56,327 research outputs found
Vortices near barriers with multiple gaps
Two models are presented for the motion of vortices near gaps in infinitely long barriers. The first model considers a line vortex for which the exact nonlinear trajectories satisfying the governing two-dimensional Euler equations are obtained analytically. The second model considers a finite-area patch of constant vorticity and is based on conformal mapping and the numerical method of contour surgery. The two models enable a comparison of the trajectories of line vortices and vortex patches. The case of a double gap formed by an island lying between two headlands is considered in detail. It is noted that Kelvin's theorem constrains the circulation around the island to be a constant and thus forces a time-dependent volume flux between the islands and the headlands. When the gap between the island and a headland is small this flux requires arbitrarily large flow speeds through the gap. In most examples the centroid of the patch is constrained to follow closely the trajectory of a line vortex of the same circulation. Exceptions occur when the through-gap flow forces the vortex patch close to an edge of the island where it splits into two with only part of the vortex passing through the gap. In general the part squeezing through a narrow gap returns to near-circular to have a diameter significantly larger than the gap width
Quantum Theory of Superresolution for Two Incoherent Optical Point Sources
Rayleigh's criterion for resolving two incoherent point sources has been the
most influential measure of optical imaging resolution for over a century. In
the context of statistical image processing, violation of the criterion is
especially detrimental to the estimation of the separation between the sources,
and modern farfield superresolution techniques rely on suppressing the emission
of close sources to enhance the localization precision. Using quantum optics,
quantum metrology, and statistical analysis, here we show that, even if two
close incoherent sources emit simultaneously, measurements with linear optics
and photon counting can estimate their separation from the far field almost as
precisely as conventional methods do for isolated sources, rendering Rayleigh's
criterion irrelevant to the problem. Our results demonstrate that
superresolution can be achieved not only for fluorophores but also for stars.Comment: 18 pages, 11 figures. v1: First draft. v2: Improved the presentation
and added a section on the issues of unknown centroid and misalignment. v3:
published in Physical Review
Gaia in-orbit realignment. Overview and data analysis
The ESA Gaia spacecraft has two Shack-Hartmann wavefront sensors (WFS) on its
focal plane. They are required to refocus the telescope in-orbit due to launch
settings and gravity release. They require bright stars to provide good signal
to noise patterns. The centroiding precision achievable poses a limit on the
minimum stellar brightness required and, ultimately, on the observing time
required to reconstruct the wavefront. Maximum likelihood algorithms have been
developed at the Gaia SOC. They provide optimum performance according to the
Cr\'amer-Rao lower bound. Detailed wavefront reconstruction procedures, dealing
with partial telescope pupil sampling and partial microlens illumination have
also been developed. In this work, a brief overview of the WFS and an in depth
description of the centroiding and wavefront reconstruction algorithms is
provided.Comment: 14 pages, 6 figures, 2 tables, proceedings of SPIE Astronomical
Telescopes + Instrumentation 2012 Conference 8442 (1-6 July 2012
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