Dynamic range extension method for phase-contrast optical coherence elastography

Abstract

The present invention discloses a dynamic range extension method for phase-contrast optical coherence elastography. By leveraging the uncertainty of a network model in an uncertainty learning framework, a pixel-level displacement tracking method that can directly reflect the level of phase decorrelation noise is constructed. This method can solve the phase decorrelation problem caused by excessive deformation without changing the structure of the existing PC-OCE measurement system, thereby extending the dynamic range of PC-OCE.

Description

Technical Field

[0001] The present invention relates to the technical field of phase-contrast optical coherence elastic imaging, and in particular to a dynamic range expansion method for phase-contrast optical coherence elastic imaging. Background Art

[0002] Phase-Contrast Optical Coherence Elastography (PC-OCE) utilizes the high sensitivity of tomographic interferometry phase changes to achieve full-field, high-precision measurement of the internal strain distribution of materials, making it the most promising method for characterizing internal mechanical properties.

[0003] The measurement steps of PC-OCE generally include: 1) collecting interference spectrum data during the deformation process of the sample; 2) demodulating the interference spectrum data based on Fourier transform to obtain the differential wrapped phase field of the sample under different deformation states; 3) calculating the gradient distribution of the differential wrapped phase field along the depth direction to obtain the strain field; 4) based on the calculated strain field and the mechanical loading prior information of the sample, obtaining the elastic modulus and other mechanical property information of the sample. It can be seen that the key to whether PC-OCE can achieve accurate elastic imaging lies in its acquisition of high-quality differential wrapped phase images. However, when the sample deformation is too large, it will cause pixel-level displacement of scattered speckles at the same position, that is, phase decorrelation. Phase decorrelation will add additional speckle phase noise to the interference spectrum, affecting the final phase imaging quality. In extreme cases, the phase fringe signal will be submerged in the decorrelation noise (see Figure 5 Therefore, the existence of phase decorrelation limits the deformation measurement range of existing PC-OCE, resulting in a low measurement dynamic range.

[0004] Existing technical solutions to the phase decorrelation problem are mainly divided into hardware solutions and software solutions. The hardware solution mainly uses a high-speed camera to continuously and quickly collect interference spectrum data during the sample deformation process, and then calculates the strain distribution under large deformation conditions through incremental superposition to solve the phase decorrelation problem. The software solution mainly uses the branch cutting method of spatial phase unwrapping to construct a phase tracking method with optimized number of phase residual points, realizing pixel-level displacement tracking before and after large deformation, and solving the phase decorrelation problem without changing the PC-OCE hardware structure.

[0005] However, for the hardware solution, its main disadvantage is that the incremental superposition calculation method will lead to error accumulation and propagation, resulting in a low signal-to-noise ratio of PC-OCE imaging, which is difficult to meet the needs of actual tomographic measurement scenarios. In addition, the hardware solution requires a specially designed spectrometer integrated with a high-speed camera, which is difficult to integrate hardware, and because there is an upper limit on the camera acquisition frame rate, it is difficult to fundamentally overcome phase decorrelation. For the software solution, its main disadvantage is that the phase tracking method uses the minimum number of phase residual points as the optimization goal, but the phase residual points essentially reflect the singular points of the phase space unwrapping, which is difficult to quantitatively characterize the decorrelation noise in the elastic imaging process. This results in the solution being not very robust in actual measurements, and the tracking effect is heavily dependent on prior information such as window size, resulting in poor practicality. Summary of the Invention

[0006] The purpose of the present invention is to overcome the deficiencies of the prior art and provide a method for dynamic range extension for phase-contrast optical coherence elastography with strong robustness and high practicality.

[0007] To achieve the above objectives, the technical solutions provided by the present invention are:

[0008] Dynamic range extension method for phase contrast optical coherence elastography, including:

[0009] S1, PC-OCE collects the interference spectrum signals I1(k, y) and I2(k, y) before and after the sample deformation, where k is the wave number of the laser and y is the spatial coordinate of the cross section;

[0010] S2. Perform Fourier transform on the interference spectrum signals I1(k, y) and I2(k, y), and obtain their respective wrapped phases φ1(z, y) and φ2(z, y) by calculating the argument, where z represents the depth coordinate;

[0011] S3. Select a sub-region of size M×M on the deformed wrapped phase φ2(z, y), and the center point (ξ, η) of the sub-region is the pixel to be phase tracked;

[0012] S4, performing pixel-level displacement (Δξ, Δη) on the sub-area described in step S3 in the horizontal and vertical directions, and calculating the differential wrapping phase corresponding to the pixel-level displacement;

[0013] S5. Construct and train a Bayesian deep neural network with a U-Net++ structure, where the input of the network is the differential wrapped phase and the output is the model uncertainty of the phase gradient. Use Bayesian inference to obtain the optimal posterior probability density distribution of the network weights.

[0014] S6. Send the differential wrapped phase obtained in step S4 into the trained Bayesian deep convolutional network of U-Net++ structure to obtain the corresponding model uncertainty;

[0015] S7, constructing an energy optimization equation for the model uncertainty obtained in step S6 to find the pixel-level displacement corresponding to the minimum energy;

[0016] S8. Based on the deformed wrapped phase φ1(z, y) obtained in step S2, each pixel is processed according to steps S3 to S7 to obtain a pixel-level horizontal displacement field Δξ*(m, n) and an axial displacement field Δη*(m, n);

[0017] S9. Perform pixel-level displacement compensation processing under phase decorrelation based on the pixel-level horizontal displacement field Δξ*(m,n) and axial displacement field Δη*(m,n) obtained in step S8 to achieve dynamic range expansion.

[0018] Furthermore, the formula for calculating the differential wrapped phase is as follows:

[0019]

[0020] Where j represents the imaginary unit, Arg represents the principal value of the complex argument, and (m,n) are the spatial coordinates of the discretized phase image. Δξ and Δη are the pixel-level displacements of the sub-region in the horizontal and vertical directions, respectively. Δφ corresponds to the deformation of the sub-region. The larger the deformation, the denser the phase fringes.

[0021] Furthermore, the calculation formula of the model uncertainty is as follows:

[0022]

[0023] Among them, μ (l) is the phase gradient output of the lth network, is the average phase gradient output of L networks; (m,n) is the spatial coordinate after discretization of the phase image.

[0024] Furthermore, the energy optimization equation is constructed as follows:

[0025]

[0026] Among them, σ(m,n,Δξ,Δη) is the model uncertainty, (Δξ * ,Δη * ) is the pixel-level displacement corresponding to the minimum energy; (Δξ, Δη) is the pixel-level displacement of the sub-region along the horizontal and vertical directions; Represents a set of integers.

[0027] Furthermore, pixel-level displacement compensation processing is performed under phase decorrelation, and the formula used is as follows:

[0028]

[0029] Wherein, j represents the imaginary unit; Arg represents the argument of the complex number; exp is the exponential signal; φ1 is the phase calculated according to step S2 before the sample is deformed, and φ2 is the phase calculated according to step S2 after the sample is deformed; (Δξ, Δη) is the pixel-level displacement of the sub-area in the horizontal and vertical directions; (Δξ * ,Δη * ) is the pixel-level displacement corresponding to the minimum energy; (m,n) is the spatial coordinate after the phase image is discretized.

[0030] Compared with the existing technology, the principles and advantages of this technical solution are as follows:

[0031] This technical solution uses the uncertainty of the network model in the uncertainty learning framework to construct a pixel-level displacement tracking method that can directly reflect the level of phase decorrelation noise. Without changing the structure of the existing PC-OCE measurement system, it can solve the phase decorrelation problem caused by excessive deformation, thereby expanding the dynamic range of PC-OCE. BRIEF DESCRIPTION OF THE DRAWINGS

[0032] 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.

[0033] Figure 1 This is a principle flow chart of the dynamic range extension method for phase contrast optical coherence elastography of the present invention;

[0034] Figure 2 A schematic diagram of a model uncertainty acquisition principle for characterizing the phase decorrelation noise level in the dynamic range extension method for phase contrast optical coherence elastography of the present invention;

[0035] Figure 3 This is a schematic diagram of the principle of pixel-level displacement tracking based on minimization of model uncertainty energy in the dynamic range extension method for phase-contrast optical coherence elastography of the present invention;

[0036] Figure 4 This is a diagram showing the effect of differential wrapping phase measurement after adopting the dynamic range extension method for phase contrast optical coherence elastography of the present invention;

[0037] Figure 5This is the differential wrapping phase diagram obtained by PC-OCE measurement when the deformation increases in the prior art. DETAILED DESCRIPTION

[0038] The present invention will be further described below in conjunction with specific embodiments:

[0039] like Figure 1 As shown, the dynamic range extension method for phase contrast optical coherence elastography described in this embodiment includes:

[0040] S1, PC-OCE collects the interference spectrum signals I1(k,y) and I2(k,y) before and after the sample deformation, where k is the wave number of the laser and y is the spatial coordinate of the cross section;

[0041] S2. Perform Fourier transform on the interference spectrum signals I1(k, y) and I2(k, y), and obtain their respective wrapped phases φ1(z, y) and φ2(z, y) by calculating the argument, where z represents the depth coordinate; the size of the deformed wrapped phase φ2(z, y) is 450×450;

[0042] S3. Select a sub-region of size 20×20 on the deformed wrapped phase φ2(z, y). The center point (ξ, η) of the sub-region is the pixel to be phase tracked.

[0043] S4, performing pixel-level displacement (Δξ, Δη) on the sub-area described in step S3 in the horizontal and vertical directions, and calculating the differential wrapping phase corresponding to the pixel-level displacement;

[0044] In this step, the formula for calculating the differential wrapping phase is as follows:

[0045]

[0046] Where j represents the imaginary unit, Arg represents the principal value of the complex argument, and (m,n) are the spatial coordinates of the discretized phase image. Δξ and Δη are the pixel-level displacements of the sub-region in the horizontal and vertical directions, respectively. Δφ corresponds to the deformation of the sub-region. The larger the deformation, the denser the phase fringes.

[0047] S5. Construct and train a Bayesian deep neural network with a U-Net++ structure, where the input of the network is the differential wrapped phase and the output is the model uncertainty of the phase gradient. The optimal posterior probability density distribution of the network weights is obtained using the Bayesian inference method, such as Figure 2 As shown;

[0048] The calculation formula for the model uncertainty σ(m,n,Δξ,Δη) is as follows:

[0049]

[0050] Among them, μ (l) is the phase gradient output of the lth network, is the average phase gradient output of L networks; (m,n) is the spatial coordinate after discretization of the phase image.

[0051] S6. Send the differential wrapped phase obtained in step S4 into the trained Bayesian deep convolutional network of U-Net++ structure to obtain the corresponding model uncertainty;

[0052] S7, construct an energy optimization equation for the model uncertainty obtained in step S6 to find the pixel-level displacement corresponding to the minimum energy. The pixel-level displacement tracking principle based on the minimum energy of the model uncertainty is as follows: Figure 3 As shown;

[0053] The constructed energy optimization equation is as follows:

[0054]

[0055] Among them, σ(m,n,Δξ,Δη) is the model uncertainty, (Δξ * ,Δη * ) is the pixel-level displacement corresponding to the minimum energy; (Δξ, Δη) is the pixel-level displacement of the sub-region along the horizontal and vertical directions; Represents a set of integers.

[0056] S8. Based on the deformed wrapped phase φ1(z, y) obtained in step S2, each pixel is processed according to steps S3 to S7 to obtain the pixel-level horizontal displacement field Δξ. * (m,n) and axial displacement field Δη * (m,n);

[0057] The formula used is as follows:

[0058]

[0059] Wherein, j represents the imaginary unit; Arg represents the argument of the complex number; exp is the exponential signal; φ1 is the phase calculated according to step S2 before the sample is deformed, and φ2 is the phase calculated according to step S2 after the sample is deformed.

[0060] S9, pixel-level horizontal displacement field Δξ obtained in step S8 * (m,n) and axial displacement field Δη * (m,n), pixel-level displacement compensation processing is performed under phase decorrelation to achieve dynamic range expansion.

[0061] like Figure 4As shown in the figure, as the deformation increases, the PC-OCE differential wrapped phase is completely submerged in the decorrelation noise due to severe phase decorrelation (see the differential wrapped phase before tracking). After using the solution of the embodiment of the present invention, the differential wrapped phase fringe signal submerged in the phase decorrelation noise is well restored. Therefore, the solution of the embodiment of the present invention can handle large sample deformations, effectively solving the dynamic range problem of PC-OCE.

[0062] 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 dynamic range extension for phase contrast optical coherence elastography, characterized in that: include: S1, PC-OCE collects the interference spectrum signals I1(k, y) and I2(k, y) before and after the sample deformation, where k is the wave number of the laser and y is the spatial coordinate of the cross section; S2. Perform Fourier transform on the interference spectrum signals I1(k, y) and I2(k, y), and obtain their respective wrapped phases φ1(z, y) and φ2(z, y) by calculating the argument, where z represents the depth coordinate; S3. Select a sub-region of size M×M on the deformed wrapped phase φ2(z, y), and the center point (ξ, η) of the sub-region is the pixel to be phase tracked; S4, performing pixel-level displacement (Δξ, Δη) on the sub-area described in step S3 in the horizontal and vertical directions, and calculating the differential wrapping phase corresponding to the pixel-level displacement; S5. Construct and train a Bayesian deep neural network with a U-Net++ structure, where the input of the network is the differential wrapped phase and the output is the model uncertainty of the phase gradient. Use Bayesian inference to obtain the optimal posterior probability density distribution of the network weights. S6. Send the differential wrapped phase obtained in step S4 into the trained Bayesian deep convolutional network of U-Net++ structure to obtain the corresponding model uncertainty; S7, constructing an energy optimization equation for the model uncertainty obtained in step S6 to find the pixel-level displacement corresponding to the minimum energy; S8. Based on the deformed wrapped phase φ1(z, y) obtained in step S2, process each pixel according to steps S3 to S7 to obtain a pixel-level horizontal displacement field Δξ*(m, n) and an axial displacement field Δη*(m, n); S9. Perform pixel-level displacement compensation processing under phase decorrelation based on the pixel-level horizontal displacement field Δξ*(m,n) and axial displacement field Δη*(m,n) obtained in step S8 to achieve dynamic range expansion.

2. The dynamic range extension method for phase contrast optical coherence elastography according to claim 1, characterized in that: The formula for calculating the differential wrapped phase is as follows: Where j represents the imaginary unit, Arg represents the principal value of the complex argument, (m, n) are the spatial coordinates after the discretization of the phase image; Δξ and Δη are the pixel-level displacements of the sub-region in the horizontal and vertical directions, respectively; Δφ corresponds to the deformation of the sub-region. The larger the deformation, the denser the phase fringes.

3. The dynamic range extension method for phase contrast optical coherence elastography according to claim 1, characterized in that: The calculation formula of model uncertainty is as follows: Among them, μ (l) is the phase gradient output of the lth network, is the average phase gradient output of L networks; (m, n) is the spatial coordinate of the discretized phase image.

4. The dynamic range extension method for phase contrast optical coherence elastography according to claim 1, characterized in that: The constructed energy optimization equation is as follows: Among them, σ(m, n, Δξ, Δη) is the model uncertainty, (Δξ * , Δη * ) is the pixel-level displacement corresponding to the minimum energy; (Δξ, Δη) is the pixel-level displacement of the sub-region along the horizontal and vertical directions; Represents a set of integers.

5. The dynamic range extension method for phase contrast optical coherence elastography according to claim 1, characterized in that: The pixel-level displacement compensation processing under phase decorrelation is performed using the following formula: Wherein, j represents the imaginary unit; Arg represents the argument of the complex number; exp is the exponential signal; φ1 is the phase calculated according to step S2 before the sample is deformed, and φ2 is the phase calculated according to step S2 after the sample is deformed; (Δξ, Δη) is the pixel-level displacement of the sub-area in the horizontal and vertical directions; (Δξ * , Δη * ) is the pixel-level displacement corresponding to the minimum energy; (m, n) is the spatial coordinate after the phase image is discretized.

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