A constructive theory of sampling for image synthesis using reproducing kernel bases

Sampling a scene by tracing rays and reconstructing an image from such pointwise samples is fundamental to computer graphics. To improve the efficacy of these computations, we propose an alternative theory of sampling. In contrast to traditional formulations for image synthesis, which appeal to nonconstructive Dirac deltas, our theory employs constructive reproducing kernels for the correspondence between continuous functions and pointwise samples. Conceptually, this allows us to obtain a common mathematical formulation of almost all existing numerical techniques for image synthesis. Practically, it enables novel sampling based numerical techniques designed for light transport that provide considerably improved performance per sample. We exemplify the practical benefits of our formulation with three applications: pointwise transport of color spectra, projection of the light energy density into spherical harmonics, and approximation of the shading equation from a photon map. Experimental results verify the utility of our sampling formulation, with lower numerical error rates and enhanced visual quality compared to existing techniques

A Monte Carlo Template based analysis for Air-Cherenkov Arrays

We present a high-performance event reconstruction algorithm: an Image Pixel-wise fit for Atmospheric Cherenkov Telescopes (ImPACT). The reconstruction algorithm is based around the likelihood fitting of camera pixel amplitudes to an expected image template. A maximum likelihood fit is performed to find the best-fit shower parameters. A related reconstruction algorithm has already been shown to provide significant improvements over traditional reconstruction for both the CAT and H.E.S.S. experiments. We demonstrate a significant improvement to the template generation step of the procedure, by the use of a full Monte Carlo air shower simulation in combination with a ray-tracing optics simulation to more accurately model the expected camera images. This reconstruction step is combined with an MVA-based background rejection. Examples are shown of the performance of the ImPACT analysis on both simulated and measured (from a strong VHE source) gamma-ray data from the H.E.S.S. array, demonstrating an improvement in sensitivity of more than a factor two in observation time over traditional image moments-fitting methods, with comparable performance to previous likelihood fitting analyses. ImPACT is a particularly promising approach for future large arrays such as the Cherenkov Telescope Array (CTA) due to its improved high-energy performance and suitability for arrays of mixed telescope types.Comment: 13 pages, 10 figure

Predicting the number of giant arcs expected in the next generation wide-field surveys from space

In this paper we estimate the number of gravitational arcs detectable in a wide-field survey such as that which will be operated by the Euclid space mission, assuming a {\Lambda}CDM cosmology. We use the publicly available code MOKA to obtain realistic deflection angle maps of mock gravitational lenses. The maps are processed by a ray-tracing code to estimate the strong lensing cross sections of each lens. Our procedure involves 1) the generation of a light-cone which is populated with lenses drawn from a theoretical mass-function; 2) the modeling of each single lens using a triaxial halo with a NFW (Navarro-Frenk-White) density profile and theoretical concentration-mass relation, including substructures, 3) the determination of the lensing cross section as a function of redshift for each lens in the light-cone, 4) the simulation of mock observations to characterize the redshift distribution of sources that will be detectable in the Euclid images. We focus on the so-called giant arcs, i.e. gravitational arcs characterized by large length-to-width ratios (l/w > 5, 7.5 and 10). We quantify the arc detectability at different significances above the level of the background. Performing 128 different realizations of a 15,000 sq. degree survey, we find that the number of arcs detectable at 1{\sigma} above the local background will be 8912,2914, and 1275 for l/w>5, 7.5 and 10, respectively. The expected arc numbers decrease to 2409, 790, and 346 for a detection limit at 3{\sigma} above the background level. From our analysis, we find that most of the lenses which contribute to the lensing optical depth are located at redshifts 0.4<zl<0.7 and that the 50% of the arcs are images of sources at zs > 3. This is the first step towards the full characterization of the population of strong lenses that will be observed by Euclid. [abridged]Comment: replaced to match the accepted version by MNRAS, 12 pag, 10 fig - more references adde

Weighing simulated galaxy clusters using lensing and X-ray

We aim at investigating potential biases in lensing and X-ray methods to measure the cluster mass profiles. We do so by performing realistic simulations of lensing and X-ray observations that are subsequently analyzed using observational techniques. The resulting mass estimates are compared among them and with the input models. Three clusters obtained from state-of-the-art hydrodynamical simulations, each of which has been projected along three independent lines-of-sight, are used for this analysis. We find that strong lensing models can be trusted over a limited region around the cluster core. Extrapolating the strong lensing mass models to outside the Einstein ring can lead to significant biases in the mass estimates, if the BCG is not modeled properly for example. Weak lensing mass measurements can be largely affected by substructures, depending on the method implemented to convert the shear into a mass estimate. Using non-parametric methods which combine weak and strong lensing data, the projected masses within R200 can be constrained with a precision of ~10%. De-projection of lensing masses increases the scatter around the true masses by more than a factor of two due to cluster triaxiality. X-ray mass measurements have much smaller scatter (about a factor of two smaller than the lensing masses) but they are generally biased low by 5-20%. This bias is ascribable to bulk motions in the gas of our simulated clusters. Using the lensing and the X-ray masses as proxies for the true and the hydrostatic equilibrium masses of the simulated clusters and averaging over the cluster sample we are able to measure the lack of hydrostatic equilibrium in the systems we have investigated.Comment: 27 pages, 21 figures, accepted for publication on A&A. Version with full resolution images can be found at http://pico.bo.astro.it/~massimo/Public/Papers/massComp.pd

Integral Field Unit Observations of NGC 891: Kinematics of the Diffuse Ionized Gas Halo

We present high and moderate spectral resolution spectroscopy of diffuse ionized gas (DIG) emission in the halo of NGC 891. The data were obtained with the SparsePak integral field unit at the WIYN Observatory. The wavelength coverage includes the [NII]6548,6583, Halpha, and [SII]6716,6731 emission lines. Position-velocity (PV) diagrams, constructed using spectra extracted from four SparsePak pointings in the halo, are used to examine the kinematics of the DIG. Using two independent methods, a vertical gradient in azimuthal velocity is found to be present in the northeast quadrant of the halo, with magnitude approximately 15-18 km/s/kpc, in agreement with results from HI observations. The kinematics of the DIG suggest that this gradient begins at approximately 1 kpc above the midplane. In another part of the halo, the southeast quadrant, the kinematics are markedly different, and suggest rotation at about 175 km/s, much slower than the disk but with no vertical gradient. We utilize an entirely ballistic model of disk-halo flow in an attempt to reproduce the kinematics observed in the northeast quadrant. Analysis shows that the velocity gradient predicted by the ballistic model is far too shallow. Based on intensity cuts made parallel to the major axis in the ballistic model and an Halpha image of NGC 891 from the literature, we conclude that the DIG halo is much more centrally concentrated than the model, suggesting that hydrodynamics dominate over ballistic motion in shaping the density structure of the halo. Velocity dispersion measurements along the minor axis of NGC 891 seem to indicate a lack of radial motions in the halo, but the uncertainties do not allow us to set firm limits.Comment: 31 pages, 10 figures. Accepted for publication in the Astrophysical Journa

Source-lens clustering effects on the skewness of the lensing convergence

The correlation between source galaxies and lensing potentials causes a systematic effect on measurements of cosmic shear statistics, known as the source-lens clustering (SLC) effect. The SLC effect on the skewness of lensing convergence, $S_3$, is examined using a nonlinear semi-analytic approach and is checked against numerical simulations. The semi-analytic calculations have been performed in a wide variety of generic models for the redshift distribution of source galaxies and power-law models for the bias parameter between the galaxy and dark matter distributions. The semi-analytic predictions are tested successfully against numerical simulations. We find the relative amplitude of the SLC effect on $S_3$ to be of the order of five to forty per cent. It depends significantly on the redshift distribution of sources and on the way the bias parameter evolves. We discuss possible measurement strategies to minimize the SLC effects.Comment: 14 pages, 14 figures, accepted for publication in MNRA