmental requirement and high energy utilization rate, and is a wavefront restoration technology with wide application prospect and research value. However, the conventional single-frame focal plane inversion technology has a multi-solution problem, which can lead to inaccurate test effect. Although the phase difference method can overcome the problem, the phase difference method needs to detect light intensity information at two positions of a focal plane and a defocusing plane, and has a complex structure. Other wavefront inversion methods based on single-frame focal plane images have various limitations and do not fundamentally solve the problem of recovery accuracy of phase inversion.
Therefore, the invention provides a wavefront restoration method of a four-step phase type Fresnel zone plate combined neural network based on a mixed focal length.
Disclosure of Invention
The invention aims to solve the technical problems that: under the condition that only one far-field light spot image is acquired, the far field contains part of in-focus information and part of defocus information, then a neural network is combined to utilize far-field images to invert a unique solution of a near-field wave front phase, and the accuracy and the instantaneity of wave front restoration are ensured. The invention provides a wavefront restoration method based on a mixed focal length four-step phase type Fresnel zone plate and a neural network, which designs a four-step Fresnel zone plate with one focal length in one quadrant and the other focal length in the other quadrant, breaks through the rotation overturning symmetry of near-field wavefront, fundamentally solves the problem of multiple solutions, and can obtain a final restoration result without the need of iterative optimization with high time consumption by combining a neural network technology with strong nonlinear fitting capability, thereby realizing a more real-time and efficient wavefront detection-free self-adaptive optical wavefront restoration method.
The invention adopts the technical proposal that: a quick wave front restoring method of four-step phase type Fresnel zone plate selects a data set fully sampled in a sample space for a Convolutional Neural Network (CNN) to fit a mapping relation between far-field light spots and near-field wave front phases, after network training is converged, far-field light spot images imaged by a mixed focal length Fresnel zone plate are input, and corresponding wave front Zernike mode coefficients can be obtained, iterative operation is not needed in the mapping solving process, calculation time is reduced, and the method comprises the following specific implementation steps:
step 1: the four-step phase type Fresnel zone plate based on the mixed focal length is designed, and the four-step phase type Fresnel zone plate comprises the distribution of the mixed focal length, an entrance pupil radius, a focal length difference, a phase step width, a phase step height and diffraction efficiency parameter design;
step 2: verifying whether the four-step phase type Fresnel zone plate based on the mixed focal length designed in the step 1 can simultaneously obtain far-field light intensity distribution of a single-frame point light source on one focal length focal plane of the four-step phase type Fresnel zone plate based on the mixed focal length, wherein the light intensity utilization rate is more than eighty percent, the light spot radius is larger than five pixels, and otherwise, the neural network is difficult to extract characteristics of a small number of pixels;
step 3: if the step 2 can be realized, introducing random aberration conforming to an atmospheric transmission model into ideal parallel light by using the four-step phase type Fresnel zone plate with the mixed focal length designed in the step 1, recording far-field light spots and near-field wave front data, respectively taking far-field light spot images detected by a CCD and near-field wave front Zernike mode coefficients (or near-field wave surfaces) corresponding to the far-field light spot images as samples and labels to manufacture a wave front restoration data set of the four-step phase type Fresnel zone plate combined neural network based on the mixed focal length, and if the step 2 cannot be realized, repeatedly executing the step 1 to design the four-step phase type Fresnel zone plate based on the mixed focal length until the step 2 is realized;
step 4: configuring a deep learning environment and building a neural network;
step 5: randomly extracting 80% of samples in the data set as a training set for the network to learn the mapping relation between far-field light spots and near-field wave fronts; randomly extracting half of the remaining 20% of samples from the data set as a verification set for adjusting network super parameters and verifying algorithm effectiveness, and finally taking the remaining 10% of samples as a test set for unbiased estimation;
step 6: and replacing different neural networks for testing, recording the test set result, and selecting the network structure with the optimal performance according to the final result.
The first and third quadrants of the four-step phase type Fresnel zone plate with the mixed focal length in the step 1 are focal length values, the second and fourth quadrants are focal length values different from the first and third quadrants, and far-field imaging can be guaranteed to contain part of in-focus information and part of out-of-focus information only when the CCD is placed on the focal plane of the first, third or second and fourth quadrants, so that the purpose of breaking the near-field wave surface overturning rotational symmetry is achieved, and the problem of multiple solutions is solved.
The difference value of focal length values of the first quadrant, the third quadrant, the second quadrant and the fourth quadrant in the four-step phase type Fresnel zone plate with the mixed focal length in the step 1 can confirm a proper defocus amount according to a traditional phase difference method, is more beneficial to improving the accuracy of wavefront restoration, and is preferably a defocus amount with a wavelength of about.
In the step 2, a four-step type with higher diffraction efficiency and moderate step number is selected for design, and the step width and the step height directly influence the diffraction efficiency.
Wherein, the number of samples of the data set in the step 3 should be at least thirty thousand groups, that is, the samples should be sufficiently sampled in the sample space.
The dividing modes of the training set, the verification set and the test set in the step 5 can be changed appropriately according to the actual requirements and the size of the data set.
Compared with the prior art, the invention has the advantages that:
(1) The four-step phase type Fresnel zone plate with the mixed focal length has higher diffraction efficiency and can overcome the problem of multiple solutions only by one far-field facula image;
(2) The four-step Fresnel zone plate with various defocus and various phase step heights is designed in a simulation manner, design parameters with higher restoration accuracy are determined by using a neural network training test, and the accuracy of restoring 62-step Zernike mode coefficients can reach the wavefront restoration residual error of 0.008 wavelength;
(3) The invention has no traditional wavefront sensor and additional modulation device, simple structure and easy operation, and the imaging equipment only needs one CCD camera;
(4) The neural network introduces channel attention and spatial attention mechanisms, so that the network focuses on important local information more, inhibits useless information, does not need iteration, has strong instantaneity, replaces various network test network performances to select a network structure with optimal wave front restoration effect, and predicts that the wave surface reasoning time of a frame is less than 4ms.
Drawings
Fig. 1 is a schematic diagram of the working principle of a control algorithm of a rapid wavefront restoration method of a four-step phase type fresnel zone plate;
FIG. 2 is a flow chart of a method for rapid wavefront restoration of a four-step phase type Fresnel zone plate according to the present invention;
FIG. 3 is a schematic diagram of a four-step phase Fresnel zone plate wave front-free sensing based on a hybrid focal length;
fig. 4 is a schematic diagram of a neural network architecture adopted in the present invention, where fig. 4 (a) is a neural network overall structure, fig. 4 (b) is a channel attention module, and fig. 4 (c) is a spatial attention module.
Detailed Description
The present invention will be further described in detail below with reference to the accompanying drawings, in order to make the objects, technical solutions and advantages of the present invention more apparent.
Fig. 1 is a schematic diagram of a fast wavefront restoration method of a four-step phase type fresnel zone plate. Fig. 2 is a working flow chart of a fast wavefront restoration method of a four-step phase type fresnel zone plate, which comprises the following specific implementation processes:
step 1: designing a four-step phase type Fresnel zone plate with a mixed focal length, and placing a CCD on a focal plane of one of a first quadrant, a third quadrant or a second quadrant and a fourth quadrant of the four-step phase type Fresnel zone plate with the mixed focal length. The four-step phase type Fresnel zone plate of the mixed focal length has the following relevant parameters: the center wavelength is 520nm, the entrance pupil diameter is 12mm, the focal length of the first quadrant and the third quadrant is 50cm, the focal length of the second quadrant and the fourth quadrant is 52cm, the number of steps is 4, the equal interval distribution is realized, the phase distribution of adjacent arc bands of the first quadrant is 0,0.5 pi, pi and 1.5 pi in sequence, and the phase distribution of adjacent arc bands of the second quadrant is 0,0.65 pi,1.3 pi and 1.95 pi in sequence. Fig. 3 is a schematic diagram of a four-step phase type fresnel zone plate with a mixed focal length, and fig. 3 is a schematic diagram of a four-step phase type fresnel zone plate without wavefront sensing based on the mixed focal length;
step 2: verifying whether the Fresnel zone plate designed in the step 1 can obtain far field light intensity distribution in different forms on a focal plane of one of a first quadrant focal length, a third quadrant focal length or a second quadrant focal length and a fourth quadrant focal length through the Fresnel zone plate aiming at the positive defocused near field wave front beam and the negative defocused near field wave front beam respectively;
step 3: if the step 2 can be realized, collecting far-field light spots and near-field wave front data imaged by the four-step phase type Fresnel zone plate with the mixed focal length according to the step 1, placing a CCD on a focal plane of one of the focal lengths of the first quadrant, the third quadrant or the second quadrant and the fourth quadrant, respectively taking Zernike mode coefficients corresponding to far-field images of the focal plane and near-field wave front as samples and labels in the data set, and if the step 2 can not be realized, repeatedly executing the step 1 to design the sensor again until the step 2 is realized;
step 4: configuring a deep learning environment, building a CNN, and FIG. 4 is a schematic diagram of an attention mechanism CNN architecture of the present invention: the attention mechanism CNN architecture contains 11 total layers, of which there are 1 input layer, 4 convolution layers, 4 pooling layers, 2 fully connected layers and add channel attention mechanism and spatial injectionA mechanism of force. The input layer inputs far-field image samples of 224 x 224 size. The convolution kernel sizes of the 4-layer convolution layers are 5×5, 4×4 and 4×4, and the channel numbers of the 4-layer convolution layers are 16, 32 and 32. The pooling layers all select the largest pooling, and the step sizes of the pooling layers are all 2. The number of nodes of the two full-connection layers is 200 and 62 respectively. The network outputs 4 to 65 th order Zernike coefficients. CNN selects Adam function as gradient descent function, initial learning rate is 10 -3 . To avoid network overfitting, batch regularization is introduced for each layer of convolutional layers. The Epoch is set to 1000 and the batch size is set to 64.
Step 5: randomly extracting 80% of samples in the data set as a training set for the network to learn the mapping relation between far-field light spots and near-field wave fronts; half of the remaining 20% of the samples in the data set are arbitrarily extracted as a verification set for adjusting network super parameters and verifying algorithm validity, and the remaining 10% of the samples are finally used as a test set for unbiased estimation.
After the training is carried out to enable the network to be converged, only a single-frame focal plane light intensity image is input into the network, and the network can output near-field wavefront information corresponding to the far-field light spot. The iterative operation is not involved in the process, the calculation speed is greatly improved, and the simulation result shows that the time required for completing one-time wave front restoration can be less than 4 milliseconds.
In step 1, the focal length of the first quadrant and the third quadrant of the four-step phase type Fresnel zone plate with the mixed focal length is set to be f 13 The focal length of the second and fourth quadrants is f 24 According to zone plate theory, the nth zone radius can be expressed as:
wherein λ is the optical wavelength, r 13_n An nth zone radius, r, representing the first and third quadrants 24_n Representing the second and the thirdThe nth zone radius of the four quadrants. The four adjacent zones of the four-step phase type Fresnel zone plate with mixed focal length have phase differences, and the modulation phases of the first quadrant and the third quadrant can be expressed as:
the modulation phases of the second and fourth quadrants can be expressed as:
therefore, the wavefront complex amplitude of the rear surface of the four-step phase fresnel zone plate of the hybrid focal length is expressed as:
in U near (x 1 ,y 1 0) is near-field optical wave complex amplitude of the front surface of the four-step phase type Fresnel zone plate with the mixed focal length.
According to the Fresnel diffraction basic theory, when the CCD camera target surface is positioned behind the mixed focal length four-step phase type Fresnel zone plate 13 The far field spot complex amplitude can be expressed as:
in (x) 2 +y 2 ) For far-field spatial two-dimensional coordinates, λ is wavelength, k=2pi/λ is wavenumber,representing the fourier transform.
In step 4, the attention mechanism is added to enable the network to sequentially infer the attention weight along the two dimensions of the channel and the space when an intermediate feature map is given, and then the attention weight is multiplied by the original feature map to adaptively adjust the features. The attention mechanism module is a lightweight generic module that can be seamlessly integrated into any CNN architecture, with negligible overhead, and can perform end-to-end training with the underlying CNN.
The channel attention mechanism is meaningful to pay attention to what features are. In order to summarize the spatial features, two modes of global average pooling and maximum pooling are adopted to respectively utilize different information:
the input is a characteristic F of hxw×c (hxw represents pixel size), and global max pooling and averaging pooling of a space are performed first to obtain two channel descriptions of 1×1×c. Then, they are respectively sent into a two-layer neural network, the number of the neurons of the first layer is C/r, the activation function is Relu, the number of the neurons of the second layer is C, and the two-layer neural networks are shared. Then adding the obtained two features, and obtaining a weight coefficient M through a Sigmoid activation function c . Finally, the input features F and M c Multiplication results in a new feature after scaling.
After the channel attention module, it makes sense to re-introduce the spatial attention module to focus on where the features are:
similarly to the channel attention, given a characteristic F of hxw×c, a maximum pooling and an average pooling of one channel dimension are performed first to obtain two hxw×i channel descriptions, and the two descriptions are spliced together according to the channels. Then, through a 7×7 convolution layer, the activation function is Sigmoid to obtain the weight coefficient M s . Finally, the input features F and M s Multiplication results in a new feature after scaling.
The two modules of channel attention and spatial attention can be combined together in a parallel or sequential manner, and the invention finds that the sequential combination and focusing of the channel attention in front can achieve better effect, so that the two modules are added to the back of the second layer of convolution layer and the last layer of convolution layer respectively in a serial manner of channel attention and spatial attention.
While the invention has been described with respect to specific embodiments thereof, it will be appreciated that the invention is not limited thereto, but rather encompasses modifications and substitutions within the scope of the present invention as will be appreciated by those skilled in the art.
Claims (5)
1. A rapid wavefront restoration method of a four-step phase type Fresnel zone plate is characterized by comprising the following steps:
step 1: the four-step phase type Fresnel zone plate based on the mixed focal length is designed, and the four-step phase type Fresnel zone plate comprises the distribution of the mixed focal length, an entrance pupil radius, a focal length difference, a phase step width, a phase step height and diffraction efficiency parameter design;
step 2: verifying whether the four-step phase type Fresnel zone plate based on the mixed focal length designed in the step 1 can simultaneously obtain far-field light intensity distribution of a single-frame point light source on one focal length focal plane of the four-step phase type Fresnel zone plate based on the mixed focal length, wherein the light intensity utilization rate is more than eighty percent, the light spot radius is larger than five pixels, and otherwise, the neural network is difficult to extract characteristics of a small number of pixels;
step 3: if the step 2 can be realized, introducing random aberration conforming to an atmospheric transmission model into ideal parallel light by using the four-step phase type Fresnel zone plate with the mixed focal length designed in the step 1, recording far-field light spots and near-field wave front data, and respectively taking far-field light spot images detected by a CCD and near-field wave front Zernike mode coefficients or near-field wave surfaces corresponding to the far-field light spot images as samples and labels to manufacture a wavefront restoration data set of the four-step phase type Fresnel zone plate combined neural network based on the mixed focal length, and if the step 2 can not be realized, repeatedly executing the step 1 to design the four-step phase type Fresnel zone plate based on the mixed focal length until the step 2 is realized;
step 4: configuring a deep learning environment and building a neural network;
step 5: selecting a sample of the first 90% of the data set as a training set for the network to learn the nonlinear mapping relation between the far-field light spot and the Zernike mode coefficient; the rest 10% of data set is used as a verification set for adjusting network super parameters and verifying algorithm effectiveness, and finally 1000 groups of data which are consistent with the same data distribution with the training set and the verification set are additionally manufactured as a test set for testing a model, residual analysis is carried out on the output predictive Zernike mode coefficient and the actual tag Zernike mode coefficient, and the accuracy and the instantaneity of the method are measured;
step 6: changing different neural networks to test, recording test set results, and selecting a network structure with optimal performance according to the final results;
and in the step 1, the first quadrant and the third quadrant of the four-step phase type Fresnel zone plate with mixed focal length are focal length values, the second quadrant and the fourth quadrant are focal length values different from the first quadrant and the third quadrant, and the CCD is placed on the focal plane of the first quadrant, the third quadrant or the second quadrant and the fourth quadrant.
2. The method for rapid wavefront restoration of a four-step phase type fresnel zone plate according to claim 1, characterized by comprising the steps of: and (2) confirming a defocus amount according to a traditional phase difference method by using focal length differences of a first quadrant, a third quadrant, a second quadrant and a fourth quadrant in the four-step phase type Fresnel zone plate with the mixed focal length in the step (1), and selecting the defocus amount of one wavelength.
3. The method for rapid wavefront restoration of a four-step phase type fresnel zone plate according to claim 1, characterized by comprising the steps of: and in the step 2, a four-step type is selected for design.
4. The method for rapid wavefront restoration of a four-step phase type fresnel zone plate according to claim 1, characterized by comprising the steps of: the number of samples of the data set in the step 3 is at least thirty-thousand, that is, the data set is fully sampled in the sample space.
5. The method for rapid wavefront restoration of a four-step phase type fresnel zone plate according to claim 1, characterized by comprising the steps of: the dividing modes of the training set, the verification set and the test set in the step 5 are properly changed according to actual requirements and the size of the data set.
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