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 $P(x,dy dz)$ which gives the probability that the pair of daughters' characteristics is around $(y,z)$, given that the mother's characteristic is $x$. Note that $y$, the characteristic of the daughter of type 0, and $z$, that of the daughter of type 1, may be conditionally dependent given $x$, 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 $\lambda/D$ 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&