Angular Spectrum Research Articles

A candidate field for deep imaging of the Epoch of Reionization observed with MWA

Abstract Deep imaging of structures from the Cosmic Dawn (CD) and the Epoch of Reionization (EoR) in five targeted fields is one of the highest priority scientific objectives for the Square Kilometre Array (SKA). Selecting ‘quiet’ fields, which allow deep imaging, is critical for future SKA CD/EoR observations. Pre-observations using existing radio facilities will help estimate the computational capabilities required for optimal data quality and refine data reduction techniques. In this study, we utilize data from the Murchison Widefield Array (MWA) Phase II extended array for a selected field to study the properties of foregrounds. We conduct deep imaging across two frequency bands: 72–103 MHz and 200–231 MHz. We identify up to 2,576 radio sources within a 5-degree radius of the image center (at RA (J2000) 8h, Dec (J2000) 5○), achieving approximately 80 % completeness at 7.7 mJy and 90 % at 10.4 mJy for 216 MHz, with a total integration time of 4.43 hours and an average RMS of 1.80 mJy. Additionally, we apply a foreground removal algorithm using Principal Component Analysis (PCA) and calculate the angular power spectra of the residual images. Our results indicate that nearly all resolved radio sources can be successfully removed using PCA, leading to a reduction in foreground power. However, the angular power spectra of the residual map remains over an order of magnitude higher than the theoretically predicted CD/EoR 21 cm signal. Further improvements in data reduction and foreground subtraction techniques will be necessary to enhance these results.

Measuring anisotropies in the PTA band with cross-correlations

Abstract The astrophysical gravitational wave background in the nanohertz (nHz) band is expected to be primarily composed of the superposition of signals from binaries of supermassive black holes. The spatial discreteness of these sources introduces shot noise, which, in certain regimes, would overwhelm efforts to measure the anisotropy of the gravitational wave background. Moreover, the fact the time-residual map has a finite angular resolution and the presence of pulsar noise, affects our ability to construct the angular power spectrum of the anisotropy from a time-residual map (finite resolution noise). In this work, we explicitly demonstrate, starting from first principles, that cross-correlating a gravitational wave background map with a sufficiently dense galaxy survey can mitigate this issue. This approach could potentially reveal underlying properties of the gravitational wave background that would otherwise remain obscured. We quantify both the shot noise and the finite resolution noise level and show that cross-correlating the gravitational wave background with a galaxy catalog improves by more than one order of magnitude the prospects for a first detection of the background anisotropy by a gravitational wave observatory operating in the nHz frequency range. In particular, we find that with a futuristic scenario with an effective number of frequencies equal to Nf = 10, the detection of the spectral amplitude can be achieved combining the first 20 multipoles, with a threshold to resolve single events SKA-like. Increasing observation time, pulsar number or reducing the pulsar white noise considerably improves the detection significance.

Convection Anisotropies of Cosmic Rays in Highly Magnetized Plasma

Abstract Recently, Y. Zhang & S. Liu proposed a turbulent convection model for multiscale anisotropies of cosmic rays (CRs), with an assumption of isotropic diffusion such that the anisotropies are statistically isotropic. However, this assumption may be unrealistic for TeV CRs, whose observations have revealed the significance of the local interstellar background magnetic field. To meet the difficulty, the turbulent convection scenario needs to be extended to cover anisotropic diffusion. In this paper, we focus on the parallel diffusion with isotropic pitch-angle scattering, which may be an approximation to the transport process driven by weak hydromagnetic waves in a magnetic flux tube, where fluctuations of the wave velocities lead to the turbulent convection. The consequence is the breaking of the statistical isotropy, while the overall shape of the angular power spectrum, C ℓ ¯ ∝ ℓ − γ − 1 (ℓ ≫ 1), remains similar to that in the isotropic diffusion model, where ℓ is degrees of spherical harmonics and γ is the turbulence spectral index of the convection field. It is then expected that the power-law index of the TeV CR small-scale angular power spectrum can be explained with the Kolmogorov law γ = 5/3, irrespective of the background magnetic field to some extent.

A measurement of Galactic synchrotron emission using MWA drift scan observations

Abstract Studying the diffuse Galactic synchrotron emission (hereafter, DGSE) at arc-minute angular scale is important to remove the foregrounds for the cosmological 21-cm observations. Statistical measurements of the large-scale DGSE can also be used to constrain the magnetic field and the cosmic ray electron density of our Galaxy’s interstellar medium (ISM). Here, we have used the Murchison Widefield Array (MWA) drift scan observations at 154.2 MHz to measure the angular power spectrum (C ℓ ) of the DGSE of a region of the sky from right ascension (RA) 349° to 70.3° at the fixed declination –26.7°. In this RA range, we have chosen 24 pointing centers (PCs), for which we have removed all the bright point sources above ∼ 430 mJy (3σ), and applied the Tapered Gridded Estimator (TGE) on residual data to estimate the C ℓ . We use the angular multipole range 65 ≤ ℓ ≤ 650 to fit the data with a model, , where we interpret the model as the combination of a power law (∝ ℓ–β) nature of the DGSE and a constant part due to the Poisson fluctuations of the residual point sources. We are able to fit the model for six PCs centered at α = 352.5°, 353°, 357°, 4.5°, 4° and 1°. We run the Markov Chain Monte Carlo (MCMC) ensemble sampler to get the best-fit values of the parameters A, β and C for these PCs. We see that the values of A vary in the range 155 to 400 mK2, whereas the β varies in the range 0.9 to 1.7. We find that the value of β is consistent at 2 – σ level with the earlier measurement of the DGSE at similar frequency and angular scales.

Single-path interferometric technique for measuring the orbital angular momentum spectrum of a structured light beam

Single-path interferometric technique for measuring the orbital angular momentum spectrum of a structured light beam

Toward Ultra‐High‐Capacity Meta‐Optics Storage: 3D Data Cube Encrypted via Arbitrary Spatial Coordinates

Abstract Optical holographic data storage technologies are increasingly critical for next‐generation information systems due to their advantages in storage density, stability, and security. However, current holographic storage approaches are limited by a small number of optical degrees of freedom, restricting both the multiplexing capacity and the expansion of independent channels, and by fixed spatial coordinate encoding, which hinders full utilization of 3D spatial information in Fresnel holography. Here, a 3D data encryption cube storage strategy is proposed and experimentally demonstrated, based on arbitrary holographic coordinate definition within the Fresnel region, enabled by an on‐chip meta‐device. By leveraging guided‐wave‐driven detour phase manipulation and optimizing the light field via an angular spectrum method integrated with a gradient descent algorithm, up to 160 spatially distinct holographic channels are realized with an equivalent storage density reaching over 200 000 dpi. Each spatial coordinate inherently serves as an encryption key, enabling secure and spatially selective data retrieval. Simultaneously, the proposed scheme suppresses zero‐order diffraction, enhancing holographic reconstruction fidelity. This work offers a promising pathway toward high‐capacity, high‐security optical storage and 3D holographic applications.

Revisiting the Relationship Between the Scale Factor (a(t)) and Cosmic Time (t) Using Numerical Analysis

Background: Current cosmological fits typically assume a direct relation between cosmic time (t) and the scale factor (a(t)), yet this ansatz remains largely untested across diverse observations. Objectives: We (i) test whether a single power-law scaling (a(t)∝tα) can reproduce late- and early-time cosmological data and (ii) explore whether a dynamically evolving (α(t)), modeled as a scalar–tensor field, naturally induces directional asymmetry in cosmic evolution. Methods: We fit a constant-α model to four independent datasets: 1701 Pantheon+SH0ES supernovae, 162 gamma-ray bursts, 32 cosmic chronometers, and the Planck 2018 TT spectrum (2507 points). The CMB angular spectrum is mapped onto a logarithmic distance-like scale (μ=log10Dℓ), allowing for unified likelihood analysis. Each dataset yields slightly different preferred values for H0 and α; therefore, we also perform a global combined fit. For scalar–tensor dynamics, we integrate α(t) under three potentials—quadratic, cosine, and parity breaking (α3sinα)—and quantify directionality via forward/backward evolution and Lyapunov exponents. Results: (1) The constant-α model achieves good fits across all datasets. In combined analysis, it yields H0≃70kms−1Mpc−1 and α≃1.06, outperforming ΛCDM globally (ΔAIC≃401254), though ΛCDM remains favored for some low-redshift chronometer data. High-redshift GRB and CMB data drive the improved fit. Numerical likelihood evaluations are approximately three times faster than for ΛCDM. (2) Dynamical α(t) models exhibit time-directional behavior: under asymmetric potentials, forward evolution displays finite Lyapunov exponents (λL∼10−3), while backward trajectories remain confined (λL<0), realizing classical arrow-of-time emergence without entropy or quantum input. Limitations: This study addresses only homogeneous background evolution; perturbations and physical derivations of potentials remain open questions. Conclusions: The time-scaling approach offers a computationally efficient control scenario in cosmological model testing. Scalar–tensor extensions naturally introduce classical time asymmetry that is numerically accessible and observationally testable within current datasets. Code and full data are available.

From few to many maps: A fast map-level emulator for extreme augmentation of cosmic microwave background systematics datasets

Generating massive sets of end-to-end simulations of time-ordered data (TOD) for Monte Carlo analyses in cosmic microwave background (CMB) experiments typically incurs exceedingly high computational costs. To address this challenge, we introduce a novel, fast, and efficient generative model built upon scattering covariances, the most recent iteration of the scattering transform statistics. This model is designed to augment by several orders of magnitude the number of map simulations in datasets of computationally expensive CMB instrumental systematics simulations, including their non-Gaussian and inhomogeneous features. Unlike conventional neural network-based algorithms, this generative model requires only a minimal number of training samples, making it highly compatible with the computational constraints of typical CMB simulation campaigns. While our primary focus is on spherical data, the framework is inherently versatile and readily applicable to 1D and 2D planar data, leveraging the localized nature of scattering statistics. We validated the method using realistic simulations of CMB systematics, which are particularly challenging to emulate, and performed extensive statistical tests to confirm its ability to produce new statistically independent approximate realizations. Remarkably, even when trained on as few as ten simulations, the emulator closely reproduces key summary statistics -- including the angular power spectrum, scattering coefficients, and Minkowski functionals -- and provides pixel covariance estimates with substantially reduced sample noise compared to those obtained without augmentation. The proposed approach has the potential to shift the paradigm in simulation campaign design. Instead of producing large numbers of low- or medium-accuracy simulations, future pipelines can focus on generating a few high-accuracy simulations that are then efficiently augmented using such a generative model. This promises significant benefits not only for current and forthcoming cosmological surveys such as Planck LiteBIRD Simons Observatory, CMB-S4, Euclid, and Rubin-LSST, but also for diverse fields including oceanography and climate science. We make both the general framework for scattering transform statistics HealpixML and the emulator CMBSCAT available to the community.

Calibration requirements for epoch of reionization 21-cm signal observations. Part IV. Bias and variance with time and frequency correlated residual gains

Observation of multifrequency angular power spectrum of the redshifted 21-cm brightness temperature fluctuation from the neutral hydrogen holds the key to understand the structure formation and its evolution during the reionization and post-reionization era. A major challenge in observing the neutral hydrogen arises from presence of strong foreground signals in the frequency range of interest. Mitigating the direct effect of foregrounds are being addressed through various techniques in literature. An additional second order effect arises, in presence of foreground, with limited accuracy in time and frequency dependent gain calibrations. This manifests as the residual gain and bandpass error in the observed data, introduces bias and increases uncertainty in the estimates ofmultifrequency angular power spectrum. In this work, we present an analytic method to estimate the bias and excess uncertainty in the estimates of multifrequency angular power spectrum in presence of residual gain and bandpass errors. We use this framework to estimate the effect of these errors for detection of redshifted 21-cm emission from a redshift of ∼ 8 with the upcoming SKA1-Low. Due to the high baseline density at the required range of angular multipoles, the SKA1-Low is found to be a tuned instrument for the redshifted 21-cm signal detection. We find that, there are scenario with residual gain and bandpass errors where there can be significant bias in these estimates. Certain foreground mitigation strategies, is expected to reduce a part of the bias. The detailed study of different aspects of gain and bandpass errors and their relative effects are discussed. We find, with assumed models of gain and bandpass errors, signal detection is possible at this redshift with 128 hours of observations. However, to achieve this one needs to have better calibration accuracy than present day interferometers.

Electrochemical engineering of wide photonic bandgap in silicon nanostructures for omnidirectional mirror applications

Abstract We report the optimized design and theoretical analysis of broadband omnidirectional mirrors made of silicon nanostructures. The design principle is based on regulating the electrochemical etching process of single-crystalline silicon substrates in an acidic solution using a train of sinusoidal current waveforms with tightly-spaced frequencies. The individual frequency of the etching current waveform is calibrated to produce a specific photonic band in the reflectance spectrum. A linear relationship is obtained between the frequency of the current signal and the resonant position of the photonic band. The frequency range of the etching waveform is selected to produce a broad photonic peak resulting from the bandgap overlap among multiple photonic bands associated with the individual frequency of each current signal. The transfer matrix method is utilized to calculate the angular reflectance spectra of the experimentally obtained omnidirectional mirrors for both transverse electric (TE) and transverse magnetic (TM) polarization of the incident light. Good agreement is found between the experimental and theoretical reflectivity spectra.

Single Probe Enabled Refraction-Corrected Transcranial Passive Acoustic Mapping Through Macaque Calvaria.

In microbubble (MB) cavitation-mediated blood-brain barrier (BBB) opening, prior knowledge of the skull's sound speed properties is required to correct phase aberration and achieve accurate localization of the cavitation source using transcranial passive acoustic mapping (TPAM). Current approaches predominantly rely on CT scans to generate an empirically sound speed map (SSM) for correction after registering the two imaging modalities. This increases hardware complexity and cost while introducing additional errors from the registration process and the empirical sound speed values in the SSM. Here, we propose an all-ultrasound (US), single-probe method for refraction-corrected TPAM. This method first deploys the head wave technique to reconstruct an approximate multilayer SSM of the skull. This SSM is then combined with the heterogeneous angular spectrum approach (ASA) for PAM to efficiently reconstruct refraction-corrected TPAM images. In the in vitro hydrophone and MB cavitation experiments using two whole macaque calvariae, we showed that the source localization error could be reduced to a submillimeter scale with the proposed method in the area where the F-number is less than 1.2. Compared to the cases without phase aberration correction, the localization error was reduced by about 1.8-5.9 times in the corrected cases, clearly demonstrating the effectiveness of the proposed method for transcranial acoustic source localization. We also showed that the proposed method achieved comparable performance on correcting source localization to the CT-corrected method. These preliminary results suggest that our method represents a low-cost solution for monitoring transcranial MB cavitation activity, particularly in the cortical regions, which could facilitate the investigation of MB-mediated focused therapies in the brain and warrants further study for clinical translation.

On the initial conditions of the νHDM cosmological model

ABSTRACT The $\nu$HDM is the only cosmological model based on Milgromian dynamics (MOND) with available structure formation simulations. While MOND accounts for galaxies, with a priori predictions for spirals and ellipticals, a light sterile neutrino of 11 eV can assist in recovering scaling relations on the galaxy-cluster scales. In order to perform MONDian cosmological simulations in this theoretical approach, initial conditions derived from a fit to the angular power spectrum of cosmic microwave background (CMB) fluctuations are required. In this work, we employ CosmoSIS to perform a Bayesian study of the $\nu$HDM model. Using the best-fitting values of the posterior, the CMB power spectrum is re-evaluated. The excess of power in the transfer function implies a distinct evolution scenario, which can be used further as an input for a set of hydro-dynamical calculations. The resulting values $H_{0} \approx 56$ km s$^{-1}$ Mpc$^{-1}$ and $\Omega _{m_0}\approx$ 0.5 are far from agreement with respect to the best-fitting ones in the canonical Cold Dark Matter model, but may be significant in MONDian cosmology. The assumed Planck CMB initial conditions are only valid for the lambda cold dark matter ($\Lambda$CDM) cosmology. This work constitutes a first step in an iterative procedure needed to disentangle the model dependence of the derived initial density and velocity fields.

Detection of Metal Impurity Particles in Lead-Acid Battery Electrolyte Based on Lens-Free Digital Holography Technology.

Lead-acid batteries, widely used in energy storage and power systems, are susceptible to performance degradation due to metal impurities such as iron, copper, and tin. Traditional methods like ICP-OES are accurate but costly and complex. Therefore, this study proposes a new method based on lens-free digital holography (LDH) to detect and distinguish metal impurities in lead-acid battery electrolytes. The study uses a compact setup with a green LED light source and a CMOS camera to capture holographic images of impurities. The technique reconstructs clear particle images using angular spectrum algorithms and analyzes their reconstruction distances and gray-scale differences for identification. Results show that copper particles have a reconstruction distance of 1406.4µm and a total gray-scale difference of 4.4681; tin particles have a reconstruction distance of 1414.85µm and a total gray-scale difference of 0.5344; iron hydroxide has a reconstruction distance of 1647.85µm and the total gray-scale difference of 13.5789. By combining these parameters, the method effectively distinguishes between copper, tin, and iron particles, even in mixed solutions. This cost-effective and efficient method offers a promising alternative for rapid and accurate detection of metal impurities in lead-acid battery electrolytes, with potential applications in battery maintenance and quality control.

Angularly Resolved Tip‐Enhanced Raman Spectroscopy

Despite intensive research in tip‐enhanced Raman spectroscopy (TERS), the angular distribution of Raman scattering in the TERS gap remains experimentally unreported leaving its relevance to the TERS signal formation to be seldomly discussed. Here, we investigate the angular distribution of the tip‐enhanced Raman signal in the Fourier plane using a model system composed of flat‐lying cobalt (II) hexadecafluoro‐phthalocyanine (CoPcF16) molecules physically adsorbed on a smooth gold surface. Both in‐plane and out‐of‐plane vibrational modes are observed, where the out‐of‐plane Raman modes at about 678 cm‐1 and 740 cm‐1 have different angular intensity distributions than those of in‐plane Raman modes at 1309 cm‐1 and 1373 cm‐1. We interpret the angular spectrum of the TERS signal considering the molecular vibrational modes computed with density functional theory (DFT) for the free and gold‐deposited, and the directed Raman scattering by the gap‐mode predicted by Finite‐Difference Time‐Domain (FDTD) simulations. We contend that the TERS gap directs the Raman vibrational modes differently, leading to distinct angularly distributed Raman scattering intensities. These findings emphasize the non‐negligible role of the TERS detection scheme in understanding spectral features, such as the relative peak intensity ratio variations for studying molecular orientations, or for monitoring chemical reactions.

Angularly Resolved Tip-Enhanced Raman Spectroscopy.

Despite intensive research in tip-enhanced Raman spectroscopy (TERS), the angular distribution of Raman scattering in the TERS gap remains experimentally unreported leaving its relevance to the TERS signal formation to be seldomly discussed. Here, we investigate the angular distribution of the tip-enhanced Raman signal in the Fourier plane using a model system composed of flat-lying cobalt (II) hexadecafluoro-phthalocyanine (CoPcF16) molecules physically adsorbed on a smooth gold surface. Both in-plane and out-of-plane vibrational modes are observed, where the out-of-plane Raman modes at about 678 cm-1 and 740 cm-1 have different angular intensity distributions than those of in-plane Raman modes at 1309 cm-1 and 1373 cm-1. We interpret the angular spectrum of the TERS signal considering the molecular vibrational modes computed with density functional theory (DFT) for the free and gold-deposited, and the directed Raman scattering by the gap-mode predicted by Finite-Difference Time-Domain (FDTD) simulations. We contend that the TERS gap directs the Raman vibrational modes differently, leading to distinct angularly distributed Raman scattering intensities. These findings emphasize the non-negligible role of the TERS detection scheme in understanding spectral features, such as the relative peak intensity ratio variations for studying molecular orientations, or for monitoring chemical reactions.

The case for a low matter density in dynamical dark energy model from local probes

In this paper, we investigate, through a Bayesian study, the ability of a local low matter density [Formula: see text], in discrepancy with the value usually inferred from the CMB angular power spectrum, to accommodate observations from local probes without being in tension with the local values of the Hubble constant [Formula: see text] or the matter fluctuation [Formula: see text] parameters. For that, we combine multiple local probes, with the criteria that they either can constrain the matter density parameter independently from the CMB constraints, or can help in doing so after making their relevant observations more model independent by relaxing their relevant calibration parameters. We assume however, either a dynamical dark energy model, or the standard [Formula: see text]CDM model, when computing the corresponding theoretical observables. We also add the latest Baryonic Acoustic Oscillations (BAO) measurements from the DESI year one release to some of our MCMC runs. We found that, within [Formula: see text]CDM model, for different combinations of our probes, we can accommodate a low matter density along with the [Formula: see text] and [Formula: see text] values usually obtained from local probes, providing we promote the sound drag [Formula: see text] component in BAO calculations to a free parameter, and that even if we combine with the Pantheon [Formula: see text] Supernova sample, an addition that was found in previous work to mitigate our concordance. Assuming [Formula: see text]CDM, we also found that relaxing [Formula: see text] allow us to accommodate [Formula: see text], [Formula: see text] and [Formula: see text] within their local values, with still however a preference for [Formula: see text] values far from [Formula: see text]CDM. However, when including Pantheon+ Supernova sample, we found that the latter preference for high matter density pushes [Formula: see text] to values much smaller than the ones usually obtained from local probes, mitigating by then a low matter density solution to the two common tensions. We conclude therefore that a low matter density value helps in preserving the concordance within [Formula: see text]CDM model, even with recent BAO DESI measurements or extended to high redshift supernovae sample, while the dynamical dark energy model ultimately fails to solve all tensions at once within our low density matter hypothesis.

Spiral sampling algorithm for calculating the complex orbital angular momentum spectrum

The orbital angular momentum (OAM) spectrum is a critical parameter for OAM-based applications, as it reflects the OAM components of the measured light field. However, traditional definition-based algorithms for determining the OAM spectrum are time-consuming and dependent on extensive prior knowledge. To solve it, we propose what we believe to be a novel method for calculating the complex OAM spectrum. Our approach utilizes spiral sampling and Fourier transform, followed by appropriate filtering and inverse Fourier transform to retrieve the radial coefficients of arbitrary OAM components. Both simulation and experimental results validate the effectiveness of our method. This algorithm provides a powerful tool for future OAM-based applications.

Accurate measurement for the orbital angular momentum spectrum in scattering media based on a Faraday atomic filter.

The orbital angular momentum (OAM) of beams has important applications in various fields such as large-capacity data transmission, imaging, and quantum information. So the precise measurement of the OAM spectrum is critical. Here, we present a direct and efficient method for measuring the OAM spectrum in a scattering medium using a Faraday atomic filter. Experimental results show that the Faraday atomic filter offers significant advantages in accurately identifying OAM under scattering media when compared to the results in the filterless device and the polarizer. Our work presents a novel, to the best of our knowledge, approach to precisely measure the OAM spectrum of vortex beams in complex scattering environments and will contribute to the advancement of various applications, including optical communications, lidar, and others.

Acoustic hologram-enabled simultaneous multi-target blood-brain barrier opening (AH-SiMBO)

Focused ultrasound-induced blood-brain barrier (BBB) opening enables targeted brain drug delivery. However, achieving simultaneous multi-target BBB opening across various depths and regions remains challenging and cost-prohibitive. Here we address these challenges by employing encoded acoustic holograms combined with a single-element plane-wave transducer to generate precise focused acoustic fields. The holograms designed using an iterative angular spectrum approach and fabricated via 3D printing produce single or multiple foci at different depths and regions, which are confirmed by simulations and hydrophone-based measurements. Beam steering capability is demonstrated and further validated in vivo. We design a hologram with less than 10% variation in amplitude across different foci and successfully achieve biplane multi-target ( ≥3) BBB opening in the bilateral hippocampus and medial septum of mice in a single sonication session with no adverse effects. This innovative acoustic holographic approach for simultaneous multi-target BBB opening is time-efficient and cost-effective, presenting broad potential applications in brain drug delivery and neuromodulation.

Multifocal plasma zone plate generated through holographic method

Plasma-based zone plates present an advanced method for high-power laser focusing, yet controlling the positions and intensities of the focal points remains challenging. To overcome these limitations, we propose a multifocal plasma zone plate (MFPZP) utilizing holography theory to achieve precise control of multiple focal points with the same intensities. In our approach, the MFPZP is generated by modulating plasma with multiple co-propagating spherical waves. We develop the theoretical framework and demonstrate the formation and function of the MFPZP using particle-in-cell simulations and angular spectrum method. This work improves upon our previous method by allowing precise control of focal lengths and intensities.