Random two-step tilt phase shift wavefront detection method based on deep learning

Abstract

The invention discloses a random two-step inclined phase shift wavefront detection method based on deep learning, and solves the problems of harsh requirements on a measurement environment and large measurement errors in the prior art. The method comprises the following steps: carrying out analogue simulation to obtain two interferogram databases; establishing a neural network model, and dividing the interferogram database into a training set and a test set; inputting the training set into the neural network model for training to obtain a trained neural network model; inputting the test set into the trained neural network model for testing, and outputting a wavefront phase calculation value; calculating an error between the wavefront phase calculation value and the wavefront phase simulation value until a new neural network model is obtained; and obtaining multiple frames of interference fringe patterns of the to-be-detected optical element, inputting the interference fringe patterns into the new neural network model, and outputting a real wavefront phase of the to-be-detected optical element, thereby realizing random two-step inclined phase shift wavefront detection based on deep learning. The method is simple in operation and high in measurement precision.

Description

Technical Field

[0001] The present invention relates to a method for wavefront detection of an optical system, and specifically to a random two-step tilt phase-shifting wavefront detection method based on deep learning. Background Art

[0002] Wavefront detection plays a crucial role in an optical system. Through wavefront detection, aberrations in the optical system can be identified and quantified, and corresponding measures can be taken for correction. Wavefront detection is crucial for improving imaging quality and resolution, especially in applications with extremely high requirements for the performance of optical systems, such as astronomical observations, biomedical imaging, and precision engineering.

[0003] The commonly used method for traditional wavefront detection is phase-shifting interference detection. By using multiple frames of interference patterns, the tilt phase-shifting error caused by the phase shifter and environmental vibration is solved, and the phase demodulation of the interference fringes is performed through an equal-step algorithm to achieve high-precision wavefront reconstruction. Since multiple frames of interference patterns need to be collected in this method and the phase-shifting step size must be set according to strict equal intervals or fixed step sizes, the acquisition is time-consuming. At the same time, environmental vibration and air disturbance will bring large errors to the finally restored phase. In addition, most traditional phase-shifting interference detection methods perform phase demodulation through interference patterns, that is, first obtain the wrapped phase, and then use the unwrapping algorithm and Zernike polynomial fitting method to obtain wavefront information. The wavefront reconstruction process is complex and the reconstruction time is long. At the same time, the method of using Zernike polynomials to obtain the wavefront restricts the shape of the optical system to be measured, and cannot test optical systems with non-circular apertures. In addition, the wavefront information obtained by the method of Zernike polynomial fitting only has low-frequency surface shape information, lacking intermediate-frequency (ripple) and high-frequency (roughness) information. Therefore, traditional wavefront detection methods are limited in practical applications because they cannot reflect all the information of the wavefront.

[0004] Compared with the traditional phase-shifting interference detection method, the random tilt two-step phase-shifting detection method can shorten the time for image acquisition and phase reconstruction, but there is a problem of decreased phase reconstruction accuracy due to the reduction of phase-shifting fringe patterns. Currently, there are many methods for realizing random tilt two-step phase-shifting detection. For example, the Chinese invention patent with publication number CN107179058A discloses a two-step phase-shifting algorithm based on structural light contrast optimization. In order to make up for the decreased phase reconstruction accuracy caused by the two-step phase-shifting fringe patterns, this method introduces a contrast optimization algorithm to reduce the phase reconstruction error. This method incorporates the influence of ambient light into the change of structural light contrast, and obtains more accurate phase information by optimizing and correcting the contrast distribution. Another example is the Chinese invention patent with publication number CN111707216A, which discloses a surface shape detection method based on random two-step phase-shifting, and reduces the calculation time for extracting the phase-shifting amount or restoring the phase by optimizing the random two-step phase-shifting algorithm.

[0005] The above methods all optimize the reconstruction accuracy of two-step phase-shifting by improving the backend algorithm. However, the acquisition of the interference pattern still realizes phase-shifting through a certain mechanical motion mechanism, which has high requirements for the phase-shifting accuracy of the phase shifter. Moreover, the phase-shifting amount error of the phase shifter and the tilt error during phase-shifting are not considered in the algorithm. Therefore, the acquisition of the interference pattern is relatively sensitive to changes in the system environment. At the same time, the reconstruction algorithms also use Zernike polynomials for fitting, and the aforementioned problems still exist.

[0006] In addition, the Chinese invention patent with publication number CN114136466A discloses a transverse shearing interference measurement device and method for realizing instantaneous two-step phase-shifting, and the Chinese invention patent with publication number CN106019913A discloses a 90° phase-shifting and calibration system and method based on two-step phase-shifting coaxial holography technology. Both of these two methods are based on the two-step phase-shifting method, and improve the phase reconstruction quality by changing the device. However, their optical paths are relatively complex, with large debugging difficulties, poor stability, and extremely easy to introduce additional errors, and they are not universal for the system wavefront test. Although this method can solve the phase-shifting error brought by the phase shifter itself, it cannot solve the tilt phase-shifting error brought by environmental vibration.

[0007] In summary, there is an urgent need for a high-precision, fast, efficient, and convenient detection means to achieve wavefront detection. Summary of the Invention

[0008] The object of the present invention is to solve the technical problems of large errors in the traditional phase-shifting interference detection method and the inability to reflect all the information of the wavefront, as well as the technical problem of the decline in phase reconstruction accuracy caused by the reduction of phase-shifting fringe patterns in the random tilt two-step phase-shifting detection method, and to provide a random two-step tilt phase-shifting wavefront detection method based on deep learning.

[0009] To achieve the above object, the technical solution provided by the present invention is as follows:

[0010] A random two-step tilt phase-shifting wavefront detection method based on deep learning, characterized in that it includes the following steps:

[0011] Step 1: Based on the light intensity expression of the interference pattern, obtain a wavefront phase simulation value and two frames of interference fringe patterns through simulation, and introduce interference factors to obtain two interference pattern databases; the interference factors include random tilt, noise, light intensity non-uniformity, random roughness, and surface profile waviness information;

[0012] Step 2: Establish a neural network model, use the interference pattern databases obtained in Step 1 as input parameters, and divide them into a training set and a test set;

[0013] Step 3: Input the training set into the neural network model for training to obtain a trained neural network model;

[0014] Step 4: Input the test set into the trained neural network model for testing and output the calculated value of the wavefront phase;

[0015] Step 5: Calculate the error between the calculated value of the wavefront phase output in Step 4 and the simulated value of the wavefront phase in Step 1. If the error meets the preset requirements, use the neural network model trained in Step 3 as the new neural network model; otherwise, return to Step 2 and optimize the neural network model through the loss function until the error between the calculated value of the wavefront phase output in Step 4 and the simulated value of the wavefront phase in Step 1 meets the preset requirements;

[0016] Step 6: Obtain multiple frames of interference fringe patterns of the optical element to be measured, input them into the new neural network model in Step 5, and output the true wavefront phase of the optical element to be measured, thereby realizing random two-step tilt phase-shifting wavefront detection based on deep learning.

[0017] Further, Step 1 is specifically:

[0018] Based on the light intensity expression I j (x, y) = I 0 (x, y) + I′(x, y) × cos[φ(x, y) + δ j , obtain a simulated value of the wavefront phase and two frames of interference fringe patterns through simulation, and introduce interference factors to obtain two interference pattern databases; where I j (x, y) represents the light intensity of any pixel in the two frames of interference fringe patterns, j = 1, 2; I 0 (x, y) represents the background light; I′(x, y) represents the modulated light; δ j represents the phase shift amount of the j-th frame of interference fringe pattern, and define the phase shift amount δ 1 = 0 of one of the frames of interference fringe patterns; φ(x, y) represents the simulated value of the wavefront phase, which is the low-frequency phase information represented by the Zernike polynomial;

[0019] The random tilt refers to the random tilt interference factor introduced into another frame of interference fringe pattern, and the phase shift amount δ 2 of this interference fringe pattern = δ + k × x + q × y; where δ represents the phase shift value, and δ ∈ (0, π), k represents the tilt amount of the phase shift plane around the X-axis during the phase shift process, q represents the tilt amount of the phase shift plane around the Y-axis during the phase shift process, and x, y respectively represent the pixel values along the X-axis and Y-axis directions in the phase shift plane;

[0020] The light intensity non-uniformity is obtained by simulating the background light and the modulated light using the Gaussian function.

[0021] Furthermore, in step 2, the neural network model is established based on the U-net network, which includes a feature fusion module and a feature mapping module; the feature fusion module includes two Resnet18 networks, which are used to implement image segmentation, feature extraction, classification, splicing, and fusion; the feature mapping module includes an encoder and a decoder, and the encoder is used to extract low-level features and high-level features; the decoder is used to fuse the low-level features and high-level features and output the test results.

[0022] Furthermore, step 3 specifically includes:

[0023] 3.1. Input the training set into the neural network model. The two Resnet18 networks of the neural network model respectively perform segmentation, feature extraction, and classification on the input training set, and then perform multi-dimensional splicing to obtain a two-channel feature map;

[0024] 3.2. Use 1×1 convolution to reduce the dimension of the two-channel feature map to obtain a single-channel feature map, and then splice and fuse it to obtain a feature fusion map;

[0025] 3.3. Extract the low-level features and high-level features in the feature fusion map through the encoder of the feature mapping module, then use the decoder to restore its resolution, and fuse the low-level features and high-level features to obtain the trained neural network model.

[0026] Furthermore, in step 3.1, there is also a step of using the RFB module for multi-branch convolution structure and dilated convolution to increase the receptive field of each feature after splitting after feature extraction and classification.

[0027] Furthermore, in step 3.2, there is also a step of performing data dimension reduction processing through the max pooling layer after obtaining the single-channel feature map, and at the same time increasing the network non-linearity through the leakyReLU activation function.

[0028] Furthermore, in step 5, the loss function uses the L 1 loss to calculate the gradient, and its expression is:

[0029]

[0030] In the formula, n is the total number of pixels in the output result map of the neural network model, is the pixel value of the output result map of the neural network model, and y i is the pixel value of the theoretical wavefront image, where 1 ≤ i ≤ n.

[0031] Further, in step 6, the interference fringe pattern of the optical element to be measured is obtained by an interference pattern acquisition device; the interference pattern acquisition device includes a laser, a converging lens, a beam expander, a beam splitter prism, a reference mirror, and an imaging detector;

[0032] The laser is a frequency conversion laser;

[0033] The converging lens, the beam expander, the beam splitter prism, and the reference mirror are arranged in sequence along the outgoing light path of the laser. Among them, the converging lens and the beam expander form a beam expansion and collimation system for adjusting the outgoing light into a parallel beam;

[0034] The reference mirror is located on the transmitted light path of the beam splitter prism, and the imaging detector is located on the reflected light path of the beam splitter prism; the beam splitter prism is used to divide the parallel beam into two beams of light. One beam of light is reflected and enters the imaging detector, and the other beam of light is transmitted, reaches the optical element to be measured after passing through the reference mirror, is reflected by the optical element to be measured and then returns to the beam splitter prism along the original path, and interferes with the reflected beam of light and then enters the imaging detector, thereby realizing the acquisition and imaging of the interference fringe pattern.

[0035] Further, in step 6, by randomly adjusting the pitch angles of the optical element to be measured and the reference mirror, different interference fringe patterns can be obtained.

[0036] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0037] 1. The present invention uses two-step phase shift to realize wavefront detection. Only two frames of interference fringe patterns are required and interference factors are randomly added, and then trained by a neural network model to obtain a new trained neural network model. After that, the interference fringe pattern of the optical element to be measured is input, and the true wavefront phase of the optical element to be measured can be output. This method reduces the number of interference pattern acquisitions, shortens the phase reconstruction time, and can obtain more accurate and complete phase information.

[0038] 2. The present invention is modeled and trained based on deep learning, which can eliminate tilt shift, compensate the accuracy of the phase shifter, and has low environmental requirements for the phase shifter.

[0039] 3. Based on deep learning, the present invention can directly solve the wavefront phase information without using Zernike fitting surface in practical applications, can accurately reflect the low-frequency, medium-frequency and high-frequency information of the wavefront, and can thus more comprehensively and completely reconstruct the system wavefront.

[0040] 4. The present invention can compensate the phase shift accuracy of the phase shifter, breaks through the limitations of high standards and strict requirements for the test environment in interference measurement, and provides guidance for in-situ detection of interference measurement. BRIEF DESCRIPTION OF THE DRAWINGS

[0041] Figure 1 It is a schematic flow chart of an embodiment of the present invention;

[0042] Figure 2 It is a schematic flow chart of obtaining the interference pattern database through simulation in step 1 of the embodiment of the present invention;

[0043] Figure 3 It is a neural network model diagram in step 2 of the embodiment of the present invention;

[0044] Figure 4 It is a schematic structural diagram of the interference pattern acquisition device in step 6 of the embodiment of the present invention.

[0045] The description of the reference numerals is as follows:

[0046] 1 - Laser; 2 - Converging lens; 3 - Beam expander; 4 - Beam splitter prism; 5 - Reference mirror; 6 - Optical element to be measured; 7 - Imaging detector. Detailed implementation manners

[0047] The inventive concept of the present invention is: based on a deep learning model, wavefront detection can be directly achieved through two frames of interference fringe patterns, without first obtaining the wrapped phase through traditional methods and then using the unwrapping algorithm and Zernike polynomial fitting to obtain wavefront information. The present invention establishes a data set through simulation according to the influencing factors encountered in actual tests. First, based on the light intensity formula of the interference pattern, formulas such as the interference measurement light source and phase shifter error, influencing factors including uneven illumination, random tilt of the phase shifter, random noise, roughness, and waviness are established on the original basic phase information; then, a neural network model for obtaining wavefront information is established by improving the U-net network, which can directly recover the wavefront phase information based on the deep learning network without Zernike fitting, retaining the low-frequency, medium-frequency, and high-frequency information of the original wavefront.

[0048] To make the purpose, advantages, and features of the present invention clearer, the following further details the present invention in conjunction with the accompanying drawings and specific embodiments. Those skilled in the art should understand that these embodiments are only used to explain the technical principle of the present invention, and the purpose is not to limit the protection scope of the present invention.

[0049] As Figure 1 shown, this embodiment provides a random two-step tilt phase-shifting wavefront detection method based on deep learning, including the following steps:

[0050] Step 1, in combination with Figure 1 and Figure 2 shown, a wavefront phase simulation value is obtained through simulation based on the light intensity expression of the interference pattern, and at the same time, two frames of interference fringe patterns are obtained. Then, interference factors are simulated and introduced into the interference fringe patterns to obtain two interference pattern databases; the interference factors include information such as random tilt, noise, uneven illumination, random roughness, and surface waviness.

[0051] To improve the accuracy of the established network model, a large amount of data needs to be provided for model training. Therefore, in this embodiment, based on the light intensity expression I of the interference pattern j (x,y) = I 0 (x,y) + I′(x,y) × cos[φ(x,y) + δ j , first, two frames of interference fringe patterns are simulated and generated. Assuming that there are m×n pixel points in each frame of the interference fringe pattern, then I j (x,y) represents the light intensity of any pixel point (x,y) in the two frames of interference fringe patterns, where j = 1, 2; I 0 (x,y) represents the background light; I′(x,y) represents the modulated light; δ j represents the phase shift amount of the j-th frame of the interference fringe pattern. It is defined that the phase shift amount δ of one of the frames of the interference fringe pattern 1 = 0; φ(x,y) represents the simulated value of the wavefront phase, which is the low-frequency phase information represented by the Zernike polynomial.

[0052] To compensate for the phase shift error introduced by the phase shifter in the interference measurement, a random tilt is introduced to the other frame of the interference fringe pattern during the simulation. Then, the phase shift amount δ of this interference fringe pattern 2 = δ + k×x + q×y; where δ represents the phase shift value. Considering that the cosine function is an even function and has periodicity, then δ ∈ (0,π), k represents the tilt amount of the phase shift plane around the X-axis during the phase shift process, and q represents the tilt amount of the phase shift plane around the Y-axis during the phase shift process. In the coordinate values of the phase shift plane, the direction along the optical axis is defined as the Z-axis direction, and the X / Y axes are the Cartesian coordinate systems that satisfy the right-hand rule. The x and y in the above formula are the pixel values of the phase shift plane in this coordinate system. In addition, the phase and the pixel values of the phase shift plane have a one-to-one correspondence relationship.

[0053] Since the light source used in the interference measurement is a laser light source, considering that the beam output by the laser is a Gaussian beam, the background light and the modulation degree are both simulated using the Gaussian function shown in the following formula:

[0054] a×exp[b×(x 2 +y 2 )]

[0055] where a represents the amplitude and b represents the waist radius of the Gaussian beam. This step will introduce the influencing factor of light intensity non-uniformity to the obtained interference pattern.

[0056] Based on the above settings, a series of phase-shifting interference fringe patterns affected by multiple factors such as random tilt, noise, and uneven illumination can be generated. Then, information such as simulated random roughness and surface waviness is randomly added. Finally, an interference pattern database of two frames of interference fringe patterns is obtained, and the simulated value of the wavefront phase is directly known at this time, which is composed of the phase of each point.

[0057] Step 2: Establish a neural network model. Using the two interference pattern databases obtained in Step 1 as the total database, take this total database as the input parameter, and divide this input parameter into a training set and a test set. At this time, both the training set and the test set include the data information of two interference patterns.

[0058] As Figure 3 shown, the neural network model of this embodiment is established based on the U-net network. It mainly includes a feature fusion module and a feature mapping module. Of course, it also includes other core modules of the traditional U-net network, such as the RFB module (receptive field block), etc. The feature fusion module of this embodiment includes two Resnet18 networks, which are used to implement image segmentation, feature extraction, classification, splicing, and fusion. The feature mapping module includes an encoder and a decoder. Among them, the encoder is used to extract low-level features and high-level features; the decoder is used to perform fusion calculations on the low-level features and high-level features and output the test results. This neural network model can realize the preprocessing process of the input data and has no requirement for the resolution of the input interference pattern.

[0059] Step 3: Input the training set into this neural network model for training to obtain the trained neural network model. Specifically:

[0060] 3.1. Input the training set into this neural network model. First, the two Resnet18 networks of the neural network model are used to separately segment, extract features, and classify the input training set; then, the RFB module is used for multi-branch convolutional structure and dilated convolution to increase the receptive field of each feature after splitting. This process helps the neural network model better understand various target and background information in the image, thereby improving the accuracy and speed of detection; then, multi-dimensional Concat splicing is performed to obtain a two-channel feature map.

[0061] 3.2. Use 1×1 convolution to reduce the dimension of the two-channel feature map to output a single-channel feature map. To achieve information interaction between the two interference patterns, data dimensionality reduction processing can be performed through the max-pooling layer. At the same time, the leakyReLU activation function is used to increase the nonlinearity of the network, and then splicing and fusion are performed to achieve the fusion of interference fringe features.

[0062] 3.3 After completing feature fusion, rich low-level and high-level features in the feature fusion map are extracted by the encoder of the feature mapping module, and then the decoder is used to restore its resolution, and the low-level and high-level features are fused to obtain an accurate result with context information, thereby completing the training of the neural network model and obtaining the trained neural network model.

[0063] In this embodiment, the output layer of the network model is mainly modified by adding a 1×1 convolutional layer and using the leaky Relu activation function to non-linearly transform the feature map, and finally the output result is obtained to obtain the corresponding true wavefront. LeakyReLU is an improved algorithm based on the ReLU activation function, which allows a small part of the values on the negative axis to pass through (multiplied by a small slope α), solving the problem of dead neurons that may occur in ReLU.

[0064] Step 4: Input the test set into the trained neural network model for testing and output the calculated value of the wavefront phase.

[0065] Step 5: Calculate the error between the calculated value of the wavefront phase output in Step 4 and the simulated value of the wavefront phase described in Step 1. If the error meets the preset requirements, the trained neural network model is used as the new neural network model. If the error does not meet the preset requirements, return to Step 2 and iterate and optimize the neural network model through the loss function until the error between the calculated value of the wavefront phase output in Step 4 and the simulated value of the wavefront phase described in Step 1 meets the preset requirements, thereby obtaining a new neural network model. Input two frames of interference fringe images into the new neural network model, and the wavefront corresponding to the interference fringe images can be obtained.

[0066] In this embodiment, the loss function uses L 1 loss to calculate the gradient, and its expression is:

[0067]

[0068] In the formula, n is the total number of pixels in the output result map of the neural network model, is the pixel value of the output result map of the neural network model, y i is the pixel value of the theoretical wavefront image, and 1 ≤ i ≤ n.

[0069] The loss function is used to measure the gap between the network output result and the labeled image (theoretical wavefront image). Through cyclic iteration, the output result can be made infinitely close to the theoretical wavefront image. The purpose of the neural network training iteration is to make the loss function approach 0. In this embodiment, the network training process is set to 200 epochs (which can also be adjusted according to the training situation), and the early stopping method is set to prevent overfitting. That is, when the loss of the training set no longer decreases, or the decrease degree in consecutive k epochs (the value of k can be set as required) is less than a certain threshold, the network stops training in advance.

[0070] The loss function can obtain the difference between the output phase information result map after modeling and the ideal phase map, and then perform iteration and optimization, continuously adjusting the feature problems in the model, and finally obtaining the optimal result to achieve the optimal model. To prevent the training from not converging effectively due to the too small real wavefront, the real wavefront information can be amplified before the output image.

[0071] Step 6: Obtain the wavefront phase interference fringe maps of multiple frames of the optical element to be measured, and input them into the new neural network model described in Step 5, then the real wavefront phase of the optical element to be measured can be output, thus realizing the random two-step tilt phase-shifting wavefront detection based on deep learning.

[0072] This method overcomes the problems of the traditional method of obtaining the wavefront using Zernike polynomials, and does not need to restrict the shape of the measured system and optical elements. It can directly obtain the surface shape information of the low-frequency wavefront, as well as the intermediate-frequency (ripple) and high-frequency (roughness) information.

[0073] Since the previous model establishment was all carried out based on the data obtained from simulation, but considering that there are certain differences between the data obtained from simulation and the data obtained from experiments, therefore, a large amount of wavefront information to be measured needs to be selected. Based on this, in this embodiment, a series of wavefront phase interference fringe maps of the optical element to be measured are obtained through the interference image acquisition device, and then imported into the new neural network model obtained in Step 5, and the wavefront phase of the optical element to be measured can be obtained. Based on this new neural network model, the wavefront information of the optical element to be measured can be extracted with high precision and high robustness.

[0074] As Figure 4 shown, the interference image acquisition device of this embodiment includes a laser 1, a converging lens 2, a beam expander 3, a beam splitter prism 4, a reference mirror 5 and an imaging detector 7. Among them, the laser 1 is a frequency conversion laser; the converging lens 2, the beam expander 3, the beam splitter prism 4, and the reference mirror 5 are arranged in sequence along the outgoing light path of the laser 1. Among them, the converging lens 2 and the beam expander 3 form an expanding and collimating system for adjusting the outgoing light into a parallel beam.

[0075] The standard mirror 5 is located on the transmission optical path of the beam splitting prism 4, and the imaging detector 7 is located on the reflection optical path of the beam splitting prism 4; the beam splitting prism 4 is used to divide the parallel beam into two beams of light, one of which is reflected into the imaging detector 7, and the other is transmitted and then reaches the optical element 6 to be measured through the standard mirror 5, and then is reflected by the optical element 6 to be measured and returns to the beam splitting prism 4 along the original path, and interferes with the reflected beam of light and then enters the imaging detector 7, so as to realize the acquisition and imaging of the interference fringe pattern.

[0076] When using this interference pattern acquisition device, first place all the devices on the air-bearing platform, turn on the light source of the laser 1, and place a light screen behind the laser 1. Translate the light screen back and forth to adjust the pitch angle of the laser 1 until the position of the laser spot on the light screen remains unchanged.

[0077] Then remove the light screen and place the converging lens 2 and the beam expander lens 3 to achieve the purpose of beam expansion and collimation. During this process, move the rear light screen to verify whether the beam after beam expansion and collimation is a parallel beam.

[0078] Then, the parallel beam is split into two beams of light by the 1:1 beam splitting prism 4. Among them, the transmitted beam is incident on the standard mirror 5, and the incident beam that is not perpendicular to the standard mirror 5 will be reflected outside the field of view, and the incident beam that is perpendicularly incident on the standard mirror 5 is irradiated on the optical element 6 to be measured after passing through the standard mirror 5. Then, after being reflected by the optical element 6 to be measured, the beam returns to the beam splitting prism 4 along the original path, interferes with the beam reflected by the beam splitting prism 4, and finally is collected by the imaging detector 7.

[0079] Finally, by randomly adjusting the pitch angles of the optical element 6 to be measured and the standard mirror 5, two interference fringe patterns can be obtained. The interference fringe patterns are input into the computer through the imaging detector 7. The new neural network model described above has been loaded in the computer here, and then the wavefront phase information of the optical element 6 to be measured can be directly obtained through this new neural network model.

[0080] The present invention establishes a model of fringes and wavefronts based on an end-to-end neural network, realizes that the wavefront of the optical element can be directly solved only with two frames of interference fringe patterns, can compensate for the phase shift accuracy of the phase shifter (including the phase shift amount error and the tilt error during phase shift), reduces the complexity of the measurement system, reduces the calculation time for extracting the phase shift amount or restoring the phase, is simple to operate, and has high measurement accuracy. At the same time, it can also compensate for the wavefront reconstruction error introduced by noise and the calibration error of the test system (i.e., uneven illumination). Therefore, this technology can break through the limitations of high standards and strict requirements for the test environment in interference measurement and provide guidance for in-situ detection of interference measurement.

[0081] The model established by the present invention based on deep learning has no resolution requirement for the input image, and the wavefront information can be solved without phase extraction and phase unwrapping, and the tilt phase-shifting error caused by phase shifting can be compensated, and the requirements for the phase shifter and the test environment are extremely low. The true wavefront information can be directly obtained through two interference patterns. Therefore, the present invention can break through the limitations of high standards and strict requirements for the test environment in interferometric measurement, and provide a direction for in-situ detection of interferometric measurement.

[0082] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit them. Although the present invention has been described in detail with reference to the foregoing embodiments, those of ordinary skill in the art should understand that they can still modify the technical solutions described in the foregoing embodiments, or perform equivalent replacements for some or all of the technical features, but these modifications or replacements do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the present invention.

Claims

1. A random two-step tilt phase shift wavefront detection method based on deep learning, characterized in that: The following steps are involved: Step 1: Based on the light intensity expression of the interference pattern, a wavefront phase simulation value and two interference fringe patterns are obtained by simulation, and interference factors are introduced to obtain two interference pattern databases; the interference factors include random tilt, noise, illumination unevenness, random roughness and surface waviness information; Step 2: Establish a neural network model, use the interference pattern database obtained in step 1 as input parameters, and divide it into a training set and a test set; Step 3: input the training set into the neural network model for training to obtain a trained neural network model; Step 4: Input the test set into the trained neural network model for testing, and output the wavefront phase calculation value; Step 5, calculating the error between the wavefront phase calculation value outputted from step 4 and the wavefront phase simulation value described in step 1. If the error meets the preset requirements, the neural network model trained in step 3 is used as a new neural network model; otherwise, returning to step 2, and optimizing the neural network model through the loss function until the error between the wavefront phase calculation value outputted from step 4 and the wavefront phase simulation value described in step 1 meets the preset requirements; Step 6: Obtain multiple frames of interference fringe patterns of the optical element to be tested, input them into the new neural network model described in step 5, and output the real wavefront phase of the optical element to be tested, thereby realizing random two-step tilt phase shift wavefront detection based on deep learning.

2. The random two-step tilt phase shift wavefront detection method based on deep learning according to claim 1 is characterized in that: Step 1 is as follows: Light intensity expression based on interference pattern I j (x,y)=I0(x,y)+I′(x,y)×cos[φ(x,y)+δ j ], a wavefront phase simulation value and two interference fringe patterns are obtained by simulation, and interference factors are introduced to obtain two interference pattern databases; among them, I j (x, y) represents the light intensity of any pixel in the two-frame interference fringe pattern, j = 1, 2; I0(x, y) represents the background light; I′(x, y) represents the modulated light; δ j represents the phase shift of the j-th frame interference fringe pattern, and defines the phase shift of one frame interference fringe pattern as δ1=0; φ(x, y) represents the wavefront phase simulation value, which is the low-frequency phase information represented by the Zernike polynomial; The random tilt refers to the random tilt interference factor introduced into another frame of the interference fringe pattern, and the phase shift of the interference fringe pattern is δ2=δ+k×x+q×y; wherein δ represents the phase shift value, and δ∈(0,π), k represents the tilt of the phase shift plane around the X axis during the phase shift process, q represents the tilt of the phase shift plane around the Y axis during the phase shift process, and x and y represent the pixel values ​​along the X axis and Y axis directions in the phase shift plane, respectively; The illumination unevenness is obtained by simulating the background light and the modulated light using a Gaussian function.

3. The random two-step tilt phase shift wavefront detection method based on deep learning according to claim 1 is characterized in that: In step 2, the neural network model is established based on the U-net network, which includes feature fusion module and feature mapping module; the feature fusion module includes two Resnet18 networks for realizing image segmentation, feature extraction, classification, splicing and fusion; The feature mapping module includes an encoder and a decoder, wherein the encoder is used to extract low-level features and high-level features; The decoder is used to fuse the low-level features with the high-level features and output the test results.

4. The random two-step tilt phase shift wavefront detection method based on deep learning according to claim 3 is characterized in that: Step 3 is as follows: 3.

1. Input the training set into the neural network model. The two Resnet18 networks of the neural network model segment, extract features and classify the input training set respectively, and then perform multi-dimensional splicing to obtain a dual-channel feature map; 3.

2. Use 1×1 convolution to reduce the dimension of the dual-channel feature map to obtain a single-channel feature map, and then concatenate and fuse them to obtain a feature fusion map; 3.

3. The encoder of the feature mapping module is used to extract the low-level features and high-level features in the feature fusion map, and then the decoder is used to restore its resolution, and the low-level features and high-level features are fused to obtain the trained neural network model.

5. The random two-step tilt phase shift wavefront detection method based on deep learning according to claim 4 is characterized in that: Step 3.1 also includes the step of performing multi-branch convolution structure and dilated convolution through the RFB module to increase the receptive field of each feature after splitting after feature extraction and classification.

6. The random two-step tilt phase shift wavefront detection method based on deep learning according to claim 5 is characterized in that: Step 3.2 also includes the steps of performing data dimensionality reduction through the maximum pooling layer after obtaining the single-channel feature map, and increasing the network nonlinearity through the leakyReLU activation function.

7. The random two-step tilt phase shift wavefront detection method based on deep learning according to claim 1 is characterized in that: In step 5, the loss function uses L1 loss for gradient calculation, and its expression is: Where n is the total number of pixels in the output result image of the neural network model, is the pixel value of the neural network model output result image, y i is the pixel value of the theoretical wavefront image, 1≤i≤n.

8. The random two-step tilt phase shift wavefront detection method based on deep learning according to claim 1 is characterized in that: In step 6, the interference fringe pattern of the optical element to be measured is obtained by an interference pattern acquisition device; The interference pattern acquisition device comprises a laser (1), a converging lens (2), a beam expanding lens (3), a beam splitting prism (4), a standard mirror (5) and an imaging detector (7); The laser (1) is a frequency-converting laser; The converging lens (2), the beam expanding lens (3), the beam splitting prism (4), and the standard mirror (5) are arranged in sequence along the outgoing light path of the laser (1), wherein the converging lens (2) and the beam expanding lens (3) form a beam expanding and collimating system for adjusting the outgoing light into a parallel beam; The standard mirror (5) is located on the transmission light path of the beam splitter prism (4), and the imaging detector (7) is located on the reflection light path of the beam splitter prism (4); the beam splitter prism (4) is used to split the parallel light beam into two paths of light, one path of light is reflected and enters the imaging detector (7), and the other path of light is transmitted and reaches the optical element to be measured (6) through the standard mirror (5), and then returns to the beam splitter prism (4) along the original path after being reflected by the optical element to be measured (6), and enters the imaging detector (7) after interfering with the reflected path of light, thereby realizing the collection and imaging of the interference fringe pattern.

9. The random two-step tilt phase shift wavefront detection method based on deep learning according to claim 8, characterized in that: In step 6, different interference fringe patterns can be obtained by randomly adjusting the pitch angles of the optical element to be measured (6) and the standard mirror (5).

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