Block strain field measurement method for phase contrast optical coherence elastography

Abstract

The invention discloses a body strain field measurement method for phase contrast optical coherence elastography, which can solve the problem of speckle decorrelation caused by large displacement on the basis of not changing the structure of the existing Phs-OCE measurement system by means of a pixel-level displacement tracking principle for directly reflecting the speckle decorrelation noise level constructed by virtue of the uncertainty of a three-dimensional model. Moreover, the method is still effective when the pixel-level displacement perpendicular to the monitoring plane exists, and improves the dynamic measurement range of Phs-OCE. In addition, the Bayesian deep neural network of the three-dimensional U-Net + + structure provided by the invention can be used for subsequent strain calculation, and the time required from differential wrapping phase to strain is remarkably shortened. And meanwhile, the Bayesian deep neural network of the three-dimensional U-Net + + structure has certain robustness, and the dependence on the phase reconstruction effect on strain calculation is relatively small, so that the practicability of body strain field measurement is improved.

Description

Technical Field

[0001] The invention relates to the technical field of computational imaging, and in particular to a method for measuring a volume strain field for phase-contrast optical coherence elastic imaging. Background Art

[0002] Phase-contrast optical coherence tomography (Phs-OCE) is a non-contact measurement technique used to visualize defects inside materials or tissues and quantify their mechanical behavior. It can be used for full-field deformation measurement inside transparent and translucent objects, with nanometer-level displacement measurement sensitivity and micrometer-level strain measurement sensitivity, which is essential for measuring the mechanical properties of materials. The key to this technology is to measure the phase difference information of light to capture the tiny displacements and strains inside the material. By analyzing the phase changes before and after the material is subjected to force, Phs-OCE can generate high-resolution tomographic strain fields. However, high-strain rate materials often exhibit large deformations during testing, and the reference pixels on their phase monitoring images are prone to offset by more than integer pixels, and are prone to pixel-level offsets perpendicular to the monitoring plane, resulting in random phase differences and inducing speckle decorrelation, which will affect the accuracy of subsequent estimated strain distribution.

[0003] In order to overcome speckle decorrelation and achieve phase reconstruction, researchers have developed many image tracking algorithms to monitor the displacement between pixels, and reconstruct phase information by comparing and moving the pixel offset trajectory. For example, researchers have developed a phase volume correlation method (PVC), which is a technology for matching pixel subsets based on the three-dimensional residual point number of the differentially wrapped phase map. It can track displacements in three-dimensional space, track the pixel-level offset between the monitoring plane and the perpendicular to the monitoring plane, and achieve displacement tracking of complex deformation distributions, overcome speckle decorrelation, and complete phase reconstruction. After that, three-dimensional unwrapping is performed to obtain the corresponding displacement field, and the displacement field is strain calculated using methods such as the three-dimensional least squares method to obtain the bulk strain distribution of the sample. However, there are also some problems in such a bulk strain calculation process, such as the following points:

[0004] (1) The calculation of the number of three-dimensional residual points in the PVC method results in low computational efficiency, making it difficult to apply to industrial on-site online detection.

[0005] (2) In the process of calculating the volume strain, it is necessary to perform three-dimensional window unwrapping. This process is easily contaminated by noise and requires manual parameter adjustment, which is difficult to meet the actual needs of complex deformation inside the sample.

[0006] In summary, although the existing methods to overcome speckle decorrelation, such as PVC combined with three-dimensional least squares method, can provide three-dimensional volume strain measurement, they have problems in computational efficiency and noise resistance. Therefore, it is necessary to further explore a method for measuring volume strain field for phase contrast optical coherence elastic imaging. Summary of the invention

[0007] The purpose of the present invention is to overcome the deficiencies of the prior art and provide a method for measuring the volume strain field for phase contrast optical coherence elastic imaging.

[0008] To achieve the above purpose, the technical solution provided by the present invention is:

[0009] A method for measuring volume strain field for phase contrast optical coherence elastic imaging, comprising:

[0010] S1. Continuous interference spectra of the material before and after the reaction are collected by a phase contrast optical coherence tomography elastic imaging system, and phase differential estimation is performed using the wrapped phase information in the spectral signal to obtain a differential wrapped phase map, thereby achieving real-time monitoring of the material deformation process;

[0011] S2, selecting a de-correlation region that needs to be phase reconstructed according to the obtained differential wrapped phase image, wherein the de-correlation region is represented as a volume set of de-correlation regions in a three-dimensional space;

[0012] S3. According to the selected decorrelation region, a sub-region of size (2×M+1, 2×M+1) is selected as a retrieval unit on the (2×M+1) deformed wrapped phase map D, where M is the sub-region size, and the center point (ζ, η, γ) of the sub-region is the pixel point to be phase tracked; then, the block of the sub-region is pixel-level shifted (Δξ, Δη, Δγ) along the horizontal direction, the vertical direction and the direction perpendicular to the monitoring plane, and the differential wrapped phase map corresponding to the pixel-level shift is calculated;

[0013] S4. Construct and train a Bayesian deep neural network with a three-dimensional U-Net++ structure;

[0014] S5, inputting the differential wrapped phase map corresponding to the pixel-level displacement obtained in step S3 into the trained three-dimensional U-Net++ structure Bayesian deep neural network to obtain the corresponding three-dimensional phase gradient; and then calculating the corresponding three-dimensional model uncertainty based on the corresponding three-dimensional phase gradient;

[0015] S6. Constructing an energy optimization equation for finding the pixel-level displacement corresponding to the minimum energy based on the uncertainty of the three-dimensional model;

[0016] S7, based on the decorrelated region selected in step S2, each pixel point on the deformed three-dimensional wrapped phase image is processed according to steps S3 to S6 to obtain a pixel-level horizontal displacement field Δζ * (i, j, k), axial displacement field Δη * (i, j, k) and the displacement field Δγ perpendicular to the monitoring plane * (i, j, k); then, according to the displacement fields in the three directions, the deformed three-dimensional wrapped phase is subjected to pixel-level displacement compensation processing under phase decorrelation to obtain a three-dimensional differential wrapped phase map φ after phase reconstruction;

[0017] S8, inputting the three-dimensional differential wrapped phase image φ after phase reconstruction into a Bayesian deep neural network with a three-dimensional U-Net++ structure for multiple predictions to obtain an average value μ of the three-dimensional phase gradient;

[0018] S9. Calculate the three-dimensional volume strain ε based on the average value μ of the three-dimensional phase gradient calculated in step S8.

[0019] Furthermore, the phase difference estimation is performed using the wrapped phase information in the spectral signal, specifically:

[0020] The phase difference operation is performed on the three-dimensional continuous area in the material, and the operation process is expressed as:

[0021] φ(i,j,k)=Arg{exp{j·[φ R (i,j,k)-φ D (i,j,k)]}}

[0022] Where j represents the imaginary unit; Arg represents the argument of a complex number; φ R represents the wrapping phase before deformation, φ D represents the wrapped phase after deformation; φ(i, j, k) represents the phase at (i, j) on the kth differential wrapped phase image.

[0023] Furthermore, the Bayesian deep neural network of the three-dimensional U-Net++ structure is based on Unet++, uses a 3D-Convolutional layer and a 3D-Maxpool with concrete dropout for downsampling, uses a 3D-Up-sampling layer for upsampling, and finally uses a Merged convolution layer for output.

[0024] Furthermore, the formula for calculating the uncertainty of the three-dimensional model is as follows:

[0025]

[0026] Among them, μ (l) is the three-dimensional phase gradient output by the lth network; is the average value of the three-dimensional phase gradient output of L networks; (x, y, z) is the spatial coordinate after the discretization of the three-dimensional phase map; (Δζ, Δη, Δγ) is the pixel-level displacement of the sub-area in the horizontal, axial and perpendicular directions to the monitoring plane.

[0027] Furthermore, the energy optimization equation constructed based on the uncertainty of the three-dimensional model is as follows:

[0028]

[0029] Among them, σ(x, y, z, Δζ, Δη, Δγ) is the uncertainty of the three-dimensional model; (Δζ * , Δη * , Δγ * ) is the pixel-level displacement corresponding to the minimum energy; Represents a set of integers.

[0030] Furthermore, the deformed three-dimensional wrapped phase is subjected to pixel-level displacement compensation processing under phase decorrelation, and the compensation processing formula is as follows:

[0031]

[0032] Where j represents the imaginary unit; Arg represents the argument of a complex number; exp is the exponential signal; φ R Represents the wrapping phase image before deformation, Represents the deformed wrapped phase obtained after displacement compensation processing based on the displacement fields in three directions.

[0033] Furthermore, the calculation formula for obtaining the three-dimensional body strain ε based on the average value μ of the three-dimensional phase gradient obtained in step S8 is as follows:

[0034]

[0035] Among them, λ c is the central wavelength of the light source, and n is the refractive index of the material being measured.

[0036] In the speckle decorrelation problem, when there is a pixel-level displacement perpendicular to the monitoring plane, existing technologies often require a lot of time to calculate, and the subsequent strain calculation depends on the effect of phase reconstruction.

[0037] Compared with the prior art, the principles and advantages of this technical solution are as follows:

[0038] By using the uncertainty of the three-dimensional model to construct a pixel-level displacement tracking method that directly reflects the decorrelation noise level of the speckle, the decorrelation problem caused by large displacement can be solved without changing the structure of the existing Phs-OCE measurement system. It is still effective when there is a pixel-level displacement perpendicular to the monitoring plane, thereby improving the dynamic measurement range of Phs-OCE. In addition, the Bayesian deep neural network with a three-dimensional U-Net++ structure proposed in this technical solution can be used for subsequent strain calculations, significantly reducing the time required from differential wrapped phase to strain. At the same time, the Bayesian deep neural network with a three-dimensional U-Net++ structure has a certain degree of robustness, and its dependence on the effect of phase reconstruction in strain calculation is relatively small, thereby improving the practicality of bulk strain field measurement. BRIEF DESCRIPTION OF THE DRAWINGS

[0039] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the services required for use in the embodiments or the prior art descriptions are briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative work.

[0040] Figure 1 It is a principle flow chart of a method for measuring volume strain field for phase contrast optical coherence elastic imaging of the present invention;

[0041] Figure 2 is the phase difference image of four adjacent continuous cross sections;

[0042] Figure 3 A schematic diagram for selecting a decorrelation region on a phase difference image;

[0043] Figure 4 A schematic diagram of mobile retrieval of a unit retrieval block in three-dimensional space;

[0044] Figure 5 A schematic diagram of calculating three-dimensional phase gradient using a Bayesian deep neural network with a three-dimensional U-Net++ structure;

[0045] Figure 6 Phase reconstruction effect diagram for different sub-area sizes;

[0046] Figure 7 This is a phase reconstruction effect diagram obtained by using the method of the present invention;

[0047] Figure 8 It is a comparison diagram of strain effects between the method of the present invention and the three-dimensional least squares method;

[0048] Fig. 9It is a comparison chart of the time consumption of the method of the present invention and other three-dimensional methods (PVC+three-dimensional least square method). DETAILED DESCRIPTION

[0049] The present invention will be further described below in conjunction with specific embodiments:

[0050] like Figure 1 As shown, the method for measuring the volume strain field for phase contrast optical coherence elastic imaging described in this embodiment includes the following steps:

[0051] S1. Continuous interference spectra of the material before and after the reaction are collected by a phase contrast optical coherence tomography elastic imaging system, and phase differential estimation is performed using the wrapped phase information in the spectral signal to obtain a differential wrapped phase map, thereby achieving real-time monitoring of the material deformation process;

[0052] In this step, the phase difference estimation is performed using the wrapped phase information in the spectral signal, specifically:

[0053] The phase difference operation is performed on the three-dimensional continuous area in the material, and the operation process is expressed as:

[0054] φ(i,j,k)=Arg{exp{j·[φ R (i,j,k)-φ D (i, j, k)]}}

[0055] Where j represents the imaginary unit; Arg represents the argument of a complex number; φ R represents the wrapping phase before deformation, φ D represents the wrapped phase after deformation; φ(i, j, k) represents the phase at (i, j) on the kth differential wrapped phase image;

[0056] The differential wrapped phase diagram of four adjacent sections is as follows Figure 2 shown.

[0057] S2. Based on the obtained differential wrapped phase map, first confirm the coverage of the decorrelated area to evaluate the decorrelation degree of the area, and at the same time narrow the calculation range and reduce the calculation time. Figure 3 The red framed area shown in (a) is used as the search range and the de-correlation area that needs phase reconstruction. It is represented as a set of blocks in the de-correlation area in three-dimensional space, as shown in Figure 4 Shown in red in (a).

[0058] S3. According to the selected decorrelation region, a sub-region of size (2×M+1, 2×M+1) is selected on the (2×M+1 deformed wrapped phase image D) as a retrieval unit, where M is the sub-region size, and the center point (ζ, η, γ) of the sub-region is the pixel to be phase tracked; Figure 3 As shown in the white box in (a), it is represented as a set of blocks in the sub-area in three-dimensional space, such as Figure 4 As shown in (b), they together constitute a sub-region block in three-dimensional space.

[0059] Next, the volume blocks of the sub-area are subjected to pixel-level displacement (Δξ, Δη, Δγ) along the horizontal direction, vertical direction and direction perpendicular to the monitoring plane, and the differential wrapped phase map corresponding to the pixel-level displacement is calculated;

[0060] S4. Construct and train a three-dimensional U-Net++ Bayesian deep neural network (3D U-Net++BNN), such as Figure 5 As shown in the figure, this network is based on Unet++, using 3D-Convolutional layer and 3D-Maxpool with concrete dropout for downsampling, 3D-Up-sampling layer for upsampling, and finally Mergedconvolution layer for output.

[0061] S5, inputting the differential wrapped phase map corresponding to the pixel-level displacement obtained in step S3 into the trained three-dimensional U-Net++ structure Bayesian deep neural network to obtain the corresponding three-dimensional phase gradient; and then calculating the corresponding three-dimensional model uncertainty based on the corresponding three-dimensional phase gradient;

[0062] The formula for calculating the uncertainty of the three-dimensional model is as follows:

[0063]

[0064] Among them, μ (l) is the three-dimensional phase gradient output by the lth network; is the average value of the three-dimensional phase gradient output of L networks; (x, y, z) is the spatial coordinate after the discretization of the three-dimensional phase map; (Δζ, Δη, Δγ) is the pixel-level displacement of the sub-area in the horizontal, axial and perpendicular directions to the monitoring plane.

[0065] S6. Based on the uncertainty of the three-dimensional model, an energy optimization equation is constructed to find the pixel-level displacement corresponding to the minimum energy. The equation is as follows:

[0066]

[0067] Among them, σ(x, y, z, Δζ, Δη, Δγ) is the uncertainty of the three-dimensional model; (Δζ * , Δη * , Δγ * ) is the pixel-level displacement corresponding to the minimum energy; represents an integer set. The pixel-level displacement tracking principle based on the minimum uncertainty energy of the three-dimensional model is as follows Figure 1 As shown in (b).

[0068] S7, based on the decorrelated region selected in step S2, each pixel point on the deformed three-dimensional wrapped phase image is processed according to steps S3 to S6 to obtain a pixel-level horizontal displacement field Δζ * (i, j, k), axial displacement field Δη * (i, j, k) and the displacement field Δγ perpendicular to the monitoring plane * (i, j, k); then, according to the displacement fields in the three directions, the deformed three-dimensional wrapped phase is subjected to pixel-level displacement compensation processing under phase decorrelation to obtain a three-dimensional differential wrapped phase map φ after phase reconstruction;

[0069] In this step, the deformed three-dimensional wrapped phase is subjected to pixel-level displacement compensation processing under phase decorrelation. The compensation processing formula is as follows:

[0070]

[0071] Where j represents the imaginary unit; Arg represents the argument of a complex number; exp is the exponential signal; φ R Represents the wrapping phase image before deformation, Represents the deformed wrapped phase obtained after displacement compensation processing based on the displacement fields in three directions.

[0072] Through the above steps, the speckle decorrelation problem caused by large displacement can be overcome, and it is still effective when there is a pixel-level displacement perpendicular to the monitoring plane, thereby expanding the measurement range of Phs-OCE.

[0073] S8, inputting the three-dimensional differential wrapped phase image φ after phase reconstruction into a Bayesian deep neural network with a three-dimensional U-Net++ structure for multiple predictions to obtain an average value μ of the three-dimensional phase gradient;

[0074] S9, based on the average value μ of the three-dimensional phase gradient obtained in step S8, the three-dimensional body strain ε is calculated using the following formula:

[0075]

[0076] Among them, λ c is the central wavelength of the light source, and n is the refractive index of the material being measured.

[0077] In order to prove the effectiveness and superiority of the method of the present invention, the following experiments were performed:

[0078] The de-correlated phase information collected during the curing process of the photocurable resin material is phase reconstructed. Here, the entire three-dimensional differential wrapping phase image is selected for phase reconstruction, such as Figure 6 As shown, (a), (b), (c), and (d) are phase reconstruction effects of different sub-area sizes, and the corresponding sizes are M=0, M=2, M=8, and M=20. It can be seen that the best phase reconstruction effect is the differential wrapped phase image shown in (d), which shows that the method of the present invention can obtain a better phase reconstruction effect when the sub-area size is appropriate.

[0079] Then we compared it with other methods (PVC), and the results are as follows Figure 7 shown. Figure 7 (a) is the differential wrapped phase image where speckle decorrelation occurs. Figure 7 (b) is the differential wrapped phase image of phase reconstruction using the PVC method. Figure 7 (c) is a differential wrapped phase image obtained by phase reconstruction using the method of the present invention. It can be seen that the method of the present invention can achieve the same phase reconstruction effect as other three-dimensional phase reconstruction methods (PVC), and the sub-region size of both methods is M=20.

[0080] Then the strain calculation is performed on the differential wrapped phase image, and the results are as follows Figure 8 As shown, Figure 8 (a) Figure 7 (b) Calculated by the three-dimensional least squares method, Figure 8 (b) Figure 7 (c) After prediction by the Bayesian deep neural network with a three-dimensional U-Net++ structure, the formula It can be seen that the strain (b) obtained by the method of the present invention is better than the strain (a) obtained by the three-dimensional least squares method, which reflects the effectiveness of the method of the present invention in strain calculation.

[0081] Finally, the comparison results on time efficiency are as follows Fig. 9 As shown, combined Figure 6 It can be seen from the data that under the condition that phase reconstruction (M=20) and strain calculation can be completed well, the time required by the method of the present invention is significantly less than that of other three-dimensional methods (PVC+three-dimensional least squares method), and as the sub-area increases, the superiority of the method of the present invention in time efficiency becomes more significant. The above experimental results prove that the three-dimensional volume strain rapid measurement technology proposed by the present invention can effectively solve the speckle dephasing problem caused by large deformation of the sample, improve the dynamic measurement capability of Phs-OCE, shorten the calculation time, and enhance its practicality.

[0082] The embodiments described above are only preferred embodiments of the present invention and are not intended to limit the scope of implementation of the present invention. Therefore, all changes made according to the shape and principle of the present invention should be included in the protection scope of the present invention.

Claims

1. A method for measuring volumetric strain field for phase contrast optical coherence elastic imaging, characterized in that: include: S1. Continuous interference spectra of the material before and after the reaction are collected by a phase contrast optical coherence tomography elastic imaging system, and phase differential estimation is performed using the wrapped phase information in the spectral signal to obtain a differential wrapped phase map, thereby achieving real-time monitoring of the material deformation process; S2, selecting a de-correlation region that needs to be phase reconstructed according to the obtained differential wrapped phase image, wherein the de-correlation region is represented as a volume set of de-correlation regions in a three-dimensional space; S3. According to the selected de-correlation region, a sub-region of size (2×M+1, 2×M+1) is selected as a retrieval unit on the (2×M+1) deformed wrapped phase map D, where M is the sub-region size, and the center point (ζ, η, γ) of the sub-region is the pixel to be phase tracked; then, the block of the sub-region is pixel-level shifted (Δζ, Δη, Δγ) along the horizontal direction, the vertical direction and the direction perpendicular to the monitoring plane, and the differential wrapped phase map corresponding to the pixel-level shift is calculated; S4. Construct and train a Bayesian deep neural network with a three-dimensional U-Net++ structure; S5, inputting the differential wrapped phase map corresponding to the pixel-level displacement obtained in step S3 into the trained three-dimensional U-Net++ structure Bayesian deep neural network to obtain the corresponding three-dimensional phase gradient; and then calculating the corresponding three-dimensional model uncertainty based on the corresponding three-dimensional phase gradient; S6. Constructing an energy optimization equation for finding the pixel-level displacement corresponding to the minimum energy based on the uncertainty of the three-dimensional model; S7, based on the decorrelated region selected in step S2, each pixel point on the deformed three-dimensional wrapped phase image is processed according to steps S3 to S6 to obtain a pixel-level horizontal displacement field Δζ * (i, j, k), axial displacement field Δη * (i, j, k) and the displacement field Δγ perpendicular to the monitoring plane * (i, j, k); then, according to the displacement fields in the three directions, the deformed three-dimensional wrapped phase is subjected to pixel-level displacement compensation processing under phase decorrelation to obtain a three-dimensional differential wrapped phase map φ after phase reconstruction; S8, inputting the three-dimensional differential wrapped phase image φ after phase reconstruction into a Bayesian deep neural network with a three-dimensional U-Net++ structure for multiple predictions to obtain an average value μ of the three-dimensional phase gradient; S9. Calculate the three-dimensional volume strain ε based on the average value μ of the three-dimensional phase gradient calculated in step S8.

2. The method for measuring bulk strain field for phase contrast optical coherence elastic imaging according to claim 1, characterized in that: The phase difference estimation is performed using the wrapped phase information in the spectral signal, specifically: The phase difference operation is performed on the three-dimensional continuous area in the material, and the operation process is expressed as: φ(i,j,k)=Arg{exp{j·[φ R (i, j, k)-φ D (i, j, k)]}} Where j represents the imaginary unit; Arg represents the argument of a complex number; φ R represents the wrapping phase before deformation, φ D represents the wrapped phase after deformation; φ(i, j, k) represents the phase at (i, j) on the kth differential wrapped phase image.

3. The method for measuring bulk strain field for phase contrast optical coherence elastic imaging according to claim 1, characterized in that: The Bayesian deep neural network of the three-dimensional U-Net++ structure is based on Unet++, uses a 3D-Convolutional layer and a 3D-Maxpool with concrete dropout for downsampling, uses a 3D-Up-sampl ing layer for upsampling, and finally uses a Merged convolution layer for output.

4. The method for measuring bulk strain field for phase contrast optical coherence elastic imaging according to claim 1, characterized in that: The formula for calculating the uncertainty of the three-dimensional model is as follows: Among them, μ (l) is the three-dimensional phase gradient output by the lth network; is the average value of the three-dimensional phase gradient output of L networks; (x, y, z) is the spatial coordinates after the discretization of the three-dimensional phase map; (Δζ, Δη, Δγ) is the pixel-level displacement of the sub-area in the horizontal, axial and perpendicular directions to the monitoring plane.

5. The method for measuring bulk strain field for phase contrast optical coherence elastic imaging according to claim 1, characterized in that: The energy optimization equation constructed based on the uncertainty of the three-dimensional model is as follows: Among them, σ(x, y, z, Δζ, Δη, Δγ) is the uncertainty of the three-dimensional model; (Δζ * , Δη * , Δγ * ) is the pixel-level displacement corresponding to the minimum energy; Represents a set of integers.

6. The method for measuring volume strain field for phase contrast optical coherence elastic imaging according to claim 1, characterized in that: The deformed three-dimensional wrapped phase is subjected to pixel-level displacement compensation processing under phase decorrelation. The compensation processing formula is as follows: Where j represents the imaginary unit; Arg represents the argument of a complex number; exp is the exponential signal; φ R Represents the wrapping phase image before deformation, Represents the deformed wrapped phase obtained after displacement compensation processing based on the displacement fields in three directions.

7. The method for measuring volume strain field for phase contrast optical coherence elastic imaging according to claim 1, characterized in that: The calculation formula for obtaining the three-dimensional volume strain ε based on the average value μ of the three-dimensional phase gradient obtained in step S8 is as follows: Among them, λ c is the central wavelength of the light source, and n is the refractive index of the material being measured.

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