9,524 research outputs found
Limit theorems for bifurcating Markov chains. Application to the detection of cellular aging
We propose a general method to study dependent data in a binary tree, where
an individual in one generation gives rise to two different offspring, one of
type 0 and one of type 1, in the next generation. For any specific
characteristic of these individuals, we assume that the characteristic is
stochastic and depends on its ancestors' only through the mother's
characteristic. The dependency structure may be described by a transition
probability which gives the probability that the pair of
daughters' characteristics is around , given that the mother's
characteristic is . Note that , the characteristic of the daughter of
type 0, and , that of the daughter of type 1, may be conditionally dependent
given , and their respective conditional distributions may differ. We then
speak of bifurcating Markov chains. We derive laws of large numbers and central
limit theorems for such stochastic processes. We then apply these results to
detect cellular aging in Escherichia Coli, using the data of Stewart et al. and
a bifurcating autoregressive model.Comment: Published in at http://dx.doi.org/10.1214/105051607000000195 the
Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute
of Mathematical Statistics (http://www.imstat.org
Euler Scheme and Tempered Distributuions
Given a smooth R^d-valued diffusion, we study how fast the Euler scheme with
time step 1/n converges in law. To be precise, we look for which class of test
functions f the approximate expectation E[f(X^{n,x}_1)] converges with speed
1/n to E[f(X^x_1)]. If X is uniformly elliptic, we show that this class
contains all tempered distributions, and all measurable functions with
exponential growth. We give applications to option pricing and hedging, proving
numerical convergence rates for prices, deltas and gammas.Comment: 26 page
Coronagraphic Low Order Wavefront Sensor: Principle and Application to a Phase-Induced Amplitude Coronagraph
High contrast coronagraphic imaging of the immediate surrounding of stars
requires exquisite control of low-order wavefront aberrations, such as tip-tilt
(pointing) and focus. We propose an accurate, efficient and easy to implement
technique to measure such aberrations in coronagraphs which use a focal plane
mask to block starlight. The Coronagraphic Low Order Wavefront Sensor (CLOWFS)
produces a defocused image of a reflective focal plane ring to measure low
order aberrations. Even for small levels of wavefront aberration, the proposed
scheme produces large intensity signals which can be easily measured, and
therefore does not require highly accurate calibration of either the detector
or optical elements. The CLOWFS achieves nearly optimal sensitivity and is
immune from non-common path errors. This technique is especially well suited
for high performance low inner working angle (IWA) coronagraphs. On
phase-induced amplitude apodization (PIAA) type coronagraphs, it can
unambiguously recover aberrations which originate from either side of the beam
shaping introduced by the PIAA optics. We show that the proposed CLOWFS can
measure sub-milliarcsecond telescope pointing errors several orders of
magnitude faster than would be possible in the coronagraphic science focal
plane alone, and can also accurately calibrate residual coronagraphic leaks due
to residual low order aberrations. We have demonstrated 1e-3 lambda/D pointing
stability in a laboratory demonstration of the CLOWFS on a PIAA type
coronagraph
The pupil-swapping coronagraph
A new coronagraph that performs destructive interference between copies of the telescope pupil in which "slices" have been swapped is studied in this paper. A fourth-order "pupil-swapping coronagraph" is particularly attractive for direct imaging of extrasolar terrestrial planets: it achieves 100% throughput at 1.4 lambda/d on a square pupil (72.5% at 1.77 lambda/d on a circular pupil), is compatible with a central obstruction and spiders, l/d and delivers sharp images of off-axis sources. Direct detection of extrasolar terrestrial planets appears theoretically feasible on a 2 to 3 m visible-wavelength telescope in space
High resolution imaging with Fresnel interferometric arrays: suitability for exoplanet detection
We propose a new kind of interferometric array that yields images of high
dynamic range and large field. The numerous individual apertures in this array
form a pattern related to a Fresnel zone plate. This array can be used for
astrophysical imaging over a broad spectral bandwidth spanning from the U.V.
(50 nanometers) to the I.R. (20 microns). Due to the long focal lengths
involved, this instrument requires formation-flying of two space borne vessels.
We present the concept and study the S/N ratio in different situations, then
apply these results to probe the suitability of this concept to detect
exoplanets.Comment: 12 pages, 19 figures, to be published in A&
Ground-based adaptive optics coronagraphic performance under closed-loop predictive control
The discovery of the exoplanet Proxima b highlights the potential for the
coming generation of giant segmented mirror telescopes (GSMTs) to characterize
terrestrial --- potentially habitable --- planets orbiting nearby stars with
direct imaging. This will require continued development and implementation of
optimized adaptive optics systems feeding coronagraphs on the GSMTs. Such
development should proceed with an understanding of the fundamental limits
imposed by atmospheric turbulence. Here we seek to address this question with a
semi-analytic framework for calculating the post-coronagraph contrast in a
closed-loop AO system. We do this starting with the temporal power spectra of
the Fourier basis calculated assuming frozen flow turbulence, and then apply
closed-loop transfer functions. We include the benefits of a simple predictive
controller, which we show could provide over a factor of 1400 gain in raw PSF
contrast at 1 on bright stars, and more than a factor of 30 gain on
an I = 7.5 mag star such as Proxima. More sophisticated predictive control can
be expected to improve this even further. Assuming a photon noise limited
observing technique such as High Dispersion Coronagraphy, these gains in raw
contrast will decrease integration times by the same large factors. Predictive
control of atmospheric turbulence should therefore be seen as one of the key
technologies which will enable ground-based telescopes to characterize
terrrestrial planets.Comment: Accepted to JATI
Phase-Induced Amplitude Apodization of Telescope Pupils for Extrasolar Terrestrial Planet Imaging
In this paper, an alternative to the classical pupil apodization techniques
(use of an amplitude pupil mask) is proposed. It is shown that an apodized
pupil suitable for imaging of Extrasolar planets can be obtained by reflection
of an unapodized flat wavefront on 2 mirrors. By carefully choosing the shape
of these 2 mirrors, it is possible to obtain a contrast better than 10^{9} at a
distance smaller than 2 \lambda/d from the optical axis. Because this technique
preserves both the angular resolution and light gathering capabilities of the
unapodized pupil, it allows efficient detection of terrestrial extrasolar
planets with a 1.5m telescope in the visible.Comment: 9 pages, 9 figures, Accepted for publication in A&A. Postscript file
with full-resolution figures can be found at
http://www.naoj.org/staff/guyon/publications/PIAA.p
Speckle noise reduction techniques for high-dynamic range imaging
High-dynamic range imaging from space in the visible, aiming in particular at
the detection of terrestrial exoplanets, necessitates not only the use of a
coronagraph, but also of adaptive optics to correct optical defects in real
time. Indeed, these defects scatter light and give birth to speckles in the
image plane. Speckles can be cancelled by driving a deformable mirror to
measure and compensate wavefront aberrations. In a first approach, targeted
speckle nulling, speckles are cancelled iteratively by starting with the
brightest ones. This first method has demonstrated a contrast better than 1e9
in laboratory. In a second approach, zonal speckle nulling, the total energy of
speckles is minimized in a given zone of the image plane. This second method
has the advantage to tackle simultaneously all speckles from the targeted zone,
but it still needs better experimental demonstration.Comment: 7 pages, 3 figures, in Optical techniques for direct imaging of
exoplanets (a special issue of Comptes Rendus de Physique
Closed-loop focal plane wavefront control with the SCExAO instrument
This article describes the implementation of a focal plane based wavefront
control loop on the high-contrast imaging instrument SCExAO (Subaru
Coronagraphic Extreme Adaptive Optics). The sensor relies on the Fourier
analysis of conventional focal-plane images acquired after an asymmetric mask
is introduced in the pupil of the instrument. This absolute sensor is used here
in a closed-loop to compensate the non-common path errors that normally affects
any imaging system relying on an upstream adaptive optics system.This specific
implementation was used to control low order modes corresponding to eight
zernike modes (from focus to spherical). This loop was successfully run on-sky
at the Subaru Telescope and is used to offset the SCExAO deformable mirror
shape used as a zero-point by the high-order wavefront sensor. The paper
precises the range of errors this wavefront sensing approach can operate within
and explores the impact of saturation of the data and how it can be bypassed,
at a cost in performance. Beyond this application, because of its low hardware
impact, APF-WFS can easily be ported in a wide variety of wavefront sensing
contexts, for ground- as well space-borne telescopes, and for telescope pupils
that can be continuous, segmented or even sparse. The technique is powerful
because it measures the wavefront where it really matters, at the level of the
science detector.Comment: 9 pages, 14 figures, accepted for publication by A&
- …