Microholographic method for holographic particle imaging of single high-density body

Abstract

The invention discloses a microholographic method # imgabs0 # for holographic particle imaging of a single high-density body. The microholographic method # imgabs0 # aims to solve the problems that an existing holographic particle imaging technology is limited in the aspects of resolution and particle concentration, and a linear approximation model of a traditional method such as compressed holography (CH) fails under high particle density. According to the method, a micro forward propagation model is established by adopting a micro programming normal form, and an inverse problem is solved by utilizing an automatic differentiation (AD) technology. Through numerical simulation and optical experiment verification, the method can effectively improve imaging precision and particle density, is superior to an existing method such as CH-FASTA in particle positioning precision, has robustness to noise, can reconstruct high-density particles of different sizes more accurately, and has a wide application prospect.

Description

Technical Field

[0001] The invention belongs to the technical field of holographic imaging, and in particular relates to a differentiable holographic method for single high-density holographic particle imaging. Background Art

[0002] Digital holography (DH) is a powerful 3D imaging method with wide applications in many fields such as materials science and bio-imaging. In 3D particle imaging, it can achieve quantitative measurements by recording the 2D holograms generated by light passing through particles and digitally reconstructing the particle information. However, traditional holographic particle imaging methods have some limitations. For example, the traditional method of reconstructing 3D particle fields based on online holograms is plagued by the twin image problem and requires additional post-processing to eliminate artifacts. In addition, the difference between 2D measurements and 3D targets and the phase-free nature of the measurements make it challenging to clearly reconstruct volume particles.

[0003] To improve the reconstruction accuracy, some methods such as compressed holography (CH) and deep learning have emerged. CH has made progress by solving the inverse problem through iterative optimization solvers, but the linear approximation-based method is only applicable to weakly scattering objects. At high particle density, the linear assumption gradually fails, leading to erroneous particle reconstruction. In the case of high-density particles, the enhanced scattering phenomenon will lead to lower signal-to-noise ratio and increased position uncertainty. Although deep learning can map holograms to three-dimensional particle distributions, it faces challenges in interpretability, robustness and generalization, especially when dealing with new experimental data and large-volume and high-density particle reconstruction.

[0004] Existing technologies such as the linear approximation model of CH have many problems in actual imaging scenarios, such as the pre-measurement of the reference beam and the calibration of the camera-container distance may not be feasible, and the linear approximation is not applicable to various nonlinear factors of high-density particles, resulting in inaccurate reconstruction. At the same time, existing methods such as 3D deconvolution technology can improve the reconstruction quality, but cannot restore accurate and dense 3D particles. Summary of the invention

[0005] The present invention proposes a three-dimensional differentiable holographic method By adopting the differentiable programming paradigm, establishing a differentiable forward propagation model, and using automatic differentiation (AD) technology to solve the inverse problem, this method can more effectively solve the particle imaging problem, overcome the limitations of existing technologies, and improve imaging accuracy and particle density.

[0006] The specific technical solution of the present invention is:

[0007] A differentiable holographic method for single high-density holographic particle imaging, characterized in that the method comprises the following steps:

[0008] S1. Establish the forward model: discretize the three-dimensional particle volume into N discrete slices. The forward model is The model is established by applying the angular spectrum method (ASM) from the farthest plane to the farthest plane to the closest plane, taking into account the multiple scattering effects of high-density particles and without the need for pre-measurement of the reference beam. At the same time, the camera-container distance z o ;

[0009] S2. Solve the inverse problem: Formulate the problem as a minimization problem st|o|-1≤0,∠o=0, where and R TV It is a regularization term involving the l1 norm and the total change. The gradient of the objective function is calculated through automatic differentiation (AD) technology, the object-related parameters and the camera-container distance are updated, and the solution is iterated until convergence. BRIEF DESCRIPTION OF THE DRAWINGS

[0010] The drawings described herein are used to provide a further understanding of the embodiments of the present invention, constitute a part of this application, and do not constitute a limitation of the embodiments of the present invention. In the drawings:

[0011] Figure 1 : Schematic diagram of the online holographic setup and the associated beam propagation model.

[0012] Figure 2 : Hologram and probability density distribution under different particle densities.

[0013] Figure 3 : Distribution of light propagation within the particle volume under different particle densities.

[0014] Figure 4 : MDE curves of the method of the present invention and the CH-FASTA method under different particle densities.

[0015] Figure 5 : Reconstructing the spatial distribution of particle positions at different particle densities.

[0016] Figure 6 : yz cross-sectional projection of reconstructed particles at different particle densities.

[0017] Figure 7 : The case of reconstructing particle positions for smaller particle sizes.

[0018] Figure 8 : MDE curves of the method of the present invention and the CH-FASTA method when noise is introduced.

[0019] Fig. 9 : Reconstructed particle situation and evolution with and without distance optimization.

[0020] Fig.10: Hologram and probability density distribution under high scattering effect.

[0021] Fig.11 : Display of relevant experimental results.

[0022] Fig.12 : Display of sample particle reconstruction results.

[0023] Fig.13 : Particle distribution and reconstruction results of different samples.

[0024] Fig.14 : Display of sparse and high-density particle reconstruction.

[0025] Fig.15 :Display of high-density particles in different xy slice planes. DETAILED DESCRIPTION

[0026] In order to make the objectives, technical solutions and advantages of the present invention more clearly understood, the present invention is further described in detail below in conjunction with embodiments and drawings. The exemplary embodiments of the present invention and their description are only used to explain the present invention and are not intended to limit the present invention.

[0027] A differentiable holographic method for single high-density holographic particle imaging, characterized in that the method comprises the following steps:

[0028] S1. The scattering effect was verified by changing the particle density. It was found that as the particle density increased, the hologram generated by the multi-layer slicing method changed from diffraction stripes to a speckle-like pattern, and its probability density distribution also changed from Gaussian distribution to non-Gaussian distribution, while the hologram distribution of the traditional propagation method remained unchanged, proving that the multi-layer slicing method can effectively simulate the scattering behavior, while the traditional method cannot.

[0029] S2. The present invention The method is compared with the classic CH-FASTA algorithm, and the mean Euclidean distance error (MDE) is calculated at different particle densities. The results show that The method can achieve sub-pixel accuracy at all tested densities, while the accuracy of the CH-FASTA method decreases as the particle density increases. The spatial distribution and yz cross-sectional projections are also used to intuitively demonstrate the In addition, the test of smaller 10-um particles also proved The stability and advantages of the method.

[0030] S3. The noise robustness of the method is evaluated by introducing Gaussian noise with different signal-to-noise ratios into the hologram. The results show that The method is remarkably resistant to noise, with MDE being approximately one pixel lower than the CH-FASTA method at all evaluated noise levels. A simulation experiment also demonstrates that using distance z0 as an optimization variable can improve reconstruction accuracy.

[0031] S4. The multi-layer slice propagation method was experimentally verified. The hologram was captured using a specific container, particle, sensor, and light source setup. It was observed that the hologram exhibited a speckle-like pattern and the probability density distribution conformed to the Rician-like distribution of high scattering effect, which was consistent with the numerical simulation results.

[0032] S5. Experiments were conducted on two samples containing different numbers of particles to verify the particle imaging accuracy. The distance z0 was optimized in the experiment, and the optimized distance was verified to be effective by back propagation. By comparing the results of particle reconstruction by the method of the present invention and the CH-FASTA method, it was shown that the method of the present invention can accurately reconstruct high-density particles of different sizes, while the CH-FASTA method cannot accurately reconstruct a large number of real particles. In addition, experiments in a water environment further demonstrated the advantages of the method of the present invention at different particle densities, and visual comparisons showed that the method of the present invention can more accurately locate particles and will not incorrectly reconstruct particles.

Claims

1. A differentiable holographic method for imaging a single high-density holographic particle, characterized in that The method comprises the following steps: S1. Establish a forward model: Discretize the three-dimensional particle volume into N discrete slices. The forward model is The model is established by applying the angular spectrum method (ASM) from the farthest plane to the farthest plane to the closest plane, taking into account the multiple scattering effects of high-density particles and without the need for pre-measurement of the reference beam. At the same time, the camera-container distance z o ; S2. Solve the inverse problem: Formulate the problem as a minimization problem st|o|-1≤0,∠o=0, where and R TV It is a regularization term involving the l1 norm and the total change. The gradient of the objective function is calculated through automatic differentiation (AD) technology, the object-related parameters and the camera-container distance are updated, and the solution is iterated until convergence. S2. The differentiable holographic method according to claim 1, characterized in that The method can realize single high-density holographic particle imaging, thereby improving imaging accuracy and particle density. S3. The differentiable holographic method according to claim 1, characterized in that The method is robust to noise and can maintain high particle positioning accuracy in the presence of noise. S4. The differentiable holographic method according to claim 1, characterized in that The method described is able to accurately reconstruct high-density particles of different sizes.

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