25,381 research outputs found
Interpolating point spread function anisotropy
Planned wide-field weak lensing surveys are expected to reduce the
statistical errors on the shear field to unprecedented levels. In contrast,
systematic errors like those induced by the convolution with the point spread
function (PSF) will not benefit from that scaling effect and will require very
accurate modeling and correction. While numerous methods have been devised to
carry out the PSF correction itself, modeling of the PSF shape and its spatial
variations across the instrument field of view has, so far, attracted much less
attention. This step is nevertheless crucial because the PSF is only known at
star positions while the correction has to be performed at any position on the
sky. A reliable interpolation scheme is therefore mandatory and a popular
approach has been to use low-order bivariate polynomials. In the present paper,
we evaluate four other classical spatial interpolation methods based on splines
(B-splines), inverse distance weighting (IDW), radial basis functions (RBF) and
ordinary Kriging (OK). These methods are tested on the Star-challenge part of
the GRavitational lEnsing Accuracy Testing 2010 (GREAT10) simulated data and
are compared with the classical polynomial fitting (Polyfit). We also test all
our interpolation methods independently of the way the PSF is modeled, by
interpolating the GREAT10 star fields themselves (i.e., the PSF parameters are
known exactly at star positions). We find in that case RBF to be the clear
winner, closely followed by the other local methods, IDW and OK. The global
methods, Polyfit and B-splines, are largely behind, especially in fields with
(ground-based) turbulent PSFs. In fields with non-turbulent PSFs, all
interpolators reach a variance on PSF systematics better than
the upper bound expected by future space-based surveys, with
the local interpolators performing better than the global ones
Difference image photometry with bright variable backgrounds
Over the last two decades the Andromeda Galaxy (M31) has been something of a
test-bed for methods aimed at obtaining accurate time-domain relative
photometry within highly crowded fields. Difference imaging methods, originally
pioneered towards M31, have evolved into sophisticated methods, such as the
Optimal Image Subtraction (OIS) method of Alard & Lupton (1998), that today are
most widely used to survey variable stars, transients and microlensing events
in our own Galaxy. We show that modern difference image (DIA) algorithms such
as OIS, whilst spectacularly successful towards the Milky Way bulge, may
perform badly towards high surface brightness targets such as the M31 bulge.
Poor results can occur in the presence of common systematics which add spurious
flux contributions to images, such as internal reflections, scattered light or
fringing. Using data from the Angstrom Project microlensing survey of the M31
bulge, we show that very good results are usually obtainable by first
performing careful photometric alignment prior to using OIS to perform
point-spread function (PSF) matching. This separation of background matching
and PSF matching, a common feature of earlier M31 photometry techniques, allows
us to take full advantage of the powerful PSF matching flexibility offered by
OIS towards high surface brightness targets. We find that difference images
produced this way have noise distributions close to Gaussian, showing
significant improvement upon results achieved using OIS alone. We show that
with this correction light-curves of variable stars and transients can be
recovered to within ~10 arcseconds of the M31 nucleus. Our method is simple to
implement and is quick enough to be incorporated within real-time DIA
pipelines. (Abridged)Comment: 12 pages. Accepted for publication in MNRAS. Includes an expanded
discussion of DIA testing and results, including additional lightcurve
example
Local interpolation schemes for landmark-based image registration: a comparison
In this paper we focus, from a mathematical point of view, on properties and
performances of some local interpolation schemes for landmark-based image
registration. Precisely, we consider modified Shepard's interpolants,
Wendland's functions, and Lobachevsky splines. They are quite unlike each
other, but all of them are compactly supported and enjoy interesting
theoretical and computational properties. In particular, we point out some
unusual forms of the considered functions. Finally, detailed numerical
comparisons are given, considering also Gaussians and thin plate splines, which
are really globally supported but widely used in applications
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