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Abstract: When an object is illuminated by a source, the resulting exit wave is a complex function intricately connected to the object's structure. Generally speaking, the wave's modulus corresponds to the object's transmittance, while its phase represents the cumulative phase shift relative to free space, caused by the object's refractive index as the wave traverses it. Therefore, to fully characterise the object, both the modulus and phase of the exit wave are required. However, detectors only measure the intensities (the modulus squared) of the waves striking the detector. The modulus can thus be easily obtained by taking the square root of the measured intensity. The phase, on the other hand, is much more challenging to determine. Any potential phase configuration could theoretically produce the same measured intensity, leading to what is known as the 'Phase Retrieval Problem', whereby the true phases that were lost during the experiment are not easily recovered. Ptychography offers a possible solution to the phase retrieval problem. Multiple diffraction intensity patterns are obtained by scanning a finite probe over an extended specimen with sufficient overlap between adjacent illumination positions. Combined with suitable iterative reconstruction algorithms, these measured diffraction patterns can be effectively utilised to accurately determine both the amplitude and phase of the object's exit wave, providing a robust approach that significantly enhances the ability to retrieve complete structural information about a specimen. Ptychography can be combined with X-ray absorption spectroscopy by using an X-ray beam of tuneable energies at each scan position. The diffraction patterns are now collected when the X-rays are scanned over absorption edges of specific elements, providing chemical information, in addition to high resolution reconstructions. This method has been dubbed 'Spectro-Ptychography'. Our work aims to push the limits of ptychography by employing it to analyse various butterfly scales. These scales are intricate self-assemblies of proteins that form complex structures. Beyond exhibiting pigment colour—where specific compounds absorb particular wavelengths of light—butterfly scales are also remarkable examples of structural colour, where their unique structures manipulate light in specific ways. We will showcase the application of spectro-ptychography on butterfly scales and demonstrate how we extracted detailed 3D spatial and chemical information from the dataset, aiding in our understanding of both 'pigment colour' and 'structural colour'. Preliminary results reveal distinct chemical variations in the carbon and oxygen signatures across different regions of a butterfly scale. By segmenting the scale into defined classes, we gain deeper insights into the chemical compositions of each specific segment, enhancing our understanding of its complex structure.

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Abstract: ances in high-resolution electron microscopy have enabled remarkable insights into both biological and materials science, particularly in the detailed structural imaging of small particles and complex materials interfaces. Yet, as resolution increases, the effective depth of field (DOF) of Transmission Electron Microscopy (TEM) narrows, creating new challenges for accurately imaging thick samples. Traditional phase retrieval approaches rely on contrast transfer functions (CTF) and projection approximations (PA) that linearize image formation physics. While effective at near-atomic resolutions, these methods lose critical phase information, limiting resolution in cases that require a full 3D reconstruction of complex structures. The maximum achievable contrast in Transmission Electron Microscopy (TEM) for small particles, including biomolecules, is theoretically set by the scattering cross sections of these particles. Our previous work has shown that, under ideal conditions, computational phase retrieval can reach this theoretical limit by precisely modeling electron-matter interactions1. However, the real-world limitations of TEM—such as noise, sample damage, and heterogeneity in imaging conditions—create a gap between theoretical predictions and actual experimental outcomes, especially for challenging samples like small or flexible biomolecules. This theory-experiment gap has historically hindered the ability to fully exploit TEM for resolving fine structural details in complex materials. First-principles simulations struggle to account for the empirical effects present in real data, including variations in ice thickness, specific particle damage, and environmental noise. To address this gap, we integrate these theoretical models into Physics-Informed Neural Networks (PINNs), which incorporate the physical laws governing electron scattering directly into the machine learning framework.

Open Access

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Abstract: Imaging of nanoscale magnetic textures within extended material systems is of critical importance to both fundamental research and technological applications. While high-resolution magnetic imaging of thin nanoscale samples is well established with electron and soft x-ray microscopy, the extension to micrometer-thick systems currently requires hard x rays, which limits high-resolution imaging to rare-earth magnets. Here, we overcome this limitation by establishing soft x-ray magnetic imaging of micrometer-thick systems using the pre-edge phase x-ray magnetic circular dichroism signal, thus making possible the study of a wide range of magnetic materials. By performing dichroic spectroptychography, we demonstrate high spatial resolution imaging of magnetic samples up to 1.7  μ⁢m thick, an order of magnitude higher than conventionally possible with soft x-ray absorption-based techniques. We demonstrate the applicability of the technique by harnessing the pre-edge phase to image thick chiral helimagnets, and naturally occurring magnetite particles, gaining insight into their three-dimensional magnetic configuration. This new regime of magnetic imaging makes possible the study of extended non-rare-earth systems that have until now been inaccessible, including magnetic textures for future spintronic applications, non-rare-earth permanent magnets for energy harvesting, and the magnetic configuration of giant magnetofossils.

Open Access

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Abstract: Ewald sphere curvature correction, which extends beyond the projection approximation, stretches the shallow depth of field in cryo-EM reconstructions of thick particles. Here we show that even for previously assumed thin particles, reconstruction artifacts which we refer to as ghosts can appear. By retrieving the lost phases of the electron exitwaves and accounting for the first Born approximation scattering within the particle, we show that these ghosts can be effectively eliminated. Our simulations demonstrate how such ghostbusting can improve reconstructions as compared to existing state-of-the-art software. Like ptychographic cryo-EM, our Ghostbuster algorithm uses phase retrieval to improve reconstructions, but unlike the former, we do not need to modify the existing data acquisition pipelines.

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Abstract: The complexity of self-assembled photonic structures like butterfly wing scales spans 3–4 orders of magnitude in length scales. These monolithic structures produced by single cells on a butterfly wing typically measure a few hundred micrometres across, with intricate features going well below the nanometre scale. While this complexity makes the self-assembly of these structures fascinating, imaging and capturing this gamut of complexity is extremely challenging. The available imaging methods can either capture the overall field of view at a lower resolution (scanning electron microscopy (SEM)) or can capture high-resolution details of the structure at a specific region (resin section transmission electron microscopy) [1]. Further, three-dimensional (3D) characterization techniques either can only image the topology of a single surface (atomic force microscopy) [1] or are limited to fewer synchrotron facilities (ptychographic x-ray tomography (PXCT)) [2], rendering them impractical to promptly test a large number of scales for gene expression studies.