Circular Gaussian Research Articles

Reordering of point-vortex lattices under anisotropic diffraction: far-field analysis

Abstract A study of the far-field complex amplitude obtained from initially ordered arrays of N × M point-vortices with equal unitary topological charge embedded in carrier beams with different geometry is presented. This can be understood as the final stationary configuration after the dynamical evolution of the vortices upon propagation, and our aim is to investigate the impact of a geometric anisotropy on the diffraction process by using an elliptic Gaussian beam as a carrier and a rectangular vortex lattice. For comparison, illumination by a circular Gaussian beam and a plane wave diffracted by a rectangular aperture are also analyzed. We show that vortices tend to cluster in some regions under high eccentricity of the carrier and there can be an entire redistribution of the vortices depending on the size of the initial array with respect to the size of the carrier, which inherits some geometric characteristics of the latter.

Estimating the Optically Pumped Threshold Fluence of Thin‐Film Gain Media Using Arbitrary Excitation Beams

Optically pumped threshold fluences are a widely reported metric to benchmark the performance of thin‐film gain media and lasers. Estimating the threshold fluence for nonhomogeneous beams, such as a circular Gaussian excitation, is not trivial since the average fluence depends on the estimated spot diameter. Using an exemplary lead halide perovskite film, the inversion volume at different pump energies is mapped. It is shown that the peak fluence of an arbitrary spatial beam profile is more relevant at the threshold, as it provides an upper bound to the threshold fluence. Also, simple conversion factors to estimate the peak fluence using Gaussian excitation beams are provided and the methodology to arbitrary profiles is extrapolated. Furthermore, it is advocated for using flat‐top or uniform stripe excitations to unambiguously extract the threshold fluence, since these excitations display minor discrepancies between the average and peak fluence, and keep the inversion volume relatively constant during the measurement.

Deblurring of Beamformed Images in the Ocean Acoustic Waveguide Using Deep Learning-Based Deconvolution

A horizontal towed linear coherent hydrophone array is often employed to estimate the spatial intensity distribution of incident plane waves scattered from the geological and biological features in an ocean acoustic waveguide using conventional beamforming. However, due to the physical limitations of the array aperture, the spatial resolution after conventional beamforming is often limited by the fat main lobe and the high sidelobes. Here, we propose a method originated from computer vision deblurring based on deep learning to enhance the spatial resolution of beamformed images. The effect of image blurring after conventional beamforming can be considered a convolution of beam pattern, which acts as a point spread function (PSF), and the original spatial intensity distributions of incident plane waves. A modified U-Net-like network is trained on a simulated dataset. The instantaneous acoustic complex amplitude is assumed following circular complex Gaussian random (CCGR) statistics. Both synthetic data and experimental data collected from the South China Sea Experiment in 2021 are used to illustrate the effectiveness of this approach, showing a maximum 700% reduction in a 3 dB width over conventional beamforming. A lower normalized mean square error (NMSE) is provided compared with other deconvolution-based algorithms, such as the Richardson–Lucy algorithm and the approximate likelihood model-based deconvolution algorithm. The method is applicable in various acoustic imaging applications that employ linear coherent hydrophone arrays with one-dimensional conventional beamforming, such as ocean acoustic waveguide remote sensing (OAWRS).

Heliospheric Diffusion of Stochastic Parker Spirals in Radially Evolving Solar Wind Turbulence

We present a stochastic field line mapping model where the interplanetary magnetic field lines are described by a density distribution function satisfying a Fokker–Planck equation that is solved numerically. Due to the spiral geometry of the nominal Parker field and to the evolving nature of solar wind turbulence, the heliospheric diffusion of the magnetic field lines is both heterogeneous and anisotropic, including a radial component. The longitudinal distributions of the magnetic field lines are shown to be close to circular Gaussian distributions, although they develop a noticeable skewness. The magnetic field lines emanating from the Sun are found to differ, on average, from the spirals predicted by Parker. Although the spirals remain close to Archimedean, they are here underwound, on average. Our model predicts a spiral angle that is smaller by ∼5° than the Parker spiral angle at Earth’s orbit for the same solar wind speed of V sw = 400 km s−1. It also predicts an angular position on the solar disk of the best magnetically connected footpoint to an observer at 1 au that is shifted westward by ∼10° with respect to the Parker’s field model. This significantly changes the angle of the most probable magnetic connection between possible sources on the Sun and observers in the inner heliosphere. The results have direct implications for the heliospheric transport of “scatter-free” electrons accelerated in the aftermath of solar eruptions.

Orthogonal Expanded Memory Polynomial Model for Circular Complex Gaussian Processes

Orthogonal Expanded Memory Polynomial Model for Circular Complex Gaussian Processes

First GMVA observations with the upgraded NOEMA facility: VLBI imaging of BL Lacertae in a flaring state

We analyze a single-epoch Global mm-VLBI Array (GMVA) observation of the blazar BL\,Lacertae (BL\,Lac) at 86\,GHz from April 2021. The participation of the upgraded, phased Northern Extended Millimetre Array (NOEMA) adds additional sensitivity to the GMVA, which has facilitated the imaging of BL\,Lac during an unprecedentedly strong gamma -ray flare. We aim to explore the nature of the inner subparsec jet of BL\,Lac and the impact of the NOEMA participation in the observation. For the data reduction, we employed two advanced automatic pipelines: rPICARD for the flux density calibration as well as the model-agnostic signal stabilization and GPCAL for the antenna leakage calibration. The conventional hybrid imaging (CLEAN\,$+$\,amplitude and phase self-calibration) was applied to the calibrated visibilities to generate final VLBI images. We performed a ridge-line analysis and Gaussian model-fits on the final jet image to derive the jet parameters. In our data, the presence of NOEMA improves the image sensitivity by a factor of 2.5. The jet shows a clear wiggling structure within 0.4\,mas from the core. Our ridge-line analysis suggests the presence of a helical jet structure (i.e., a sinusoidal pattern). Six circular Gaussian components were fitted to the inner jet region. We estimated an apparent brightness temperature of sim 3\,times \,1012\,K in the two innermost components. They are likely to be highly boosted by relativistic beaming effect. We find four significant polarized knots in the jet. Interestingly, two of them are located in the core region. Finally, we suggest a number of physical scenarios to interpret our results.

Method Comparison for Simulating Non-Gaussian Beams and Diffraction for Precision Interferometry.

In the context of simulating precision laser interferometers, we use several examples to compare two wavefront decomposition methods-the Mode Expansion Method (MEM) and the Gaussian Beam Decomposition (GBD) method-for their precision and applicability. To assess the performance of these methods, we define different types of errors and study their properties. We specify how the two methods can be fairly compared and based on that, compare the quality of the MEM and GBD through several examples. Here, we test cases for which analytic results are available, i.e., non-clipped circular and general astigmatic Gaussian beams, as well as clipped circular Gaussian beams, in the near, far, and extremely far fields of millions of kilometers occurring in space-gravitational wave detectors. Additionally, we compare the methods for aberrated wavefronts and their interaction with optical components by testing reflections from differently curved mirrors. We find that both methods can generally be used for decomposing non-Gaussian beams. However, which method is more accurate depends on the optical system and simulation settings. In the given examples, the MEM more accurately describes non-clipped Gaussian beams, whereas for clipped Gaussian beams and the interaction with surfaces, the GBD is more precise.

Evolution and particle trapping dynamics of circular Pearcey-Airy Gaussian vortex beams in tightly focused systems.

This study investigates the propagation and evolution of self-focusing circular Pearcey-Airy Gaussian vortex beams (CPAGVB) through high numerical aperture objective lenses. CPAGVB demonstrates a unique light field distribution compared to the circular Pearcey vortex beam and circular Airy Gaussian vortex beam. By adjusting optical distribution factors, main radii, and off-axis vortex pair positions, a variety of light field structures can be generated, including asymmetric micro-optical bottles, quasi-flat-top beam micro-optical bottles, and dual optical bottles. The particle trapping performance of CPAGVB is examined, revealing a gradient force eight orders of magnitude larger than its scattering force, up to twice the peak gradient force, and 2.5 times the scattering force of CAGVB. Further analysis of lateral power flow density, spin density vector, and total angular momentum distribution at the focal plane unveils the dynamics of particle motion toward the center. The Gouy phase difference under varying main radii reveals two types of normalized spin density vectors, characterized by helical and oscillating distributions. Additionally, the study examines the two-dimensional polarization ellipse distribution at the focal plane, elucidating the formation of central polarization singularities with axial vortices and the impact of peripheral polarization rearrangement on phase singularities. This research advances the comprehension of CPAGVB's distinctive properties and potential applications in micro-optical systems and particle manipulation.

Abnormally autofocusing vortex Swallowtail Gaussian vector beam with low spatial coherence

The precondition for the application of light beams is the ability to devise light distribution with high precision. Controlling more dimensions for structured light fields is an effective method to improve the ability to devise light distribution. The Swallowtail beam, due to its rich regulatory parameters, provides the possibility to design a light field with a specific intensity distribution. Utilizing the Swallowtail beam as a foundation, we design its initial phase, polarization, and coherent structure, and propose a partially coherent azimuthally polarized circular vortex Swallowtail Gaussian beam (PCAPCVSGB) in our paper. This beam exhibits an abnormal self-focusing ability and forms an easily adjustable optical potential well at the focal plane, providing another effective tool for achieving optical manipulation. In addition, the PCAPCVSGB also shows an interesting vector property. It possesses a stable polarization singularity even with changes in coherence and topological charges, which exhibits a potential application value in optical communication.

Phase congruency based on derivatives of circular symmetric Gaussian function: an efficient feature map for image quality assessment

Image quality assessment (IQA) has become a hot issue in the area of image processing, which aims to evaluate image quality automatically by a metric being consistent with subjective evaluation. The first stage of conventional IQA model design is the quality-aware feature selection. Taking advantages of early visual feature, Phase congruency (PC) operates in frequency domain to measure local structures such as edges, corners, lines, etc., by computing the local amplitudes and local energies in multiple scales. Conventional local PC features are calculated with log-Gabor-based filtrations in several orientations, and usually combined with other features for IQA model design. Generally, a directional filter is sensitive to the changes on specific direction, and insensitive to other directions. This leads to multi-directional calculation and much time consumption in practical applications. Recently, researchers suggested that spatially circular symmetric filters, such as gradient magnitude (GM) and Laplacian of Gaussian (LoG), are highly efficient quality features and hence have been widely used in various IQA model designs. With the odd-symmetric and even-symmetric properties of GM and LoG operators, the two features are a suitable pair for PC compositions and can be computed uniformly by a Gaussian function with one scale factor. In this regard, we propose to combine GM and LoG signals to construct a new PC model with non-directional property. With ability to catch different types of distortions, the proposed PC feature can be promoted to a full-reference IQA model simply with average pooling or standard deviation pooling, and shows state-of-the-art performance compared with existing methods. Furthermore, our proposed PC algorithm can take the place of conventional PC component in well-known FSIM metric, which achieves improved performance and spends less in computation cost. This study suggests that the proposed circular symmetric PC feature is a highly efficient quality feature and can be exclusively used in IQA model designs.

The hidden side of cosmic star formation at z > 3

Our current understanding of the cosmic star formation history at z > 3 is primarily based on UV-selected galaxies (Lyman-break galaxies, i.e., LBGs). Recent studies of H-dropouts (HST-dark galaxies) have revealed that we may be missing a large proportion of star formation that is taking place in massive galaxies at z > 3. In this work, we extend the H-dropout criterion to lower masses to select optically dark or faint galaxies (OFGs) at high redshifts in order to complete the census between LBGs and H-dropouts. Our criterion (H > 26.5 mag & [4.5] < 25 mag) combined with a de-blending technique is designed to select not only extremely dust-obscured massive galaxies but also normal star-forming galaxies (typically E(B − V) > 0.4) with lower stellar masses at high redshifts. In addition, with this criterion, our sample is not contaminated by massive passive or old galaxies. In total, we identified 27 OFGs at zphot > 3 (with a median of zmed = 4.1) in the GOODS-ALMA field, covering a wide distribution of stellar masses with log(M⋆/M⊙) = 9.4 − 11.1 (with a median of log(M⋆med/M⊙) = 10.3). We find that up to 75% of the OFGs with log(M⋆/M⊙) = 9.5 − 10.5 were neglected by previous LBGs and H-dropout selection techniques. After performing an optical-to-millimeter stacking analysis of the OFGs, we find that rather than being limited to a rare population of extreme starbursts, these OFGs represent a normal population of dusty star-forming galaxies at z > 3. The OFGs exhibit shorter gas depletion timescales, slightly lower gas fractions, and lower dust temperatures than the scaling relation of typical star-forming galaxies. Additionally, the total star formation rate (SFRtot = SFRIR + SFRUV) of the stacked OFGs is much higher than the SFRUVcorr (SFRUV corrected for dust extinction), with an average SFRtot/SFRUVcorr = 8 ± 1, which lies above (∼0.3 dex) the 16–84th percentile range of typical star-forming galaxies at 3 ≤ z ≤ 6. All of the above suggests the presence of hidden dust regions in the OFGs that absorb all UV photons, which cannot be reproduced with dust extinction corrections. The effective radius of the average dust size measured by a circular Gaussian model fit in the uv plane is Re(1.13 mm) = 1.01 ± 0.05 kpc. After excluding the five LBGs in the OFG sample, we investigated their contributions to the cosmic star formation rate density (SFRD). We found that the SFRD at z > 3 contributed by massive OFGs (log(M⋆/M⊙) > 10.3) is at least two orders of magnitude higher than the one contributed by equivalently massive LBGs. Finally, we calculated the combined contribution of OFGs and LBGs to the cosmic SFRD at z = 4 − 5 to be 4 × 10−2 M⊙ yr−1 Mpc−3, which is about 0.15 dex (43%) higher than the SFRD derived from UV-selected samples alone at the same redshift. This value could be even larger, as our calculations were performed in a very conservative way.

SCMA Codebook for Uplink Rician Fading Channels

In this letter, the codebook design criteria for uplink Rician fading channels are explored. The probability distribution of the weighted sums of the Rician random variables from each frequency resource is derived based on the independent non-central circular complex Gaussian random variable. Then, considering the pairwise error probability, the key performance indicators of multidimensional constellations for uplink Rician channels are explored. A sub-optimal optimization approach is deployed to generate an enhanced codebook for various Rician scenarios. Finally, numerical results are provided to verify the key performance indicators in the uplink Rician fading channels.

Transverse energy propagation and interference of elliptical Gaussian beams

Elliptical Gaussian beam (EGB) has many different physical properties from circular Gaussian beam. In this paper, the transverse energy flux and intensity of one and two coherent EGBs are studied. In our simulation, the transverse energy flux and intensity varying with waist ratio are discussed in detail. It has been found that through increasing the waist ratio, the transverse energy flux after interference would be strengthened significantly. Although the transverse energy flux is much weaker than the longitudinal energy flux, its signal to noise ratio has been verified to be strong enough for detection. Our derivations are still reasonable for another simulation with general experimental parameters. The simulation results are considered to be helpful for some physical experiments using the transverse energy flux of Gaussian beam, such as an important application in electromagnetic response produced by interaction of high-frequency gravitational waves.

Commissioning of a synchrotron-based proton beam therapy system for use with a Monte Carlo treatment planning system

This work tackles the commissioning and validation of a novel combination of a synchrotron-based proton beam therapy system (Hitachi, Ltd.) for use with a Monte Carlo treatment planning system (TPS). Four crucial aspects in this configuration have been investigated: (1) Monte Carlo-based correction performed by the TPS to the measured integrated depth-dose curves (IDD), (2) circular spot modelling with a single Gaussian function to characterize the synchrotron physical spot, which is elliptical, (3) the modelling of the range shifter that enables using only one set of measurements in open beams, and (4) the Monte Carlo dose calculation model in small fields.Integrated depth-dose curves were measured with a PTW Bragg peak chamber and corrected, with a Monte Carlo model, to account for energy absorbed outside the detector. The elliptical spot was measured by IBA Lynx scintillator, EBT3 films and PTW microDiamond. The accuracy of the TPS (RayStation, RaySearch Laboratories) at spot modelling with a circular Gaussian function was assessed.The beam model was validated using spread-out Bragg peak (SOBP) fields. We took single-point doses at several depths through the central axis using a PTW Farmer chamber, for fields between 2 × 2cm and 30 × 30cm. We checked the range-shifter modelling from open-beam data. We tested clinical cases with film and an ionization chamber array (IBA Matrix).Sigma differences for spots fitted using 2D images and 1D profiles to elliptical and circular Gaussian models were below 0.22 mm. Differences between SOBP measurements at single points and TPS calculations for all fields between 5 × 5 and 30 × 30cm were below 2.3%. Smaller fields had larger differences: up to 3.8% in the 2 × 2cm field. Mean differences at several depths along the central axis were generally below 1%. Differences in range-shifter doses were below 2.4%. Gamma test (3%, 3 mm) results for clinical cases were generally above 95% for Matrix and film.Approaches for modelling synchrotron proton beams have been validated. Dose values for open and range-shifter fields demonstrate accurate Monte Carlo correction for IDDs. Elliptical spots can be successfully modelled using a circular Gaussian, which is accurate for patient calculations and can be used for small fields. A double-Gaussian spot can improve small-field calculations. The range-shifter modelling approach, which reduces clinical commissioning time, is adequate.

Controllable Self‐Focusing Circular Vortex Pearcey Gaussian Beam with Low Spatial Coherence

AbstractA new type of controllable self‐focusing circular vortex Pearcey Gaussian beam, which can create an optical potential well with adjustable depth and width at the center of the beam by adjusting the coherent width and the number of topological charges, is introduced. As the coherent width increases, the intensity becomes lower in the dark notch caused by the topological charges, which are consistent with the experimental results. In addition, the self‐focusing location and the strength of the circular vortex Pearcey Gaussian beam can be controlled by the spatial coherence in the simulation.

Complex source point theory of paraxial and nonparaxial elliptical Gaussian beams.

Using the operator transformation technology, we extend the circular Gaussian beam based virtual (complex) sources method to investigate the paraxial and nonparaxial propagation properties of the elliptical Gaussian beams (EGBs) with planar or cylindrical wavefronts travelling in free space. The paraxial approximation analysis reveals the self-reappearance and self-focusing propagation features for the EGBs with cylindrical wavefront under proper parameter conditions. We further introduce the nonparaxial theory to derive the analytical expressions for the field distribution of an EGB in free space, and confirm that these intriguing propagation features can still be observed with added nonparaxial correction. Comparing with the paraxial approximation results, it is worth noting that there is a clear deviation of the on-axial intensity and phase distributions near the self-focusing position on the basis of nonparaxial correction solution. Our results reveal that the anisotropic diffraction of light propagating through homogeneous medium or free space is possible. The approach in this work can easily be generalized to other beam models with elliptical geometry, which allows us to correctly predict some important information about their near field propagation characteristics for various applications.

On-axis polarization of beams radiated by electromagnetic circularly coherent sources.

On-axis spectral density and degree of polarization of beams radiated by electromagnetic (EM) sources with circular correlations are shown to be finely controlled by changing the source parameters. We reveal, in particular, that in this beam class, unlike for all previously known stationary beams, it is possible to control independently the dynamics of the on-axis spectral density and the degree of polarization. This was enabled by the obtained analytical expression for the on-axis polarization matrix, derived for general EM sources with circular coherence and Gaussian spectral density across the source plane. A simple experimental scheme for generating a broad class of EM circularly coherent sources is devised involving only a line source, a lens, and a transparency, possibly anisotropic.

Flat-Top Line-Shaped Beam Shaping and System Design.

In this study, the circular Gaussian spot emitted by a laser light source is shaped into a rectangular flat-top beam to improve the scanning efficiency of a selective laser sintering scanning system. A CO2 laser with a power of 200 W, wavelength of 10.6 μm, and spot diameter of 9 mm is shaped into a flat-top spot with a length and width of 0.5 × 0.1 mm, and the mapping function and flat-top Lorentzian function are calculated. We utilize ZEMAX to optimize the aspherical cylindrical lens of the shaping system and the cylindrical lens of the focusing system. We then calculate the energy uniformity of the flat-top line-shaped beam at distances from 500 to 535 mm and study the zoom displacement of the focusing lens system. The results indicated that the energy uniformity of the flat-top beam was greater than 80% at the distances considered, and the focusing system must precisely control the displacement of the cylindrical lens in the Y-direction to achieve precise zooming.

Automated Femoral Landmark Detection from Pelvic X-Rays

Surgical planning requires the identification of anatomical landmarks on medical images pre, intra, and post-procedures. Landmark detection on X-rays is thus an important, though time intensive, step to ensure good surgical outcomes. The operative workflow can be made more efficient by using machine learning approaches to automate the detection of landmarks. These models could also assist with the development of robotic surgical procedures, as robotic approaches to surgery require the robotic device to orient itself to the patient's anatomy. Previously described models are effective, but complex, making it difficult for landmark identification to occur in real-time in a robotic system. We propose a streamlined approach to landmark detection on pelvis radiographs that achieves similar accuracy to gold-standard manual annotations. To train and evaluate the network, 902 pelvic radiographs (382 Outlet view, 520 AP view) were annotated with 22 landmarks and split into training (n = 700), validation (n = 99), and testing (n = 103) set. A U-Net architecture with five encoding layers and five decoding layers was used. Landmark labels were converted into 128 × 128 × 22 heatmap array by placing a Gaussian blur filter (5% of image size) over each landmark in order to generate a single 128 × 128 layer of the array, thus generating the 22 layers of the overall heatmap array with one landmark heatmap on each layer. Each layer was an array of 0 except a circular Gaussian around the area of the landmark. A 256 × 256 array representing the image was fed into the U-Net architecture, which outputted a 128 × 128 × 22 heatmap array. Intersection over union loss was used to train the network. Following training for 100 epochs, the algorithm was able to predict the position of 22 clinically relevant landmarks with an average error of 2.36±.5 mm compared to ground-truth annotations made by trained experts and musculoskeletal radiologists with experience in pelvic scan analysis. The network was able to accurately determine the position of relevant landmarks. It was able to do this despite highly variable contrast and brightness in the dataset. Prediction accuracy was invariant to view (AP: 2.27±.51 mm, Outlet: 2.45±.64 mm). A prediction took 1.13±.07 seconds. The network is able to rapidly provide accurate femoral landmarks on a radiograph of the pelvis. This will allow for the automation of numerous clinically relevant measurements. Additionally, an important avenue of further research is exploring whether automated use of these measurements can aid in the prediction of femur fractures in machine learning models.

Rotation of degree of coherence and redistribution of transverse energy flux induced by non-circular degree of coherence of twisted partially coherent sources.

It is known that a twisted Gaussian Schell-model (TGSM) beam with elliptical Gaussian amplitude will rotate its beam spot upon propagation because of the vortex structure of the transverse energy flux. In this paper, we study a special kind of twisted partially coherent beams named twisted Hermite-Gaussian correlated Schell model (HGCSM) beam whose degree of coherence (DOC) is non-circularly symmetric but the source amplitude is of the circular Gaussian profile. Our results reveal that the beam spot (average intensity distribution) does not rotate during propagation even if the circular symmetry of the beam spot is broken. However, the DOC pattern shows the rotation under propagation. From the investigation of the transverse energy flux and OAM density flux, we attribute the nontrivial rotation phenomenon to the redistribution of the transverse energy flux by non-circular DOC. Furthermore, based on Hyde's approach [J. Opt. Soc. Am. A37, 257 (2020)10.1364/JOSAA.381772], we introduce a method for the generation of this class of twisted partially coherent sources. The non-rotation of the beam spot and rotation of the DOC are demonstrated in experiment.