Two-dimensional Power Spectrum Research Articles

Impact of astrophysical effects on the dark matter mass constraint with 21 cm intensity mapping

ABSTRACT We present an innovative approach to constraining the non-cold dark matter model using a convolutional neural network (CNN). We perform a suite of hydrodynamic simulations with varying dark matter particle masses and generate mock 21 cm radio intensity maps to trace the dark matter distribution at z = 3 in the postreionization epoch. Our proposed method complements the traditional power-spectrum analysis. We compare the results of the CNN classification between the mock maps with different dark matter masses with those from the two-dimensional power spectrum of the differential brightness temperature map of 21 cm radiation. We find that the CNN outperforms the power spectrum. Moreover, we investigate the impact of baryonic physics on the dark matter model constraint, including star formation, self-shielding of H i gas, and ultraviolet background model. We find that these effects may introduce some contamination in the dark matter constraint, but they are insignificant compared to the system noise of the SKA instruments.

Influence of sources with a spectral peak in the detection of Cosmic Dawn and Epoch of Reionization

ABSTRACT Foreground removal is one of the biggest challenges in the detection of the Cosmic Dawn (CD) and Epoch of Reionization (EoR). Various foreground subtraction techniques have been developed based on the spectral smoothness of foregrounds. However, the sources with a spectral peak (SP) at megahertz may break down the spectral smoothness at low frequencies (<1000 MHz). In this paper, we cross-match the GaLactic and Extragalactic All-sky Murchison Widefield Array (GLEAM) extragalactic source catalogue with three other radio source catalogues, covering the frequency range 72 MHz–1.4 GHz, to search for sources with spectral turnover. 4423 sources from the GLEAM catalogue are identified as SP sources, representing ≈3.2 per cent of the GLEAM radio source population. We utilize the properties of SP source candidates obtained from real observations to establish simulations and test the impact of SP sources on the extraction of CD/EoR signals. We statistically compare the differences introduced by SP sources in the residuals after removing the foregrounds with three methods, which are polynomial fitting, principal component analysis, and fast independent component analysis. Our results indicate that the presence of SP sources in the foregrounds has a negligible influence on extracting the CD/EoR signal. After foreground subtraction, the contribution from SP sources to the total power in the two-dimensional power spectrum within the EoR window is approximately 3–4 orders of magnitude lower than the CD/EoR signal.

Accurate, automatic determination of astigmatism and phase with Ctfplotter in IMOD

Ctfplotter in the IMOD software package is a flexible program for determination of CTF parameters in tilt series images. It uses a novel approach to find astigmatism by measuring defocus in one-dimensional power spectra rotationally averaged over a series of restricted angular ranges. Comparisons with Ctffind, Gctf, and Warp show that Ctfplotter’s estimated astigmatism is generally more reliable than that found by these programs that fit CTF parameters to two-dimensional power spectra, especially at higher tilt angles. In addition to that intrinsic advantage, Ctfplotter can reduce the variability in astigmatism estimates further by summing results over multiple tilt angles (typically 5), while still finding defocus for each individual image. Its fitting strategy also produces better phase estimates. The program now includes features for tuning the sampling of the power spectrum so that it is well-represented for analysis, and for determining an appropriate fitting range that can vary with tilt angle. It can thus be used automatically in a variety of situations, not just for fitting tilt series, and has been integrated into the SerialEM acquisition software for real-time determination of focus and astigmatism.

Evaluation of deep-learning image reconstruction for chest CT examinations at two different dose levels.

The aims of the present study were to, for both a full-dose protocol and an ultra-low dose (ULD) protocol, compare the image quality of chest CT examinations reconstructed using TrueFidelity (Standard kernel) with corresponding examinations reconstructed using ASIR-V (Lung kernel) and to evaluate if post-processing using an edge-enhancement filter affects the noise level, spatial resolution and subjective image quality of clinical images reconstructed using TrueFidelity. A total of 25 patients were examined with both a full-dose protocol and an ULD protocol using a GE Revolution APEX CT system (GE Healthcare, Milwaukee, USA). Three different reconstructions were included in the study: ASIR-V 40%, DLIR-H, and DLIR-H with additional post-processing using an edge-enhancement filter (DLIR-H + E2). Five observers assessed image quality in two separate visual grading characteristics (VGC) studies. The results from the studies were statistically analyzed using VGC Analyzer. Quantitative evaluations were based on determination of two-dimensional power spectrum (PS), contrast-to-noise ratio (CNR), and spatial resolution in the reconstructed patient images. For both protocols, examinations reconstructed using TrueFidelity were statistically rated equal to or significantly higher than examinations reconstructed using ASIR-V 40%, but the ULD protocol benefitted more from TrueFidelity. In general, no differences in observer ratings were found between DLIR-H and DLIR-H + E2. For the three investigated image reconstruction methods, ASIR-V 40% showed highest noise and spatial resolution and DLIR-H the lowest, while the CNR was highest in DLIR-H and lowest in ASIR-V 40%. The use of TrueFidelity for image reconstruction resulted in higher ratings on subjective image quality than ASIR-V 40%. The benefit of using TrueFidelity was larger for the ULD protocol than for the full-dose protocol. Post-processing of the TrueFidelity images using an edge-enhancement filter resulted in higher image noise and spatial resolution but did not affect the subjective image quality.

Wavelet-Based Transmissibility for Structural Damage Detection

Short-time, abrupt events—such as earthquakes and other shock loadings—often lead to damage that is difficult to detect in structures using output-only vibration measurements. The time-variant transmissibility is proposed to tackle this problem. The approach is based on two-dimensional wavelet power spectra. The time-frequency transmissibility and relevant coherence function are used for structural damage detection in structural elements in buildings. Numerical simulations and experimental tests are used in these investigations. The results are compared with the classical transmissibility and time-variant input-output wavelet approach. The paper shows that output-only measurements and wavelet-based transmissibility can be used to monitor abrupt damage-related changes to structural dynamics.

Modelling annual scintillation arc variations in PSR J1643−1224 using the Large European Array for Pulsars

ABSTRACT In this work, we study variations in the parabolic scintillation arcs of the binary millisecond pulsar PSR J1643−1224 over five years using the Large European Array for Pulsars (LEAP). The two-dimensional (2D) power spectrum of scintillation, called the secondary spectrum, often shows a parabolic distribution of power, where the arc curvature encodes the relative velocities and distances of the pulsar, ionized interstellar medium, and Earth. We observe a clear parabolic scintillation arc, which varies in curvature throughout the year. The distribution of power in the secondary spectra is inconsistent with a single scattering screen, which is fully 1D or entirely isotropic. We fit the observed arc curvature variations with two models: an isotropic scattering screen and a model with two independent 1D screens. We measure the distance to the scattering screen to be in the range 114–223 pc, depending on the model, consistent with the known distance of the foreground large-diameter H ii region Sh 2-27 (112 ± 17 pc), suggesting that it is the dominant source of scattering. We obtain only weak constraints on the pulsar’s orbital inclination and longitude of ascending node, since the scintillation pattern is not very sensitive to the pulsar’s motion and the screen is much closer to the Earth than the pulsar. More measurements of this kind – where scattering screens can be associated with foreground objects – will help to inform the origins and distribution of scattering screens within our galaxy.

Magnetic turbulence and long-range correlation studies in the GOLEM tokamak

The small university-scale tokamak GOLEM equipped with the electric and magnetic probes becomes a test bench for studying the plasma turbulence and Zonal Flows, which are the essential processes affecting the plasma confinement. The broadband (f BB < 250 kHz) magnetic turbulence was detected for the first time using the Mirnov probes. The two-dimensional (frequency–wavelength) Fourier power spectra S(k, f) of the magnetic turbulence indicate the turbulence poloidal propagation. The long-range correlations (LRC) between the signals of magnetic and electric probes installed at different toroidal cross-sections were detected in the low-frequency range (f LRC < 60 kHz), which is similar to the plasma potential LRC range observed in other devices.

Enhanced light extraction efficiency of an LED package by a surface-mounted amorphous photonic structure.

In this study, we propose a low-cost, simple and feasible post-processing approach to improve the light extraction efficiency (LEE) of LED packages. Amorphous photonic structures (APSs) with only short-range order are fabricated from anodic aluminum oxide (AAO) and transferred to intermediate polymer stamp (IPS) by nanoimprint technology. The IPS with APSs is directly mounted onto the surface of an LED package, where the LEE is achieved as 94.6%. The scanning electron microscope (SEM) images of AAO templates and imprinted IPS are analyzed by radial distribution function and diameter histogram. The far-field patterns of APS-mounted LED packages are measured in electroluminescence (EL). The three-dimensional finite-difference time-domain (3D-FDTD) calculations of transmittance of APSs confirm that they improve the light extraction above the critical angle. Two-dimensional Fourier power spectra from SEM images of APSs are also calculated. The LEE enhancement is attributed to that the APSs have short-range order on a length scale comparable to emission wavelength of LED. We provide novel multistage simulations in a simplified FDTD model for the LED package. Finally, we discuss the influence of the morphology of APSs on the LEE of the APS mounted LEDs.

Development of a Quantitative Method Based on the Hill-Shading Technique for Assessing Morphological Changes in the Bone During Image-Guided Radiotherapy for Bone Metastasis

We hypothesized that positioning corrections matching the image in image-guided radiotherapy (IGRT) for bone metastasis contain information on temporal structural changes in irradiated bone metastatic lesions during the treatment period. To extract and quantify these changes, a hill-shading technique was used to emphasize the characteristics of the structure. Spatial frequency components of the bone lesions were described based on hillshading transformations of the images, and a quantification method was suggested. The matching images of 11 patients who received IGRT for lytic bone metastases were evaluated retrospectively. The hill-shading technique was applied to images of both metastatic lesions and normal bone outside the irradiation field. Outlined bone microstructures were analyzed by a two-dimensional power spectrum using fast Fourier transformation, and the frequency components were quantified. Correlations between the frequency components and cumulative radiation doses were analyzed between the irradiated metastatic bone and normal bone outside the irradiation field. The high-frequency components of the metastatic bone lesion images decreased by a mean of 7% (minimum:−0.2%, maximum: −13.2%) following cumulative irradiation doses of 20–30 Gy versus 0–10 Gy. In the normal bone outside the irradiation field, high-frequency components increased by a mean of 0.07% (minimum:−2.0%, maximum: +4.4%) following irradiation doses of 20–30 Gy versus 0–10 Gy. High-frequency components were significantly different between the normal bone and bone metastases following radiotherapy (p &lt;0.0001). Hill-shading transformation of matching images obtained during the treatment period enabled adaptation and evaluation of irradiation-induced changes in the microstructure of bone metastatic lesions.

AI-assisted superresolution cosmological simulations – II. Halo substructures, velocities, and higher order statistics

ABSTRACT In this work, we expand and test the capabilities of our recently developed superresolution (SR) model to generate high-resolution (HR) realizations of the full phase-space matter distribution, including both displacement and velocity, from computationally cheap low-resolution (LR) cosmological N-body simulations. The SR model enhances the simulation resolution by generating 512 times more tracer particles, extending into the deeply nonlinear regime where complex structure formation processes take place. We validate the SR model by deploying the model in 10 test simulations of box size 100 h−1 Mpc, and examine the matter power spectra, bispectra, and two-dimensional power spectra in redshift space. We find the generated SR field matches the true HR result at per cent level down to scales of k ∼ 10 h Mpc−1. We also identify and inspect dark matter haloes and their substructures. Our SR model generates visually authentic small-scale structures that cannot be resolved by the LR input, and are in good statistical agreement with the real HR results. The SR model performs satisfactorily on the halo occupation distribution, halo correlations in both real and redshift space, and the pairwise velocity distribution, matching the HR results with comparable scatter, thus demonstrating its potential in making mock halo catalogues. The SR technique can be a powerful and promising tool for modelling small-scale galaxy formation physics in large cosmological volumes.

Broad Coverage Precoding for 3D Massive MIMO with Huge Uniform Planar Arrays.

In this paper, we propose a novel broad coverage precoder design for three-dimensional (3D) massive multi-input multi-output (MIMO) equipped with huge uniform planar arrays (UPAs). The desired two-dimensional (2D) angle power spectrum is assumed to be separable. We use the per-antenna constant power constraint and the semi-unitary constraint which are widely used in the literature. For normal broad coverage precoder design, the dimension of the optimization space is the product of the number of antennas at the base station (BS) and the number of transmit streams. With the proposed method, the design of the high-dimensional precoding matrices is reduced to that of a set of low-dimensional orthonormal vectors, and of a pair of low-dimensional vectors. The dimensions of the vectors in the set and the pair are the number of antennas per column and per row of the UPA, respectively. We then use optimization methods to generate the set of orthonormal vectors and the pair of vectors, respectively. Finally, simulation results show that the proposed broad coverage precoding matrices achieve nearly the same performance as the normal broad coverage precoder with much lower computational complexity.

Singularity-Exponent-Domain Image Feature Transform.

Combining the generalized fractal theory and the time-frequency distribution, the image feature decomposition in the singularity exponent domain is studied in this paper. With the theoretical derivation and quantitative analysis, the singularity-exponent-domain image feature transform (SIFT) method is proposed to analyze and process images from new feature dimensions. If one derives from the generalized fractal characteristics of the image, the two-dimensional frequency variables of the 2D time-frequency transform of the image can be used to estimate the two-dimensional singularity power spectrum (SPS) in the space dimension. As a consequence, it leads to the SPS distribution of the original image in the spatial domain, i.e., SIFT images. Based on the SIFT, the feature transform images with different singularity exponent and feature curves of singularity power spectrum with respect to different physical regions can thus be obtained. The SIFT is rigorously derived from the 2D-SPS and the Pseudo Wigner-Ville distribution (PWVD). In addition, the feature images based on the SIFT is proved to be the SNR independence in the GWN background. In order to validate the effectiveness of feature extraction, the proposed methodology is tested on the breast ultrasound images, the visual images, and the synthetic aperture radar (SAR) images. Furthermore, the SAR target detection method based on the SIFT images is proposed, and the experiment results indicate that the proposed algorithm is superior in performance to the traditional CFAR or 2D-SPS method. In fact, this new SIFT is promising to provide a technical approach for image feature extraction, target detection, and recognition.

Precision Orbital Dynamics from Interstellar Scintillation Arcs for PSR J0437–4715

Abstract Intensity scintillations of radio pulsars are known to originate from interference between waves scattered by the electron density irregularities of interstellar plasma, often leading to parabolic arcs in the two-dimensional power spectrum of the recorded dynamic spectrum. The degree of arc curvature depends on the distance to the scattering plasma and its transverse velocity with respect to the line of sight. We report the observation of annual and orbital variations in the curvature of scintillation arcs over a period of 16 yr for the bright millisecond pulsar, PSR J0437−4715. These variations are the signature of the relative transverse motions of Earth, the pulsar, and the scattering medium, which we model to obtain precise measurements of parameters of the pulsar’s binary orbit and the scattering medium itself. We observe two clear scintillation arcs in most of our &gt;5000 observations, and we show that they originate from scattering by thin screens located at distances D 1 = 89.8 ± 0.4 pc and D 2 = 124 ± 3 pc from Earth. The best-fit scattering model we derive for the brightest arc yields the pulsar’s orbital inclination angle, i = 137.°1 ± 0.°3, and longitude of ascending node, Ω = 206.°3 ± 0.°4. Using scintillation arcs for precise astrometry and orbital dynamics can be superior to modeling variations in the diffractive scintillation timescale, because the arc curvature is independent of variations in the level of turbulence of interstellar plasma. This technique can be used in combination with pulsar timing to determine the full three-dimensional orbital geometries of binary pulsars and provides parameters essential for testing theories of gravity and constraining neutron star masses.

Martian Topographic Roughness Spectra and Its Influence on Bistatic Radar Scattering

There are few studies on predicting fully bistatic scattering from the rough surface of Mars, though some bistatic radar observations have been made, such as in the MARS EXPRESS mission. To better understand the interaction of radar signals with a planetary surface in bistatic radar observations, the topographic-scale roughness of Mars, characterized by a two-dimensional power spectrum density (2D-PSD), is examined in view of its global roughness variations and scale dependence on geological units. The analysis shows that the Martian 2D-PSD is strongly dependent on the geological units and that it lies between Gaussian and exponential functions, with a power index equal to 1.9. The bistatic scattering coefficients are calculated by an advanced integral equation model (AIEM) with the 2D-PSD as the input. It shows that the specific surface roughness spectrum and the dielectric inhomogeneity should be taken into account in interpreting the bistatic radar scattering response.

A Monte Carlo Implementation of Galactic Free–Free Emission for the EoR Foreground Models

Abstract The overwhelming foreground causes severe contamination on the detection of 21 cm signal during the Epoch of Reionization (EoR). Among various foreground components, the Galactic free–free emission is less studied, so that its impact on the EoR observation remains unclear. To better constrain this emission, we perform Monte Carlo simulation of Hα emission, which comprises direct and scattered Hα radiation from H ii regions and warm ionized medium (WIM). The positions and radii of H ii regions are quoted from the Wide-Field Infrared Survey Explorer H ii catalog, and the WIM is described by an axisymmetric model. The scattering is off dust and free electrons that are realized by applying an exponential fitting to the HI4PI H i map and an exponential disk model, respectively. The simulated Hα intensity, the Simfast21 software, and the latest SKA1-Low layout configuration are employed to simulate the SKA “observed” images of Galactic free–free emission and the EoR signal. By analyzing the one-dimensional power spectra, we find that the Galactic free–free emission can be about 105.4–102.1, 105.0–101.7, and 104.3–101.1 times more luminous than the EoR signal on scales of in the 116–124, 146–154, and 186–194 MHz frequency bands, respectively. We further calculate the two-dimensional power spectra inside the EoR window and show that the power leaked by Galactic free–free emission can still be significant, as the power ratios can reach about 110%–8000%, 30%–2400%, and 10%–250% on scales of in three frequency bands. Therefore, we indicate that the Galactic free–free emission should be carefully treated in future EoR detections.

The Impact of Realistic Foreground and Instrument Models on 21 cm Epoch of Reionization Experiments

Abstract Predictions for the ability of 21 cm interferometric experiments to discriminate Epoch of Reionization (EoR) signal models are typically limited by the simplicity of data models, whereby foreground signals and characteristics of the instrument are often simplified or neglected. To move toward more realistic scenarios, we explore the effects of applying more realistic foreground and instrument models to the 21 cm signal, as well as the ability to estimate astrophysical parameters with these additional complexities. We use a highly optimized version of 21cmFAST, integrated into 21cmMC, to generate lightcones of the brightness temperature fluctuation for Bayesian parameter estimation. We include a statistical point-source foreground model and an instrument model based on the Murchison Widefield Array scaled in observation time to have an effective sensitivity similar to the future Square Kilometre Array. We also extend the current likelihood prescription to account for the presence of beam convolution and foregrounds, the two-dimensional power spectrum (PS), and the correlation of PS modes. We use frequency bands between 150 and 180 MHz to constrain the ionizing efficiency (ζ), the minimum virial temperature of halos ( ), the soft X-ray emissivity per unit star formation rate (SFR) (L X /SFR), and the X-ray energy threshold (E 0). We find that the inclusion of realistic foregrounds and instrumental components biases the parameter constraints, due to unaccounted for cross-power between the EoR signal, foregrounds, and thermal noise. This causes estimates of ζ to be biased by up to 5σ, but the estimates of T vir, L X /SFR and E 0 remain unaffected and are all within 1σ.

Deep multiredshift limits on Epoch of Reionization 21 cm power spectra from four seasons of Murchison Widefield Array observations

Abstract We compute the spherically averaged power spectrum from four seasons of data obtained for the Epoch of Reionization (EoR) project observed with the Murchison Widefield Array (MWA). We measure the EoR power spectrum over k = 0.07–3.0 h Mpc−1 at redshifts $z$ = 6.5–8.7. The largest aggregation of 110 h on EoR0 high band (3340 observations), yields a lowest measurement of (43 mK)2 = 1.8 × 103 mK2 at k = 0.14 h Mpc−1 and $z$ = 6.5 (2σ thermal noise plus sample variance). Using the Real-Time System to calibrate and the CHIPS pipeline to estimate power spectra, we select the best observations from the central five pointings within the 2013–2016 observing seasons, observing three independent fields and in two frequency bands. This yields 13 591 2-min snapshots (453 h), based on a quality assurance metric that measures ionospheric activity. We perform another cut to remove poorly calibrated data, based on power in the foreground-dominated and EoR-dominated regions of the two-dimensional power spectrum, reducing the set to 12 569 observations (419 h). These data are processed in groups of 20 observations, to retain the capacity to identify poor data, and used to analyse the evolution and structure of the data over field, frequency, and data quality. We subsequently choose the cleanest 8935 observations (298 h of data) to form integrated power spectra over the different fields, pointings, and redshift ranges.

Filaments and striations: anisotropies in observed, supersonic, highly magnetized turbulent clouds

ABSTRACTStars form in highly magnetized, supersonic turbulent molecular clouds. Many of the tools and models that we use to carry out star formation studies rely upon the assumption of cloud isotropy. However, structures like high-density filaments in the presence of magnetic fields and magnetosonic striations introduce anisotropies into the cloud. In this study, we use the two-dimensional power spectrum to perform a systematic analysis of the anisotropies in the column density for a range of Alfvén Mach numbers ($\operatorname{\mathcal {M}_{\text{A}}}=0.1{\!-\!10}$) and turbulent Mach numbers ($\operatorname{\mathcal {M}}=2{\!-\!20}$), with 20 high-resolution, three-dimensional turbulent magnetohydrodynamic simulations. We find that for cases with a strong magnetic guide field, corresponding to $\operatorname{\mathcal {M}_{\text{A}}}\lt 1$, and $\operatorname{\mathcal {M}}\lesssim 4$, the anisotropy in the column density is dominated by thin striations aligned with the magnetic field, while for $\operatorname{\mathcal {M}}\gtrsim 4$ the anisotropy is significantly changed by high-density filaments that form perpendicular to the magnetic guide field. Indeed, the strength of the magnetic field controls the degree of anisotropy and whether or not any anisotropy is present, but it is the turbulent motions controlled by $\operatorname{\mathcal {M}}$ that determine which kind of anisotropy dominates the morphology of a cloud.

A chromospheric resonance cavity in a sunspot mapped with seismology

Sunspots are intense collections of magnetic fields that pierce through the Sun’s photosphere, with their signatures extending upwards into the outermost extremities of the solar corona1. Cutting-edge observations and simulations are providing insights into the underlying wave generation2, configuration3,4 and damping5 mechanisms found in sunspot atmospheres. However, the in situ amplification of magnetohydrodynamic waves6, rising from a few hundreds of metres per second in the photosphere to several kilometres per second in the chromosphere7, has, until now, proved difficult to explain. Theory predicts that the enhanced umbral wave power found at chromospheric heights may come from the existence of an acoustic resonator8–10, which is created due to the substantial temperature gradients experienced at photospheric and transition region heights11. Here, we provide strong observational evidence of a resonance cavity existing above a highly magnetic sunspot. Through a combination of spectropolarimetric inversions and comparisons with high-resolution numerical simulations, we provide a new seismological approach to mapping the geometry of the inherent temperature stratifications across the diameter of the underlying sunspot, with the upper boundaries of the chromosphere ranging between 1,300 ± 200 km and 2,300 ± 250 km. Our findings will allow the three-dimensional structure of solar active regions to be conclusively determined from relatively commonplace two-dimensional Fourier power spectra. The techniques presented are also readily suitable for investigating temperature-dependent resonance effects in other areas of astrophysics, including the examination of Earth–ionosphere wave cavities12. Spectropolarimetric data combined with high-resolution numerical simulations reveal a resonance cavity above a highly magnetic sunspot. This technique conclusively determines the three-dimensional structure of solar active regions from relatively commonplace two-dimensional data.

Contribution of Radio Halos to the Foreground for SKA EoR Experiments

The overwhelming foreground contamination is one of the primary impediments to probing the Epoch of Reionization (EoR) through measuring the redshifted 21 cm signal. Among various foreground components, radio halos are less studied and their impacts on the EoR observations are still poorly understood. In this work, we employ the Press-Schechter formalism, merger-induced turbulent re-acceleration model, and the latest SKA1-Low layout configuration to simulate the SKA "observed" images of radio halos. We calculate the one-dimensional power spectra from simulated images and find that radio halos can be about $10^4$, $10^3$ and $10^{2.5}$ times more luminous than the EoR signal on scales of $0.1\,\text{Mpc}^{-1} < k < 2\,\text{Mpc}^{-1}$ in the 120-128, 154-162, and 192-200 MHz bands, respectively. By examining the two-dimensional power spectra inside properly defined EoR windows, we find that the power leaked by radio halos can still be significant, as the power ratios of radio halos to the EoR signal on scales of $0.5\,\text{Mpc}^{-1} \lesssim k \lesssim 1\,\text{Mpc}^{-1}$ can be up to about 230-800%, 18-95%, and 7-40% in the three bands, when the 68% uncertainties caused by the variation of the number density of bright radio halos are considered. Furthermore, we find that radio halos located inside the far side-lobes of the station beam can also impose strong contamination within the EoR window. In conclusion, we argue that radio halos are severe foreground sources and need serious treatments in future EoR experiments.