A refractive index reconstruction method

Abstract

This invention discloses a refractive index reconstruction method, belonging to the field of optical measurement technology, comprising: acquiring the moiré fringes of the flow field to be measured; obtaining a standard moiré fringe deflection angle distribution using the moiré fringes of the flow field to be measured based on Fourier analysis and the multigrid method; inputting the obtained standard moiré fringe deflection angle distribution into a preset convolutional neural network to obtain a predicted flow field refractive index distribution; performing a Radon transform on the obtained predicted flow field refractive index distribution to obtain a predicted moiré fringe deflection angle distribution; substituting the standard moiré fringe deflection angle distribution and the predicted moiré fringe deflection angle distribution into an error function to determine the error value; determining a convergent convolutional neural network based on the convergence state of the error value; and using the convergent convolutional neural network to calculate the standard flow field refractive index distribution. This invention provides a refractive index reconstruction method that effectively reduces the complexity and theoretical difficulty of the calculation process.

Description

Technical Field

[0001] The invention relates to a refractive index reconstruction method, belonging to the technical field of optical measurement. Background Art

[0002] When using moiré tomography to detect high-temperature complex flow fields, the accuracy of refractive index reconstruction is particularly important, which greatly affects the key parameters of the flow field to be measured, such as temperature, density and other detection results. However, so far, refractive index reconstruction relies on traditional filtered back projection methods and algebraic reconstruction methods, which not only have a relatively complex calculation process, but also have high theoretical difficulty, greatly increasing the workload of technicians. Related research will be of great significance for realizing refractive index reconstruction of high-temperature complex flow fields using moiré tomography technology and expanding the field of technology. Summary of the invention

[0003] The purpose of the present invention is to overcome the deficiencies in the prior art and provide a refractive index reconstruction method that effectively reduces the complexity and theoretical difficulty of the calculation process.

[0004] To achieve the above objectives, the present invention is implemented by adopting the following technical solutions:

[0005] The present invention provides a refractive index reconstruction method, comprising:

[0006] Obtaining moiré fringes of the flow field to be measured;

[0007] Based on Fourier analysis and multi-grid method, the standard moiré fringe deflection angle distribution is obtained by using the moiré fringe of the flow field to be measured.

[0008] The obtained standard moiré fringe deflection angle distribution is input into a preset convolutional neural network to obtain the predicted flow field refractive index distribution;

[0009] The predicted flow field refractive index distribution is subjected to Radon transformation to obtain the predicted Moire fringe deflection angle distribution;

[0010] Substituting the standard moiré fringe deflection angle distribution and the predicted moiré fringe deflection angle distribution into the error function to determine the error value;

[0011] Determine the converged convolutional neural network according to the convergence state of the error value;

[0012] The convergent convolutional neural network is used to calculate the refractive index distribution of the standard flow field.

[0013] Furthermore, the method of obtaining the standard moiré fringe deflection angle distribution by using the moiré fringe of the flow field to be measured based on Fourier analysis and multi-grid method specifically includes:

[0014] Perform Fourier transform on the moiré fringes of the flow field to be measured to obtain the moiré fringes frequency domain information;

[0015] Extract a side lobe from the frequency domain information of the moiré fringe and translate it to the origin of the frequency domain and perform inverse Fourier transform;

[0016] The moiré fringe wrapping phase is calculated based on the result after inverse Fourier transform;

[0017] The moiré fringe wrapping phase is contracted and extended multiple times to obtain the wrapping phase under different coarse and fine grids;

[0018] The wrapped phases under different coarse and fine grids are iterated by residual error at the wrapped position to obtain the real phase distribution of the moiré fringes;

[0019] The standard moiré fringe deflection angle distribution is calculated based on the true phase distribution of the moiré fringe.

[0020] Furthermore, the step of inputting the obtained standard moiré fringe deflection angle distribution into a preset convolutional neural network to obtain a predicted flow field refractive index distribution specifically includes:

[0021] Inputting the obtained standard moiré fringe deflection angle distribution into a preset convolutional neural network to obtain a feature map with the same resolution output by the convolution layer in the preset convolutional neural network;

[0022] After activating the feature map of the same resolution, input it into the pooling layer for maximum pooling calculation to obtain the next layer of low-resolution feature map;

[0023] The next layer of low-resolution feature maps is downsampled multiple times to obtain the lowest layer feature map;

[0024] Deconvolution is performed on the lowest layer feature map to obtain the previous layer high-resolution feature map;

[0025] Performing a jump connection between a high-resolution feature map of a previous layer and a feature map of the same resolution to obtain a new feature map corresponding to the high-resolution feature map of the previous layer;

[0026] After convolution and activation calculations on the new feature map, multiple upsampling calculations are performed to obtain the predicted flow field refractive index distribution.

[0027] Furthermore, the Radon transform of the obtained predicted flow field refractive index distribution to obtain the predicted moiré fringe deflection angle distribution specifically includes:

[0028] X'=R(Y')

[0029] Among them, R is the Radon transform operator, Y' is the predicted flow field refractive index distribution, and X' is the predicted moiré fringe deflection angle distribution.

[0030] Furthermore, substituting the standard moiré fringe deflection angle distribution and the predicted moiré fringe deflection angle distribution into the error function to determine the error value specifically includes:

[0031]

[0032] Wherein, L is the error value, X' is the predicted moiré fringe deflection angle distribution, X is the standard moiré fringe deflection angle distribution, R is the Radon transform operator, F is the mapping from input to output of the preset convolutional neural network, M is the total number of rows of the standard moiré fringe deflection angle distribution, N is the total number of columns of the standard moiré fringe deflection angle distribution, m is the row index of the standard moiré fringe deflection angle distribution, and n is the column index of the standard moiré fringe deflection angle distribution.

[0033] Furthermore, determining the convergent convolutional neural network according to the convergence state of the error value specifically includes:

[0034] Determine whether the error value converges;

[0035] If yes, the preset convolutional neural network is used as the converged convolutional neural network;

[0036] If not, update the network parameters of the preset convolutional neural network, use the updated preset convolutional neural network to return to execute the step of obtaining the predicted flow field refractive index distribution and its subsequent steps until the error value converges, and use the current updated preset convolutional neural network as the converged convolutional neural network.

[0037] Furthermore, the use of the convergent convolutional neural network to calculate the refractive index distribution of the standard flow field specifically includes:

[0038] Obtaining moiré fringes of the flow field to be measured;

[0039] The standard moiré fringe deflection angle distribution obtained by using the moiré fringes of the flow field to be measured based on Fourier analysis and the multi-grid method is input into a convergent convolutional neural network, and the result output by the convergent convolutional neural network is the standard flow field refractive index distribution.

[0040] Compared with the prior art, the beneficial effects achieved by the present invention are:

[0041] The standard flow field refractive index distribution can be obtained by inputting the standard Moire fringe deflection angle distribution into the trained and updated convergent convolutional neural network. The standard flow field refractive index distribution can be intelligently reconstructed without the need for labeled data, effectively reducing the complexity and theoretical difficulty of the calculation process. BRIEF DESCRIPTION OF THE DRAWINGS

[0042] Figure 1 is a flow chart of a refractive index reconstruction method provided by an embodiment of the present invention;

[0043] Figure 2 It is a moiré tomography technology experimental device for a refractive index reconstruction method provided by an embodiment of the present invention;

[0044] In the figure: 1. Laser light source; 2. Beam expansion and collimation system; 3. Flow field to be measured; 4. Ronchi grating; 5. Imaging lens; 6. Receiving screen; 7. Filter aperture. DETAILED DESCRIPTION

[0045] The present invention will be further described below in conjunction with the accompanying drawings. The following embodiments are only used to more clearly illustrate the technical solutions of the present invention and are not intended to limit the protection scope of the present invention.

[0046] Embodiment 1:

[0047] like Figure 1 As shown, this embodiment discloses a refractive index reconstruction method, and the present invention is further described in detail below through specific implementation schemes:

[0048] S1: Obtain the moiré fringes of the flow field to be measured;

[0049] By adopting Figure 2 The moiré tomography experimental device shown in the figure obtains the moiré fringes of the flow field to be measured. Specifically, the laser light source generates a laser that forms a parallel beam through a beam expansion and collimation system. The parallel beam passes through the flow field to be measured to carry the flow field information to be measured, and forms overlapping interference fringes of different orders after passing through the Ronchi grating. After passing through the imaging lens and the filter aperture, the first order of moiré fringes is obtained and presented on the receiving screen. Finally, CDD1 inputs the moiré fringes into the computer. It should be noted that CDD2 is used to take photos of the flow field to be measured and input the photos of the flow field to be measured into the computer.

[0050] S2: Based on Fourier analysis and multi-grid method, the standard moiré fringe deflection angle distribution is obtained by using the moiré fringe of the flow field to be measured, including the following steps:

[0051] S21: Performing Fourier transform on the moiré fringes of the flow field to be measured to obtain frequency domain information of the moiré fringes;

[0052] W=F{I}

[0053] Among them, I is the moiré fringe of the flow field to be measured, W is the frequency domain information of the moiré fringe, and F is the Fourier transform.

[0054] S22: extract a side lobe in the frequency domain information of the moiré fringe and translate it to the origin of the frequency domain and perform inverse Fourier transform;

[0055] c=F -1 {W'}

[0056] Where W' is a side lobe in the frequency domain information of the moiré fringe, c is the result after inverse Fourier transform, and F -1 is the inverse Fourier transform.

[0057] S23: Calculate the moiré fringe wrapping phase according to the result after inverse Fourier transform;

[0058]

[0059] Where ψ is the moiré fringe wrapping phase, Im[·] and Re[·] represent the imaginary and real parts of c(x,y), respectively, and c is the result after inverse Fourier transform.

[0060] S24: The moiré fringe wrapped phase is contracted and extended multiple times to obtain the wrapped phase under different coarse and fine grids;

[0061] The shrinkage calculation formula is:

[0062]

[0063] Among them, c ij is the point in the i-th row and j-th column on the coarse grid, f ij is the point in the i-th row and j-th column on the fine grid.

[0064] The extension calculation formula is:

[0065]

[0066] In this embodiment, the moiré fringe wrapping phase is specifically subjected to the above-mentioned contraction and extension three times to obtain the wrapping phase under different coarse and fine grids.

[0067] S25: Iterate the residual error of the wrapped phase under different coarse and fine grids to obtain the real phase distribution of the moiré fringe;

[0068] Use 0 as the initial value to iterate the calculation of Ae=r:

[0069] r=ρ-Aψ'

[0070] Among them, r is the residual, A is the differential coefficient matrix, ψ' is the wrapped phase under different coarse and fine grids, and ρ is the Laplace operator of the true phase, that is: Where φ is the true phase. When the iteration is completed until the residual converges, the phase distribution on the fine grid is the true phase.

[0071] S26: Calculate the standard Moiré fringe deflection angle distribution based on the Moiré fringe true phase distribution.

[0072]

[0073] in, is the standard moiré fringe deflection angle distribution, φ(x, y) is the moiré fringe true phase distribution, d is the grating constant, △ is the grating spacing, n0 is the ambient refractive index in the measurement, and α is the grating angle.

[0074] S3: Inputting the obtained standard moiré fringe deflection angle distribution into a preset convolutional neural network to obtain a predicted flow field refractive index distribution, including the following steps:

[0075] S31: inputting the obtained standard moiré fringe deflection angle distribution into a preset convolutional neural network to obtain a feature map with the same resolution output by the convolution layer in the preset convolutional neural network;

[0076] Among them, the preset convolutional neural network is a u-net network, and it can also be set to other convolutional neural networks according to actual needs.

[0077] S32: Activate the feature map of the same resolution and input it into the pooling layer to perform maximum pooling calculation to obtain the next layer of low-resolution feature map;

[0078] The input feature map is divided into 2×2 sub-regions, and the maximum value of each sub-region is taken to represent each sub-region, which is used as the value of the corresponding sub-region of the next layer of feature map, thereby obtaining the next layer of low-resolution feature map.

[0079] S33: The next layer of low-resolution feature maps are downsampled multiple times to obtain the lowest layer feature map;

[0080] Assume that the feature map is downsampled s times, then the value of the kth image pixel after downsampling once is:

[0081]

[0082] Among them, p k is the value of the kth image pixel after downsampling once, I i is the value of the i-th pixel in the feature map, and win(k) is the k-th s×s submatrix of the feature map.

[0083] In this embodiment, the next layer of low-resolution feature maps is subjected to the above-mentioned downsampling calculation three times to obtain the lowest layer feature map.

[0084] S34: Deconvolute the lowest layer feature map to obtain the previous layer high-resolution feature map;

[0085] Each point in the lowest layer feature map is filled with 0, and then convolved with the convolution kernel to obtain the high-resolution feature map of the previous layer.

[0086] S35: performing a jump connection between the previous high-resolution feature map and the feature map with the same resolution to obtain a new feature map corresponding to the previous high-resolution feature map;

[0087] The feature map of the same resolution at the same layer in the downsampling process is concatenated with the high-resolution feature map on the channel to obtain a new feature map.

[0088] S36: After convolution and activation calculations are performed on the new feature map, a predicted flow field refractive index distribution is obtained through multiple upsampling calculations.

[0089] Assume that the new feature map is upsampled s times, then the value of the k-th image pixel after upsampling once is:

[0090]

[0091] Among them, q k is the value of the kth image pixel after upsampling once, I i is the value of the i-th pixel in the new feature map, and win(k) is the k-th s×s submatrix of the new feature map.

[0092] In this embodiment, the new feature map is convolved and activated, and then subjected to the above-mentioned upsampling calculation three times to obtain the predicted flow field refractive index distribution.

[0093] S4: performing Radon transformation on the obtained predicted flow field refractive index distribution to obtain the predicted moiré fringe deflection angle distribution;

[0094] The calculation formula is:

[0095] X'=R(Y')

[0096] Among them, R is the Radon transform operator, Y' is the predicted flow field refractive index distribution, and X' is the predicted moiré fringe deflection angle distribution.

[0097] S5: Substituting the standard moiré fringe deflection angle distribution and the predicted moiré fringe deflection angle distribution into the error function to determine the error value;

[0098] The error value is calculated as follows:

[0099]

[0100] Wherein, L is the error value, X' is the predicted moiré fringe deflection angle distribution, X is the standard moiré fringe deflection angle distribution, R is the Radon transform operator, F is the mapping from input to output of the preset convolutional neural network, M is the total number of rows of the standard moiré fringe deflection angle distribution, N is the total number of columns of the standard moiré fringe deflection angle distribution, m is the row index of the standard moiré fringe deflection angle distribution, and n is the column index of the standard moiré fringe deflection angle distribution.

[0101] S6: Determine the converged convolutional neural network according to the convergence state of the error value, specifically including:

[0102] Determine whether the error value converges;

[0103] If yes, the preset convolutional neural network is used as the converged convolutional neural network;

[0104] If not, update the network parameters of the preset convolutional neural network, use the updated preset convolutional neural network to return to execute the step of obtaining the predicted flow field refractive index distribution and its subsequent steps until the error value converges, and use the current updated preset convolutional neural network as the converged convolutional neural network.

[0105] S7: Calculating the refractive index distribution of the standard flow field using the convergent convolutional neural network, specifically including:

[0106] Obtaining moiré fringes of the flow field to be measured;

[0107] Based on the above-mentioned Fourier analysis and multi-grid method, the standard moiré fringe deflection angle distribution obtained by using the moiré fringes of the flow field to be measured is input into the convergent convolutional neural network, and the result finally output by the convergent convolutional neural network is the standard flow field refractive index distribution. The present invention can obtain the standard flow field refractive index distribution by inputting the standard moiré fringe deflection angle distribution into the trained and updated convergent convolutional neural network, and can intelligently reconstruct the standard flow field refractive index distribution without the need for labeled data, effectively reducing the complexity and theoretical difficulty of the calculation process.

[0108] Those skilled in the art will appreciate that the embodiments of the present application may be provided as methods, systems, or computer program products. Therefore, the present application may adopt the form of a complete hardware embodiment, a complete software embodiment, or an embodiment in combination with software and hardware. Moreover, the present application may adopt the form of a computer program product implemented in one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) that include computer-usable program code.

[0109] The present application is described with reference to the flowcharts and / or block diagrams of the methods, devices (systems), and computer program products according to the embodiments of the present application. It should be understood that each process and / or box in the flowchart and / or block diagram, as well as the combination of the processes and / or boxes in the flowchart and / or block diagram, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing device to generate a machine, so that the instructions executed by the processor of the computer or other programmable data processing device generate instructions for implementing the processes in the flowchart and / or block diagram. Figure 1 A process or multiple processes and / or boxes Figure 1 A device that provides the functions specified in a block or multiple blocks.

[0110] These computer program instructions may also be stored in a computer readable memory capable of directing a computer or other programmable data processing device to operate in a specific manner, so that the instructions stored in the computer readable memory produce an article of manufacture including an instruction device, which implements the process Figure 1 A process or multiple processes and / or boxes Figure 1 A function specified in one or more boxes.

[0111] These computer program instructions can also be loaded onto a computer or other programmable data processing device so that a series of operating steps are executed on the computer or other programmable device to produce a computer-implemented process, thereby providing instructions for implementing the process. Figure 1 A process or multiple processes and / or boxes Figure 1 The steps for the functions specified in one or more boxes.

[0112] The above is only a preferred embodiment of the present invention. It should be pointed out that for ordinary technicians in this technical field, several improvements and modifications can be made without departing from the technical principles of the present invention. These improvements and modifications should also be regarded as the scope of protection of the present invention.

Claims

1. A refractive index reconstruction method, characterized in that: include: Obtaining moiré fringes of the flow field to be measured; Based on Fourier analysis and multi-grid method, the standard moiré fringe deflection angle distribution is obtained by using the moiré fringe of the flow field to be measured. The obtained standard moiré fringe deflection angle distribution is input into a preset convolutional neural network to obtain the predicted flow field refractive index distribution; The predicted flow field refractive index distribution is subjected to Radon transformation to obtain the predicted Moire fringe deflection angle distribution; Substituting the standard moiré fringe deflection angle distribution and the predicted moiré fringe deflection angle distribution into the error function to determine the error value; Determine the converged convolutional neural network according to the convergence state of the error value; The convergent convolutional neural network is used to calculate the refractive index distribution of the standard flow field; The method of obtaining the standard moiré fringe deflection angle distribution by using the moiré fringe of the flow field to be measured based on Fourier analysis and multi-grid method specifically includes: Perform Fourier transform on the moiré fringes of the flow field to be measured to obtain the moiré fringes frequency domain information; Extract a side lobe from the frequency domain information of the moiré fringe and translate it to the origin of the frequency domain and perform inverse Fourier transform; The moiré fringe wrapping phase is calculated based on the result after inverse Fourier transform; The moiré fringe wrapping phase is contracted and extended multiple times to obtain the wrapping phase under different coarse and fine grids; The wrapped phases under different coarse and fine grids are iterated by residual error at the wrapped position to obtain the real phase distribution of the moiré fringes; The standard moiré fringe deflection angle distribution is calculated based on the moiré fringe real phase distribution; The step of inputting the obtained standard moiré fringe deflection angle distribution into a preset convolutional neural network to obtain a predicted flow field refractive index distribution specifically includes: Inputting the obtained standard moiré fringe deflection angle distribution into a preset convolutional neural network to obtain a feature map with the same resolution output by the convolution layer in the preset convolutional neural network; After activating the feature map of the same resolution, input it into the pooling layer for maximum pooling calculation to obtain the next layer of low-resolution feature map; The next layer of low-resolution feature maps is downsampled multiple times to obtain the lowest layer feature map; Deconvolution is performed on the lowest layer feature map to obtain the previous layer high-resolution feature map; Performing a jump connection between a high-resolution feature map of a previous layer and a feature map of the same resolution to obtain a new feature map corresponding to the high-resolution feature map of the previous layer; After convolution and activation calculations are performed on the new feature map, the predicted flow field refractive index distribution is obtained through multiple upsampling calculations; The step of performing Radon transformation on the obtained predicted flow field refractive index distribution to obtain the predicted moiré fringe deflection angle distribution specifically includes: ， in, is the Radon transform operator, To predict the refractive index distribution of the flow field, To predict the distribution of moiré fringe deflection angles; Substituting the standard moiré fringe deflection angle distribution and the predicted moiré fringe deflection angle distribution into the error function to determine the error value specifically includes: ， in, is the error value, To predict the deflection angle distribution of moiré fringes, is the standard Moire fringe deflection angle distribution, is the Radon transform operator, To preset the mapping from input to output of the convolutional neural network, is the total number of rows of standard moiré fringe deflection angle distribution, is the total number of columns of the standard moiré fringe deflection angle distribution, is the row index of the standard moiré fringe deflection angle distribution, is the column index of the standard moiré fringe deflection angle distribution.

2. The refractive index reconstruction method according to claim 1, characterized in that: Determining the convergent convolutional neural network according to the convergence state of the error value specifically includes: Determine whether the error value converges; If yes, the preset convolutional neural network is used as the converged convolutional neural network; If not, update the network parameters of the preset convolutional neural network, use the updated preset convolutional neural network to return to execute the step of obtaining the predicted flow field refractive index distribution and its subsequent steps until the error value converges, and use the current updated preset convolutional neural network as the converged convolutional neural network.

3. The refractive index reconstruction method according to claim 1, characterized in that: The method of using the convergent convolutional neural network to calculate the refractive index distribution of the standard flow field specifically includes: Obtaining moiré fringes of the flow field to be measured; The standard moiré fringe deflection angle distribution obtained by using the moiré fringes of the flow field to be measured based on Fourier analysis and the multi-grid method is input into a convergent convolutional neural network, and the result output by the convergent convolutional neural network is the standard flow field refractive index distribution.

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