785 research outputs found
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
Approximation and Reconstruction from Attenuated Radon Projections
Attenuated Radon projections with respect to the weight function are shown to be closely related to the orthogonal
expansion in two variables with respect to . This leads to an algorithm
for reconstructing two dimensional functions (images) from attenuated Radon
projections. Similar results are established for reconstructing functions on
the sphere from projections described by integrals over circles on the sphere,
and for reconstructing functions on the three-dimensional ball and cylinder
domains.Comment: 25 pages, 3 figure
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
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
Chromatic polynomials of some sunflower mixed hypergraphs
The theory of mixed hypergraphs coloring has been first introduced by Voloshin in 1993 and it has been growing ever since. The proper coloring of a mixed hypergraph H = (X; C;D) is the coloring of the vertex set X so that no D-hyperedge is monochromatic and no C-hyperedge is polychromatic. A mixed hypergraph with hyperedges of type D, C or B is commonly known as a D-, C-, or B-hypergraph respectively, where B = C = D. D-hypergraph colorings are the classic hypergraph colorings which have been widely studied. The chromatic polynomial P(H;λ) of a mixed hypergraph H is the function that counts the number of proper λ-colorings, which are mappings. Recently, Walter published [15] some results concerning the chromatic polynomial of some non-uniform D-sunflower. In this paper, we present an alternative proof of his result and extend his formula to those of non-uniform C-sunflowers and B-sunflowers. Some results of a new but related member of sunflowers are also presented
Foundation of an analytical proton beamlet model for inclusion in a general proton dose calculation system
We have developed a model for proton depth dose and lateral distributions
based on Monte Carlo calculations (GEANT4) and an integration procedure of the
Bethe-Bloch equation (BBE). The model accounts for the transport of primary and
secondary protons, the creation of recoil protons and heavy recoil nuclei as
well as lateral scattering of these contributions. The buildup, which is
experimentally observed in higher energy depth dose curves, is modeled by
inclusion of two different origins: 1. Secondary reaction protons with a
contribution of ca. 65 % of the buildup (for monoenergetic protons). 2. Landau
tails as well as Gaussian type of fluctuations for range straggling effects.
All parameters of the model for initially monoenergetic proton beams have been
obtained from Monte Carlo calculations or checked by them. Furthermore, there
are a few parameters, which can be obtained by fitting the model to measured
depth dose curves in order to describe individual characteristics of the
beamline - the most important being the initial energy spread. We find that the
free parameters of the depth dose model can be predicted for any intermediate
energy from a couple of measured curves.Comment: Eclipse implementatio
Rethinking data-driven point spread function modeling with a differentiable optical model
In astronomy, upcoming space telescopes with wide-field optical instruments
have a spatially varying point spread function (PSF). Specific scientific goals
require a high-fidelity estimation of the PSF at target positions where no
direct measurement of the PSF is provided. Even though observations of the PSF
are available at some positions of the field of view (FOV), they are
undersampled, noisy, and integrated into wavelength in the instrument's
passband. PSF modeling represents a challenging ill-posed problem, as it
requires building a model from degraded observations that can infer a
super-resolved PSF at any wavelength and position in the FOV. Our model, coined
WaveDiff, proposes a paradigm shift in the data-driven modeling of the point
spread function field of telescopes. We change the data-driven modeling space
from the pixels to the wavefront by adding a differentiable optical forward
model into the modeling framework. This change allows the transfer of
complexity from the instrumental response into the forward model. The proposed
model relies on stochastic gradient descent to estimate its parameters. Our
framework paves the way to building powerful, physically motivated models that
do not require special calibration data. This paper demonstrates the WaveDiff
model in a simplified setting of a space telescope. The proposed framework
represents a performance breakthrough with respect to the existing
state-of-the-art data-driven approach. The pixel reconstruction errors decrease
6-fold at observation resolution and 44-fold for a 3x super-resolution. The
ellipticity errors are reduced at least 20 times, and the size error is reduced
more than 250 times. By only using noisy broad-band in-focus observations, we
successfully capture the PSF chromatic variations due to diffraction. Code
available at https://github.com/tobias-liaudat/wf-psf.Comment: Submitted. Without appendix: 42 pages, 10 figures, 4 table
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