Nanoscale Imaging & ML Spectroscopy

• NISMA is an integrated framework combining advanced nano-imaging and spectroscopy with machine learning for precise, automated phase mapping at nanoscales.
• The methodology employs advanced techniques like PCA, autoencoders, and Gaussian mixture models to reduce data complexity and extract quantitative physical parameters.
• It enhances reproducibility and speed by automating feature extraction, enabling high-throughput, robust analysis of structural, electronic, and chemical phenomena in materials.

Nanoscale Imaging and Spectroscopy with Machine-learning Assistance (NISMA) refers to an integrated paradigm in materials characterization where advanced nano-imaging and spectroscopic platforms are combined with machine learning algorithms for robust, high-throughput quantification and mapping of structural, electronic, magnetic, or chemical phenomena at nanometer length scales. The methodology is characterized by the synergistic interplay between high-resolution physical measurement modalities—such as scanning probe microscopies, optical near-field or X-ray spectroscopies, and electron microscopy—and statistical or data-driven models that extract, classify, and quantify local features from dense multidimensional datasets. The resulting framework enables not only imaging with spatial resolution beyond classical limits but also quantification and segmentation of structural phases, chemical states, or functional responses with improved accuracy, speed, and robustness.

1. Integration of Machine Learning in Nano-imaging Workflows

NISMA approaches are defined by the explicit use of machine learning models (PCA, GMM, deep CNNs, Bayesian inference, NMF, autoencoders, and hybrid/physics-informed architectures) to analyze hyperspectral or multidimensional data acquired from advanced nano-imaging or spectroscopy experiments.

For example, in phase mapping of strained SrSnO₃ films using nano-infrared spectroscopy, principal component analysis (PCA) is used first to reduce the dimensionality of hyperspectral s-SNOM data. The first three principal components capture the dominant spectral variance across spatial pixels. Subsequently, a Gaussian Mixture Model (GMM) operating in the reduced principal component space assigns each pixel to one of four statistically defined clusters. These clusters correspond to physical phases—specifically, edge and bulk regions of tetragonal and orthorhombic domains—identified through their distinct vibrational and electronic (phonon and plasma) spectral responses (Bragg et al., 23 Jul 2025).

This unsupervised machine learning segmentation is robust against noise, results in highly reproducible quantitative phase maps, and obviates the need for subjective manual feature extraction. Similar unsupervised and supervised learning protocols—including CNN-based extraction of atomic identities from STM topographs (Lafleur et al., 17 Oct 2024), and NMF-based “blind source separation” for chemical unmixing in STEM-EDX data (Jany et al., 2017, Chen et al., 23 May 2024)—serve as central pillars across the NISMA landscape.

2. Nanoscale Imaging and Spectroscopy Modalities

NISMA builds upon nano-imaging platforms that break conventional spatial and/or spectral limits. Representative techniques include:

• Scattering-type scanning near-field optical microscopy (s-SNOM): s-SNOM and nano-FTIR allow vibrational and free-electron plasma responses to be recorded at sub-diffraction resolution (~10–50 nm) (Bragg et al., 23 Jul 2025). Local optical spectra are acquired pixel-wise, providing hyperspectral data cubes for further ML analysis.
• Energy-dispersive X-ray spectroscopy (EDX-SEM/TEM): STEM-EDX generates elemental maps at nanometer scales. Machine-learning deconvolution separates the contributions of nanostructures, substrates, and background from overlapping signals, enabling accurate quantification (Jany et al., 2017, Chen et al., 23 May 2024).
• STM/AFM and local spectroscopy: High-resolution topography and site-resolved electronic spectra are inputted to ML classifiers for automated identification of atomic or molecular species (Lafleur et al., 17 Oct 2024).
• Coherent X-ray imaging and near-field optical techniques: Hyperspectral imaging across vibrational (IR, far-IR) or X-ray absorption edges provides compositional discrimination at nanoscales, with phase and amplitude information accessible in the imaging (Johnson et al., 2020).

Data from these methods are often multi-dimensional (spatial × spectral), necessitating dimensionality reduction, clustering, and regression for physical property mapping.

3. Machine Learning Pipelines for Phase Identification and Quantification

A defining operational feature of NISMA is the use of unsupervised pipelines to analyze large, complex datasets. The canonical steps are:

1. Dimensionality Reduction: PCA or autoencoders compress high-dimensional spectra to a tractable latent space, preserving the salient variance for classification (Bragg et al., 23 Jul 2025, A et al., 2022).
2. Clustering: Gaussian mixture models (GMM), k-means, or hierarchical clustering in the low-dimensional space statistically assign each data point (pixel or spectrum) to a phase (Bragg et al., 23 Jul 2025, Meneses et al., 2022).
3. Cluster-specific Quantification: For each phase, average spectra are computed and fitted to microscopic models (e.g., Drude–Lorentz) to extract physical parameters: phonon energy, plasma frequency, carrier effective mass, etc.
4. Automated or guided model fitting and regression: Parameters such as screened plasma frequency (ω_p,sc) are associated with the Drude oscillator and directly inferred via ML-driven nonlinear fitting. These yield further physical quantities (carrier density, effective mass, electron-phonon coupling strength).
5. Output: High-fidelity phase maps, quantitative physical parameter images, and statistical uncertainty estimates.

The adoption of such workflows provides statistical control, reproducibility, and resistance to subjective user bias.

4. Quantitative Mapping and Physical Parameter Extraction

NISMA approaches leverage measured hyperspectral responses to generate spatially resolved maps of key material properties. In the context of phase coexistence in strained SrSnO₃, local reflectance and absorption spectra from four identified phases are averaged and then fit to the Drude–Lorentz dielectric function model:

$$\epsilon(\omega) = \epsilon_{\infty} - \frac{\omega_p^2}{\omega (\omega + i\gamma_p)} + \frac{A_{TO}^2}{\omega_{TO}^2 - \omega^2 - i\gamma_{TO}\omega}$$

where $\omega_p$ is the plasma frequency (related to carrier density and effective mass), $\omega_{TO}$ is the transverse optical phonon frequency, and $A_{TO}$, $\gamma_p$, and $\gamma_{TO}$ are model parameters. The observed spread in $\omega_{p,\text{sc}}$ between edge and bulk regions is directly translated into spatial maps of carrier effective mass and mobility.

In (Bragg et al., 23 Jul 2025), the paper finds that the orthorhombic edge phase exhibits a screened plasma frequency $\omega_{p,\text{sc}} \approx 4090~\text{cm}^{-1}$ (effective mass ∼29% higher) compared to tetragonal edge ($\omega_{p,\text{sc}} \approx 4650~\text{cm}^{-1}$), highlighting how nanoscale phase coexistence modulates optoelectronic properties in a spatially inhomogeneous manner.

Analogous quantitative extractions—such as atomic percent composition in STEM-EDX via ZAF correction after NMF unmixing (Chen et al., 23 May 2024), or direct identification of atomic species in STM via DNN classifiers (Lafleur et al., 17 Oct 2024)—are foundational across NISMA-enabled platforms.

5. Applications Across Complex Material Systems

The ability of NISMA to combine spatially resolved imaging or spectroscopy with data-driven phase and property mapping has broad applicability across scientific domains:

• Complex oxides and correlated materials: Enables direct mapping and quantification of coexisting structural/electronic phases or domain boundaries that impact transport, ferroic, or catalytic properties (Bragg et al., 23 Jul 2025).
• Catalysis and nanocomposites: Supports chemical quantification and spatial identification of active phases in supported nanoparticle systems, trace dopant mapping, and interface analysis (Chen et al., 23 May 2024).
• Functional semiconductors and quantum materials: Facilitates phase diagram mapping, optoelectronic property localization, and heterostructure characterization at scales relevant for device engineering.
• Nanofabrication and quantum information: Automates the identification and classification of atomic sites/species relevant for atomic assembly or device fabrication (Lafleur et al., 17 Oct 2024).

Broader use in biology, earth science, and nanoelectronics is plausible wherever complex nanoscale structure/function relationships are critical.

6. Advantages, Limitations, and Future Directions

NISMA delivers key advantages:

• Unbiased segmentation: Automated, statistical phase mapping replaces subjective manual segmentation, facilitating reproducibility.
• High-fidelity quantification: Robustness against noise and experimental variability, with statistical confidence from large data ensembles.
• Scalability: Amenable to large datasets generated by modern fast-acquisition nano-imaging modalities.
• Physical interpretability: Integration of first-principles models and physical constraints (e.g., Drude–Lorentz, ZAF corrections, sum rules) alongside data-driven inference (Bragg et al., 23 Jul 2025, Chen et al., 23 May 2024).

Limitations include:

• Dependence on data quality: Artifacts or systematic errors in hyperspectral data can propagate through the machine learning pipeline.
• Model transferability: Physical models and clustering criteria may require adaptation across different material systems or measurement modalities.
• Interpretability of machine learning assignments: Unsupervised clusters must be linked to physically meaningful phases by additional analysis or validation.

Emerging directions include integration with real-time data acquisition, multi-modal or multi-dimensional data fusion, autonomous experimental platforms (reinforcement learning–driven probe placement), uncertainty quantification in ML-driven property inference, and application to nontrivial topological, quantum, or biological nano-systems.

7. Representative Data Analysis Workflow in NISMA (Example Table)

Step	Method	Output
Hyperspectral imaging	s-SNOM, nano-FTIR, EDX	Multidimensional data cube
Dimensionality reduction	PCA, autoencoder	Principal component map
Clustering/segmentation	GMM, k-means, CNN	Phase/region assignments per pixel
Spectral quantification	Model fitting (e.g., Drude–Lorentz; ZAF)	Local physical parameters
Spatial mapping	Cluster/parameter image	Final phase/property maps

The above workflow—summarizing the approach described in (Bragg et al., 23 Jul 2025, Chen et al., 23 May 2024, Lafleur et al., 17 Oct 2024)—captures the core operational logic of NISMA: from high-dimensional measurement to quantitative, interpretable nano-maps with minimal human bias.

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NISMA enables robust, automated, and reproducible nano-imaging and spectroscopy workflows that combine advanced physical measurement with machine learning–based data segmentation and quantification. This integration supports detailed spatially resolved physical property mapping in complex and heterogeneous materials, greatly expanding the analytical power and scope of modern nanocharacterization platforms.