Extreme ultraviolet lithography method based on iterative frequency mask
By combining iterative frequency masks and adaptive learning rate schedulers, the problems of low reconstruction quality and poor noise resistance in stacked diffraction imaging are solved, achieving efficient and stable reconstruction results. In particular, it significantly improves computational efficiency and reconstruction quality in low overlap and high noise environments.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- ZHEJIANG UNIV
- Filing Date
- 2025-07-21
- Publication Date
- 2026-06-23
AI Technical Summary
Existing stacked diffraction imaging algorithms suffer from low reconstruction quality, poor noise resistance, and are prone to getting trapped in local minima under low overlap and high noise conditions, and also have low computational efficiency.
An extreme ultraviolet (EUV) stacked diffraction imaging method based on iterative frequency masks is adopted. Through physical-driven iterative spatial frequency mask design and an adaptive learning rate scheduler, combined with a GPU-accelerated batch optimization model, multi-level spatial frequency masks are constructed by progressively optimizing from low frequency to high frequency, and the learning rate is dynamically adjusted to improve reconstruction stability and noise resistance.
It significantly improves reconstruction quality and convergence speed, enhances robustness to noise and stacking ratio, increases computational efficiency by 10 to 100 times, and can provide high-quality reconstruction results under complex imaging conditions.
Smart Images
Figure CN120927618B_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the field of computational imaging, and more specifically to an extreme ultraviolet light stacked diffraction imaging method based on iterative frequency masks. Background Technology
[0002] Stacked diffraction imaging for extreme ultraviolet light is an important area of computational imaging and image processing technology, and a key research direction in coherent diffraction imaging. It involves scanning and illuminating a sample across multiple overlapping regions to acquire diffraction intensity patterns, and then using numerical reconstruction algorithms to reconstruct the sample's complex amplitude information (i.e., amplitude and phase). This technology overcomes the resolution limitations of traditional optical systems and is widely used in fields such as biological tissue observation and semiconductor detection. Because it does not require a high-performance lens system, it offers advantages such as low cost and high resolution.
[0003] Existing classic stacked diffraction imaging algorithms can be divided into methods based on alternating projection and methods based on optimization.
[0004] Alternating projection-based methods were the first to be proposed and have been widely used, offering advantages such as intuitive algorithm structure and ease of implementation. These methods approximate the true complex amplitude information by alternately constraining projections between the imaging domain (spatial domain) and the diffraction domain (frequency domain). Typical methods include error inversion methods, differential mapping methods, and stacked iterative engines and their improved versions. These methods have clear steps, are easy to code and implement, and exhibit fast convergence speeds under high overlap and low noise conditions. However, they also face challenges such as the reconstruction results being highly dependent on the initial estimate, requiring high overlap diffraction images, poor noise resistance, and difficulty in handling complex scenes.
[0005] Optimization-based methods formalize the phase reconstruction problem as a nonlinear optimization problem, inferring the target image by minimizing the difference between the predicted diffraction pattern and the actual measurement results. Typical methods include gradient descent-based reconstruction methods and alternating direction multiplier methods. These methods have low requirements for the reconstruction rate of the diffraction image and high reconstruction accuracy, but they are susceptible to local minima and may converge to suboptimal solutions, and still face the problem of weak noise resistance.
[0006] Although alternating projection methods and optimization-based reconstruction methods differ significantly in their technical implementation paths—the former focusing on local iterative updates in the spatial domain and the latter on minimizing global loss—these algorithms primarily emphasize different spatial update strategies while uniformly processing the entire spectrum, neglecting the inherent structure and importance of frequency information during reconstruction. The contribution of frequency components to stacked diffraction imaging is progressive: low-frequency structures construct the basic features of objects and are generally easier to acquire; while high-frequency details improve resolution and are crucially dependent on accurate low-frequency recovery.
[0007] To address this limitation, this invention utilizes an iterative spatial frequency mask to introduce a frequency-progressive reconstruction strategy into extreme ultraviolet (EUV) stacked diffraction imaging. This decomposes the complex inverse problem into a series of optimization processes from low to high frequencies, thereby achieving higher quality and more robust stacked diffraction imaging reconstruction. Compared to other methods, this invention offers the following advantages: 1. In the low-frequency stage, low-frequency subproblems typically have better condition numbers, making the initial stage more conducive to convergence; 2. The structured optimization path provides a progression from simple to complex, helping to avoid getting trapped in local minima; 3. The frequency mask introduces implicit regularization, thereby improving the performance of the ill-posed inverse problem. Summary of the Invention
[0008] This invention aims to improve the reconstruction quality, convergence speed, and noise resistance of stacked diffraction imaging reconstruction methods. This invention proposes an extreme ultraviolet (EUV) stacked diffraction imaging method based on iterative frequency masks. Through a physically driven iterative spatial frequency mask design and an adaptive learning rate scheduler, the reconstruction quality, robustness to noise and stacking rate, and convergence stability of EUV stacked diffraction imaging are significantly improved.
[0009] The technical solution of the present invention includes the following steps:
[0010] The method of the present invention includes the following steps:
[0011] S1. Use an extreme ultraviolet coherent light source to scan and irradiate the target to be reconstructed, and collect diffraction intensity patterns at each scanning position.
[0012] S2. Based on the position information and diffraction intensity patterns of all scanning positions, obtain the initial probe function and the initial reconstruction target function; at the same time, initialize the auxiliary variable tensor, the Lagrange multiplier tensor, and the adaptive learning rate.
[0013] S3. Construct a multi-level spatial frequency mask.
[0014] In step S3, a multi-level spatial frequency mask is constructed through the following process: the zero point of the zero-order Bessel function is used as the dividing point to divide the frequency domain into multiple frequency sub-intervals. The spatial frequency mask of each frequency sub-interval is constructed by combining the cutoff radius of each frequency sub-interval with a super Gaussian filter. The spatial frequency masks of all frequency sub-intervals constitute a multi-level spatial frequency mask.
[0015] The spatial frequency mask M of the l-th level frequency sub-interval l Set it according to the following formula:
[0016]
[0017] In the formula, M l(f) represents the mask value at spatial frequency coordinate f in the l-th frequency sub-interval, where f represents the spatial frequency coordinate, |f| represents the frequency radius at spatial frequency coordinate f, and r l Let represent the cutoff radius of the l-th frequency sub-interval, n be the exponent of the super-Gaussian function, and L represent the total number of frequency sub-intervals.
[0018] The cutoff radius of the l-th frequency sub-interval is set according to the following formula:
[0019]
[0020] In the formula, r max J represents the maximum frequency indicated by the diffraction intensity pattern. 0,l+1 J represents the (l+1)th zero of the zero-order Bessel function. 0,L+1 This represents the (L+1)th zero of the zero-order Bessel function.
[0021] S4. Based on the position information and diffraction intensity pattern of all scanning positions, use a multi-level spatial frequency mask to update the probe function, reconstruction objective function, auxiliary variable tensor and Lagrange multiplier tensor step by step from the low frequency sub-interval to the high frequency sub-interval. The optimal probe function and optimal reconstruction objective function are used as the reconstruction result.
[0022] Step S4 is as follows:
[0023] S4.1. Obtain the current adaptive learning rate based on the reconstruction error, frequency level, and gradient behavior.
[0024] In step S4.1, the adaptive learning rate includes the probe adaptive learning rate and the reconstruction target adaptive learning rate;
[0025] When the current frequency sub-interval is the l-th level frequency sub-interval, the probe adaptive learning rate and the reconstruction target adaptive learning rate are obtained by the following formulas:
[0026]
[0027] In the formula, The current adaptive learning rate is represented by z, which is either P or O, where P and O represent the probe and the reconstruction target, respectively. error (e (l) () represents the adjustment factor based on reconstruction error, e (l) f represents the reconstruction error. freq (l) represents the adjustment factor based on frequency level l, f osc (g( l-w )) represents the detection of g( based on gradient oscillation. 1-w The adjustment factor of g( l-w ) represents the gradient history of the past w iterations.
[0028] S4.2 Using the current probe function and reconstruction target function, combined with the current auxiliary variable tensor and Lagrange multiplier tensor, calculate the gradients of the probe and reconstruction target based on the diffraction intensity patterns at all scan positions.
[0029] In step S4.2, when the current frequency sub-interval is the l-th level frequency sub-interval, the gradients of the probe and the reconstructed target are obtained by the following formulas:
[0030]
[0031] In the formula, O l and P l S represents the current reconstruction target and the current probe function, respectively. l Aux represents the auxiliary variable tensor. l Represents the Lagrange multiplier tensor; A batch This indicates a batch sampling operator, which simultaneously reconstructs the target O from the current location based on the position information of the scanned location. l Extract all probe illumination regions to form a reconstructed target tensor of shape [J,H,W]. A represents batch The inverse transform; [ j Let j represent the j-th channel of the tensor, [] * To denote the conjugate of a complex number, || 2 denoted as the square of the L2 norm, and ∈ denotes a small constant to prevent division by zero; Indicates the gradient of the probe. This represents the gradient of the reconstruction target.
[0032] Furthermore, in step S4.2, a GPU-accelerated batch processing optimization model can be used to process the diffraction intensity patterns at each scanning position in parallel.
[0033] S4.3. Based on the current adaptive learning rate obtained in step S4.1, the gradients of the probe and the reconstruction target obtained in step S4.2, and the spatial frequency mask of the current frequency sub-interval, update the probe function and the reconstruction target function.
[0034] In step S4.3, when the current frequency sub-interval is the l-th level frequency sub-interval, the probe function and the reconstruction target function are updated using the following formula:
[0035]
[0036] In the formula, P l+1 P represents the updated probe function. l Indicates the current probe function. This represents the current adaptive learning rate. This represents the probe gradient after being processed by the spatial frequency mask of the current frequency sub-interval;
[0037] O l+1 Denotes the updated reconstruction objective function, O l This represents the current reconstruction objective function. This represents the adaptive learning rate of the current reconstruction target. This represents the reconstructed target gradient after processing with a spatial frequency mask in the current frequency sub-interval;
[0038] Among them, the probe gradient after spatial frequency masking of the current frequency sub-interval and the reconstructed target gradient after spatial frequency masking of the current frequency sub-interval It is obtained through the following formula:
[0039]
[0040] In the formula, and These represent the gradients of the probe and the reconstructed target, respectively, after being processed by the spatial frequency mask of the current frequency sub-interval. Indicates Fourier transform, M represents the inverse Fourier transform. l This represents the spatial frequency mask for the current frequency sub-interval.
[0041] S4.4 Based on the updated probe function and reconstruction objective function, obtain the new auxiliary variable tensor and Lagrange multiplier tensor.
[0042] In step S4.4, when the current frequency subinterval is the l-th level frequency subinterval, the new auxiliary variable tensor and Lagrange multiplier tensor are calculated using the following formulas:
[0043]
[0044] In the formula, μ represents an intermediate variable. This represents the phase projection operator, which projects the complex field into a form that matches the measured intensity. l+1 Let P represent the reconstruction target tensor obtained from the updated reconstruction objective function. l+1 This represents the updated probe function, Aux. l S represents the current Lagrange multiplier tensor; l+1 This represents a new round of auxiliary variable tensors. Indicates Fourier transform, This represents the inverse Fourier transform. Let I represent the spatial frequency mask for the current frequency sub-interval, I represent the diffraction intensity pattern tensor with shape [J,H,W], and β represent the ADMM penalty parameter. Aux represents the inverse operation of the phase projection operator; l+1 This represents the new round of Lagrange multiplier tensors.
[0045] S4.5. Take the next level frequency sub-interval as the new current frequency sub-interval and return to step S4.1.
[0046] S4.6 Repeat steps S4.1 to S4.5 until the iteration conditions are met. The iteration ends, and the optimal probe function and the optimal reconstruction objective function are obtained.
[0047] In step S4.6, the iteration ends when any of the following iteration conditions are met:
[0048] a. Reach the preset maximum number of iterations;
[0049] b. The relative error change over multiple consecutive iterations is less than the preset relative error change threshold;
[0050] c. The reconstruction error is lower than the preset reconstruction error threshold.
[0051] In summary, this invention discloses an extreme ultraviolet (EUV) stacked diffraction imaging method based on iterative frequency masks to address technical problems such as low reconstruction quality and sensitivity to noise and overlap rate in EUV stacked diffraction imaging reconstruction. The method employs a physically driven iterative spatial frequency mask design, constructing a frequency mask based on the zero points of the zero-order Bessel function, and uses a super-Gaussian filter to simulate the frequency response characteristics of a real optical system. Furthermore, the method incorporates a multi-level adaptive learning rate scheduler that dynamically adjusts the learning rate based on reconstruction error, frequency level, and gradient behavior, significantly improving reconstruction stability. A GPU-accelerated batch processing optimization model further enhances reconstruction performance by 10–100 times. Experimental results demonstrate that the method exhibits significant advantages in reconstruction quality, convergence speed, and robustness to low stacking rates and high-noise environments, making it valuable for applications in stacked diffraction imaging.
[0052] The beneficial effects of this invention are:
[0053] 1. This invention innovatively proposes an extreme ultraviolet light stacked diffraction imaging method based on iterative frequency masks, which solves the key technical problems of unstable reconstruction quality and convergence of traditional reconstruction algorithms in low overlap and high noise environments.
[0054] 2. This invention introduces a frequency progressive reconstruction strategy for the first time. By using a stepwise optimization method from low frequency to high frequency, it effectively utilizes the hierarchical structure of frequency information, which significantly improves the accuracy and stability of reconstruction.
[0055] 3. This invention designs a multi-level adaptive learning rate scheduler that can dynamically adjust the learning rate according to reconstruction error, frequency level and gradient behavior, effectively overcoming the technical bottleneck of traditional methods that are prone to divergence in the high-frequency reconstruction stage.
[0056] 4. The method of this invention can also be combined with a GPU-accelerated batch processing optimization model to transform serial iteration into parallel computing, significantly improving computing efficiency by 10 to 100 times, and providing an efficient technical solution for large-scale point cloud reconstruction.
[0057] 5. It effectively solves the problems of weak convergence, sensitivity to noise and stacking ratio of traditional methods, and shows significant advantages in reconstruction quality, convergence speed and robustness to low stacking ratio and high noise environment. Especially in the complex imaging conditions faced in practical applications, it can stably provide high-quality reconstruction results. Attached Figure Description
[0058] Figure 1 This is a flowchart of the method of the present invention;
[0059] Figure 2 Reconstruction results under different overlap rates;
[0060] Figure 3 This is a frequency-progressive reconstruction process based on simulation data.
[0061] Figure 4 This is a comparison chart of reconstruction results based on real data. Detailed Implementation
[0062] The present invention will be further described below with reference to the accompanying drawings and embodiments.
[0063] The flowchart of the method of the present invention is as follows Figure 1 As shown, the specific steps include:
[0064] S1. Use an extreme ultraviolet coherent light source to scan and irradiate the target to be reconstructed, and collect diffraction intensity patterns at each scanning position.
[0065] S2. Based on the location information and diffraction intensity patterns of all scanned positions, obtain the initial probe function and the initial reconstruction target function. Simultaneously, initialize the auxiliary variable tensor, the Lagrange multiplier tensor, and the adaptive learning rate.
[0066] S3. Construct a multi-level spatial frequency mask.
[0067] Specifically, in step S3, a multi-level spatial frequency mask is constructed through the following process: using the zeros of the zero-order Bessel function as dividing points, the entire frequency domain is divided into multi-level annular frequency sub-intervals. Based on the cutoff radius of each frequency sub-interval and combined with a super-Gaussian filter, a spatial frequency mask for each frequency sub-interval is constructed. All spatial frequency masks for the frequency sub-intervals constitute a multi-level spatial frequency mask. In this process, by employing a super-Gaussian filter, the frequency response characteristics of a real optical system can be simulated.
[0068] Specifically: If the zeros of the zero-order Bessel function are denoted as J... 0,1 J 0,2 J 0,3 , ..., J 0,L+1 (Arranged in ascending order), the dividing point corresponding to the first-level frequency sub-interval is J. 0,1 and J 0,2 The cutoff radius of the first-order frequency sub-interval
[0069] More specifically, the spatial frequency mask M of the l-th frequency sub-interval l Set it according to the following formula:
[0070]
[0071] In the formula, M l (f) represents the mask value at spatial frequency coordinate f in the l-th frequency sub-interval, where f represents the spatial frequency coordinate, |f| represents the frequency radius at spatial frequency coordinate f, and r l The cutoff radius of the l-th frequency sub-interval is given by , n is the exponent of the super-Gaussian function used to simulate the smooth transition of frequency response caused by aberrations in actual optical systems, and L represents the total number of frequency sub-intervals.
[0072] The cutoff radius of the l-th frequency sub-interval is set according to the following formula:
[0073]
[0074] In the formula, r max J represents the maximum frequency indicated by the diffraction intensity pattern. 0,l+1 J represents the (l+1)th zero of the zero-order Bessel function. 0,L+1 This represents the (L+1)th zero of the zero-order Bessel function.
[0075] S4. Based on the position information and diffraction intensity pattern of all scanning positions, use a multi-level spatial frequency mask to update the probe function, reconstruction objective function, auxiliary variable tensor and Lagrange multiplier tensor step by step from the low frequency sub-interval to the high frequency sub-interval. The optimal probe function and optimal reconstruction objective function are used as the reconstruction result.
[0076] In step S4, the reconstruction and update process of each sub-interval is activated sequentially according to frequency, so that low-frequency information is accurately reconstructed first, and then high-frequency details are gradually introduced, thereby improving the overall reconstruction quality and stability. Step S4 is specifically as follows:
[0077] S4.1. Use an adaptive learning rate scheduler to dynamically adjust the learning rate based on the reconstruction error, frequency level, and gradient behavior to obtain the current adaptive learning rate. In this step, dynamically adjusting the learning rate can improve the stability of the reconstruction process.
[0078] In step S4.1, the adaptive learning rate includes the probe adaptive learning rate and the reconstruction target adaptive learning rate. When the current frequency sub-interval is the l-th level frequency sub-interval, the probe adaptive learning rate and the reconstruction target adaptive learning rate are obtained using the following formulas:
[0079]
[0080] In the formula, The current adaptive learning rate is represented by z, which is either P or O, where P and O represent the probe and the reconstruction target, respectively. error (e ( l)) represents the adjustment factor based on reconstruction error, e ( l) represents the reconstruction error, f freq (l) represents the adjustment factor based on frequency level l, f osc (g( l-w )) represents gradient oscillation detection (i.e., gradient behavior) g( l-w The adjustment factor of g( l-w ) represents the gradient history of the past w iterations.
[0081] The adaptive learning rate scheduler automatically reduces the learning rate as the algorithm progresses to higher frequency levels to accommodate finer update requirements and prevent instability caused by high-frequency components. Furthermore, by detecting gradient oscillations, the scheduler adjusts the learning rate in a timely manner to stabilize the optimization process, effectively mitigating the divergence and oscillation problems commonly found in layer-by-layer reconstruction.
[0082] S4.2 Using the current probe function and reconstruction target function, combined with the current auxiliary variable tensor and Lagrange multiplier tensor, calculate the gradients of the probe and reconstruction target based on the diffraction intensity patterns at all scan positions.
[0083] Preferably, in step S4.2, a GPU-accelerated batch processing optimization model is used to process the diffraction intensity patterns of each scanning position in parallel, thereby improving computational efficiency and increasing reconstruction speed.
[0084] In step S4.2, when the current frequency sub-interval is the l-th level frequency sub-interval, the gradients of the probe and the reconstructed target are obtained by the following formulas:
[0085]
[0086] In the formula, O l and P l S represents the current reconstruction target and the current probe function, respectively. l Aux represents the auxiliary variable tensor used to decompose the original optimization problem into more easily solvable subproblems. l S represents the Lagrange multiplier tensor used to connect the original variable and the auxiliary variable. l and Aux l The shapes are all [J,H,W], where J is the number of scan positions, and H and W are the height and width of the detector. T denotes the transpose of a matrix; A batch This indicates a batch sampling operator, which simultaneously reconstructs the target O from the current location based on the position information of the scanned location. l Extract all probe illumination regions to form a reconstructed target tensor of shape [J,H,W]. A represents batch The inverse transform; [ j Let j represent the j-th channel of the tensor, [] * To denote the conjugate of a complex number, || 2 Let L2 norm be the squared form, and ∈ denote a small constant to prevent division by zero; in the final result, Indicates the gradient of the probe. This represents the gradient of the reconstruction target.
[0087] S4.3. Using the gradient descent method, update the probe function and the reconstruction target function based on the current adaptive learning rate obtained in step S4.1, the gradient of the probe and the reconstruction target obtained in step S4.2, and the spatial frequency mask of the current frequency sub-interval.
[0088] In step S4.3, when the current frequency sub-interval is the l-th level frequency sub-interval, the probe function and the reconstruction target function are updated using the following formula:
[0089]
[0090] In the formula, P l+1 P represents the updated probe function. l This represents the current probe function (i.e., the probe function updated in the previous iteration). This represents the current adaptive learning rate. This represents the probe gradient after being processed by the spatial frequency mask of the current frequency sub-interval;
[0091] O l+1 Denotes the updated reconstruction objective function, O l This represents the current reconstruction objective function (i.e., the reconstruction objective function updated in the previous iteration). This represents the adaptive learning rate of the current reconstruction target. This represents the reconstructed target gradient after processing with a spatial frequency mask in the current frequency sub-interval;
[0092] Among them, the probe gradient after spatial frequency masking of the current frequency sub-interval and the reconstructed target gradient after spatial frequency masking of the current frequency sub-interval It is obtained through the following formula:
[0093]
[0094] In the formula, and These represent the gradients of the probe and the reconstructed target, respectively, after being processed by the spatial frequency mask of the current frequency sub-interval. Indicates Fourier transform, M represents the inverse Fourier transform. l This represents the spatial frequency mask for the current frequency sub-interval.
[0095] S4.4 Based on the updated probe function and reconstruction objective function, obtain the new auxiliary variable tensor and Lagrange multiplier tensor.
[0096] In step S4.4, when the current frequency subinterval is the l-th level frequency subinterval, the new auxiliary variable tensor and Lagrange multiplier tensor are calculated using the following formulas:
[0097]
[0098] In the formula, μ represents an intermediate variable. This represents the phase projection operator, which projects the complex field into a form that matches the measured intensity. l+1 Let P represent the reconstruction target tensor obtained from the updated reconstruction objective function. l+1 S represents the updated probe function; l+1 This represents the auxiliary variable tensor for the new round, i.e., the diffraction field reconstructed in the (l+1)th round. Indicates Fourier transform, This represents the inverse Fourier transform. Let I represent the spatial frequency mask for the current frequency sub-interval, I represent the diffraction intensity pattern tensor with shape [J,H,W], and β represent an ADMM penalty parameter with manually set variation rules, used to balance the weights between data fidelity terms and constraint terms. Aux represents the inverse operation of the phase projection operator; l+1 This represents the new round of Lagrange multiplier tensors.
[0099] S4.5. Take the next level frequency sub-interval as the new current frequency sub-interval and return to step S4.1.
[0100] S4.6 Repeat steps S4.1 to S4.5 until the iteration conditions are met. The iteration ends, and the optimal probe function and the optimal reconstruction objective function are obtained.
[0101] In step S4.6, the iteration ends when any of the following iteration conditions are met:
[0102] a. Reach the preset maximum number of iterations;
[0103] b. The relative error change over multiple consecutive iterations is less than the preset relative error change threshold;
[0104] c. The reconstruction error is lower than the preset reconstruction error threshold.
[0105] Reconstruction error refers to the following: using the reconstruction target function and probe function obtained from the current reconstruction, a forward propagation is performed (simulating the process of obtaining diffraction images through sampling), resulting in a set of diffraction images corresponding to the scanning position. The MSE loss is calculated using this set of diffraction images and the actual acquired diffraction intensity pattern, and the calculated MSE value is the reconstruction error.
[0106] Furthermore, the imaging methods also include:
[0107] S5. Post-process the reconstruction results using the phase unwinding algorithm and / or spatial domain normalization algorithm to obtain the final reconstruction result.
[0108] Specific embodiments of the present invention are as follows:
[0109] Example 1
[0110] This experimental example uses diffraction images acquired by a simulated far-field diffraction and a real stacked diffraction optical experimental platform as examples. The method of this invention is used to perform stacked diffraction imaging to recover the amplitude and phase of the object.
[0111] This embodiment specifically includes the following steps:
[0112] S1. Data Acquisition: The target to be reconstructed is scanned and irradiated using an extreme ultraviolet coherent light source, and diffraction intensity patterns at each scanning position are acquired.
[0113] This step specifically involves using a precision displacement stage to scan and sample the target in a two-dimensional plane at preset step sizes. At each scanning position, the system uses an extreme ultraviolet coherent light source as a probe to illuminate the target. When the coherent beam passes through or reflects from the target, the probe interacts with the target to generate an outgoing wave containing complex amplitude information. A charge-coupled device (CCD) or complementary metal-oxide-semiconductor (CMOS) sensor is used to record the diffraction intensity pattern in the far field. During this process, because the detection device can only record light intensity and cannot directly acquire phase information, phase information is lost.
[0114] S2. Reconstruction Initialization: Based on the position information and diffraction intensity patterns of all scanned positions, obtain the initial probe function and the initial reconstruction target function; simultaneously, initialize the auxiliary variable function S. 0 AUX 0 .
[0115] This step specifically involves: based on the acquired diffraction intensity pattern and its corresponding scanning position information, making preliminary estimates of the probe function and the size of the reconstructed target. The initialization of the reconstructed target is determined by the scanning range, step size, and overlap rate, using random initialization or a full-one matrix as the starting point. The initialization of the probe is determined by the effective detection area and size of the sensor, using a Gaussian beam model to determine the initial function. Subsequently, based on the detector size (height and width), the frequency response characteristics of the actual optical system, and the reconstruction quality requirements, the total frequency level L is determined, typically ranging from 100 to 600.
[0116] In this embodiment, the probe and reconstructed target sizes are initially estimated based on the size of the local diffraction image and the corresponding scanning position information. The Gaussian beam model and the all-1 matrix are used as the initial functions for the probe and the reconstructed target, respectively, and the total frequency level L = 300 is determined.
[0117] S3. Generate multi-level spatial frequency masks.
[0118] Using the zeros of the zero-order Bessel function as frequency boundaries, for a total frequency level L, L+1 zeros of the Bessel function are calculated, with J... 0,1 and J 0,2 As the two boundaries corresponding to the first-level frequency sub-interval, J 0, 2 and J 0,3 As the two boundaries corresponding to the second-level frequency sub-intervals, and so on, the entire frequency domain is divided into multi-level ring-shaped frequency sub-intervals. This division method ensures a finer division in the low-frequency region, while the high-frequency region has looser intervals, which is consistent with the characteristic that low-frequency information in optical imaging systems usually contains more reliable structural information.
[0119] Subsequently, a spatial frequency mask is constructed using a super-Gaussian filter based on the cutoff radius of each frequency sub-interval. By replacing the ideal hard cutoff mask with a super-Gaussian filter to simulate the smooth transition characteristics of the frequency response in a real optical system, not only is the actual frequency response of the physical system more closely approximated, but the Gibbs phenomenon caused by hard cutoff in the spatial domain is also effectively suppressed, thus improving the quality of the reconstructed image.
[0120] In this embodiment, the exponent of the superGaussian function is set to 6.
[0121] S4, Reconstructing step by step from low frequency to high frequency.
[0122] In this step, the probe function and reconstruction objective function are updated based on an adaptive learning rate scheduler and a batch optimization model. The adaptive learning rate scheduler automatically reduces the learning rate as the algorithm progresses to higher frequency levels to adapt to finer update requirements and prevent instability caused by high-frequency components. Furthermore, by detecting gradient oscillations, the scheduler adjusts the learning rate in a timely manner to stabilize the optimization process, effectively mitigating common divergence and oscillation problems in layered reconstruction. In addition, the batch optimization model improves the reconstruction speed by nearly 100 times. The method proposed in this invention has significant advantages in robustness against noise and overlap ratios. By sampling the same region with different step sizes and number of positions, diffraction patterns with different overlap ratios are obtained. Figure 2 The reconstruction results of this method are shown at some challenging overlap rates.
[0123] S5. Post-process the results, using phase unwinding algorithm and spatial domain normalization to make the reconstruction results more reasonable, and output the final result.
[0124] Example 2
[0125] This embodiment uses a Camera Man image as the reconstruction target and simulated coherent light as the probe to couple and generate simulated stacked diffraction image data. The reconstruction is then performed using the method of this invention. The reconstruction process meets the intended design of the invention; the probe and reconstruction target gradually reconstruct information from low frequencies to high frequencies, resulting in increasingly richer information and more abundant details. Figure 3 Several representative stages were shown.
[0126] Example 3
[0127] In this embodiment, diffraction images were acquired under two conditions: low overlap rate and normal noise (a) and normal overlap rate and high noise (b). Reconstruction was performed using the method of this invention. The reconstruction results of the objective function of this invention were compared with other existing methods. The results are as follows: Figure 4 As shown.
[0128] Experimental results show that this method is significantly better than other methods in terms of reconstruction performance at low overlap rates, robustness to noise, and reconstruction speed.
[0129] While the present invention has been disclosed above with reference to preferred embodiments, it is not intended to limit the invention. Those skilled in the art can make various modifications and refinements without departing from the spirit and scope of the invention. Therefore, the scope of protection of the present invention shall be determined by the claims.
Claims
1. An extreme ultraviolet (EUV) stacked diffraction imaging method based on iterative frequency masks, characterized in that, Includes the following steps: S1. Use an extreme ultraviolet coherent light source to scan and irradiate the target to be reconstructed, and collect diffraction intensity patterns at each scanning position; S2. Based on the position information and diffraction intensity patterns of all scanning positions, obtain the initial probe function and the initial reconstruction target function; at the same time, initialize the auxiliary variable tensor, the Lagrange multiplier tensor, and the adaptive learning rate. S3. Construct a multi-level spatial frequency mask; S4. Based on the diffraction intensity patterns at all scanning positions, use a multi-level spatial frequency mask to update the probe function, reconstruction target function, auxiliary variable tensor, and Lagrange multiplier tensor step by step from low frequency to high frequency. The optimal probe function and optimal reconstruction target function are used as the reconstruction results. Step S4 is as follows: S4.
1. Obtain the current adaptive learning rate based on the reconstruction error, frequency level, and gradient behavior; In step S4.1, the adaptive learning rate includes the probe adaptive learning rate and the reconstruction target adaptive learning rate; When the current frequency sub-interval is the l-th level frequency sub-interval, the probe adaptive learning rate and the reconstruction target adaptive learning rate are obtained by the following formulas: In the formula, This represents the current adaptive learning rate, where z is either P or O, and P and O represent the probe and the reconstruction target, respectively. This represents the adjustment factor based on the reconstruction error. Indicates reconstruction error. Indicates frequency level The adjustment factor, Indicates gradient oscillation detection The adjustment factor, Indicates the past Gradient history of each iteration; S4.2 Using the current probe function and reconstruction target function, combined with the current auxiliary variable tensor and Lagrange multiplier tensor, calculate the gradients of the probe and reconstruction target based on the diffraction intensity patterns at all scanning positions; In step S4.2, when the current frequency sub-interval is the l-th level frequency sub-interval, the gradients of the probe and the reconstructed target are obtained by the following formulas: In the formula, and These represent the current reconstruction target and the current probe function, respectively. Represents an auxiliary variable tensor. Represents the Lagrange multiplier tensor; This indicates a batch sampling operator, which simultaneously reconstructs the target from the current location based on the scanned position information. Extract all probe illumination areas and form a shape as Reconstruction target tensor , express inverse transform; This represents the j-th channel of the tensor. To represent the conjugate of a complex number, Represents the square of the L2 norm. This represents a small constant that prevents division by zero. Indicates the gradient of the probe. The gradient representing the reconstruction target; S4.
3. Based on the current adaptive learning rate obtained in step S4.1, the gradients of the probe and the reconstruction target obtained in step S4.2, and the spatial frequency mask of the current frequency sub-interval, update the probe function and the reconstruction target function. In step S4.3, when the current frequency sub-interval is the l-th level frequency sub-interval, the probe function and the reconstruction target function are updated using the following formula: In the formula, This represents the updated probe function. Indicates the current probe function. This represents the current adaptive learning rate. This represents the probe gradient after being processed by the spatial frequency mask of the current frequency sub-interval; This represents the updated reconstruction objective function. This represents the current reconstruction objective function. This represents the adaptive learning rate of the current reconstruction target. This represents the reconstructed target gradient after processing with a spatial frequency mask in the current frequency sub-interval; Among them, the probe gradient after spatial frequency masking of the current frequency sub-interval and the reconstructed target gradient after spatial frequency masking of the current frequency sub-interval It is obtained through the following formula: In the formula, and These represent the gradients of the probe and the reconstructed target, respectively, after being processed by the spatial frequency mask of the current frequency sub-interval. {} denotes Fourier transform, {} denotes the inverse Fourier transform. This represents the spatial frequency mask for the current frequency sub-interval; S4.
4. Based on the updated probe function and reconstruction target function, obtain the new auxiliary variable tensor and Lagrange multiplier tensor; In step S4.4, when the current frequency subinterval is the l-th level frequency subinterval, the new auxiliary variable tensor and Lagrange multiplier tensor are calculated using the following formulas: In the formula, Indicates intermediate variables. This represents the phase projection operator, which projects the complex field into a form that matches the measured intensity. This represents the reconstruction target tensor obtained from the updated reconstruction objective function. This represents the updated probe function. This represents the current Lagrange multiplier tensor; This represents a new round of auxiliary variable tensors. This represents the spatial frequency mask for the current frequency sub-interval, where I represents the diffraction intensity pattern tensor with the following shape. , This represents the ADMM penalty parameter. This represents the inverse operation of the phase projection operator; This represents the new round of Lagrange multiplier tensors; S4.
5. Take the next level frequency sub-interval as the new current frequency sub-interval and return to step S4.1; S4.6 Repeat steps S4.1 to S4.5 until the iteration conditions are met. The iteration ends, and the optimal probe function and the optimal reconstruction objective function are obtained.
2. The extreme ultraviolet light stacked diffraction imaging method based on iterative frequency mask according to claim 1, characterized in that: In step S3, a multi-level spatial frequency mask is constructed through the following process: the zero point of the zero-order Bessel function is used as the dividing point to divide the frequency domain into multiple frequency sub-intervals. The spatial frequency mask of each frequency sub-interval is constructed by combining the cutoff radius of each frequency sub-interval with a super Gaussian filter. The spatial frequency masks of all frequency sub-intervals constitute a multi-level spatial frequency mask.
3. The extreme ultraviolet light stacked diffraction imaging method based on iterative frequency masks according to claim 2, characterized in that: Spatial frequency mask for the l-th level frequency sub-interval Set it according to the following formula: In the formula, Represents the spatial frequency coordinates in the l-th level frequency sub-interval Mask value at that location, Represents spatial frequency coordinates. Represents spatial frequency coordinates The frequency radius at that location, This represents the cutoff radius of the l-th frequency sub-interval. is the exponent of the superGaussian function, and L represents the total number of frequency subintervals; The cutoff radius of the l-th frequency sub-interval is set according to the following formula: In the formula, This indicates the maximum frequency represented by the diffraction intensity pattern. This represents the (l+1)th zero of the zero-order Bessel function. This represents the (L+1)th zero of the zero-order Bessel function.
4. The extreme ultraviolet light stacked diffraction imaging method based on iterative frequency mask according to claim 1, characterized in that: In step S4.6, the iteration ends when any of the following iteration conditions are met: a. Reach the preset maximum number of iterations; b. The relative error change over multiple consecutive iterations is less than the preset relative error change threshold; c. The reconstruction error is lower than the preset reconstruction error threshold.
5. The extreme ultraviolet light stacked diffraction imaging method based on iterative frequency mask according to claim 1, characterized in that: In step S4.2, a GPU-accelerated batch processing optimization model is used to process the diffraction intensity patterns at each scanning position in parallel.