arXiv subjects

Kartik Ayyer

Publications and source records attributed to Kartik Ayyer.

At least 19 recordsLinked to original sources

arXiv2025

Single-particle incoherent diffractive imaging and amplified spontaneous emission in copper nanocubes

We demonstrate element-specific incoherent diffractive imaging (IDI) of single copper nanocubes using intensity correlations of K$α$ fluorescence at a hard X-ray free-electron laser. Combining single particle diffraction classification with IDI, we retrieve the form factor of 88 nm cubes with 20 nm resolution, extending IDI to the destructive single-particle regime with a large gain in resolution. IDI visibility drops sharply above a fluence of $10^2$ J/cm$^2$, consistent with the assumption of amplified spontaneous emission. Our results reveal fundamental limits for high-fluence nanoimaging towards future single-particle X-ray imaging.

physics.optics↗

arXiv2025

Nonlinear phenomena in X-ray fluorescence from single nanoparticles under extreme conditions

Materials exposed to intense femtosecond X-ray pulses with energies above their K-shell absorption edge can enter an extremely ionized state, which could give rise to nonlinear phenomena, such as saturable absorption and reverse saturable absorption. In this work, we investigate these effects on single copper nanoparticles irradiated by an X-ray free-electron laser pulse. We study the properties of the K$α$ fluorescence for two different short pulse durations and three X-ray incident energies below and above the K-shell absorption edge, and correlate these with incident fluence estimates based on coherent diffraction. We observe that the incident fluence of the pulse and not its duration, is the main factor that modulates the nonlinear response, which leads to an effective shortening of the fluorescence emission. Our findings have implications for fluorescence-based methods for imaging single particles using transiently coherent fluorescence, or diffractive imaging through transient resonances.

physics.optics↗

arXiv2025

Single-Particle X-ray Scattering Reveals a High Local Supersaturation of Precursors as the Origin of CoO Assembly Formation

Single-particle small-angle X-ray scattering (SP-SAXS) enables quantitative morphological analysis by recording diffraction snapshots from isolated particles using X-ray free-electron laser (XFEL) pulses. Unlike conventional X-ray techniques, which average over the entire illuminated sample volume, SP-SAXS resolves low-contrast, less abundant, or transient species within heterogeneous particle populations that would otherwise remain hidden. Here, we apply SP-SAXS to investigate the solvothermal formation of CoO nanocrystal assemblies from a Co(acac)$_3$ precursor in benzyl alcohol. The single-particle data reveal amorphous, uniform-density Co(acac)$_2$ spheres as transient intermediates that directly crystallize into cavernous CoO nanocrystal assemblies, which explains why CoO forms as hierarchical aggregates rather than as isolated nanocrystals. These results demonstrate that SP-SAXS provides a powerful framework for disentangling morphological heterogeneity in nanoparticle formation processes.

cond-mat.mes-hall↗

arXiv2025

High-background X-ray single particle imaging enabled by holographic enhancement with 2D crystals

X-ray single particle imaging (SPI) has offered the potential to visualize structures of biomolecules at near-atomic resolution. However, state-of-the-art structures at X-ray free electron lasers (XFELs) are limited to moderate resolution, primarily due to background scattering. We computationally explore a modified SPI technique based on holographic enhancement from a strongly scattering 2D crystal lattice placed near the object. The Bragg peaks from the crystal enable structure retrieval even for background levels up to 10$^{5}$ times higher than the object signal. This method could enable SPI at more widely accessible synchrotron sources, where even detection of objects before radiation damage is nearly impossible currently, supports practical fixed-target sample delivery, and enables high-resolution imaging under near-native conditions. Numerical simulations with a custom reconstruction algorithm to recover the latent parameters show the potential to improve the achievable resolution while also expanding the accessibility to the technique.

physics.optics↗

arXiv2025

SPRING: an effective and reliable framework for image reconstruction in single-particle Coherent Diffraction Imaging

Coherent Diffraction Imaging (CDI) is an experimental technique to gain images of isolated structures by recording the light scattered off the sample. In principle, the sample density can be recovered from the scattered light field through a straightforward Fourier Transform operation. However, only the amplitude of the field is recorded, while the phase is lost during the measurement process and has to be retrieved by means of suitable, well-established phase retrieval algorithms. In this work, we present SPRING, an analysis framework tailored to X-ray Free Electron Laser (XFEL) single-shot single-particle diffraction data that implements the Memetic Phase Retrieval method to mitigate the shortcomings of conventional algorithms. We benchmark the approach on experimental data acquired in two experimental campaigns at SwissFEL and European XFEL. Imaging results on isolated nanostructures reveal unprecedented stability and resilience of the algorithm's behavior on the input parameters, as well as the capability of identifying the solution in conditions hardly treatable so far with conventional methods. A user-friendly implementation of SPRING is released as open-source software, aiming at being a reference tool for the coherent diffraction imaging community at XFEL and synchrotron facilities.

physics.optics↗

arXiv2025

Direct observation of the exciton polaron by serial femtosecond crystallography on single CsPbBr$_3$ quantum dots

The outstanding opto-electronic properties of lead halide perovskites have been related to the formation of polarons. Nevertheless, the observation of the atomistic deformation brought about by one electron-hole pair in these materials has remained elusive. Here, we measure the diffraction patterns of single CsPbBr$_3$ quantum dots (QDs) with and without resonant excitation in the single exciton limit using serial femtosecond crystallography (SFX). By reconstructing the 3D differential diffraction pattern, we observe small shifts of the Bragg peaks indicative of a crystal-wide deformation field. Building on DFT calculations, we show that these shifts are consistent with the lattice distortion induced by a delocalized electron and a localized hole, forming a mixed large/small exciton polaron. This result creates a clear picture of the polaronic deformation in CsPbBr$_3$ QDs, highlights the exceptional sensitivity of SFX to lattice distortions in few-nanometer crystallites, and establishes an experimental platform for future studies of electron-lattice interactions.

cond-mat.mtrl-sci↗

arXiv2024

Observation of Aerosolization-induced Morphological Changes in Viral Capsids

Single-stranded RNA viruses co-assemble their capsid with the genome and variations in capsid structures can have significant functional relevance. In particular, viruses need to respond to a dehydrating environment to prevent genomic degradation and remain active upon rehydration. Theoretical work has predicted low-energy buckling transitions in icosahedral capsids which could protect the virus from further dehydration. However, there has been no direct experimental evidence, nor molecular mechanism, for such behaviour. Here we observe this transition using X-ray single particle imaging of MS2 bacteriophages after aerosolization. Using a combination of machine learning tools, we classify hundreds of thousands of single particle diffraction patterns to learn the structural landscape of the capsid morphology as a function of time spent in the aerosol phase. We found a previously unreported compact conformation as well as intermediate structures which suggest an incoherent buckling transition which does not preserve icosahedral symmetry. Finally, we propose a mechanism of this buckling, where a single 19-residue loop is destabilised, leading to the large observed morphology change. Our results provide experimental evidence for a mechanism by which viral capsids protect themselves from dehydration. In the process, these findings also demonstrate the power of single particle X-ray imaging and machine learning methods in studying biomolecular structural dynamics.

q-bio.BM↗

arXiv2024

Resolving non-equilibrium shape variations amongst millions of gold nanoparticles

Nanoparticles, exhibiting functionally relevant structural heterogeneity, are at the forefront of cutting-edge research. Now, high-throughput single-particle imaging (SPI) with x-ray free-electron lasers (XFELs) creates unprecedented opportunities for recovering the shape distributions of millions of particles that exhibit functionally relevant structural heterogeneity. To realize this potential, three challenges have to be overcome: (1) simultaneous parametrization of structural variability in real and reciprocal spaces; (2) efficiently inferring the latent parameters of each SPI measurement; (3) scaling up comparisons between $10^5$ structural models and $10^6$ XFEL-SPI measurements. Here, we describe how we overcame these three challenges to resolve the non-equilibrium shape distributions within millions of gold nanoparticles imaged at the European XFEL. These shape distributions allowed us to quantify the degree of asymmetry in these particles, discover a relatively stable `shape envelope' amongst nanoparticles, discern finite-size effects related to shape-controlling surfactants, and extrapolate nanoparticles' shapes to their idealized thermodynamic limit. Ultimately, these demonstrations show that XFEL SPI can help transform nanoparticle shape characterization from anecdotally interesting to statistically meaningful.

cond-mat.mes-hall↗

arXiv2023

Nanoscale X-ray imaging with high spectral sensitivity using fluorescence intensity correlations

This paper introduces Spectral Incoherent Diffractive Imaging (SIDI) as a novel method for achieving dark-field imaging of nanostructures with heterogeneous oxidation states. With SIDI, shifts in photoemission profiles can be spatially resolved, enabling the independent imaging of the underlying emitter distributions contributing to each spectral line. In the X-ray domain, this approach offers unique insights beyond the conventional combination of diffraction and X-ray Emission Spectroscopy (XES). When applied at X-ray Free-Electron Lasers (XFELs), SIDI promises to be a versatile tool for investigating a broad range of systems, offering unprecedented opportunities for detailed characterization of heterogeneous nanostructures for catalysis and energy storage, including of their ultrafast dynamics.

physics.optics↗

arXiv2023

Ab Initio Spatial Phase Retrieval via Intensity Triple Correlations

Second-order intensity correlations from incoherent emitters can reveal the Fourier transform modulus of their spatial distribution, but retrieving the phase to enable completely general Fourier inversion to real space remains challenging. Phase retrieval via the third-order intensity correlations has relied on special emitter configurations which simplified an unaddressed sign problem in the computation. Without a complete treatment of this sign problem, the general case of retrieving the Fourier phase from a truly arbitrary configuration of emitters is not possible. In this paper, a general method for ab initio phase retrieval via the intensity triple correlations is described. Simulations demonstrate accurate phase retrieval for clusters of incoherent emitters which could be applied to imaging stars or fluorescent atoms and molecules. With this work, it is now finally tractable to perform Fourier inversion directly and reconstruct images of arbitrary arrays of independent emitters via far-field intensity correlations alone.

physics.optics↗

arXiv2022

Holographic single particle imaging for weakly scattering, heterogeneous nanoscale objects

Single particle imaging (SPI) at X-ray free electron lasers (XFELs) is a technique to determine the 3D structure of nanoscale objects like biomolecules from a large number of diffraction patterns of copies of these objects in random orientations. Millions of low signal-to-noise diffraction patterns with unknown orientation are collected during an X-ray SPI experiment. The patterns are then analyzed and merged using a reconstruction algorithm to retrieve the full 3D-structure of particle. The resolution of reconstruction is limited by background noise, signal-to-noise ratio in diffraction patterns and total amount of data collected. We recently introduced a reference-enhanced holographic single particle imaging methodology [Optica 7,593-601(2020)] to collect high enough signal-to-noise and background tolerant patterns and a reconstruction algorithm to recover missing parameters beyond orientation and then directly retrieve the full Fourier model of the sample of interest. Here we describe a phase retrieval algorithm based on maximum likelihood estimation using pattern search dubbed as MaxLP, with better scalability for fine sampling of latent parameters and much better performance in the low signal limit. Furthermore, we show that structural variations within the target particle are averaged in real space, significantly improving robustness to conformational heterogeneity in comparison to conventional SPI. With these computational improvements, we believe reference-enhanced SPI is capable of reaching sub-nm resolution biomolecule imaging.

eess.IV↗

arXiv2022

On the use of multilayer Laue lenses with X-ray Free Electron Lasers

Multilayer Laue lenses were used for the first time to focus x-rays from an X-ray Free Electron Laser (XFEL). In an experiment, which was performed at the European XFEL, we demonstrated focusing to a spot size of a few tens of nanometers. A series of runs in which the number of pulses per train was increased from 1 to 2, 3, 4, 5, 6, 7, 10, 20 and 30 pulses per train, all with a pulse separation of 3.55 us, was done using the same set of lenses. The increase in the number of pulses per train was accompanied with an increase of x-ray intensity (transmission) from 9% to 92% at 5 pulses per train, and then the transmission was reduced to 23.5 % when the pulses were increased further. The final working condition was 30 pulses per train and 23.5% transmission. Only at this condition we saw that the diffraction efficiency of the MLLs changed over the course of a pulse train, and this variation was reproducible from train to train. We present the procedure to align and characterize these lenses and discuss challenges working with the pulse trains from this unique x-ray source.

physics.acc-ph↗

arXiv2021

Unsupervised learning approaches to characterize heterogeneous samples using X-ray single particle imaging

One of the outstanding analytical problems in X-ray single particle imaging (SPI) is the classification of structural heterogeneity, which is especially difficult given the low signal-to-noise ratios of individual patterns and that even identical objects can yield patterns that vary greatly when orientation is taken into consideration. We propose two methods which explicitly account for this orientation-induced variation and can robustly determine the structural landscape of a sample ensemble. The first, termed common-line principal component analysis (PCA) provides a rough classification which is essentially parameter-free and can be run automatically on any SPI dataset. The second method, utilizing variation auto-encoders (VAEs) can generate 3D structures of the objects at any point in the structural landscape. We implement both these methods in combination with the noise-tolerant expand-maximize-compress (EMC) algorithm and demonstrate its utility by applying it to an experimental dataset from gold nanoparticles with only a few thousand photons per pattern and recover both discrete structural classes as well as continuous deformations. These developments diverge from previous approaches of extracting reproducible subsets of patterns from a dataset and open up the possibility to move beyond studying homogeneous sample sets and study open questions on topics such as nanocrystal growth and dynamics as well as phase transitions which have not been externally triggered.

eess.IV↗

arXiv2020

New aerodynamic lens injector for single particle diffractive imaging

An aerodynamic lens injector was developed specifically for the needs of single-particle diffractive imaging experiments at free-electron lasers. Its design allows for quick changes of injector geometries and focusing properties in order to optimize injection for specific individual samples. Here, we present results of its first use at the FLASH free-electron-laser facility. Recorded diffraction patterns of polystyrene spheres are modeled using Mie scattering, which allowed for the characterization of the particle beam under diffractive-imaging conditions and yield good agreement with particle-trajectory simulations.

physics.ins-det↗

arXiv2020

An encryption-decryption framework for validating single-particle imaging

We propose an encryption-decryption framework for validating diffraction intensity volumes reconstructed using single-particle imaging (SPI) with x-ray free-electron lasers (XFELs) when the ground truth volume is absent. This framework exploits each reconstructed volumes' ability to decipher latent variables (e.g. orientations) of unseen sentinel diffraction patterns. Using this framework, we quantify novel measures of orientation disconcurrence, inconsistency, and disagreement between the decryptions by two independently reconstructed volumes. We also study how these measures can be used to define data sufficiency and its relation to spatial resolution, and the practical consequences of focusing XFEL pulses to smaller foci. This framework overcomes critical ambiguities in using Fourier Shell Correlation (FSC) as a validation measure for SPI. Finally, we show how this encryption-decryption framework naturally leads to an information-theoretic reformulation of the resolving power of XFEL-SPI, which we hope will lead to principled frameworks for experiment and instrument design.

physics.data-an↗

arXiv2020

3D diffractive imaging of nanoparticle ensembles using an X-ray laser

We report the 3D structure determination of gold nanoparticles (AuNPs) by X-ray single particle imaging (SPI). Around 10 million diffraction patterns from gold nanoparticles were measured in less than 100 hours of beam time, more than 100 times the amount of data in any single prior SPI experiment, using the new capabilities of the European X-ray free electron laser which allow measurements of 1500 frames per second. A classification and structural sorting method was developed to disentangle the heterogeneity of the particles and to obtain a resolution of better than 3 nm. With these new experimental and analytical developments, we have entered a new era for the SPI method and the path towards close-to-atomic resolution imaging of biomolecules is apparent.

physics.app-ph↗

arXiv2020

Photon statistics and signal to noise ratio for incoherent diffraction imaging

Intensity interferometry is a well known method in astronomy. Recently, a related method called incoherent diffractive imaging (IDI) was proposed to apply intensity correlations of x-ray fluorescence radiation to determine the 3D arrangement of the emitting atoms in a sample. Here we discuss inherent sources of noise affecting IDI and derive a model to estimate the dependence of the signal to noise ratio (SNR) on the photon counts per pixel, the temporal coherence (or number of modes), and the shape of the imaged object. Simulations in two- and three-dimensions have been performed to validate the predictions of the model. We find that contrary to coherent imaging methods, higher intensities and higher detected counts do not always correspond to a larger SNR. Also, larger and more complex objects generally yield a poorer SNR despite the higher measured counts. The framework developed here should be a valuable guide to future experimental design.

physics.optics↗

arXiv2020

Low-signal limit of X-ray single particle imaging

An outstanding question in X-ray single particle imaging experiments has been the feasibility of imaging sub 10-nm-sized biomolecules under realistic experimental conditions where very few photons are expected to be measured in a single snapshot and instrument background may be significant relative to particle scattering. While analyses of simulated data have shown that the determination of an average image should be feasible using Bayesian methods such as the EMC algorithm, this has yet to be demonstrated using experimental data containing realistic non-isotropic instrument background, sample variability and other experimental factors. In this work, we show that the orientation and phase retrieval steps work at photon counts diluted to the signal levels one expects from smaller molecules or with weaker pulses, using data from experimental measurements of 60-nm PR772 viruses. Even when the signal is reduced to a fraction as little as 1/256, the virus electron density determined using ab initio phasing is of almost the same quality as the high-signal data. However, we are still limited by the total number of patterns collected, which may soon be mitigated by the advent of high repetition-rate sources like the European XFEL and LCLS-II.

eess.IV↗