Single-frame interferogram demodulation method based on convolutional neural network

Abstract

The invention discloses a single-frame interference pattern demodulation method based on a convolutional neural network, and the specific steps are as follows: constructing a convolutional neural network (CNN) for phase demodulation of a single-frame interference pattern; combining an experimental interference system, establishing an interference data simulation model, and making a data set required for CNN training, wherein the data set includes a wrapped phase, a wrapped order, and an interference pattern; using the interference pattern in the data set as the input of the CNN, and the corresponding wrapped phase and wrapped order in the data set as the output of the CNN, and training the network; inputting the interference pattern collected by the interferometer into the trained network model, and the network outputs the wrapped phase and wrapped order; summing the wrapped phase and wrapped order to obtain the absolute phase of the interference pattern. The invention can solve the phase from a single interference pattern with high precision, and does not require a phase unpacking process, has high measurement efficiency and measurement accuracy, and has broad application prospects in the fields of interferometry.

Description

Technical Field

[0001] The invention belongs to the field of interference measurement and machine learning, and in particular relates to a single-frame interference pattern demodulation method based on a convolutional neural network (CNN for short). Background Art

[0002] Optical interferometry is recognized as one of the most effective methods for optical surface measurement due to its non-contact, fast, and high nanoscale measurement accuracy. In the interferometer, the measured surface is encoded in the interference pattern. Therefore, the demodulation of the interference pattern is crucial in interferometric measurement, and its demodulation accuracy and demodulation speed directly affect the performance of the interferometer.

[0003] As the most commonly used method for high-precision phase extraction, time phase-shifting interferometry requires a stable measurement environment during the measurement process. Therefore, it is not suitable for measurements under unstable conditions such as vibration and turbulence, such as online detection at the processing site or detection of large-aperture components under a long interference cavity. At present, there are three main methods to solve this problem: single-frame interferogram demodulation (SFID) technology, random phase-shifting interferometry (RPSI) technology, and spatial phase-shifting interferometry (SPSI) technology. SFID technology includes fast Fourier transform (FFT), polar coordinate transformation (PCT), and regularized phase tracker (RPT). Compared with the phase shift method, the SFID method has lower accuracy and inherent limitations in application. For example, FFT is only applicable to open straight stripes, while PCT is only applicable to circular stripes. The RPT method requires manual parameter setting, and the calculation process is time-consuming, which is not suitable for real-time measurement. RPSI mainly includes principal component analysis (PCA) and iterative algorithms. The accuracy of the PCA method is affected by the number of fringes, and the tilt phase shift error caused by vibration cannot be eliminated. The iterative algorithm takes a long time, and its accuracy depends on the accuracy of the initial value of the iteration and the uniformity of the background intensity and modulation. SPSI generally uses prisms, diffraction elements or micro-polarization elements to perform spatial polarization phase shift on light, thereby obtaining four phase-shifted interference patterns at the same time. SPSI increases the complexity of the system and introduces systematic errors. It also has disadvantages such as reduced resolution of interference patterns, inaccurate phase shift, and difficulty in interferogram registration. Moreover, no matter which method is used, only a discontinuous wrapped phase can be directly obtained. In order to obtain the true surface of the measured part, phase unwrapping is required, and this process reduces the efficiency of the measurement.

[0004] As a data-driven machine learning technology, CNN has developed rapidly in recent years and has been widely used in various fields. In the field of optics, CNN has been applied to image preprocessing, phase recovery, phase unwrapping, super-resolution imaging, lensless imaging, and system calibration. However, there are few studies on the application of CNN to high-precision surface measurement. In 2019, Feng et al. first applied CNN to high-precision phase demodulation of a single fringe pattern with a root mean square accuracy of 0.016λ, but this method is only applicable to periodic straight stripes. Kando et al. used CNN to recover the phase from a closed fringe pattern, but the relative root mean square accuracy was only 0.027. Liu et al. proposed a demodulation method to extract the Zernike coefficients of the target to be measured from a single interferogram, but this method loses the high-frequency information of the measured part and is not suitable for complex surfaces that cannot be fitted with Zernike polynomials with high precision. Summary of the invention

[0005] The purpose of the present invention is to provide a single-frame interference pattern demodulation method based on a convolutional neural network, which solves the problem that traditional methods are difficult to achieve high-precision and rapid detection under unstable conditions such as online detection at the processing site and detection of large-aperture components under a long interference cavity.

[0006] The technical solution to achieve the purpose of the present invention is: a single-frame interference pattern demodulation method based on a convolutional neural network, comprising the following steps:

[0007] S1. Construct a convolutional neural network model CNN for phase demodulation of single-frame interference patterns;

[0008] S2. Combine the experimental interference system to establish an interference data simulation model and produce the data set required for CNN training. The data set includes simulated package phase, simulated package order and simulated interference pattern.

[0009] S3, using the simulated interference pattern in the data set as the input of the CNN, and the corresponding simulated package phase and simulated package order in the data set as the output of the CNN, training the CNN to obtain a trained CNN;

[0010] S4, input the interference pattern collected by the experimental interference system into the trained CNN, and the CNN outputs the package phase and package order;

[0011] S5, summing the wrapping phase and the wrapping order to obtain the absolute phase of the interference pattern;

[0012] Compared with the prior art, the present invention has the following significant advantages:

[0013] (1) The present invention is based on CNN high-precision phase demodulation. After training CNN with a training set, the input interference pattern can be directly converted into the output wrapped phase and wrapped order. There is no need to perform the phase unwrapping process, and it has good measurement efficiency. Simulation and experimental results show that the time required to demodulate a single-frame interference pattern is only 0.02 seconds.

[0014] (2) The present invention demodulates a single-frame interference pattern through CNN, and there is no systematic error caused by the phase shifting method, and no complex demodulation algorithm is required, so the method has high solution accuracy. The experimental results of the method of the present invention are compared with the experimental results of the Zygo interferometer. The method of the present invention has a root mean square accuracy better than 0.01λ (λ=632.8nm). BRIEF DESCRIPTION OF THE DRAWINGS

[0015] Figure 1 It is a flow chart of a single-frame interference pattern demodulation method based on a convolutional neural network of the present invention.

[0016] Figure 2 It is a network structure diagram of the present invention.

[0017] Figure 3 Graph 1 is a structural diagram of the residual block of the present invention.

[0018] Figure 4 is the input interference pattern.

[0019] Figure 5 is the wrapped phase plot of the corresponding output.

[0020] Figure 6 is the corresponding output package level graph.

[0021] Figure 7 is the absolute phase diagram. DETAILED DESCRIPTION

[0022] The present invention will be described in detail below in conjunction with the accompanying drawings.

[0023] Combination Figure 1 The single-frame interferogram demodulation method based on convolutional neural network of the present invention simultaneously extracts the package phase and the package order distribution of the single-frame interferogram without additional expansion processing, and includes the following steps:

[0024] S1. Construct a convolutional neural network model CNN for phase demodulation of single-frame interference patterns.

[0025] Figure 2The network structure described in S1 is shown, where each solid line box represents a corresponding feature map, and each dotted line box represents a corresponding unit. The specific structure of CNN is as follows: the CNN includes 1 input unit, 4 downsampling units and 4 upsampling units. The interference pattern is used as the input of CNN, that is, the input data of the input unit is sequentially output after passing through 1 convolution block (convblock) and 2 residual blocks (resblock), wherein the convolution block includes a batch normalization layer (BN), an excitation layer (ReLU) and a convolution layer arranged in sequence; the output data of the input unit is used as the input data of the first downsampling unit, and the data is output after passing through 1 maximum pooling layer, 1 convolution block and 2 residual blocks in sequence; the output data of the first downsampling unit is used as the input data of the second downsampling unit, and the data is output after passing through 1 maximum pooling layer, 1 convolution block and 2 residual blocks in sequence; the output data of the second downsampling unit is used as the input data of the third downsampling unit, and the data is output after passing through 1 maximum pooling layer, 1 convolution block and 2 residual blocks in sequence; the output data of the third downsampling unit is used as the input data of the fourth downsampling unit, and the data is output after passing through 1 maximum pooling layer, 1 convolution block and 2 residual blocks and 1 upsampling layer in sequence; the output data of the fourth downsampling unit is used as the input data of the The input data of the first upsampling unit is connected with the output data of the third downsampling unit through the connection layer, and then sequentially passes through 1 convolution block, 2 residual blocks and 1 upsampling layer to output data; the output data of the first upsampling unit is used as the input data of the second upsampling unit, connected with the output data of the second downsampling unit through the connection layer, and then sequentially passes through 1 convolution block, 2 residual blocks and 1 upsampling layer to output data; the output data of the second upsampling unit is used as the input data of the third upsampling unit, connected with the output data of the first downsampling unit through the connection layer, and then sequentially passes through 1 convolution block, 2 residual blocks and 1 upsampling layer to output data. The output data of the first upsampling unit is connected, and then successively passes through 1 convolution block, 2 residual blocks and 1 upsampling layer to output the data; the output data of the third upsampling unit is used as the input data of the fourth upsampling unit, connected with the output data of the input unit through the connection layer, and then successively passes through 1 convolution block, 2 residual blocks and 1 convolution layer to output the wrapped phase and the wrapped level, and the convolution layer uses a tanh function to limit the output to [-1, 1], and the value range of [-1, 1] corresponds linearly to the value range of the wrapped phase ([-π, π]).

[0026] Figure 3 The structural diagram of the residual block is shown. The residual block consists of two consecutive convolution blocks and a jump connection from input data. The input data passes through two consecutive convolution blocks and is added to the input data of the jump connection and output.

[0027] S2. Combined with the experimental interference system, an interference data simulation model is established to produce the data set required for CNN training. The data set includes simulated package phase, simulated package order and simulated interference pattern, as follows:

[0028] S21. In the process of establishing the data set, a data set for CNN training is generated through a data simulation model. The data set includes three parts: wrapped phase, wrapped order, and interference pattern. The interference pattern can be expressed as:

[0029]

[0030] Where I(x, y) is the light intensity distribution of the simulated interference pattern, A(x, y) is the background intensity, B(x, y) is the modulation amplitude, is the phase to be recovered. First, the following random phase distribution is generated using Zernike polynomials:

[0031]

[0032] where a i is the i-th Zernike basis function Z i The coefficients are numbered i = 1, 2, 3, ..., n. The simulation uses the first 36 Zernike polynomials. The Zernike coefficients are generated by a random function, where a1 is 0, a2, a3 ranges from [0, 5], a4 ranges from [-5, 5], a5 to a9 ranges from [-0.3, 0.3], and a 10 ~a 36 The value range of is [-0.03, 0.03]. The first term represents the axial displacement, which does not affect the shape of the phase, so a1 is set to 0. The second and third terms represent the tilt, and the fourth term is the defocus. Items 5-9 are raw aberrations, which are usually the main aberrations of the measured part. The rest are higher-order aberrations, which are usually small.

[0033] After the phase S22 is generated, the corresponding simulation package phase and simulation package order can be obtained by formula (3):

[0034]

[0035] Where <> is a rounding operator, Φ(x, y) is the simulated wrapping phase, and m(x, y) is the simulated wrapping order. The simulated wrapping order at the center of the interference pattern is 0. M is the maximum wrapping number of the phase, which is a positive integer. Considering the possible number of interference fringes and numerical stability in actual measurement, M is set to 8, that is, the maximum number of fringes in the interference pattern is less than 16.

[0036] S23, generate background intensity and modulation amplitude. It can be assumed that the reference light and the test light have the same intensity distribution, but different intensity amplitudes, that is,

[0037] I t (x, y) = wI r (x, y) (4)

[0038] In the formula, t (x, y) is the test light intensity, I r (x, y) is the reference light intensity, w is the ratio of the two light intensities. w is [0.2, 1]

[0039] Then, the background intensity and modulation amplitude are expressed as:

[0040] A(x,y)=(w+1)I r (x,y) (5)

[0041]

[0042] Interferometers usually use laser light sources whose intensity satisfies Gaussian distribution. Therefore, the reference light intensity can be expressed as:

[0043]

[0044] Where A0 is the intensity amplitude. x0 and y0 represent the offset of the point in the x and y directions, which are randomly generated in the range of [-0.2, 0.2]. σ is the beam width, which is randomly generated in the range of [0.9, 1, 1]. Combining equations (1) and (4)-(7), the normalized intensity of any point in the simulated interference pattern should satisfy

[0045]

[0046] S24. The present invention simulates the background noise of the actual interferometer as much as possible. First, the reference light intensity of the Zygo interferometer is collected and Gaussian fitting is performed on it. Then, the fitting term is subtracted from the reference light intensity, and the difference is the background noise sample of the Zygo interferometer. Since the noise collected by the interferometer includes more pixels than the simulated interference pattern, a noise with the same pixel size as the simulated interference pattern is randomly intercepted from it each time and added to I (x, y) to obtain a simulated reference light. Gaussian noise is added to the simulated reference light to enhance the diversity of the data.

[0047] S25. Generate a simulated interference pattern according to the simulated reference light and the generated random phase.

[0048] S3. Take the simulated interference pattern in the data set as the input of CNN, and the corresponding simulated package phase and simulated package order in the data set as the output of CNN, train the CNN, and obtain the trained CNN.

[0049] In the present invention, the interference pattern in the data set is used as the input of CNN, the wrapping phase and wrapping order corresponding to the interference pattern in the data set are used as the output of CNN, and the mean square error (MSE) is used as the loss function Loss, which is defined as follows:

[0050]

[0051] Where C is the number of samples, sample number j = 1, 2...C, x i and i are output data and true value data respectively. The present invention uses an adaptive moment estimation method (Adam) to optimize the weights during the training process. The learning rate (lr) is the variable value defined by formula (11). The network was trained for a total of 120 cycles, with a batchsize of 8 and 512 steps per cycle. The network was implemented under the Tensorflow platform and the Keras framework. The training process takes about 28 hours. After about 100 trainings, the loss function values ​​of the training set and the validation set converged.

[0052]

[0053] S4. The interference pattern collected by the experimental interference system is input into the trained CNN, and the CNN outputs the package phase and package order.

[0054] S5. Sum the wrapping phase and the wrapping order to obtain the absolute phase of the interference pattern.

[0055] In this example, simulation data is used to verify the proposed method. After network training, the average solution time of each interference pattern is 0.02 seconds using the generated test set. Figure 4 The input interference pattern is shown, and the output is Figure 5 The wrapped phase and Figure 6 The package level shown, the two outputs are added to get Figure 7 The absolute phase is shown.

[0056] In summary, the present invention can calculate the phase with high precision from a single interference pattern, and does not require a phase unpacking process, has high measurement efficiency and measurement accuracy, and has broad application prospects in fields such as interferometry.

Claims

1. A single-frame interference pattern demodulation method based on convolutional neural network, characterized in that: The following steps are involved: S1. Construct a convolutional neural network model CNN for phase demodulation of single-frame interference patterns; S2. Combine the experimental interference system to establish an interference data simulation model and produce the data set required for CNN training. The data set includes simulated package phase, simulated package order and simulated interference pattern. S3, using the simulated interference pattern in the data set as the input of the CNN, and the corresponding simulated package phase and simulated package order in the data set as the output of the CNN, training the CNN to obtain a trained CNN; S4, input the interference pattern collected by the experimental interference system into the trained CNN, and the CNN outputs the package phase and package order; S5, summing the wrapping phase and the wrapping order to obtain the absolute phase of the interference pattern; The CNN includes 1 input unit, 4 downsampling units and 4 upsampling units. The specific structure is as follows: The interference graph is used as the input of CNN, i.e., the input data of the input unit, and outputs data after passing through one convolution block and two residual blocks in sequence; The output data of the input unit is used as the input data of the first downsampling unit, and is output after passing through 1 maximum pooling layer, 1 convolution block and 2 residual blocks in sequence; The output data of the first downsampling unit is used as the input data of the second downsampling unit, and the data is output after passing through 1 maximum pooling layer, 1 convolution block and 2 residual blocks in sequence; The output data of the second downsampling unit is used as the input data of the third downsampling unit, and is output after passing through 1 maximum pooling layer, 1 convolution block and 2 residual blocks in sequence; The output data of the third downsampling unit is used as the input data of the fourth downsampling unit, and is output after passing through 1 maximum pooling layer, 1 convolution block, 2 residual blocks and 1 upsampling layer in sequence; The output data of the fourth down-sampling unit is used as the input data of the first up-sampling unit. The first up-sampling unit is connected with the output data of the third down-sampling unit via a connection layer, and then outputs the data after passing through one convolution block, two residual blocks and one up-sampling layer in sequence. The output data of the first upsampling unit is used as the input data of the second upsampling unit. The second upsampling unit is connected to the output data of the second downsampling unit via a connection layer, and then outputs data after passing through 1 convolution block, 2 residual blocks and 1 upsampling layer in sequence; The output data of the second upsampling unit is used as the input data of the third upsampling unit. The third upsampling unit is connected to the output data of the first downsampling unit via a connection layer, and then outputs data after passing through one convolution block, two residual blocks and one upsampling layer in sequence. The output data of the third upsampling unit is used as the input data of the fourth upsampling unit. The fourth upsampling unit is connected to the output data of the input unit via a connection layer, and then sequentially outputs the wrapped phase and the wrapped level via one convolution block, two residual blocks and one convolution layer; In S2, combined with the experimental interference system, an interference data simulation model is established to produce the data set required for CNN training. The specific steps are as follows: S21. The light intensity distribution I(x, y) of the simulated interference pattern satisfies the formula: Among them, A(x, y) is the background intensity, B(x, y) is the modulation amplitude, is the phase distribution; Generate a random phase distribution using Zernike polynomials: Among them, a i is the ith Zemike basis function Z i The coefficients of , the coefficient serial number i = 1, 2, 3, ..., n; the simulation uses the first 36 Zernike polynomials, and the Zernike coefficients are generated by a random function; S22, according to random phase distribution Get the corresponding simulated package phase and simulated package order: Where <> is a rounding operator, Φ(x, y) is the simulated wrapping phase, m(x, y) is the simulated wrapping order; the wrapping order at the center of the interference pattern is 0; M is the maximum wrapping number of the phase, which is a positive integer; S23, establish the intensity model of the reference light and the test light to generate the background intensity and modulation amplitude of the data simulation model, wherein the intensity distribution of the reference light and the test light is the same, and the reference light intensity I r (x, y) and test light intensity I t (x, y) has a proportional relationship: I t (x,y)=wI r (x,y) (4) In the formula, I t (x, y) is the test light intensity, I r (x, y) is the reference light intensity, w is the ratio of the two light intensities; the background intensity A(x, y) and the modulation amplitude B(x, y) are expressed as: A(x,y)=(w+1)I r (x,y) (5) The reference light intensity I r (x, y) satisfies Gaussian distribution, expressed as: Where A0 is the intensity amplitude, x0 and y0 correspond to the offset of the point in the x and y directions, and σ is the reference light beam width; Combining equations (1), (4)-(7), the conditions for the normalized intensity I(x, y) of any point in the simulated interference pattern to satisfy are: S24, simulate the background noise of the interferometer, the steps are as follows: S24.

1. Collect the reference light intensity of the interferometer and perform Gaussian fitting on it; S24.2, subtract the fitted term from the reference light intensity, and the difference is the background noise sample of the interferometer; S24.3, randomly intercept a noise with the same pixel size as the simulated interference pattern from the background noise sample of the interferometer each time and add it to I(x, y), and then add Gaussian noise to obtain simulated reference light; S25. Generate a simulated interference pattern according to the simulated reference light and the generated random phase.

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