Training method of neural network model and phase estimation method

Abstract

The application relates to a training method of a neural network model for phase estimation of an interferogram and a phase estimation method of an interferogram based on the neural network model. The training method of the neural network model for phase estimation of an interferogram comprises the following steps: acquiring a training interferogram and a real phase map thereof; inputting the training interferogram into a neural network model; acquiring a predicted phase map output by the neural network model; calculating a loss function value between the predicted phase map and the real phase map; and training the neural network model by gradient back propagation by minimizing the loss function value. In this way, the features of different scales of the interferogram are learned by the neural network model based on Unet++, and accurate estimation of the phase map corresponding to the interferogram is obtained.

Description

Technical Field

[0001] This application relates to the field of optical measurement technology, and more specifically, to a training method for a neural network model for phase estimation of interferograms and a phase estimation method for interferograms based on the neural network model. Background Technology

[0002] Interferometry is a crucial technique in optical measurement due to its high sensitivity and accuracy, leading to its widespread application. This technique utilizes coherent light to interfere with the measured object, forming a fringe pattern. Analyzing this fringe pattern is the core of interferometry. Fringe pattern analysis primarily involves extracting the fringe phase, which contains information about the measured object.

[0003] Traditional phase extraction methods are mainly divided into two categories: phase shifting and spatial demodulation. Both methods have their advantages and disadvantages.

[0004] Phase-shifting methods include two different approaches: time-domain and spatial-domain. Time-domain phase-shifting requires piezoelectric ceramics for phase shifting, generating multiple images. It is time-consuming and sensitive to instrument vibration and interference. Spatial-domain phase-shifting generates fringes of different phases using polarization devices and displays them on a single image frame. It requires no additional time and is highly stable against external interference, but its accuracy is lower due to the resolution limitations of CCD cameras. Furthermore, both time-domain and spatial-domain phase-shifting methods require specialized components, resulting in hardware costs.

[0005] Single-frame interferometric fringe analysis without phase shifting has been a hot research topic, with spatial demodulation methods being the mainstream approach. This method employs Fourier transform analysis, also known as the Fourier transform method. It can derive the phase from a single-frame interferogram, but is often susceptible to noise and uneven lighting. Furthermore, it is unsuitable for analyzing closed fringes, which are quite common in industry, such as Newton's rings. Analyzing Newton's rings can estimate physical parameters such as the radius of curvature and position of spherical elements, the vertex offset of fiber optic connector endfaces, and fiber height. Even if we can convert closed fringes into open fringes by introducing a carrier wave, this carrier modulation, achieved through tilting or defocusing, introduces additional errors, leading to a decrease in accuracy.

[0006] Furthermore, the phases obtained by both the phase-shifting method and the spatial demodulation method are entangled, and both require the use of an unwinding algorithm. However, the unwinding algorithm is very susceptible to noise and interference, which leads to a decrease in accuracy.

[0007] Therefore, it is necessary to develop simpler methods for analyzing interference fringes that do not require phase shifting, modulation, or unwinding.

[0008] Deep learning is a method that learns and analyzes patterns based on massive amounts of data. Due to its strong data fitting ability, it has shown remarkable performance in many application fields.

[0009] Based on this, this application aims to provide a phase estimation scheme for interferograms based on deep learning. Summary of the Invention

[0010] This application provides a method for training a neural network model for phase estimation of interferograms and a method for phase estimation of interferograms based on the neural network model. It learns the features of interferograms at different scales by using a Unet++-based neural network model to obtain an accurate estimate of the phase map corresponding to the interferogram.

[0011] According to one aspect of this application, a method for training a neural network model for phase estimation of an interferogram is provided, comprising: acquiring a training interferogram and its true phase map; inputting the training interferogram into a neural network model, the neural network model having N convolutional layer branches, wherein the i-th convolutional layer branch has a plurality of cascaded N+1-i convolutional layers, 1≤i≤N, wherein the output feature map of the first convolutional layer in the i-th convolutional layer branch is downsampled and input into the first convolutional layer in the (i+1)-th convolutional layer branch, the output feature map of the j-th convolutional layer in the (i+1)-th convolutional layer branch is upsampled and input into the (j+1)-th convolutional layer in the i-th convolutional layer branch, 1≤j≤N+1-i, and the output feature map of each convolutional layer in the i-th convolutional layer branch is input to each of its downstream convolutional layers; acquiring a predicted phase map output by the neural network model; calculating a loss function value between the predicted phase map and the true phase map; and training the neural network model by minimizing the loss function value using gradient backpropagation.

[0012] In the training method of the neural network model for phase estimation of interferograms described above, obtaining the training interferogram includes: capturing a predetermined object using a predetermined image acquisition device to obtain the training interferogram.

[0013] In the training method of the neural network model for phase estimation of interferograms described above, obtaining training interferograms by photographing a predetermined object with a predetermined image acquisition device includes: obtaining multiple interferograms with multiple phases by photographing the predetermined object with the predetermined image acquisition device based on a multi-step phase shifting method; and obtaining an interferogram without phase shifting as the training interferogram.

[0014] In the training method of the neural network model for phase estimation of interferograms described above, the number of branches of the convolutional layer of the neural network model is 4, the number of convolutional kernels doubles starting from 32, and the size of the convolutional kernels is 5×5.

[0015] In the training method of the neural network model used for phase estimation of interferograms described above, each convolutional layer includes a ResBlock convolutional block.

[0016] In the above-described training method for a neural network model for phase estimation of interferograms, before inputting the training interferogram into the neural network model, the method further includes: cropping or augmenting the training interferogram.

[0017] In the training method of the neural network model for phase estimation of interferograms described above, image cropping or image augmentation of the training interferogram includes: cropping the training interferogram when the number of branches in the convolutional layer is less than or equal to a predetermined threshold; and augmenting the training interferogram when the number of branches in the convolutional layer is greater than the predetermined threshold.

[0018] In the training method of the neural network model for phase estimation of interferograms described above, image cropping or image augmentation of the training interferogram includes: when the training interferogram is cropped, the number of pixels in the cropped image is sufficient to fit an ideal sphere.

[0019] In the training method of the neural network model used for phase estimation of interferograms described above, the loss function value is the root mean square error loss function value, expressed as:

[0020]

[0021] F1 (i) and F2 (i) These are the matrix representations of the predicted phase map and the true phase map corresponding to the i-th interferogram among a total of k interferograms, and the size of the matrix of the predicted phase map and the true phase map is m×n.

[0022] In the training method of the neural network model used for phase estimation of interferograms described above, the loss function value is the relative root mean square error loss function value, expressed as:

[0023]

[0024] F1 (i) a,b and F2 (i) a,b These are the pixel values ​​at position (a, b) in the predicted phase map and the true phase map corresponding to the i-th interferogram among a total of k interferograms.

[0025] According to another aspect of this application, a phase estimation method for an interferogram is provided, comprising: acquiring an interferogram to be estimated; and inputting the interferogram to be estimated into a neural network model trained based on the training method for a neural network model for phase estimation of an interferogram as described above, to obtain a phase map corresponding to the interferogram to be estimated.

[0026] The phase estimation method for the interferogram described above further includes: calculating at least one of the radius of curvature, vertex offset, and fiber height of the predetermined object based on the phase diagram.

[0027] The training method for the neural network model for phase estimation of interferograms and the phase estimation method for interferograms based on the neural network model provided in this application can learn the importance of features at different depths through the Unet++-based neural network model, thereby obtaining an accurate phase map of the interferogram. Attached Figure Description

[0028] Various other advantages and benefits of this application will become apparent to those skilled in the art upon reading the detailed description of the preferred embodiments below. The accompanying drawings are for illustrative purposes only and are not intended to limit the scope of this application. It is obvious that the drawings described below are merely some embodiments of this application, and those skilled in the art can obtain other drawings based on these drawings without any inventive effort. Furthermore, the same reference numerals denote the same parts throughout the drawings.

[0029] Figure 1 The diagram shows the interference fringe pattern at the end face of the optical fiber.

[0030] Figure 2 The illustration shows a schematic overall flow of the fiber endface phase estimation method according to an embodiment of this application.

[0031] Figure 3 The diagram illustrates a schematic U-net network structure used for fiber end-face phase estimation.

[0032] Figure 4 The illustration shows a flowchart of a method for training a neural network model for phase estimation of an interferogram according to an embodiment of this application.

[0033] Figure 5 The illustration shows a schematic diagram of a training interferogram and its true phase diagram according to an embodiment of this application.

[0034] Figure 6 The diagram illustrates a schematic U-net++ network structure.

[0035] Figure 7The illustration shows a schematic diagram of a ResBlock convolutional block used in a neural network model according to an embodiment of this application.

[0036] Figure 8 The illustration shows a flowchart of an interferogram phase estimation method according to an embodiment of this application.

[0037] Figure 9 The diagram illustrates the predicted phase results of the preferred neural network model architecture.

[0038] Figure 10 A more general example of phase estimation for simulated interferograms is shown.

[0039] Figure 11 A more general example of phase estimation for a real interferogram is shown.

[0040] Figure 12 A schematic diagram illustrating the error of the phase estimation method for the interferogram according to an embodiment of this application against noise is shown. Detailed Implementation

[0041] Hereinafter, exemplary embodiments according to this application will be described in detail with reference to the accompanying drawings. Obviously, the described embodiments are merely some embodiments of this application, and not all embodiments of this application. It should be understood that this application is not limited to the exemplary embodiments described herein.

[0042] Application Overview

[0043] Fiber optic connectors, used to connect light sources to optical fibers, optical fibers to optical fibers, and optical fibers to detectors in optical fiber communication, are among the most widely used passive devices in optical communication. Their main body is composed of an optical fiber ceramic ferrule, with a micro-hole in the center used to fix the optical fiber.

[0044] The end-face quality and geometry of fiber optic connectors directly affect the transmission efficiency of optical signals. If there are defects in the end-face grinding of the connector connecting two optical fibers, the insertion loss and return loss of the connector will increase, which will reduce the optical signal performance of the optical link and may even cause the optical signal to fail to transmit.

[0045] To better determine the quality of manufactured fiber optic connectors, the International Electrotechnical Commission (IEC) has a series of requirements for the three-dimensional morphological parameters of the connector end face. All manufactured fiber optic connectors must undergo testing and detailed information on the end face grinding condition must be provided. This information must include a three-dimensional image and a two-dimensional contour display of the fiber end face, as well as key parameters such as radius of curvature, vertex offset, fiber height (fiber concavity / protrusion), and end face tilt angle. These indicators are used to determine whether the connector meets the usage standards. The fiber end face is also measured using interferometry. By performing interferometric imaging on the fiber optic connector, the resulting interference fringe pattern is shown below. Figure 1 As shown. Figure 1 The diagram illustrates the interference fringe pattern at the fiber end face. (For example...) Figure 1 As shown, the entire image consists of Newton's rings and a dark spot. The Newton's rings are formed because the entire end face is a microsphere, which will appear after interference imaging. The dark spot is located at the fiber core. Because the refractive index of the fiber core and the insert material is different, the dark spot will affect part of the interference fringe pattern.

[0046] Because the fiber end-face interference pattern contains not only Newton's rings but also dark spots caused by the fiber core, which create fringe shading, and because the fiber core and ferrule are made of different materials with different refractive indices, the shadow cast by the fiber core not only shades the fringes but also causes some fringe deformation. Furthermore, since fiber height parameters are more precise than other parameters, typically measured in nanometers (nm), phase analysis is often required to ensure estimation accuracy. Additionally, surface roughness is also obtained from the morphology distribution reconstructed from the phase. Therefore, the inspection method for fiber optic connector end faces usually involves extracting the phase of the fiber end-face interference fringe pattern to obtain the end-face morphology distribution, which can then be used for parameter estimation.

[0047] In the interferogram of an optical fiber end face, the phase of the fringe pattern is consistent with the size of the fringe pattern, representing a point-to-point mapping relationship. Existing phase analysis methods for fringe patterns are mainly based on phase shifting methods using multiple patterns and Fourier transform methods using single patterns. These methods have some shortcomings in estimating the phase of closed fringe patterns. Therefore, in this application, a deep learning convolutional neural network is used to estimate the phase of closed fringe patterns.

[0048] In this embodiment of the application, besides the interferogram of spherical surfaces such as the fiber end face, as mentioned above, during interferometric measurement, various fringe patterns can also be formed by interferometric imaging of other types of objects under test to perform general surface shape measurements. Furthermore, in this embodiment of the application, the interferogram does not need to be a closed-shape annular interferogram; it can also be an open fringe formed from a portion of an annular interferogram, such as a portion of Newton's rings.

[0049] Therefore, the phase estimation method of the interferogram according to the embodiments of this application can be used for phase estimation of the interferometric imaging of various types of objects under test, and is not limited to phase estimation of Newton's rings on spherical surfaces such as fiber end faces.

[0050] Specifically, deep learning is used to estimate the phase of a closed fringe pattern. The convolutional neural network used directly outputs the corresponding phase pattern from the input fringe pattern, as follows: Figure 2 As shown. Figure 2 The illustration shows a schematic overall flow of the phase estimation method for interferograms according to an embodiment of this application. For the input fringe pattern, the output of the neural network is an image of the same size as the input, mapped point-to-point.

[0051] Furthermore, in the embodiments of this application, the output phase map is an unwrapped phase map, that is, the phase map of the interferogram can be obtained without any further post-processing of the neural network output.

[0052] For example, the chosen neural network could be U-net, which uses upsampling, downsampling, and skip connections to enrich the information at each layer, compensating for the information lost during continuous downsampling. Figure 3 The illustration shows a schematic U-net network structure used for phase estimation of interferograms.

[0053] Indicative training methods

[0054] Figure 4 The illustration shows a flowchart of a method for training a neural network model for phase estimation of an interferogram according to an embodiment of this application.

[0055] like Figure 4 As shown, the training method for a neural network model for phase estimation of interferograms according to an embodiment of this application includes the following steps.

[0056] Step S110: Obtain the training interferogram and its true phase map. Specifically, Figure 5 The illustration shows a schematic diagram of a training interferogram and its actual phase diagram according to an embodiment of this application. Figure 5 As shown, the training interferogram is the real interferogram as shown in 5(a), and the real phase diagram is the phase diagram corresponding to the real interferogram as shown in 5(b).

[0057] Specifically, to obtain a true interferogram, a dedicated image acquisition device can be used to photograph the predetermined object under test, such as the fiber optic end face. For example, the Mars-ML400 manufactured by Hangzhou Qiyue Co., Ltd. can be used to capture the fiber optic end face interferogram. Specifically, the Mars-ML400 measures the fiber optic end face interferogram based on the five-step phase-shifting method (each phase shift is π / 2, so the last image is theoretically the same as the first image). Therefore, by measuring each fiber optic connector end face using the Mars-ML400, five cropped fiber optic end face interferograms with an image size of 223×223, contained within the measured area (corresponding to a physical size of 140um-250um), are obtained. However, since phase estimation of a single carrier-free fiber optic end face interferogram is required in this embodiment, only the first and fifth interferograms without phase shifting in each interferometric imaging can be selected.

[0058] Those skilled in the art will understand that, although the above example uses the fiber end face, for other objects under test, the interferogram to be trained can also be obtained by using a predetermined image acquisition device to capture images. Furthermore, a multi-step phase-shifting method can also be used when capturing images with the predetermined image acquisition device.

[0059] Then, based on the real interferogram, the corresponding real phase diagram is obtained by calculation, for example, by the phase shift method based on multiple diagrams and the Fourier transform method based on a single diagram, which will not be elaborated here.

[0060] Therefore, in the training method of the neural network model for phase estimation of interferograms according to the embodiments of this application, obtaining the training interferogram includes: capturing a predetermined object by a predetermined image acquisition device to obtain the interferogram to be trained.

[0061] Furthermore, in the training method of the neural network model for phase estimation of interferograms according to the embodiments of this application, obtaining the training interferogram by photographing a predetermined object with a predetermined image acquisition device includes: photographing the predetermined object with a predetermined image acquisition device based on a multi-step phase shifting method to obtain multiple interferograms with multiple phases; and obtaining an interferogram without phase shifting as the training interferogram.

[0062] Furthermore, nonlinear normalization can be performed on the true phase diagram.

[0063] Step S120: Input the interferogram to be trained into a neural network model. The neural network model has N convolutional layer branches. The i-th convolutional layer branch has multiple cascaded N+1-i convolutional layers, 1≤i≤N. The output feature map of the first convolutional layer in the i-th convolutional layer branch is downsampled and then input into the first convolutional layer in the (i+1)-th convolutional layer branch. The output feature map of the j-th convolutional layer in the (i+1)-th convolutional layer branch is upsampled and then input into the (j+1)-th convolutional layer in the i-th convolutional layer branch, 1≤j≤N+1-i. The output feature map of each convolutional layer in the i-th convolutional layer branch is input into each of its downstream convolutional layers.

[0064] Here, in this embodiment of the application, the neural network model is a convolutional neural network called U-net++. Figure 6 The diagram illustrates a schematic U-net++ network structure. Among them, Figure 6 The diagram illustrates the U-net++ network structure with 5 convolutional layer branches. (Example:) Figure 6 As shown, the first convolutional layer branch in the five convolutional layer branches has five cascaded convolutional layers, the same number as the convolutional layer branches. Furthermore, for each increment in the branch number, the number of cascaded convolutional layers it contains decreases by one; that is, the second convolutional layer branch has four cascaded convolutional layers, and so on, until the fifth convolutional layer branch has one convolutional layer.

[0065] The output feature map of the first convolutional layer in each convolutional layer branch is downsampled and then input into the first convolutional layer in the next convolutional layer branch, such as... Figure 6 The solid arrow pointing downwards to the right indicates downsampling. Except for the first convolutional layer branch, the output feature map of each convolutional layer in each branch is upsampled and then input into the next convolutional layer of the previous branch, as shown below. Figure 6 The solid arrow pointing to the upper right indicates upsampling. Furthermore, within each convolutional layer branch, the upstream convolutional layer (i.e., Figure 6 The output feature map of the leftmost convolutional layer is input into each of its downstream convolutional layers (i.e., ...). Figure 6 (The convolutional layer on the right). That is, within each convolutional layer branch, the feature maps are not only passed backward layer by layer, but also skip connections.

[0066] Here, the neural network model according to the embodiments of this application is still based on the encoder-decoder structure design. Its multiple convolutional layer branches are designed to adapt to different features of various datasets. Since the importance of features at different levels of the neural network varies for different datasets, multiple convolutional layer branches enable the neural network to learn the importance of features at different depths. Furthermore, through feature fusion via downsampling and upsampling between multiple convolutional layer branches, features at all depths can be utilized, allowing the neural network to autonomously learn the importance of features at different depths. Moreover, this neural network model shares a single feature extractor, eliminating the need to train multiple encoders and requiring only one encoder to be trained. When features at different levels are needed, they are reconstructed through different decoder paths. Furthermore, in the neural network model according to the embodiments of this application, the cascaded convolutional layers in each convolutional layer branch have corresponding long and short connections. This not only integrates features from different levels but also allows the large number of parameters in the deep network to be significantly reduced within an acceptable accuracy range.

[0067] Specifically, for each convolutional layer of the neural network model, the number and size of the convolutional kernels can be set. For example, the number of convolutional kernels can be doubled starting from 16 or doubled starting from 32, and the size of the convolutional kernels can be 3×3 or 5×5.

[0068] Experiments showed that the neural network model performed best when the number of convolutional layer branches was 4, the number of convolutional kernels doubled starting from 32, and the kernel size was 5×5. Compared to the neural network model with 5 convolutional layer branches, it had fewer parameters, reduced hardware resource requirements, shortened testing time, and was more suitable for practical applications, while also maintaining accuracy. Specific experimental data and results will be detailed below.

[0069] Therefore, in the training method of the neural network model for phase estimation of interferograms according to the embodiments of this application, the number of convolutional layer branches of the neural network model is 4, the number of convolutional kernels is doubled starting from 32, and the size of the convolutional kernels is 5×5.

[0070] Furthermore, in this embodiment, each convolutional layer may include a predetermined convolutional block, such as a regular initial convolutional block. Preferably, each convolutional layer includes a ResBlock convolutional block, such as... Figure 7 As shown. Figure 7The illustration shows a schematic diagram of a ResBlock convolutional block used in a neural network model according to an embodiment of this application. The residual learning framework of the ResBlock convolutional block makes it easier to optimize than direct mapping, thereby enabling it to handle degradation problems at greater network depths. Furthermore, the residual connections of the ResBlock convolutional block, combined with the dense skip connections in the neural network model, can improve the gradient flow during network training. This design ensures the possibility of training deep networks with a large number of parameters.

[0071] Furthermore, since the feature map needs to be downsampled multiple times in the neural network model, the training interferogram can be preprocessed to meet the size requirements of the downsampled feature map.

[0072] Specifically, for an image of size 223×223 acquired by Mars-ML400, image cropping can be performed, such as cropping its image edges, to obtain a 208×208 image. That is, according to the principle of spherical fitting, these data are sufficient to fit an ideal sphere.

[0073] Alternatively, the original 223×223 image can be augmented, for example by zero-padding one row and one column, to make it a 224×224 image. After obtaining the phase map, the padded row and column data can be removed after obtaining the topography from the phase map to obtain an estimated phase of the original size.

[0074] Furthermore, in this embodiment, the preprocessing of the training interferogram can be based on the number of branches in the convolutional layer. That is, when the number of branches in the convolutional layer is less than or equal to a predetermined threshold, image cropping is performed on the training interferogram, and when the number of branches in the convolutional layer is greater than the predetermined threshold, image augmentation is performed on the training interferogram.

[0075] For example, for a 208×208 image, a U-net++ network with four convolutional layer branches is used, while for a 224×224 image, a U-net++ network with five convolutional layer branches is used.

[0076] Therefore, in the training method of the neural network model for phase estimation of interferograms according to the embodiments of this application, before inputting the training interferogram into the neural network model, it further includes: image cropping or image augmentation of the training interferogram.

[0077] Furthermore, in the training method of the neural network model for phase estimation of interferograms according to the embodiments of this application, image cropping or image augmentation of the training interferogram includes: cropping the training interferogram when the number of branches of the convolutional layer is less than or equal to a predetermined threshold; and augmenting the training interferogram when the number of branches of the convolutional layer is greater than the predetermined threshold.

[0078] Furthermore, in the training method of the neural network model for phase estimation of interferograms according to the embodiments of this application, image cropping or image augmentation of the training interferogram includes: when the training interferogram is image cropped, the number of pixels in the cropped image is sufficient to fit an ideal sphere.

[0079] Step S130: Obtain the predicted phase map output by the neural network model. Here, as... Figure 3 As shown, the obtained predicted phase map is also a phase map similar to the real phase map. This is because the prediction accuracy of the neural network model varies and there is an error between the real phase map and the real phase map.

[0080] Step S140: Calculate the loss function value between the predicted phase map and the true phase map. Specifically, in this embodiment, the loss function value can be the root mean square error (RMSE) loss function value, expressed as:

[0081]

[0082] F1 (i) and F2 (i) These are the matrix representations of the predicted phase map and the true phase map corresponding to the i-th interferogram among a total of k interferograms, and the size of the matrix of the predicted phase map and the true phase map is m×n.

[0083] In the training method of the neural network model used for phase estimation of interferograms described above, the loss function value is the relative root mean square error loss function value, expressed as:

[0084]

[0085] F1 (i) a,b and F2 (i) a,b These are the pixel values ​​at position (a, b) in the predicted phase map and the true phase map corresponding to the i-th interferogram among a total of k interferograms.

[0086] Step S150: Train the neural network model by minimizing the loss function value using gradient backpropagation. Specifically, in this embodiment, the AdamW optimizer can be used to optimize the gradient backpropagation.

[0087] Additionally, in this embodiment, other hyperparameters may include a basic learning rate 1e. -3 Weight decay of 0.1, learning rate adjustment strategy: cosine decay, batch size: 512, number of training rounds: 30.

[0088] Indicative estimation method

[0089] Figure 8 The illustration shows a flowchart of an interferogram phase estimation method according to an embodiment of this application.

[0090] like Figure 8 As shown, the phase estimation method for the interferogram according to an embodiment of this application includes: step S210, obtaining the interferogram to be estimated; and step S220, inputting the interferogram to be estimated into the trained neural network model to obtain the phase map of the optical fiber end face.

[0091] Here, those skilled in the art will understand that the specific details of the phase estimation method for interferograms according to the embodiments of this application are exactly the same as the corresponding details in the training method of the neural network model for phase estimation of interferograms according to the embodiments of this application as described above, and will not be repeated here.

[0092] Thus, after obtaining the phase diagram of the predetermined object, such as the fiber end face, other parameters of the predetermined object, such as radius of curvature, vertex offset, and fiber height, can be further calculated.

[0093] Therefore, the phase estimation method for the interferogram according to the embodiments of this application further includes: calculating at least one of the radius of curvature, vertex offset, and fiber height of the predetermined object based on the phase map of the predetermined object.

[0094] Effect verification

[0095] During the performance verification, a total of 121,000 pairs of fiber end-face interferograms and phase maps were first obtained, of which 120,000 pairs were used as the training set and the remaining 100 pairs were used as the test set. The training and testing of the network can be implemented on a single NVIDIA Quartron RTX 5000 GPU, for example, based on the Python TensorFlow framework.

[0096] Furthermore, during training, the optimizer can be, for example, Adam, and the batch size can be set to, for example, 16. Through experimentation, the initial learning rate was determined to be 1×10⁻⁶. -4 The training criterion is that when the loss function values ​​of the training set and the test set no longer decrease continuously and become stable (when the loss function values ​​no longer decrease after more than 10 training cycles), the initial learning rate will be reduced to 1 / 10 of the original. After two changes in the initial learning rate, training will stop when the loss function values ​​no longer decrease continuously and become stable.

[0097] As described above, for the neural network model according to the embodiments of this application, different numbers of convolutional layer branches, initial number of convolutional kernels, and kernel sizes can be set. The following shows the test data of neural network models with different network architectures, where (a,b) represent (initial number of convolutional kernels and kernel size).

[0098] Table 1. Comparison of fiber endface phase estimation performance of U-net++ for different network architectures

[0099]

[0100] We can see that the number of branches in the convolutional layer is 4, the number of initial convolutional kernels doubles starting from 32, and the network structure with a convolutional kernel size of 5×5 performs best. Figure 9 The diagram illustrates the predicted phase results of the preferred neural network model architecture. Wherein, Figure 9 (a) shows the true phase after translation, (b) shows the predicted phase of the neural network model, (c) shows a comparison of the x-axis cross-sections of (a) and (b) (the two solid lines represent the true phase and the predicted phase, respectively), and (d) shows a comparison of the y-axis cross-sections of (a) and (b) (the two solid lines represent the true phase and the predicted phase, respectively). Figure 9 As shown in (a) to (d), the phase recovered by the network is very close to the true phase after translation, and the predicted phase RMSE = 0.0738 (RRMSE = 0.9597%). Furthermore, it can be seen from the two side views that the network also predicts the roughness of the topography to a certain extent.

[0101] After obtaining the phase map, the predicted phase can be used to calculate the radius of curvature, vertex offset, and fiber height. Test results for some real fiber interferograms are shown in Table 2 below.

[0102] [Table 2] Estimation results of interferogram parameters of real fiber endface using U-net++

[0103]

[0104]

[0105] The absolute errors of the test on 100 real test sets were averaged and statistically analyzed. The absolute errors of the radius of curvature, vertex offset and fiber height were ±0.04mm, ±0.31um and ±2.13nm, respectively.

[0106] As can be seen, the surface results of the effect verification have reached the commercial level. Further improvements can be made in accuracy and the surface roughness can be more accurately characterized. This also lays the foundation for the development of a fiber end face interferometer based on a single-frame carrierless design.

[0107] Figure 10 A more general example of phase estimation for simulated interferograms is shown. Wherein, Figure 10 (a) shows a simulated interferogram. Figure 10 (b) shows the true phase diagram. Figure 10 (c) shows an estimated phase map according to an embodiment of this application, and Figure 10 (d) shows the error between the true phase map and the estimated phase map.

[0108] Figure 11 A more general example of phase estimation for a real interferogram is shown. Wherein, Figure 11 (a) shows the actual interferogram. Figure 11 (b) shows the true phase diagram. Figure 11 (c) shows an estimated phase map according to an embodiment of this application, and Figure 11 (d) shows the error between the true phase map and the estimated phase map.

[0109] Figure 12 A schematic diagram illustrating the error of the phase estimation method for the interferogram according to an embodiment of this application against noise is shown. Figure 12 As can be seen, the phase estimation method of the interferogram according to the embodiments of this application is robust to both Gaussian noise and Poisson noise.

[0110] The basic principles of this application have been described above with reference to specific embodiments. However, it should be noted that the advantages, benefits, and effects mentioned in this application are merely examples and not limitations, and should not be considered as essential features of each embodiment of this application. Furthermore, the specific details disclosed above are for illustrative and facilitative purposes only, and are not limitations. These details do not limit the application to the necessity of employing the aforementioned specific details for implementation.

[0111] The block diagrams of devices, apparatuses, devices, and systems involved in this application are merely illustrative examples and are not intended to require or imply that they must be connected, arranged, or configured in the manner shown in the block diagrams. As those skilled in the art will recognize, these devices, apparatuses, devices, and systems can be connected, arranged, and configured in any manner. Words such as “comprising,” “including,” “having,” etc., are open-ended terms meaning “including but not limited to,” and are used interchangeably with them. The terms “or” and “and” as used herein refer to the terms “and / or,” and are used interchangeably with them unless the context clearly indicates otherwise. The term “such as” as used herein refers to the phrase “such as but not limited to,” and is used interchangeably with it.

[0112] It should also be noted that in the apparatus, equipment, and methods of this application, the components or steps can be disassembled and / or recombined. These disassemblies and / or recombinations should be considered as equivalent solutions of this application.

[0113] The above description of the disclosed aspects is provided to enable any person skilled in the art to make or use this application. Various modifications to these aspects will be readily apparent to those skilled in the art, and the general principles defined herein can be applied to other aspects without departing from the scope of this application. Therefore, this application is not intended to be limited to the aspects shown herein, but rather to be accorded the widest scope consistent with the principles and novel features disclosed herein.

[0114] The above description has been given for purposes of illustration and description. Furthermore, this description is not intended to limit the embodiments of this application to the forms disclosed herein. Although numerous exemplary aspects and embodiments have been discussed above, those skilled in the art will recognize certain variations, modifications, alterations, additions, and sub-combinations thereof.

Claims

1. A method for training a neural network model for phase estimation of interferograms, characterized in that, include: Obtain the interferograms used for training and testing, as well as their true phase maps; The training interferogram is input into a neural network model, which has N convolutional layer branches. The i-th convolutional layer branch has multiple cascaded N+1-i convolutional layers. In this process, the output feature map of the first convolutional layer in the i-th convolutional layer branch is downsampled and then input into the first convolutional layer in the (i+1)-th convolutional layer branch, and the output feature map of the j-th convolutional layer in the (i+1)-th convolutional layer branch is upsampled and then input into the (j+1)-th convolutional layer in the i-th convolutional layer branch. And the output feature map of each convolutional layer in the i-th convolutional layer branch is input to each convolutional layer downstream of it; Obtain the predicted phase map output by the neural network model; Calculate the loss function value between the predicted phase map and the true phase map; as well as, The neural network model is trained by backpropagating the gradient by minimizing the value of the loss function. Within each convolutional layer branch, in addition to being passed back layer by layer, the feature maps are also skipped, so that the output feature maps of the upstream convolutional layers are all input to each downstream convolutional layer. Each convolutional layer includes a ResBlock convolutional block, which employs residual connections.

2. The training method for the neural network model for phase estimation of interferograms according to claim 1, wherein, Obtaining the training interferogram includes: Interferograms for training are obtained by photographing a predetermined object using a predetermined image acquisition device.

3. The training method for the neural network model for phase estimation of interferograms according to claim 2, wherein, Obtaining training interferograms by photographing predetermined objects using predetermined image acquisition equipment includes: Multiple interferograms with multiple phases are obtained by capturing images of the predetermined object using a predetermined image acquisition device based on a multi-step phase-shifting method; and, An interferogram without phase shift is obtained as the training interferogram.

4. The training method for the neural network model for phase estimation of interferograms according to claim 1, wherein, The neural network model has 4 branches in its convolutional layer, the number of convolutional kernels doubles starting from 32, and the kernel size is 5×5.

5. The training method for a neural network model for phase estimation of interferograms according to claim 1, further comprising, before inputting the training interferogram into the neural network model: The training interferogram is then cropped or augmented.

6. In the training method for the neural network model for phase estimation of interferograms according to claim 5, image cropping or image augmentation of the training interferogram includes: If the number of branches in the convolutional layer is less than or equal to a predetermined threshold, the training interferogram is cropped. as well as, If the number of branches in the convolutional layer is greater than a predetermined threshold, image augmentation is performed on the training interferogram.

7. In the training method for the neural network model for phase estimation of interferograms according to claim 1, image cropping or image augmentation of the training interferogram includes: When the training interferogram is cropped, the number of pixels in the cropped image is sufficient to fit an ideal sphere.

8. In the training method of the neural network model for phase estimation of interferograms according to claim 1, the loss function value is the root mean square error loss function value, expressed as: ； in and They are the total In the interference diagram, the first The matrix representation of the predicted phase map and the true phase map corresponding to the Zhang interferogram, and the size of the matrix of the predicted phase map and the true phase map is . .

9. In the training method of the neural network model for phase estimation of interferograms according to claim 1, the loss function value is the relative root mean square error loss function value, expressed as: ； in and They are the total In the interference diagram, the first The predicted phase map corresponding to the Zhang interferogram and the actual phase map, position The pixel value.

10. A phase estimation method for interferograms, characterized in that, include: Obtain the interferogram to be estimated; and ， The interferogram to be estimated is input into the neural network model trained based on the training method for a neural network model for phase estimation of an interferogram according to any one of claims 1 to 9, so as to obtain a phase map corresponding to the interferogram to be estimated.

11. The phase estimation method for interferograms according to claim 10, further comprising: Based on the phase diagram, at least one of the radius of curvature, vertex offset, and fiber height of the predetermined object is calculated.

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