Resampling images in Fourier domain

When simulating sky images, one often takes a galaxy image $F(x)$ defined by a set of pixelized samples and an interpolation kernel, and then wants to produce a new sampled image representing this galaxy as it would appear with a different point-spread function, a rotation, shearing, or magnification, and/or a different pixel scale. These operations are sometimes only possible, or most efficiently executed, as resamplings of the Fourier transform $\tilde F(u)$ of the image onto a $u$-space grid that differs from the one produced by a discrete Fourier transform (DFT) of the samples. In some applications it is essential that the resampled image be accurate to better than 1 part in $10^3$, so in this paper we first use standard Fourier techniques to show that Fourier-domain interpolation with a wrapped sinc function yields the exact value of $\tilde F(u)$ in terms of the input samples and kernel. This operation scales with image dimension as $N^4$ and can be prohibitively slow, so we next investigate the errors accrued from approximating the sinc function with a compact kernel. We show that these approximations produce a multiplicative error plus a pair of ghost images (in each dimension) in the simulated image. Standard Lanczos or cubic interpolators, when applied in Fourier domain, produce unacceptable artifacts. We find that errors $<1$ part in $10^3$ can be obtained by (1) 4-fold zero-padding of the original image before executing the $x\rightarrow u$ DFT, followed by (2) resampling to the desired $u$ grid using a 6-point, piecewise-quintic interpolant that we design expressly to minimize the ghosts, then (3) executing the DFT back to $x$ domain.Comment: Typographical and one algebraic correction, to appear in PASP March 201

Optimizing weak lensing mass estimates for cluster profile uncertainty

Weak lensing measurements of cluster masses are necessary for calibrating mass-observable relations (MORs) to investigate the growth of structure and the properties of dark energy. However, the measured cluster shear signal varies at fixed mass M_200m due to inherent ellipticity of background galaxies, intervening structures along the line of sight, and variations in the cluster structure due to scatter in concentrations, asphericity and substructure. We use N-body simulated halos to derive and evaluate a weak lensing circular aperture mass measurement M_ap that minimizes the mass estimate variance <(M_ap - M_200m)^2> in the presence of all these forms of variability. Depending on halo mass and observational conditions, the resulting mass estimator improves on M_ap filters optimized for circular NFW-profile clusters in the presence of uncorrelated large scale structure (LSS) about as much as the latter improve on an estimator that only minimizes the influence of shape noise. Optimizing for uncorrelated LSS while ignoring the variation of internal cluster structure puts too much weight on the profile near the cores of halos, and under some circumstances can even be worse than not accounting for LSS at all. We briefly discuss the impact of variability in cluster structure and correlated structures on the design and performance of weak lensing surveys intended to calibrate cluster MORs.Comment: 11 pages, 5 figures; accepted by MNRA

Use of entanglement in quantum optics

Several recent demonstrations of two-particle interferometry are reviewed and shown to be examples of either color entanglement or beam entanglement. A device, called a number filter, is described and shown to be of value in preparing beam entanglements. Finally, we note that all three concepts (color and beam entaglement, and number filtering) may be extended to three or more particles

Characterization and correction of charge-induced pixel shifts in DECam

Interaction of charges in CCDs with the already accumulated charge distribution causes both a flux dependence of the point-spread function (an increase of observed size with flux, also known as the brighter/fatter effect) and pixel-to-pixel correlations of the Poissonian noise in flat fields. We describe these effects in the Dark Energy Camera (DECam) with charge dependent shifts of effective pixel borders, i.e. the Antilogus et al. (2014) model, which we fit to measurements of flat-field Poissonian noise correlations. The latter fall off approximately as a power-law r^-2.5 with pixel separation r, are isotropic except for an asymmetry in the direct neighbors along rows and columns, are stable in time, and are weakly dependent on wavelength. They show variations from chip to chip at the 20% level that correlate with the silicon resistivity. The charge shifts predicted by the model cause biased shape measurements, primarily due to their effect on bright stars, at levels exceeding weak lensing science requirements. We measure the flux dependence of star images and show that the effect can be mitigated by applying the reverse charge shifts at the pixel level during image processing. Differences in stellar size, however, remain significant due to residuals at larger distance from the centroid.Comment: typo and formatting fixes, matches version published in JINS

Assessing the psychometric properties of dream content questionnaires

The present study was the first of its kind to systematically explore the psychometric properties of dream content questionnaires as measures of dream experience. One hundred and six University students filled out the Dream Content Questionnaire (DCQ) and kept a 14-day dream diary on two separate occasions, in addition to filling out the NEO-PI-R and Multidimensional Personality Questionnaire and measures of spatial ability and imaginativeness. The DCQ's reliability was acceptable, as was its discriminant and construct validity. Six of eight predicted relationships between trait personality and DCQ reported dream content were significant. In contrast, dream diaries showed instability over time and were unrelated to personality traits. The DCQ's concurrent validity could not be adequately appraised due to the inconsistency in dream diary content over time. The results suggest that questionnaires may be used to measure dream experience; however, the precise utility of dream questionnaires remains unclear. The findings raise important questions concerning measures of dream experience

Symmetry without Symmetry: Numerical Simulation of Axisymmetric Systems using Cartesian Grids

We present a new technique for the numerical simulation of axisymmetric systems. This technique avoids the coordinate singularities which often arise when cylindrical or polar-spherical coordinate finite difference grids are used, particularly in simulating tensor partial differential equations like those of 3+1 numerical relativity. For a system axisymmetric about the z axis, the basic idea is to use a 3-dimensional Cartesian (x,y,z) coordinate grid which covers (say) the y=0 plane, but is only one finite-difference-molecule--width thick in the y direction. The field variables in the central y=0 grid plane can be updated using normal (x,y,z)--coordinate finite differencing, while those in the y \neq 0 grid planes can be computed from those in the central plane by using the axisymmetry assumption and interpolation. We demonstrate the effectiveness of the approach on a set of fully nonlinear test computations in 3+1 numerical general relativity, involving both black holes and collapsing gravitational waves.Comment: 17 pages, 4 figure

An ongoing secondary task can reduce the illusory truth effect

IntroductionPeople are more likely to believe repeated information—this is known as the Illusory Truth Effect (ITE). Recent research on the ITE has shown that semantic processing of statements plays a key role. In our day to day experience, we are often multi-tasking which can impact our ongoing processing of information around us. In three experiments, we investigate how asking participants to engage in an ongoing secondary task in the ITE paradigm influences the magnitude of the effect of repetition on belief.MethodsUsing an adapted ITE paradigm, we embedded a secondary task into each trial of the encoding and/or test phase (e.g., having participants count the number of vowels in a target word of each trivia claim) and calculated the overall accuracy on the task.ResultsWe found that the overall ITE was larger when participants had no ongoing secondary task during the experiment. Further, we predicted and found that higher accuracy on the secondary task was associated with a larger ITE.DiscussionThese findings provide initial evidence that engaging in an ongoing secondary task may reduce the impact of repetition. Our findings suggest that exploring the impact of secondary tasks on the ITE is a fruitful area for further research

Constraining the expansion history of the universe from the red shift evolution of cosmic shear

We present a quantitative analysis of the constraints on the total equation of state parameter that can be obtained from measuring the red shift evolution of the cosmic shear. We compare the constraints that can be obtained from measurements of the spin two angular multipole moments of the cosmic shear to those resulting from the two dimensional and three dimensional power spectra of the cosmic shear. We find that if the multipole moments of the cosmic shear are measured accurately enough for a few red shifts the constraints on the dark energy equation of state parameter improve significantly compared to those that can be obtained from other measurements.Comment: 17 pages, 4 figure