Centroid Position Research Articles

Direct tool for quantitative analysis of cell/object dynamic behavior – metastasis and far beyond

IntroductionThe dynamics and depth of invasion as well as the ability of cancer cells to penetrate the walls of lymphatic or blood vessels represent critical survival-influencing factors in cancer patients. Depending on the cell type and tissue environment, cancer cell invasion differ in terms of motility mechanism and migration modes. Thus, there is the need of effective models allowing not only for single cell invasion potential assessment but also for collective migration and expansive growth evaluation in 3D microenvironment e.g. basement membranes. To meet this task, the specimens should be compared and analyzed in terms of the dynamics of movement and the evolution of the shape. ObjectivesOur main objective was development of the mathematical method that enables fast and credible calculation of parameters of shape and position, namely standard deviations (σX, σY), centroid position (μX, μY) and correlation coefficient ρ, based only on the contour of the aggregate. MethodsIn order to accomplish this goal we measured geometrical properties of aggregates of RGM1 cells seeded in 3D Geltrex basement membrane. Referential microscopic images were taken 24 and 48 h after seeding and cell group dynamics was registered over 8 h periods using time lapse microscopy. ResultsBased on gathered data, we managed to develop and fully test universal numerical tool allowing for estimation of statistical parameters of cell groups and aggregates which then allows for the precise evaluation of their behavior within microenvironment with time. ConclusionWe conclude, that our tool is suitable for any research on the metastatic potential and motility of cancer cells in a given microenvironment, regardless of the migration mechanism, which together with the advanced analysis like cell single-cell transcriptomic, proteomic, and chromatin accessibility data may allow to identify precise targets for anti-cancer therapies, to predict the degree of malignancy of neoplastic lesions as well as it can be useful during architecting therapeutic strategies. Moreover, the developed tool seems to be broadly applicable for assessment of behavioural dynamics of any population.

Research on Indoor 3D Positioning Model Using Improved Triangular Centroid Position Algorithm Based on UWB

The indoor positioning technology of an ultra-wideband (UWB) can play an excellent supplementary role in satellite navigation and has broad application prospects. However, if strong interference exists, the measurement data based on UWB will fluctuate abnormally, which seriously affects the accuracy of positioning. In view of the above problems, based on the combination of mathematical modeling, this paper starts from the subject data, and proposes a positioning method suitable for non-interference/interference conditions and an abnormal data identification method to improve the positioning accuracy. The specific scheme includes data preprocessing model establishment and solution, positioning model establishment and solution, migration application of positioning model, interfering data identification model establishment and solution, and movement track positioning model establishment and solution.

Surface Imaging-Guided Adaptive Radiotherapy (ART): Imaging Protocol and Verification for Inter- and Intra-Fractional Motion Managements

<h3>Purpose/Objective(s)</h3> CBCT-guided adaptive radiotherapy (CT-ART) has proven to account for inter-fractional anatomic changes. However, no commercial solution for intra-fractional respiratory motion management existed in CT-ART. Therefore, we investigated intra-fractional motion-managed treatment strategies in CT-ART (or Image-guided RT: IGRT) using optical surface imaging combined with <i>in-situ</i> CBCTs. <h3>Materials/Methods</h3> Eight of ten cancer patients with mobile lower lung or upper abdominal malignancies have completed CT-ART (or IGRT) using Ethos radiotherapy in an IRB-approved clinical trial (phase I). Four of the eight patients underwent additional MR simulations, including cine MRIs, to estimate the tumor/abdominal skin motion correlation. In CT-ART, a pre-configured gating window (±2 mm in vertical position) on surface imaging was used for manually triggering intra-fractional CBCT and treatment beam irradiation in breath-hold (six patients for exhalation and two patients for inhalation). A donut-shaped imaging-surrogate on patient's abdomen was used to localize Region of Interest (ROI) of the abdomen on CBCTs. Two inter-fractional CBCTs at exhalation and inhalation in each fraction were acquired to verify the tumor/imaging-surrogate motions range. Intra-fractional CBCTs were used to quantify the residual motion of the tumor/imaging-surrogate within the pre-configured gating window. Tumor motion was measured by tracking the position of a tumor centroid. <h3>Results</h3> The pre-configured gating window on surface imaging was confirmed based on the correlation of the tumor and abdominal skin motions using cine MRIs. Thirty-six pairs of inter-fractional CBCTs and 100 intra-fractional CBCTs from 36 fractions were analyzed (13 fractions for IGRT and 23 for ART). In the motion range study from the inter-fractional CBCTs, the values of mean ± std were 17.3 ± 12.0 mm in the SI direction for the tumors and 16.6 ± 7.9 mm in the AP direction for the imaging-surrogate, respectively. The residual motion of the imaging-surrogate from intra-fractional CBCTs was 2.5 ± 2.1 mm for SI, 2.3 ± 2.0 mm for RL, and 2.1 ± 2.3 mm for AP directions. The residual motion of the tumors was 2.4 ± 3.1 mm for SI, 2.3 ± 2.3 mm for RL, and 2.2 ± 2.0 mm for AP directions. Trends in the residual motion during the course of treatment fractions and over time through delivery were stable. Inter-fractional residual motions of the tumors were 2.3 ± 0.8 mm for SI, 2.3 ± 0.6 mm for RL, and 2.2 ± 0.7 mm for AP directions. Intra-fractional residual motions of the tumors were 2.4 ± 0.9 mm for SI, 2.4 ± 0.7 mm for RL, and 3.2 ± 1.3 mm for AP. <h3>Conclusion</h3> We demonstrated the inter- and intra-fractional motion-managed treatment strategies in CBCT-guided ART using surface imaging. Since the residual motion of the tumors was comparable to that of the imaging-surrogate within clinical PTV margins (5 mm) but a bit larger than the pre-configured gating window, additional caution is needed with intra-fractional motion management in CT-ART using the optical surface imaging.

Shack–Hartmann wavefront sensor based on Kalman filter

The Shack–Hartmann wavefront sensor (SHWFS) traditionally employs the center of gravity (CoG), windowing, and thresholding CoG (TCoG) algorithms to measure wavefront aberrations. Nevertheless, these algorithms yield low accuracy in a low signal-to-noise ratio (SNR) environment, and therefore, we propose a measurement algorithm based on the Kalman filter to correct the three algorithms’ centroid position of the Shack–Hartmann spot. When the Euclidean distance between the reference centroid in a sub-aperture and the measurement centroid exceeds a certain threshold, the sub-apertures centroid position is untrusted and must be corrected. Several simulation experiments are conducted in three environments: no noise, Poisson noise, and Gaussian noise; they demonstrate that the proposed algorithm effectively improves the centroid’s accuracy by more than 10% and ensures real-time performance for the adaptive optics system. In addition, experimental results on wavefront reconstruction tasks reveal that our algorithm produces wavefronts close to the original.

Assessment of intrafractional prostate motion and its dosimetric impact in MRI-guided online adaptive radiotherapy with gating

PurposeThis study aimed to evaluate the intrafractional prostate motion captured during gated magnetic resonance imaging (MRI)-guided online adaptive radiotherapy for prostate cancer and analyze its impact on the delivered dose as well as the effect of gating.MethodsSagittal 2D cine-MRI scans were acquired at 4 Hz during treatment at a ViewRay MRIdian (ViewRay Inc., Oakwood Village, OH, USA) MR linac. Prostate shifts in anterior–posterior (AP) and superior–inferior (SI) directions were extracted separately. Using the static dose cloud approximation, the planned fractional dose was shifted according to the 2D gated motion (residual motion in gating window) to estimate the delivered dose by superimposing and averaging the shifted dose volumes. The dose of a hypothetical non-gated delivery was reconstructed similarly using the non-gated motion. For the clinical target volume (CTV), rectum, and bladder, dose–volume histogram parameters of the planned and reconstructed doses were compared.ResultsIn total, 174 fractions (15.7 h of cine-MRI) from 10 patients were evaluated. The average (±1 σ) non-gated prostate motion was 0.6 ± 1.0 mm in the AP and 0.0 ± 0.6 mm in the SI direction with respect to the centroid position of the gating boundary. 95% of the shifts were within [−3.5, 2.7] mm in the AP and [−2.9, 3.2] mm in the SI direction. For the gated treatment and averaged over all fractions, CTV D98% decreased by less than 2% for all patients. The rectum and the bladder D2% increased by less than 3% and 0.5%, respectively. Doses reconstructed for gated and non-gated delivery were similar for most fractions.ConclusionA pipeline for extraction of prostate motion during gated MRI-guided radiotherapy based on 2D cine-MRI was implemented. The 2D motion data enabled an approximate estimation of the delivered dose. For the majority of fractions, the benefit of gating was negligible, and clinical dosimetric constraints were met, indicating safety of the currently adopted gated MRI-guided treatment workflow.

Language universal font watermarking with multiple cross-media robustness

The rapid development of digital devices and the increasing demand for copyright protection and leakage tracing of documents result in new demands for robust text watermarking. It becomes more important for a utility text watermarking scheme to have robustness in cross-media channels since the camera shooting operation to papers or screens has become very convenient. To achieve the corresponding cross-media robustness, this paper proposes a font-based text watermarking scheme, which is applicable to most commonly used languages while the previous works were usually designed for specific languages. To generate fonts with high efficiency, we propose a novel glyph centroid modification-based font generation algorithm, which can automatically create target-similar fonts. And we design an effective watermarking scheme that utilizes the relative centroid position (RCP) of glyphs to represent watermark signals. Compared with existing font-based text watermarking schemes that artificially design fonts, the proposed scheme ensures higher efficiency by generating the font codebook automatically. In addition, the proposed RCP-based watermarking scheme can achieve the robustness against lossy compression and several kinds of cross-media distortions. The watermark message can be extracted without the need to recognize the semantic information of glyphs by optical character recognition (OCR).

NDG-CAM: Nuclei Detection in Histopathology Images with Semantic Segmentation Networks and Grad-CAM.

Nuclei identification is a fundamental task in many areas of biomedical image analysis related to computational pathology applications. Nowadays, deep learning is the primary approach by which to segment the nuclei, but accuracy is closely linked to the amount of histological ground truth data for training. In addition, it is known that most of the hematoxylin and eosin (H&E)-stained microscopy nuclei images contain complex and irregular visual characteristics. Moreover, conventional semantic segmentation architectures grounded on convolutional neural networks (CNNs) are unable to recognize distinct overlapping and clustered nuclei. To overcome these problems, we present an innovative method based on gradient-weighted class activation mapping (Grad-CAM) saliency maps for image segmentation. The proposed solution is comprised of two steps. The first is the semantic segmentation obtained by the use of a CNN; then, the detection step is based on the calculation of local maxima of the Grad-CAM analysis evaluated on the nucleus class, allowing us to determine the positions of the nuclei centroids. This approach, which we denote as NDG-CAM, has performance in line with state-of-the-art methods, especially in isolating the different nuclei instances, and can be generalized for different organs and tissues. Experimental results demonstrated a precision of 0.833, recall of 0.815 and a Dice coefficient of 0.824 on the publicly available validation set. When used in combined mode with instance segmentation architectures such as Mask R-CNN, the method manages to surpass state-of-the-art approaches, with precision of 0.838, recall of 0.934 and a Dice coefficient of 0.884. Furthermore, performance on the external, locally collected validation set, with a Dice coefficient of 0.914 for the combined model, shows the generalization capability of the implemented pipeline, which has the ability to detect nuclei not only related to tumor or normal epithelium but also to other cytotypes.

Automatic pointer meters recognition system based on line scan vision

The automatic recognition of pointers is of great significance for efficiently collecting measurements from industrial instruments. In this paper, an automatic pointer meter recognition system based on line scan vision is developed. A line scan camera is used to capture images of the pointer of a pointer meter. Light-spot centroid algorithm is implemented to determine the centroid position of the pointer. The captured images can record the dynamic movement of the pointer, thereby enabling condition monitoring in industrial processes. Experimental results show that the proposed pointer meter extraction method is robust against interference and that a characteristic segmentation classifier produces more accurate detection results than other approaches.

Controllable Peculiar Spin‐Dependent Transverse and In‐Plane Shifts of Airy Beam

AbstractGenerally, most of the photonic spin Hall effect (SHE) are investigated based on the Gaussian beam, and the research of the photonic SHE in novel beams with non‐Gaussian distribution is relatively rare. The Airy beam is one of the novel beams whose initial field distribution is asymmetric and tunable. Thus, it is necessary to explore the photonic SHE in the Airy beam. Here analytical solutions for the transverse and in‐plane shifts of the Airy beam are derived, and the peculiar photonic SHE of the Airy beam is systematically researched. The theoretical research results show that the transverse shifts of the left‐ and right‐handed circularly polarized beams are asymmetric, and the in‐plane shifts of the left‐ and right‐handed circularly beams are identical. More importantly, the variation rules of the transverse and in‐plane shifts with the incident centroid position are obtained, and the incident centroid position is regulated by the decay factor of the Airy beam. That is, the spin‐dependent transverse and in‐plane shift can be manipulated flexibly and purposefully by adjusting the beam parameter. It is believed these findings will provide more ideas for exploring the application of the photonic SHE based on novel beams.

Numerical Study on the Influence of Model Uncertainties on the Transport of Underwater Spilled Oil.

Oil pollution influences marine biology, ecology, and regional sustainable development capacity, but model uncertainties limit the ability of the numerical model to accurately predict the transport and fate of the underwater oil spill. Based on a three-dimensional underwater oil spill model validated by satellite images of the oil slick at the sea surface, the Penglai 19-3 oil spill accident in the Bohai Sea was simulated; in addition, several sensitivity experiments were set up to investigate the influence of model uncertainties in the background wind, current, start time of the oil spill, and spill site on the transport of underwater spilled oil in the Penglai 19-3 oil spill accident. The experimental results indicate that the uncertainty in the background wind has a certain impact on the simulated centroid position at the sea surface, and little effect on the simulated underwater results, while the uncertainty in the background current has a significant influence on the transport of the underwater spilled oil both at the sea surface and underwater. An uncertainty of 24 h in the start time of the oil spill can cause more than 1 time larger than the benchmark case displacement of the oil spill centroid point and sweeping area at the sea surface, as the periodic tidal current is the main constituent of the ocean current in the Bohai Sea. The uncertainty in the spill site has a large influence on the final position of the oil spill centroid point, but the oil spill trajectories do not intersect with each other within 48 h, which makes it possible to identify the oil spill platform from the actual observations. The influence of uncertainties in the important model inputs and key model parameters on the transport of underwater spilled oil in the Penglai 19-3 oil spill accident is evaluated for the first time, which is of substantial significance for improving the prediction accuracy of the transport and fate of underwater oil spills.

Sensitivity analysis of low-order plasma moments reconstruction for RFX-mod2 tokamak operations

The reconstruction of total plasma current and plasma centroid position from low-order moments of toroidal current density is presented for RFX-mod2 shaped tokamak equilibria. DEMO-like shape conditions and negative triangularity plasmas are considered in the analysis. The impact of a single sensor failure on the reconstruction is investigated by performing a sensitivity analysis at each possible poloidal position of the faulty sensor. The effects of using mono-axial or bi-axial sensors are also quantified. The minimum number of sensors necessary to estimate both the total plasma current and the centroid position within a certain level of accuracy has been assessed for the wide plasma shape conditions of the considered equilibria.

Characterization model of silicon dioxide melting based On image analysis

The silicon dioxide is the hardest part to melt among the iron tailing components, the melting behavior of iron tailing can be represented by the melting behavior of silicon dioxide. Estimating the real-time melting rate of silicon dioxide in the time sequence provide guidance for the tailing addition and heat compensation in the process of slag cotton preparation, also indirectly improved the direct fiber forming technology of blast furnace slag. The position of silicon dioxide particles in the high-temperature molten pool during the melting process is changing constantly, using a strong weighted distance centroid algorithm to rack the centroid position of silicon dioxide particles during the melting process, and present the motion trail of centroid of silicon dioxide. In the paper, extracting indexes which represent the edge outline characteristics of silicon dioxide during the melting process of silicon dioxide using Snake active contour algorithm combined with Sobel operator, include shape, perimeter and area. Using the extracted skeleton characteristics, a three-dimensional skeleton generation model is created. From the skeleton data, estimating the volume of silicon dioxide and determine the parameter formula for the actual melting rate of silicon dioxide. The silicon dioxide melting rate at each moment is calculated by numerical simulation. The results of the Hough test circle and the silicon dioxide melting rate are verified. The rationality of the model is further determined.

Identification of vehicle axle loads based on visual measurement

Monitoring vehicle axle loads is very important for preventing infrastructure degradation and traffic accidents. However, developing an accurate, cost-effective, and easy-to-implement axle load identification technology still remains challenging. In this study, a vehicle axle load identification method based on visual measurement is proposed. The principle of the method is that each axle load of the vehicle is determined based on the vehicle unsprung masses, the ratio of vehicular sprung mass to unsprung mass, and the centroid position of the sprung mass. While the vehicle unsprung masses can be treated as a known with the vehicle model identified, the mass ratio can be predicted from the visually captured free damped vibrations of the vehicle as it passes over a speed bump. To be more specific, the vibration responses of a vehicle passing over a speed bump are firstly measured by a camera, and the vehicle system matrix, which is composed of the mass matrix, stiffness matrix, and damping matrix, can be obtained from the vehicle responses. The axle load can then be determined based on the element ratios in the system matrix of the vehicle whose unsprung masses are known. The performance of the proposed method was evaluated by numerical simulations and field tests. The results show that the errors of the simulation results are all less than 1% under ideal conditions. In the field test, the average error in identifying axle loads at different vehicle speeds was 7.01% when the vehicle speed was below 20 m s−1, which proved the accuracy and effectiveness of the proposed method. This study has demonstrated a novel application of computer vision technology to identify the axle loads of moving vehicles. The proposed method does not require installation of sensors on the roadway or the vehicle, making it a promising alternative for traditional weigh-in-motion systems.

Effects of free-play or introducing artificial rules on tactical behavior based on soccer-team lines: A pilot study

Team-lines structures are particular subsystems determined strategically by the formation chosen by the team coach, and despite its relevance, no study has analyzed training effects on tactical behavior based on team lines. This study aimed to assess the effects of modified games playing freely and introducing artificial rules on tactical behavior based on team lines during the team-possession game phase in two youth-soccer categories. Two Spanish under-14s (U-14s: n = 16) and under-16s (U-16s: n = 16) teams took part in the study. Each team was divided into two groups, free-play and conditioned, that faced each other during three 7-min eight-on-eight games in four training sessions. The free-play group played freely without restrictions, while the conditioned group played constrained by artificial rules (i.e. a minimum number of touches, no return pass allowed, forward pass after a back pass) that modified the cooperative motor interactions between teammates. Tactical behavior was assessed by the three geometrical primitives’ representations (i.e. node: change in the centroid position (CCP), line: interpersonal distance between teammates (dyads), and area: surface area (SA)) and their time series approximate entropy (ApEn) normalized measures in subgroups based on team lines (goalkeeper – defenders, defenders – midfielders, and midfielders – forward) before and after the training intervention in an eight-on-eight game using a local positioning system (LPS). The results suggest that the short-term training intervention affected considerably (i.e. Cohen’s d≥ moderate) U-14s team lines’ behavior, especially those who played freely. On the other hand, U-16s’ tactical behavior based on team lines barely changed (i.e. Cohen’s d≤ small). It seems that playing freely for several training sessions could strengthen the tactical behavior of each line, enhancing team lines’ regularity in youth-soccer categories.

What to expect from dynamical modelling of cluster haloes – II. Investigating dynamical state indicators with Random Forest

ABSTRACT We investigate the importance of various dynamical features in predicting the dynamical state (ds) of galaxy clusters, based on the Random Forest (RF) machine-learning approach. We use a large sample of galaxy clusters from the Three Hundred Project of hydrodynamical zoomed-in simulations, and construct dynamical features from the raw data as well as from the corresponding mock maps in the optical, X-ray, and Sunyaev–Zel’dovich (SZ) channels. Instead of relying on the impurity based feature importance of the RF algorithm, we directly use the out-of-bag (oob) scores to evaluate the importance of individual features and different feature combinations. Among all the features studied, we find the virial ratio, η, to be the most important single feature. The features calculated directly from the simulations and in three dimensions carry more information on the ds than those constructed from the mock maps. Compared with the features based on X-ray or SZ maps, features related to the centroid positions are more important. Despite the large number of investigated features, a combination of up to three features of different types can already saturate the score of the prediction. Lastly, we show that the most sensitive feature η is strongly correlated with the well-known half-mass bias in dynamical modelling. Without a selection in ds, cluster haloes have an asymmetric distribution in η, corresponding to an overall positive half-mass bias. Our work provides a quantitative reference for selecting the best features to discriminate the ds of galaxy clusters in both simulations and observations.

Quantitative evaluation of segmentation accuracy of subsegmental infarcts using 2DSTE and synthetic ultrasonic data in a spheroidal model of the left ventricle

ObjectiveEvaluation of the accuracy of the segmentation of simulated subsegmental infarcts using 2DSTE. MethodsSynthetic ultrasonic data were obtained using the FIELD II package and meshes obtained from FEM simulations of deformation of left ventricular (LV) models of a healthy LV and LVs with different infarcts. Hierarchical block matching method was applied to estimate displacements. Longitudinal and circumferential strain components were estimated and then averaged over small subsegments resulting from division of AHA 17 segments no 7 and 12. The infarcts were segmented in strain maps using three thresholds differing in sensitivity and specificity. The exact infarct location derived from FEM meshes and another one obtained from FEM derived displacement maps served as the references. The classification accuracy (ACC) and centroid position error (CPE) were used to assess the results of segmentation. ResultsACC does not drop below 0.92 and 0.85 when segmentation was done using error-free and 2DSTE estimated longitudinal strain maps, respectively. ACC does not drop below 0.90 and 0.75 in the same conditions for the circumferential strain maps. The mean CPE does not exceed 2 mm and 3 mm for infarct segmented from estimated longitudinal and circumferential strain maps, respectively. ConclusionReduction of the strain averaging area when using 2DSTE appeared necessary for detection and segmentation of small simulated infarcts (down to 9 mm diameter) as global strain measures showed insufficient sensitivity. SignificanceThe advantage of strain averaging over a reduced area for segmentation of small simulated infarcts when using the 2DSTE technique has been demonstrated.

Effect of proton beam irradiation on the tracking efficiency of CMOS image sensors

A star tracker provides accurate space positioning and reference for satellites, intercontinental strategic missiles, and other spacecrafts. However, the main imaging unit of the star sensor – the image sensor – is affected by the space radiation environment and, in turn, affects the precision with which the star is located by the star tracker. In this study, the parameter degradation of a CMOS image sensor (CIS) after proton irradiation with different fluences was investigated. An outfield test platform for star map collection was built using the star sensor lens and image collection system. The influence of dark current, dark-current nonuniformity, and photo-response nonuniformity of the irradiated CIS on the star diagonal distance measurement error and star-point centroid position detection accuracy was studied. The results showed that with increasing proton fluences, the CIS noise increased, leading to an increase in the error in the measured diagonal distance of the star and a decrease in the star’s position detection accuracy. Among these parameters, the dark current plays the greatest role in influencing the measurement accuracy of the star tracker. Furthermore, when a tracker is exposed to space radiation with fluences that are same as those used in this experiment, it is beneficial to reduce the integration time. This reduction in the time will decrease the noise and improve the position measurement accuracy.

The Lyman Alpha Reference Sample

Aims. We use Hubble Space Telescope data of 45 nearby star-forming galaxies to investigate properties of Lyman-alpha (Lyα) halos, Lyα morphology, and the star-forming characteristics of galaxies. We study how the morphology of Lyα emission is related to other Lyα observables. Furthermore, we study the interdependencies of Lyα morphological quantities. Methods. We studied the spatial extent of Lyα using surface brightness profiles in the following two ways (i) using circular apertures and (ii) within faint Lyα isophotes. We also measured the average intensity and the size of the regions with a high star formation rate density. The morphology of the galaxies was quantified by computing centroid position, axis ratio, and position angle in the Lyα, ultraviolet continuum, and I band maps. Results. We found that galaxies with more extended star-forming regions possess larger Lyα halos. Furthermore, galaxies with more elongated Lyα morphology are also more extended in Lyα. Our data suggest that Lyα bright galaxies appear rounder in their Lyα morphology, and there is less of a contribution from their Lyα halo to their overall luminosity. We compared our results with studies at high redshift and found that whilst the Lyα extent in the inner regions of the galaxies in our sample are similar to the high-z Lyα emitters (LAEs), Lyα halos are more extended in high-z LAEs. Conclusions. Our analysis suggests that the Lyα morphology affects the measurement of other observable quantities concerning Lyα emission, and some of the conclusions drawn from high redshift LAEs might be biased towards galaxies with specific Lyα shapes. In particular, faint Lyα emitters have larger Lyα scale lengths and halo fractions. This implies that faint Lyα emitters are harder to detect at high redshift than previously believed.

Kerr-Newman black hole lensing of relativistic massive particles in the weak-field limit

The gravitational lensing of relativistic neutral massive particles caused by a Kerr-Newman black hole is investigated systematically in the weak-field limit. Based on the Kerr-Newman metric in Boyer-Lindquist coordinates, we first derive the analytical form of the equatorial gravitational deflection angle of a massive particle in the third post-Minkowskian approximation. The resulting bending angle, which is found to be consistent with the result in the previous work, is adopted to solve the popular Virbhadra-Ellis lens equation. The analytical expressions for the main observable properties of the primary and secondary images of the particle source are thus obtained beyond the weak-deflection limit, within the framework of standard perturbation theory. The observables include the positions, magnifications, and gravitational time delays of the individual images, the differential time delay, and the total magnification and centroid position. The explicit forms of the correctional effects induced by the deviation of the initial velocity of the massive particle from the speed of light on the observables of the lensed images are then achieved. Finally, serving as an application of the formalism, the supermassive black hole at the Galactic Center, Sagittarius ${\mathrm{A}}^{*}$, is modeled to be a Kerr-Newman lens. The magnitudes of the velocity-induced correctional effects on the practical lensing observables as well as the possibilities to detect them in this scenario are also analyzed.

On-demand measurement of higher topological charges using Hadamard-coded apertures with a DMD

The diffraction of an orbital angular momentum (OAM) beam behind slits and polygon apertures has enabled the measurement of light’s topological charge (TC). In this work, we present a simple technique to measure higher TCs using Hadamard-coded apertures programmed in a digital micromirror device (DMD). Apart from pattern recognition, a common approach in relating the topological properties of the beam with its diffraction, we demonstrate that we can determine TCs from m=±1 to ±10 using the position of diffracted intensity centroid R. We show thru experiments and simulations that indeed the centroids of the diffracted beams move depending on the magnitude and the sign of the TC, and the order N of the Hadamard aperture. Based on our results, distinguishing the TC of a beam is easier when |m|>5. Lastly, we infer the source of the movement of the centroid using simple interference of three points derived from a Hadamard N = 2. By tracing the position of the zeroth-order maxima in the interference, we relate the maximum intensity position with the intensity centroid position in the diffraction. Our technique is crucial for determining higher-order modes whose TC are difficult to determine with the currently available methods.