Laminated diffraction imaging reconstruction method and system based on subgradient projection regularization

Abstract

The invention belongs to the field of coherent diffraction imaging, and particularly discloses a laminated diffraction imaging reconstruction method and system based on subgradient projection regularization. According to the method and the device, a spatial variation gradient weighting function is further introduced into the laminated diffraction imaging reconstruction model according to a convex problem optimization theory of sub-gradient projection to adaptively adjust and update the step length, and the iteration convergence speed is improved. According to the method, the convergence speed in the support domain can be improved in a balanced manner by punishing or suppressing the extreme step length in the updating process without introducing any additional calculation overhead. Moreover, the method does not need any hardware modification, can be directly compatible with a laminated diffraction imaging model, reduces the parameter sensitivity of an iterative algorithm in the reconstruction process, and can achieve robust convergence without fine parameter adjustment.

Description

Technical Field

[0001] The present application belongs to the field of coherent diffraction imaging, and more specifically, to a stacked diffraction imaging reconstruction method and system based on sub-gradient projection regularization. Background Art

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

[0003] Different from coherent diffraction imaging that only uses a single diffraction field to restore the amplitude and phase information of the sample to be measured, stacked diffraction imaging technology (ePIE, see Ultramicroscopy 2009, 109(4): 338-343) uses a translation stage to drive the sample to move laterally in a plane. The detector collects multiple overlapping diffraction fields of the probe in real space, using rich redundant information to achieve improvements in resolution, imaging field of view, and robustness.

[0004] In recent years, the reconstruction methods applied to stacked diffraction have been greatly developed, and the idea of ​​sub-gradient projection has also been applied to the reconstruction process of samples and probes. Compared with the traditional ePIE, the stacked diffraction reconstruction method based on sub-gradient projection (see Journal of Applied Crystallography 2024, 57: 1085-1097) adds information about the current update gradient to the update algorithm, and can adaptively adjust the update step size when the gradient is small, thereby avoiding falling into the local minimum, so that the sample and probe can obtain better reconstruction results. However, both ePIE and the stacked diffraction reconstruction method based on sub-gradient projection have the problem of slow reconstruction convergence speed. At the same time, the existing algorithms require complex and sophisticated parameter adjustment processes to ensure that the iterative reconstruction process can converge to a suitable result. Summary of the invention

[0005] In view of the defects of the prior art, the purpose of the present application is to provide a stacked diffraction imaging reconstruction method and system based on sub-gradient projection regularization, aiming to solve the problems of slow convergence speed and the need for fine-tuning parameters in the existing stacked diffraction imaging reconstruction method.

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

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

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

[0009] S3. By multiplying the probe and the sample to be tested, the emitted light formed after the interaction between the sample to be tested and the probe at each scanning position is simulated;

[0010] S4. simulating the process of the outgoing light propagating to the detector plane through 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, keeping the phase information unchanged, and obtaining an updated simulated diffraction light field at each scanning position;

[0012] S6. The updated simulated diffraction light field is updated to obtain updated outgoing light at each scanning position in the sample plane through a reverse propagation model;

[0013] S7. According to the emitted light before and after the update in S3 and S6, the samples to be tested and the probes at each scanning position are updated at the same time, and the updated step size is adaptively adjusted according to the spatially varying gradient weighting function;

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

[0015] Preferably, the simultaneous updating of the samples to be tested and the probes at each scanning position is specifically as follows:

[0016]

[0017] Among them, O n (r) and O n ′(r) respectively represent the samples to be tested before and after updating at the nth scanning position, P(r) and P ′ (r) represents the probe before and after the update, r represents the coordinate in real space, λ O , P denote the iterative search step size parameters of the sample and probe, ΔΨ n represents the difference in complex amplitude of the emitted light before and after the update; represents the square of the matrix Frobenius norm, () + Indicates that when the operation result is less than 0, it is taken as 0, and when it is greater than or equal to 0, it is taken as the operation result itself. O With α P represent the tuning parameters of the sample and probe respectively, ξ represents the tuning parameters about convergence; * represents the conjugate matrix of the complex matrix.

[0018] Preferably, λ O , P The value range is (0,1).

[0019] Preferably, α O With α P The value range is (0,1).

[0020] Preferably, the root mean square error MSE between the simulated diffracted light field intensity and the measured diffracted light field intensity is calculated and used as an indicator of reconstruction convergence:

[0021]

[0022] Among them, n (u) represents the simulated diffraction light field at the nth scanning position, I n (u) represents the diffraction intensity signal actually measured by the detector at the nth scanning position, ∑ n Indicates that the variable is summed over all scan positions.

[0023] The second aspect of the present application relates to a stacked 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 is used to execute the program stored in the memory. 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 also includes: a stacked diffraction imaging optical system,

[0027] The stacked diffraction imaging optical system is used to obtain diffraction light field signals of the probe in the plane at different scanning positions through a predetermined scanning path, and send the signals to the processor.

[0028] It can be understood that the beneficial effects of the second aspect mentioned above can be found in the relevant description of the first aspect mentioned above, and will not be repeated here.

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

[0030] (1) This application proposes a stacked 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 into the stacked diffraction imaging reconstruction model to adaptively adjust the update step size and improve the iterative convergence speed. This method can achieve a balanced improvement in the convergence speed within the support domain by penalizing or suppressing the extreme step size in the update process without introducing any additional computational overhead; unlike the existing methods that require a complex and sophisticated parameter adjustment process, the newly added α O With α PIt has extremely strong parameter stability, and all parameters do not need fine-tuning, which further optimizes the testing process.

[0031] (2) The device of the present application does not increase the complexity of the system, is directly compatible with the stacked diffraction imaging model, and has wide applicability. BRIEF DESCRIPTION OF THE DRAWINGS

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

[0033] Figure 2 A flow chart of a stacked diffraction imaging reconstruction method based on sub-gradient projection regularization provided in an embodiment of the present application.

[0034] Figure 3 The diagrams of the samples to be tested and the probes involved in the simulation experiment provided in the embodiments of the present application.

[0035] Figure 4 A schematic diagram of the convergence speed of the stacked diffraction imaging reconstruction method based on sub-gradient projection regularization provided in an embodiment of the present application and the original method.

[0036] Throughout the 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 diaphragm, 4- Focusing lens, 5- Sample to be measured, 6- Detector, 7- Beam splitter prism. DETAILED DESCRIPTION

[0038] In order to make the purpose, technical solution and advantages of the present application more clearly understood, the present application is further described in detail below in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present application and are not used to limit the present application.

[0039] The term "and / or" in this article is a description of the association relationship of associated objects, indicating that there can be three relationships. For example, A and / or B can represent: A exists alone, A and B exist at the same time, and B exists alone. The symbol " / " in this article indicates that the associated objects are in an or relationship, for example, A / B means A or B.

[0040] The terms "first" and "second" in the specification and claims herein are used to distinguish different objects rather than to describe a specific order of the objects. For example, a first response message and a second response message are used to distinguish different response messages rather than to describe a specific order of the response messages.

[0041] In the embodiments of the present application, words such as "exemplary" or "for example" are used to indicate examples, illustrations or descriptions. Any embodiment or design described as "exemplary" or "for example" in the embodiments of the present application should not be interpreted as being more preferred or more advantageous than other embodiments or designs. Specifically, the use of words such as "exemplary" or "for example" is intended to present related concepts in a specific way.

[0042] In the description of the embodiments of the present application, unless otherwise specified, "multiple" means two or more than two. For example, multiple processing units refer to two or more processing units, etc.; multiple elements refer to two or more elements, etc.

[0043] The embodiments of the present application are described below in conjunction with the drawings in the embodiments of the present application.

[0044] The present application provides a stacked diffraction imaging reconstruction method based on sub-gradient projection regularization, comprising the following steps:

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

[0046] Figure 1 The optical path principle diagram of the stacked diffraction imaging system provided in the embodiment of the present application, the arrangement of the components in the stacked diffraction imaging system is as follows: a small laser module 1, a beam expander 2, an adjustable aperture diaphragm 3, a focusing lens 4, a sample to be measured 5, a detector 6 and a beam splitter prism 7. Among them, Figure 1 In the transmission imaging system in (a), the incident light is focused by the focusing lens 4 onto the surface of the sample 5 to be measured, and the resulting outgoing light propagates in space and directly enters the detector 6. Figure 1 In the reflective imaging system in (b), the outgoing light formed by the probe and the sample 5 to be measured is reflected into the beam splitter prism 7 and then enters the detector 6.

[0047] Step S2: Adjust the optical path system, use a small laser module 1 with an operating wavelength of 522.1nm as the light source, and output the required collimated laser beam. The beam is expanded by the beam expander 2. The beam size is precisely adjusted by the adjustable aperture diaphragm 3 to ensure that the beam meets subsequent requirements. The collimated parallel beam after expansion and size adjustment is focused by the 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, about 2mm, to ensure that the beam forms a probe of appropriate size on the sample to be tested.

[0048] Step S3: Fix the sample 5 to be tested on a precise two-axis translation stage, set the scanning path so that the sample moves horizontally on a plane perpendicular to the optical axis, and the scanning method is as follows: Figure 1In order to ensure the reconstruction quality, the overlap rate of adjacent probes needs to be guaranteed. The fixed detector 6 is 15 mm behind the sample 5 to collect the actual diffraction light field signal I at different scanning positions. n (u), where n is the nth scanning position in the plane and u is the frequency domain coordinate (in the reflective stack diffraction system, the diffraction signal needs to be transmitted to the detector 6 through the beam splitter prism 7).

[0049] Step S4: The diffraction light field signals I at different scanning positions recorded by the detector in step S3 are n (u) is substituted into the reconstruction algorithm of stacked diffraction, and the amplitude and phase information of the sample and probe to be tested are iteratively reconstructed using the stacked diffraction imaging reconstruction method based on the sub-gradient projection regularization.

[0050] Figure 2 A flowchart of a stacked diffraction imaging reconstruction method based on sub-gradient projection regularization provided in an embodiment of the present application. Figure 2 As shown, the detailed steps of the stacked diffraction imaging reconstruction method based on sub-gradient projection regularization are as follows:

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

[0052] S4.2: According to the scanning path preset in step S3, the sample to be tested interacts with the probe to form an emission light function at each scanning position The propagation of the outgoing light function in space conforms to the light field scalar diffraction model, 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: Complete amplitude replacement in the 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, and keep the phase information unchanged in the process, so as to obtain the updated simulated diffraction light field Ψ at each scanning position n ′ (u):

[0057]

[0058] S4.4: The updated simulated diffraction light field is propagated back to the sample plane to form an updated output light function at each scanning position

[0059]

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

[0061] S4.5: According to the emitted light before and after the update in S3 and S6, the samples to be tested and the probes at each scanning position are updated simultaneously, and the step length of the update is adaptively adjusted according to the spatially varying gradient weighting function:

[0062]

[0063] in, represents the difference between the emitted light before and after the update. * represents the conjugate matrix of the complex matrix, represents the square of the matrix Frobenius norm, () + Indicates that when the operation result is less than 0, 0 is taken (when it is greater than or equal to 0, the operation result itself is taken). n (r) and O n ′(r) are the samples to be tested before and after the update at the nth scanning position, P(r) and P′(r) represent the probes before and after the update, and r is used to refer to the coordinates in the real space. O , P They represent the iterative search step parameters of the sample and probe, respectively, and the optimal value range is (0,1), α O With α P Represent the tuning parameters of the sample and probe respectively, ξ represents the tuning parameter, according to the cost function Make adjustments and updates.

[0064] S4.6: Calculate the root mean square error between the intensity of the diffracted light field simulated by S4.2 and the intensity of the diffracted light field measured by S4, and use this as an indicator of reconstruction convergence:

[0065]

[0066] When the calculated root mean square error is greater than the preset threshold, steps S4.2-S4.5 are repeated until the root mean square error is less than the threshold, at which time it can be determined that the algorithm has converged.

[0067] S4.7: When the algorithm reaches a convergence state, the amplitude and phase information of the reconstructed probe and the sample to be tested obtained by iterative calculation can be output.

[0068] Compared with the ePIE algorithm and the stacked diffraction reconstruction method based on sub-gradient projection, this application further introduces a spatially varying gradient weighting function in the stacked diffraction imaging reconstruction model based on the convex problem optimization theory of sub-gradient projection to adaptively adjust the update step size, which is used to adjust when the update step size has an extreme value. Without adding additional computational overhead, the reconstruction accuracy is guaranteed while greatly improving the convergence speed. Unlike the existing methods that require a complex and sophisticated parameter adjustment process, the method described in this application has extremely strong parameter stability and further optimizes the test process.

[0069] Figure 3 It is the amplitude and phase pattern of the sample to be tested and the probe involved in the simulation experiment process provided in the embodiment of the present application.

[0070] like Figure 3 As shown in (a) and (c), the size of the sample to be tested used in the simulation experiment is 768×768 pixels, and (a) and (c) record its amplitude and phase information respectively. A Gaussian probe with a size of 256×256 pixels is 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 wavelength of the probe is set to 522.1nm, and the focal length of the focusing lens is set to 25mm. According to the size of the sample to be tested, the number of scanning positions in the plane is set to 17×17. Figure 1 The detector collected 289 actual diffraction light fields in total. The sample to be tested was reconstructed using the stacked diffraction imaging reconstruction method based on the sub-gradient projection regularization. The amplitude and phase of the sample to be tested in the simulation results are shown in Figure 2. 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] The simulation results show that the amplitude and phase of the sample and probe to be tested are reconstructed with high contrast and high definition. In the reconstructed sample amplitude, the corner edge part will be blurred because the edge probe lacks overlapping redundant data. In the middle area with sufficient redundant information, the features of the reconstructed part perform well in terms of resolution and contrast.

[0072] Figure 4 The following is a schematic diagram of the convergence of the stacked diffraction imaging reconstruction method based on sub-gradient projection regularization and the original method. Curve A in the figure is the result of iterative calculation of the original stacked diffraction imaging reconstruction method based on sub-gradient projection, and curve B is the result of iterative calculation of the stacked diffraction imaging reconstruction method based on sub-gradient projection regularization proposed in this application. Figure 3The samples and probes in the simulation reconstruction are reconstructed. When each iteration is 1000 times, the method proposed in the present application has a significant improvement in convergence speed compared with the original method.

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

[0074] It should be understood that the above-mentioned device is used to execute the method in the above-mentioned embodiment. The implementation principle and technical effect of the corresponding program module in the device are similar to those described in the above-mentioned method. The working process of the device can refer to the corresponding process in the above-mentioned method, which will not be repeated here.

[0075] Based on the method in the above embodiment, an embodiment of the present application provides a computer-readable storage medium, which stores a computer program. When the computer program runs on a processor, the processor executes the method in the above embodiment.

[0076] Based on the method in the above embodiment, an embodiment of the present application provides a computer program product. When the computer program product runs on a processor, the processor executes the method in the above embodiment.

[0077] It is understandable that the processor in the embodiment of the present application may be a central processing unit (CPU), or other general-purpose processors, digital signal processors (DSP), application-specific integrated circuits (ASIC), field programmable gate arrays (FPGA) or other programmable logic devices, transistor logic devices, hardware components or any combination thereof. The general-purpose processor may be a microprocessor or any conventional processor.

[0078] The method steps in the embodiments of the present application can be implemented by hardware or by a processor executing software instructions. The software instructions can be composed of corresponding software modules, and the software modules 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, mobile hard disks, CD-ROMs, or any other form of storage medium known in the art. An exemplary storage medium is coupled to a processor so that the processor can read information from the storage medium 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 be located in an ASIC.

[0079] In the above embodiments, it can be implemented in whole or in part by software, hardware, firmware or any combination thereof. When implemented using software, it can be implemented in whole or in part 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, the process or function described in the embodiment of the present application is generated in whole or in part. The computer may be a general-purpose computer, a special-purpose computer, a computer network, or other programmable device. The computer instructions may be stored in a computer-readable storage medium or transmitted through the computer-readable storage medium. The computer instructions may be transmitted from a website site, a computer, a server or a data center to another website site, a computer, a server or a data center by wired (e.g., coaxial cable, optical fiber, digital subscriber line (DSL)) or wireless (e.g., infrared, wireless, microwave, etc.) means. The computer-readable storage medium may be any available medium that a computer can access or a data storage device such as a server or a data center that includes one or more available media integrated. The available medium may be a magnetic medium (e.g., a floppy disk, a hard disk, a tape), an optical medium (e.g., a DVD), or a semiconductor medium (e.g., a solid-state drive (SSD)), etc.

[0080] It should be understood that the various numerical numbers involved in the embodiments of the present application are only used for the convenience of description and are not used to limit the scope of the embodiments of the present application.

[0081] It will be easily understood by those skilled in the art that the above description is only a preferred embodiment of the present application and is not intended to limit the present application. Any modifications, equivalent substitutions and improvements made within the spirit and principles of the present application shall be included in the scope of protection of the present application.

Claims

1. A stacked diffraction imaging reconstruction method based on sub-gradient projection regularization, characterized in that: include: S1. Obtaining 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 and the sample to be tested, the emitted light formed after the interaction between the sample to be tested and the probe at each scanning position is simulated; S4. simulating the process of the outgoing light propagating to the detector plane through the corresponding propagation model, so as to obtain the simulated diffraction light field at each scanning position in the sample plane; S5. replacing the amplitude of the simulated diffraction light field at each scanning position with the actually measured light field intensity information, keeping the phase information unchanged, and obtaining an updated simulated diffraction light field at each scanning position; S6. The updated simulated diffraction light field is updated to obtain updated outgoing light at each scanning position in the sample plane through a reverse propagation model; S7. According to the emitted light before and after the update in S3 and S6, the samples to be tested and the probes at each scanning position are updated at the same time, and the updated step size is adaptively adjusted according to the spatially varying gradient weighting function; S8. Repeat steps S3 to S7 for all scanning positions until the iteration stop condition is met, and output the reconstructed complex amplitude information of the probe and the sample.

2. The reconstruction method according to claim 1, characterized in that: The simultaneous updating of the samples to be tested and the probes at each scanning position is specifically as follows: Among them, O n (r) and O n ′(r) respectively represent the samples to be tested before and after updating at the nth scanning position, P(r) and P ′ (r) represents the probe before and after the update, r represents the coordinate in real space, λ O , P denote the iterative search step parameters of the sample and probe, ΔΨ n represents the difference in complex amplitude of the emitted light before and after the update; represents the square of the matrix Frobenius norm, () + Indicates that when the operation result is less than 0, it is taken as 0, and when it is greater than or equal to 0, it is taken as the operation result itself. O With α P represent the tuning parameters of the sample and probe respectively, ξ represents the tuning parameters about convergence; * represents the conjugate matrix of the complex matrix.

3. The reconstruction method according to claim 2, characterized in that: λ O , P The value range is (0,1).

4. The reconstruction method according to claim 2, characterized in that: α O With α P The value range is (0,1).

5. The reconstruction method according to claim 1, characterized in that: The root mean square error (MSE) between the simulated diffracted light field intensity and the measured diffracted light field intensity is calculated and used as an indicator of reconstruction convergence: Among them, n (u) represents the simulated diffraction light field at the nth scanning position, I n (u) represents the diffraction intensity signal actually measured by the detector at the nth scanning position, ∑ n Indicates that the variable is summed over all scan positions.

6. A stacked diffraction imaging reconstruction system based on sub-gradient projection regularization, characterized in that: include: at least one memory for storing a computer program; At least one processor is used to execute the program stored in the memory. When the program stored in the memory is executed, the processor is used to execute the reconstruction method according to any one of claims 1 to 5.

7. The reconstruction system according to claim 6, characterized in that: Also includes: Laminated diffraction imaging optical system, The stacked diffraction imaging optical system is used to obtain diffraction light field signals of the probe in the plane at different scanning positions through a predetermined scanning path, and send the signals to the processor.

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