Three-Dimensional Scattering Research Articles

Phaseless inverse scattering with a parametrized spatial spectral volume integral equation for finite scatterers in the soft x-ray regime

Soft x-ray wafer-metrology experiments are characterized by low signal-to-noise ratios and lack phase information, which both cause difficulties with the accurate three-dimensional profiling of small geometrical features of structures on a wafer. To this end, we extend an existing phase-based inverse-scattering method to demonstrate a sub-nanometer and noise-robust reconstruction of the targets by synthetic soft x-ray scatterometry experiments. The targets are modeled as three-dimensional finite dielectric scatterers embedded in a planarly layered medium, where a scatterer’s geometry and spatial permittivity distribution are described by a uniform polygonal cross section along its height. Each cross section is continuously parametrized by its vertices and homogeneous permittivity. The combination of this parametrization of the scatterers and the employed Gabor frames ensures that the underlying linear system of the spatial spectral Maxwell solver is continuously differentiable with respect to the parameters for phaseless inverse-scattering problems. In synthetic demonstrations, we demonstrate the accurate and noise-robust reconstruction of the parameters without any regularization term. Most of the vertex parameters are retrieved with an error of less than λ/13 with λ=13.5nm, when the ideal sensor model with shot noise detects at least five photons per sensor pixel. This corresponds to a signal-to-noise ratio of 3.5 dB. These vertex parameters are retrieved with an accuracy of λ/90 when the signal-to-noise ratio is increased to 10 dB, or approximately 100 photons per pixel. The material parameters are retrieved with errors ranging from 0.05% to 5% for signal-to-noise ratios between 10 dB and 3.5 dB.

A Three-Dimensional Hydrophobic Surface-Enhanced Raman Scattering Sensor via a Silver-Coated Polytetrafluoroethylene Membrane for the Direct Trace Detection of Molecules in Water.

We report a three-dimensional (3D) SERS substrate consisting of a silver nanoparticle (AgNP) coating on the skeleton-fiber surfaces of a polytetrafluoroethylene (PTFE) membrane. Simple thermal evaporation was employed to deposit Ag onto the PTFE membrane to produce grape-shaped AgNPs. The 3D-distributed AgNPs exhibit not only strong localized surface plasmon resonance (LSPR) but also strong hydrophobic performance. High-density hotspots via silver nano-grape structures and nanogaps, the large 3D interaction volume, and the large total surface area, in combination with the hydrophobic enrichment of the specimen, facilitate high-sensitivity sensing performance of such a SERS substrate for the direct detection of low-concentration molecules in water. An enhancement factor of up to 1.97 × 1010 was achieved in the direct detection of R6G molecules in water with a concentration of 10-13 mol/L. The lowest detection limit of 100 ppt was reached in the detection of melamine in water. Such a SERS sensor may have potential applications in food-safety control, environmental water pollution monitoring, and biomedical analysis.

Analyzing Three-dimensional Tip Near-field Scattering of Infrared Polaritons through Peak Force Scattering-type Near-field Optical Microscopy.

Analyzing Three-dimensional Tip Near-field Scattering of Infrared Polaritons through Peak Force Scattering-type Near-field Optical Microscopy.

Neural Operator-Based Surrogate Solver for Free-Form Electromagnetic Inverse Design

Neural operators have emerged as a powerful tool for solving partial differential equations in the context of scientific machine learning. Here, we implement and train a modified Fourier neural operator as a surrogate solver for electromagnetic scattering problems and compare its data efficiency to existing methods. We further demonstrate its application to the gradient-based nanophotonic inverse design of free-form, fully three-dimensional electromagnetic scatterers, an area that has so far eluded the application of deep learning techniques.

Three-Dimensional Surface-Enhanced Raman Scattering Platform with Hotspots Built by a Nano-mower for Rapid Detection of MRSA.

Methicillin-resistant Staphylococcus aureus (MRSA) has become one of the greatest threats to human health due to its strong drug resistance, wide distribution range, and high infection rate. Rapid identification of MRSA strains is very important for accurate diagnosis and early treatment of MRSA infections. Here, we introduced an Exo III-assisted nanomotor mower to build 3D hotspots for rapid detection of MRSA by surface-enhanced Raman scattering (SERS). As the bacteria bound to the aptamer, two trigger chains were released from the double-stranded structure, and the nano-mowers were activated by opening a hairpin probe on gold nanoparticles (AuNPs). With the continued cleavage of Exo III and cyclic release of the trigger chain, multiple hairpin DNAs on the AuNPs were cleaved to increase the motor power. The resulting nano-mower continued slicing protective DNA from larger AuNPs, exposing the AuNPs. Without the protection of DNA, Mg2+ in the buffer induced spontaneous aggregation of the AuNPs, and a large number of hotspots were formed for SERS measurements. Under optimal conditions, MRSA can be detected within 40 min, and the concentration of MRSA showed a good linear relationship with the SERS intensity at 1342 cm-1, with a limit of detection as low as 1 CFU/mL and a wide linear range (100 to 107 CFU/mL). This strategy creates a rapid bacterial detection method that performs well on actual samples utilizing portable Raman spectroscopy instruments, with potential applications in food detection, water detection, clinical treatment, and diagnosis.

ZnO nanoparticles functionalized SWCNTs as highly sensitive SERS substrate for heavy metal ions detection

This report presents the most effective and novel approach to fabricate a three-dimensional (3D) Surface-Enhanced Raman Scattering (SERS) substrate for detection of heavy metal ions in the environment. Firstly, Single Wall Carbon Nanotubes (SWCNTs) are synthesized by Plasma Enhanced Chemical Vapor Deposition (PECVD) technique at low temperature. Then, the surface of SWCNTs is functionalized by Zinc Oxide nanoparticles (ZnO NPs) using thermal evaporation technique to achieve ZnO@SWCNTs nanocomposite film as a SERS substrate. The ZnO@SWCNTs with 3D nanostructure increases the coverage of plasmonic nanostructure. The effect of intertube and interparticle coupling generates the multitude ‘hot spots’ with a strong SERS effect. Different characterization techniques- Field Emission Scanning Electron Microscope (FESEM), X-Ray Diffraction (XRD), UV–Vis and Raman spectroscopy were performed. For detection of heavy metal ions, the Raman spectra are recorded for samples of different metal ions- Pb2+, Hg2+, Cd2+, Cu2+, and As2+. The proposed substrate demonstrates high sensitivity, selectivity and very low Limit of detection of the order of 0.225 nM with high stability and repeatability for Pb2+. Therefore, the proposed ZnO@SWCNTs nanocomposite SERS substrate can be used as a powerful tool for the detection of heavy metal ion- Pb2+ in aqueous solutions for a green environment.

Ultrasound simulation of blood with different red blood cell aggregations and concentrations

Considerable progress of ultrasound simulation on blood has enhanced the characterizing of red blood cell (RBC) aggregation. A novel simulation method aims at modeling the blood with different RBC aggregations and concentrations is proposed. The modeling process is as follows: (i) A three-dimensional scatterer model is first built by a mapping with a Hilbert space-filling curve from the one-dimensional scatterer distribution. (ii) To illustrate the relationship between the model parameters and the RBC aggregation level, a variety of blood samples are prepared and scanned to acquire their radiofrequency signals in-vitro. (iii) The model parameters are determined by matching the Nakagami-distribution characteristics of envelope signals simulated from the model with those measured from the blood samples. Nakagami metrics m estimated from 15 kinds of blood samples (hematocrits of 20%, 40%, 60% and plasma concentrations of 15%, 30%, 45%, 60%, 75%) are compared with metrics estimated by their corresponding models (each with different eligible parameters). Results show that for the three hematocrit levels, the mean and standard deviation of the root-mean-squared deviations of m are 0.27 ± 0.0026, 0.16 ± 0.0021, 0.12 ± 0.0018 respectively. The proposed simulation model provides a viable data source to evaluate the performance of the ultrasound-based methods for quantifying RBC aggregation.

Silver Nanoparticle-Decorated Chitosan Aerogels as Three-Dimensional Porous Surface-Enhanced Raman Scattering Substrates for Ultrasensitive Detection

Silver Nanoparticle-Decorated Chitosan Aerogels as Three-Dimensional Porous Surface-Enhanced Raman Scattering Substrates for Ultrasensitive Detection

Three-Dimensional Elastic Scattering Coefficients and Enhancement of the Elastic Near Cloaking

This paper is concerned with the elastic near cloaking for the Lamé system in three-dimensions using the notion of elastic scattering coefficients (ESC). Accordingly, the ESC of arbitrary three-dimensional objects are designed and some of their properties are discussed using elements of the elastic layer potential theory. Then, near-cloaking structures, coined as ESC-vanishing-structures, are constructed for the elastic cloaking at a fixed frequency or a band of frequencies. These multi-layered structures are designed so that their first few significant ESC vanish ahead of transformation-elastodynamics. The invisibility effect is achieved as the arbitrary elastic object inside the cloak has near-zero scattering cross-section for a band of frequencies. The cloaking effect for the Lamé system is significantly enhanced by the proposed near-cloaking structures.

An Improved Subspace-Regularized DBIM-MLGFIM Method for Three-Dimensional Inverse Scattering Problems

The repetitive computation of the forward problem in distorted Born iterative method (DBIM)-type inversion method is time-consuming and memory-costly, especially in dealing with 3-D inverse scattering problem. An improved subspace-regularized DBIM is proposed for the efficient solution of the 3-D inverse problem, which introduces the multilevel Green’s function interpolation method (MLGFIM) to accelerate the computation of the forward problem. In order to stabilize the inversion, an improved subspace-regularized DBIM is used with one new subspace-regularized induced current term in the cost function in virtue of truncated singular value decomposition (TSVD). To further reduce the computation burden, the incident field induced with updated inhomogeneous background medium is used approximately as the total field in the cost function, which saves one forward solver calculation in each iteration. Besides, the resource-intensive multiplication of inhomogeneous Green’s function can be avoided, which further improves the efficiency. Three numerical and two Fresnel experimental examples are given to demonstrate both the efficiency of the forward solver and the accuracy of the inversion algorithm.

ISAR Image Matching and Three-Dimensional Scattering Imaging Based on Extracted Dominant Scatterers

This paper studies inverse synthetic aperture radar (ISAR) image matching and three-dimensional (3D) scattering imaging based on extracted dominant scatterers. In the condition of a long baseline between two radars, it is easy for obvious rotation, scale, distortion, and shift to occur between two-dimensional (2D) radar images. These problems lead to the difficulty of radar-image matching, which cannot be resolved by motion compensation and cross-correlation. What is more, due to the anisotropy, existing image-matching algorithms, such as scale invariant feature transform (SIFT), do not adapt to ISAR images very well. In addition, the angle between the target rotation axis and the radar line of sight (LOS) cannot be neglected. If so, the calibration result will be smaller than the real projection size. Furthermore, this angle cannot be estimated by monostatic radar. Therefore, instead of matching image by image, this paper proposes a novel ISAR imaging matching and 3D imaging based on extracted scatterers to deal with these issues. First, taking advantage of ISAR image sparsity, radar images are converted into scattering point sets. Then, a coarse scatterer matching based on the random sampling consistency algorithm (RANSAC) is performed. The scatterer height and accurate affine transformation parameters are estimated iteratively. Based on matched scatterers, information such as the angle and 3D image can be obtained. Finally, experiments based on the electromagnetic simulation software CADFEKO have been conducted to demonstrate the effectiveness of the proposed algorithm.

Three-Dimensional Time-Harmonic Electromagnetic Scattering Problems from Bianisotropic Materials and Metamaterials: Reference Solutions Provided by Converging Finite Element Approximations

A recently developed theory is applied to deduce the well posedness and the finite element approximability of time-harmonic electromagnetic scattering problems involving bianisotropic media in free-space or inside waveguides. In particular, three example problems are considered of which one deals with scattering from plasmonic gratings that exhibit bianisotropy while the other two deal with bianisotropic obstacles inside waveguides. The hypotheses that guarantee the reliability of the numerical results are verified, and the ranges of the constitutive parameters of the media involved for which the finite element solutions are guaranteed to be reliable are deduced. It is shown that, within these ranges, there can be significant bianisotropic effects for the practical media considered as examples. The ensured reliability of the obtained results can make them useful as benchmarks for other numerical approaches. To the best of our knowledge, no other tool can guarantee reliable solutions.

An Efficient Technique for Solving Inhomogeneous Electromagnetic Inverse Scattering Problems

The electromagnetic inverse scattering approach seeks to obtain the electric characteristics of a scatterer using information about the source and the scattered data. The inverse scattering problem usually suffers from limited knowledge about the scatterer used, which makes its solution more challenging than the forward problem. This paper presents an inversion approach to estimating the unknown electric properties of a two- and three-dimensional inhomogeneous scatterer. The presented approach considers the inverse scattering problem as a global minimization problem with a meshless forward formulation for the computation of the scattered electromagnetic field. Various simulated annealing cooling schedules are applied and assessed to solve the problem, and the results of several case studies are presented for both two- and three-dimensional electromagnetic inverse scattering problems.

基于有限邻域辐射传输的三维云层多次散射近似模型

基于有限邻域辐射传输的三维云层多次散射近似模型

Convexification for a Three-Dimensional Inverse Scattering Problem with the Moving Point Source

For the first time, we develop in this paper the globally convergent convexification numerical method for a coefficient inverse problem for the three-dimensional Helmholtz equation for the case whe...

基于有限邻域辐射传输的三维云层多次散射近似模型

基于有限邻域辐射传输的三维云层多次散射近似模型

Measuring the Three-Dimensional Volume Scattering Functions of Microsphere Suspension: Design and Laboratory Experiments

The measurement of the volume scattering function (VSF) of suspended particles is an ongoing research topic since it has the potential to provide a rapid, nondestructive means of analyzing hydrosols. Despite the success of scattering theory, the measurement of multidirectional scattering intensity distributions over a wide, continuous range of scattering angles and multiple scattering planes, which is described by a three-dimensional VSF (3D VSF), has proven to be difficult. To measure the 3D VSF of submicron particles suspended in water, a measurement approach is proposed, built and tested with several standard submicron particles with diameters ranging from 60 nm to 1 μm. The experimental results indicate that the proposed setup can obtain an accurate 3D VSF for scattering angles from 21° to 160° and azimuthal angles from 1° to 179°. Comparisons between the experiment and theory show a high level of consistency for particles with diameters less than 200 nm. The variation in the VSF in response to the polarization direction of the incident light is also discussed. Both the experiment and theory show the potential of the device to detect the 3D VSF of marine submicron biological particles.

Three-Dimensional Surface-Enhanced Raman Scattering Platforms: Large-Scale Plasmonic Hotspots for New Applications in Sensing, Microreaction, and Data Storage.

Surface-enhanced Raman scattering (SERS) is a molecular-specific spectroscopic technique that provides up to 1010-fold enhancement of signature Raman fingerprints using nanometer-scale 0D to 2D platforms. Over the past decades, 3D SERS platforms with additional plasmonic materials in the z-axis have been fabricated at sub-micrometer to centimeter scale, achieving higher hotspot density in all x, y, and z spatial directions and higher tolerance to laser misalignment. Moreover, the flexibility to construct platforms in arbitrary sizes and 3D shapes creates attractive applications besides traditional SERS sensing. In this Account, we introduce our library of substrate-based and substrate-less 3D plasmonic platforms, with an emphasis on their non-sensing applications as microlaboratories and data storage labels. We aim to provide a scientific synopsis on these high-potential yet currently overlooked applications of SERS and ignite new scientific discoveries and technology development in 3D SERS platforms to tackle real-world issues. One highlight of our substrate-based SERS platforms is multilayered platforms built from micrometer-thick assemblies of plasmonic particles, which can achieve up to 1011 enhancement factor. As an alternative, constructing 3D hotspots on non-plasmonic supports significantly reduces waste of plasmonic materials while allowing high flexibility in structural design. We then introduce our emerging substrate-less plasmonic capsules including liquid marbles and colloidosomes, which we further incorporate the latter within an aerosol to form centimeter-scale SERS-active plasmonic cloud, the world's largest 3D SERS platform to date. We then discuss the various emerging applications arising only from these 3D platforms, in the fields of sensing, microreactions, and data storage. An important novel sensing application is the stand-off detection of airborne analytes that are several meters away, made feasible with aerosolized plasmonic clouds. We also describe plasmonic capsules as excellent miniature lab-in-droplets that can simultaneously provide in situ monitoring at the molecular level during reaction, owing to their ultrasensitive 3D plasmonic shells. We highlight the emergence of 3D SERS-based data storage platforms with 10-100-fold higher storage density than 2D platforms, featuring a new approach in the development of level 3 security (L3S) anti-counterfeiting labels. Ultimately, we recognize that 3D SERS research can only be developed further when its sensing capabilities are concurrently strengthened. With this vision, we foresee the creation of highly applicable 3D SERS platforms that excel in both sensing and non-sensing areas, providing modernsolutions in the ongoing Fourth Industrial Revolution.

On the alignment of 3D EBSD data collected by serial sectioning technique

Three-dimensional Electron Back Scattering Diffraction (3D-EBSD) is a technique for microstructure characterization that works by sequential sectioning via mechanical polishing, Focused Ion Beam (FIB) milling or layer ablation by laser. In this technique, consecutive steps of sample preparation and EBSD measurement are employed to extract 2D-EBSD sections and to reconstruct the 3D microstructure. The 3D data collected by the serial sectioning technique, suffer from misalignment between the adjacent sections. In the present work, serial sectioning by mechanical polishing was employed to collect 3D EBSD data of a dual-phase (DP) steel sample. A previously developed algorithm based on the minimization of misorientation between the neighboring sections was utilized to accurately align the consecutive sections. The reconstructed microstructure was then used to validate the accuracy of the alignment algorithm. The results show that the alignment procedure has successfully improved the reconstructed 3D microstructure and produced reconstructed sections, which in terms of microstructural parameters (i.e. grain size and morphology), image quality and kernel average misorientation distribution resemble the results of a directly measured EBSD experiment and can be used to differentiate the 3D morphology and crystallography of martensite from ferrite in DP steels.

Mathematical Model Taking into Account Nonlocal Effects of Plasmonic Structures on the Basis of the Discrete Source Method

The discrete source method is used to develop and implement a mathematical model for solving the problem of scattering electromagnetic waves by a three-dimensional plasmonic scatterer with nonlocal effects taken into account. Numerical results are presented whereby the features of the scattering properties of plasmonic particles with allowance for nonlocal effects are demonstrated depending on the direction and polarization of the incident wave.