Accurately determining elemental distributions within functional materials at the nanoscale is crucial for understanding their properties and device performance. Multimodal imaging techniques, such as combining X-ray ptychography (providing high-resolution structural information) with XRF microscopy (providing elemental distribution), offer a powerful approach. However, XRF microscopy resolution is limited by the X-ray probe size, resulting in a convolution effect between the probe profile and the sample's elemental distribution. While deconvolution methods exist, they are often unsuitable for the specific convolution problem in XRF microscopy. Deep learning methods, especially deep residual networks, have shown promise in solving various computational imaging problems, including image super-resolution. This paper explores applying a deep residual network to enhance the resolution of XRF microscopy by learning a mapping function between low-resolution and high-resolution XRF images. This approach is advantageous as it avoids the need for complex numerical modeling and is data-driven.

The paper reviews existing multimodal imaging techniques, highlighting the limitations of XRF microscopy's resolution compared to ptychography. It discusses existing image deblurring techniques and their shortcomings in addressing the convolution problem inherent to XRF. The paper then examines the application of deep learning to computational imaging problems, particularly image super-resolution, focusing on the capabilities of deep residual networks. The authors note the novelty of applying ML methods to deconvolute the X-ray probe profile from XRF images.

The study employs a multimodal approach, simultaneously acquiring XRF and ptychography data using the Hard X-ray Nanoprobe Beamline (HXN) at NSLS-II. Two different hard X-ray nanoprobes (focused by a Fresnel Zone Plate (FZP) and Multilayer Laue Lenses (MLLs)) were used. The X-ray probe profile is obtained from ptychographic reconstruction. The core of the method is a residual dense network (RDN) model trained to map low-resolution XRF images (convolved with the probe profile) to high-resolution images. The RDN architecture consists of feature extraction, fusion, and upsampling modules. Residual dense blocks (RDBs) are used to extract hierarchical features, and an efficient sub-pixel convolutional neural network performs upsampling. The model uses a combined loss function (mean squared error and Pearson correlation coefficient) during training. Two datasets were used for training: one generated by convolving simulated high-resolution images (from the Caltech-256 dataset) with the experimentally obtained probe profiles, and another directly using experimental low-resolution XRF images from NMC samples, simulating the on-the-fly scanning process. The Adam optimizer was used for training, with a learning rate of 10⁻³ that decreases by half every 15 epochs. The upscaling factor was determined by the ratio of the pixel size of the XRF images and the probe profile. The trained model was then applied to experimental XRF datasets from NMC cathode material with a concentration gradient.

The RDN model successfully enhanced the spatial resolution of both simulated and experimental XRF images. The results from the two different focusing methods (FZP and MLLs) demonstrated the robustness of the model. For the NMC samples, the resolution was improved from 94.8 nm (FZP) and 57.4 nm (MLLs) to 22.0 nm (FZP) and 24.5 nm (MLLs), respectively. Qualitative analysis of the enhanced images revealed finer details in elemental distribution, which are highly consistent with the ptychography results. The quantitative analysis of the elemental percentages (Ni, Mn, and Co) in the NMC particles showed that the overall concentration profiles remained similar before and after the image enhancement process. This indicates the robustness of the proposed method in preserving elemental information during resolution enhancement. The improved resolution allows better visualization of micro-cracks, voids, and fractures within the NMC particles, offering valuable insights into the degradation mechanism of these materials. The ML model outperformed traditional bicubic interpolation in terms of peak signal-to-noise ratio (PSNR).

The successful enhancement of the spatial resolution in both simulated and experimental data validates the effectiveness of the proposed ML-based approach. The consistency between the enhanced XRF images and the ptychography images suggests the method effectively decouples the effect of the X-ray probe profile and the scanning scheme, mimicking a deconvolution process similar to ptychography. The ability to improve resolution using different X-ray focusing techniques (FZP and MLLs) highlights the method's general applicability. The preservation of elemental concentrations during the enhancement further emphasizes the model's robustness. The enhanced resolution of the XRF tomography reconstructions provides unprecedented insights into the microstructure and degradation mechanisms of NMC cathode materials, which is a significant advancement over previous techniques.

This research introduces a powerful ML-based method for enhancing the spatial resolution of XRF microscopy. By leveraging simultaneous ptychography data to determine the X-ray probe profile, and utilizing a trained RDN model to deconvolute the probe's effect from the XRF signal, significant resolution improvements are achieved. The method's broad applicability across various focusing techniques and material systems is demonstrated. Future research directions could include expanding the training dataset for improved model generalization, incorporating physical models (such as self-absorption effects) into the training process, exploring transfer learning techniques for faster adaptation to new probe profiles, and developing the RDN model to incorporate the probe profile directly as an input.

The performance of the RDN model is dependent on the accuracy of the X-ray beam profile obtained from ptychography. The model's performance might be limited by the limitations in the simulated training data, although it still performed well on experimental data. Retraining is required when the X-ray beam profile changes, although transfer learning can mitigate this. The effective overlap ratio between adjacent scanning spots affects the upper limit of resolution enhancement.