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

Detectability of CMB tensor B modes via delensing with weak lensing galaxy surveys

We analyze the possibility of delensing CMB polarization maps using foreground weak lensing (WL) information. We build an estimator of the CMB lensing potential out of optimally combined projected potential estimators to different source redshift bins. Our estimator is most sensitive to the redshift depth of the WL survey, less so to the shape noise level. Estimators built using galaxy surveys like LSST and SNAP yield a 30-50% reduction in the lensing B-mode power. We illustrate the potential advantages of a 21-cm survey by considering a fiducial WL survey for which we take the redshift depth zmax and the effective angular concentration of sources n as free parameters. For a noise level of 1 muK arcmin in the polarization map itself, as projected for a CMBPol experiment, and a beam with FWHM=10 arcmin, we find that going to zmax=20 at n=100 gal/sqarcmin yields a delensing performance similar to that of a quadratic lensing potential estimator applied to small-scale CMB maps: the lensing B-mode contamination is reduced by almost an order of magnitude. In this case, there is also a reduction by a factor of ~4 in the detectability threshold of the tensor B-mode power. At this CMB noise level, there is little gain from sources with zmax>20. The delensing gains are lost if the CMB beam exceeds ~20 arcmin. The delensing efficiency and useful zmax depend acutely on the CMB map noise level, but beam sizes below 10 arcmin do not help. Delensing via foreground sources does not require arcminute-resolution CMB observations, a substantial practical advantage over the use of CMB observables for delensing.Comment: 10 pages, 5 figures; accepted for publication in Physical Review

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

Improved Parameters and New Lensed Features for Q0957+561 from WFPC2 Imaging

New HST WFPC2 observations of the lensed double QSO 0957+561 will allow improved constraints on the lens mass distribution and hence will improve the derived value of H$_0$. We first present improved optical positions and photometry for the known components of this lens. The optical separation between the A and B quasar images agrees with VLBI data at the 10 mas level, and the optical center of the primary lensing galaxy G1 coincides with the VLBI source G' to within 10 mas. The best previous model for this lens (Grogin and Narayan 1996) is excluded by these data and must be reevaluated. Several new resolved features are found within 10\arcsec of G1, including an apparent fold arc with two bright knots. Several other small galaxies are detected, including two which may be multiple images of each other. We present positions and crude photometry of these objects.Comment: 7 pages including 2 postscript figures, LaTeX, emulateapj style. Also available at http://www.astro.lsa.umich.edu:80/users/philf/www/papers/list.htm