Generative adversarial autoencoder for noise reduction in x-ray images

Abstract

A method for reducing noise in X-ray images is disclosed. The method comprises the step of receiving a plurality of X-ray images acquired at a predefined location on a semiconductor substrate. Among the plurality of X-ray images, a plurality of pairs are selected, and each pair comprises (i) two copies of the same X-ray image or (ii) two different X-ray images. A generator is applied to reduce noise in each pair of X-ray images, and the generator is trained to deceive a discriminator of a Generative Adversarial Network (GAN) in determining whether each pair comprises (i) two copies of the same X-ray image or (ii) two different X-ray images. When the generator is successfully trained to deceive the discriminator, the trained generator is applied to reduce noise in at least one additional X-ray image acquired at a selected location on the semiconductor substrate.

Description

Technology Field

[0001] (Cross-reference to related applications)

[0002] This application claims the benefit of U.S. provisional patent application No. 63 / 753,468 filed on February 4, 2025, the disclosure of said application is incorporated herein by reference.

[0003] (Field of Invention)

[0004] The present invention generally relates to X-ray image processing, and in particular to a method and system for reducing noise in digital X-ray scattering images using machine learning techniques. Background Technology

[0005] X-ray critical dimension (XCD) analysis and other X-ray imaging techniques used in semiconductor manufacturing and material characterization rely on digital X-ray scattering imaging. These images are inherently affected by multiple sources of noise, including Poisson noise arising from the photon counting process and hardware-induced noise such as electron interference, detector defects, and mechanical instability. Such noise can limit the precision, accuracy, and throughput of measurements. While reducing noise in X-ray images is essential to improving the quality of X-ray analysis (e.g., XCD measurements), current noise reduction image generation techniques require increased sampling rates and extended image acquisition times, which consequently reduces the throughput of the X-ray system. means of solving the problem

[0006] One embodiment of the present invention provides a method for reducing noise in X-ray images, the method comprising the step of receiving a plurality of X-ray images acquired at a predefined location on a semiconductor substrate. Among the plurality of X-ray images, a plurality of pairs are selected, each pair comprising (i) two copies of the same X-ray image or (ii) two different X-ray images. A generator is applied to reduce noise in each pair of X-ray images, and the generator is trained to deceive a discriminator of a Generative Adversarial Network (GAN) in determining whether each pair comprises (i) two copies of the same X-ray image or (ii) two different X-ray images. After the generator is successfully trained to deceive the discriminator, the trained generator is applied to reduce noise in one or more additional X-ray images acquired at a selected location on the semiconductor substrate.

[0007] In some embodiments, the generator and the discriminator together constitute a Generative Adversarial Autoencoder (GAAE) that combines a Variational Autoencoder (VAE) architecture with a Generative Adversarial Network (GAN). In other embodiments, the generator includes an encoder and a decoder, wherein the encoder is configured to compress each X-ray image into a latent representation, and the decoder is configured to reconstruct a noise-reduced X-ray image from the latent representation. In yet another embodiment, the discriminator is configured to receive as input a pair of latent representations generated by the encoder, and the encoder is trained so that the discriminator cannot distinguish whether the pair of latent representations originated from two copies of the same X-ray image or from two different X-ray images.

[0008] In some embodiments, the discriminator is configured to receive as input a pair of noise-reduced X-ray images generated by a decoder, and the decoder is trained such that the discriminator cannot distinguish whether the pair of noise-reduced X-ray images originated from two copies of the same X-ray image or from two different X-ray images. In other embodiments, the Generative Adversarial Autoencoder (GAAE) is trained using (a) an intershot loss configured to measure the difference between noise-reduced X-ray images generated from two different X-ray images in a pair, and (b) a weighted combination of one or more loss functions selected from the following list of loss functions: (i) a reconstruction loss configured to maintain similarity between the noise-reduced X-ray image and the corresponding X-ray image; (ii) a Kullback-Leibler (KL) divergence loss configured to normalize the latent representation to approximate a standard normal distribution; (iii) a generator loss configured to measure how successfully the encoder deceives the discriminator; and (iv) a discriminator loss configured to measure the discriminator's ability to distinguish whether the pair originated from two copies of the same X-ray image or from two different X-ray images. In another embodiment, the learning of the GAAE is stopped when at least the inter-shot loss reaches saturation and no longer improves.

[0009] In some embodiments, a generative adversarial autoencoder (GAAE) is trained to reduce both Poisson noise generated during the photon counting process and hardware-induced noise, including at least one of electronic interference, detector defects, or mechanical vibrations. In other embodiments, if the generator is successfully trained to deceive the discriminator, the discriminator is discarded and only the generator is applied to reduce noise in the one or more additional X-ray images.

[0010] In some embodiments, the plurality of X-ray images comprises a repeatability set of images acquired by successive shots at predefined locations on a semiconductor substrate. In other embodiments, the method also comprises the steps of: calculating a discriminator loss for at least one pair; comparing the discriminator loss with a predefined threshold; and generating an indication of an abnormal sign in the plurality of X-ray images if the discriminator loss exceeds the predefined threshold.

[0011] According to one embodiment of the present invention, a system for reducing noise in X-ray images is further provided, the system comprising: (1) an interface configured to receive a plurality of X-ray images acquired at a predefined location on a semiconductor substrate; and (2) a processor configured to perform the following: (a) select a plurality of pairs from the plurality of X-ray images, wherein each pair is selected to include (i) two copies of the same X-ray image or (ii) two different X-ray images; (b) apply a generator to reduce noise in each pair of X-ray images, wherein the generator is trained to deceive a discriminator of a Generative Adversarial Network (GAN) to determine whether each pair includes (i) two copies of the same X-ray image or (ii) two different X-ray images; and (c) after the generator is successfully trained to deceive the discriminator, apply the trained generator to reduce noise in at least one additional X-ray image acquired at a selected location on a semiconductor substrate.

[0012] The present invention will be more fully understood by referring to the following detailed description of embodiments and the accompanying drawings. Brief explanation of the drawing

[0013] FIG. 1 is a block diagram schematically illustrating a system for reducing noise in an X-ray image according to one embodiment of the present invention. FIG. 2 is a flowchart schematically illustrating a method for reducing noise in an X-ray image according to one embodiment of the present invention. Specific details for implementing the invention

[0014] (outline)

[0015] X-ray imaging and analysis techniques, such as X-ray critical dimension analysis used in semiconductor manufacturing, rely on digital X-ray scattering images that are inherently affected by various noise sources. This noise can include Poisson noise arising from the photon counting process, as well as hardware-induced noise such as electron interference, detector defects, and mechanical instability. These noise sources limit the precision, accuracy, and throughput of measurements. Reducing noise in X-ray images is essential to ensure high-quality measurements and analyses. However, conventional image noise reduction methods generally require increasing the number of samples or extending image acquisition times, which reduces the throughput of the X-ray system.

[0016] The embodiments of the invention described herein provide a method and system for reducing noise in digital X-ray scattering images using a novel machine learning architecture. The architecture is configured to effectively reduce both Poisson noise and hardware-induced noise while maintaining high throughput while preserving important structural details.

[0017] In some embodiments, a learning and inference system for reducing noise in X-ray images includes an interface and a processor. The interface is configured to receive a plurality of X-ray images acquired at a predefined location on a semiconductor substrate (e.g., a semiconductor wafer, also referred to herein for convenience as a wafer). During a learning phase, the processor is configured to select a plurality of pairs of X-ray images from the received plurality of X-ray images, each pair of images consisting of (i) two copies of the same X-ray image or (ii) two different X-ray images.

[0018] In some embodiments, during the training phase, the processor is configured to apply a generator to reduce noise for each pair of X-ray images. In this example, the generator includes a variational autoencoder (hereinafter also referred to as an autoencoder for convenience) implemented within a neural network (NN). The autoencoder is trained to deceive a discriminator based on a Generative Adversarial Network (GAN) configuration implemented within the neural network, and the discriminator is configured to determine whether each pair of images consists of two copies of the same X-ray image or two different X-ray images. In some embodiments, if the generator (e.g., the autoencoder) is successfully trained to deceive the discriminator, during the inference phase, the processor is configured to apply the trained autoencoder to reduce noise in at least one additional X-ray image acquired at a selected location on the wafer. In particular, a discriminator is not required in an actual production environment. In this embodiment, the interface is configured to receive a single image acquired by an X-ray analysis system, and the processor is configured to reduce noise in the acquired image by applying a learned autoencoder. Based on the noise-reduced image, the processor is configured to perform X-ray analysis, such as measuring the critical dimension (CD) of a predefined pattern contained in a metal layer, dielectric layer, or semiconductor layer formed inside or on top of the wafer.

[0019] In some embodiments, the technology disclosed herein integrates two existing machine learning models, namely (i) a Variational Autoencoder (VAE) and (ii) a Generative Adversarial Network (GAN), to form an integrated framework referred herein as a Generative Adversarial Autoencoder (GAAE). The VAE component includes an encoder configured to compress (and optionally reduce noise) a noisy X-ray image into a latent representation and a decoder configured to reconstruct a noise-reduced image from said latent space. The GAN component includes a generator, which may include an encoder alone or a combination of an encoder and a decoder, and also includes a discriminator configured to provide adversarial feedback to improve noise reduction performance. By integrating the encoding-decoding capabilities provided by the autoencoder architecture of VAE with the adversarial learning of GAN, GAAE is configured to leverage the strengths of both machine learning models to effectively reduce noise in X-ray images while preserving fine structural details essential for precise critical dimension analysis.

[0020] In some embodiments, during the learning phase, GAAE is configured to receive pairs of noisy X-ray images captured at the same measurement point on a semiconductor wafer. X-ray images captured at the same measurement point are referred to herein as a repeatability set. The repeatability set may include images acquired as successive shots at the same location or images acquired from redundant detectors measuring the same point. Each image in each pair of images is processed by an encoder to generate a latent representation. A discriminator receives a pair of latent representations or a pair of noise-reduced images and attempts to determine whether the pairs originated from the same base X-ray image or from different images within the repeatability set. At the same time, the encoder and decoder are trained to deceive the discriminator, so that the discriminator cannot distinguish them, thereby causing noise-reduced images generated from different noisy inputs at the same measurement point to appear as similar to each other as possible.

[0021] In some embodiments, after the learning phase is completed, the discriminator is discarded, and only the encoder-decoder pair is used to reduce noise in new X-ray images in real time. When a new noisy X-ray image is provided as input (e.g., by an X-ray system), the trained generator is configured to process the noisy X-ray image to produce a high-quality X-ray image with reduced Poisson noise and hardware noise. Adversarial learning enables effective generalization to new data, thereby preserving important details necessary for accurate X-ray critical dimension analysis while maintaining image fidelity. As previously described, only a single X-ray image is required as input during the operation phase, and paired images from a repeatable set are not required.

[0022] In some embodiments, the technology disclosed herein offers significant advantages over conventional noise reduction methods. GAAE can effectively reduce not only Poisson noise inherent in the photon counting process but also hardware-induced noise such as electronic interference, detector defects, beam blocker instability, and mechanical vibration, thereby outperforming conventional methods that typically handle only one type of noise. The GAAE architecture is configured to preserve the microstructural details of X-ray images essential for precise critical dimension analysis of high aspect ratio nanostructures, thereby overcoming the limitations of conventional noise reduction algorithms that can blur or distort important features of X-ray images. By eliminating the need to increase measurement time for noise reduction, this technology enables image acquisition time to be reduced without compromising precision. For example, in some embodiments, image acquisition time can be reduced by up to 50% while maintaining the required measurement accuracy. Furthermore, the adversarial learning process enables the neural network to effectively generalize to multiple noise types and combinations thereof, as well as to previously unobserved data acquired from various locations on the wafer, ensuring consistent performance across different samples and measurement conditions.

[0023] In some embodiments, the disclosed system may be implemented in two configurations. In the first configuration, GAAE is directly integrated into an X-ray Critical Dimension (XCD) tool or another X-ray scattering measurement system as part of a real-time X-ray measurement processing pipeline, with a processing latency of less than about 100 milliseconds per image. When the X-ray system acquires a measurement, the processor of the XCD tool is configured to automatically input the noisy X-ray image into a trained GAAE model, said GAAE model trained to reduce noise in the image while preserving important structural details. This process is fully automated and requires no operator intervention. In the second configuration, GAAE is deployed to a processing unit as a software-based standalone post-processing tool. An operator or applied scientist can input previously acquired noisy X-ray images from any XCD analysis tool into the standalone software, which reduces the noise in the image and outputs a high-quality X-ray image for subsequent analysis. This standalone approach is particularly suitable for facilities that already possess X-ray measurement equipment but wish to improve measurement accuracy and throughput without hardware upgrades.

[0024] In some embodiments, the primary application of the disclosed technology is the improvement of X-ray critical dimension (XCD) analysis, but the technology may also be applied to other X-ray analysis and imaging methods. For example, the disclosed technology may be implemented in X-ray reflectivity (XRR), X-ray fluorescence (XRF), X-ray diffraction imaging (XRDI), X-ray diffraction of single-crystal and polycrystalline materials, and other X-ray imaging and measurement techniques where noise reduction is required.

[0026] (System Description)

[0027] FIG. 1 is a block diagram schematically illustrating a system (11) for reducing noise in an X-ray image according to one embodiment of the present invention. In some embodiments, the system (11) is configured to receive a noise-containing X-ray image obtained from a semiconductor substrate and to generate a noise-reduced X-ray image suitable for high-precision critical dimension analysis as well as other applications. In addition, in some embodiments, the system (11) is configured to incorporate machine learning technology to effectively reduce hardware-induced noise, such as electronic interference, detector defects, beam blocker instability, and mechanical vibration, as well as Poisson noise inherent in the photon counting process.

[0028] In the exemplary configuration illustrated in FIG. 1, the system (11) includes an interface (21), a processor (22), and a display (23). In some embodiments, the interface (21) is configured to receive a plurality of X-ray images (12) acquired by an X-ray analysis system (not shown in the drawing) at a predefined location on a semiconductor substrate (not shown in the drawing), such as a semiconductor wafer (hereinafter also referred to as a wafer for convenience) used in the manufacture of an integrated circuit (IC) device. The plurality of X-ray images (12) acquired at the same measurement point are referred to herein as a repeatability set. The repeatability set may include from two X-ray images (12) to thousands of X-ray images (12). In this example, the repeatability set includes X-ray images (12a), X-ray images (12b), X-ray images (12c), X-ray images (12d), and additional X-ray images (not shown in the drawing) obtained by consecutive shots at the same location, each shot capturing the same basic structural information but containing different levels of noise due to various noise sources described below. Alternatively, the repeatability set may consist of images obtained from redundant detectors measuring the same point simultaneously. By using the repeatability set in this way, the system (11) can capture the variability of noise inherent in the measurement process while ensuring that the basic signal remains consistent across the images.

[0029] In some embodiments, the processor (22) is operatively connected to the interface (21) and is configured to reduce noise in the received X-ray image (12) using a learned generative adversarial autoencoder (GAAE) (77) as described in detail below. The processor (22) may include one or more general-purpose processors, digital signal processors (DSPs), graphics processing units (GPUs), or specialized machine learning accelerators such as one or more tensor processing units (TPUs) configured to efficiently perform neural network operations. In some embodiments, the processor (22) is programmed with software to perform the functions described herein. The software may be downloaded to the processor (22) in electronic form, for example, over a network, or alternatively or additionally provided or stored on non-transitory tangible media such as magnetic, optical, or electronic memory. In some embodiments, the display (23) is operatively connected to the processor (22) and is configured to display the noise-reduced X-ray image (16) and analysis results to an operator.

[0030] In some embodiments, the processor (22) is configured to implement a variational autoencoder (VAE), referred to herein as an autoencoder (33), and the autoencoder (33) constitutes part of a generative adversarial autoencoder (GAAE) (77) that integrates a VAE architecture and a generative adversarial network (GAN) architecture. This combination is configured to effectively reduce noise in an X-ray image (12) while preserving important details by leveraging the advantages of machine learning and deep learning models, respectively. The autoencoder (33) includes an encoder (44) and a decoder (55). In some embodiments, the GAAE (77) further includes a discriminator (66) that improves noise reduction performance by providing adversarial feedback during the learning process. Additionally, in some embodiments, the generator of the GAN may include only an encoder (44) or a combination of an encoder (44) and a decoder (55) depending on the specific implementation.

[0031] In some embodiments, the encoder (44) receives a noisy X-ray image, such as an X-ray image (12a) or an X-ray image (12b), as input and is configured to compress the image into a latent representation. The latent representation is an internal compression form of the image that captures essential features of the image while reducing dimensionality, and in some embodiments, provides the effect of reducing noise from the noisy X-ray image. Since the latent representation is smaller in size than the input image, this induces the encoder (44) to learn and prioritize the features most important for representing the actual signal. For example, the encoder (44) may be configured to generate an encoded feature vector (14a) from the X-ray image (12a) and an encoded feature vector (14b) from the X-ray image (12b). By compressing the image into a low-dimensional latent space, the encoder (44) learns how to distinguish important structural information from noise and retains only the features meaningful for representing the actual signal in a noise-free or noise-reduced state. In some embodiments, the encoder (44) is configured to add a controlled amount of random noise to the latent representation as part of a variational autoencoder architecture, which helps prevent overfitting and improves generalization performance.

[0032] In another embodiment, the encoder (44) is configured to generate encoded feature vectors (14a) and (14b) by adding different amounts of random noise to a potential representation from an X-ray image (12) containing a single randomly selected noise.

[0033] In some embodiments, the decoder (55) receives encoded feature vectors such as encoded feature vector (14a) and encoded feature vector (14b) and is configured to reconstruct a noise-reduced X-ray image (16) from these latent representations. In the reconstruction process, the decoder (55) is configured to expand the compressed latent representations into the entire image space to generate a noise-reduced X-ray image (16a) from the encoded feature vector (14a) and a noise-reduced X-ray image (16b) from the encoded feature vector (14b). The output noise-reduced X-ray images (16a) and (16b) each preserve essential structural details of the acquired X-ray images (12a) and (12b), respectively, while suppressing noise components filtered during the encoding process. In some embodiments, the decoder (55) is configured to operate as a noise remover configured to generate a clean and consistent image (16) and to effectively reduce Poisson noise and hardware-induced noise.

[0034] In some embodiments, the discriminator (66) is implemented as a neural network (NN) configured to receive input pairs and determine whether each input pair originates from the same base X-ray image (12) or from different X-ray images (12) within a set of repeatability. In particular, this architecture is distinguished from a conventional Generative Adversarial Network (GAN) discriminator that evaluates whether an image is real or fake. In the disclosed embodiment, the discriminator (66) is configured to evaluate (i) noise-reduced image pairs such as noise-reduced images (16a) and (16b), or (ii) latent representation pairs such as encoded feature vectors (14a) and (14b) to determine whether the input pair originates from the same base X-ray image (12) or from different X-ray images (12a, 12b) acquired at the same measurement point.

[0035] In some embodiments, the discriminator (66) is configured to receive pairs of encoded feature vectors, such as encoded feature vector (14a) and encoded feature vector (14b), generated by the encoder (44). In other embodiments, the discriminator (66) is configured to receive pairs of X-ray images, such as noise-reduced X-ray image (16a) and noise-reduced X-ray image (16b), generated by the decoder (55). Both of these configurations have been tested and may be optionally used for training the Generative Adversarial Autoencoder (GAAE) (77) depending on specific implementation requirements.

[0036] In some embodiments, during the learning phase of the autoencoder (33), the processor (22) is configured to select a plurality of image pairs from a plurality of X-ray images (12) received through the interface (21). Each image pair includes (i) two copies of the same X-ray image (e.g., X-ray image (12c)) or (ii) two different X-ray images selected from a set of repetitions (e.g., X-ray image (12a) and X-ray image (12b), or X-ray image (12c) and X-ray image (12d)). In some embodiments, the image pairs are randomly selected from a set of repetitions, so that the processor (22) does not know in advance whether a particular X-ray image pair (12) is two copies of the same image or two different images. This random selection strategy is a key element of the adversarial learning process and provides the discriminator (66) with examples of both pairs of X-ray images originating from the same source and pairs of X-ray images originating from different sources.

[0037] In some embodiments, for each pair of X-ray images (12), the processor (22) is configured to process the pair of X-ray images (12) by applying an autoencoder (33). Each pair of X-ray images (12) passes through an encoder (44) to generate a corresponding encoded feature vector (14). For example, an X-ray image (12a) is encoded to generate an encoded feature vector (14a), and an X-ray image (12b) is encoded to generate an encoded feature vector (14b). In some embodiments, the encoded feature vector (14) is processed by a decoder (55) to generate a noise-reduced X-ray image (16).

[0038] In some embodiments, the discriminator (66) is configured to receive an encoded feature vector pair (14) or a noise-reduced image pair (16) and attempts to classify whether the pairs originated from the same base X-ray image (e.g., image (12c)) or from different images (e.g., image (12a) and image (12b)).

[0039] In some embodiments, the learning process includes simultaneously optimizing an autoencoder (33) (including an encoder (44) and a decoder (55)) and a discriminator (66) having conflicting goals. The autoencoder (33) is trained to deceive the discriminator (66) by generating an output that prevents the discriminator (66) from distinguishing whether the output is from the same X-ray image or from different X-ray images. The purpose of this training is to ensure that noise-reduced images (e.g., image (16a) and image (16b)) generated from different shots within a repeatability set are indistinguishable from each other, that is, to make them appear substantially similar or identical. At the same time, the discriminator (66) is trained to improve this ability to distinguish. Due to these adversarial learning dynamics, the autoencoder (33) is induced to generate consistent noise-reduced images across different noise inputs obtained at the same measurement point, and as a result, learns a method to effectively reduce noise while preserving the actual underlying signal.

[0040] In some embodiments, the autoencoder (33) is trained using a weighted combination of multiple loss functions to balance different learning objectives. In this embodiment, the reconstruction loss function prevents the autoencoder (33) from generating random or irrelevant outputs by ensuring that the noise-reduced X-ray image (16a) is very similar to the corresponding input X-ray image (12a) and that the noise-reduced X-ray image (16b) is very similar to the corresponding input X-ray image (12b). The reconstruction loss is configured to restrict the noise reduction process so that the output inherits the essential features of the original noise X-ray image (12). Without these constraints, the autoencoder (33) could generate the same output for empty images or all inputs, which could formally easily deceive the discriminator (66) but could not achieve the required noise reduction objective.

[0041] In some embodiments, the Kullback-Ibler (KL) divergence loss function is configured to normalize the encoded latent distribution associated with the encoded feature vectors (14a, 14b) to approximate a standard normal prior distribution. This normalization promotes a latent space that is smooth, continuous, and consistently organized across different inputs, thereby improving the generalization performance of the autoencoder (33), reducing the possibility of overfitting of the noise remover, and enabling more stable learning dynamics and more reliable performance even under previously unobserved noise conditions and sample variations. Additionally, the KL divergence loss function is configured to limit parameters of the latent representation, such as the mean and variance used for sampling, thereby affecting the effective level of stochastic variation introduced during the latent variable sampling process. This serves as a technical component of the variational autoencoder architecture, contributing to preventing the latent encoding from becoming overly deterministic and preventing the network from repeatedly generating the same output for the same input when sampling is enabled.

[0042] In some embodiments, the generator loss function is configured to evaluate how effectively the encoder (44) and decoder (55) deceive the discriminator (66). The generator loss function induces that the noise-reduced X-ray images (16) generated by the autoencoder (33) are indistinguishable from one another regardless of their origin. Here, the origin may be an X-ray image containing the same noise (e.g., X-ray image (12c)) or different noise-reduced X-ray images acquired at the same measurement point (e.g., X-ray image (12a) and X-ray image (12b)). That is, the generator loss function induces the encoder (44) and decoder (55) to produce a consistent and source-invariant output so that the discriminator (66) cannot determine whether a pair of noise-reduced images (16) originated from the same original X-ray image or from different X-ray images at the same measurement point. In this context, the generator loss function quantitatively measures how successfully the encoder (44) deceives the discriminator (66).

[0043] In some embodiments, the discriminator loss function is configured to measure the ability of the discriminator (66) to accurately classify whether input pairs originate from the same X-ray image (e.g., X-ray image (12c)) or from different X-ray images (e.g., X-ray image (12a) and X-ray image (12b)). The discriminator loss function induces the discriminator (66) to perform this distinction more precisely, and accordingly, the autoencoder (33) is trained to generate more consistent and high-quality noise-reduced output to deceive the discriminator (66). That is, the discriminator loss function serves to continuously improve the discriminant performance of the discriminator (66), and this improvement in discriminant performance acts as learning pressure on the generator-side autoencoder (33), thereby inducing learning in a direction where noise-reduced X-ray images generated from different noise inputs are matched to reflect the same actual signal.

[0044] In some embodiments, the between-shot loss function is configured to compare noise-reduced images, e.g., noise-reduced X-ray image (16a) and noise-reduced X-ray image (16b), generated from different shots of the same measurement point, and to penalize any discrepancy between them. In some embodiments, the between-shot loss function includes the mean squared difference between the noise-reduced images. This between-shot loss function is configured to enforce consistency across the noise-reduced images (16) generated from the iteration set, thereby preventing the autoencoder (33) from generating random output or creating arbitrary details, and ensuring that the noise-reduced images (16) reflect the actual underlying signal rather than noise fluctuations. The smaller the difference between the noise-reduced images generated from different shots, the more successful the learning is evaluated. In some embodiments, learning is stopped when the between-shot loss function reaches saturation and no longer improves. This means that it is no longer possible to further reduce the difference between the noise-reduced images generated from different shots within the iteration set. This saturation point is used as a termination criterion for the learning process.

[0045] In another embodiment, a generative adversarial autoencoder (GAAE) (77) may be trained using a weighted combination comprising (a) a shot-to-shot loss configured to measure the difference between two noise-reduced X-ray images generated from a pair of a single source image (12) or different images (12), and (b) one or more loss functions selected from the loss functions previously exemplified. The loss functions include (i) a reconstruction loss configured to maintain similarity between the noise-reduced X-ray image and the corresponding X-ray image, (ii) a Kullback-Leibler (KL) divergence loss configured to adjust the level of the encoded latent distribution to approximate a standard normal distribution, (iii) a generator loss configured to measure how successfully the encoder deceives the discriminator, and (iv) a discriminator loss configured to measure the discriminator's ability to distinguish whether the pair originated from two copies of the same X-ray image or from two different X-ray images.

[0046] In some embodiments, the weighted combination of loss functions is configured so that the autoencoder (33) is forced to take different images as input and reduce the noise in them to make them substantially the same, rather than taking the same image as input and adding noise to make them look different. This is achieved through a balance between a reconstruction loss function configured to prevent the output from deviating excessively from the input and a shot-to-shot loss function that induces the output generated from different inputs to be as similar as possible. The specific weights assigned to each loss function can be adjusted according to the characteristics of the X-ray imaging system, the type of noise present in the acquired X-ray image (12), and the requirements of the application, such as image quality or measurement precision.

[0047] In some embodiments, after the learning phase is completed, the discriminator (66) is discarded, and only the autoencoder (33), consisting of the encoder (44) and the decoder (55), is retained for operational use (e.g., production environment). This is an important distinction between the learning phase and the operational phase. During the operational phase, the interface (21) is configured to receive a single noise X-ray image (e.g., X-ray image (12a)) acquired by the X-ray analysis system without the need for paired images from the repeatability set.

[0048] In some embodiments, the processor (22) is configured to apply a learned autoencoder (33) to process a single-noise X-ray image (12a) and to generate a high-quality X-ray image (e.g., a noise-reduced X-ray image (16a)) with reduced Poisson noise and hardware-induced noise.

[0049] In some embodiments, adversarial learning performed during the learning phase enables the autoencoder (33) to effectively generalize to new and previously unobserved data acquired at various locations on the semiconductor substrate. That is, the learning may be performed using a noisy X-ray image (12) acquired at a first location on the wafer, and in the operation phase, the learned autoencoder (33) is configured to process a single-noise X-ray image acquired at a second location different from the first location.

[0050] In some embodiments, this generalization capability ensures consistent noise reduction performance across different samples, locations, and measurement conditions, thereby maintaining image fidelity and preserving important structural details necessary for accurate X-ray critical dimension analysis or other types of X-ray analysis based on the noise-reduced X-ray image (16). Also, in some embodiments, the learned autoencoder (33) is configured to process new images in real time (e.g., within a delay of about 100 milliseconds), enabling high-throughput operations without the delay associated with conventional noise reduction methods that require an increase in the number of samples or an extension of the image acquisition time.

[0051] In some embodiments, the processor (22) is configured to perform X-ray analysis based on the noise-reduced X-ray image (16). For example, the processor (22) can measure critical dimensions of a predefined pattern present in a metal layer, dielectric layer, or semiconductor layer formed inside or on top of a semiconductor substrate. The image quality improved through the noise reduction process enables more precise measurements of internal structures of IC devices, such as high aspect ratio nanostructures, which is essential for quality control in the semiconductor manufacturing process. Additionally, in some embodiments, the display (23) is configured to display the noise-reduced X-ray image (16) and the analysis results so that a user of the X-ray analysis system can review them.

[0052] In some embodiments, the autoencoder (33) is configured to effectively reduce both Poisson noise and hardware-induced noise from the X-ray image (12). Poisson noise is caused by the statistical characteristics of the photon counting process in the X-ray detector and appears as random fluctuations in pixel intensity following a Poisson distribution. The level of Poisson noise is related to the number of detected photons, and if conventional techniques are applied, more photons must be collected to reduce Poisson noise, which increases image acquisition time and consequently reduces the throughput of the X-ray analysis system. Additionally, hardware-induced noise may include electronic interference from system components, detector defects such as non-uniform pixel responses or non-functional pixels (dead pixels), instability of the beam blocker, and mechanical vibrations that cause blurring or distortion of the image.

[0053] In some embodiments, by acquiring multiple X-ray images at the same measurement point and learning using a repeatable dataset that captures both types of noise variability, the autoencoder (33) learns to distinguish between noise components and true underlying diffraction signals. This adversarial learning process is combined with shot-to-shot loss to ensure that the autoencoder (33) produces a consistent output across various noise sources, effectively suppressing statistical and systematic noise sources while preserving microstructural details essential for precise critical dimension analysis.

[0054] In some embodiments, the disclosed technology offers several advantages over conventional noise reduction methods. The Generative Adversarial Autoencoder (GAAE) (77) is configured to effectively reduce both Poisson noise and hardware-induced noise, surpassing conventional technologies that typically handle only a single type of noise. Additionally, the architecture is configured to preserve the microstructural details of the X-ray image, which are essential for precise critical dimension analysis of high aspect ratio nanostructures, thereby overcoming the limitations of conventional noise reduction algorithms that can blur or distort important features. The technology of the present disclosure eliminates the need to increase measurement time for noise reduction, thereby enabling a reduction in the acquisition time of the X-ray image without compromising precision. For example, in some embodiments, the acquisition time of the noisy X-ray image (12) can be reduced by up to about 50% while maintaining measurement precision, and, for example, the maximum 3σ error can be maintained at about 0.4% to less than 0.5%. This throughput improvement is achieved because the learned autoencoder (33) can effectively reduce noise even on a single image acquired with a relatively short acquisition time, instead of requiring multiple images or long exposures to achieve an acceptable noise level like conventional averaging techniques.

[0055] In some embodiments, the system (11) may be implemented in various configurations. In a first configuration, the autoencoder (33) is directly integrated into an X-ray threshold dimension (XCD) tool or other type of measurement system as part of a real-time X-ray measurement processing pipeline. When the X-ray detector acquires an X-ray image (12), the processor (22) is configured to automatically input the noisy image (12) into a trained autoencoder (33), which is trained to reduce the noise in the X-ray image (12) while preserving important structural details. This integrated configuration improves the throughput and productivity of the X-ray imaging and analysis system by enabling X-ray imaging and analysis to be performed fully automated without operator intervention and by allowing the XCD tool to provide measurements of sufficiently high precision without increasing exposure time.

[0056] In some embodiments, in the second configuration, the autoencoder (33) is deployed as a standalone post-processing tool separate from the X-ray measurement hardware. In this configuration, the interface (21) may include a network interface or file input mechanism configured to receive previously acquired noisy X-ray images (12) from any X-ray analysis tool (e.g., X-ray threshold dimension (XCD) analysis tool). In this embodiment, the processor (22) is configured to (i) apply the learned autoencoder (33) to reduce the noise in the received X-ray images (12) and (ii) output a high-quality, noise-reduced X-ray image (16) for subsequent analysis. Such a standalone configuration is particularly suitable for facilities that already possess X-ray measurement equipment but wish to improve the measurement accuracy and throughput of the X-ray system without hardware upgrades. Additionally, the standalone tool can be applied to previously acquired data to improve the accuracy of previous measurements and enable new analyses that were difficult to perform with the originally acquired noisy X-ray images (12).

[0057] In some embodiments, the primary application of the system (11) is to improve X-ray critical dimension analysis in semiconductor manufacturing processes as previously described. However, the technology disclosed herein may be applied to other X-ray analysis and imaging methods. For example, the system (11) may be configured to reduce noise in images acquired using X-ray reflectivity (XRR), X-ray fluorescence (XRF), X-ray diffraction imaging (XRDI), X-ray diffraction of single-crystal and polycrystalline materials, and other X-ray imaging and measurement technologies where noise reduction is beneficial for improving measurement precision and accuracy. Additionally, the technology disclosed herein may be applied to noise reduction of other types of signals receiving a repeatability set consisting of a plurality of signals acquired at predefined locations and / or conditions. The signals may include, but are not limited to, image, acoustic, ultrasonic signals, etc. For example, the technology disclosed in this specification may also be applied in other applications, such as in the field of materials science or medical imaging, when observing structures formed inside and / or on a substrate using imaging methods such as electron microscopes, ion microscopes, and optical microscopes.

[0058] In other embodiments, alternative neural network architectures may be used instead of or in addition to the Generative Adversarial Autoencoder (GAAE) configuration described above. For example, a Conditional Generative Adversarial Network (cGAN) can be used to guide the generation process by integrating class labels or other metadata. Additionally, a Residual Network (ResNet) can be integrated to reduce information loss through skip connections and more effectively capture fine features. Furthermore, by applying attention mechanisms such as self-attention, high-importance regions within the image can be highlighted, thereby improving the quality of noise reduction, particularly in specific areas prone to noise. Through these improvements, a more flexible and robust neural network capable of effectively handling various noise characteristics that may be present in the measurement data can be implemented.

[0059] In some embodiments, alternative loss functions may be used to further enhance noise reduction performance. For example, by incorporating a perceptual loss based on features extracted from a pre-trained neural network, the preservation of visual quality and essential structural details may be prioritized. Additionally, various aspects of image quality may be simultaneously optimized by applying a multi-objective optimization strategy that combines the mean squared error (MSE) and the structural similarity index (SSIM). Furthermore, by using cycle consistency or contrastive learning techniques, the noise-reduced image may be made to accurately preserve the underlying physical characteristics of the original data.

[0060] The specific configuration and structure of the learning method of the system (11) illustrated in FIG. 1 are presented as examples to explain the specific problems that the embodiments of the present invention aim to solve and to explain how these embodiments can be applied to improve the noise reduction performance of an image noise reduction system and an X-ray analysis system. However, the embodiments of the present invention are not limited to these specific example systems, and the principles disclosed herein may be similarly applied to various analysis systems based on other imaging methods as well as to X-ray-based systems.

[0061] FIG. 2 is a flowchart schematically illustrating a method for reducing noise in an X-ray image (12) according to an embodiment of the present invention.

[0062] The present method comprises integrating a variational autoencoder (VAE), referred to herein as an autoencoder (33), and the generative adversarial network (GAN) described above into an integrated framework referred to as a generative adversarial autoencoder (GAAE) (77), said integrated framework being configured to effectively reduce Poisson noise and hardware-induced noise while preserving important structural details and maintaining high throughput.

[0063] The present method begins with an image reception step (100), in which a processor (22) receives a plurality of noise-containing X-ray images (12) acquired at a predefined location on the semiconductor substrate of the aforementioned wafer via an interface (21). The plurality of X-ray images (12) acquired at the same measurement point are referred to herein as a repeatability set. The repeatability set may include images acquired from a plurality of shots performed consecutively at the same location by an X-ray imaging and analysis system, each shot capturing the same basic structural information but containing different noise realizations. Alternatively, the repeatability set may consist of images acquired by a redundant detector measuring the same point simultaneously. The X-ray images (12) included in the repeatability set may contain Poisson noise originating from the photon counting process, as well as hardware-derived noise including electron interference, detector defects, beam blocker instability, and mechanical vibration.

[0064] In the image selection step (102), the processor (22) may randomly select a plurality of image pairs from a plurality of X-ray images (12). Each image pair comprises (i) two copies of the same X-ray image (e.g., X-ray image (12c)) or (ii) two different X-ray images selected from a set of iterations (e.g., X-ray image (12a) and X-ray image (12b)). In some embodiments, the pairs are randomly selected from a set of iterations, so that the generative adversarial autoencoder (GAAE) (77) does not know in advance whether a given image pair consists of two copies of the same image or two different images. This random selection strategy provides the discriminator (66) with examples of both identical source image pairs and different source image pairs, which forms the core of the adversarial learning process. Through such pair selection, the generative adversarial autoencoder (GAAE) (77) can learn the difference between noise variation and the actual base signal by comparing how images acquired at the same measurement point appear differently due to noise.

[0065] In the first noise reduction step (104), the processor (22) applies an autoencoder (33) to reduce the noise contained in each pair of X-ray images (12). The autoencoder (33) includes an encoder (44) and a decoder (55). The encoder (44) is configured to compress each noisy X-ray image into a latent representation, such as an encoded feature vector (14a) and an encoded feature vector (14b), thereby capturing essential features while reducing dimensionality. The decoder (55) is configured to reconstruct a noise-reduced X-ray image (16) from the latent representation, for example, generating a noise-reduced X-ray image (16a) and a noise-reduced X-ray image (16b) from the encoded feature vector (14a) and the encoded feature vector (14b), respectively. During the first noise reduction step (104), the autoencoder (33) is trained to deceive the discriminator (66) of the Generative Adversarial Network (GAN), and the discriminator (66) is configured to determine whether a pair of noise-reduced X-ray images (16a, 16b) is based on (i) a noise-reduced version generated from two copies of the same X-ray image (12c) or (ii) a noise-reduced version generated from two different X-ray images (12a, 12b). The discriminator (66) receives as input a pair of latent representations generated by the encoder (44), e.g., an encoded feature vector (14a) and an encoded feature vector (14b), or a pair of noise-reduced X-ray images (16a, 16b) generated by the decoder (55). In some embodiments, the discriminator (66) attempts to determine whether the input pair originated from the same base X-ray image (12c) or from different X-ray images (12a, 12b) within a repeatability set.

[0066] In the autoencoder learning step (106), the processor (22) trains the autoencoder (33) to deceive the discriminator (66). The learning process includes adversarial learning that simultaneously improves and optimizes the autoencoder (33) and the discriminator (66) having conflicting goals. Specifically, the autoencoder (33) is trained to produce an output that prevents the discriminator (66) from distinguishing whether the output originated from the same X-ray image (12c) or from different X-ray images (12a, 12b) acquired at the same measurement point. At the same time, the discriminator (66) is trained to more accurately determine whether the output originated from the same source or from different sources. Due to these adversarial learning dynamics, the autoencoder (33) is induced to produce a consistent noise-reduced image across different noise inputs acquired at the same measurement point, thereby learning a method to effectively reduce noise while preserving the actual basis signal.

[0067] In some embodiments, during the autoencoder learning step (106), the autoencoder (33) is trained using a weighted combination of multiple loss functions to balance different learning objectives, as described in detail in FIG. 1. Additionally, in some embodiments, training is stopped when the intershot loss reaches a saturation state and no longer decreases significantly. This indicates that the difference between noise-reduced images generated from different shots within the iterative set has reached a state where it can no longer be further reduced, and this saturation point is used as a training termination condition.

[0068] When the autoencoder (33) is successfully trained to deceive the discriminator (66), the method proceeds to a second noise reduction step (108) that terminates the method. In the second noise reduction step (108), the discriminator (66) is discarded, and the processor (22) applies the trained autoencoder (33) to reduce the noise of at least one additional X-ray image acquired at a selected location on the semiconductor substrate during production mode. In the second noise reduction step (108), only a single noisy X-ray image is required as input, and accordingly, paired images from the iterative set are no longer needed. The trained autoencoder (33) processes the single noisy X-ray image to generate a high-quality noise-reduced X-ray image with reduced Poisson noise and hardware noise levels. Adversarial learning performed during the autoencoder learning phase (106) enables the autoencoder (33) to effectively generalize to new (unknown) X-ray images acquired at various locations on the wafer, thereby ensuring consistent noise reduction performance across different samples, locations on the wafer, and measurement conditions.

[0069] In some embodiments, the discriminator (66) may be used as an anomaly or tool drift detector. In this scenario, after the X-ray system captures a plurality of X-ray images (12), the processor (22) is configured to automatically perform the image reception step (100), the image selection step (102), and the first noise reduction step (104), but is configured to stop before the autoencoder learning step (106). Instead, the processor (22) is configured to calculate the discriminator loss and compare the calculated discriminator loss with a predefined threshold. If the discriminator loss exceeds the threshold, this indicates the presence of data anomalies or tool drift, and accordingly, automatic adjustment or retraining of the Generative Adversarial Autoencoder (GAAE) (77) may be triggered.

[0070] In some embodiments, based on the noise-reduced X-ray image generated in the second noise reduction step (108), the processor (22) is configured to perform X-ray analysis, such as measuring the critical dimensions of a predefined pattern existing in a metal layer, dielectric layer, or semiconductor layer formed inside or on the semiconductor substrate. The image quality enhanced by the noise reduction process enables more precise measurements of high aspect ratio nanostructures, which is essential for quality control in the semiconductor manufacturing process.

[0071] In some embodiments, the method illustrated in FIG. 2 offers several advantages over conventional noise reduction methods. The Generative Adversarial Autoencoder (GAAE) (77) is configured to effectively reduce not only Poisson noise inherent in the photon counting process but also hardware-induced noise such as electronic interference, detector defects, beam blocker instability, and mechanical vibration, thereby outperforming conventional methods that typically handle only a single type of noise. Furthermore, the method overcomes the limitations of conventional noise reduction algorithms that can blur or distort important features of X-ray images by preserving the microstructural details of X-ray images that are essential for precise critical dimension analysis of high aspect ratio nanostructures. Moreover, the method eliminates the need to increase measurement time for noise reduction, enabling shorter data acquisition times without compromising measurement precision as described in detail in FIG. 1.

[0072] In some embodiments, the method illustrated in FIG. 2 may be implemented in two configurations. In the first configuration, the method is performed by a processor directly integrated into an X-ray critical dimension (XCD) tool or other critical dimension measurement system as part of a real-time X-ray measurement processing pipeline. When the X-ray system acquires measurement data, the processor automatically performs an image reception step (100), an image selection step (102), a first noise reduction step (104), an autoencoder learning step (106), and a second noise reduction step (108) to reduce noise in the X-ray image while preserving important structural details. This process is performed in a fully automated manner and does not require operator intervention. In the second configuration, the method is performed by a standalone post-processing tool. In this case, an operator or applied scientist may input a previously acquired noisy X-ray image from any XCD analysis tool into the standalone software, and the standalone software performs the steps of the method to reduce noise in the X-ray image and outputs a high-quality refined image for subsequent analysis. This standalone configuration is particularly suitable for facilities that already possess X-ray measurement equipment but wish to improve measurement accuracy and throughput without hardware upgrades.

[0073] In some embodiments, the primary application of the method illustrated in FIG. 2 is to improve X-ray critical dimension (XCD) analysis, but the method can also be applied to other X-ray analysis and imaging methods. For example, the method can be applied to X-ray reflectance (XRR), X-ray fluorescence (XRF), X-ray diffraction imaging (XRDI), X-ray diffraction of single-crystal and polycrystalline materials, as well as other X-ray imaging and measurement techniques where noise reduction is required.

[0074] While the embodiments described herein primarily address noise reduction in X-ray images, the methods and systems disclosed herein may also be applied to imaging methods other than X-rays. For example, the methods and systems may be used to reduce noise generated during image acquisition in various imaging methods, such as electron microscopes, ion microscopes, and optical imaging devices used in semiconductor processes, as well as in other materials science applications. Furthermore, the technology disclosed herein may also be applied to applications that receive a repeatable set consisting of multiple signals acquired using predefined locations and / or predefined signal acquisition conditions within an appropriate time interval (e.g., from microseconds to minutes), such as medical imaging and defense applications.

[0075] Accordingly, it should be understood that the embodiments described above are merely illustrative and that the present invention is not limited to what is specifically illustrated and described above. Rather, the scope of the present invention includes not only combinations and partial combinations of the various features described above, but also variations and modifications that are obvious to those skilled in the art and are not disclosed in the prior art. Furthermore, the documents incorporated by reference in this patent application should be considered as an integral part of the components of this application. However, if a term defined in a document incorporated by reference conflicts with a term defined explicitly or implicitly in this specification, only the definition in this specification shall apply.

Claims

Claim 1 A method for reducing noise in X-ray images, comprising: receiving a plurality of X-ray images acquired at a predefined location on a semiconductor substrate; selecting from the plurality of X-ray images a plurality of pairs, each comprising (i) two copies of the same X-ray image or (ii) two different X-ray images; applying a generator to reduce noise in each pair of X-ray images, wherein the generator is trained to deceive a discriminator of a Generative Adversarial Network (GAN) in determining whether each pair comprises (i) two copies of the same X-ray image or (ii) two different X-ray images; and, when the generator is successfully trained to deceive the discriminator, applying a trained generator to reduce noise in at least one additional X-ray image acquired at a selected location on the semiconductor substrate. Claim 2 A method for reducing noise in X-ray images according to claim 1, wherein the generator and the discriminator together form a Generative Adversarial Autoencoder (GAAE) that combines a Variational Autoencoder (VAE) architecture and a GAN. Claim 3 A method for reducing noise in an X-ray image according to claim 2, wherein the generator comprises an encoder and a decoder, the encoder is configured to compress each X-ray image into a latent representation, and the decoder is configured to reconstruct a noise-reduced X-ray image from the latent representation. Claim 4 A method for reducing noise in an X-ray image according to claim 3, wherein the discriminator is configured to receive a latent representation pair generated by the encoder, and the encoder is trained such that the discriminator cannot distinguish whether the latent representation pair is derived from two copies of the same X-ray image or from two different X-ray images. Claim 5 A method for noise reduction of an X-ray image according to claim 3, wherein the discriminator is configured to receive a pair of noise-reduced X-ray images generated by the decoder, and the decoder is trained such that the discriminator cannot distinguish whether the pair of noise-reduced X-ray images is derived from two copies of the same X-ray image or from two different X-ray images. Claim 6 A method for noise reduction of an X-ray image according to claim 3, wherein the GAAE is trained using (a) a shot-to-shot loss configured to measure the difference between noise-reduced X-ray images generated from two different pairs of X-ray images and (b) a weighted combination of one or more loss functions selected from a list of loss functions, wherein the list of loss functions includes: (i) a reconstruction loss configured to ensure that the noise-reduced X-ray image remains similar to the corresponding X-ray image; (ii) a Kullback-Leibler (KL) divergence loss configured to regularize the latent representation to approximate a standard normal distribution; (iii) a generator loss configured to measure how successfully the encoder deceives the discriminator; and (iv) a discriminator loss configured to measure the ability of the discriminator to distinguish whether the pair originated from two copies of the same X-ray image or from two different X-ray images. Claim 7 A method for reducing noise in an X-ray image according to claim 6, characterized in that the learning of the GAAE is stopped when at least the inter-shot loss reaches a saturation state and is no longer improved. Claim 8 A noise reduction method for an X-ray image according to claim 2, characterized in that the GAAE is learned to reduce all hardware-induced noise, including at least one of Poisson noise and electronic interference, detector defects, or mechanical vibrations occurring during the photon counting process. Claim 9 A method for reducing noise in an X-ray image according to claim 2, characterized in that when the generator is successfully trained to deceive the discriminator, the discriminator is discarded and only the generator is applied to reduce noise in the at least one additional X-ray image. Claim 10 A method for reducing noise in an X-ray image, characterized in that, in any one of claims 1 to 9, the plurality of X-ray images comprises a repeatable set of images obtained through a series of shots at a predetermined location on the semiconductor substrate. Claim 11 A method for reducing noise in X-ray images, characterized in that, in any one of claims 1 to 9, it further comprises the steps of: calculating a discrimination loss for at least one pair; comparing the discrimination loss with a predefined threshold value; and generating an indication of an abnormal sign in the plurality of X-ray images in response to the discrimination loss exceeding the predefined threshold value. Claim 12 A noise reduction system for X-ray images comprises: an interface configured to receive a plurality of X-ray images acquired at a predefined location on a semiconductor substrate; and a processor, wherein the processor comprises: From the plurality of X-ray images above, (i) two copies of the same X-ray image or (ii) a plurality of pairs including two different X-ray images are selected; A generator is applied to reduce noise in each pair of X-ray images, wherein the generator is trained to deceive a discriminator of a Generative Adversarial Network (GAN) in determining whether each pair consists of (i) two copies of the same X-ray image or (ii) two different X-ray images; and A noise reduction system for X-ray images, characterized in that when the generator is successfully trained to deceive the discriminator, the trained generator is configured to apply to at least one additional X-ray image acquired at a selected location on the semiconductor substrate to reduce noise. Claim 13 A noise reduction system for X-ray images according to claim 12, characterized in that the generator and the discriminator together form a Generative Adversarial Autoencoder (GAAE) that combines a Variational Autoencoder (VAE) architecture and the GAN. Claim 14 A noise reduction system for X-ray images according to claim 13, wherein the generator comprises an encoder and a decoder, the encoder is configured to compress each X-ray image into a latent representation, and the decoder is configured to reconstruct a noise-reduced X-ray image from the latent representation. Claim 15 A noise reduction system for X-ray images according to claim 14, wherein the discriminator is configured to receive latent representation pairs generated by the encoder, and the encoder is trained such that the discriminator cannot distinguish whether the latent representation pairs originated from two copies of the same X-ray image or from two different X-ray images. Claim 16 A noise reduction system for X-ray images according to claim 14, wherein the discriminator is configured to receive a pair of noise-reduced X-ray images generated by the decoder, and the decoder is trained such that the discriminator cannot distinguish whether the pair of noise-reduced X-ray images is derived from two copies of the same X-ray image or from two different X-ray images. Claim 17 A noise reduction system for X-ray images according to claim 14, wherein the GAAE is trained using (a) a shot-to-shot loss configured to measure the difference between noise-reduced X-ray images generated from two pairs of different X-ray images and (b) a weighted combination of one or more loss functions selected from a list of loss functions, wherein the list of loss functions includes: (i) a reconstruction loss configured to ensure that the noise-reduced X-ray image remains similar to the corresponding X-ray image; (ii) a Kullback-Leibler (KL) divergence loss configured to regularize the latent representation to approximate a standard normal distribution; (iii) a generator loss configured to measure how successfully the encoder deceives the discriminator; and (iv) a discriminator loss configured to measure the discriminator's ability to distinguish whether the pair originated from two copies of the same X-ray image or from two different X-ray images. Claim 18 A noise reduction system for X-ray images according to claim 17, characterized in that the learning of the GAAE is stopped when at least the inter-shot loss reaches a saturation state and is no longer improved. Claim 19 A noise reduction system for X-ray images according to claim 13, wherein the GAAE is trained to reduce all hardware-induced noise, including at least one of Poisson noise and electronic interference, detector defects, or mechanical vibrations occurring during the photon counting process. Claim 20 A noise reduction system for X-ray images according to claim 13, characterized in that when the generator is successfully trained to deceive the discriminator, the discriminator is discarded and only the generator is applied to reduce noise in the at least one additional X-ray image. Claim 21 A noise reduction system for X-ray images according to any one of claims 12 to 20, wherein the plurality of X-ray images comprises a repeatable set of images obtained through a series of shots at the predetermined positions on the semiconductor substrate. Claim 22 A noise reduction system for X-ray images according to any one of claims 12 to 20, wherein the processor is further configured to calculate a discrimination loss for at least one pair, compare the discrimination loss with a predefined threshold, and generate an indication of an abnormal sign in a plurality of X-ray images when the discrimination loss exceeds the predefined threshold.

Images