Angular Spectrum Research Articles

LiteBIRD science goals and forecasts. A case study of the origin of primordial gravitational waves using large-scale CMB polarization

We study the possibility of using the LiteBIRD satellite B-mode survey to constrain models of inflation producing specific features in CMB angular power spectra. We explore a particular model example, i.e. spectator axion-SU(2) gauge field inflation. This model can source parity-violating gravitational waves from the amplification of gauge field fluctuations driven by a pseudoscalar “axionlike” field, rolling for a few e-folds during inflation. The sourced gravitational waves can exceed the vacuum contribution at reionization bump scales by about an order of magnitude and can be comparable to the vacuum contribution at recombination bump scales. We argue that a satellite mission with full sky coverage and access to the reionization bump scales is necessary to understand the origin of the primordial gravitational wave signal and distinguish among two production mechanisms: quantum vacuum fluctuations of spacetime and matter sources during inflation. We present the expected constraints on model parameters from LiteBIRD satellite simulations, which complement and expand previous studies in the literature. We find that LiteBIRD will be able to exclude with high significance standard single-field slow-roll models, such as the Starobinsky model, if the true model is the axion-SU(2) model with a feature at CMB scales. We further investigate the possibility of using the parity-violating signature of the model, such as the TB and EB angular power spectra, to disentangle it from the standard single-field slow-roll scenario. We find that most of the discriminating power of LiteBIRD will reside in BB angular power spectra rather than in TB and EB correlations.

P‐50: Multi‐depth‐SGD Based Tilted Plane Diffraction Propagation for Holographic Near‐eye Displays

To facilitate the practical application of wearable holographic near‐eye displays, the propagation between non‐parallel planes is essential for the hologram generation of off‐axis projection onto the holographic‐optical‐element (HOE) based combiners. However, existing methods, particularly the angular spectrum rotation‐based approach for generating tilted plane holograms, encounter challenges such as gradient loss when integrated with the stochastic gradient descent (SGD) algorithm. In this paper, we present a novel method for generating a tilted plane hologram using multi‐depth‐SGD, effectively mitigating the gradient loss issue.

Finding origins of CMB anomalies in the inflationary quantum fluctuations

In this paper, we present compelling evidence for the parity asymmetry (a discrete symmetry separate from isotropy) in the Cosmic Microwave Background (CMB) map, measured through two-point temperature correlations. Any asymmetry associated with discrete symmetries, such as parity, challenges our understanding of quantum physics associated with primordial physics rather than LCDM (Λ Cold-Dark-Matter) itself. We commence by conducting a comprehensive analysis of the Planck CMB, focusing on the distribution of power in low-multipoles and temperature anticorrelations at parity conjugate points in position space. We find tension with the near scale-invariant power-law power spectrum of Standard Inflation (SI), with p-values of the order 𝒪(10-4 - 10-3). Alternatively, we explore the framework of direct-sum inflation (DSI), where a quantum fluctuation arises as a direct sum of two components evolving forward and backward in time at parity conjugate points in physical space. This mechanism results in a parity-asymmetric scale-dependent power spectrum, particularly prominent at low-multipoles, without any additional free model parameters. Our findings indicate that DSI is consistent with data on parity asymmetry, the absence of power at θ > 60°, and power suppression at low-even-multipoles which are major data anomalies in the SI model. Furthermore, we discover that the parameters characterizing the hemispherical power asymmetry anomaly become statistically insignificant when the large SI quadrupole amplitude is reduced to align with the data. DSI explains this low quadrupole with a p-value of 3.5%, 39 times higher than SI. Combining statistics from parameters measuring parity and low-ℓ angular power spectrum, we find that DSI is 50-650 times more probable than SI. In summary, our investigation suggests that while CMB temperature fluctuations exhibit homogeneity and isotropy, they also display parity-asymmetric behavior consistent with predictions of DSI. This observation provides a tantalizing evidence for the quantum mechanical nature of gravity.

Improvement of optical wave propagation simulations: the scaled angular spectrum method for far-field and focal analysis

In the field of optics, accurately simulating wave propagation is essential for both theoretical insights and practical applications. This study introduces the scaled angular spectrum method (Sc-ASM) for simulating far-field and focal patterns, overcoming the limitations inherent in the standard angular spectrum method (ASM) by allowing variable sampling intervals between source and observation planes. Comparative analysis with the Rayleigh–Sommerfeld integral demonstrates Sc-ASM's superior accuracy in estimating the far-field patterns of beams with complex phase structures. Our results underscore Sc-ASM’s potential to set a new benchmark in optical simulations, significantly advancing optical system design and the study of wave propagation.

Soft Contact Lens Engraving Characterization by Wavefront Holoscopy.

Permanent engravings on contact lenses provide information about the manufacturing process and lens positioning when they are placed on the eye. The inspection of their morphological characteristics is important, since they can affect the user's comfort and deposit adhesion. Therefore, an inverted wavefront holoscope (a lensless microscope based on Gabor's principle of in-line digital holography) is explored for the characterization of the permanent marks of soft contact lenses. The device, based on an in-line transmission configuration, uses a partially coherent laser source to illuminate the soft contact lens placed in a cuvette filled with a saline solution for lens preservation. Holograms were recorded on a digital sensor and reconstructed by back propagation to the image plane based on the angular spectrum method. In addition, a phase-retrieval algorithm was used to enhance the quality of the recovered images. The instrument was experimentally validated through a calibration process in terms of spatial resolution and thickness estimation, showing values that perfectly agree with those that were theoretically expected. Finally, phase maps of different engravings for three commercial soft contact lenses were successfully reconstructed, validating the inverted wavefront holoscope as a potential instrument for the characterization of the permanent marks of soft contact lenses. To improve the final image quality of reconstructions, the geometry of lenses should be considered to avoid induced aberration effects.

Propagation of elliptical Gaussian vortex beam based on angular spectrum representation

Vortex beams with hollow elliptical ring structure have attracted broad interest in applications such as micro-particle trapping and manipulation. The paper investigates the dependence of the hollow elliptic ring structure of vortex beams on the beam order and the topological charge, while propagating in the near- and far-field zones. The electric field of the beam is formulated by using the angular spectrum method, which satisfies rigorously Maxwell's equation. The electric field, linear momentum and orbital angular momentum are calculated. Numerical results show that the hollow elliptical ring structure approximately remains unchanged over a finite propagation distance, accompanied by a rotation whose angle depends on the topological charge. In the far-field zone, the ring structure is broken, leading to two bright spots and several dark islands. It is found that the beam profile in the near-field zone is mainly related to the beam order but in the far-field zone is primarily affected by the topological charge. The results presented in the paper may be useful in predicting and explaining the interaction between the elliptic hollow Gaussian vortex beam and the micro-particles, such as the movement of micro-particles along the orbit and the rolling rotation.

Broadband angular spectrum analog processors based on all-dielectric metasurfaces

Broadband angular spectrum analog processors based on all-dielectric metasurfaces

Unbiased estimation of gravitational-wave anisotropies from noisy data

One of the most exciting targets of current and future gravitational-wave observations is the angular power spectrum of the astrophysical GW background. This cumulative signal encodes information about the large-scale structure of the Universe, as well as the formation and evolution of compact binaries throughout cosmic time. However, the finite rate of compact binary mergers gives rise to , which introduces a significant bias in measurements of the angular power spectrum if not explicitly accounted for. Previous work showed that this bias can be removed by cross-correlating GW sky maps constructed from different observing times. However, this work considered an idealized measurement scenario, ignoring detector specifics and in particular noise contributions. Here we extend this temporal cross-correlation method to account for these difficulties, allowing us to implement the first unbiased anisotropic search pipeline for LIGO-Virgo-KAGRA data. In doing so, we show that the existing pipeline is biased , due to previously neglected subleading contributions to the noise covariance. We apply our pipeline to mock LIGO data, and find that our improved analysis will be crucial for stochastic searches from the current observing run (O4) onwards. Published by the American Physical Society 2024

A unified linear intrinsic alignment model for elliptical and disc galaxies and the resulting ellipticity spectra

Alignments of disc galaxies were thought to result from tidal torquing, where tidal field of the cosmic large-scale structure exert torquing moments onto dark matter haloes, determining their angular momentum and ultimately the orientation of galactic discs. In this model, resulting intrinsic ellipticity correlations are typically present on small scales, but neither observations nor simulations have found empirical evidence; instead, simulations point at the possibility that alignments of disc galaxies follow a similar alignment model as elliptical galaxies, but with a weaker alignment amplitude. In our article we make the case for the theory of linear alignments resulting from tidal distortions of the galactic disc, investigate the physical properties of this model and derive the resulting angular ellipticity spectra, as they would appear as a contribution to weak gravitational lensing in surveys such as Euclid’s. We discuss in detail on the statistical and physical properties of tidally induced alignments in disc galaxies, as they are relevant for mitigation of alignment contamination in weak lensing data, comment on the consistency between the alignment amplitude in spiral and elliptical galaxies and finally, estimate their observability with a Euclid-like survey.

Evaluating the beam shape coefficients of Bessel–Gauss beams with radial quadrature: a comparison with angular spectrum decomposition and finite series methods

The Bessel–Gauss beam (BGB) stands as a physically realizable beam extensively employed in applications such as micromanipulation and optical trapping. In these contexts, the assessment of beam shape coefficients (BSCs) becomes imperative. Previous research reveals that the BSCs of the BGBs obtained with different methods deviate from each other under certain circumstances. In this paper, the formulation of BSCs employs the radial quadrature method, and a comparative analysis is conducted with counterparts formulated using the angular spectrum decomposition and the finite series technique. Contributions stemming from evanescent waves and the situation of the BSC blowing-ups are discussed, offering a deep insight of pertinent BSC evaluation methods. The paper provides an alternative approach for calculating the BSCs of the BGBs.

Calibration-free deep optics for depth estimation with precise simulation

Monocular depth estimation is an important computer vision task widely explored in fields such as autonomous driving, robotics, and more. Recently, deep optics approaches that optimize diffractive optical elements (DOEs) with differentiable frameworks have improved depth estimation performance. However, they only consider on-axis point spread functions (PSFs) and are highly dependent on system calibration. We propose a precise end-to-end paradigm combining ray tracing and angular spectrum diffraction. With this approach, we jointly trained a DOE and a reconstruction network for depth estimation and image restoration. Compared with conventional deep optics approaches, we accurately simulate both on-axis and off-axis PSFs, eliminating the need for calibration. We have validated the high similarity between captured PSFs and simulated ones at 19.4∘ field-of-view (FOV). Our optimized phase mask and network achieve state-of-the-art performance among semantic-based monocular depth estimation and existing deep optics methods. During real-world experiments, our prototype camera shows depth distributions similar to the Intel D455 infrared structured light camera.

Fast emulation of two-point angular statistics for photometric galaxy surveys

ABSTRACT We develop a set of machine-learning-based cosmological emulators, to obtain fast model predictions for the C(ℓ) angular power spectrum coefficients, characterizing tomographic observations of galaxy clustering and weak gravitational lensing from multiband photometric surveys (and their cross-correlation). A set of neural networks are trained to map cosmological parameters into the coefficients, achieving, with respect to standard Boltzmann solvers, a speed-up of $\mathcal {O}(10^3)$ in computing the required statistics for a given set of cosmological parameters, with an accuracy better than 0.175 per cent (<0.1 per cent for the weak lensing case). This corresponds to $\lesssim 2~{{\ \rm per\ cent}}$ of the statistical error bars expected from a typical Stage IV photometric surveys. Such overall improvement in speed and accuracy is obtained through (i) a specific pre-processing optimization, ahead of the training phase, and (ii) an effective neural network architecture. Compared to previous implementations in the literature, we achieve an improvement of a factor of 5 in terms of accuracy, while training a considerably lower amount of neural networks. This results in a cheaper training procedure and a higher computational performance. Finally, we show that our emulators can recover unbiased posteriors when analysing synthetic Stage-IV galaxy survey data sets.

The Weyl expansion for the scalar and vector spherical wave functions

The Weyl expansion technique, also known as the angular spectrum expansion, expresses an outgoing spherical wave as a linear combination of plane waves. The scalar spherical waves are the solutions of the homogeneous Helmholtz equation and therefore have direct relation to the scalar multipole fields. This paper gives the Weyl expansion of multipole fields, scalar and vector, of any degree and order for spherical wave functions. The expressions are given in closed form for the scalar, , and vector, , , multipole fields, evaluated across a plane orthogonal to any given direction. In the case of scalar spherical multipoles, the spherical gradient operator has been used, while for the vector spherical multipoles, the vector spherical wave operator has been constructed.

Overmodulation and phase correction of virtual images propagated by holographic curved waveguide for near-eye display

Generally, current type of waveguide used for near-eye displays is planar waveguide, which belongs to flat panel display. Compared to display system in three-dimensional space, flat panel display limits people's view of the 3-D world and is not conducive to the integration of virtual and reality. This paper proposes a holographic curved waveguide system for near-eye display. In order to analyze the propagation process of light beam in waveguide, an iterative algorithm is established based on angular spectrum theory to get the intensity distribution from each total internal reflection point. According to the simulation results and experimental phenomenon, we have developed phase compensation measures for overmodulation during beam propagation in the waveguide. The research shows that using curved waveguide can achieve beam transmission with less aberration after introducing an appropriate phase compensation in a distance, and it can also achieve beam transmission with lossless energy within a large radius range. Experiments have proven that the final coupling effect is basically consistent with the simulation results, this means that our proposal about curved waveguide has potential application value in near-eye display systems.

Tomographic cross correlations between galaxy surveys and the CMB gravitational lensing potential. Effect of the redshift bin mismatch

Upcoming surveys of the large-scale structure of our Universe will employ a large coverage area of about half of the sky and will significantly increase the observational depth. With these surveys, we will be able to cross-correlate cosmic microwave background (CMB) gravitational lensing and galaxy surveys divided into narrow redshift bins to map the evolution of the cosmological parameters with redshift. We study the effect of the redshift bin mismatch of objects that is due to photometric redshift errors in tomographic cross-correlation measurements. We used the code FLASK to create Monte Carlo simulations of the Vera C. Rubin Observatory Legacy Survey of Space and Time (LSST) and Planck CMB lensing convergence. We simulated log-normal fields and divided galaxies into nine redshift bins with the Gaussian and modified Lorentzian photometric redshift errors. To estimate the parameters, we used angular power spectra of CMB lensing and galaxy density contrast fields and the maximum likelihood estimation method. We show that even with simple Gaussian errors with a standard deviation of $ the galaxy auto-power spectra in tomographic bins are offset by $2-15<!PCT!>$. The estimated cross-power spectra between galaxy clustering and CMB lensing are also biased, with smaller deviations $<5<!PCT!>$. As a result, the $ $ parameter deviates between $0.2-1.2\ due to the redshift bin mismatch of the objects. We propose a computationally fast and robust method based on the scattering matrix approach to correct for the redshift bin mismatch of the objects. The estimates of the parameters in tomographic studies such as the linear galaxy bias, the cross-correlation amplitude, and $ $ are biased due to the redshift bin mismatch of the objects. The biases in these parameters are alleviated with our scattering matrix approach.

Single shot depth-resolved imaging through dynamic turbid media

Guide star assisted wavefront shaping techniques have been exploited for focusing and imaging through turbid media by addressing a scatter inverse pattern. However, the turbid medium is required to be steady before finding the proper correction pattern, which limits applications in focusing and imaging through dynamic media, such as turbid water or blood. This study proposes a holography-based dual-polarization computational wavefront shaping method for imaging objects at variant depths behind dynamic turbid media. The orthogonal polarized output speckles of a point source (considered as a guide star) and an object are simultaneously recorded in holograms in separate regions of a single CCD camera. The holograms of the point source and object are subjected to the same distortion regardless of whether the media is static or dynamic. The hologram of the point source is used to determine the correction phase pattern for the distortion, while that of the object is used to record the complex scattered wavefront of the object. To reconstruct a clear object image, the wavefront of the scattered object is digitally corrected using the correction phase pattern and is then transferred to the image plane by calculating the transmission of the angular spectrum. Benefiting from the autofocusing feature of digital holography, objects at different depths can be recovered from a single shot hologram pair. The potential applications of the proposed method in diverse dynamic scattering media are demonstrated by imaging through a moving diffuser, turbid water, and pig blood with optical depth beyond 10.

Sidelobe suppression for accelerating beams

Although the control of trajectory, amplitude and beam-width in accelerating beams have been extensively investigated, sidelobes manipulation of such beams, which is required in many applications, has been surprisingly under-researched. This paper presents an approach for the generating of accelerating beams with significantly reduced sidelobes. The proposed method encompasses a two-step angular spectrum design, including employing a general model to establish the phase distribution and applying a stochastic parallel gradient descent (SPGD) algorithm to optimize the binary amplitude modulation. Experimental results confirm that the sidelobe intensity of accelerating beams can be reduced by over 50% with our method, thereby enhancing their applicability in many fields, such as micro-machining, particle manipulation, and optical communication.

Harmonic analysis of discrete tracers of large-scale structure

It is commonplace in cosmology to analyze fields projected onto the celestial sphere, and in particular density fields that are defined by a set of points e.g. galaxies. When performing an harmonic-space analysis of such data (e.g. an angular power spectrum) using a pixelized map one has to deal with aliasing of small-scale power and pixel window functions. We compare and contrast the approaches to this problem taken in the cosmic microwave background and large-scale structure communities, and advocate for a direct approach that avoids pixelization. We describe a method for performing a pseudo-spectrum analysis of a galaxy data set and show that it can be implemented efficiently using well-known algorithms for special functions that are suited to acceleration by graphics processing units (GPUs). The method returns the same spectra as the more traditional map-based approach if in the latter the number of pixels is taken to be sufficiently large and the mask is well sampled. The method is readily generalizable to cross-spectra and higher-order functions. It also provides a convenient route for distributing the information in a galaxy catalog directly in harmonic space, as a complement to releasing the configuration-space positions and weights, and a route to spectral apodization. We make public a code enabling the application of our method to existing and upcoming datasets.

Magnification and evolution bias of transient sources: GWs and SNIa

Third-generation gravitational wave (GW) observatories such as the Einstein Telescope and Cosmic Explorer, together with the LSST survey at the Vera Rubin Observatory, will yield an abundance of extra-galactic transient objects. This opens the exciting possibility of using GW sources and Supernovae Type Ia (SNIa) as luminosity distance tracers of large-scale structure for the first time.The large volumes accessible to these surveys imply that we may need to include relativistic corrections, such as lensing and Doppler magnification. However, the amplitude of these effects depends on the magnification and evolution biases of the transient sources, which are not yet understood.In this paper we develop comprehensive frameworks to address and model these biases for both populations of transient objects; in particular, we define how to compute these biases for GW sources. We then analyse the impact of magnification and evolution biases on the relativistic corrections and on the angular power spectrum of these sources. We show that correct modelling and implementation of these biases is crucial for measuring the cross-correlations of transient sources at higher redshifts.

Orbital angular momentum spectrum of model partially coherent beams in turbulence

The use of partial coherence has been extensively studied as a potential solution to mitigate the destructive effects of atmospheric turbulence in optical applications involving the free space propagation of light. However, in OAM-based optical systems, reducing coherence leads to the broadening of the orbital angular momentum (OAM) spectrum, consequently increasing the cross-talk between adjacent modes. In this paper, we have investigated three fundamental classes of partially coherent OAM beams under the influence of turbulence. The aim is to identify a distinct type of partially coherent beam (PCB) in which the reduction in coherence results in higher resistance of the OAM spectrum against atmospheric disturbances. It is demonstrated that, for a specific propagation distance, we can prepare a PCB in which the benefits of reducing coherence outweigh its drawbacks.