Two-dimensional Power Spectrum Research Articles

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.

Interface depth modelling of gravity data and altitude variations: a Bayesian neural network approach

Modelling of anomalous geological source from the gravity data is vital for understanding the crustal/sub-crustal interface depths and associated hazard assessment. Two-dimensional radial power spectra have usually been used to infer average depth of protuberant geological structures, which lack details of dimensional comprehension of lateral interfaces. Here in this study, we implement jointly scaled conjugate gradient-based Bayesian neural network (SCG-BNN) scheme with variogram modelling to carve out shallow and deeper interfaces of complex geological terrain of Eastern Indian Shield, India, using Bouguer gravity anomaly (BGA) and altitude variations data. Our “learner codes” uses the SCG-BNN optimization algorithm to build up a statistical model involving appropriate control parameters for the modelling of shallow and deeper interfaces. We have also compared the proposed SCG-BNN modelling results with the results of both conventional artificial neural networks (ANNs) schemes (e.g. conjugate gradient-based ANNs (CG-ANN) and SCG-ANN) and support vector regression (SVR) modelling to demonstrate the robustness of the underlying method. Comparative analysis suggests that the SCG-BNN model produced superior results than the results of CG-ANN, SCG-ANN and SVR models. The results based on SCG-BNN analysis and variogram modelling have identified the existence of three conspicuous fault structures, namely Malda–Kishanganj Fault, Munger–Saharsha Ridge Marginal Fault and Katihar Fault. The analyses also significantly minimize prediction error in three independent datasets (viz. training, validation and test), enhancing the precision of estimated shallow and deeper interface depths and thereby extenuating feasibility of “SCG-BNN” learner code. We, therefore, conclude that the underlying approach is robust to model various interface depths and generate precisely variation in the shallow and deeper interfaces with appropriate input data from altitude variation and BGA. The “SCG-BNN learner scheme” may potentially be used to exploit interface depths from several other complex tectonic regions.

Application of fractal dimension for quantifying noise texture in computed tomography images.

Evaluation of noise texture information in CT images is important for assessing image quality. Noise texture is often quantified by the noise power spectrum (NPS), which requires numerous image realizations to estimate. This study evaluated fractal dimension for quantifying noise texture as a scalar metric that can potentially be estimated using one image realization. The American College of Radiology CT accreditation phantom (ACR) was scanned on a clinical scanner (Discovery CT750, GE Healthcare) at 120kV and 25 and 90mAs. Images were reconstructed using filtered back projection (FBP/ASIR 0%) with varying reconstruction kernels: Soft, Standard, Detail, Chest, Lung, Bone, and Edge. For each kernel, images were also reconstructed using ASIR 50% and ASIR 100% iterative reconstruction (IR) methods. Fractal dimension was estimated using the differential box-counting algorithm applied to images of the uniform section of ACR phantom. The two-dimensional Noise Power Spectrum (NPS) and one-dimensional-radially averaged NPS were estimated using established techniques. By changing the radiation dose, the effect of noise magnitude on fractal dimension was evaluated. The Spearman correlation between the fractal dimension and the frequency of the NPS peak was calculated. The number of images required to reliably estimate fractal dimension was determined and compared to the number of images required to estimate the NPS-peak frequency. The effect of Region of Interest (ROI) size on fractal dimension estimation was evaluated. Feasibility of estimating fractal dimension in an anthropomorphic phantom and clinical image was also investigated, with the resulting fractal dimension compared to that estimated within the uniform section of the ACR phantom. Fractal dimension was strongly correlated with the frequency of the peak of the radially averaged NPS curve, having a Spearman rank-order coefficient of 0.98 (P-value<0.01) for ASIR 0%. The mean fractal dimension at ASIR 0% was 2.49 (Soft), 2.51 (Standard), 2.52 (Detail), 2.57 (Chest), 2.61 (Lung), 2.66 (Bone), and 2.7 (Edge). A reduction in fractal dimension was observed with increasing ASIR levels for all investigated reconstruction kernels. Fractal dimension was found to be independent of noise magnitude. Fractal dimension was successfully estimated from four ROIs of size 64×64 pixels or one ROI of 128×128 pixels. Fractal dimension was found to be sensitive to non-noise structures in the image, such as ring artifacts and anatomical structure. Fractal dimension estimated within a uniform region of an anthropomorphic phantom and clinical head image matched that estimated within the ACR phantom for filtered back projection reconstruction. Fractal dimension correlated with the NPS-peak frequency and was independent of noise magnitude, suggesting that the scalar metric of fractal dimension can be used to quantify the change in noise texture across reconstruction approaches. Results demonstrated that fractal dimension can be estimated from four, 64×64-pixel ROIs or one 128×128 ROI within a head CT image, which may make it amenable for quantifying noise texture within clinical images.

Multi-phase Turbulence Density Power Spectra in the Perseus Molecular Cloud

Abstract We derive two-dimensional spatial power spectra of four distinct interstellar medium tracers, H i, 12CO(J = 1–0), 13CO(J = 1–0), and dust, in the Perseus molecular cloud, covering linear scales ranging from ∼0.1 pc to ∼90 pc. Among the four tracers, we find the steepest slopes of −3.23 ± 0.05 and −3.22 ± 0.05 for the uncorrected and opacity-corrected H i column density images. This result suggests that the H i in and around Perseus traces a non-gravitating, transonic medium on average, with a negligible effect from opacity. On the other hand, we measure the shallowest slope of −2.72 ± 0.12 for the 2MASS dust extinction data and interpret this as the signature of a self-gravitating, supersonic medium. Possible variations in the dust-to-gas ratio likely do not alter our conclusion. Finally, we derive slopes of −3.08 ± 0.08 and −2.88 ± 0.07 for the 12CO(1–0) and 13CO(1–0) integrated intensity images. Based on theoretical predictions for an optically thick medium, we interpret these slopes of roughly −3 as implying that both CO lines are susceptible to the opacity effect. While simple tests for the impact of CO formation and depletion indicate that the measured slopes of 12CO(1–0) and 13CO(1–0) are not likely affected by these chemical effects, our results generally suggest that chemically more complex and/or fully optically thick media may not be a reliable observational tracer for characterizing turbulence.

Joint Bayesian estimation of tensor and lensing B modes in the power spectrum of CMB polarization data

We investigate the performance of a simple Bayesian fitting approach to correct the cosmic microwave background (CMB) B-mode polarization for gravitational lensing effects in the recovered probability distribution of the tensor-to-scalar ratio. We perform a two-dimensional power spectrum fit of the amplitude of the primordial B-modes (tensor-to-scalar ratio, $r$) and the amplitude of the lensing B-modes (parameter $A_{lens}$), jointly with the estimation of the astrophysical foregrounds including both synchrotron and thermal dust emissions. Using this Bayesian framework, we forecast the ability of the proposed CMB space mission LiteBIRD to constrain $r$ in the presence of realistic lensing and foreground contributions. We compute the joint posterior distribution of $r$ and $A_{lens}$, which we improve by adopting a prior on $A_{lens}$ taken from the South Pole Telescope (SPT) measurement. As it applies to the power spectrum, this approach cannot mitigate the uncertainty on $r$ that is due to E-mode cosmic variance transferred to B-modes by lensing, unlike standard delensing techniques that are performed on maps. However, the method allows to correct for the bias on $r$ induced by lensing, at the expense of a larger uncertainty due to the increased volume of the parameter space. We quantify, for different values of the tensor-to-scalar ratio, the trade-off between bias correction and increase of uncertainty on $r$. For LiteBIRD simulations, which include foregrounds and lensing contamination, we find that correcting the foreground-cleaned CMB B-mode power spectrum for the lensing bias, not the lensing cosmic variance, still guarantees a $3\sigma$ detection of $r=5\times 10^{-3}$. The significance of the detection is increased to $6\sigma$ when the current SPT prior on $A_{lens}$ is adopted.

Influence of hypersonic turbulence in plasma sheath on synthetic aperture radar imaging

On the basis of the fractal theory and measurements of hypersonic turbulence, the spectral index, and two-dimensional (2D) power spectrum of the refractive index fluctuation are derived, and the 2D band-limited Weierstrass fractal function is applied to simulate the refractive index fluctuation in hypersonic turbulence. Thus, the impact of hypersonic turbulence on synthetic aperture radar (SAR) imaging system is simulated using the fractal phase screen method. Results show that the resolution of SAR imaging is severely deteriorated under the influence of hypersonic turbulence. The phase error caused by the turbulence microstructures in the plasma sheath becomes more apparent with the increase in the fractal dimension of the hypersonic turbulence. The larger Reynolds number associated with the hypersonic turbulence results in a more evident microstructure fluctuation and inferior imaging quality. Furthermore, when an aircraft flies at high speed, the azimuth focus is considerably sensitive to the turbulence microstructure along the direction of flow field. Consequently, hypersonic turbulence in the plasma sheath has a significantly larger effect on the azimuth than on the range in point-target imaging.

Predicting acoustic backscattering from bioturbated seafloors

Seabed roughness is an important property for high-frequency scattering. However, for certain littoral environments, the surficial roughness of the seabed is often continuously being modified by hydrodynamic and biologic forces. For example, ocean surface waves may create orbital ripples on sand seafloors which are characterized by anisotropic roughness, and acoustic scattering from such a seafloor would be strongly aspect-dependent. Yet bottom-dwelling organisms rework the sediment, returning the structured seabed relief to random isotropic roughness, where acoustic scattering is more uniform with respect to the aspect ensonified. In this talk, we will utilize both analytic expressions as well as procedural generation methods to predict the two-dimensional roughness equilibrium power spectra of rippled and bioturbated seafloors, and the resulting impact on acoustic scattering prediction.

Texture features for object salience

Although texture is important for many vision-related tasks, it is not used in most salience models. As a consequence, there are images where all existing salience algorithms fail. We introduce a novel set of texture features built on top of a fast model of complex cells in striate cortex, i.e., visual area V1. The texture at each position is characterised by the two-dimensional local power spectrum obtained from Gabor filters which are tuned to many scales and orientations. We then apply a parametric model and describe the local spectrum by the combination of two one-dimensional Gaussian approximations: the scale and orientation distributions. The scale distribution indicates whether the texture has a dominant frequency and what frequency it is. Likewise, the orientation distribution attests the degree of anisotropy. We evaluate the features in combination with the state-of-the-art VOCUS2 salience algorithm. We found that using our novel texture features in addition to colour improves AUC by 3.8% on the PASCAL-S dataset when compared to the colour-only baseline, and by 62% on a novel texture-based dataset.

Optimal Gabor filter-based edge detection of high spatial resolution remotely sensed images

Edge extraction from high spatial resolution (HSR) remotely sensed images is one of the essential tasks for image segmentation and object identification. We present an optimal Gabor-based edge detection method which mainly focuses on selecting optimal parameters, including central frequency and spectrum scale, for Gabor filter. The central frequency is automatically optimized by phase randomization and the human visual system-based structure similarity index. Next, the optimal spectrum scale is determined based on two-dimensional power spectrum density. The edge detection method is comprehensively discussed in the analysis of parameter sensitivity, overall performance, and comparative tests with several widely used methods. Qualitative and quantitative experimental studies, performed on six test images with various spatial resolution, show that the proposed method provides a promising solution to edge detection from HSR remotely sensed images.

A High-Resolution Foreground Model for the MWA EoR1 Field: Model and Implications for EoR Power Spectrum Analysis

AbstractThe current generation of experiments aiming to detect the neutral hydrogen signal from the Epoch of Reionisation (EoR) is likely to be limited by systematic effects associated with removing foreground sources from target fields. In this paper, we develop a model for the compact foreground sources in one of the target fields of the MWA’s EoR key science experiment: the ‘EoR1’ field. The model is based on both the MWA’s GLEAM survey and GMRT 150 MHz data from the TGSS survey, the latter providing higher angular resolution and better astrometric accuracy for compact sources than is available from the MWA alone. The model contains 5 049 sources, some of which have complicated morphology in MWA data, Fornax A being the most complex. The higher resolution data show that 13% of sources that appear point-like to the MWA have complicated morphology such as double and quad structure, with a typical separation of 33 arcsec. We derive an analytic expression for the error introduced into the EoR two-dimensional power spectrum due to peeling close double sources as single point sources and show that for the measured source properties, the error in the power spectrum is confined to highk⊥modes that do not affect the overall result for the large-scale cosmological signal of interest. The brightest 10 mis-modelled sources in the field contribute 90% of the power bias in the data, suggesting that it is most critical to improve the models of the brightest sources. With this hybrid model, we reprocess data from the EoR1 field and show a maximum of 8% improved calibration accuracy and a factor of two reduction in residual power ink-space from peeling these sources. Implications for future EoR experiments including the SKA are discussed in relation to the improvements obtained.

MEASUREMENT OF A REDSHIFT-SPACE POWER SPECTRUM FOR BOSS GALAXIES AND THE GROWTH RATE AT REDSHIFT 0.57

ABSTRACT We present a measurement of the two-dimensional (2D) redshift-space power spectrum for the Baryon Oscillation Spectroscopic Survey Data Release 11 CMASS galaxies in the northern Galactic cap based on the method developed by Jing &amp; Börner. In this method, we first measure the 2D redshift-space correlation function and obtain the 2D power spectrum based on Fourier transform of the correlation function. The method is tested with an N-body mock galaxy catalog, which demonstrates that the method can yield an accurate and unbiased measurement of the redshift-space power spectrum given that the input 2D correlation function is correct. Compared with previous measurements in literature that are usually based on direct Fourier transform in redshift space, our method has the advantages that the window function and shot noise are fully corrected. Thus, our measurement can facilitate a direct comparison with the theoretical predictions. Our 2D power spectrum, by construction, can reproduce the 2D correlation function, and it can reproduce, for example, the 2D power spectrum of Beutler et al. accurately if ours is convolved with the window function they provided. We then develop a method to measure the structure growth rate, by separating the anisotropic redshift-space power spectrum from the isotropic real-space power spectrum. We have carefully corrected for the nonlinearities in the mapping from real space to redshift space, according to the theoretical model of Zhang et al. Finally, we obtain the measurement of structure growth rate f( )σ 8( ) = 0.438 ± 0.037 at the effective redshift = 0.57. The result is useful for constraining cosmological parameters. The measurements of the 2D power spectrum will be released soon.

DELAY SPECTRUM WITH PHASE-TRACKING ARRAYS: EXTRACTING THE H i POWER SPECTRUM FROM THE EPOCH OF REIONIZATION

ABSTRACT The detection of redshifted 21 cm emission from the epoch of reionization (EoR) is a challenging task owing to strong foregrounds that dominate the signal. In this paper, we propose a general method, based on the delay spectrum approach, to extract H i power spectra that are applicable to tracking observations using an imaging radio interferometer ("Delay Spectrum with Imaging Arrays"). Our method is based on modeling the H i signal taking into account the impact of wide field effects such as the w-term, which are then used as appropriate weights in cross-correlating the measured visibilities. Our method is applicable to any radio interferometer that tracks a phase center and could be utilized for arrays such as the Murchison Widefield Array (MWA), Low Frequency Array (LOFAR), Giant Meterwave Radio Telescope (GMRT), Donald C. Backer Precision Array for Probing the Epoch of Reionization (PAPER), and HERA. In the literature the delay spectrum approach has been implemented for near-redundant baselines using drift scan observations. In this paper we explore the scheme for non-redundant tracking arrays. This is the first application of delay spectrum methodology to such data to extract the H i signal. We analyze 3 hr of MWA tracking data on the EoR1 field. We present both two-dimensional ( ) and one-dimensional (k) power spectra from the analysis. Our results are in agreement with the findings of other pipelines developed to analyze the MWA EoR data.

RZ Leonis Minoris bridging between ER Ursae Majoris-type dwarf nova and nova-like system

AbstractWe observed RZ LMi, which is renowned for its extremely short (∼19 d) supercycle and is a member of a small, unusual class of cataclysmic variables called ER UMa-type dwarf novae, in 2013 and 2016. In 2016, the supercycles of this object substantially lengthened in comparison to the previous measurements to 35, 32, and 60 d for three consecutive superoutbursts. We consider that the object virtually experienced a transition to the nova-like state (permanent superhumper). This observed behavior reproduced the prediction of the thermal-tidal instability model extremely well. We detected a precursor in the 2016 superoutburst and detected growing (stage A) superhumps with a mean period of 0.0602(1) d in 2016 and in 2013. Combined with the period of superhumps immediately after the superoutburst, the mass ratio is not as small as in WZ Sge-type dwarf novae, having orbital periods similar to RZ LMi. By using least absolute shrinkage and selection operator (Lasso) two-dimensional power spectra, we detected possible negative superhumps with a period of 0.05710(1) d. We estimated an orbital period of 0.05792 d, which suggests a mass ratio of 0.105(5). This relatively large mass ratio is even above that of ordinary SU UMa-type dwarf novae, and it is also possible that the exceptionally high mass-transfer rate in RZ LMi may be a result of a stripped secondary with an evolved core in a system evolving toward an AM CVn-type object.

Relation between one- and two-dimensional noise power spectra of magnetic resonance images.

Our purpose in this study was to elucidate the relation between the one-dimensional (1D) and two-dimensional (2D) noise power spectra (NPSs) in magnetic resonance imaging (MRI). We measured the 1D NPSs using the slit method and the radial frequency method. In the slit method, numerical slits 1 pixel wide and L pixels long were placed on a noise image (128×128pixels) and scanned in the MR image domain. We obtained the 1D NPS using the slit method (1D NPS_Slit) and the 2D NPS of the noise region scanned by the slit (2D NPS_Slit). We also obtained 1D NPS using the radial frequency method (1D NPS_Radial) by averaging the NPS values on the circumference of a circle centered at the origin of the original 2D NPS. The properties of the 1D NPS_Slits varied with L and the scanning direction in PROPELLER MRI. The 2D NPS_Slit shapes matched that of the original 2D NPS, but were compressed by L/128. The central line profiles of the 2D NPS_Slits and the 1D NPS_Slits matched exactly. Therefore, the 1D NPS_Slits reflected not only the NPS values on the central axis of the original 2D NPS, but also the NPS values around the central axis. Moreover, the measurement precisions of the 1D NPS_Slits were lower than those of the 1D NPS_Radial. Consequently, it is necessary to select the approach applied for 1D NPS measurements according to the data acquisition method and the purpose of the noise evaluation.

3D Imaging of Retinal Pigment Epithelial Cells in the Living Human Retina.

PurposeDysfunction of the retinal pigment epithelium (RPE) underlies numerous retinal pathologies, but biomarkers sensitive to RPE change at the cellular level are limited. In this study, we used adaptive optics optical coherence tomography (AO-OCT) in conjunction with organelle motility as a novel contrast mechanism to visualize RPE cells and characterize their 3-dimensional (3D) reflectance profile.MethodsUsing the Indiana AO-OCT imaging system (λc = 790 nm), volumes were acquired in the macula of six normal subjects (25–61 years). Volumes were registered in 3D with subcellular accuracy, layers segmented, and RPE and photoreceptor en face images extracted and averaged. Voronoi and two-dimensional (2D) power spectra analyses were applied to the images to quantify RPE and cone packing and cone-to-RPE ratio.ResultsAdaptive optics OCT revealed two distinct reflectance patterns at the depth of the RPE. One is characterized by the RPE interface with rod photoreceptor tips, the second by the RPE cell nuclei and surrounding organelles, likely melanin. Increasing cell contrast by averaging proved critical for observing the RPE cell mosaic, successful in all subjects and retinal eccentricities imaged. Retinal pigment epithelium mosaic packing and cell thickness generally agreed with that of histology and in vivo studies using other imaging modalities.ConclusionsWe have presented, to our knowledge, the first detailed characterization of the 3D reflectance profile of individual RPE cells and their relation to cones and rods in the living human retina. Success in younger and older eyes establishes a path for testing aging effects in larger populations. Because the technology is based on OCT, our measurements will aid in interpreting clinical OCT images.

Contamination of the Epoch of Reionization power spectrum in the presence of foregrounds

We construct foreground simulations comprising spatially correlated extragalactic and diffuse Galactic emission components and calculate the `intrinsic' (instrument-free) two-dimensional spatial power spectrum and the cylindrically and spherically averaged three-dimensional k-space power spectra of the Epoch of Reionization (EoR) and our foreground simulations using a Bayesian power spectral estimation framework. This leads us to identify a model dependent region of optimal signal estimation for our foreground and EoR models, within which the spatial power in the EoR signal relative to foregrounds is maximised. We identify a target field dependent region, in k-space, of intrinsic foreground power spectral contamination at low k_perp and k_parallel and a transition to a relatively foreground-free intrinsic EoR window in the complement to this region. The contaminated region of k-space demonstrates that simultaneous estimation of the EoR and foregrounds is important for obtaining statistically robust estimates of the EoR power spectrum; biased results will be obtained from methodologies that ignore their covariance. Using simulated observations with frequency dependent uv-coverage and primary beam, with the former derived for HERA in 37-antenna and 331-antenna configuration, we recover instrumental power spectra consistent with their intrinsic counterparts. We discuss the implications of these results for optimal strategies for unbiased estimation of the EoR power spectrum.

Impact of bowtie filter and object position on the two-dimensional noise power spectrum of a clinical MDCT system.

Noise characteristics of clinical multidetector CT (MDCT) systems can be quantified by the noise power spectrum (NPS). Although the NPS of CT has been extensively studied in the past few decades, the joint impact of the bowtie filter and object position on the NPS has not been systematically investigated. This work studies the interplay of these two factors on the two dimensional (2D) local NPS of a clinical CT system that uses the filtered backprojection algorithm for image reconstruction. A generalized NPS model was developed to account for the impact of the bowtie filter and image object location in the scan field-of-view (SFOV). For a given bowtie filter, image object, and its location in the SFOV, the shape and rotational symmetries of the 2D local NPS were directly computed from the NPS model without going through the image reconstruction process. The obtained NPS was then compared with the measured NPSs from the reconstructed noise-only CT images in both numerical phantom simulation studies and experimental phantom studies using a clinical MDCT scanner. The shape and the associated symmetry of the 2D NPS were classified by borrowing the well-known atomic spectral symbols s, p, and d, which correspond to circular, dumbbell, and cloverleaf symmetries, respectively, of the wave function of electrons in an atom. Finally, simulated bar patterns were embedded into experimentally acquired noise backgrounds to demonstrate the impact of different NPS symmetries on the visual perception of the object. (1) For a central region in a centered cylindrical object, an s-wave symmetry was always present in the NPS, no matter whether the bowtie filter was present or not. In contrast, for a peripheral region in a centered object, the symmetry of its NPS was highly dependent on the bowtie filter, and both p-wave symmetry and d-wave symmetry were observed in the NPS. (2) For a centered region-ofinterest (ROI) in an off-centered object, the symmetry of its NPS was found to be different from that of a peripheral ROI in the centered object, even when the physical positions of the two ROIs relative to the isocenter were the same. (3) The potential clinical impact of the highly anisotropic NPS, caused by the interplay of the bowtie filter and position of the image object, was highlighted in images of specific bar patterns oriented at different angles. The visual perception of the bar patterns was found to be strongly dependent on their orientation. The NPS of CT depends strongly on the bowtie filter and object position. Even if the location of the ROI with respect to the isocenter is fixed, there can be different symmetries in the NPS, which depend on the object position and the size of the bowtie filter. For an isolated off-centered object, the NPS of its CT images cannot be represented by the NPS measured from a centered object.

Wavelet analysis methods for radiography of multidimensional growth of planar mixing layers.

The counter-propagating shear campaign is examining instability growth and its transition to turbulence in the high-energy-density physics regime using a laser-driven counter-propagating flow platform. In these experiments, we observe consistent complex break-up of and structure growth in a tracer layer placed at the shear flow interface during the instability growth phase. We present a wavelet-transform based analysis technique capable of characterizing the scale- and directionality-resolved average intensity perturbations in static radiographs of the experiment. This technique uses the complete spatial information available in each radiograph to describe the structure evolution. We designed this analysis technique to generate a two-dimensional power spectrum for each radiograph from which we can recover information about structure widths, amplitudes, and orientations. The evolution of the distribution of power in the spectra for an experimental series is a potential metric for quantifying the structure size evolution as well as a system's evolution towards isotropy.

Extension of the Archaean Madibe-Kraaipan granite-greenstone terrane in southeast Botswana: Constraints from gravity and magnetic data

The main goal of this study is to use suitably processed potential field data between longitude 24°E to 26°E and latitude 25°S to 26.5°S to gain a better geological and structural understanding of the extension of the Madibe-Kraaipan granite-greenstone terrane in southeast Botswana. Specifically, 150 new gravity measurements at 2–4 km intervals are reduced and later merged with existing gravity data in Botswana and South Africa for an integrated crustal interpretation with regional aeromagnetic data.Gravity and aeromagnetic anomalies of the region present partly coincident medium to high amplitude regions alternating with low zones. Analysis of the data revealed the existence of relatively narrow NS trending rocks of dense and high magnetic intensity extending to the village of Mmathethe, corresponding to the northern extent of the Kraaipan greenstone belt. Much of the north-central area forms a broad magnetic low and gravity high implying Kraaipan metavolcanic rocks are more extensively developed in this area than previously recognized, under a blanket of Kalahari sediments that are ∼55 m thick as indicated by borehole data. The whole area lies within an ENE-trending Pre-Transvaal dyke swarm visible on the regional aeromagnetic data and much clearer on (proprietary) high resolution aeromagnetic data. The derivative and analytic signal techniques applied for both gravity and magnetic data spatially map the greenstone belt and multiple granite plutons very well.Depth estimates obtained by the 3D Euler method in combination with two-dimensional power spectrum technique locate the high magnetic intensity horizon at around 4.0 km. The depths were further confirmed by gravity model results along two profiles across the granite-greenstone terrane in Botswana and South Africa in a W-E direction. The models show generally steep-sided bodies of comparable width with a maximum depth extent of 4.7 km for the greenstones and 4.4 km for the younger plutons. The distribution and configuration of the greenstones and plutons suggest assembly of this Kaapvaal craton western domain by plate tectonic processes. Episodic intrusion of granitoids into Kraaipan greenstone successions led to deformation of the belt with significance to Au and Au-PGE mineralization. The mapped structures could be important for groundwater exploration in this dry farming terrane.