Highly sensitive 2D X-ray absorption spectroscopy via physics informed machine learning

X-ray absorption spectroscopy (XAS), particularly XANES, is widely used to characterize element-specific valence states and local environments but conventional bulk XANES misses spatial heterogeneity. 2D XANES imaging via scanning fluorescence X-ray microscopy offers high sensitivity but is slow for large areas and dynamic studies. Full-field transmission X-ray microscopy (TXM) achieves high spatial resolution, high throughput, and large field of view, but suffers from relatively poor sensitivity due to low signal-to-noise ratio (SNR). Accurate background (white-field) normalization is critical; variations in the incident beam intensity/profile induce systematic errors that conventional denoising methods cannot remove, leading to unreliable chemical-state mapping, especially at low concentrations. This study aims to develop a physics-informed deep-learning method that reliably separates smooth beam background from sample signal in TXM-XANES stacks, improving SNR and enabling robust, quantitative oxidation-state mapping. The approach further targets adaptability to new datasets via self-supervised learning to handle transfer to different edges/materials and low-abundance species.

The paper contrasts scanning XRF-XANES (high sensitivity, nanoscale resolution, but slow) with full-field TXM-XANES (fast, large FOV, high resolution, but low SNR). Prior denoising approaches (e.g., non-local means, total variation regularization, BM3D) effectively mitigate random noise (e.g., Poisson) but cannot correct beam-profile-induced systematic normalization errors due to lack of beam physics priors. Recent deep neural networks excel in image tasks such as denoising, inpainting, and super-resolution (e.g., residual dense networks, RRDB/ESRGAN), motivating a learned approach augmented with domain knowledge. The authors leverage the known energy dependence of X-ray attenuation and simplified spectral models to regularize learning across the spectroscopic dimension, addressing limitations of purely image-based denoisers.

- Data acquisition context: TXM-XANES collects paired object and background (white-field) images at multiple incident energies to assemble 3D stacks (2D space × energy). Beam energy range example: 8.2–8.8 keV (Ni K-edge), 90 energy points; exposure 0.05 s per image. - Problem: Imperfect background normalization due to random variations in beam intensity/profile introduces spatially varying systematic errors that corrupt spectra, especially in low-absorption regions. - Model architecture: A Residual-in-Residual Dense Block (RRDB) network built from Residual Dense Blocks (RDBs) with local residual connections and dense feature concatenations. Input: noisy XANES image stack across energies. Output: predicted smooth background images (one per energy). The focus is on estimating and removing background rather than directly predicting foreground/sample structure to accommodate diverse morphologies with limited training data. - Training data generation (supervised stage): Synthetic–experimental fusion. Each training image is a superposition of (i) simulated sample absorption images (Lambert–Beer law; energy-dependent attenuation coefficients from Xraylib) providing known ‘ground-truth’ foreground; and (ii) experimentally measured beam intensity profiles collected at the FXI beamline over months, decomposed into a smooth background (ground-truth background via Gaussian filtering, 7×7 kernel) and high-frequency random (Poisson-like) noise. The goal is to predict the clean smooth background from noisy composites. - Physics-informed losses across image and spectral dimensions: 1) Image-wise background prediction losses per energy: L1 MSE and L2 VGG feature loss between predicted and clean (smoothed) background images. 2) Spectral-domain consistency via a simplified spectral model I(E) = A μ(E) + B E + C, where μ(E) is the known element’s linear attenuation coefficient (from Xraylib). After background removal, spectra are fitted at each pixel to obtain maps of parameters A (absorption ‘thickness’ proportional to material amount), B, C. Three additional losses enforce spectroscopic consistency: - L5: MSE between fitted thickness A from predicted images and thickness from ground-truth images. - L3: MSE between reconstructed low-frequency spectroscopic images (from fitted A, B, C via the model) and the predicted denoised images. - L4: VGG feature loss between the same pair to align perceptual/structural content. These losses promote faster convergence, training stability, and improved denoising, especially at low absorption. - Application to experimental data: The trained model is applied to two TXM-XANES measurements of the same Ni(OH)2+LiOH precursor area to assess consistency and to multiple elements (Ni, Co, Mn, Fe) for generality. - Self-supervised ‘production’ step for transfer to new datasets/edges (e.g., low Co content ~10% with weak edge response): Without ground truth backgrounds, the workflow uses a subset of pre-edge and post-edge images to fine-tune the model iteratively: 1) Feed raw images through the pretrained model to get preliminary denoised images. 2) Fit thickness A (and B, C) using the full stack and fix A. 3) Create training batches by randomly sampling pre-/post-edge images; define two losses: (i) total-variation regularization on predicted background-normalized images to enforce smoothness; (ii) MSE between the background-normalized images and reconstructed images from the spectral model with fixed A. Iterate to progressively improve SNR and background normalization without labeled data. - Implementation/code: Provided via PyXAS package with pretrained models. Data collected at NSLS-II FXI beamline.

- Background normalization improvement and spectral SNR: - On two independent measurements of the same Ni precursor area, the ML-corrected images exhibit spatially even backgrounds and significantly cleaner spectra. ROI with low Ni concentration (ROI #2) previously yielded inconsistent or unphysical valence (e.g., +2.77 vs. <+2); after ML correction, spectra fit well to Ni2+/Ni3+ references with consistent oxidation-state results across measurements. - Pixel-wise Ni3+ fraction maps from the two measurements become nearly identical after ML denoising. The ratio map of Ni3+ fractions (Measurement I / Measurement II) over particle regions follows a Gaussian with mean ≈ 1 and standard deviation σ = 0.006, implying <1.8% difference for 99.7% of pixels (3σ). - Generality and transfer: - The pretrained model, trained on simulated Ni, effectively denoises experimental XANES at other edges (Co, Mn, Fe) in most cases. - For low Co content (~10%) in LiNi0.85Co0.1Mn0.05O2, direct application showed limited improvement; the self-supervised production step (1–3 iterations) markedly increased spectral SNR and reduced fitting variance in Co3+ maps. - Chemical-state insights enabled by improved SNR: - Co valence in pristine LiNi0.85Co0.1Mn0.05O2 varies from ~+2.7 to +3, contrary to the common assumption of strictly +3. Ni valence is also spatially non-uniform. - K-means clustering revealed three clusters with average valences: cluster 1 (center): Co +2.93, Ni +2.96; cluster 2 (bottom): Co +2.84, Ni +2.89; cluster 3 (sides): Co +3.00, Ni +2.90. Regions with higher Co concentration tend to show lower Co valence (notably cluster 2), indicating a correlation between composition and valence. - Practical impact: - The approach can reduce TXM-XANES experiment time by up to half by enabling pre-acquisition of background images and eliminating repeated sample in/out motions, beneficial for dynamic experiments. It also reduces registration errors.

The study addresses the central challenge of systematic background normalization errors in full-field TXM-XANES that degrade SNR and bias chemical-state quantification. By explicitly modeling and predicting the smooth beam background with a RRDB network and enforcing spectral-domain constraints based on a physics-informed attenuation model, the method effectively separates background from sample signal. This yields robust and consistent oxidation-state maps even in low-absorption regions and across repeated measurements. The self-supervised production step further enhances transferability to new datasets, especially for weak-edge signals (e.g., low Co content), by leveraging invariant thickness A and pre-/post-edge subsets without requiring labeled backgrounds. The improved SNR enables detection of subtle, spatially heterogeneous valence distributions and correlations with composition, offering insights into synthesis–property relationships in layered oxides. Beyond accuracy, the approach can streamline data acquisition workflows, reducing time and alignment overhead by decoupling background collection from per-energy sample motions. The generality across elements arises because the simplified spectral model retains only the step-like edge dependence μ(E), which is similar in form across edges once energy is rescaled.

This work introduces a physics-informed deep-learning framework for TXM-XANES that predicts and removes smooth beam background, substantially improving spectral SNR and enabling accurate, consistent oxidation-state mapping at nanoscale resolution. The supervised training blends simulated foregrounds with experimentally measured backgrounds and is regularized by image- and spectrum-domain losses grounded in a simplified attenuation model. A self-supervised production step adapts the model to new datasets lacking labels, significantly enhancing transferability, especially for low-abundance elements. The method reveals spatial heterogeneity in Co and Ni valence states and their correlation with composition in LiNi0.85Co0.1Mn0.05O2, insights not accessible with conventional processing. Practically, it can halve experimental time and reduce registration errors by allowing pre-acquired backgrounds. Future work could extend the physics priors to multi-edge scenarios, incorporate uncertainty quantification for spectral fits, and apply the approach to other spectro-microscopies and dynamic in situ/operando measurements.

- Transferability: The pretrained model may underperform on datasets with weak edge steps (low concentration elements) or unseen background patterns/morphologies, requiring the self-supervised production step to adapt. - Spectral model assumptions: The simplified model I(E)=A μ(E)+B E + C assumes other edges are sufficiently far; additional step terms are needed otherwise. Deviations or complex post-edge fine structure (‘white line’, EXAFS wiggles) are not explicitly modeled in training losses. - Ground truth backgrounds: Clean backgrounds are approximated by Gaussian filtering of measured white-fields; residual biases could impact supervision. - Foreground diversity: The network is not trained to predict diverse foreground structures; it focuses on background estimation, which may limit performance if background–foreground interactions violate assumptions. - Low-signal regimes: For very low concentrations, residual normalization errors may still be comparable to signal variations even after correction. - Generalization across beamlines: Different source/optics configurations may require additional fine-tuning for optimal performance.