Category: 7. Science

Using the Wide Field Camera 3 (WFC3) instrument aboard the NASA/ESA Hubble Space Telescope, astronomers have captured a stunning new image of the spiral galaxy NGC 7456.

NGC 7456 was discovered by the British astronomer John Herschel on September 4, 1834.

This galaxy lies approximately 51 million light-years away from Earth in the constellation of Grus.

Otherwise known as ESO 346-26, IRAS 22594-3950 or LEDA 70304, it has a diameter of 117,100 light-years.

NGC 7456 is a member of the LDC 1547 galaxy group, a gathering of 16 large galaxies.

“In the Hubble image we see in fine detail the patchy spiral arms of this galaxy, followed by clumps of dark, obscuring dust,” the Webb astronomers said.

“Blossoms of glowing pink are rich reservoirs of gas where new stars are forming, illuminating the clouds around them and causing the gas to emit this tell-tale red light.”

“The Hubble program which collected these data is focused on stellar activity just like this, tracking new stars, clouds of hydrogen and star clusters to learn how the galaxy has evolved through time,” they added.

“Hubble, with its ability to capture visible, ultraviolet and some infrared light, is not the only observatory focused on NGC 7456.”

“ESA’s XMM-Newton satellite has imaged X-rays from the galaxy on multiple occasions, discovering a number of so-called ultraluminous X-ray sources.”

“These small, compact objects emit terrifically powerful X-rays, much more than would be expected for their size.”

“We are still trying to pin down what powers these extreme objects, and NGC 7456 contributes a few more examples.”

“On top of that, the region around the galaxy’s supermassive black hole is spectacularly bright and energetic, making NGC 7456 an active galaxy.”

“Whether looking at its core or its outskirts, at visible light or X-rays, this galaxy has something interesting to show.”

An international team of researchers have successfully derived a quantum version of Bayes’ rule, a cornerstone of probability theory

Their discovery was published on August 28, 2025, in Physical Review Letters and examines how beliefs are updated in the quantum world, where normal physics rules no longer apply

The research was conducted by Professor Valerio Scarani from the Centre for Quantum Technologies and the National University of Singapore, Assistant Professor Ge Bai from the Hong Kong University of Science and Technology, and Professor Francesco Buscemi from Nagoya University in Japan.

Understanding Bayes’ rule

Bayes’ rule was developed in the 18th century by mathematician Thomas Bayes and is a method used to update the probability of a hypothesis based on new evidence. It’s used across a range of fields from medical diagnosis and weather forecasting to data science and machine learning.

Put simply, Bayes’ rule enables individuals to update their expectations in response to new information becoming available. For example, if a person believes they might have the flu and then receives a positive test result, Bayes’ rule helps quantify how much more likely it is that they are actually sick.

This rule is grounded in the idea of conditional probability. It works by updating an individual’s prior belief to a new belief (called the posterior) that takes new information into account.

Bayes’ role in the quantum world

Although the classical Bayes’ rule is well understood, its application in the quantum realm has remained elusive. Quantum systems behave differently from classical ones; they are governed by probabilities and wavefunctions that describe the likelihood of finding a particle in a particular state.

Previously, researchers had proposed several quantum analogues of Bayes’ rule, but none had been derived from a fundamental principle of quantum mechanics. The team adopted a new approach by focusing on how beliefs should adapt in response to new quantum measurements, while maintaining as close a connection as possible to the principle of minimum change.

The principle of minimum change

The principle of minimum change states that when new information is received, beliefs should be adjusted as little as necessary to fit the latest facts. In classical Bayes’ rule, this is reflected mathematically by minimising the distance between the original and updated probability distributions.

To translate this into the quantum domain, the team employed a concept known as quantum fidelity, which measures the closeness of two quantum states to each other. Their goal was to maximise fidelity, or in other words, find the slightest change in belief that still accounts for the observed data.

This led them to derive a quantum Bayes’ rule by maximising fidelity between two mathematical objects representing the forward and reverse processes of measurement and belief update.

Connecting to the Petz map

The team found that in specific scenarios, their newly derived equations matched a well-known mathematical tool in quantum information theory, known as the Petz recovery map. This map, introduced in the 1980s, was considered a promising candidate for a quantum version of Bayes’ rule due to its valuable properties. Still, it had never been derived from first principles before.

Now, with this new research, researchers have not only validated the Petz map’s role in quantum reasoning but also opened the door to new applications, such as quantum error correction and quantum machine learning.

Quantum potential: What does this mean for the future?

The researchers are now exploring whether the principle of minimum change can lead to other quantum analogues by applying it to different mathematical measures. Their findings could further close the gap between classical and quantum reasoning, contributing to the foundation of future quantum technologies.

We performed constrained spherical deconvolution (CSD) and particle-filtering tractography (PFT) with anatomical priors^27,28 on DWI data of 39 healthy participants of the BIL&GIN database (Fig. 1A)²⁹. All tractograms were registered to MNI space³⁰, and the SLS was extracted for each individual leveraging the regions of interest (ROIs) of the JHU cortical atlas (Fig. 1B)³¹. Individual SLS were then concatenated. The N39 SLS was then parceled into sub-SLS using a cortex-to-cortex pairing approach, in which each frontal gyrus was systematically paired with every other gyrus of the same hemisphere as defined by the JHU template (Fig. 1C). sub-SLS from the right hemisphere were flipped and concatenated with their left hemisphere homologous (Fig. 1D). Out of the 119 possible ROI combinations, the cortex-to-cortex pairing approach led to the extraction of 96 non-empty sub-SLS tractograms. Of these, 45 contained more than 200 streamlines and were subsequently processed with QuickBundlesX clustering for the initial exclusion of implausible streamlines based on their geometrical features (Fig. 1D)³². These sub-SLS revealed a defined wiring of connections linking the 4 frontal gyri of the lateral convexity (i.e., IFG, MFG, superior frontal gyrus (SFG), and PrCG) to several regions covering the lateral surface of the parietal (i.e., angular gyrus (AG), postcentral gyrus (PoCG), superior parietal gyrus (SPG) and supramarginal gyrus (SMG)), temporal (i.e., ITG, MTG, STG and temporal pole (T-pole)) and occipital cortices (i.e., inferior (IOG) and middle occipital gyri (MOG)), and a restricted section of the basal temporal cortex (i.e., fusiform gyrus (FuG)) (Fig. 2). Connections involving the FuG, IOG, and T-pole were null when paired with the SFG. On the medial surface, connectivity was confined to the precuneus (PrCu). Conversely, 74 ROI combinations, consisting of 33 empty tractograms (Fig. 2, black circles) and 41 with less than 200 streamlines in both hemispheres (Fig. 2, gray circles), were deemed non-viable. They included the entire connectivity of the fronto-orbital region (lateral fronto-orbital gyrus (LFOG), middle fronto-orbital gyrus (MFOG), and rectus gyrus (RG)) as well as connections to the cuneus (Cu), lingual gyrus (LG), parahippocampal gyrus (PHG), entorhinal cortex (ENT), and superior occipital gyrus (SOG). Additionally, as noted earlier, connections between the SFG and the IOG, FuG, and T-pole were null.

It shows the 45 viable gyral combinations identified with the cortex-to-cortex pairing approach, along with combinations that resulted in empty tractograms (black circles) or tractograms containing less than 200 streamlines each (gray circles). Viable sub-SLS were classified as anatomically plausible and validated (green), anatomically plausible but not validated (yellow), and anatomically implausible (red) based on their correspondence with ex-vivo dissection data and adherence to anatomical principles of fibers distribution. AG angular gyrus, Cu cuneus, ENT entorhinal cortex, FuG fusiform gyrus, IFG inferior frontal gyrus, IOG inferior occipital gyrus, ITG inferior temporal gyrus, LFOG lateral fronto-orbital gyrus, LG lingual gyrus, MFG middle frontal gyrus, MFOG medial fronto-orbital gyrus, MOG middle occipital gyrus, MTG middle temporal gyrus, PHG parahippocampal gyrus, PoCG postcentral gyrus, PrCG precentral gyrus, PrCu precuneus, SFG superior frontal gyrus, SMG supramarginal gyrus, SOG superior occipital gyrus, SPG superior parietal gyrus, STG superior temporal gyrus, RG rectus gyrus, T-pole temporal pole.

Sub-SLS tractography templates description

This section is dedicated to the anatomical description of the 45 sub-SLS tractography templates obtained with the cortex-to-cortex pairing approach and after the removal of streamlines classified as implausible based on their geometrical features, as represented in Fig. 2. For this description, templates are grouped based on the frontal gyrus from which they originate.

Inferior frontal gyrus

Connections between the IFG and the inferior parietal lobule (IPL), namely AG and SMG, primarily originate from pars opercularis (pOp) and pars triangularis (pTri), with only a few streamlines reaching the dorsal and posterior pars orbitalis (pOrb). These connections course longitudinally within the deep WM of the central region of the hemisphere, running parallel the Sylvian fissure before resurfacing laterally to reach their parietal target. Connections to the AG mostly terminate in its anterior part, while those to the SMG are more evenly distributed. The IFG-PoCG template follows a similar but shorter course, parallelling the Sylvian fissure. For this connection, terminations in the IFG are more densely distributed in pOp and become sparser in pTri, with no streamline reaching pOrb. Posterior terminations cover only the most ventral part of the PoCG. The two templates representing connections to the dorso-medial parietal cortex, namely IFG-SPG and IFG-PrCu, follow a similar anatomical course to the connections described above up to the level of the PoCG, where they shift dorsally to reach their respective targets. These connections arise primarily from pOp, with only a few streamlines reaching pTri, particularly for the IFG-PrCu template, and reach anterior SPG and anterior PrCu. Connections between the IFG and the temporal lobe follow the same longitudinal course as the IFG-parietal connections up to the deep WM at the level of the AG. At this point, streamlines arch around the posterior ramus of the Sylvian fissure, then proceed ventrally with a transverse orientation. After entering the deep WM of the temporal lobe, they proceed towards their target temporal gyrus and start fanning to resurface laterally. While their fanning enlarges both anteriorly and posteriorly for connections to the ITG, MTG, STG, and FuG, connections to the T-pole follow a postero-anterior direction as they traverse the deep WM of the dorsal temporal lobe, parallelling the Sylvian fissure ventrally. Connections reaching the STG and the MTG arise uniformly from both pOp and pTri, with fewer streamlines originating from pOrb, while connections with the FuG, ITG, and T-pole almost exclusively originate from pOp. Posteriorly, connections to the FuG cover only the mid-segment of the ROI. While connections to the ITG, MTG, and STG distribute equally along the posterior ⅔ of the whole gyri, connections to the T-pole correspond to the anterior continuation of these connections. For what concerns connections with the occipital cortex, the IFG-MOG template follows a course similar to IFG-parietal connections, while the IFG-IOG template is more akin to IFG-temporal connections. Indeed, the IFG-MOG template has an overall longitudinal orientation, whereas IFG-IOG fibers arch around the Sylvian fissure, spanning the boundary between the temporal and occipital cortices before fanning out posteriorly to reach the anterior portion of IOG.

Middle frontal gyrus

Connections between the MFG and the IPL originate from the posterior ⅔ of the MFG ROI. After leaving the gyrus, streamlines travel posteriorly within the deep WM of the central region, maintaining a longitudinal orientation along the z-axis (streamlines course at the same height from the posterior end of the MFG to the AG and SMG). Streamlines resurface laterally at the level of the gyrus they terminate into. Posterior terminations are homogeneously distributed across both the AG and SMG ROIs. Templates of connections from the MFG to the PoCG, SPG, and PrCu exhibit a more compact course compared to connections to the IPL, and course slightly dorsal to them. Streamlines connecting to the SPG display more anterior terminations in MFG, covering the posterior ⅔ of the ROI similarly to the IPL connections. In contrast, streamlines to the PoCG and PrCu tend to terminate more posteriorly in the MFG, within the posterior third of the region. Streamlines of the MFG-PoCG template resurface laterally after passing the level of the central sulcus, with posterior terminations covering only the middle third and the inferior part of the dorsal third of the PoCG ROI. Connections from the MFG to the SPG and PrCu shift slightly vertically after passing the level of the postcentral sulcus, reaching the anterior part of the SPG and the entire PrCu ROI. Connections between the MFG and the ITG, MTG, and STG are more widespread, covering the posterior ⅔ of the MFG ROI. In contrast, connections to the FuG and the T-pole tend to arise more posteriorly in MFG, with the MFG-T-pole template covering only the very posterior aspect of the frontal ROI. After coursing longitudinally in the deep WM of the frontal and parietal lobes, MFG-temporal streamlines arch around the Sylvian fissure at the level of the IPL and enter the temporal cortex along a transverse course. Connections to the FuG terminate in the mid-segment of the FuG ROI, while connections to the ITG, MTG, and STG span the posterior ⅔ of the lateral temporal gyri. Connections to the T-pole traverse the deep WM of the superior temporal lobe and extend anteriorly. For what concerns connections with the occipital cortex, the MFG-MOG template resembles in its course MFG-parietal connections, while MFG-IOG conforms with MFG-temporal connections, arching around the Sylvian fissure and coursing ventrally with a transverse orientation before fanning posteriorly to reach the anterior end of the IOG ROI. The MFG-MOG template terminates in the anterior MOG.

Superior frontal gyrus

Connections between the SFG and the parietal lobe originate solely from the posterior third of the SFG. Templates reaching the PoCG, SPG, PrCu, and AG follow a longitudinal course through the deep WM of the dorsal central region. Contrarily, connections reaching the SMG leave the SFG ventrally, follow a main transverse orientation up to the level of the deep WM below the ventral PrCG and abruptly turn longitudinally before traveling posteriorly to the anterior SMG. Terminations in the PoCG cover only the most dorsal portion of the ROI, while connections to the SPG and PrCu cover the entire gyri. The AG is mainly covered in its antero-dorsal part. Connectivity between the SFG and the occipital cortex is represented by the sole SFG-MOG template. It resembles the SFG-AG template in its course, but extends further posteriorly to the anterior MOG. SFG-temporal connections involve only the posterior halves of the ITG, MTG, and STG. These streamlines leave the posterior half of the SFG ventrally and traverse the frontal lobe with a transverse orientation, up to the level of the dorsal IFG. Here, they abruptly switch course to a longitudinal orientation, reaching the deep WM of the IPL before arching into the temporal lobe. Streamlines fan laterally, both posteriorly and anteriorly, at the level of their respective temporal gyrus.

Precentral gyrus

The PrCG-PoCG template represents the only pattern of connectivity between adjacent gyri of the SLS. It consists of U-shaped fibers that span the entire extent of both gyri. Connections between the PrCG and the IPL arise from the ventral half of the PrCG ROI. After coursing briefly through the deep WM of the central region, streamlines resurface laterally, terminating homogeneously along the entire cortical surface of both the AG and SMG. The fanning of these streamlines is larger anteriorly to accommodate for the involvement of the PrCG ROI, which develops primarily along the z-axis. Connections between the PrCG and the SPG or the PrCu originate more dorsally in the PrCG than those to the IPL. Streamlines connecting to the SPG originate from the dorsal half of the PrCG, while those reaching the PrCu originate from the most dorsal third of this region. Streamlines of the PrCG-SPG template group in the deep WM below the PoCG and then turn slightly vertically to reach the anterior half of the SPG, while PrCG-PrCu connections remain dorsal and cover the anterior ⅔ of PrCu. Connections between the PrCG and the temporal lobe arise from the ventral half of the PrCG. Streamlines connecting to the ITG and the MTG are uniformly distributed along this portion of the PrCG ROI, those to the T-pole and the FuG arise more dorsally compared to the others, and those to STG seed only in the most ventral end of the region. Streamlines of the PrCG-temporal templates travel longitudinally up to the deep WM below the IPL, arch around the Sylvian fissure, and follow a transverse course until they reach the deep WM of their target gyrus. Connections to the FuG terminate in the mid-segment of the ROI, while those to the ITG, MTG, and STG cover the posterior ⅔ of the respective gyri. Connections to the T-pole extend more anteriorly, paralleling the Sylvian fissure ventrally, and cover the anterior third of the temporal lobe. As previously described for IFG and MFG, the PrCG-MOG template follows a similar course to PrCG-parietal connections, while streamlines of the PrCG-IOG template arch into the temporal lobe, crossing the boundary between temporal and occipital cortices, and fan posteriorly.

Sub-SLS ex-vivo dissection

Layer-by-layer Klingler microdissection of 6 left and 4 right hemispheres resulted in the identification of 24 dissection layers (henceforth referred to as epochs – abbreviated as “epo” when referring to a specific dissection layer) representing connections of the SLS. In some specimens, (abbreviated as “spc” when referring to a specific specimen) both fronto-parietal and fronto-temporal connectivity were exposed while proceeding with a latero-medial dissection approach (e.g., Fig. 3, spc-01, spc-06, spc-07, spc-10, spc-12, spc-15, and spc-19). Occasionally, fronto-parietal connectivity could be exposed on two subsequent epochs of the same specimen: a lateral one revealing more superficial and shorter fibers, and a medial one revealing deeper and longer ones (e.g., Fig. 3, spc-02 and spc-07). 3D digital models of each epoch were reconstructed with photogrammetry and aligned to the radiological space of each specimen^25,33. A detailed anatomical analysis of the trajectory of the dorsal fibers leaving the frontal cortex and connecting to any other cortex of the same hemisphere was carried out on these models. Each sub-SLS connection visible on the texture of the models was manually annotated with the CloudCompare “Segment Tool” following a cortex-to-cortex pairing approach, compatible with the one adopted for the parcellation of tractography data. The identified sub-SLS annotated on the different epochs are listed and represented in Fig. 3.

The annotation of the sub-SLS across 24 epochs according to the cortex-to-cortex pairing approach revealed the anatomical features of 22 sub-SLS previously identified with tractography. SPC specimen, EPO epoch. AG angular gyrus, FuG fusiform gyrus, IFG inferior frontal gyrus, IOG inferior occipital gyrus, ITG inferior temporal gyrus, MFG middle frontal gyrus, MTG middle temporal gyrus, PoCG postcentral gyrus, PrCG precentral gyrus, SFG superior frontal gyrus, SMG supramarginal gyrus, SPG superior parietal gyrus, STG superior temporal gyrus.

Cortex-to-cortex annotation of the SLS connections on the specimens resulted in the identification of 22 sub-SLS, all of which were also previously reconstructed with tractography and represented by sub-SLS templates. These annotations depict connections between the IFG with the IPL (i.e., AG and SMG) as well as with the ITG and MTG. Connections linking the MFG and the PrCG to the lateral aspect of the parietal (i.e., AG, SMG, PoCG, and SPG) and temporal cortices (i.e., STG, MTG, and ITG) were also traced, alongside those to the IOG. The SFG-AG connection was the only sub-SLS identified from the SFG. Fibers reaching the FuG were visible just in one specimen, where they connected to the PrCG.

While the manual annotation of sub-SLS connections on the dissection models confirmed the existence of these connectivity patterns, the concurrent analysis of all the sub-SLS annotations across epochs revealed several organizational principles of the WM fibers of the SLS. Shorter fibers were found to course more superficially, while longer fibers ran more deeply. Specifically, fronto-parietal connections, being shorter by nature, were found on more superficial epochs compared to fronto-temporal fibers, which required the removal of overlaying tissue (e.g., spc-01 and spc-02 epo-06 vs. epo-07 in Fig. 3). While this observation aligns with the classical description of the SLF/AF complex³⁴, we also noted that this organizational principle holds within individual connections defined by specific termination territories. For instance, MFG-AG connection in spc-02 was identified on two consecutive epochs (see Fig. 3, spc-02, epo-05 and epo-06 in orange). On epo-05, MFG-AG appears as a short connection involving only posterior MFG, while on epo-06, deeper fibers extend to reach anterior MFG. This latero-medial organizational pattern contributes to a layered architecture of WM fibers of the SLS, which also respects a ventro-dorsal organization. Ventral regions connect to other ventral regions through fibers coursing ventrally, while dorsal regions are connected to other dorsal regions through fibers coursing dorsally. This is particularly evident in fronto-parietal epochs. For instance, in epo-06 of spc-01 connections between the IFG and the AG course more ventrally compared to those between the MFG and the AG. Conversely, connections between the PrCG and the AG remain dorsal if originating from dorsal PrCG and ventral if arising from ventral PrCG. As seen in epo-07 of spc-02, this organizational layout also applies to fronto-temporal connections. In the case of PrCG-ITG fibers, those arising from the dorsal part of the PrCG after the splitting of the gyrus remain more external as they arch into the temporal lobe (i.e., farther from the posterior end of the Sylvian fissure) compared to fibers originating from the ventral part of the PrCG, which run closer to the Sylvian fissure. Thus, the ventro-dorsal organization in fronto-temporal connections translates into a mirrored pattern relative to the Sylvian fissure. Specifically, connections more ventral in the frontal cortex tend to connect to more dorsal regions in the temporal cortex, following the shape of the Sylvian fissure closely. Interestingly, as fronto-temporal fibers of the SLS arise more dorsally in the frontal cortex and thus course farther from the Sylvian fissure, the shift from a longitudinal course in the frontal and parietal cortices to a transverse course in the temporal cortex becomes less steep. Eventually, this results in an inversion in the fanning of temporal fibers – from more anteriorly directed for internal connections to more posteriorly directed for external connections. This trend culminates in fibers bending posteriorly to reach the occipital cortex, as shown in epo-05 of spc-16.

Sub-SLS templates anatomical evaluation with BraDiPho

All the 45 sub-SLS tractography templates were non-linearly registered to the radiological space of the 10 3D models of ex-vivo dissection for anatomical evaluation (Fig. 1E). Of these, 22 sub-SLS templates obtained with tractography were matched with their corresponding anatomical annotations from ex-vivo dissection, as described in the previous section. Quantitative overlap scores between tractography reconstructions and the corresponding manual annotations on the photogrammetric models of ex-vivo dissection are reported in Supplementary Data 1 and visualized in Supplementary Fig. 1. Across all matched sub-SLS templates, the average overlap between modalities was 88.15% ± 11.60% (mean ± SD; min 67.8%; max 100%). It is important to note that a degree of spatial mismatch may be expected, as tractography is registered to the T1 of the specimens before starting the dissection and minor shifts in tissue conformation occur during the dissection process, particularly as tissues relax following removal of overlying structures.

Based on the representation of the sub-SLS in the ex-vivo dissection models, the tractography templates were further refined. Initially, the selection of plausible streamlines was made without reference to the anatomical features of the sub-SLS, relying instead on plausibility judgment based on the geometrical characteristics of the streamlines. Moreover, this process involved broad clusters encompassing a wide array of streamlines, sometimes intermingling both plausible and implausible ones, possibly leading to the rejection of some plausible streamlines along with implausible ones. While rejecting some plausible streamlines would typically not be problematic in most cases due to the redundancy of tractography, with the correction for density bias in creation of the templates it could result in the loss of relevant reconstructions. Therefore, once anatomical information was obtained through the one-to-one comparison of in-vivo tractography and ex-vivo dissection data, the selection of plausible streamlines was re-performed in Tractome. This allowed for a more selective, connection-specific filtering of implausible streamlines^35,36. The re-evaluation of the sub-SLS templates resulted in a more comprehensive and anatomically informed representation of WM connections, with improved coverage of their anatomical extent as suggested by the dissection data. These anatomically plausible and validated sub-SLS templates are shown in green in Fig. 1. A graphical summary of the anatomical evaluation process with BraDiPho is provided for each template in Supplementary Fig. 1.

The remaining 23 sub-SLS tractography templates were not found in our dissection data. These templates were classified as anatomically plausible but not validated or anatomically implausible based on the information gathered through dissection. The anatomically plausible but not validated templates (Fig. 2, yellow templates) represent connections that were reconstructed with tractography but could not be confirmed in our dissections, although their anatomical course remains consistent with anatomically plausible and validated connections. For instance, the existence of very medial connections, such as those from the MFG/PrCG/SFG to the PrCu, between SFG and dorsal PoCG, and between SFG and SPG, could not be proven, but they could not be excluded either. Indeed, these connections could not be exposed by our latero-medial dissection approach, which was not optimal for exposing such WM pathways. Similarly, connections to the MOG were not found in our dissections, as the dissection of purely longitudinal fibers stopped at the level of the AG. Dissection of the temporal cortex also did not extend to the T-pole, and rarely revealed connections to the basal surface of the hemisphere. The only specimen showing connections to the FuG (i.e., PrCG-FuG, see Fig. 3) was spc-06. Indeed, its unique anatomical configuration showing a “bulge” of the FuG interposing between the ITG and the IOG on the ventral lateral aspect of the convexity allowed the exposure of fibers connecting to this region through a latero-medial dissection approach. Additionally, connections with the IFG were only observed in 3 specimens, leaving anatomically plausible connections such as IFG-PoCG, IFG-STG, and IFG-IOG unproven.

On the other hand, we classified as anatomically implausible those sub-SLS templates showing abrupt changes of direction (Fig. 2, red templates). For instance, sub-SLS templates between the SFG and the temporal cortex (ITG, MTG, and STG) leave the posterior half of the SFG ventrally and traverse the posterior frontal cortex transversally up to the IFG before joining the other fronto-temporal connections of the SLS. Similarly, connections of the SFG-SMG template leave the SFG ventrally, travel vertically up to the level of the IFG, and then abruptly bend longitudinally toward the SMG. A similar but opposed shift in direction is seen in the IFG-SPG and IFG-PrCu templates, which travel longitudinally from the IFG up to the postcentral sulcus, before shifting vertically to reach the dorsal and medial parietal cortices. No such abrupt changes in direction were observed in the ex-vivo dissection of the SLS, therefore, these templates were classified as anatomically implausible. These directional shifts are likely caused by the intersection of longitudinal fibers with the anterior transverse system in the frontal lobe or with projection fibers of the pyramidal tract in the parietal lobe, leading the tractography algorithm to follow undesired directions.

sub-SLS templates replication study

The replication analysis of the sub-SLS tractography templates carried out on the three HCP test-retest tractography datasets distributed on brainlife.io³⁷ with the Fast Streamline Search approach³⁸ revealed a good agreement across tractography reconstructions derived from two different DWI acquisition protocols (i.e., BIL&GIN vs. HCP). Overall, we achieved 0.77 ± 0.27 average wDSC (i.e., dice coefficient on voxels weighted for streamline density) for test and test_run_2 and 0.78 ± 0.26 for retest. When considering only anatomically plausible and validated templates, mean wDSC spiked to 0.92 ± 0.08 for all HCP datasets, while it attested to 0.72 ± 0.29, 0.71 ± 0.3, and 0.71 ± 0.31 for test, test_run_2, and retest respectively, when considering anatomically plausible but not validated templates. On the other hand, wDSC dropped to 0.39 ± 0.22, 0.37 ± 0.19, and 0.43 ± 0.18 when considering sub-SLS templates deemed anatomically implausible. All measurements, including further streamline- and voxel-based similarity measurements on top of wDSC (i.e., bundle adjacency, dice coefficient, density correlation, overlap and overreach) are available in Supplementary Data 2, also reporting mean and standard deviations calculated considering all the templates together as well as filtered according to the classification of the templates (anatomically plausible and validated in green, anatomically plausible but not validated in yellow, and anatomically implausible in red). Single tractography reconstructions and voxel masks showing the overlap between the sub-SLS provided in the present work and sub-SLS extracted from each HCP dataset are displayed in Supplementary Fig. 2 with the respective wDSC. Of note, while on average wDSC dropped for anatomically implausible templates, the visualization provided in Supplementary Fig. 2 shows that implausible streamlines following the exact same course of the ones extracted on the N39 BIL&GIN dataset could also be found in the three HCP datasets. This reinforces the importance of relying on direct anatomical explorations to make tractography-based inferences on the architecture of WM pathways, independently from the characteristic of DWI and tractography.

sub-SLS templates characterization

A numerical description of each anatomically plausible sub-SLS tractography template—both validated and not validated (Fig. 2, green and yellow templates, respectively)—is provided through shape analysis (Supplementary Data 3)³⁹. Additionally, we provide the mean coordinates of both anterior and posterior terminations for each of these templates in MNI space, with “anterior” indicating frontal terminations (Supplementary Data 4).

sub-SLS templates topological organization

The study of the SLS wiring through ex-vivo dissection and the annotation of different sub-SLS on photogrammetric models revealed key organizational principles of the WM fibers of this system. We analyzed the sub-SLS tractography templates to test for the occurrence of the same medio-lateral and dorso-ventral patterns of fiber distribution identified in the dissection study. The combined visualization of centroids of the sub-SLS templates originating in the IFG, MFG, and SFG shows that IFG connections start, course, and terminate more ventrally compared to MFG connections, which in turn are more ventral compared to SFG connections (Fig. 4, middle column, top row, in yellow, orange, and bordeaux, respectively). As previously described in the dissection data, this ordered layout is respected when streamlines bend into the temporal cortex, and defines their distance from the Sylvian fissure when arching around it (i.e., the more dorsal in the frontal cortex, the farther they course from the Sylvian fissure). Connections originating in the PrCG, which parallels the central sulcus and spans the most posterior part of the frontal lobe with a dorso-vental configuration, overlay to those arising from the other frontal gyri (Fig. 4, third column).

Centroids representing the SLS connectivity for each frontal gyrus are shown in the first (IFG, MFG, SFG) and second columns (PrCG, bottom row), with parietal, temporal, and occipital connections in green, blue, and pink, respectively. A concatenation of the centroids representing sub-SLS templates originating from the IFG (yellow), MFG (orange), and SFG (bordeaux) is provided in the second column, top row. The third column icon displays all anatomically plausible sub-SLS centroids together with IFG connections in yellow, MFG connections in orange, SFG connections in bordeaux and PrCG connections in red). AG angular gyrus, FuG fusiform gyrus, IFG inferior frontal gyrus, IOG inferior occipital gyrus, ITG inferior temporal gyrus, MFG middle frontal gyrus, MOG middle occipital gyrus, MTG middle temporal gyrus, PoCG postcentral gyrus, PrCG precentral gyrus, PrCu precuneus, SFG superior frontal gyrus, SMG supramarginal gyrus, SOG superior occipital gyrus, SPG superior parietal gyrus, STG superior temporal gyrus, T-pole temporal pole.

The dorso-ventral organization of fibers observed by considering all the frontal gyri together is respected also at the level of the single gyrus (Fig. 4, icons dedicated to IFG, MFG, SFG, and PrCG in the first and second columns). Connections arising in the PrCG provide an illustrative example. As it can be observed in Fig. 4, (second column, PrCG icon) fronto-parietal connections, depicted in green, are organized according to a ventro-dorsal layout, with a sequential organization orderly displaying, from ventral to dorsal, PrCG-SMG, PrCG-AG, PrCG-PoCG (whose centroid lies in the middle of the gyrus, as the connection spans the whole extent of both PrCG and PoCG), PoCG-SPG, and PrCG-PrCu. This organization respects the arrangement of cortical gyri in the parietal cortex, and drives the distribution of the fibers. The same principle applies to connections between the PrCG and both the lateral aspect of the temporal cortex and the occipital lobe. Connections from the PrCG to the STG terminate more ventrally in the PrCG compared to those reaching the MTG, which, in turn, are more ventral than those reaching the ITG. Accordingly, as we proceed from ventral to dorsal in the PrCG – and inversely from dorsal to ventral in the temporal cortex -, streamlines shift from coursing close to the Sylvian fissure to following a more distant trajectory. Similarly, connections to the IOG arise more ventrally in the PrCG compared to those reaching the MOG, and this dorso-ventral organization persists along their entire course. Connections to the T-pole and to the FuG demonstrate a similar organization, forming an additional deeper layer. Indeed, as seen in all the icons of Fig. 4 dedicated to each single gyrus, fronto-parietal connections, depicted in green, are the most superficial, followed by connections to the lateral temporal cortex and to the occipital lobe, which are themselves more superficial compared to connections reaching the anterior temporal lobe (i.e., T-pole) and the basal temporal cortex (i.e., FuG).

This medio-lateral layering reflects the length of streamlines, with shorter connections coursing more superficially and longer connections traveling deeper. This principle is shown in Fig. 5A, B, where streamlines are color-coded based on their distance from the cortex. More superficial fibers (yellow) cover shorter distances, while longer fibers (dark red), travel more deeply. Supplementary Fig. 3 provides the same color-coded representation for each sub-SLS template, further demonstrating that this organizational principle applies broadly across the SLS, even when considering only part of the system. Statistical analysis revealed a significant positive correlation between the length of each streamline and its distance from the cortex (Pearson’s r = 0.689, p < 0.001) (Fig. 5C).

Streamlines of the SLS are color-coded to reflect their distance from the cortex, with more superficial fibers shown in yellow, and deeper fibers shown in dark red (A and B, lateral and medial views, respectively). This color gradient illustrates the medio-lateral organization of the SLS, where shorter connections course more superficially, and longer connections travel deeper. The scatterplot in (C) shows a positive correlation between streamline length and distance from the cortex (Pearson’s r = 0.689, p < 0.001), confirming the consistency of this organizational principle across the SLS.

In 2017, astronomers detected ‘Oumuamua, an interstellar object passing through our solar system. Its unusual shape and acceleration patterns defy conventional explanations, leading to various hypotheses, including the possibility of it being an artificial object. However, no consensus has been reached, and ‘Oumuamua remains an unresolved enigma in modern astronomy.

The total lunar eclipse on 7 September 2025 will be visible from the UK as the Moon rises, meaning the Moon will already be eclipsed when it emerges above the horizon.

In fact, totality will have ended about 15 minutes after the Moon pops up above the horizon (as seen from the centre of the UK).

That means, if you want to photograph the 7 September lunar eclipse from the UK, you’ll want to catch it as close to the horizon as possible.

There are many ways to photograph a lunar eclipse and, as you’d expect, some methods work better than others.

Of course, the wild card will be the weather, which caused a lot of issues for much of the UK during the lunar eclipse in March 2025.

All we can do is keep our fingers crossed and hope for crisp, clear, haze-free skies this time around.

Fortunately, with the final partial phase lasting just over an hour, there’s a decent window of opportunity to capture something worthwhile.

Using a smartphone

A smartphone is perfectly acceptable for photographing a lunar eclipse, but the Moon’s apparent diameter of around half a degree will result in a small lunar disc.

Yes, you can zoom in with your phone, but the best results will come from staying within your phone’s optical zoom range.

Beyond that, you’re into digital zooming territory, which is no better than enlarging the image in post-processing using an image editor.

The software increases the number of pixels in the image by interpolating between actual recorded data, filling in gaps with synthetic information.

Get more advice with our guide on how to photograph the Moon with a smartphone.

Camera and lens

A better bet for photographing a lunar eclipse is to use a dedicated camera fitted with a lens of at least 400mm focal length on a full-frame sensor.

This setup will allow you to capture the Moon as a detailed disc with visible surface features.

Mounting the camera on a fixed platform – or, even better, a tracking mount – will help you achieve excellent, sharp images.

The bright lunar surface that is exposed after totality won’t typically require long exposures and so is unlikely to be subject to trailing.

However, if you allow the bright surface to over-expose, you should be able to pull out some of the beautiful umbral colours in the darker part of the shadowed regions.

For this, you’ll need slightly longer exposures, which is where a tracking mount becomes especially useful.

Planetary camera

Another method is to use a planetary camera setup with a wide enough field of view to be able to capture the entire Moon in a single frame.

Planetary setups typically use multi-frame imaging, collecting numerous shots of the same target over a short period of time.

Software such as AutoStakkert! (freeware) can then analyse, quality-assess, register and stack the frames to generate a final image with a higher signal-to-noise ratio than the individual frames.

The trick here is to make sure you don’t extend the capture session too long, otherwise the movement of Earth’s shadow will blur the edge more than usual.

Find out more in our guide to stacking images of the Moon.

6 tips for photographing the September 2025 lunar eclipse

Plan your location

Keep an eye on the weather and, if you’re prepared to put in a little extra effort, identify some alternative locations that might be clear in case you’re clouded out.

Pick sites with unobstructed views in the required direction. From the centre of the UK, the Moon rises at azimuth 100° or just south (right) of east.

Practise, practise, practise

Choose your setup(s) and practise with the Moon on evenings ahead of the eclipse, especially if you intend to relocate on eclipse day.

As a bare minimum, use a DSLR or equivalent with a 400mm or longer lens.

Take your phone for atmospheric shots too, such as the Belt of Venus into which the Moon will rise.

Prepare your camera lens

On evenings before the lunar eclipse, focus your lens as accurately as possible on the Moon.

Then, with the lens set to manual focus, use a length of low-tack electrical tape to secure the focus ring so it can’t rotate.

When the Moon rises on 7 September, the show will already be under way, so you need to be as ready as possible.

Identify where the Moon will rise

To pinpoint exactly where the Moon will appear, visit your chosen location on a night before the eclipse.

Wait for the sky to darken and Saturn to become visible.

Set your camera’s clock accurately (ideally using UT), then take a wide or mid shot of the horizon where you expect the Moon to rise, exposing to capture stars.

Use a stargazing app

Download your images and inspect their EXIF headers using freeware like FastStone.

With a planetarium app, identify stars near the horizon and their azimuths by entering the shot’s date and time. Note the azimuths of visible horizon features.

Using the same app, confirm where the Moon will rise on 7 September.

Give yourself plenty of time

On the night, set up in good time.

Don’t be surprised if the Moon doesn’t show when expected: low haze can easily hide it. Binoculars will very helpful.

Use a low to mid ISO and an aperture around f/8–f/11. Short exposures will capture the bright surface, but try longer ones to reveal colour in the shadowed regions.

If you photograph the 7 September 2025 lunar eclipse, share your images with us by emailing contactus@skyatnightmagazine.com

The joint European Space Agency (ESA) and NASA Solar Orbiter spacecraft has tracked electrons traveling at nearly the speed of light back to the sun, finding they originated in different types of solar outbursts.

Solar Orbiter detected these so-called Solar Energetic Electrons (SEEs) in space after being accelerated to high energies, and researchers were able to pinpoint their source in an attempt to better understand the physics of the sun.

Near-field ptychography is a scanning phase-contrast imaging technique, which recovers the illumination and the sample transmission function from overlapping scan positions. Multi-slice reconstructions extend the capabilities of ptychography to the imaging of optically thick specimens. It was initially used in FFP²⁷ and has recently been introduced for the near-field regime²⁴. Multi-slice ptychography enables multiple layers of a 3D sample to be recovered.

The minimum thickness of layers distinguishable in multi-slice ptychography is described by the depth of field of the imaging system. In general, the depth of field (DOF) in ptychography is defined as:

where (delta _r) is the lateral resolution, (lambda) the wavelength of the illumination, and c a constant reported to be between 1.0 and 5.2^28,29,30. Stockmar et al. defined (c:=1.0) for NFP²⁸. Hu et al. define the depth resolution for near-field multi-slice ptychography based on raytracing as:

where (z_1+z_2) is the propagation distance between the focus of the cone beam and the detector and D is the beam diameter on the detector²⁴. For small angles, as generally valid for X-ray optics, one can rewrite Eq. (2) with the numerical aperture as (textit{NA}approx 0.5cdot D/(z_1+z_2)). Defining (NA) in terms of the Abbe criterion is identical to Eq. (1) with (c=1.0), so this again matches the definition by Stockmar et al.²⁸. The achievable resolution in NFP is slice dependent since the pixel size of each slice depends on the individual focus-to-slice distance. Therefore, the DOF in NFP, as defined by Eqs. (1) and (2), is also slice dependent.

Although NFP is a lensless imaging technique that does not use an objective lens, the achievable depth resolution as described in Eq. (2) is directly related to the numerical aperture of the lens placed upstream of the sample. To achieve superior lateral and depth resolution, high-NA lenses should be used.

Many in-situ studies require bulky reaction environments. For this reason, a high penetration depth of the illuminating beam is required, which can be achieved by using hard X-rays. MLLs are the optics type with the highest NA in the hard X-ray range and were therefore utilized for this setup. In our experiment, we set the photon energy to (E =) 18 keV. A set of MLLs for horizontal and vertical focusing created a focal spot of 30 nm (times) 24 nm (see supplementary material Fig. S10). The MLLs were illuminated fully coherently for the in-situ series shown in Fig. 3. For the other measurements prefocusing compound reflective lenses located 54 m upstream of the MLLs were used. These reduced the spatial coherence length at the MLL position to 15 µm in the horizontal and 85 µm in the vertical direction and led to a partially coherent illumination. In near-field imaging, coherence over the first Fresnel zone width would be sufficient³¹ and the coherence length for all measurements is well above this limit. As shown schematically in Fig. 1, the focused beam was cleaned from other diffraction orders by a rectangular pinhole. The sample was positioned on a piezo scanner between 0.63 and 3.00 mm downstream of the focal plane and diffraction patterns were recorded at a distance of 3.29 m behind the sample by an Eiger X 4M in-vacuum detector. Further details of the setup can be found in the Methods.

The scans were reconstructed using the ePIE³² algorithm for the single-slice case and the 3PIE²⁷ algorithm for the multi-slice case. In the reconstruction, the wavefield is propagated between the slices and between the sample and the detector using a Fresnel propagator. Details of the reconstruction parameters for each scan are tabulated in the supplementary material. In contrast to FFP, NFP is modeled with a cone beam geometry. For efficient image reconstruction, the cone beam must be converted to a parallel-beam geometry, which is done by applying the Fresnel scaling theorem³³. The pixel size and the propagation distance of each slice are scaled accordingly. This step requires the knowledge of the distance between the focus and the sample, measured during the experiment. In this work, the focus-to-sample distance and the distances between slices were refined interactively by performing reconstructions with the aforementioned distances varied by (pm 10%) around the expected value. The values that produced a flat phase profile for the illumination and visually good results for the slices were chosen for the final reconstruction. The adjustments in the 3PIE algorithm can be found in the supplementary material. In our experiment, the divergent MLL-beam had a size of 11.3 mm (times) 12.6 mm on the detector, with a propagation distance of 3.29 m between sample and detector. Using Eq. (2), it is found that the depth resolution is (DOFapprox 275 cdot delta _r). At a source-size-limited lateral resolution of (delta _r=) 30 nm the achievable depth resolution with our setup is therefore (DOF=) 8 µm.

Capabilities for ex-situ imaging

We first characterize our method by imaging cuprous oxide nanoparticles synthesized ex situ on both sides of a 225 µm-thick polyimide foil, as conceptually illustrated in Fig. 2a. Details of the image acquisition are described in the Methods—Scanning parameters section. The reconstructed illuminating beam (Fig. 2b) shows a relatively flat phase profile (indicated by the colors), as it is expected in near-field imaging without a diffuser¹⁰. The grid-like structure visible in the amplitude of the illumination (indicated by the brightness) is caused by the layered structure of the multilayer Laue lenses. Structure in the illumination is in general beneficial for a robust reconstruction in ptychography^34,35 and even more important in NFP. For efficient phase retrieval, NFP relies on a structured illumination^10,15. The structure is conventionally realized with a diffuser, such as sand paper, positioned in front of the lens. The use of MLLs, whose slight imperfections produce an inherently structured wavefield, made a diffuser unnecessary in our work.

For the multi-slice reconstruction, the polyimide foil is a model specimen with two distinct planes of cuprous oxide cubes on either side of the foil, slice 1 and slice 2, as shown in Fig. 2a. A conventional NFP reconstruction of the foil, treating the object as optically thin, is shown in Fig. 2c. The features on the upstream side of the foil are well resolved and sharp, while the cuprous oxide cubes on the back side appear blurred (see blue arrow in the figure). This indicates that the single-slice approximation for the object is not sufficient to model the thicker sample. To resolve both sides of the foil, beam propagation effects between the different layers must be taken into account. With multi-slice NFP, the individual slices can be sharply recovered. Slice 1 (Fig. 2e) shows the particles located on the upstream side of the foil and slice 2 (Fig. 2f) the nanocubes on the downstream side. The pixelwise sum of the two slices, shown in Fig. 2d, exhibits sharp edges for all features of both layers. Due to the cone-beam geometry, the effective pixel sizes are not the same for the two object slices. The pixel size for slice 1, which is closer to the focus, is 64.7nm and for slice 2 it is 69.8nm. To create the pixelwise slice sum in Fig. 2d as a parallel projection, we scaled the pixel size of slice 2 to match the pixel size of slice 1 using the scikit-image³⁶ resize function.

Background fluctuations (brighter and darker areas without any sharp edges) are apparent in the reconstructions of the slices and cancel out in the sum of the two. These low-frequency image artifacts are often present in multi-slice ptychography^30,37, typically caused by the short propagation distance between the slices. The maximum width between two points in one plane, for which interference effects can be observed after propagation over an effective distance (z_textrm{eff}), can be estimated by the first Fresnel zone radius (r_F)³⁸:

where (lambda) denotes the X-ray wavelength. This effectively limits the lowest spatial frequency that can be recovered for a given propagation distance.

In the multi-slice reconstructions, the scattering of the polyimide foil was neglected, and the wavefield propagated between the two slices. In reality, though, the polyimide foil introduces a phase shift. However, this effect is negligible at the used photon energy for a homogeneous foil of the given thickness. Applying Eq. (2) with a lateral resolution of (delta _r=) 102.6 nm, the DOF for this scan was equal to 27.5 µm while the reconstructed slices were separated by 225 µm, which is well above the DOF limit. Here, we demonstrated multi-slice NFP on an ex-situ model sample; in the next step we show its capabilities for in-situ imaging of chemical reactions.

Near-field multi-slice ptychography of ex-situ cuprous oxide nanoparticles deposited on both sides of a polyimide foil. (a) schematic of the sample placed 2840 µm downstream of the focus of the X-ray beam with the two particle layers separated by a 225 µm-thick polyimide foil. (b) shows the corresponding reconstructed illumination with a size of 8.5 µm (times) 10 µm. (c) reconstruction of the scan assuming a single optically thin object. (d) summed phase of the multi-slice reconstruction shown in (e) first slice (upstream) and (f) second slice (downstream). The particles on the downstream side of the foil (slice 2) appear blurred in the single slice reconstruction (see e. g. the blue arrow), while they are well resolved in the reconstruction of the second slice and in the sum of the slices.

In-situ imaging of the galvanic replacement reaction of cuprous oxide nanocubes with gold

The galvanic replacement reaction of cuprous oxide nanocubes with gold acts as a model reaction for in-situ multi-slice NFP. We mounted our reaction cell for in-situ imaging of nanoparticle growth³⁹ at a distance of 3.0 mm behind the focal plane. The polyimide foil with the cuprous oxide cubes is placed on the upstream side of the reaction container. The downstream window is an empty polyimide foil, which is separated by 1 mm from the upstream window using a PTFE-frame between them. The resulting reaction container is enclosed in a metal casing (for photographs of the cell see supplementary material Fig. S5). The reaction solution containing the gold precursor is injected between the two polyimide windows. The pre-synthesized cuprous oxide nanocubes are attached to a polyimide foil and, over the course of the reaction, the cuprous oxide is replaced by gold, as schematically shown in Fig. 3a,b. The reaction conditions are described in the Methods—Synthesis procedure and details can be found in Grote et al.³⁹.

The in-situ series of the galvanic replacement reaction of (hbox {Cu}_2 hbox {O}) with Au was measured over 4.2h. A single ptychographic scan spanned a field of view of 10 µm (times) 10 µm and required a total scan time of 9.6 min. The reconstruction parameters can be found in the supplementary material Table S2.

For this in-situ series, the DOF was 21 µm and the two reconstructed slices were separated by 1 mm. Scattering by the reaction solution was neglected and the distance between the two windows was modeled with a free-space propagator. In the post-processing step, a high-pass filter was applied to the reconstructed phase images of the upstream window to reduce low-frequency artifacts. We used the scikit-image³⁶ Butterworth filter with a cutoff frequency ratio of 0.018.

At the beginning of the reaction at 0.0 h (Fig. 3c), the upstream polyimide foil was covered with (hbox {Cu}_2 hbox {O}) cubes with an edge length of 150 nm to 250 nm (see Supplementary Fig. S7). The reaction solution containing the gold precursor (20 mM (hbox {HAuCl}_4)) was slowly injected into the cell with a syringe pump. In the first phase of the reaction, Au particles formed on the surface of the nanocubes. In the second phase, the Au particles grew larger and fused together, (hbox {Cu}_2 hbox{O}) was further oxidized and dissolved, and the cubes became less dense in their centers. The final stage of the reaction was the formation of hollow Au nanocages, similar like observed in our FFP experiments reported previously.³⁹

Between 0.0 h and 2.8 h (Fig. 3c–f), a growth of the particles could be observed. A beam dump between 3.0 h and 3.8 h after the start of the reaction did not allow data acquisition during this period. In the first scan after the beam dump (at 3.8 h, Fig. 3g), the particles appeared hollow and in the subsequent scans the hollow structures seemed to connect. The growth in the first phase can be attributed to Au particles forming on the (hbox {Cu}_2 hbox {O}) surface. The galvanic replacement reaction progressed during the beam dump and at 3.8 h after the start of the reaction the hollow cages resembled the expected final result. The later Au deposition (Fig. 3h) can be attributed to beam damage. This is also evidenced by Au deposition on the downstream window of the reaction container (see Fig. S8 in the supplementary material), which is not the case in comparable ex-situ laboratory experiments.

For this in-situ series, the spatial resolution determined by Fourier-ring correlation was between 88 nm and 129 nm (see supplementary material Fig. S2), which is comparable to the spatial resolution achieved in a similar experiment with FFP³⁹. The average dose per projection was 0.36 MGy with a dose rate of 1.28 kGy/s, which corresponds to a reduction in dose by a factor of 2.5 for a given field of view and a reduction of the dose rate by more than two orders of magnitude compared to the FFP results. The dose and dose rate were calculated according to the procedure reported by Grote et al.³⁹. The significantly reduced dose rate is a result of the large illumination. However, the cumulative dose is comparable and, therefore, so is the spatial resolution.

The growth and formation of the hollow cages was clearly observed. This study demonstrates the competitiveness of NFP for in-situ imaging with reduced dose rate and improved temporal resolution while maintaining high spatial resolution. NFP is an excellent method for radiation sensitive samples. However, beam damage is a complex process with many experimental parameters to consider, such as beam size, photon energy and more. Björling et al. describe comprehensively the interplay between experimental parameters and free-radical formation in aqueous solutions¹⁷.

The spatial resolution of the scans was between 129 nm for the early scans, without significant beam damage, and 88 nm for the later scans, with significant beam damage, where we observe additionally to galvanic replacement a deposition of gold in the exposed areas of the sample. The increased size and thickness of the gold particles leads to an increased phase shift and thus an increased X-ray optical contrast, thereby improving the spatial resolution of the reconstructions of later scans. The resolution of all scans was close to or below the size of two pixels. Therefore, they can be described as pixel size limited when the resolution is considered in terms of the Nyquist-Shannon limit. In future experiments, the use of a detector with a smaller pixel size could improve the spatial resolution for similar temporal resolution and dose. Alternatively, an improved resolution could potentially be achieved by reducing the demagnified pixel size using a two-stage Fresnel propagator as described by Witte et al.⁴⁰.

In-situ near-field multislicing ptychography of cuprous oxide nanocubes undergoing a galvanic replacement reaction. (a) Schematic of the galvanic replacement reaction. Gold particles form on the surface of the cuprous oxide cubes, (hbox {Cu}^{2+}) dissolves over the course of the reaction and hollow gold nanocages form (adapted from³⁹). (b) Schematic of the reaction container. A polyimide foil with pre-synthesized cuprous oxide and a clean foil encapsulate the reaction solution with the gold precursor. (c)–(h) In-situ galvanic replacement reaction over 4.2 h. Multi-slice near-field reconstructions of the upstream window (phase shift).

In-situ imaging at highest spatial resolution

In a second in-situ series of the same reaction, our aim was to achieve imaging with an even higher spatial resolution. The reaction cell was moved to a position 630 µm downstream of the focal plane of the MLLs. By moving the sample closer to the focal plane, the magnification was increased by a factor of 4.75 to (M=5223) and the pixel size in the first slice was reduced by the same factor to 14.4 nm. The reaction was running for 1.0 h when the scan shown in Fig. 4 was recorded. The distance between the upstream and downstream window was 1.2 mm, slightly larger than in the previous experiment. However, this is within the assembly tolerances of the reaction container.

Figure 4b shows a single-slice reconstruction, where the sample was treated as a single, optically thin object. A big inclusion in the polyimide foil is clearly visible in the background in the lower left corner. The polyimide foils often contain inclusions from additives used as slipping agents in the production process^41,42 (see supplementary material Fig. S6), which compromise the reconstruction of the layer of interest containing the nanoparticles.

To optimize the resolution of the plane of interest and to remove any inclusions obscuring the view on the nanoparticles, we recovered four distinct slices (Fig. 4c–f) in a multi-slice reconstruction (see Table S2 in the supplementary material for specific reconstruction parameters). The two slices of the upstream window of the reaction cell (slice 1 and slice 2) are separated by 125 µm. The exit window is located 1200 µm downstream of the second slice and divided into two slices separated by 62.5 µm.

A distance of 630 µm between focal plane and sample may seem small to consider this measurement in the near-field imaging regime. The effective Fresnel number F for this scan is given by Eq. (4)¹⁰:

with the extent of the illumination (W^2={2.2},upmu textrm{m}times {2.5},upmu textrm{m}), the wavelength (lambda =) 0.69 Å and the effective propagation distance (z_textrm{eff}=) 630 µm. Even though the effective Fresnel number for this measurement is considerably larger than unity, the scan can still be reconstructed with a far-field propagator between the last slice and the detector. However, the slice separation achieved with the near-field multi-slice reconstruction is superior to that of the far-field reconstruction (see supplementary material Fig. S4). The contribution from other slices remaining in the plane of interest is significantly smaller, showing that the Fresnel approximation models the measurement more accurately in this case. The plane with the nanoparticles (slice 2, Fig. 4d) shows only a weak shadow of the large inclusion from slice 1 compared to the single slice reconstruction. In order to correctly evaluate the reaction process, it is of great importance to obtain an undisturbed, quantitative image of the plane of interest, which we have achieved here in the multi-slice reconstruction. The large inclusions in slices 1, 3, and 4 are surrounded by a halo. This is a well-known artifact for strongly phase-shifting features in phase-contrast imaging^43,44,45,46, resulting from the small modulation transfer of the low spatial frequencies.

The spatial resolution for slice 2, determined with Fourier ring correlation^47,48, is 30 nm. This is close to the theoretical limit given by the focal spot size of the MLLs and below the resolution limit of two times the pixel size, given by the Nyquist criterion. The reconstruction can therefore be described as pixel size limited. The resolution for the other slices was 48 nm for the first slice, 84 nm for the third slice, and 130 nm for the fourth slice. The resolution of slice 1 is lower than slice 2 despite a smaller pixel size. This can be explained by a sparse sample plane for slice 1 with more than half of the scan points containing only little structural diversity and, hence, being more challenging to reconstruct. Details of the Fourier ring correlation analysis can be found in the supplementary material Fig. S3. For these spatial resolutions the slice thicknesses are all greater than the depth of field limit given by Eq. (2) (slice 1: 13 µm, slice 2: 8 µm, slice 3: 23 µm). Nevertheless, the separation of slice 3 and 4 does not appear to be perfect. The dark particle in the center of slice 3 appears as a white shadow in slice 4. The slice thickness seems to be close to the practical reconstruction limit. Hu et al. already describe that the actual thickness of the slices in X-ray NFP often has to be significantly larger than the theoretical limit given by Eq. (2)²⁴. However, applying Eq. (1) with the constant (c=1) seems to overestimate the limit for slice separation ((DOF=) 102.6 µm).

We found that in the case of hard X-ray NFP, the experiment geometry must be well known at the time of measurement, to a much better degree than in the case of FFP experiments. The reconstruction is very sensitive to inaccuracies in defocus and interslice distance, as these have a strong impact on the effective Fresnel number.

In the scans following the one shown in Fig. 2, beam damage overshadows the reaction progress (see supplementary material Fig. S9). Again, in-situ imaging is a balancing act between spatial resolution and tolerable beam damage. Nevertheless, we have shown that NFP is competitive with FFP. Multi-slice NFP extends the capabilities of the method to the imaging of optically thick specimens, making it attractive for in-situ imaging.

Imaging of nanoparticles growing in solution. (a) shows a schematic longitudinal cross-section of the chemical reactor with four distinct object planes (slices) in the direction of the X-ray beam. (b) A conventional single-slice reconstruction of the chemical reactor with nanoparticles. Applying the multi-slice approach allows to isolate four object planes corresponding to: (c) the upstream reactor’s window, (d) the inner side of the upstream window with nanoparticles, (e) the inner side of the downstream reactor’s window, and (f) the outer side of the downstream reactor’s window. (c), (e), and (f) show inclusions present in polyimide foils that otherwise obscure the view on the nanoparticles.

Frozen water is one of the most abundant substances on Earth. It is found in glaciers, on mountain peaks and in polar ice caps. Although it is a well-known material, studying its properties continues to yield fascinating results.

An international study involving ICN2, at the UAB campus, Xi’an Jiaotong University (Xi’an) and Stony Brook University (New York), has shown for the first time that ordinary ice is a flexoelectric material. In other words, it can generate electricity when subjected to mechanical deformation. This discovery could have significant implications for the development of future technological devices and help to explain natural phenomena such as the formation of lightning in thunderstorms.

The study, published in the journal Nature Physics, represents a significant step forward in our understanding of the electromechanical properties of ice. “We discovered that ice generates electric charge in response to mechanical stress at all temperatures. In addition, we identified a thin ‘ferroelectric’ layer at the surface at temperatures below -113ºC (160K). This means that the ice surface can develop a natural electric polarization, which can be reversed when an external electric field is applied—similar to how the poles of a magnet can be flipped. The surface ferroelectricity is a cool discovery in its own right, as it means that ice may have not just one way to generate electricity but two: ferroelectricity at very low temperatures, and flexoelectricity at higher temperatures all the way to 0 °C ” explains Dr Xin Wen, a member of the ICN2 Oxide Nanophysics Group and one of the study’s lead researchers. This property places ice on a par with electroceramic materials such as titanium dioxide, which are currently used in advanced technologies like sensors and capacitors.

Ice, flexoelectricity and thunderstorms

One of the most surprising aspects of this discovery is its connection to nature. The results of the study suggest that the flexoelectricity of ice could play a role in the electrification of clouds during thunderstorms, and therefore in the origin of lightning.

It is known that lightning forms when an electric potential builds up in clouds due to collisions between ice particles, which become electrically charged. This potential is then released as a lightning strike. However, the mechanism by which ice particles become electrically charged has remained unclear, since ice is not piezoelectric — it cannot generate charge simply by being compressed during a collision.

However, the study shows that ice can become electrically charged when it is subjected to inhomogeneous deformations, i.e. when it bends or deforms irregularly. “During our research, the electric potential generated by bending a slab of ice was measured. Specifically, the block was placed between two metal plates and connected to a measuring device. The results match those previously observed in ice-particle collisions in thunderstorms”, explains ICREA Prof. Gustau Catalán, leader of the Oxide Nanophysics Group at ICN2.

Thus, the results suggest that flexoelectricity could be one possible explanation for the generation of the electric potential that leads to lightning during storms.

Future perspectives

The researchers in the group are already exploring new lines of investigation aimed at exploiting these properties of ice for real-world applications. Although it is still a bit early to discuss potential solutions, this discovery could pave the way for the development of new electronic devices that use ice as an active material, which could be fabricated directly in cold environments.

Reference:

Wen, X; Ma, Q; Mannino, A; Fernandez-Serra, M; Shen, S; Catalan, G. Flexoelectricity and surface ferroelectricity of water ice. Nature Physics. (2025).

At first glance, Nam-Joon Cho’s lab at Singapore’s Nanyang Technological University looks like your typical research facility — scientists toiling away, crowded workbenches, a hum of machinery in the background. But the orange-yellow stains on the lab coats slung on hooks hint at a less-usual subject matter under study.

The powdery stain is pollen: microscopic grains containing male reproductive cells that trees, weeds and grasses release seasonally. But Cho isn’t studying irksome effects like hay fever, or what pollen means for the plants that make it. Instead, the material scientist has spent a decade pioneering and refining techniques to remodel pollen’s rigid outer shell — made of a polymer so tough it’s sometimes called “the diamond of the plant world” — transforming the grains to a jam-like consistency.