High-reliability biplane lensless on-sheet holographic microscopic phase image reconstruction method

Abstract

The invention discloses a high-reliability double-plane lensless on-sheet holographic microscopic phase image reconstruction method. The method comprises the following steps: firstly, acquiring two frames of holograms with different heights, acquiring optimized initial object plane complex amplitude distribution by utilizing a biplane intensity transmission equation, then calculating an object plane complex amplitude gradient value by adopting a biplane Wirtinger operator and updating the object plane complex amplitude gradient value, then applying complex amplitude total variation minimization and physical absorption double constraints, accelerating updating by utilizing Nesterov momentum, and finally calculating the object plane complex amplitude gradient value according to the updated object plane complex amplitude gradient value. And finally, a high-reliability object phase image is obtained through iteration. According to the method, the suitability of the non-convex optimization problem under the limited measurement condition can be effectively improved, and the calculation efficiency and precision of phase reconstruction are improved. Compared with an existing biplane phase reconstruction algorithm, the method can achieve lens-free on-sheet holographic microscopic phase image reconstruction with higher fidelity and higher imaging precision, and is suitable for processing complex samples and reconstruction scenes needing higher fidelity.

Description

Technical Field

[0001] This invention relates to the field of microscopic imaging technology, and in particular to a highly reliable method for reconstructing on-sheet holographic microscopic phase images without lenses in two planes. Background Technology

[0002] Lensless on-sheet holographic microscopy is a high-throughput microscopy technique that directly images the object under test against the surface of an image sensor without the need for any lenses. This technique uses a coherent or partially coherent light source to illuminate the object; the scattered light from the object interferes with a reference light to form a hologram, which is recorded by an image sensor. A phase retrieval algorithm is then used to accurately recover the wavefront information of the object from the recorded hologram, achieving amplitude and phase imaging. Compared to traditional optical microscopy systems that utilize imaging lenses, this technique offers significant advantages such as simple and compact structure, low cost, resolution not limited by lens aperture, and the ability to achieve high-resolution imaging over a large field of view. It has enormous application potential in portable devices and resource-constrained scenarios.

[0003] However, lensless on-sheet holographic microscopy, based on the principle of coaxial holography, suffers from severe twin image interference during phase imaging, leading to decreased image resolution and contrast and affecting the accuracy of phase imaging. Therefore, removing twin image interference and achieving high-reliability, high-precision phase imaging are the core challenges of lensless on-sheet holographic microscopy.

[0004] Traditional multi-frame holographic phase retrieval algorithms require acquiring 6 to 8 lensless on-sheet holograms with different modulation parameters by changing recording distance, illumination wavelength, illumination angle, and mask modulation. Under information redundancy, simple algorithms such as the traditional GS algorithm or TIE algorithm can effectively suppress twin interference and achieve high-precision phase reconstruction. However, multi-frame algorithms have two main limitations: first, multi-parameter modulation significantly increases the complexity of the optical system; second, data acquisition is time-consuming, making it unsuitable for real-time dynamic observation, especially limiting its application in scenarios with high temporal resolution requirements, such as live-cell imaging or industrial online inspection.

[0005] In contrast, single-frame phase retrieval algorithms only require acquiring one lensless hologram to complete the reconstruction, offering a significant advantage in data acquisition efficiency. However, single-frame phase retrieval is a severely non-convex problem, leading to significant ill-posedness in the solution process. This ill-posedness makes the algorithm prone to getting trapped in local optima. Existing single-frame phase retrieval algorithms are typically based on compressed sensing frameworks, relying on multiple prior information, including physical constraints (such as nonnegativity and absorption domain), sparse priors in the transform domain (such as spatial domain and gradient domain), and implicit priors based on image enhancement (such as BM3D matching algorithm and guided filtering) or deep neural networks, to reduce the solution space and improve the well-posedness of the non-convex problem. Although the above methods can eliminate twin interference to some extent, the reconstruction quality is still limited due to the severely insufficient information in a single-frame hologram: firstly, over-reliance on prior knowledge easily introduces reconstruction biases, manifested as phase discontinuities or structural distortions; secondly, the limited information capacity leads to the loss of high-frequency details and the amplification of artifacts. These limitations restrict the practical applicability of single-frame algorithms in handling complex samples, low signal-to-noise ratio environments, and reconstruction scenarios requiring high reliability.

[0006] To effectively alleviate the ill-posedness of non-convex problems in single-frame phase retrieval, researchers have begun studying dual-plane phase retrieval algorithms in the field of lensless holographic microscopy. The aim is to improve the well-posedness of non-convex problems from a physical perspective while maintaining data acquisition efficiency, thereby achieving high-reliability phase retrieval. Guo Cheng's team proposed a dual-plane phase retrieval algorithm based on total variational constraints. Through weighted feedback mechanisms and regularization design, the reconstructed image exhibits good resolution and noise suppression; however, the reconstructed image still lags significantly behind traditional multi-frame phase retrieval results. Winnik's team proposed a dual-plane phase retrieval framework based on conjugate gradient minimization. While possessing theoretical characteristics such as global convergence, fast convergence, and low computational cost, the lack of suitable regularization techniques limits the algorithm's reconstruction accuracy. Therefore, although theoretically dual-plane phase retrieval can balance data acquisition efficiency and imaging reliability, in the field of lensless holographic microscopy, existing dual-plane phase retrieval algorithms have not yet achieved the reconstruction results of multi-frame phase retrieval. Summary of the Invention

[0007] To address the aforementioned problems, the present invention aims to provide a highly reliable method for reconstructing phase images using dual-plane lensless on-sheet holographic microscopy, thereby improving imaging reliability and accuracy.

[0008] The technical solution to achieve the objective of this invention is as follows: a highly reliable method for reconstructing phase images using dual-plane lensless on-sheet holographic microscopy, comprising the following steps: Step S1: Acquire two frames of lensless holographic microscopic images at different heights, calculate the initial complex amplitude distribution of the object plane using the dual-plane intensity transmission equation, and use it as the estimated value of the complex amplitude of the object plane. Step S2: The estimated complex amplitude of the object plane is updated by gradient using the biplane Wirtinger operator, and then the total variation minimization and physical absorption constraints of the complex amplitude are applied. The Nesterov momentum is used to accelerate the update to obtain the updated complex amplitude of the object plane. Step S3: Determine the convergence condition of the complex amplitude of the object plane after physical absorption constraint in step S2. If the convergence condition is not met, use the final updated value in step S2 as the estimated value of the complex amplitude of the object plane and repeat step S2. If the convergence condition is met, terminate the iteration, output the complex amplitude value of the object plane after physical absorption constraint, and obtain the final reconstructed phase image.

[0009] Preferably, step S1 specifically includes: S11. Using the established lensless on-sheet holographic microscopy system, two frames of holographic micrographs at different heights are acquired, and the precise height of each hologram is calculated using an autofocus algorithm. S12. Use an image registration algorithm to register the two holographic micrographs to obtain the registered two holographic images. S13. For the two registered holograms, use the dual-plane intensity transmission equation to solve for the phase distribution of the optical field on one of the hologram planes. Combine the amplitude distribution recorded on that hologram plane to synthesize the complex amplitude distribution of the optical field on that hologram plane. S14. Using the optical field angular spectrum propagation algorithm, the complex amplitude of the optical field on the hologram plane is propagated backward to the object plane, and the initial complex amplitude distribution of the optical field on the object plane is calculated as the estimated value of the complex amplitude on the object plane.

[0010] Preferably, step S2 specifically includes: S21. Using the estimated complex amplitude of the object plane as the initial value for iteration, the gradient value of the complex amplitude of the object plane is calculated using the biplane Wirtinger operator, and the complex amplitude distribution of the object plane is updated using the gradient descent algorithm. S22. Apply the total variational minimization constraint of complex amplitude to the object plane complex amplitude updated in step S21, and update the object plane complex amplitude distribution using the near-end gradient descent algorithm. S23. Apply amplitude physical absorption constraints to the object plane complex amplitude updated in step S22, and update the object plane complex amplitude distribution. S24. The complex amplitude of the object plane updated in step S23 is updated using Nesterov momentum acceleration to obtain the updated value of the complex amplitude of the object plane.

[0011] Preferably, step S21 specifically includes: S211. Using the estimated value of the complex amplitude of the object plane as the starting value of the current iteration, and using the amplitude information of the two frames of holographic micrographs, the Wirtinger operator is used to calculate the two complex amplitude gradient values ​​of the object plane respectively. S212. Average the two gradient values ​​obtained in step S211 to obtain the global gradient: , In the formula, ▽ F 1( u m ) and ▽ F 2( u m ) represent the complex amplitude gradient values ​​of the two object planes, It is the global gradient. u m Indicates the first m The estimated complex amplitude of the object plane in the next iteration; S213. Using the global gradient described in step S212, obtain the updated complex amplitude distribution of the object plane through the gradient descent algorithm.

[0012] Preferably, step S22 specifically includes: A proximal gradient descent operator model for minimizing the total variation of complex amplitude is constructed and solved using the dual method. Spatial edge weights are introduced to locally modulate the update step size of the dual variables, and the obtained optimal dual solution is then used to update the complex amplitude distribution of the object plane. Among them, the optimal dual solution w * Obtained from the following sub-iterations: , In the formula, l represents the number of sub-iterations. γ denoted by τ, where τ represents the regularization parameter, and ▽ represents the discrete gradient operator. div ( ) denotes the discrete divergence operator. W It is the spatial edge weight, the initial dual solution ω 0 =0.

[0013] Preferably, step S3 specifically includes: Step S31: The first convergence condition is determined for the complex amplitude of the object plane after physical absorption constraint in step S2. The first convergence condition uses the sum of squared amplitude errors (…). ASSE ), can be represented as: , In the formula, and They represent the first m Second and third m- The magnitude of the complex amplitude of the object plane after a single physical absorption constraint. Nx 、N y It is the size of the image. ε It is a preset threshold; Step S32: The second convergence condition is determined for the complex amplitude of the object plane after physical absorption constraint in step S2. The second convergence condition is defined as the relative rate of change of ASSE at a preset interval of iterations, which can be expressed as: , In the formula, m and mc They represent the first m The second iteration and the first m - c iteration c This indicates the preset interval for the number of iterations. η It is a preset threshold; Step S33: Based on the first convergence condition and the second convergence condition, if neither convergence condition is met, repeat the iteration of step S2. If either convergence condition is met, terminate the iteration, output the complex amplitude value of the object plane after physical absorption constraint, and obtain the final reconstructed phase image.

[0014] As described above, this invention discloses a highly reliable dual-plane lensless on-sheet holographic microscopic phase image reconstruction method. First, a dual-plane Wirtinger operator is used for complex amplitude gradient descent update iterations. Simultaneously, an optimized initial value and a Nesterov momentum acceleration strategy are employed to improve computational efficiency and reconstruction accuracy. Furthermore, the well-posedness of the non-convex problem under finite measurement conditions is enhanced by utilizing the dual constraints of complex amplitude total variation minimization and physical absorption. This invention achieves imaging quality comparable to traditional multi-frame phase retrieval algorithms while reducing data acquisition volume. Comparison with existing dual-plane phase retrieval algorithms demonstrates that this invention's algorithm can achieve higher imaging reliability and accuracy. Attached Figure Description

[0015] Figure 1 The flowchart illustrates a highly reliable dual-plane lensless on-chip holographic microscopic phase image reconstruction method provided in this embodiment of the invention.

[0016] Figure 2 This is a schematic diagram of the lensless on-sheet holographic microscopy device provided in an embodiment of the present invention.

[0017] Figure 3 The figures show experimental results of simulated imaging of phase-type objects using different phase retrieval algorithms, as provided in embodiments of the present invention. Figure 3 (a) shows the original phase map and the phase maps reconstructed by each algorithm; Figure 3 (b) is the residual plot between the corresponding reconstructed plot and the original plot.

[0018] Figure 4 This is an experimental result image obtained using a standard polystyrene microsphere sample as an embodiment of the present invention. Figure 4 (a) is one of the two holograms acquired by the sensor; Figure 4 In the middle (b)-(g), the phase maps reconstructed by different algorithms are shown. Figure 4 (I) Thickness distribution curves of microspheres along the central diameter obtained by different algorithms were plotted.

[0019] Figure 5 The images show experimental results of imaging oral epithelial cell samples using different phase retrieval algorithms, as provided in this embodiment of the invention. The left image is a hologram acquired by the sensor; in the right image, (a1)~(a5) and (b1)~(b5) are the local magnified reconstruction results of different regions under each algorithm. Detailed Implementation

[0020] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0021] This invention discloses a highly reliable method for reconstructing phase images using dual-plane lensless on-sheet holographic microscopy.

[0022] In this embodiment, holographic microscopic images can be acquired using a lensless on-sheet holographic microscopy device constructed in our laboratory. A schematic diagram of the device structure is shown below. Figure 2 As shown. The sample to be tested is placed on the sample stage, and the height of the imaging sensor in the experimental setup from the sample is adjusted. Z k To record coaxial holographic microscopic images at different heights.

[0023] Since the distance from the light source to the sample plane is much greater than the distance from the sample plane to the sensor plane, the wavefront curvature of the illumination light wave at the sample can be ignored. Therefore, the illumination light wave can be approximated as a uniform plane wave, and the transmitted light field can be expressed as: , In the formula, U p Represents the illumination light field. u Let be the transmittance function of the sample. In this embodiment, U p It can be approximated as a constant, and its diagonalized matrix form is the identity matrix (i.e., diag (U p )= I ).

[0024] Transmitted light field U t Propagation distance in free space Z k The process of reaching the holographic recording plane can be represented by the angular spectrum propagation algorithm as follows: , Q k This represents the propagation operator from the sample plane to different recording planes. F and F -1 Let Q represent the Fourier transform and the inverse Fourier transform, respectively, and the propagation operator Q. k It can be discretized and vectorized into Q. k , It is the angular spectral transfer function, which can be expressed as: , in λ It is the illumination wavelength. f x and f y They represent along x and y Spatial frequency of the axis.

[0025] The hologram obtained by the sensor corresponds to the complex optical field. The intensity is expressed as: , The amplitude of the recorded light field is expressed as: ; After vectorizing the above formula, the forward model can be obtained: , In the formula, Indicates the first k Vectorized amplitude distribution of the second measurement The linear sampling matrix represents the forward model. M x and M y Indicates the size of the hologram. N x and N y This represents the sample size. The vectorization used here is only for simplifying algorithm derivation and interpretation, and is not necessary in the actual algorithm implementation.

[0026] Under finite measurement conditions, phase reconstruction is a non-convex optimization problem, and directly solving for the phase carries the risk of non-unique solutions and overfitting. Therefore, to improve the uniqueness and physical reliability of the solution, the problem is formulated as minimizing the amplitude-based loss function under the least squares criterion, and combining the minimization of the total variation of complex amplitude and the physical absorption constraint as regularization terms. The resulting objective function is as follows: , In the formula, τ>0 is the regularization parameter, and ||.||2 is the L2 norm of the matrix. F ( u ) is a data fidelity item. R ( u ) is a regular term.

[0027] In constructing the regularization term, we adopt a hybrid regularization strategy, which integrates the dual constraints of minimizing the total variation of complex amplitude and physical absorption. Among them, the regularization term with the minimum total variation of complex amplitude is... R 1( u ) is represented as: , In the formula, ▽ represents the discrete gradient operator, ▽{U} i,j Representation matrix f In coordinates ( i , j The gradient value at point () indicates that the gradient is calculated for the real and imaginary parts of the complex optical field respectively; Physical absorption constraint R 2( u The following is represented: , In the formula, abs () represents the amplitude operator for calculating complex numbers.

[0028] The workflow of holographic microscopic phase image reconstruction method is as follows: Figure 1 As shown, it includes the following steps:

[0029] S1. Acquire two frames of lensless holographic microscopic images at different heights. Calculate the initial complex amplitude distribution of the object plane using the dual-plane intensity transmission equation and use it as the estimated value of the complex amplitude of the object plane.

[0030] Furthermore, in this embodiment, step S1 specifically includes: S11. Using the established lensless on-sheet holographic microscopy system, acquire two holographic micrographs at different heights. Focus the holographic images at different heights to obtain the precise height of each holographic image, where the precise height... Z 1 and Z 2 was obtained through an autofocus algorithm; S12. Use an image registration algorithm to register the two holographic micrographs to obtain the registered two holographic images. S13. For the two registered holograms, use the dual-plane intensity transmission equation to solve for the phase distribution of the optical field on one of the hologram planes. Combine the amplitude distribution recorded on that hologram plane to synthesize the complex amplitude distribution of the optical field on that hologram plane. S14. Using the optical field angular spectrum propagation algorithm, the complex amplitude of the optical field on the hologram plane is propagated backward to the object plane, and the initial complex amplitude distribution of the optical field on the object plane is calculated and used as the estimated value of the complex amplitude on the object plane.

[0031] S2. The estimated complex amplitude of the object plane is updated by gradient using the biplane Wirtinger operator, and then the total variational minimum and physical absorption constraints of the complex amplitude are applied. At the same time, the Nesterov momentum is used to accelerate the update, so as to obtain the updated value of the complex amplitude of the object plane.

[0032] Furthermore, in this embodiment, step S2 specifically includes: S21. Estimate the complex amplitude of the object plane. u m As the initial values ​​for iteration, the complex amplitude gradient of the object plane is calculated using the biplane Wirtinger operator, and then updated using the gradient descent algorithm to obtain the updated complex amplitude distribution of the object plane. v m ; S211, Estimate the complex amplitude of the object plane. u m Using the current iteration starting value, the complex amplitude distribution of the light field angular spectrum propagation algorithm is calculated to propagate to the two recording planes. The amplitude is compared with the amplitude of the actual recorded hologram to calculate the amplitude error. Then, the Wirtinger operator is used to calculate the complex amplitude gradient values ​​of the two object planes. The calculation formula is as follows: , In the formula, express A k The conjugate transpose operator (backpropagation operator), u m Indicates the first m The estimated value of the complex amplitude distribution of the object plane in the next iteration; S212. Average the two gradient values ​​obtained in step S211 to obtain the global gradient: ; S213. Using the global gradient described in step S212, update the complex amplitude distribution of the object plane through the gradient descent algorithm: , In the formula, γ It is the preset step size for gradient descent, and satisfies 0 < γ ≤2 / ρ ( A H A ), ρ () represents the spectral radius; S22. The complex amplitude of the object plane obtained in step S21 v m By applying a constraint to minimize the total variation of the complex amplitude, the object plane complex amplitude distribution is updated using the proximal gradient descent algorithm. s m ; The proximal gradient descent operator that minimizes the total variation of complex amplitude is represented as follows: , The denoising problem of minimizing the total variation of complex amplitudes is solved by introducing a dual matrix. The solution is obtained by transforming it into its dual form, where w x ,w y ∈ N x ×N y Corresponding to the horizontal and vertical components of the image gradient, respectively, a Lagrangian dual objective function is established, and then the Chambolle projection algorithm is used to iteratively calculate the solution to the problem: , In the formula, w * represents the optimal dual solution of the proximal gradient descent operator, d iv ( ) denotes the discrete divergence operator, the optimal dual solution. w *This can be obtained through the following sub-iteration formula: , In the formula, l represents the number of sub-iterations. W It is the spatial edge weight, the initial dual solution ω 0 =0.

[0033] S23. The complex amplitude of the object plane obtained in step S22 s m By applying amplitude physical absorption constraints, the updated complex amplitude distribution of the object plane is obtained. u' m : , S24. Update the complex amplitude of the object plane in step S23. u' m The updated values ​​of complex amplitude on the object plane are obtained by using Nesterov momentum acceleration. um+1 ; The complex amplitude of the object plane updated in step S23 is updated using Nesterov momentum acceleration to obtain the updated value of the complex amplitude of the object plane: , In the formula, The adaptive adjustment parameter for Nesterov momentum. u ' m and u ' m-1 They represent the first m Second and third m The magnitude of the complex amplitude of the object plane after -1 physical absorption constraint. u m+1 It is the first m The updated value of the complex amplitude of the object plane obtained in the next iteration.

[0034] S3. Perform a convergence condition judgment on the complex amplitude of the object plane after physical absorption constraint in step S2. If the convergence condition is not met, take the final updated value in step S2 as the estimated value of the complex amplitude of the object plane and repeat step S2. If the convergence condition is met, terminate the iteration, output the complex amplitude value of the object plane after physical absorption constraint, and obtain the final reconstructed phase image.

[0035] Furthermore, in this embodiment, step S3 specifically includes: Step S31: The first convergence condition is determined for the complex amplitude of the object plane after physical absorption constraint in step S2. The first convergence condition uses the sum of squared amplitude errors (…). ASSE ), can be represented as: , In the formula, and They represent the first m Second and third m- The magnitude of the complex amplitude of the object plane after a single physical absorption constraint. N x 、N y It is the size of the image. ε It is a preset threshold, in this embodiment ε Set to 1×10 -8 ; Step S32: The second convergence condition is determined for the complex amplitude of the object plane after physical absorption constraint in step S2. The second convergence condition is defined as the relative rate of change of ASSE at a preset interval of iterations, which can be expressed as: , In the formula, m and mc They represent the firstm The second iteration and the first m - c iteration c This indicates the preset interval for the number of iterations. η It is a preset threshold, in this embodiment η Set to 0.01, iteration interval c Set to 100; Step S33: Based on the first convergence condition and the second convergence condition, if neither convergence condition is met, repeat the iteration of step S2. If either convergence condition is met, terminate the iteration, output the complex amplitude value of the object plane after physical absorption constraint, and obtain the final reconstructed phase image.

[0036] To verify the feasibility of the highly reliable dual-plane lensless on-sheet holographic microscopic phase image reconstruction method described in this invention, we first conducted numerical simulations. The simulation parameters were set as follows: laser wavelength 405 nm, test image resolution 512 × 512 pixels, pixel size 1.67 µm, and diffraction distance (500 + ( k -1)×25)µm. To compare the performance of the algorithm described in this invention with existing algorithms, phase retrieval reconstruction was performed using the following algorithms: the Universal TIE Solver Algorithm based on the maximum intensity assumption (US-TIE), the Gerchberg-Saxto (GS) iterative algorithm (including GS algorithms using two-frame and eight-frame holograms), classical single-frame phase retrieval algorithms such as the Constrained Complex Amplitude Total Variational Algorithm (CCTV), existing dual-plane phase retrieval algorithms such as the Dual-Plane Phase Retrieval Algorithm based on Total Variational Constraints (DPR-TV), and the algorithm described in this invention. To quantitatively evaluate the performance of each algorithm, the PSRN and SSIM values ​​of each method were experimentally calculated. Figure 3 The simulation reconstruction results of different algorithms for phase-type objects are shown, among which... Figure 3 (a) shows the original phase map and the phase maps reconstructed by each algorithm. Figure 3 (b) shows the residual map between the reconstructed image and the original image. As can be seen from the figure, in terms of phase reconstruction, the phase reconstructed by the algorithm described in this invention is very close to the original image, and the error shown in the residual map is extremely small. Its image evaluation metrics are significantly better than other algorithms, demonstrating extremely high phase reconstruction fidelity. Numerical simulation results prove that, compared with existing traditional algorithms, the algorithm described in this invention significantly reduces residual error while maintaining high reconstruction accuracy, exhibiting stronger robustness and stability.

[0037] In this embodiment, the experiment is as follows: Figure 2The illumination was performed on the device shown. The illumination source was a single-mode fiber-coupled laser (FCM405S50LM1P0, fiber laser, center wavelength 405nm), and the detector was a CMOS image sensor (DMM27UJ003-ML, The Imaging Source). The image sensor had a pixel size of 1.67μm and provided a field of view of approximately 29.85mm. 2 The distance Z between the image sensor plane and the sample plane. k The distance Z0 between the laser and the sample plane is approximately 0.4 to 1 mm, and approximately 15 cm. The sample plane is equipped with an electrically driven displacement platform (GCD-402050M, Daheng Optics) for adjusting Z0. k This allows for the acquisition of holographic microscopic images at different heights.

[0038] To quantitatively verify the accuracy of the algorithm described in this invention, we selected polystyrene microspheres with known optical properties as the reference sample for phase reconstruction. The polystyrene microspheres used had a diameter of 10 ± 0.5 μm and a refractive index of 1.59. The sample preparation process was as follows: a small amount of polystyrene microspheres were scattered on a glass slide. After the water evaporated, a refractive index matching solution (from Cargille, refractive index 1.58) was added to immerse the microspheres, and finally a coverslip was placed on top. The prepared sample was placed on the stage, and two holographic micrographs at different heights were acquired. To quantitatively compare the accuracy of phase reconstruction using the algorithm described in this invention with existing algorithms, phase reconstruction was performed using different algorithms. The experimental results are as follows: Figure 4 As shown, where Figure 4 (a) is one of the two holograms acquired by the sensor. Figure 4 (b)-(g) are phase images reconstructed by different algorithms. The results show that the existing phase retrieval algorithms exhibit blurred edges or noise interference, while the microsphere phase image reconstructed by the algorithm described in this invention has clearer edges and maintains higher phase imaging reliability. Figure 4 (I) Thickness distribution curves along the central diameter of a microsphere obtained by different algorithms were plotted. The results show that the algorithm described in this invention best matches the real data in terms of peak thickness and profile width, indicating that the algorithm described in this invention can accurately reproduce the three-dimensional distribution characteristics of the microsphere.

[0039] To verify the imaging performance of the algorithm described in this invention in complex biological samples, a representative phase-reconstruction biological sample, oral epithelial cells, was selected for experimentation. The reconstruction results were then compared and analyzed with four existing phase retrieval algorithms. The sample preparation process was as follows: First, the oral cavity was thoroughly cleaned with physiological saline to ensure a clean oral environment. Then, a sterile toothpick was used to gently scrape along the inside of the mouth 5-6 times to collect sufficient oral epithelial cells. The collected oral epithelial cells were then evenly spread on a glass slide pre-dropped with a drop of physiological saline, and finally, a coverslip was placed on top. The prepared sample was placed on the stage, and two holographic micrographs at different heights were acquired. Phase reconstruction was then performed using different phase retrieval algorithms. The experimental results are as follows: Figure 5 As shown, where Figure 5 The image on the left is a hologram acquired by the sensor. Figure 5 The right side (a1)~(a5) and (b1)~(b5) show the local magnified reconstruction results of different regions under each algorithm. Experimental results show that the algorithm described in this invention is superior to other algorithms in terms of reconstruction accuracy and detail preservation. It can not only capture the fine structural features of oral epithelial cells more comprehensively, but also significantly suppress reconstruction artifacts.

[0040] The above description of the disclosed embodiments enables those skilled in the art to make or use the invention. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of the invention. Therefore, the invention is not to be limited to the embodiments shown herein, but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. A highly reliable method for reconstructing phase images using dual-plane lensless on-sheet holographic microscopy, characterized in that, Includes the following steps: Step S1: Acquire two frames of lensless holographic microscopic images at different heights, calculate the initial complex amplitude distribution of the object plane using the dual-plane intensity transmission equation, and use it as the estimated value of the complex amplitude of the object plane. Step S2: The estimated complex amplitude of the object plane is updated by gradient using the biplane Wirtinger operator, and then the total variation minimization and physical absorption constraints of the complex amplitude are applied. The Nesterov momentum is used to accelerate the update to obtain the updated complex amplitude of the object plane. Step S3: Determine the convergence condition of the complex amplitude of the object plane after physical absorption constraint in step S2. If the convergence condition is not met, use the final updated value in step S2 as the estimated value of the complex amplitude of the object plane and repeat step S2. If the convergence condition is met, terminate the iteration, output the complex amplitude value of the object plane after physical absorption constraint, and obtain the final reconstructed phase image.

2. The highly reliable dual-plane lensless on-plate holographic microscopic phase image reconstruction method according to claim 1, characterized in that, Step S1 specifically includes: Step S11: Using the established lensless on-sheet holographic microscopy system, acquire two frames of holographic micrographs at different heights, and use an autofocus algorithm to calculate the precise height of each hologram frame; Step S12: Use an image registration algorithm to register the two holographic micrographs to obtain the registered two holographic images; Step S13: For the two registered holograms, use the dual-plane intensity transmission equation to solve for the phase distribution of the optical field on one of the hologram planes, and combine it with the amplitude distribution recorded on that hologram plane to synthesize the complex amplitude distribution of the optical field on that hologram plane. Step S14: Using the optical field angular spectrum propagation algorithm, the complex amplitude of the optical field on the hologram plane is propagated backward to the object plane, and the initial complex amplitude distribution of the optical field on the object plane is calculated as the estimated value of the complex amplitude on the object plane.

3. The highly reliable dual-plane lensless on-plate holographic microscopic phase image reconstruction method according to claim 1, characterized in that, Step S2 specifically includes: Step S21: Use the estimated value of the complex amplitude of the object plane as the initial value of the iteration, use the two-plane Wirtinger operator to calculate the gradient value of the complex amplitude of the object plane, and use the gradient descent algorithm to update the complex amplitude distribution of the object plane. Step S22: Apply the total variation minimization constraint of complex amplitude to the complex amplitude of the object plane updated in step S21, and update the complex amplitude distribution of the object plane using the near-end gradient descent algorithm; Step S23: Apply amplitude physical absorption constraints to the object plane complex amplitude updated in step S22, and update the object plane complex amplitude distribution; Step S24: Update the complex amplitude of the object plane updated in step S23 using Nesterov momentum acceleration to obtain the updated value of the complex amplitude of the object plane.

4. The highly reliable dual-plane lensless on-plate holographic microscopic phase image reconstruction method according to claim 3, characterized in that, Step S21 specifically includes: Step S211: Using the estimated value of the complex amplitude of the object plane as the starting value of the current iteration, and using the amplitude information of the two frames of holographic micrographs, the Wirtinger operator is used to calculate the two complex amplitude gradient values ​​of the object plane respectively. Step S212: Average the two gradient values ​​obtained in step S211 to obtain the global gradient: , In the formula, ▽ F 1( u m ) and ▽ F 2( u m ) represent the complex amplitude gradient values ​​of the two object planes, It is the global gradient. u m Indicates the first m The estimated complex amplitude of the object plane in the next iteration; Step S213: Using the global gradient described in step S212, obtain the updated complex amplitude distribution of the object plane through the gradient descent algorithm.

5. The highly reliable dual-plane lensless on-sheet holographic microscopic phase image reconstruction method according to claim 3, wherein step S22 specifically includes: A near-end gradient descent operator that minimizes the total variation of complex amplitude is constructed. When solving the problem using the dual method, spatial edge weights are introduced to locally modulate the update step size of the dual variables. The obtained optimal dual solution is then used to update the complex amplitude distribution of the object plane. Among them, the optimal dual solution w * Obtained from the following sub-iterations: , In the formula, l represents the number of sub-iterations, γ represents the sub-iteration step size, τ represents the regularization parameter, and ▽ represents the discrete gradient operator. div ( ) denotes the discrete divergence operator. W It is the spatial edge weight, the initial dual solution ω 0 =0.

6. The highly reliable dual-plane lensless on-plate holographic microscopic phase image reconstruction method according to claim 1, characterized in that, Step S3 specifically includes: Step S31: The first convergence condition is determined for the complex amplitude of the object plane after physical absorption constraint in step S2. The first convergence condition uses the sum of squared amplitude errors (…). ASSE ), can be represented as: ， In the formula, and They represent the first m Second and third m The magnitude of the complex amplitude of the object plane after -1 physical absorption constraint. N x 、N y It is the size of the input image. ε It is a preset threshold; Step S32: The second convergence condition is determined for the complex amplitude of the object plane after physical absorption constraint in step S2. The second convergence condition is defined as the relative rate of change of ASSE at a preset interval of iterations, which can be expressed as: , In the formula, m and mc They represent the first m The second iteration and the first m - c iteration c This indicates the preset interval for the number of iterations. η It is a preset threshold; Step S33: Based on the first convergence condition and the second convergence condition, if neither convergence condition is met, repeat the iteration of step S2. If either convergence condition is met, terminate the iteration, output the complex amplitude value of the object plane after physical absorption constraint, and obtain the final reconstructed phase image.

Images