A method for measuring bulk strain field for phase-contrast optical coherence elastography imaging

Abstract

The application discloses a kind of bulk strain field measurement methods for phase contrast optical coherence elastography, which constructs pixel-level displacement tracking principle directly reflecting speckle decorrelation noise level by means of three-dimensional model uncertainty, can solve the problem of speckle decorrelation caused by large displacement without changing the structure of existing Phs-OCE measurement system, and is still effective when there is pixel-level displacement perpendicular to the monitoring plane, improve the dynamic measurement range of Phs-OCE.In addition, the Bayesian deep neural network with three-dimensional U-Net++ structure proposed by the application can be used for subsequent strain calculation, significantly reducing the time required from differential wrapped phase to strain.At the same time, the Bayesian deep neural network with three-dimensional U-Net++ structure has certain robustness, and the dependence on the effect of phase reconstruction in strain calculation is relatively small, thereby improving the practicability of bulk strain field measurement.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of computed imaging, and in particular to a bulk strain field measurement method for phase contrast optical coherence elastography imaging. BACKGROUND

[0002] Phase contrast optical coherence elastography (Phs-OCE) is a non-contact measurement technique for visualizing internal defects of materials or tissues and quantifying their mechanical behavior. It can be used for full-field deformation measurement inside transparent and semi-transparent objects, with nanometer-level displacement measurement sensitivity and micrometer-level strain measurement sensitivity, which is crucial for measuring the mechanical properties of materials. The key to this technique is to measure the phase difference of light to capture the small displacement and strain inside the material. By analyzing the phase change before and after the material is stressed, Phs-OCE can generate high-resolution tomographic strain fields. However, high strain rate materials often exhibit large deformation during testing, and the reference pixels on the phase monitoring image are easily shifted by more than an integer pixel, and pixel-level shifts perpendicular to the monitoring plane are also likely to occur, resulting in random phase differences and inducing speckle decorrelation, which can affect the accuracy of subsequent strain distribution estimation.

[0003] To overcome speckle decorrelation and achieve phase reconstruction, researchers have developed many image tracking algorithms to monitor the displacement between pixels, and reconstruct the phase information by comparing and moving the pixel displacement trajectories. For example, researchers have developed a phase volume correlation (PVC) method, which is a technique based on three-dimensional residual point number for pixel subset matching based on differential wrapped phase maps. It can track displacement in three-dimensional space, track pixel-level shifts perpendicular to the monitoring plane, achieve displacement tracking for complex deformation distribution, overcome speckle decorrelation, and complete phase reconstruction. Then, three-dimensional unwrapping is performed to obtain the corresponding displacement field, and methods such as three-dimensional least squares are used to calculate the strain of the displacement field to obtain the bulk strain distribution of the sample. However, such bulk strain calculation process also has some problems, such as the following points:

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

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

[0006] In summary, while existing methods for overcoming speckle decorrelation, such as PVC combined with 3D least squares, can provide 3D volume strain measurements, they suffer from computational efficiency and noise immunity. Therefore, further exploration of a volume strain field measurement method for phase-contrast optical coherence elastography is needed. 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 bulk strain field for phase-contrast optical coherence elastography.

[0008] To achieve the above objectives, the technical solutions provided by the present invention are:

[0009] A method for measuring bulk strain fields for phase-contrast optical coherence elastography, comprising:

[0010] S1. Continuous interference spectra of the material before and after the reaction are collected using a phase-contrast optical coherence tomography system. The phase difference is estimated using the wrapped phase information in the spectral signal to obtain a differential wrapped phase map, enabling real-time monitoring of the material deformation process.

[0011] S2. selecting a de-correlation region requiring phase reconstruction according to the obtained differential wrapped phase map, wherein the de-correlation region is represented as a set of volume blocks of the de-correlation region in three-dimensional space;

[0012] S3. Based on the selected decorrelated region, a subregion of size (2×M+1, 2×M+1) is selected as a search unit on the (2×M+1) deformed wrapped phase image D, where M is the subregion size and the center point (ζ, η, γ) of the subregion is the pixel to be phase tracked. Next, the block of the subregion is pixel-wise shifted (Δξ, Δη, Δγ) in the horizontal and vertical directions and in the direction perpendicular to the monitoring plane, and the differential wrapped phase image corresponding to the pixel-wise shift is calculated.

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

[0014] S5. Inputting the differential wrapped phase image corresponding to the pixel-level displacement obtained in step S3 into the trained Bayesian deep neural network of the three-dimensional U-Net++ structure 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. Construct 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 de-correlated 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 the 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 pixel-level displacement compensation processing is performed on the deformed three-dimensional wrapped phase under phase decorrelation to obtain the three-dimensional differential wrapped phase map φ after phase reconstruction;

[0017] S8, inputting the phase-reconstructed three-dimensional differential wrapped phase image φ into a Bayesian deep neural network with a three-dimensional U-Net++ structure for multiple predictions to obtain the 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 within the material. 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 the 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 with a 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 of the discretized 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 under phase decorrelation. The compensation formula is as follows:

[0031]

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

[0033] Furthermore, the calculation formula for 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:

[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 existing technology, the principles and advantages of this technical solution are as follows:

[0038] By leveraging the uncertainty of the three-dimensional model to construct a pixel-level displacement tracking method that directly reflects the level of speckle decorrelation noise, this method can address the speckle decorrelation problem caused by large displacements without changing the structure of the existing Phs-OCE measurement system. This method is also effective even in the presence of pixel-level displacements perpendicular to the monitoring plane, thereby improving the dynamic measurement range of Phs-OCE. Furthermore, 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 to convert differential wrapped phase to strain. Furthermore, the Bayesian deep neural network with a three-dimensional U-Net++ structure exhibits a certain degree of robustness, and its strain calculations are relatively less dependent on the effectiveness of phase reconstruction, thereby improving the practicality of bulk strain field measurements. 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 will be 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 any creative work.

[0040] Figure 1 This is a principle flow chart of a method for measuring bulk strain field for phase-contrast optical coherence elastography according to the present invention;

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

[0042] Figure 3 Schematic diagram for selecting decorrelation regions on the phase difference image;

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

[0044] Figure 5 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 under 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 A comparison diagram of the strain effects between the method of the present invention and the three-dimensional least squares method;

[0048] Figure 9This is a comparison chart of the time consumption of the method of the present invention and other three-dimensional methods (PVC+three-dimensional least squares 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 bulk strain field for phase contrast optical coherence elastography described in this embodiment includes the following steps:

[0051] S1. Continuous interference spectra of the material before and after the reaction are collected using a phase-contrast optical coherence tomography system. The phase difference is estimated using the wrapped phase information in the spectral signal to obtain a differential wrapped phase map, enabling 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 within the material. 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 the 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 diagrams of four adjacent sections are as follows Figure 2 shown.

[0057] S2. Based on the obtained differential wrapped phase map, first confirm the coverage of the de-correlated area to evaluate the degree of de-correlation in 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 as the red block in (a).

[0058] S3. Based on the selected de-correlated 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 sub-area blocks 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 image corresponding to the pixel-level displacement obtained in step S3 into the trained Bayesian deep neural network of the three-dimensional U-Net++ structure 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 of the discretized 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 de-correlated 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 the 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 pixel-level displacement compensation processing is performed on the deformed three-dimensional wrapped phase under phase decorrelation to obtain the three-dimensional differential wrapped phase map φ after phase reconstruction;

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

[0070]

[0071] Where j represents the imaginary unit; Arg represents the argument of the complex number; exp is the exponential signal; φ R Represents the wrapped phase image before deformation, Represents the deformed wrapped phase obtained after displacement compensation 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 phase-reconstructed three-dimensional differential wrapped phase image φ into a Bayesian deep neural network with a three-dimensional U-Net++ structure for multiple predictions to obtain the average value μ of the three-dimensional phase gradient;

[0074] S9. Calculate the three-dimensional volume strain ε based on the average value μ of the three-dimensional phase gradient obtained in step S8. The calculation formula is as follows:

[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 demonstrate the effectiveness and superiority of the method of the present invention, the following experiments were performed:

[0078] The phase information of the de-correlated phase collected by the photocurable resin material during the curing process is reconstructed. Here, the entire three-dimensional differential wrapping phase image is selected for phase reconstruction, such as Figure 6 Figures (a), (b), (c), and (d) show the phase reconstruction results for different sub-region sizes, corresponding to M = 0, M = 2, M = 8, and M = 20, respectively. It can be seen that the best phase reconstruction effect is achieved with the differential wrapping phase image shown in (d), indicating that the method of the present invention can achieve good phase reconstruction results when the sub-region size is appropriate.

[0079] Then we compared it with other methods (PVC), and the results were as follows: Figure 7 shown. Figure 7 (a) is the differential wrapping phase image where speckle decorrelation occurs. Figure 7 (b) is the differential wrapped phase image using the PVC method for phase reconstruction. Figure 7 (c) is the 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), when the sub-region size of both methods is M=20.

[0080] Then the strain calculation is performed on the differential wrapped phase map, 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 of the 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 Figure 9 As shown, combined Figure 6 As can be seen from the data, under the conditions of successfully completing phase reconstruction (M = 20) and strain calculation, the method of the present invention requires significantly less time than other 3D methods (PVC + 3D least squares method). Furthermore, the time efficiency advantage of the method of the present invention becomes even more pronounced as the subregion increases. These experimental results demonstrate that the proposed rapid 3D volume strain measurement technique can effectively address the speckle dephasing problem caused by large sample deformations, enhance the dynamic measurement capabilities of Phs-OCE, shorten 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, any changes made based on the shape and principle of the present invention should be included in the scope of protection of the present invention.

Claims

1. A method for measuring bulk strain fields for phase-contrast optical coherence elastography, characterized in that: include: S1. Continuous interference spectra of the material before and after the reaction are collected using a phase-contrast optical coherence tomography system. The phase difference is estimated using the wrapped phase information in the spectral signal to obtain a differential wrapped phase map, enabling real-time monitoring of the material deformation process. S2. selecting a de-correlation region requiring phase reconstruction according to the obtained differential wrapped phase map, wherein the de-correlation region is represented as a set of volume blocks of the de-correlation region in three-dimensional space; S3. Based on the selected decorrelated region, a subregion of size (2×M+1, 2×M+1) is selected as a search unit on the (2×M+1) deformed wrapped phase image D, where M is the subregion size and the center point (ζ, η, γ) of the subregion is the pixel to be phase tracked. Next, the block of the subregion is pixel-wise shifted (Δξ, Δη, Δγ) along the horizontal, axial, and perpendicular directions to the monitoring plane, and the differential wrapped phase image corresponding to the pixel-wise shift is calculated. S4. Build and train a Bayesian deep neural network with a three-dimensional U-Net++ structure; S5. Inputting the differential wrapped phase image corresponding to the pixel-level displacement obtained in step S3 into the trained Bayesian deep neural network of the three-dimensional U-Net++ structure 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. Construct 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 de-correlated 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 the 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 pixel-level displacement compensation processing is performed on the deformed three-dimensional wrapped phase under phase decorrelation to obtain the three-dimensional differential wrapped phase map φ after phase reconstruction; S8, inputting the phase-reconstructed three-dimensional differential wrapped phase image φ into a Bayesian deep neural network with a three-dimensional U-Net++ structure for multiple predictions to obtain the 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 elastography according to claim 1, characterized in that: 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 within the material. 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 the 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 elastography according to claim 1, characterized in that: The Bayesian deep neural network with a three-dimensional U-Net++ structure is based on Unet++, uses a 3D-Convolutional layer with concrete dropout and a 3D-Maxpool for downsampling, uses a 3D-Up-sampling 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 elastography 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 coordinate of the discretized 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 elastography 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 bulk strain field for phase-contrast optical coherence elastography according to claim 1, characterized in that: The pixel-level displacement compensation processing is performed on the deformed 3D wrapped phase under phase decorrelation. The compensation processing formula is as follows: Where J represents the imaginary unit; Arg represents the argument of the complex number; exp is the exponential signal; φ R Represents the wrapped phase image before deformation, Represents the deformed wrapped phase obtained after displacement compensation based on the displacement fields in three directions.

7. The method for measuring bulk strain field for phase-contrast optical coherence elastography according to claim 1, characterized in that: The calculation formula for 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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