467 research outputs found
Astrometric signal profile fitting for Gaia
A tool for representation of the one-dimensional astrometric signal of Gaia
is described and investigated in terms of fit discrepancy and astrometric
performance with respect to number of parameters required. The proposed basis
function is based on the aberration free response of the ideal telescope and
its derivatives, weighted by the source spectral distribution. The influence of
relative position of the detector pixel array with respect to the optical image
is analysed, as well as the variation induced by the source spectral emission.
The number of parameters required for micro-arcsec level consistency of the
reconstructed function with the detected signal is found to be 11. Some
considerations are devoted to the issue of calibration of the instrument
response representation, taking into account the relevant aspects of source
spectrum and focal plane sampling. Additional investigations and other
applications are also suggested.Comment: 13 pages, 21 figures, Accepted by MNRAS 2010 January 29. Received
2010 January 28; in original form 2009 September 3
Fine compactified Jacobians
We study Esteves's fine compactified Jacobians for nodal curves. We give a
proof of the fact that, for a one-parameter regular local smoothing of a nodal
curve , the relative smooth locus of a relative fine compactified Jacobian
is isomorphic to the N\'eron model of the Jacobian of the general fiber, and
thus it provides a modular compactification of it. We show that each fine
compactified Jacobian of admits a stratification in terms of certain fine
compactified Jacobians of partial normalizations of and, moreover, that it
can be realized as a quotient of the smooth locus of a suitable fine
compactified Jacobian of the total blowup of . Finally, we determine when a
fine compactified Jacobian is isomorphic to the corresponding Oda-Seshadri's
coarse compactified Jacobian.Comment: 35 pages; final version, to appear in Math. Nac
Combinatorial aspects of nodal curves
To any nodal curve is associated the degree class group, a combinatorial
invariant which plays an important role in the compactification of the
generalised Jacobian of and in the construction of the N\'eron model of the
Picard variety of families of curves having as special fibre. In this paper
we study this invariant. More precisely, we construct a wide family of graphs
having cyclic degree class group and we provide a recursive formula for the
cardinality of the degree class group of the members of this family. Moreover,
we analyse the behaviour of the degree class group under standard geometrical
operations on the curve, such as the blow up and the normalisation of a node.Comment: 28 pages, to appear in Le Matematiche. Revised version: minor
changes, references adde
Chromaticity in all-reflective telescopes for astrometry
Chromatic effects are usually associated with refractive optics, so
reflective telescopes are assumed to be free from them. We show that
all-reflective optics still bears significant levels of such perturbations,
which is especially critical to modern micro-arcsecond astrometric experiments.
We analyze the image formation and measurement process to derive a precise
definition of the chromatic variation of the image position, and we evaluate
the key aspects of optical design with respect to chromaticity. The fundamental
requirement related to chromaticity is the symmetry of the optical design and
of the wavefront errors. Finally, we address some optical engineering issues,
such as manufacturing and alignment, providing recommendations to minimize the
degradation that chromaticity introduces into astrometry.Comment: 10 pages, 8 figure
Performance of an Algorithm for Estimation of Flux, Background, and Location on One-dimensional Signals
Optimal estimation of signal amplitude, background level, and photocentre
location is crucial to the combined extraction of astrometric and photometric
information from focal plane images, and in particular from the one-dimensional
measurements performed by Gaia on intermediate to faint magnitude stars. Our
goal is to define a convenient maximum likelihood framework, suited to
efficient iterative implementation and to assessment of noise level, bias, and
correlation among variables. The analytical model is investigated numerically
and verified by simulation over a range of magnitude and background values. The
estimates are unbiased, with a well-understood correlation between amplitude
and background, and with a much lower correlation of either of them with
location, further alleviated in case of signal symmetry. Two versions of the
algorithm are implemented and tested against each other, respectively, for
independent and combined parameter estimation. Both are effective and provide
consistent results, but the latter is more efficient because it takes into
account the flux-background estimate correlation.Comment: 13 pages; 13 figures; to be published on PAS
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