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A Digital Simulation Toolkit for Physics-Based Generation of Realistic Experimental Scanning Tunneling Microscopy Images

This paper presents a low-cost, physics-driven digital toolkit that generates large volumes of realistic, noisy Scanning Tunneling Microscopy (STM) images by simulating clean atomic structures and adding physically informed artifacts, thereby enabling the training of superior supervised denoising models that outperform unsupervised methods in preserving critical physical features like electron waves and defects.

Original authors: Huanhuan Zhao, Laxmi Bhurtel, Connor Vernachio, Fahmy Paiziah, Wonhee Ko, Arpan Biswas

Published 2026-09-30

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CC BY 4.0

Original authors: Huanhuan Zhao, Laxmi Bhurtel, Connor Vernachio, Fahmy Paiziah, Wonhee Ko, Arpan Biswas

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

To see the invisible world of atoms, scientists rely on a tool called a scanning tunneling microscope. This instrument acts like a incredibly sensitive finger, hovering just above a material's surface to map out its electronic landscape. Because the signal it uses drops off so sharply with distance, it can reveal individual atoms and the subtle waves of electrons that flow around them. However, this extreme sensitivity comes with a cost: the images are often corrupted by static and distortion. Vibrations from the building, tiny shifts in the equipment, or electronic interference can smear the picture, hiding the very details researchers need to understand how materials behave. For decades, cleaning up these images has been a struggle. Traditional methods often blur the fine lines, while newer computer programs that learn to remove noise usually fail because they lack the perfect examples needed to teach them what a clean image should look like.

A team of researchers has now solved this training problem by building a digital workshop that creates its own perfect examples. Instead of waiting for rare, pristine experimental data, they developed a physics-driven toolkit that simulates realistic images of copper and lead surfaces, then deliberately adds back the specific types of noise and distortion found in real experiments. By feeding these synthetic, paired images into advanced computer models, the team taught the software to strip away the interference without losing the delicate physical features underneath. The result is a system that not only cleans up noisy microscope photos better than previous methods but also allows scientists to uncover hidden quantum patterns, such as how electron waves shift when a magnetic field is applied.

The core challenge the researchers faced was a catch-22 in the world of artificial intelligence. To teach a computer to clean a dirty image, you usually need to show it a pair: the dirty version and the perfect, clean version. In the real world, however, a perfect, noise-free scanning tunneling microscope image does not exist. Every measurement is tainted by some form of disturbance, making it impossible to create the training data needed for the most powerful cleaning algorithms. While some scientists have tried to teach computers to guess the clean image without examples, these methods often struggle to balance removing noise with preserving the tiny, crucial details of the material's surface. The new toolkit bypasses this limitation by generating the perfect pairs from scratch.

The process begins with a computer simulation of a clean surface, specifically the atomic arrangement of copper and lead crystals. Once this ideal image is created, the toolkit acts like a digital sound engineer, layering on the specific types of static that plague real-world experiments. The researchers programmed the system to mimic five distinct sources of interference. First, they added random electronic static, similar to the hiss on a radio. Next, they simulated the slow, drifting movement of the microscope tip, which causes the image to skew or tilt. They also introduced flickering noise that varies in intensity, as well as sharp, repeating stripes caused by external vibrations. Finally, they added a curved background distortion that often appears in these measurements. By mixing these elements in varying amounts, the toolkit produces thousands of realistic, noisy images that look and behave exactly like the difficult photos taken in a laboratory.

With this vast library of synthetic data, the researchers trained two state-of-the-art computer models to become expert image cleaners. They tested these models on both the simulated images and real experimental photos of copper and lead surfaces. The results showed a clear advantage for the models trained on the synthetic data. When compared to older, unsupervised methods, the new models removed the noise more completely while keeping the atomic details sharp. In the simulated tests, the supervised models achieved significantly higher scores for image quality, successfully preserving the intricate wave patterns of electrons that other methods blurred or erased. When applied to real experimental images, the models removed the distracting scan lines and drift, revealing the underlying atomic structures and defects with remarkable clarity.

The true value of this work emerged when the researchers used the cleaned images to study a specific quantum phenomenon: how electron waves change under a magnetic field. By taking experimental photos of copper taken at different magnetic strengths and subtracting one from another, they could see how the electron patterns shifted. Without the new cleaning method, the subtraction was dominated by noise, making the patterns impossible to see. After the images were processed by the models trained on the digital toolkit, the subtraction revealed clear, consistent shifts in the electron waves. This demonstrated that the software was not just guessing or inventing details, but was actually recovering the true physical signals hidden beneath the interference.

This approach offers a general solution for a field that has long been held back by the scarcity of high-quality training data. By proving that a physics-based simulation can accurately represent the complex noise of real experiments, the toolkit opens the door for more advanced analysis of materials. It allows scientists to use powerful artificial intelligence tools to explore the atomic world with greater confidence, knowing that the images they are studying reflect the true nature of the material rather than the limitations of the machine. The work suggests that by building better digital mirrors of reality, researchers can accelerate the discovery of new materials and quantum behaviors that were previously too obscured to see.

Technical Summary: A Digital Simulation Toolkit for Physics-Based Generation of Realistic Experimental Scanning Tunneling Microscopy Images

Problem Statement
Scanning Tunneling Microscopy (STM) is a critical tool for atomic-scale surface characterization, yet its measurements are highly susceptible to noise and artifacts arising from mechanical vibrations, thermal drift, electronic interference, and feedback loop instability. While deep learning has shown promise in image denoising, its application to STM faces two primary bottlenecks: the scarcity of experimental data due to costly acquisition and, more critically, the impossibility of obtaining perfectly "clean" ground-truth images for supervised training. Existing unsupervised methods (e.g., N2V, N2V2) are computationally inexpensive but often fail to balance noise removal with the recovery of subtle physical features, sometimes introducing new artifacts or over-smoothing critical details like electron waves. Conversely, supervised methods (e.g., NAFNet, Restormer) offer superior performance but require large paired datasets of noisy and clean images, which are impractical to generate experimentally.

Methodology
To address the data availability challenge, the authors developed a low-cost, physics-driven digital toolkit capable of rapidly generating large volumes of realistic, paired clean-noisy STM images. The methodology proceeds in two main stages:

Clean Image Simulation: The toolkit simulates clean STM images based on specific material systems. The authors utilized established simulation tools (converted from MATLAB to Python) to generate images of Cu(111) surfaces with defects and triangular lattices. These simulations incorporate physical parameters such as lattice constants, scattering centers, and local density of states using the Kernel Polynomial Method (KPM).
Physics-Informed Noise Synthesis: Instead of adding generic noise, the toolkit superimposes five distinct noise and artifact functions derived from the physical characteristics of STM experiments:
- Gaussian Electronic Noise: Randomly sampled from a normal distribution.
- Row-by-Row Drift: Simulates mechanical drift where each scan line shifts relative to the previous one (up to three pixels).
- Paraboloid Background Artifacts: Adds slowly varying curved backgrounds (bowl, dome, or saddle shapes) common in scanning probe microscopy.
- 1/f Flicker Noise: Modeled as $1/f^\beta$ noise with $\beta$ randomly sampled between 1 and 3, generated via FFT-based time-domain synthesis.
- Periodic Stripe Lines: Simulates external interruptions (vibrations/resonances) as distinct, sharp bands along the scan direction.

These components are normalized, assigned random weights, and combined with the clean simulated images to create "AI-ready" paired datasets.

Key Contributions

A Generalizable Simulation Toolkit: The authors present a flexible framework that integrates multiple experimentally informed noise models, allowing for user-controlled intensity and density to mimic diverse experimental conditions.
Bridging the Supervised Learning Gap: By generating realistic paired data, the toolkit enables the training of state-of-the-art supervised denoising models (NAFNet and Restormer) for STM, a domain previously dominated by unsupervised approaches due to data constraints.
Validation on Downstream Tasks: The work demonstrates that models trained on this synthetic data can effectively denoise real experimental images and facilitate downstream scientific analysis, specifically the extraction of quantum interference patterns.

Results
The authors evaluated the efficacy of the toolkit by training supervised models (NAFNet, Restormer) on the generated data and benchmarking them against unsupervised methods (N2V, GDM) on both simulated and experimental STM images of Cu(111) and Pb(111).

Quantitative Performance: On simulated test sets, supervised models significantly outperformed unsupervised benchmarks, achieving higher PSNR (36.33 for Restormer vs. 22.81 for N2V) and SSIM (0.98 vs. 0.58) scores.
Qualitative Performance: Visual analysis of experimental images revealed that unsupervised methods either left residual noise (N2V) or over-smoothed physical features like electron wave patterns and defects (GDM). In contrast, supervised models trained on the synthetic toolkit successfully removed scan artifacts while faithfully preserving atomic defects and electron wave interference patterns.
Downstream Analysis: A case study on Cu(111) under varying magnetic fields (0T, 5T, 15T) demonstrated that denoising experimental images before subtraction (Strategy 2) yielded clearer electron wave pattern shifts compared to subtracting raw images first. This confirmed that the supervised models revealed true physical patterns rather than hallucinating artifacts.

Significance and Claims
The paper claims that the proposed digital toolkit adequately represents the complex noise characteristics present in real STM measurements, thereby facilitating the development of robust, data-driven STM analysis tools. The authors assert that supervised models trained on this synthetic data can more effectively denoise experimental images and learn subtle physical features (such as electron waves and defects) than benchmarked unsupervised approaches.

The significance of this work lies in its potential to overcome the global data availability challenge in microscopy. By providing a generalizable and extensible method for generating realistic, AI-ready data, the toolkit supports the development of advanced denoising and automation tasks across various material systems and imaging conditions, ultimately aiding in scientific discovery where experimental data is scarce or difficult to label. The authors note that while the current work focuses on noise removal and pattern revelation, future iterations will aim to better preserve the absolute physical scale of images during the denoising process.

Technical Summary: A Digital Simulation Toolkit for Physics-Based Generation of Realistic Experimental Scanning Tunneling Microscopy Images

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