A lamination diffraction imaging reconstruction method and system based on sub-gradient projection regularization

Abstract

This application belongs to the field of coherent diffraction imaging, specifically disclosing a method and system for reconstructing stacked diffraction imaging based on subgradient projection regularization. Through this application, based on the convex problem optimization theory of subgradient projection, a spatially varying gradient weighting function is further introduced into the stacked diffraction imaging reconstruction model to adaptively adjust the update step size, thereby improving the iterative convergence speed. This method can achieve a balanced improvement in convergence speed within the support domain without introducing any additional computational overhead by penalizing or suppressing extreme step sizes during the update process. Furthermore, this method requires no hardware modification, is directly compatible with stacked diffraction imaging models, and reduces the parameter sensitivity of the iterative algorithm during reconstruction, achieving robust convergence without fine-tuning.

Description

TECHNICAL FIELD

[0001] The present application belongs to the field of coherent diffraction imaging, and more particularly, relates to a superposition diffraction imaging reconstruction method and system based on subgradient projection regularization. BACKGROUND

[0002] Coherent diffraction imaging technology records the intensity distribution of the light field through a sensor, and then reconstructs the phase information that the sensor cannot directly record in an iterative calculation manner. Its lens-free high-resolution imaging method breaks through the dependence on high-quality and large numerical aperture optical lenses, and is widely used in extremely short wavelength imaging fields such as electron beam and X-ray imaging.

[0003] Unlike coherent diffraction imaging that recovers the amplitude and phase information of the sample to be measured only through a single diffraction field, the superposition diffraction imaging technology (ePIE, see Ultramicroscopy 2009, 109(4): 338-343) drives the sample to move horizontally in the plane by a displacement stage, and the detector collects multiple diffraction fields overlapping in the real space. By using the rich redundant information, the resolution, imaging field of view and robustness are improved.

[0004] In recent years, the reconstruction method applied to superposition diffraction has been greatly developed, and the idea of subgradient projection has also been applied to the reconstruction process of the sample and the probe. The superposition diffraction reconstruction method based on subgradient projection (see Journal of Applied Crystallography 2024, 57: 1085-1097) adds the information of the current update gradient in the update algorithm compared with the traditional ePIE, which can adaptively adjust the update step when the gradient is small, thereby avoiding falling into a local minimum value and making the sample and the probe get a better reconstruction result. However, both ePIE and the superposition diffraction reconstruction method based on subgradient projection have the problem of slow convergence speed of reconstruction, and the existing algorithms all need a complex and delicate parameter adjustment process to ensure that the iterative reconstruction process can converge to a suitable result. SUMMARY

[0005] In view of the defects of the prior art, the purpose of the present application is to provide a superposition diffraction imaging reconstruction method and system based on subgradient projection regularization, which aims to solve the problems of slow convergence speed and the need for fine parameter adjustment in the existing superposition diffraction imaging reconstruction method.

[0006] The first aspect of the present application relates to a superposition diffraction imaging reconstruction method based on subgradient projection regularization, comprising:

[0007] S1. Obtain the light field intensity information actually measured at each scanning position;

[0008] S2. Initialize the probe and the sample to be measured;

[0009] S3. Simulating the emergent light formed after the interaction between the probe and the sample to be measured at each scanning position by multiplying the probe and the sample to be measured;

[0010] S4. Simulating the process of the emergent light propagating to the detector plane by the corresponding propagation model, so as to obtain the simulated diffraction light field at each scanning position in the sample plane;

[0011] S5. Replacing the amplitude of the simulated diffraction light field at each scanning position with the actually measured light field intensity information, and keeping the phase information unchanged, to obtain the updated simulated diffraction light field at each scanning position;

[0012] S6. Obtaining the updated emergent light at each scanning position in the sample plane by the inverse propagation model;

[0013] S7. Updating the sample to be measured and the probe at each scanning position according to the updated and un-updated emergent light in S3 and S6, and adaptively adjusting the step length according to the spatial variation gradient weighting function;

[0014] S8. Repeating steps S3 to S7 for all scanning positions until the iteration stopping condition is met, and outputting the reconstructed complex amplitude information of the probe and the sample.

[0015] Preferably, the simultaneous updating of the sample to be measured and the probe at each scanning position is as follows:

[0016]

[0017] wherein O n (r) and O n ′(r) represent the sample to be measured before and after updating at the nth scanning position, respectively, P(r) and P ′ (r) represent the probe before and after updating, respectively, r represents the coordinate in the real space, λ O , λ P represent the iteration search step length parameters of the sample and the probe, respectively, ΔΨ n represents the complex amplitude difference between the updated and un-updated emergent light; represents the square of the matrix Frobenius norm, () + represents taking 0 when the operation result is less than 0, and taking the operation result itself when it is greater than or equal to 0, α O and α P represent the tuning parameters of the sample and the probe, respectively, and ξ represents the tuning parameter related to convergence; * represents the conjugate matrix of the complex matrix.

[0018] Preferably, the values of λ O and λ P are in the range of (0, 1).

[0019] Preferably, the value of a O The value of a P is in the range of (0, 1).

[0020] Preferably, the mean square error (MSE) between the simulated diffraction light field intensity and the measured diffraction light field intensity is calculated as an index of reconstruction convergence:

[0021]

[0022] wherein, Ψ n (u) represents the simulated diffraction light field at the nth scanning position, I n (u) represents the actual measured diffraction light intensity signal of the detector at the nth scanning position, and ∑ n represents the summation of variables for all scanning positions.

[0023] The second aspect of the present application relates to a lamination diffraction imaging reconstruction system based on sub-gradient projection regularization, comprising:

[0024] at least one memory for storing a computer program;

[0025] at least one processor for executing the program stored in the memory, and when the program stored in the memory is executed, the processor is used to execute the reconstruction method as described in the first aspect.

[0026] Preferably, it further comprises a lamination diffraction imaging optical system,

[0027] The lamination diffraction imaging optical system is used to obtain the diffraction light field signal of the probe in the plane at different scanning positions along the given scanning path and send it to the processor.

[0028] It can be understood that the beneficial effects of the above-mentioned second aspect can be referred to the related description in the first aspect, which will not be repeated here.

[0029] Overall, compared with the prior art, the above technical solutions conceived by the present application have the following beneficial effects:

[0030] (1) The present application proposes a lamination diffraction imaging reconstruction method based on sub-gradient projection regularization. According to the convex problem optimization theory of sub-gradient projection, a spatially varying gradient weighting function is further introduced in the lamination diffraction imaging reconstruction model to adaptively adjust the update step size and improve the iteration convergence speed. This method can realize the balanced improvement of convergence speed in the support domain by punishing or suppressing the extreme step size in the update process without introducing any additional calculation overhead. Unlike the complex and delicate parameter adjustment process required by existing methods, the newly added a O The value of a PIt exhibits extremely high parameter stability, and all parameters do not require fine-tuning, further optimizing the testing process.

[0031] (2) The device in this application does not increase the system complexity, is directly compatible with the stacked diffraction imaging model, and has wide applicability. Attached Figure Description

[0032] Figure 1 This is a schematic diagram of the optical path of the stacked diffraction imaging system and a schematic diagram of the lateral scanning method provided in the embodiments of this application.

[0033] Figure 2 A flowchart of a stacked diffraction imaging reconstruction method based on subgradient projection regularization provided in this application embodiment.

[0034] Figure 3 The images show the test sample and probes involved in the simulation experiments provided in this application embodiment.

[0035] Figure 4 A schematic diagram showing the convergence speed of the subgradient projection regularization-based stacked diffraction imaging reconstruction method provided in this application embodiment compared with the original method.

[0036] In all the accompanying drawings, the same reference numerals are used to denote the same elements or structures, wherein:

[0037] 1-Small laser module, 2-Beam expander, 3-Adjustable aperture stop, 4-Focusing lens, 5-Sample to be tested, 6-Detector, 7-Beam splitter. Detailed Implementation

[0038] To make the objectives, technical solutions, and advantages of this application clearer, the following detailed description is provided in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the scope of this application.

[0039] In this article, the term "and / or" describes the relationship between related objects, indicating that three relationships can exist. For example, A and / or B can represent: A existing alone, A and B existing simultaneously, or B existing alone. The symbol " / " in this article indicates that the related objects are in an "or" relationship; for example, A / B means A or B.

[0040] The terms "first" and "second," etc., used in the specification and claims herein are used to distinguish different objects, not to describe a specific order of objects. For example, "first response message" and "second response message," etc., are used to distinguish different response messages, not to describe a specific order of response messages.

[0041] In the embodiments of this application, the terms "exemplary" or "for example" are used to indicate that something is an example, illustration, or description. Any embodiment or design that is described as "exemplary" or "for example" in the embodiments of this application should not be construed as being more preferred or advantageous than other embodiments or design. Specifically, the use of the terms "exemplary" or "for example" is intended to present the relevant concepts in a specific manner.

[0042] In the description of the embodiments of this application, unless otherwise stated, "multiple" means two or more, for example, multiple processing units means two or more processing units, multiple elements means two or more elements, etc.

[0043] The embodiments of this application are described below with reference to the accompanying drawings.

[0044] This application provides a method for reconstructing stacked diffraction imaging based on subgradient projection regularization, comprising the following steps:

[0045] Step S1: Construct a stacked diffraction imaging system, including but not limited to a transmission stacked diffraction imaging system and a reflection stacked diffraction imaging system.

[0046] Figure 1 The diagram below illustrates the optical path of a stacked diffraction imaging system provided in this application. The components in the stacked diffraction imaging system are arranged sequentially as follows: a small laser module 1, a beam expander 2, an adjustable aperture stop 3, a focusing lens 4, the sample to be tested 5, a detector 6, and a beam splitter 7. Figure 1 In the transmission imaging system in (a), the incident light is focused onto the surface of the sample 5 by the focusing lens 4, and the resulting outgoing light propagates in space and then directly enters the detector 6. Figure 1 In the reflective imaging system in (b), the outgoing light generated by the probe and the sample 5 is reflected into the beam splitter 7 and then into the detector 6.

[0047] Step S2: Adjust the optical path system, using a small laser module 1 with a working wavelength of 522.1nm as the light source to output the required collimated laser beam. The beam is expanded by beam expander 2. The beam size is precisely adjusted using adjustable aperture stop 3 to ensure that the beam meets subsequent requirements. The expanded and sized collimated parallel beam is focused by focusing lens 4 with an effective focal length of 25mm. The sample to be tested 5 is placed near the back focal plane of the focusing lens, approximately 2mm away, to ensure that the beam forms a probe of appropriate size on the sample.

[0048] Step S3: Fix the sample 5 to be tested on a precision biaxial displacement stage, set the scanning path so that the sample moves laterally in a plane perpendicular to the optical axis, and the scanning method is as follows. Figure 1As shown in (c). To ensure reconstruction quality, the overlap rate of adjacent probes must be maintained. The detector 6 is fixed 15 mm behind the sample 5, and the actual diffraction field signal I at different scanning positions is acquired. n (u), where n is the nth scanning position in the plane, and u is the frequency domain coordinate (in a reflective stacked diffraction system, the diffraction signal needs to be transmitted to the detector 6 through the beam splitter 7).

[0049] Step S4: Convert the diffraction light field signals I recorded by the detector at different scanning positions in step S3. n (u) Substituted into the reconstruction algorithm of stacked diffraction, the amplitude and phase information of the sample and probe are reconstructed iteratively using the stacked diffraction imaging reconstruction method based on subgradient projection regularity.

[0050] Figure 2 This document provides a flowchart of a stacked diffraction imaging reconstruction method based on subgradient projection regularization, as illustrated in an embodiment of this application. Figure 2 As shown, the detailed steps of the stacked diffraction imaging reconstruction method based on subgradient projection regularization are as follows:

[0051] S4.1: Use the generated random matrix as the initial value guess for the sample and probe. n (r), P n (r), where r represents the real space coordinates.

[0052] S4.2: Following the pre-set scanning path in step S3, the sample to be tested interacts with the probe, forming the emitted light function at each scanning position. The propagation of the emitted light function in space conforms to the scalar diffraction model of the optical field, and the detector records the corresponding simulated diffraction light field signal Ψ. n (u):

[0053]

[0054]

[0055] Here, prop represents the scalar diffraction propagation model of light in free space.

[0056] S4.3: Perform amplitude replacement in reciprocal space, that is, replace the amplitude of the simulated diffraction light field at each scanning position in step S3 with the light field intensity information actually measured by the detector in step S1, while keeping the phase information unchanged, thereby obtaining the updated simulated diffraction light field Ψ at each scanning position. n ′ (u):

[0057]

[0058] S4.4: The updated simulated diffraction field propagates backward to the sample plane, thereby forming the updated output light function at each scanning position.

[0059]

[0060] Among them, prop -1 This represents the scalar diffraction inverse propagation model of light in free space corresponding to step S4.2.

[0061] S4.5: Based on the emitted light before and after the update in S3 and S6, simultaneously update the sample and probe at each scanning position. The update step size is adaptively adjusted according to the spatial variation gradient weighting function.

[0062]

[0063] in, This represents the difference between the emitted light after the update and before the update. * denotes the conjugate matrix of the complex matrix. Let Frobenius norm be the square of the matrix. + This means that if the result of the operation is less than 0, it takes the value 0 (if the result is greater than or equal to 0, it takes the result itself). n (r) and O n Let P'(r) and P'(r) represent the sample before and after the update at the nth scan position, respectively. P(r) and P'(r) represent the probe before and after the update, respectively, where r refers to the coordinates in real space. λ O , λ P These represent the iterative search step size parameters for the sample and probe, respectively, with an optimal value range of (0,1), α O With α P Let ξ represent the tuning parameters of the sample and probe, respectively, according to the cost function. Adjustments and updates will be made.

[0064] S4.6: The root mean square error of the simulated diffracted light field intensity in S4.2 and the measured diffracted light field intensity in S4 is used as an indicator of reconstruction convergence.

[0065]

[0066] When the calculated root mean square error is greater than the preset threshold, repeat steps S4.2-S4.5 until the root mean square error is less than the threshold. At this point, the algorithm can be determined to have converged.

[0067] S4.7: Once the algorithm reaches convergence, it can output the amplitude and phase information of the reconstructed probe and the sample under test obtained from the iterative calculation.

[0068] Compared to the ePIE algorithm and the stacked diffraction reconstruction method based on subgradient projection, this application, based on the convex problem optimization theory of subgradient projection, further introduces a spatially varying gradient weighting function into the stacked diffraction imaging reconstruction model to adaptively adjust the update step size. This function is used to adjust the update step size when it reaches an extreme value, ensuring reconstruction accuracy while significantly improving convergence speed without increasing computational overhead. Unlike existing methods that require complex and precise parameter tuning, the method described in this application exhibits extremely strong parameter stability and further optimizes the testing process.

[0069] Figure 3 These are the amplitude and phase patterns of the sample to be tested and the probe involved in the simulation experiment provided in this application embodiment.

[0070] like Figure 3 As shown in (a) and (c), the sample to be tested used in the simulation experiment had a size of 768×768 pixels. (a) and (c) respectively recorded its amplitude and phase information. A Gaussian probe with a size of 256×256 pixels was constructed to scan the sample to be tested. The amplitude and phase information of the probe are shown in... Figure 3 As shown in (e) and (g). The probe wavelength was set to 522.1 nm, and the focal length of the focusing lens was set to 25 mm. Based on the sample size, the number of in-plane scanning positions was set to 17 × 17, according to... Figure 1 The scanning method in (c) was used, and the detector acquired a total of 289 actual diffraction light fields. The sample under test was reconstructed using a stacked diffraction imaging reconstruction method based on subgradient projection canonicality. The amplitude and phase of the sample under test in the simulation results are as follows: Figure 3 As shown in (b) and (d), the amplitude and phase of the probe are as follows: Figure 3 As shown in (f) and (h).

[0071] Simulation results show that the amplitude and phase of the sample and probe are reconstructed with high contrast and high definition. In the reconstructed amplitude of the sample, the corner edges suffer from image blurring due to the lack of overlapping redundant data from the edge probes. However, in the central regions with sufficient redundant information, the reconstructed features exhibit good resolution and contrast.

[0072] Figure 4 This diagram illustrates the convergence of the subgradient projection regularization-based stacked diffraction imaging reconstruction method and the original method. Curve A in the diagram represents the result of iterative calculation using the original subgradient projection-based stacked diffraction reconstruction method, while curve B represents the result of iterative calculation using the subgradient projection regularization-based stacked diffraction imaging reconstruction method proposed in this application. The two methods are then used to... Figure 3The sample and probe were simulated and reconstructed. With 1000 iterations each, the method proposed in this application has a significant improvement in convergence speed compared with the original method.

[0073] It is understood that the detailed functional implementation of each of the above units / modules can be found in the description in the aforementioned method embodiments, and will not be repeated here.

[0074] It should be understood that the above-described device is used to execute the methods in the above embodiments. The implementation principle and technical effect of the corresponding program modules in the device are similar to those described in the above methods. The working process of the device can be referred to the corresponding process in the above methods, and will not be repeated here.

[0075] Based on the methods in the above embodiments, this application provides a computer-readable storage medium storing a computer program that, when run on a processor, causes the processor to execute the methods in the above embodiments.

[0076] Based on the methods in the above embodiments, this application provides a computer program product that, when run on a processor, causes the processor to execute the methods in the above embodiments.

[0077] It is understood that the processor in the embodiments of this application can be a central processing unit (CPU), or other general-purpose processors, digital signal processors (DSPs), application-specific integrated circuits (ASICs), field-programmable gate arrays (FPGAs), or other programmable logic devices, transistor logic devices, hardware components, or any combination thereof. A general-purpose processor can be a microprocessor or any conventional processor.

[0078] The method steps in this application embodiment can be implemented in hardware or by a processor executing software instructions. The software instructions can consist of corresponding software modules, which can be stored in random access memory (RAM), flash memory, read-only memory (ROM), programmable read-only memory (PROM), erasable programmable read-only memory (EPROM), electrically erasable programmable read-only memory (EEPROM), registers, hard disks, portable hard disks, CD-ROMs, or any other form of storage medium known in the art. An exemplary storage medium is coupled to the processor, enabling the processor to read information from and write information to the storage medium. Of course, the storage medium can also be a component of the processor. The processor and the storage medium can reside in an ASIC.

[0079] In the above embodiments, implementation can be achieved entirely or partially through software, hardware, firmware, or any combination thereof. When implemented using software, it can be implemented entirely or partially in the form of a computer program product. The computer program product includes one or more computer instructions. When the computer program instructions are loaded and executed on a computer, all or part of the processes or functions described in the embodiments of this application are generated. The computer can be a general-purpose computer, a special-purpose computer, a computer network, or other programmable device. The computer instructions can be stored in a computer-readable storage medium or transmitted through the computer-readable storage medium. The computer instructions can be transmitted from one website, computer, server, or data center to another website, computer, server, or data center via wired (e.g., coaxial cable, fiber optic, digital subscriber line (DSL)) or wireless (e.g., infrared, wireless, microwave, etc.) means. The computer-readable storage medium can be any available medium that a computer can access or a data storage device such as a server or data center that integrates one or more available media. The available medium can be a magnetic medium (e.g., floppy disk, hard disk, magnetic tape), an optical medium (e.g., DVD), or a semiconductor medium (e.g., solid-state disk (SSD)).

[0080] It is understood that the various numerical designations used in the embodiments of this application are merely for the convenience of description and are not intended to limit the scope of the embodiments of this application.

[0081] Those skilled in the art will readily understand that the above description is merely a preferred embodiment of this application and is not intended to limit this application. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of this application should be included within the scope of protection of this application.

Claims

1. A method for reconstructing stacked diffraction imaging based on subgradient projection regularization, characterized in that, include: S1. Obtain the actual measured light field intensity information at each scanning position; S2. Initialize the probe and the sample to be tested; S3. By multiplying the probe with the sample to be tested, the emitted light formed after the sample to be tested interacts with the probe at each scanning position is simulated; S4. The process of the outgoing light propagating to the detector plane is simulated using the corresponding propagation model, thereby obtaining the simulated diffraction light field at each scanning position in the sample plane. S5. Replace the amplitude of the simulated diffraction light field at each scanning position with the actual measured light field intensity information, while keeping the phase information unchanged, to obtain the updated simulated diffraction light field at each scanning position; S6. The simulated diffraction field will be updated, and the updated outgoing light at each scanning position in the sample plane will be obtained through the reverse propagation model; S7. Based on the emitted light before and after the update in S3 and S6, update the sample and probe at each scanning position simultaneously. The update step size is adaptively adjusted according to the spatial variation gradient weighting function. S8. Repeat steps S3 to S7 for all scanning positions until the iteration stop condition is met, and output the reconstructed probe and sample complex amplitude information; In step S7, the simultaneous updating of the sample and probe at each scanning position is as follows: in, and They represent the first time. The sample to be tested before and after updating at each scan position and Let represent the probe before and after the update, respectively, and let r represent the coordinates in real space. , These represent the iterative search step size parameters for the sample and probe, respectively. This represents the difference in complex amplitude between the emitted light after the update and before the update; Denotes the square of the Frobenius norm of a matrix. This means that if the result is less than 0, the value is 0; if the result is greater than or equal to 0, the value is the result itself. and These represent the tuning parameters for the sample and probe, respectively. Represents the tuning parameters with respect to convergence; This represents the conjugate matrix of a complex matrix.

2. The reconstruction method as described in claim 1, characterized in that, , The value range is (0,1).

3. The reconstruction method as described in claim 1, characterized in that, and The value range is (0,1).

4. The reconstruction method as described in claim 1, characterized in that, By calculating the root mean square error of the simulated diffraction light field intensity and the measured diffraction light field intensity. This serves as an indicator of reconstruction convergence: in, Indicates the first Simulated diffraction light field at each scanning position Indicates the first The diffraction intensity signal actually measured by the detector at each scanning position. This indicates that the variables are summed over all scan positions.

5. A stacked diffraction imaging reconstruction system based on subgradient projection regularization, characterized in that, include: At least one memory for storing computer programs; At least one processor is configured to execute a program stored in the memory, wherein when the program stored in the memory is executed, the processor is configured to perform the reconstruction method as described in any one of claims 1 to 4.

6. The reconfiguration system as described in claim 5, characterized in that, Also includes: Stacked diffraction imaging optical system The stacked diffraction imaging optical system is used to acquire the diffraction light field signal of the probe in the plane at different scanning positions along a predetermined scanning path, and send it to the processor.

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