Convergent Beam Research Articles

Exploiting commercial micro X-ray fluorescence systems for stereoscopic soft X-ray imaging

Background Commercial micro X-ray fluorescence (μXRF) systems often employ a tilted convergent beam, which can cause a misalignment between X-ray cartography and the corresponding visible images. This misalignment is typically considered a disadvantage, as it hinders the accurate spatial correlation of elemental information. However, this apparent drawback can be exploited to facilitate X-ray stereoscopy. Objective To demonstrate the use of unmodified commercial μXRF equipment to estimate the 3D configurations of metals and voids within a low-atomic-weight matrix, specifically polymethyl methacrylate, and to explore the implications for enhancing μXRF mapping techniques. This approach could have applications in materials science, archaeology, and other fields requiring non-destructive 3D chemical mapping. Methods Using unmodified commercial μXRF equipment, we leveraged both XRF and Compton scattering effects to quantitatively reconstruct the size, position, and depth of embedded tungsten, copper, and silver objects. The study specifically examines how beam divergence affects the acutance of objects located deeper within the sample. Results Our findings indicate a depth estimation bias ranging from 4% to 15% for depths between 24 mm, and a size estimation bias below 3.2%. These results validate the methodology and highlight the robustness of our approach under typical operational settings, suggesting that the technique could be applied to a wide range of samples with minimal modifications to existing μXRF systems. Conclusions The study confirms that the inclination-induced misalignment in μXRF systems can be harnessed to enhance three-dimensional imaging capabilities. Our work establishes a foundation for advancing current μXRF mapping techniques and interpretation strategies, potentially broadening the applications of μXRF in various scientific and industrial fields.

Convergent laser beam shapes: Unveiling the dynamics of Laser-induced elastic waves in composite materials

Overcoming the low signal-to-noise ratio (SNR) in laser ultrasonic testing of composite materials remains a significant challenge. Current efforts focus on enhancing SNR by inserting more energy into the material through temporal and/or spatial modulation of the laser beam. However, potential SNR improvements through wave convergence and wave energy manipulation have been overlooked. This paper addresses this gap by demonstrating the convergence of different wave types to a designated point and by showing the feasibility of directing absorbed laser energy into a specific wave type through spatial modulation of the laser beam. To achieve this, mathematical expressions for the convergent laser beams are derived. Various laser beam profiles are then introduced to the thermoelastic equations and solved using the finite element method. The sample under investigation is a transversely isotropic unidirectional carbon fiber reinforced plastic, characterized by anisotropic thermal expansion coefficients and thermal conductivities. Results reveal pronounced convergence of the intended wave type at the center due to laser beam shaping. This study showcases the ability to direct absorbed laser energy toward a specific wave type through spatial modulation of the laser beam and highlights the role of material anisotropy in energy focusing.

Real-time four-dimensional scanning transmission electron microscopy through sparse sampling

Abstract Four-dimensional scanning transmission electron microscopy (4-D STEM) is a state-of-the-art image acquisition mode used to reveal high and low mass elements at atomic resolution. The acquisition of the electron momenta at each real space probe location allows for various analyses to be performed from a single dataset, including virtual imaging, electric field analysis, as well as analytical or iterative extraction of the object induced phase shift. However, the limiting factor in 4-D STEM is the speed of acquisition which is bottlenecked by the read-out speed of the camera, which must capture a convergent beam electron diffraction (CBED) pattern at each probe position in the scan. Recent developments in sparse sampling and image inpainting (a branch of compressive sensing) for STEM have allowed for real-time recovery of sparsely acquired data from fixed monolithic detectors, Further developments in compressive sensing for 4-D STEM have also demonstrated that acquisition speeds can be increased, i.e., live video rate 4-D imaging is now possible. In this work, we demonstrate the first practical implementations of compressive 4-D STEM for real-time inference on two different scanning transmission electron microscopes.

Large-Angle Rocking Beam Electron Diffraction of Large Unit Cell Crystals Using Direct Electron Detector.

We report a large-angle rocking beam electron diffraction (LARBED) technique for electron diffraction analysis. Diffraction patterns are recorded in a scanning transmission electron microscope (STEM) using a direct electron detector with large dynamical range and fast readout. We use a nanobeam for diffraction and perform the beam double rocking by synchronizing the detector with the STEM scan coils for the recording. Using this approach, large-angle convergent beam electron diffraction (LACBED) patterns of different reflections are obtained simultaneously. By using a nanobeam, instead of a focused beam, the LARBED technique can be applied to beam-sensitive crystals as well as crystals with large unit cells. This paper describes the implementation of LARBED and evaluates the performance using silicon and gadolinium gallium garnet crystals as test samples. We demonstrate that our method provides an effective and robust way for recording LARBED patterns and paves the way for quantitative electron diffraction of large unit cell and beam-sensitive crystals.

Bifocal lenses with adjustable intensities enabled by bilayer liquid crystal structures.

In this paper, we propose bifocal lenses based on bilayer structures composed of a liquid crystal (LC) cell and LC polymer, and the relative intensity of two foci can be adjusted arbitrarily through applying an external voltage. Two LC layers have different light modulation functions: when circularly polarized light passes through the first layer, part of the outgoing light is converted with PB phase modulation and another part is not converted; followed by the second layer, PB modulation of these two parts would be simultaneously realized but with opposite signs; thus the transmitted left- and right-handed circularly polarized (LCP and RCP) light can be independently controlled. As proof-of-concept examples, longitudinal and transverse bifocal lenses are designed to split an incident LCP light into two convergent beams with orthogonal helicity, and the position of the two foci can be flexibly arranged. Benefitting from the electrically controlled polarization conversion efficiency (PCE) of the LC cell, the relative intensity of the two foci can be adjusted arbitrarily. Experimental results agree well with theoretical calculations. Besides, a broadband polarization and an edge imaging system based on the proposed bifocal LC lenses have also been demonstrated. This paper presents a simple method to design a functional multilayer LC device and the proposed bifocal lenses may have potentials in the optical interconnection, biological imaging, and optical computing.

Effect of Laser Beam Overlap Rate on Mechanical Properties of Aluminum Alloy Arc Welding with Laser Peening

This study aims to investigate the effect of the laser beam overlap rate on the mechanical properties of Al3003 aluminum alloy arc weldment with laser peening. To determine the optimal laser beam overlap rate for laser peening of the weldment, peening experiments were conducted on bead-welded and butt-welded specimens with varying overlap rates, and the effect of the beam overlap rate was analyzed. As the overlap rate increased, the residual stress changed from tensile to compressive, with the highest level of compressive residual stress at the overlap rate of 75%. Laser peening was performed on the aluminum weldment of the prototype, applying the optimal peening conditions identified earlier. As a result of comparing the residual stress, hardness, and tensile strength of the weld before and after laser peening, it was found that the tensile residual stress in the weldment was improved to a compressive residual stress of about −50 MPa or more. The hardness and tensile strength of the weld increased after peening, and the mechanical properties were also improved.

Evaluation of beam convergence driven by spherical gradient refractive index lenses based on nonparaxial beam propagation.

We utilize a theoretical method based on nonlinear beam propagation and finite difference eigenmode solver methods to precisely simulate Gaussian beam propagation in electrical fields through spherical gradient refractive index lenses. The theoretical computation uses second-order partial differentiation of propagation coordinates to generate microwave field propagation. Consequently, it offers accurate simulation results for any complex refractive index profile. The reliability of the proposed method is verified by comparing it with existing experimental and theoretical results. We employ the theoretical method to assess Gaussian beam convergence in terms of four key parameters: beam waist, maximum intensity, focal position, and Rayleigh range. The results indicate that gradient index spherical lenses have better convergence than convex thin lenses, as evidenced by a significant reduction in beam waist size. However, these lenses prompt an extremely short back focal length. Consequently, we propose a slight shift in the boundary and index distribution of spherical lenses to expand their back focal lengths.

A Web-Based Interactive Application to Simulate and Correct Distortion in Multibeam Sonars

Multibeam sonars are advanced scientific tools for estimating fish school volume and density, using multiple beams to provide comprehensive size measurements of detected targets. However, challenges remain in accurately estimating target dimensions due to beam geometric expansion and overlap, particularly in athwart-beam measurements, which tend to be overestimated with increasing distance from the transducer. We present an interactive web application that simulates distortion caused by beam overlap and expansion in multibeam sonars using simple geometric equations. Users can define sonar characteristics, such as the number of beams, swath opening, or degree of overlap, as well as specify an elliptical target’s dimensions, orientation, and distance from the transducer. The application estimates and visualises the true and distorted shapes of the target, calculating the level of distortion. It can run simulations in both forward and inverse directions, either simulating the distortion of a true school or correcting the shape of a distorted school. This tool aims to enhance the interpretation of multibeam sonar signals and improve the accuracy of target dimension estimates, facilitating more effective use of these sonars in scientific research.

A new insight into largely defocused HAADF-STEM imaging and visualization of strain field

A crystalline bilayer specimen with a semi-coherent interface can generate moiré fringes in the high-angle annular-dark field scanning transmission electron microscopy (HAADF-STEM) imaging. Moreover, when the probe is significantly defocused, this specimen can produce largely defocused probe (LDP)-STEM patterns. Although the electron channeling effect serves as the fundamental principles for HAADF-STEM imaging, its connection to the emergence of LDP-STEM patterns remains unclear. The missing link lies in identifying the location of the imaged region. To address this issue, we examined the strain field in three-dimensional space and its interaction with the convergent electron beam, taking the PbZrO3/SrTiO3 (PZO/STO) heterostructure as an example. We discovered a new intensity relationship for LDP-STEM patterns in the PZO/STO heterostructure, which can be well explained by our theory. We also found that, generated by imaging the strain zone, these patterns revealed information that might be obscured in traditional high resolution STEM images, showing a unique advantage in characterizing the strain field. Furthermore, we provided discussions on visualizing the strain field, including the misfit dislocation network and array. Our research offers a novel perspective on the LDP-STEM imaging and clarifies the approach to characterizing the strain field.

Four dimensional-scanning transmission electron microscopy study on relationship between crystallographic orientation and spontaneous polarization in epitaxial BiFeO3

Spontaneous polarization and crystallographic orientations within ferroelectric domains are investigated using an epitaxially grown BiFeO3 thin film under bi-axial tensile strain. Four dimensional-scanning transmission electron microscopy (4D-STEM) and atomic resolution STEM techniques revealed that the tensile strain applied is not enough to cause breakdown of equilibrium BiFeO3 symmetry (rhombohedral with space group: R3c). 4D-STEM data exhibit two types of BiFeO3 ferroelectric domains: one with projected polarization vector possessing out-of-plane component only, and the other with that consisting of both in-plane and out-of-plane components. For domains with only out-of-plane polarization, convergent beam electron diffraction (CBED) patterns exhibit “extra” Bragg’s reflections (compared to CBED of cubic-perovskite) that indicate rhombohedral symmetry. In addition, beam damage effects on ferroelectric property measurements were investigated by systematically changing electron energy from 60 to 300 keV.

High performance composite phosphor-in-glass film for laser-driven warm white light on patterned sapphire substrate

Phosphor-in-glass film (PiF) based on sapphire substrate (SS) is a promising laser-driven color converter. Herein, by using an optimized silicon borate glass component, high-performance Y3Al5O12:Ce3+ PiFs are successfully prepared on both flat sapphire substrate (FSS) and patterned sapphire substrate (PSS) surfaces. Compared with planar structure of FSS, PSS has a periodic arrangement of conical structures on its surface, which effectively increases the contact area between the PiF and the substrate by approximately 56%, thereby forming a more robust film composite structure. The blue laser light is affected by the structure of PSS and produces a typical diffraction effect, which realizes the dispersion of the convergent beam. This significantly expands the laser spot on PSS-PiF and improves the uniformity of light. The saturation power density of PiF-PSS (6.29 W/mm2) is found to be 91% higher than that of PiF-FSS, while maintaining a high luminous efficiency (220 lm/W) and a low correlated color temperature (4500 K). Finally, the thermal quenching mechanism of PiF with different substrate surface morphologies is compared and analyzed. The present results provide important support for designing the interface structure between SSs and PiF to achieve higher efficiency and higher saturation threshold for warm white light.

A cone-beam optical CT based on a convergent light source – Characterization and optimization

PurposeEmploying a Fresnel lens and a point-like light source to create a convergent light beam for the camera effectively minimizes stray light and enhances image quality in optical computed tomography (OCT), benefiting 3D dosimetry applications. This study outlines the development of an economical cone-beam optical computed scanner for 3D dosimetry. MethodsOptical performance was assessed by calculating modulation transfer function (MTF) with pattern charts. Stray light was evaluated by imaging a cylinder flask and a square grid with 5 mm diameter holes to determine the stray-to-primary ratio. Reconstruction quality was determined using SIRT-TV and compared with spectrophotometry attenuation coefficients, with the best regularization parameter (λ = 0.01) chosen based on contrast-to-noise ratio (CNR). Dosimetry performance was assessed by determining percentage dose depth (PDD) for a 6MV beam with a 5 × 5 cm2 field using FXO-f gel dosimeter, compared with ionization chamber data. ResultsMTF evaluation yielded ≥ 50 % agreement with pattern charts. Stray-to-primary ratio was less than 0.1 or 10 % of the total signal. Reconstruction showed low noise and artifacts, with optimal CNR at λ = 0.01. Attenuation coefficients from optical CT aligned with spectrometer measurements within 1.2 %. PDD calculated with FXO-f gel dosimeter closely matched ionization chamber data (<1.2 % difference), achieving a dose resolution of 0.1 Gy. ConclusionThe built and optimization the de optical-CT based on a convergent beam is read to perform the 3D quality assurance in clinical applications.

Ba4RuMn2O10: A Noncentrosymmetric Polar Crystal Structure with Disordered Trimers.

Phase-pure polycrystalline Ba4RuMn2O10 was prepared and determined to adopt the noncentrosymmetric polar crystal structure (space group Cmc21) based on results of second harmonic generation, convergent beam electron diffraction, and Rietveld refinements using powder neutron diffraction data. The crystal structure features zigzag chains of corner-shared trimers, which contain three distorted face-sharing octahedra. The three metal sites in the trimers are occupied by disordered Ru/Mn with three different ratios: Ru1:Mn1 = 0.202(8):0.798(8), Ru2:Mn2 = 0.27(1):0.73(1), and Ru3:Mn3 = 0.40(1):0.60(1), successfully lowering the symmetry and inducing the polar crystal structure from the centrosymmetric parent compounds Ba4T3O10 (T = Mn, Ru; space group Cmca). The valence state of Ru/Mn is confirmed to be +4 according to X-ray absorption near-edge spectroscopy. Ba4RuMn2O10 is a narrow bandgap (∼0.6 eV) semiconductor exhibiting spin-glass behavior with strong magnetic frustration and antiferromagnetic interactions.

A study on the effect of laser decontamination by beam overlap rate of crud formed on aluminum alloy

The corrosion products formed on the internal surfaces of the primary system are the major factor that generates radioactive contaminants such as oxide films and cruds during decommissioning, causing radiation exposure to workers. Thus, decontamination of nuclear facility surfaces is crucial to ensure the safe completion of decommissioning work. This study applied laser decontamination, which enables precise work while minimizing the deformation of the material surface through the control of process parameters, and investigated the characteristics of the decontaminated area. Specimens coated with Ni-ferrite on an aluminum alloy (A6061) substrate were fabricated and used in this experiment. Laser decontamination was performed using a low-power Q’switching fiber laser while varying the laser beam overlap rate and number of scans. The results of laser decontamination differed by the process parameters and material characteristics. It is determined that high decontamination efficiency can be achieved if appropriate conditions are applied.

High-speed 4-dimensional scanning transmission electron microscopy using compressive sensing techniques.

Here we show that compressive sensing allows 4-dimensional (4-D) STEM data to be obtained and accurately reconstructed with both high-speed and reduced electron fluence. The methodology needed to achieve these results compared to conventional 4-D approaches requires only that a random subset of probe locations is acquired from the typical regular scanning grid, which immediately generates both higher speed and the lower fluence experimentally. We also consider downsampling of the detector, showing that oversampling is inherent within convergent beam electron diffraction (CBED) patterns and that detector downsampling does not reduce precision but allows faster experimental data acquisition. Analysis of an experimental atomic resolution yttrium silicide dataset shows that it is possible to recover over 25 dB peak signal-to-noise ratio in the recovered phase using 0.3% of the totaldata. Lay abstract: Four-dimensional scanning transmission electron microscopy (4-D STEM) is a powerful technique for characterizing complex nanoscale structures. In this method, a convergent beam electron diffraction pattern (CBED) is acquired at each probe location during the scan of the sample. This means that a 2-dimensional signal is acquired at each 2-D probe location, equating to a 4-D dataset. Despite the recent development of fast direct electron detectors, some capable of 100kHz frame rates, the limiting factor for 4-D STEM is acquisition times in the majority of cases, where cameras will typically operate on the order of 2kHz. This means that a raster scan containing 256^2 probe locations can take on the order of 30s, approximately 100-1000 times longer than a conventional STEM imaging technique using monolithic radial detectors. As a result, 4-D STEM acquisitions can be subject to adverse effects such as drift, beam damage, and sample contamination. Recent advances in computational imaging techniques for STEM have allowed for faster acquisition speeds by way of acquiring only a random subset of probe locations from the field of view. By doing this, the acquisition time is significantly reduced, in some cases by a factor of 10-100 times. The acquired data is then processed to fill-in or inpaint the missing data, taking advantage of the inherently low-complex signals which can be linearly combined to recover the information. In this work, similar methods are demonstrated for the acquisition of 4-D STEM data, where only a random subset of CBED patterns are acquired over the raster scan. We simulate the compressive sensing acquisition method for 4-D STEM and present our findings for a variety of analysis techniques such as ptychography and differential phase contrast. Our results show that acquisition times can be significantly reduced on the order of 100-300 times, therefore improving existing frame rates, as well as further reducing the electron fluence beyond just using a faster camera.

3D electron diffraction goes multipolar.

Over 30 years ago, it was shown that bonding between atoms has a noticeable effect on convergent beam electron diffraction patterns. The paper by Olech et al. [(2024). IUCrJ, 11, 309-324] demonstrates that its influence is also clearly present in 3D electron diffraction data, opening up new possibilities for quantum crystallography.

Effect of energy distribution on laser cleaning quality of 30Cr3 ultra-high strength steel

30Cr3 is a novel ultra-high strength steel (UHSS) with excellent strength and plastic toughness, which has been mainly used in aerospace shells and stressed parts. Currently, there is still a lack of systematic research and comprehensive evaluation on the laser cleaning of this particular material. In this study, a nanosecond pulsed laser was employed for the cleaning process. First, the energy distribution model was derived, the influence of the spatial and temporal distribution of laser energy on the cleaning quality was discussed, and the cleaning experiment was conducted. The results showed that a laser energy density of 15 J/cm2, combined with the beam overlap rate 52% in the x-direction and 61% in the y-direction, can effectively remove the oxide layer and thoroughly expose the natural metal matrix. Then, under the optimum parameters, the oxygen content decreased from 22.3% to 3.4%, the Fe content increased from 54.5 to 83.4%, the Fe3+ peak disappeared in the X-ray photoelectron spectroscopy (XPS), a remelted layer of only 1 μm was observed. Last, the roughness was slightly reduced from 3.573 μm to 2.985 μm, the hardness was restored to the original hardness level of the substrate (∼260 HV), and the electron back scatter diffraction (EBSD) showed that the structure hardly changed after cleaning, the grain size was comparable to that of the matrix. These findings indicated that laser cleaning can effectively remove the oxide layer of 30Cr3 UHSS without damaging the properties of the base material, which has promising application in the cleaning of UHSS.

Influence of magnetic field on electron beam-induced Coulomb explosion of gold microparticles in transmission electron microscopy

In this work we instigated the fragmentation of Au microparticles supported on a thin amorphous carbon film by irradiating them with a gradually convergent electron beam inside the Transmission Electron Microscope. This phenomenon has been generically labeled as “electron beam-induced fragmentation” or EBIF and its physical origin remains contested. On the one hand, EBIF has been primarily characterized as a consequence of beam-induced heating. On the other, EBIF has been attributed to beam-induced charging eventually leading to Coulomb explosion. To test the feasibility of the charging framework for EBIF, we instigated the fragmentation of Au particles under two different experimental conditions. First, with the magnetic objective lens of the microscope operating at full capacity, i.e. background magnetic field B=2 T, and with the magnetic objective lens switched off (Lorenz mode), i.e. B=0 T. We observe that the presence or absence of the magnetic field noticeably affects the critical current density at which EBIF occurs. This strongly suggests that magnetic field effects play a crucial role in instigating EBIF on the microparticles. The dependence of the value of the critical current density on the absence or presence of an ambient magnetic field cannot be accounted for by the beam-induced heating model. Consequently, this work presents robust experimental evidence suggesting that Coulomb explosion driven by electrostatic charging is the root cause of EBIF.

Fiber optic photoacoustic gas sensor enhanced by multi-pass cell with overlapping phantom spots

A neotype fiber optic photoacoustic gas sensor with overlapping phantom spots based multi-pass is proposed, which greatly improves the reflection times and the length of gas absorption path. Moreover, the detection accuracy of photoacoustic spectroscopy (PAS) system is independent of the optical interference effect caused by overlapping spots, which is different from tunable diode laser absorption spectroscopy (TDLAS) technology. A mathematical model including light beam motion space, spot size and overlap discrimination of multi-pass structure based on overlapping phantom spots is established. The incident light is reflected up to dozens of times in the resonator with a diameter of only 8 mm. The emergent light does not need to converge on a photodetector, which reduces the difficulty of adjusting the optical path and promotes the realization of overlapping phantom spots. The experimental results show that the amplitude of photoacoustic signal is improved by about 40 times compared with the single spot structure. Appling high-sensitivity optical fiber cantilever to detect the sound pressure signal. The detection limit of C2H2 gas reaches 8.2 ppt. The normalized noise equivalent absorption (NNEA) coefficient of the gas sensor is achieved to be 9.3×10−11 cm−1WHz−1/2.

Vortex electromagnetic wave imaging with orbital angular momentum and waveform degrees of freedom

The vortex electromagnetic wave has shown great prospects of radar applications, due to the orbital angular momentum (OAM) degree of freedom. However, the radiation energy convergence of the OAM beam remains a hard problem to be solved for radar target imaging in realistic scenario. In this paper, an OAM beam generation method is developed exploiting the OAM and waveform degrees of freedom simultaneously, which can collimate the beams with different OAM modes. Furthermore, the echo demodulation and the imaging methods are proposed to reconstruct the target profiles in the range and azimuth domain. Simulation and experimental results both validate that the OAM-based radar imaging can achieve azimuthal super-resolution beyond the diffraction limit of the array aperture. This work can advance the system design of vortex electromagnetic wave radar and its real-world applications.