Multi-surface phase retrieval method and system based on convolutional neural network

Abstract

The application relates to the technical field of interference phase shifting, and discloses a multi-surface phase recovery method and system based on a convolutional neural network. The method takes four frames of simulated multi-surface phase shifting interferograms as input data, takes corresponding separated multi-surface fringe interferograms as labels, and trains a multi-surface phase shifting interferogram fringe separation model based on a convolutional neural network. The optimal separation model after training is used for fringe separation of the multi-surface phase shifting interferogram, and corresponding multi-surface fringe prediction interferograms are obtained. Based on the multi-surface fringe prediction interferograms, a four-step phase shifting method is used to recover the phase distribution results of the corresponding single surfaces. Only four frames of multi-surface phase shifting interferograms need to be collected, and a four-step phase shifting method is used for phase recovery, thereby reducing the wavelength tuning range required when a measured object is measured and increasing the thickness measurement range of the measured object. The convolutional neural network is used to improve the accuracy of multi-surface phase shifting interferogram separation, and the anti-noise capability is high.

Description

Technical Field

[0001] This application relates to the field of interferometric phase shifting technology, specifically to a multi-surface phase recovery method and system based on convolutional neural networks. Background Technology

[0002] In optical multi-surface interferometry, the accurate extraction of phase information from the front and back surfaces, as well as the thickness, is crucial. Phase-shifting interferometry is a widely used and effective phase extraction method in interferometry, achieving high-precision phase recovery by recording multiple frames of phase-shifting interferograms.

[0003] Currently, to achieve high-precision multi-surface interferometry, there are many classic multi-surface phase retrieval algorithms, such as the nineteen-frame phase retrieval algorithm, the least-squares-based multi-surface iterative algorithm, and the weighted multi-step phase shift retrieval algorithm. However, these multi-surface phase retrieval algorithms all require a large number of multi-surface phase shift interferograms to accurately recover the phase information.

[0004] Furthermore, in actual acquisition of multi-surface phase-shift interferograms, wavelength-tuned interferometers are commonly used to acquire the required multiple frames of multi-surface phase-shift interferograms. The thinner the component under test, the more frames of interferograms acquired, and the smaller the interference cavity length, the larger the required wavelength tuning range. However, since the output wavelength of a wavelength-tuned laser is limited (approximately 0.2633 nm), when the component is too thin or too many frames are acquired, it may result in an insufficient number of multi-surface phase-shift interferogram frames, thus making it impossible to complete the measurement. Summary of the Invention

[0005] This application provides a multi-surface phase retrieval method based on convolutional neural networks to solve the problems in the prior art, where existing multi-surface phase retrieval algorithms introduce large environmental errors due to the excessive number of interferogram frames required, and when the measured object is too thin, it is difficult to obtain a sufficient number of interferograms within a limited wavelength range.

[0006] Accordingly, this application also provides a multi-surface phase retrieval system based on a convolutional neural network, an electronic device, and a computer-readable storage medium to ensure the implementation and application of the above methods.

[0007] To address the aforementioned technical problems, this application discloses a multi-surface phase retrieval method based on a convolutional neural network, the method comprising:

[0008] Four frames of simulated multi-surface phase-shift interferograms under four different phase states are generated, along with multiple separated single-surface fringe interferograms corresponding to each frame of the simulated multi-surface phase-shift interferogram; the multiple single-surface fringe interferograms include a front surface fringe interferogram, a rear surface fringe interferogram, and a thickness fringe interferogram;

[0009] Construct a multi-surface phase-shifting interferogram fringe separation model based on convolutional neural networks;

[0010] Four frames of simulated multi-surface phase-shifting interferograms were used as input data, and the corresponding separated single-surface fringe interferograms were used as labels to train a multi-surface phase-shifting interferogram fringe separation model and obtain the optimal separation model.

[0011] The optimal separation model was used to separate the fringes of four frames of multi-surface phase-shift interferograms under four different phase states, and multiple single-surface fringe prediction interferograms were obtained under the corresponding phase states. The multiple single-surface fringe prediction interferograms include the front surface fringe prediction interferogram, the rear surface fringe prediction interferogram, and the thickness fringe prediction interferogram.

[0012] Based on multiple single-surface fringe prediction interferograms under four different phase states, the phase distribution results of the corresponding single surface are recovered using a four-step phase shift method.

[0013] This application also discloses a multi-surface phase retrieval system based on a convolutional neural network, the system comprising:

[0014] The data generation module is used to generate four frames of simulated multi-surface phase-shift interferograms under four different phase states, as well as multiple separated single-surface fringe interferograms corresponding to each frame of simulated multi-surface phase-shift interferograms; the multiple single-surface fringe interferograms include front surface fringe interferograms, back surface fringe interferograms and thickness fringe interferograms;

[0015] The model building module is used to build a multi-surface phase-shifting interferogram fringe separation model based on a convolutional neural network;

[0016] The model optimization module is used to take four frames of simulated multi-surface phase-shifting interferograms as input data and the corresponding separated single-surface fringe interferograms as labels to train the multi-surface phase-shifting interferogram fringe separation model and obtain the optimal separation model.

[0017] The separation prediction module is used to perform fringe separation on four frames of multi-surface phase-shift interferograms under four different phase states using the optimal separation model, and obtain multiple single-surface fringe prediction interferograms under the corresponding phase states; the multiple single-surface fringe prediction interferograms include front surface fringe prediction interferograms, rear surface fringe prediction interferograms and thickness fringe prediction interferograms;

[0018] The phase recovery module is used to predict interferograms based on multiple single-surface fringes under four different phase states, and recover the phase distribution results of the corresponding single surface using a four-step phase shifting method.

[0019] This application also discloses an electronic device, including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the program to implement one or more of the methods described in this application.

[0020] This application also discloses a computer-readable storage medium storing a computer program that, when executed by a processor, implements one or more of the methods described in this application.

[0021] In this application, four frames of simulated multi-surface phase-shift interferograms under four different phase states are generated, along with the corresponding separated front surface fringe interferogram, rear surface fringe interferogram, and thickness fringe interferogram. A multi-surface phase-shift interferogram fringe separation model based on a convolutional neural network is constructed. Using the four frames of simulated multi-surface phase-shift interferograms as input data and the corresponding separated single-surface fringe interferograms as labels, the multi-surface phase-shift interferogram fringe separation model is trained to obtain the optimal separation model. The optimal separation model is used to perform fringe separation on the four frames of multi-surface phase-shift interferograms under four different phase states, obtaining the predicted front surface fringe interferogram, rear surface fringe predictive interferogram, and thickness fringe predictive interferogram under the corresponding phase states. Based on the predicted single-surface fringe interferograms under four different phase states, the phase distribution results of the corresponding single surface are recovered using a four-step phase-shift method. This application only requires the acquisition of four frames of multi-surface phase-shift interferograms and employs a more mature and accurate four-step phase-shift phase recovery algorithm, significantly reducing the wavelength tuning range required for measuring the device under test and further increasing the thickness measurement range of the device under test. The method in this application is an end-to-end processing method that uses a convolutional neural network-based model to extract interferogram fringe features. This method can effectively capture complex features in multi-surface interferograms, improve the accuracy of multi-surface phase-shifting interferogram separation, and has strong noise resistance.

[0022] Additional aspects and advantages of this application will be set forth in the following description, and will become apparent from the description or may be learned by practice of this application. Attached Figure Description

[0023] The above and / or additional aspects and advantages of this application will become apparent and readily understood from the following description of the embodiments taken in conjunction with the accompanying drawings, wherein:

[0024] Figure 1 This is a flowchart of a multi-surface phase retrieval method based on convolutional neural networks;

[0025] Figure 2 This is a schematic diagram of the structure of a multi-surface phase-shifting interference pattern fringe separation model;

[0026] Figure 3 This is a schematic diagram of the training phase of a multi-surface phase-shifting interferogram fringe separation model.

[0027] Figure 4 (a) is the input data for the first set of model tests;

[0028] Figure 4 (b) Data of the front surface stripe labels for the first set of model tests;

[0029] Figure 4 (c) Output data of the front surface stripes for the first set of model tests;

[0030] Figure 4 (d) shows the thickness stripe label data from the first set of model tests;

[0031] Figure 4 (e) is the thickness stripe output data of the first set of model tests;

[0032] Figure 4 (f) shows the back surface stripe label data of the first set of model tests;

[0033] Figure 4 (g) is the back surface stripe output data of the first set of model tests;

[0034] Figure 5 (a) Front surface phase map obtained by using the four-step phase shift method to recover the front surface stripe output data of the first set of model tests;

[0035] Figure 5 (b) The error between the front surface phase map and the true phase map obtained after recovering the front surface stripe output data of the first set of model tests using the four-step phase-shifting phase method;

[0036] Figure 5 (c) The thickness phase map obtained by using the four-step phase shifting method to recover the thickness stripe output data of the first set of model tests;

[0037] Figure 5 (d) is the error between the thickness phase map and the true phase map obtained after recovering the thickness stripe output data of the first set of model tests using the four-step phase shifting method;

[0038] Figure 5 (e) The back surface phase map obtained by using the four-step phase-shifting phase method to recover the back surface stripe output data of the first set of model tests;

[0039] Figure 5 (f) represents the error between the back surface phase map and the true phase map obtained after recovering the back surface stripe output data of the first set of model tests using the four-step phase shifting phase method;

[0040] Figure 6 (a) is the input data for the second set of model tests;

[0041] Figure 6 (b) shows the front surface stripe label data for the second set of model tests;

[0042] Figure 6 (c) Output data of the front surface stripes from the second set of model tests;

[0043] Figure 6 (d) shows the thickness stripe label data from the second set of model tests;

[0044] Figure 6 (e) is the thickness stripe output data of the second set of model tests;

[0045] Figure 6 (f) shows the back surface stripe label data from the second set of model tests;

[0046] Figure 6 (g) is the back surface stripe output data of the second set of model tests;

[0047] Figure 7 (a) Front surface phase map obtained by using the four-step phase-shifting phase method to recover the front surface stripe output data of the second set of model tests;

[0048] Figure 7 (b) The error between the front surface phase map and the true phase map obtained after recovering the front surface stripe output data of the second set of model tests using the four-step phase-shifting phase method;

[0049] Figure 7 (c) The thickness phase map obtained by using the four-step phase shifting method to recover the thickness stripe output data of the second set of model tests;

[0050] Figure 7 (d) is the error between the thickness phase map and the true phase map obtained after recovering the thickness stripe output data of the second set of model tests using the four-step phase shifting method;

[0051] Figure 7 (e) The back surface phase map obtained by using the four-step phase shifting phase method to recover the back surface stripe output data of the second set of model tests;

[0052] Figure 7 (f) represents the error between the back surface phase map and the true phase map obtained after recovering the back surface stripe output data of the second set of model tests using the four-step phase-shifting phase method;

[0053] Figure 8 (a) is the input data for the third set of model tests;

[0054] Figure 8 (b) Data of the front surface stripe labels for the third set of model tests;

[0055] Figure 8 (c) Output data of the front surface stripes from the third set of model tests;

[0056] Figure 8 (d) shows the thickness stripe label data from the third set of model tests;

[0057] Figure 8 (e) shows the thickness stripe output data for the third set of tests;

[0058] Figure 8 (f) shows the back surface stripe label data from the third set of model tests;

[0059] Figure 8 (g) is the back surface stripe output data of the third group of model tests;

[0060] Figure 9 (a) Front surface phase map obtained by using the four-step phase-shifting phase method to recover the front surface stripe output data of the third group of model tests;

[0061] Figure 9 (b) The error between the front surface phase map and the true phase map obtained after recovering the front surface stripe output data of the third set of model tests using the four-step phase-shifting phase method;

[0062] Figure 9 (c) The thickness phase map obtained by using the four-step phase shifting method to recover the thickness stripe output data of the third group of model tests;

[0063] Figure 9 (d) is the error between the thickness phase map and the true phase map obtained after recovering the thickness stripe output data of the third group of model tests using the four-step phase shifting method;

[0064] Figure 9 (e) The back surface phase map obtained by using the four-step phase shifting phase method to recover the back surface stripe output data of the third set of model tests;

[0065] Figure 9 (f) represents the error between the back surface phase map and the true phase map obtained after recovering the back surface fringe output data of the third group of model tests using the four-step phase-shifting phase method;

[0066] Figure 10 A schematic diagram of the structure of a vehicle speed measurement system based on road surveillance video provided in an embodiment of this application;

[0067] Figure 11 This is a schematic diagram of the structure of an electronic device provided in an embodiment of this application. Detailed Implementation

[0068] The embodiments of this application are described in detail below. Examples of the embodiments are shown in the accompanying drawings, wherein the same or similar reference numerals denote the same or similar elements or elements having the same or similar functions throughout. The embodiments described below with reference to the accompanying drawings are exemplary and are only used to explain this application, and should not be construed as limiting this application.

[0069] Those skilled in the art will understand that, unless explicitly stated otherwise, the singular forms “a,” “an,” “the,” and “the” used herein may also include the plural forms. It should be further understood that the term “comprising” as used in this application means the presence of features, integers, steps, operations, elements, and / or components, but does not exclude the presence or addition of one or more other features, integers, steps, operations, elements, components, and / or combinations thereof. It should be understood that when we say an element is “connected” or “coupled” to another element, it can be directly connected or coupled to the other element, or there may be intermediate elements. Furthermore, “connected” or “coupled” as used herein can include wireless connections or wireless coupling. The term “and / or” as used herein includes all or any units and all combinations of one or more associated listed items.

[0070] It will be understood by those skilled in the art that, unless otherwise defined, all terms used herein (including technical and scientific terms) have the same meaning as commonly understood by one of ordinary skill in the art to which this invention pertains. It should also be understood that terms such as those defined in general dictionaries should be understood to have the same meaning as in the context of the prior art and should not be interpreted in an idealized or overly formal sense unless specifically defined as herein.

[0071] The solutions provided in this application can be executed by any electronic device, such as a terminal device or a server. The server can be a standalone physical server, a server cluster or distributed system composed of multiple physical servers, or a cloud server providing cloud computing services. The terminal can be a smartphone, tablet, laptop, desktop computer, smart speaker, smartwatch, etc., but is not limited to these. The terminal and server can be directly or indirectly connected via wired or wireless communication, which is not limited herein. Regarding the technical problems existing in the prior art, the multi-surface phase retrieval method and system based on convolutional neural networks provided in this application aim to solve at least one of the technical problems in the prior art.

[0072] The technical solution of this application and how the technical solution of this application solves the above-mentioned technical problems are described in detail below with specific embodiments. These specific embodiments can be combined with each other, and the same or similar concepts or processes may not be described again in some embodiments. The embodiments of this application will now be described with reference to the accompanying drawings.

[0073] Existing multi-surface phase retrieval algorithms require a large number of multi-surface phase-shift interferograms to accurately recover phase information. In contrast, single-surface phase retrieval algorithms require fewer interferograms and are more mature. For example, the four-step phase-shift method has advantages such as high precision, strong noise resistance, wide applicability, and simple algorithm implementation, and has good applicability and stability in the field of interferometry. Based on this, this application provides a possible implementation method, such as... Figure 1 The diagram shows a flowchart of a multi-surface phase recovery method based on a convolutional neural network. This method can be executed by any electronic device, and optionally, it can be executed on a server or a terminal device.

[0074] like Figure 1 As shown, the method may include the following steps:

[0075] Step 101: Generate four frames of simulated multi-surface phase-shifting interferograms under four different phase states, and multiple separated single-surface fringe interferograms corresponding to each frame of simulated multi-surface phase-shifting interferograms.

[0076] Multiple single-surface fringe interferograms include front surface fringe interferogram, back surface fringe interferogram, and thickness fringe interferogram.

[0077] In this embodiment, four simulated multi-surface phase-shift interferograms and corresponding separated front surface fringe interferograms, back surface fringe interferograms, and thickness fringe interferograms are generated based on Zernike polynomials, wavelength tuning principles, and interference intensity superposition theory models. The four simulated multi-surface phase-shift interferograms represent different phase conditions, with each frame adding a phase shift value of π / 2 to the previous frame.

[0078] Step 102: Construct a multi-surface phase-shifting interferogram fringe separation model based on a convolutional neural network.

[0079] Step 103: Use four frames of simulated multi-surface phase-shifting interferograms as input data and the corresponding separated single-surface fringe interferograms as labels to train the multi-surface phase-shifting interferogram fringe separation model and obtain the optimal separation model.

[0080] The input data is divided into four channels and fed into the multi-surface phase-shifting interferogram fringe separation model to learn the features of the front surface fringe, the back surface fringe, and the thickness fringe, and output the corresponding predicted interferograms of the front surface fringe, the back surface fringe, and the thickness fringe. During iterative training, the predicted interferograms of the front surface fringe, the back surface fringe, and the thickness fringe are compared with their corresponding labels (front surface fringe, back surface fringe, and thickness fringe), the loss is calculated, and the multi-surface phase-shifting interferogram fringe separation model is updated until the optimal separation model is obtained after meeting the preset conditions.

[0081] The method in this embodiment involves inputting four frames of multi-surface phase-shifting interferograms and using a convolutional neural network to separate the front surface fringes, back surface fringes, and thickness fringes from the original intersecting fringes. Therefore, the accuracy of the training data is crucial. Simultaneously, there is a one-to-one correspondence between the input data and the label data to ensure that the model can correctly learn the relationship between the input and output during training.

[0082] Step 104: Use the optimal separation model to perform fringe separation on four frames of multi-surface phase-shift interferograms under four different phase states to obtain multiple single-surface fringe prediction interferograms under the corresponding phase states.

[0083] Multiple single-surface fringe prediction interferograms include front surface fringe prediction interferogram, back surface fringe prediction interferogram, and thickness fringe prediction interferogram.

[0084] Step 105: Based on multiple single-surface fringe prediction interferograms under four different phase states, the phase distribution results of the corresponding single surface are recovered using the four-step phase shift method.

[0085] In this embodiment, four frames of simulated multi-surface phase-shift interferograms under four different phase states are generated, along with the corresponding separated front surface fringe interferogram, rear surface fringe interferogram, and thickness fringe interferogram. A multi-surface phase-shift interferogram fringe separation model based on a convolutional neural network is constructed. Using the four frames of simulated multi-surface phase-shift interferograms as input data and the corresponding separated single-surface fringe interferograms as labels, the multi-surface phase-shift interferogram fringe separation model is trained to obtain the optimal separation model. The optimal separation model is used to perform fringe separation on the four frames of multi-surface phase-shift interferograms under four different phase states, obtaining the predicted front surface fringe interferogram, rear surface fringe predictive interferogram, and thickness fringe predictive interferogram under the corresponding phase states. Based on the predicted single-surface fringe interferograms under four different phase states, the phase distribution results of the corresponding single surface are recovered using a four-step phase-shift method. In this embodiment, only four frames of multi-surface phase-shift interferograms need to be acquired, and a more mature and accurate four-step phase-shift phase recovery algorithm is used, significantly reducing the wavelength tuning range required for measuring the device under test and further increasing the thickness measurement range of the device under test. The method in this embodiment is an end-to-end processing method that uses a convolutional neural network-based model to extract interferogram fringe features. This method can effectively capture complex features in multi-surface interferograms, improve the accuracy of multi-surface phase-shifting interferogram separation, and has strong noise resistance.

[0086] As a first example, the mathematical model for the generated simulated multi-surface phase-shifting interferogram and the corresponding separated front surface fringe interferogram, back surface fringe interferogram, and thickness fringe interferogram is expressed as follows:

[0087]

[0088] In the formula, I k (x, y) represents the simulated multi-surface phase-shifting interferogram; I1 k (x, y) represents the corresponding front surface fringe interference pattern; I2 k (x, y) represents the corresponding back surface fringe interference pattern; I3 k (x, y) represents the corresponding thickness fringe interferogram; k is the number of interferogram frames (k = 1 to 4), and k is 1 in the initial interferogram; a(x, y) is the background light intensity, let a(x, y) = 0.5; b1(x, y), b2(x, y), and b3(x, y) are the modulation degrees of the front surface, back surface, and thickness, respectively, let b1(x, y) = b2(x, y) = 0.3 and b3(x, y) = 0.2; These are the front surface phase information, rear surface phase information, and thickness information to be recovered, respectively. (represented by Zernike polynomials); θ 1k (x, y), θ 2k (x, y), θ3k (x, y) represent the phase shift values ​​(θ) of the front surface, rear surface, and thickness, respectively. 11 (x, y) = θ 21 (x, y) = θ 31 (x, y) = 0), where the phase shift value of the front surface is π / 4; η k (x, y) represents noise added to the interferogram.

[0089] In the aforementioned multi-surface phase-shifting interferograms, the Zernike polynomials involved can represent optical aberrations, theoretical wavefronts, and fitted wavefronts. The process of generating simulated interferograms involves using Zernike polynomials to simulate different aberration effects, superimposing them together to generate a phase distribution, and then generating four frames of multi-surface phase-shifting interferograms.

[0090] The mathematical model for phase distribution based on Zernike polynomials is expressed as follows:

[0091]

[0092] In the formula, For the front surface phase distribution, For the rear surface phase distribution, c 1i c 2i They are and The coefficient of the i-th term in the Zernike polynomial; Z i (x,y) is the i-th term of the Zernike polynomial, and n is the total number of terms using the Zernike polynomial. In this embodiment, n = 20.

[0093] In this embodiment of the application, when collecting input data and corresponding labels, the first twenty terms of the Zernike polynomial are used to generate a phase distribution to satisfy the diversity of training data; random noise with different signal-to-noise ratios (20-100dB) is added to approximate the interferogram collected in the real environment as closely as possible.

[0094] The method in this application embodiment is applicable to the processing of multi-surface phase shift interferograms with a front surface phase shift value of π / 4.

[0095] In an optional embodiment, the multi-surface phase-shifting interferogram fringe separation model includes a downsampling module, an upsampling module, and an output layer;

[0096] The downsampling module is used to extract multiple single-surface fringe features corresponding to the input data by reducing the feature map size; the multiple single-surface fringe features include front surface fringe features, back surface fringe features, and thickness fringe features;

[0097] The upsampling module includes multiple independent upsampling parts, which are used to restore the corresponding single-surface fringe features to the size of the input data; wherein, the multiple upsampling parts correspond one-to-one with multiple single-surface fringe features;

[0098] The output layer has multiple layers, each corresponding to an upsampling section, and is used to convert the channel features of the output of the corresponding upsampling section into the corresponding separated single-surface fringe prediction interferogram.

[0099] In an optional embodiment, the downsampling module includes a first downsampling portion and a second downsampling portion;

[0100] The first downsampling part includes multiple convolutional layers; the first sampling part is used to reduce the size of the feature map by using a stride specified by the convolutional layers.

[0101] The second downsampling part consists of multiple alternating convolutional layers and max pooling layers. The second downsampling part is used to reduce the size of the feature map by utilizing the max pooling layers.

[0102] As a second example, the input data consists of four frames of simulated multi-surface phase-shifting interferograms, each image being 256*256 pixels in size and divided into four channels, which are then input into the multi-surface phase-shifting interferogram fringe separation model.

[0103] like Figure 2 As shown, the multi-surface phase-shifting interferogram fringe separation model includes a shared first downsampling part, a second downsampling part, three independent upsampling parts, and three independent output layers.

[0104] The first downsampling part consists of seven convolutional layers plus activation functions, from DownA_1 to DownA_7. In DownA_1, the input is a 4-channel simulated multi-surface phase-shifting interferogram of 256*256 pixels. Sixteen convolutional kernels with a stride of 2 and a size of 3*3 are used to extract low-level features. Then, the ReLU activation function is applied to generate a 16-channel feature map of size 128*128 pixels. Similarly, in the subsequent convolutional layers (DownA_2 to DownA_7), 32, 64, 128, 256, 512, and 1024-channel feature maps are obtained, with feature map sizes of 64*64, 32*32, 16*16, 8*8, 4*4, and 2*2, respectively. The first downsampling part reduces the size of the feature map by using a stride of 2, which allows for a greater focus on the overall feature representation and is beneficial for the network model to learn the distribution of background light intensity.

[0105] The second downsampling part consists of 7 convolutional layers + activation functions and 7 max pooling layers, from DownB_1 to DownB_7. In DownB_1, the input is a 4-channel simulated multi-surface phase-shifting interferogram of 256*256. Sixteen convolutional kernels with a stride of 1 and a size of 3*3 are used to extract the low-level features. Then, a ReLU activation function is applied to obtain a 16-channel feature map of size 256*256. Next, max pooling is performed using a filter with a stride of 2 and a size of 2*2, resulting in a 16-channel feature map of size 128*128. Similarly, in the subsequent parts (DownB_2 to DownB_7), 32, 64, 128, 256, 512, and 1024-channel feature maps are obtained, with sizes of 64*64, 32*32, 16*16, 8*8, 4*4, and 2*2, respectively. The second downsampling part reduces the size of the feature map through a max pooling layer, which can retain more feature information and is more sensitive to feature details. This is beneficial for the multi-surface phase-shifting interferogram fringe separation model to learn the features of the front surface fringe, the back surface fringe, and the thickness fringe.

[0106] Each of the three independent upsampling parts consists of seven convolutional layers + activation functions and seven bilinear interpolation upsampling layers, from UpA_1 to UpA_7, UpB_1 to UpB_7, and UpC_1 to UpC_7. Since the structures of the three independent upsampling parts are identical, this embodiment uses the UpA part as an example for explanation. In UpA_1, the input is a 2*2 2048-channel feature map obtained by concatenating the 2*2 1024-channel feature map output from DownA_7 and the 2*2 1024-channel feature map output from DownB_7. 1024 convolutional kernels with a stride of 1 and a size of 3*3 are used to extract depth features, and then a ReLU activation function is applied to generate a 2*2 1024-channel feature map. Then, a bilinear interpolation upsampling layer is used to restore the feature map size, resulting in a 4*4 1024-channel feature map. In UpA_2, the input is a 4*4 2048-channel feature map obtained by concatenating the 4*4 512-channel feature map output from DownB_6 and the 4*4 1024-channel feature map output from UpA_1. This is then passed through a convolutional layer and a bilinear interpolation upsampling layer to obtain a 1024-channel feature map of size 8*8. Similarly, in subsequent upsampling parts (UpA_3 to UpA_7), 768, 512, 320, 192, and 112-channel feature maps are obtained, with feature map sizes of 16*16, 32*32, 64*64, 128*128, and 256*256, respectively. These three independent upsampling parts are used to restore the feature images extracted in the downsampling parts to the original input image size and combine features at different resolutions.

[0107] Finally, three independent output layers are used, each consisting of three convolutional layers + activation functions and one convolutional layer, namely OutA, OutB, and OutC. Since the three independent output layers have the same structure, this embodiment uses OutA as an example for explanation. In OutA, the input is a 112-channel feature map of size 256*256 output from UpA_7. This is processed by three convolutional layers + ReLU activation functions with a stride of 1, kernel sizes of 3*3, and kernel numbers of 56, 28, and 14 respectively, resulting in a 14-channel feature map of size 256*256. Then, four convolutional kernels with a stride of 1 and a size of 1*1 are used to transform the 14-channel feature map of size 256*256 into a 4-channel feature map of size 256*256 as the final output.

[0108] In general, the embodiments of this application employ a multi-task learning method. The multi-surface phase-shifting interferogram fringe separation model extracts feature information from the input 4-channel simulated multi-surface phase-shifting interferogram through a downsampling module, resulting in a feature map with richer feature information. Then, the obtained feature information is utilized through skip connections (stitching) and upsampling modules to finally separate the corresponding front surface fringe prediction interferogram, back surface fringe prediction interferogram, and thickness fringe prediction interferogram (3 sets of independent fringes) from the multi-surface phase-shifting interferogram (cross fringes).

[0109] In an optional embodiment, four frames of simulated multi-surface phase-shifting interferograms are used as input data, and the corresponding separated single-surface fringe interferograms are used as labels to train a multi-surface phase-shifting interferogram fringe separation model to obtain the optimal separation model, including:

[0110] Acquire multiple sets of input data and corresponding labels; each set of input data includes four frames of simulated multi-surface phase-shift interferograms;

[0111] Multiple sets of input data are fed into the multi-surface phase-shifting interferogram fringe separation model to obtain multiple sets of prediction results; each set of prediction results includes multiple single-surface fringe prediction interferograms.

[0112] The loss function is used to calculate the difference between each set of predictions and the corresponding label, and the gradient of the loss function with respect to the model is also calculated.

[0113] The parameters of the gradient multi-surface phase-shifting interferogram fringe separation model are determined, and the optimal separation model is obtained when a preset number of iterations is reached.

[0114] In an optional embodiment, multiple sets of input data are fed into a multi-surface phase-shift interferogram fringe separation model to obtain multiple sets of prediction results, including:

[0115] Multiple sets of input data are shuffled in order using DataLoader, and the number of data transmitted at one time is increased before being input into the multi-surface phase-shifting interferogram fringe separation model.

[0116] Multiple sets of prediction results were obtained by using a multi-surface phase-shifting interferogram fringe separation model.

[0117] In an optional embodiment, the loss function is expressed as follows:

[0118] L = L1 + L2 + L3

[0119] Wherein, L1 is the front surface fringe loss function, used to calculate the difference between the predicted interferogram of the front surface fringe and the corresponding label; L2 is the back surface fringe loss function, used to calculate the difference between the predicted interferogram of the back surface fringe and the corresponding label; and L3 is the thickness fringe loss function, used to calculate the difference between the predicted interferogram of the thickness fringe and the corresponding label.

[0120] In an optional embodiment, the front surface fringe loss function, the back surface fringe loss function, and the thickness fringe loss function are all mean absolute error functions.

[0121] As a third example, 5000 sets of input data (four frames of simulated multi-surface phase-shift interferograms) were shuffled and their batch size (the number of data points passed to the program for training at one time) were increased by DataLoader before being input into the multi-surface phase-shift interferogram fringe separation model. Layer-by-layer calculations were performed using downsampling and upsampling modules to generate three independent prediction results (predicted interferogram of the front surface fringe, predicted interferogram of the rear surface fringe, and predicted interferogram of the thickness fringe). Each of the three prediction results was compared with its corresponding label (true value). The mean absolute error (MAE) function was used to measure the difference between the prediction result and the label, and the sum of the three MAE loss functions was used as the total loss function.

[0122] With a learning rate of 0.001, the Adam optimization algorithm is used to find the network weights that minimize the loss function.

[0123] like Figure 3 As shown, four frames of simulated multi-surface phase-shifting interferograms (input data) are separated into four frames of predicted front surface fringe interferograms, four frames of predicted back surface fringe interferograms, and four frames of predicted front surface fringe interferograms (prediction results) after being processed by the multi-surface phase-shifting interferogram fringe separation model. The corresponding label data are four frames of front surface fringe interferograms, four frames of back surface fringe interferograms, and four frames of thickness fringe interferograms, respectively. The multi-surface phase-shifting interferogram fringe separation model is trained using a loss function (MAE) and an optimizer (Adam).

[0124] Specifically, the iteration count is set to 100. In each iteration, the following steps are performed: First, forward propagation is performed to input the input data into the model and calculate the prediction result. Then, the difference between the prediction result and the labeled data is measured using a loss function. Next, backpropagation is performed to calculate the gradient of the loss function with respect to the model parameters. Finally, the Adam optimization algorithm is used to update the weights and biases of the multi-surface phase-shifting interferogram fringe separation model based on the gradient information, so that the loss function gradually decreases.

[0125] Repeat these steps until the predetermined number of iterations is reached. Each iteration trains the entire training dataset (5000 input data sets) to gradually optimize the model's performance. Finally, after 100 iterations, the optimal separation model is obtained, which can accurately separate the stripes on the input data.

[0126] The specific process is as follows:

[0127] Step 1, Data Reading: Load 5000 sets of input data (4 frames of simulated multi-surface phase-shift interferograms) using DataLoader. Calculate the predicted results using the multi-surface phase-shift interferogram fringe separation model. Its main function is to shuffle the data order (random reading) and increase Batch_size (the number of data points passed to the program for training at one time).

[0128] Step 2, Model Definition: Define the network structure of the multi-surface phase-shifting interferogram fringe separation model and define the weight initialization function.

[0129] Step 3, Loss and Optimizer: Compare the predicted results with the corresponding label (true value) data, and use the mean absolute error function (MAE) to measure the differences between the separated front surface fringe predicted interferogram, back surface fringe predicted interferogram, and thickness fringe predicted interferogram and the corresponding label data.

[0130] A loss function (MAE) and an optimizer (Adam) are defined for training the model. By setting the loss function, the mean absolute error (MAE) is calculated to measure the differences between the separated front surface fringe predicted interferogram, rear surface fringe predicted interferogram, and thickness fringe predicted interferogram and the labeled data. The mathematical models for the total loss function and the three independent MAE loss functions are expressed as follows:

[0131] L = L1 + L2 + L3

[0132]

[0133] In the formula, y 1i This is the predicted interferogram for the front surface fringes. For the front surface stripe label data, y 2i This is the predicted interferogram for the back surface fringes. For the back surface stripe label data, y 3i For thickness fringe prediction interferograms, The data represents the thickness stripe label data, where n is the number of training samples.

[0134] Among them, the separated front surface fringe interference pattern, rear surface fringe interference pattern, and thickness fringe interference pattern are shown. Figure 3 Each labeled data point corresponds to three independent MAE loss functions, which can maintain the accuracy and correlation among the three outputs while reducing training time.

[0135] This step uses the Adam optimizer to adjust the neural network parameters to their optimal state. The learning rate is adjusted at specified epochs, and the optimizer is updated using the new learning rate to minimize the loss function. The MAE loss function and the Adam optimizer are crucial components in the neural network training process. They update model parameters through backpropagation and gradient descent to minimize the loss between the predicted results and the labeled data, thereby improving network performance.

[0136] Step 4, Training Loop: Iterate through the dataset within a certain number of rounds, setting the number of iterations to 100, and execute the forward propagation, loss calculation, backpropagation, and parameter update processes. Each iteration trains the entire training data once; that is, within each round, the data batch is traversed, and the training loop is performed.

[0137] Step 5, Save the model: After each round, save the trained model file to the specified folder, and save the learning rate and loss value corresponding to each round in an Excel spreadsheet for easy analysis of model performance after training.

[0138] In this embodiment, four frames of simulated multi-surface phase-shifting interferogram data are used as a test set. The test data is input into the optimal separation model, and the separated front surface fringe prediction interferogram, rear surface fringe prediction interferogram, and thickness fringe prediction interferogram are output. The separated front surface fringe prediction interferogram, rear surface fringe prediction interferogram, and thickness fringe prediction interferogram are compared with the labeled data in Matlab to further evaluate the accuracy of the model.

[0139] The specific process is as follows:

[0140] Configure the GPU device and load the pre-test model, then load the optimal separation model into the test.

[0141] By inputting the test dataset into the optimal separation model, the fringe separation results (predicted interferograms of the front surface, the back surface, and the thickness) can be obtained. The final fringe separation results are then compared and evaluated with the labeled data. Theoretically, the fringe separation results output by the neural network model are approximately the same as those of the labeled data, with minimal differences.

[0142] A four-step phase-shifting method was used to recover the phase of the fringe separation results to verify its effectiveness. The performance of the optimal separation model was evaluated by calculating the peak-to-valley (PV) and root mean square (RMS) values ​​of the recovered phase. Finally, three sets of data (accurate to four decimal places) were selected from the test results. The test input data, label data, separation output results, and phase recovery results are shown below. Figures 4-9 As shown in Table 1, the test results are compared.

[0143] Table 1 Comparison of Test Results

[0144]

[0145]

[0146] Based on the above test results, the error between the actual multi-surface separation result and the predicted separation result of the multi-surface phase-shifting interferogram fringe separation model is extremely small, that is, the fitting effect of the multi-surface phase-shifting interferogram fringe separation model is good, and the test results in the embodiments of this application are within the ideal expectation.

[0147] Based on the same principles as the methods provided in the embodiments of this application, the embodiments of this application also provide a multi-surface phase retrieval system based on a convolutional neural network, such as... Figure 10 As shown, the system includes:

[0148] The data generation module 1001 is used to generate four frames of simulated multi-surface phase-shift interferograms under four different phase states, as well as multiple separated single-surface fringe interferograms corresponding to each frame of simulated multi-surface phase-shift interferograms; the multiple single-surface fringe interferograms include a front surface fringe interferogram, a rear surface fringe interferogram, and a thickness fringe interferogram;

[0149] Model building module 1002 is used to build a multi-surface phase-shifting interferogram fringe separation model based on a convolutional neural network;

[0150] The model optimization module 1003 is used to take four frames of simulated multi-surface phase-shifting interferograms as input data and the corresponding separated single-surface fringe interferograms as labels to train the multi-surface phase-shifting interferogram fringe separation model and obtain the optimal separation model.

[0151] The separation prediction module 1004 is used to perform fringe separation on four frames of multi-surface phase-shift interferograms under four different phase states using the optimal separation model, and obtain multiple single-surface fringe prediction interferograms under the corresponding phase states; the multiple single-surface fringe prediction interferograms include front surface fringe prediction interferograms, rear surface fringe prediction interferograms and thickness fringe prediction interferograms.

[0152] The phase recovery module 1005 is used to predict interferograms of multiple single-surface fringes based on four different phase states, and to recover the phase distribution results of the corresponding single surface using a four-step phase shifting method.

[0153] In this embodiment, four frames of simulated multi-surface phase-shift interferograms under four different phase states are generated, along with the corresponding separated front surface fringe interferogram, rear surface fringe interferogram, and thickness fringe interferogram. A multi-surface phase-shift interferogram fringe separation model based on a convolutional neural network is constructed. Using the four frames of simulated multi-surface phase-shift interferograms as input data and the corresponding separated single-surface fringe interferograms as labels, the multi-surface phase-shift interferogram fringe separation model is trained to obtain the optimal separation model. The optimal separation model is used to perform fringe separation on the four frames of multi-surface phase-shift interferograms under four different phase states, obtaining the predicted front surface fringe interferogram, rear surface fringe predictive interferogram, and thickness fringe predictive interferogram under the corresponding phase states. Based on the predicted single-surface fringe interferograms under four different phase states, the phase distribution results of the corresponding single surface are recovered using a four-step phase-shift method. In this embodiment, only four frames of multi-surface phase-shift interferograms need to be acquired, and a more mature and accurate four-step phase-shift phase recovery algorithm is used, significantly reducing the wavelength tuning range required for measuring the device under test and further increasing the thickness measurement range of the device under test. The method in this embodiment is an end-to-end processing method that uses a convolutional neural network-based model to extract interferogram fringe features. This method can effectively capture complex features in multi-surface interferograms, improve the accuracy of multi-surface phase-shifting interferogram separation, and has strong noise resistance.

[0154] The multi-surface phase retrieval system based on convolutional neural networks provided in this application can achieve… Figures 1 to 9 The various processes implemented in the method embodiments are not described in detail here to avoid repetition.

[0155] The multi-surface phase retrieval system based on convolutional neural networks in this application can execute the multi-surface phase retrieval method based on convolutional neural networks provided in this application. The implementation principles are similar. The actions performed by each module and unit in the multi-surface phase retrieval system based on convolutional neural networks in each embodiment of this application correspond to the steps in the multi-surface phase retrieval method based on convolutional neural networks in each embodiment of this application. For detailed functional descriptions of each module in the multi-surface phase retrieval system based on convolutional neural networks, please refer to the descriptions in the corresponding multi-surface phase retrieval methods based on convolutional neural networks shown above. They will not be repeated here.

[0156] Based on the same principles as the methods shown in the embodiments of this application, this application also provides an electronic device, which may include, but is not limited to, a processor and a memory; the memory for storing computer programs; and the processor for executing the multi-surface phase retrieval method based on convolutional neural networks shown in any optional embodiment of this application by calling the computer program. Compared with the prior art, the multi-surface phase retrieval method based on convolutional neural networks provided in this application only requires the acquisition of four frames of multi-surface phase-shift interferograms and adopts a more mature and accurate four-step phase-shift phase retrieval algorithm, which significantly reduces the wavelength tuning range required for measuring the test piece and further increases the thickness measurement range of the test piece. The method in this application is an end-to-end processing method that uses a convolutional neural network-based model to extract interferogram fringe features, effectively capturing complex features in multi-surface interferograms, improving the accuracy of multi-surface phase-shift interferogram separation, and exhibiting strong noise resistance.

[0157] In an alternative embodiment, an electronic device, such as Figure 11 As shown, Figure 11 The illustrated electronic device 1100 can be a server, including a processor 1101 and a memory 1103. The processor 1101 and the memory 1103 are connected, for example, via a bus 1102. Optionally, the electronic device 1100 may also include a transceiver 1104. It should be noted that in practical applications, the transceiver 1104 is not limited to one, and the structure of this electronic device 1100 does not constitute a limitation on the embodiments of this application.

[0158] Processor 1101 may be a CPU (Central Processing Unit), a general-purpose processor, a DSP (Digital Signal Processor), an ASIC (Application Specific Integrated Circuit), an FPGA (Field Programmable Gate Array), or other programmable logic devices, transistor logic devices, hardware components, or any combination thereof. It can implement or execute the various exemplary logic blocks, modules, and circuits described in conjunction with the disclosure of this application. Processor 1101 may also be a combination that implements computational functions, such as including one or more microprocessor combinations, a combination of a DSP and a microprocessor, etc.

[0159] Bus 1102 may include a pathway for transmitting information between the aforementioned components. Bus 1102 may be a PCI (Peripheral Component Interconnect) bus or an EISA (Extended Industry Standard Architecture) bus, etc. Bus 1102 can be divided into address bus, data bus, control bus, etc. For ease of representation, Figure 11 The bus is represented by a single thick line, but this does not mean that there is only one bus or one type of bus.

[0160] The memory 1103 may be a ROM (Read Only Memory) or other type of static storage device capable of storing static information and instructions, RAM (Random Access Memory) or other type of dynamic storage device capable of storing information and instructions, or an EEPROM (Electrically Erasable Programmable Read Only Memory), CD-ROM (Compact Disc Read Only Memory) or other optical disc storage, optical disc storage (including compressed optical discs, laser discs, optical discs, digital universal optical discs, Blu-ray discs, etc.), magnetic disk storage media or other magnetic storage devices, or any other medium capable of carrying or storing desired program code in the form of instructions or data structures and accessible by a computer, but not limited thereto.

[0161] The memory 1103 is used to store application code that executes the solution of this application, and its execution is controlled by the processor 1101. The processor 1101 is used to execute the application code stored in the memory 1103 to implement the content shown in the foregoing method embodiments.

[0162] Among them, electronic devices include, but are not limited to: mobile terminals such as mobile phones, laptops, digital radio receivers, PDAs (personal digital assistants), PADs (tablet computers), PMPs (portable multimedia players), and in-vehicle terminals (such as in-vehicle navigation terminals), as well as fixed terminals such as digital TVs and desktop computers. Figure 11 The electronic device shown is merely an example and should not impose any limitation on the functionality and scope of use of the embodiments of this application.

[0163] The server provided in this application can be a standalone physical server, a server cluster or distributed system composed of multiple physical servers, or a cloud server providing basic cloud computing services such as cloud services, cloud databases, cloud computing, cloud functions, cloud storage, network services, cloud communication, middleware services, domain name services, security services, CDN, and big data and artificial intelligence platforms. The terminal can be a smartphone, tablet, laptop, desktop computer, smart speaker, smartwatch, etc., but is not limited to these. The terminal and server can be directly or indirectly connected via wired or wireless communication, which is not limited herein.

[0164] This application provides a computer-readable storage medium storing a computer program that, when run on a computer, enables the computer to execute the corresponding content in the aforementioned method embodiments.

[0165] It should be understood that although the steps in the flowcharts of the accompanying figures are shown sequentially as indicated by the arrows, these steps are not necessarily executed in the order indicated by the arrows. Unless explicitly stated herein, there is no strict order restriction on the execution of these steps, and they can be executed in other orders. Moreover, at least some steps in the flowcharts of the accompanying figures may include multiple sub-steps or multiple stages. These sub-steps or stages are not necessarily completed at the same time, but can be executed at different times, and their execution order is not necessarily sequential, but can be performed alternately or in turn with other steps or at least some of the sub-steps or stages of other steps.

[0166] It should be noted that the computer-readable storage medium described above in this application can also be a computer-readable signal medium or a combination of computer-readable storage media and computer-readable storage media. Computer-readable storage media can be, for example,—but not limited to—electrical, magnetic, optical, electromagnetic, infrared, or semiconductor systems, apparatuses, or devices, or any combination thereof. More specific examples of computer-readable storage media may include, but are not limited to: electrical connections having one or more wires, portable computer disks, hard disks, random access memory (RAM), read-only memory (ROM), erasable programmable read-only memory (EPROM or flash memory), optical fiber, portable compact disk read-only memory (CD-ROM), optical storage devices, magnetic storage devices, or any suitable combination thereof. In this application, a computer-readable storage medium can be any tangible medium containing or storing a program that can be used by or in conjunction with an instruction execution system, apparatus, or device. In this application, a computer-readable signal medium can include a data signal propagated in baseband or as part of a carrier wave, carrying computer-readable program code. Such propagated data signals can take various forms, including but not limited to electromagnetic signals, optical signals, or any suitable combination thereof. A computer-readable signal medium can be any computer-readable medium other than a computer-readable storage medium, which can send, propagate, or transmit a program for use by or in connection with an instruction execution system, apparatus, or device. The program code contained on the computer-readable medium can be transmitted using any suitable medium, including but not limited to: wires, optical fibers, RF (radio frequency), etc., or any suitable combination thereof.

[0167] The aforementioned computer-readable medium may be included in the aforementioned electronic device; or it may exist independently and not assembled into the electronic device.

[0168] The aforementioned computer-readable medium carries one or more programs, which, when executed by the electronic device, cause the electronic device to perform the methods shown in the above embodiments.

[0169] According to one aspect of this application, a computer program product or computer program is provided, comprising computer instructions stored in a computer-readable storage medium. A processor of a computer device reads the computer instructions from the computer-readable storage medium and executes the computer instructions, causing the computer device to perform the multi-surface phase retrieval method and system based on convolutional neural networks provided in the various optional implementations described above.

[0170] Computer program code for performing the operations of this application can be written in one or more programming languages ​​or a combination thereof, including object-oriented programming languages ​​such as Java, Smalltalk, and C++, and conventional procedural programming languages ​​such as the "C" language or similar programming languages. The program code can be executed entirely on the user's computer, partially on the user's computer, as a standalone software package, partially on the user's computer and partially on a remote computer, or entirely on a remote computer or server. In cases involving remote computers, the remote computer can be connected to the user's computer via any type of network—including a local area network (LAN) or a wide area network (WAN)—or can be connected to an external computer (e.g., via the Internet using an Internet service provider).

[0171] The flowcharts and block diagrams in the accompanying drawings illustrate the architecture, functionality, and operation of possible implementations of systems, methods, and computer program products according to various embodiments of this application. In this regard, each block in a flowchart or block diagram may represent a module, segment, or portion of code containing one or more executable instructions for implementing a specified logical function. It should also be noted that in some alternative implementations, the functions indicated in the blocks may occur in a different order than those indicated in the drawings. For example, two consecutively indicated blocks may actually be executed substantially in parallel, and they may sometimes be executed in reverse order, depending on the functions involved. It should also be noted that each block in the block diagrams and / or flowcharts, and combinations of blocks in the block diagrams and / or flowcharts, can be implemented using a dedicated hardware-based system that performs the specified function or operation, or using a combination of dedicated hardware and computer instructions.

[0172] The modules described in the embodiments of this application can be implemented in software or hardware. The names of the modules do not necessarily limit the module itself; for example, a model building module can also be described as "a model building module for building a multi-surface phase-shifting interferogram fringe separation model based on a convolutional neural network".

[0173] The above description is merely a preferred embodiment of this application and an explanation of the technical principles employed. Those skilled in the art should understand that the scope of disclosure in this application is not limited to technical solutions formed by specific combinations of the above-described technical features, but should also cover other technical solutions formed by arbitrary combinations of the above-described technical features or their equivalents without departing from the above-described concept. For example, technical solutions formed by substituting the above features with (but not limited to) technical features with similar functions disclosed in this application.

Claims

1. A multi-surface phase retrieval method based on convolutional neural networks, characterized in that, The method includes: Four frames of simulated multi-surface phase-shift interferograms under four different phase states are generated, along with multiple separated single-surface fringe interferograms corresponding to each frame of the simulated multi-surface phase-shift interferogram; the multiple single-surface fringe interferograms include a front surface fringe interferogram, a rear surface fringe interferogram, and a thickness fringe interferogram; A multi-surface phase-shifting interferogram fringe separation model based on a convolutional neural network is constructed. The model includes a downsampling module, an upsampling module, and an output layer. The downsampling module extracts multiple single-surface fringe features corresponding to the input data by reducing the feature map size. These single-surface fringe features include front surface fringe features, back surface fringe features, and thickness fringe features. The upsampling module includes multiple independent upsampling parts, which restore the corresponding single-surface fringe features to the size of the input data. Each upsampling part corresponds one-to-one with a single-surface fringe feature. The output layer has multiple layers, each corresponding one-to-one with a specific upsampling part, and is used to convert the channel features output by the corresponding upsampling part into a predicted interferogram of the separated single-surface fringe. Four frames of simulated multi-surface phase-shifting interferograms are used as input data, and the corresponding separated single-surface fringe interferograms are used as labels to train the multi-surface phase-shifting interferogram fringe separation model and obtain the optimal separation model. The optimal separation model is used to perform fringe separation on four frames of multi-surface phase-shift interferograms under four different phase states to obtain multiple single-surface fringe prediction interferograms under the corresponding phase states; the multiple single-surface fringe prediction interferograms include a front surface fringe prediction interferogram, a rear surface fringe prediction interferogram, and a thickness fringe prediction interferogram. Based on multiple single-surface fringe prediction interferograms under four different phase states, the phase distribution results of the corresponding single surface are recovered using a four-step phase shift method.

2. The multi-surface phase retrieval method based on convolutional neural networks according to claim 1, characterized in that, The downsampling module includes a first downsampling part and a second downsampling part; The first downsampling portion includes multiple convolutional layers; the first downsampling portion is used to reduce the size of the feature map by using a stride specified by the convolutional layers; The second downsampling portion includes multiple alternating convolutional layers and max pooling layers, and the second downsampling portion is used to reduce the size of the feature map by utilizing the max pooling layers.

3. The multi-surface phase retrieval method based on convolutional neural networks according to claim 1, characterized in that, The process involves using four frames of simulated multi-surface phase-shift interferograms as input data and the corresponding separated single-surface fringe interferograms as labels to train the multi-surface phase-shift interferogram fringe separation model and obtain the optimal separation model, including: Acquire multiple sets of input data and corresponding labels; each set of input data includes four frames of simulated multi-surface phase-shift interferograms; Multiple sets of input data are input into the multi-surface phase-shifting interferogram fringe separation model to obtain multiple sets of prediction results; each set of prediction results includes multiple single-surface fringe prediction interferograms. The difference between each set of predictions and the corresponding label is calculated using a loss function, and the gradient of the loss function with respect to the model is also calculated. The parameters of the multi-surface phase-shifting interferogram fringe separation model are updated based on the gradient, and the optimal separation model is obtained when a preset number of iterations is reached.

4. The multi-surface phase retrieval method based on convolutional neural networks according to claim 3, characterized in that, The expression for the loss function is: in, This is the front surface fringe loss function, used to calculate the difference between the predicted interferogram of the front surface fringe and the corresponding label. This is the back surface fringe loss function, used to calculate the difference between the predicted back surface fringe interferogram and the corresponding label. This is the thickness fringe loss function, used to calculate the difference between the predicted interferogram of thickness fringe and the corresponding label.

5. The multi-surface phase retrieval method based on convolutional neural networks according to claim 4, characterized in that, The front surface fringe loss function, the rear surface fringe loss function, and the thickness fringe loss function are all mean absolute error functions.

6. The multi-surface phase retrieval method based on convolutional neural networks according to claim 3, characterized in that, The process involves inputting multiple sets of input data into the multi-surface phase-shifting interferogram fringe separation model to obtain multiple sets of prediction results, including: Multiple sets of input data are shuffled in order using DataLoader, and the number of data transmitted at one time is increased before being input into the multi-surface phase-shifting interferogram fringe separation model. Multiple sets of prediction results were obtained through the multi-surface phase-shifting interferogram fringe separation model.

7. A multi-surface phase retrieval system based on a convolutional neural network, characterized in that, The system includes: The data generation module is used to generate four frames of simulated multi-surface phase-shift interferograms under four different phase states, as well as multiple separated single-surface fringe interferograms corresponding to each frame of simulated multi-surface phase-shift interferograms; the multiple single-surface fringe interferograms include a front surface fringe interferogram, a rear surface fringe interferogram, and a thickness fringe interferogram; A model building module is used to construct a multi-surface phase-shifting interferogram fringe separation model based on a convolutional neural network. The multi-surface phase-shifting interferogram fringe separation model includes a downsampling module, an upsampling module, and an output layer. The downsampling module extracts multiple single-surface fringe features corresponding to the input data by reducing the feature map size. These multiple single-surface fringe features include front surface fringe features, back surface fringe features, and thickness fringe features. The upsampling module includes multiple independent upsampling parts, which restore the corresponding single-surface fringe features to the size of the input data. Each upsampling part corresponds one-to-one with a single-surface fringe feature. The output layer has multiple layers, each corresponding one-to-one with one of the upsampling parts, and is used to convert the channel features output by the corresponding upsampling part into the corresponding separated single-surface fringe predicted interferogram. The model optimization module is used to take four frames of simulated multi-surface phase-shifting interferograms as input data and the corresponding separated single-surface fringe interferograms as labels to train the multi-surface phase-shifting interferogram fringe separation model and obtain the optimal separation model. The separation prediction module is used to perform fringe separation on four frames of multi-surface phase-shift interferograms under four different phase states using the optimal separation model, and obtain multiple single-surface fringe prediction interferograms under the corresponding phase states; the multiple single-surface fringe prediction interferograms include a front surface fringe prediction interferogram, a rear surface fringe prediction interferogram, and a thickness fringe prediction interferogram. The phase recovery module is used to predict interferograms based on multiple single-surface fringes under four different phase states, and recover the phase distribution results of the corresponding single surface using a four-step phase shifting method.

8. An electronic device, characterized in that, It includes a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor, when executing the program, implements the method of any one of claims 1-6.

9. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores a computer program that, when executed by a processor, implements the method of any one of claims 1-6.

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