Searching for faint companions with VLTI/PIONIER. I. Method and first results

Context. A new four-telescope interferometric instrument called PIONIER has recently been installed at VLTI. It provides improved imaging capabilities together with high precision. Aims. We search for low-mass companions around a few bright stars using different strategies, and determine the dynamic range currently reachable with PIONIER. Methods. Our method is based on the closure phase, which is the most robust interferometric quantity when searching for faint companions. We computed the chi^2 goodness of fit for a series of binary star models at different positions and with various flux ratios. The resulting chi^2 cube was used to identify the best-fit binary model and evaluate its significance, or to determine upper limits on the companion flux in case of non detections. Results. No companion is found around Fomalhaut, tau Cet and Regulus. The median upper limits at 3 sigma on the companion flux ratio are respectively of 2.3e-3 (in 4 h), 3.5e-3 (in 3 h) and 5.4e-3 (in 1.5 h) on the search region extending from 5 to 100 mas. Our observations confirm that the previously detected near-infrared excess emissions around Fomalhaut and tau Cet are not related to a low-mass companion, and instead come from an extended source such as an exozodiacal disk. In the case of del Aqr, in 30 min of observation, we obtain the first direct detection of a previously known companion, at an angular distance of about 40 mas and with a flux ratio of 2.05e-2 \pm 0.16e-2. Due to the limited u,v plane coverage, its position can, however, not be unambiguously determined. Conclusions. After only a few months of operation, PIONIER has already achieved one of the best dynamic ranges world-wide for multi-aperture interferometers. A dynamic range up to about 1:500 is demonstrated, but significant improvements are still required to reach the ultimate goal of directly detecting hot giant extrasolar planets.Comment: 11 pages, 6 figures, accepted for publication in A&

Expanding the Family of Grassmannian Kernels: An Embedding Perspective

Modeling videos and image-sets as linear subspaces has proven beneficial for many visual recognition tasks. However, it also incurs challenges arising from the fact that linear subspaces do not obey Euclidean geometry, but lie on a special type of Riemannian manifolds known as Grassmannian. To leverage the techniques developed for Euclidean spaces (e.g, support vector machines) with subspaces, several recent studies have proposed to embed the Grassmannian into a Hilbert space by making use of a positive definite kernel. Unfortunately, only two Grassmannian kernels are known, none of which -as we will show- is universal, which limits their ability to approximate a target function arbitrarily well. Here, we introduce several positive definite Grassmannian kernels, including universal ones, and demonstrate their superiority over previously-known kernels in various tasks, such as classification, clustering, sparse coding and hashing

A geometric Newton method for Oja's vector field

Newton's method for solving the matrix equation $F(X)\equiv AX-XX^TAX=0$ runs up against the fact that its zeros are not isolated. This is due to a symmetry of $F$ by the action of the orthogonal group. We show how differential-geometric techniques can be exploited to remove this symmetry and obtain a ``geometric'' Newton algorithm that finds the zeros of $F$. The geometric Newton method does not suffer from the degeneracy issue that stands in the way of the original Newton method

Two-sided Grassmann-Rayleigh quotient iteration

The two-sided Rayleigh quotient iteration proposed by Ostrowski computes a pair of corresponding left-right eigenvectors of a matrix $C$. We propose a Grassmannian version of this iteration, i.e., its iterates are pairs of $p$-dimensional subspaces instead of one-dimensional subspaces in the classical case. The new iteration generically converges locally cubically to the pairs of left-right $p$-dimensional invariant subspaces of $C$. Moreover, Grassmannian versions of the Rayleigh quotient iteration are given for the generalized Hermitian eigenproblem, the Hamiltonian eigenproblem and the skew-Hamiltonian eigenproblem.Comment: The text is identical to a manuscript that was submitted for publication on 19 April 200

The geometry of nonlinear least squares with applications to sloppy models and optimization

Parameter estimation by nonlinear least squares minimization is a common problem with an elegant geometric interpretation: the possible parameter values of a model induce a manifold in the space of data predictions. The minimization problem is then to find the point on the manifold closest to the data. We show that the model manifolds of a large class of models, known as sloppy models, have many universal features; they are characterized by a geometric series of widths, extrinsic curvatures, and parameter-effects curvatures. A number of common difficulties in optimizing least squares problems are due to this common structure. First, algorithms tend to run into the boundaries of the model manifold, causing parameters to diverge or become unphysical. We introduce the model graph as an extension of the model manifold to remedy this problem. We argue that appropriate priors can remove the boundaries and improve convergence rates. We show that typical fits will have many evaporated parameters. Second, bare model parameters are usually ill-suited to describing model behavior; cost contours in parameter space tend to form hierarchies of plateaus and canyons. Geometrically, we understand this inconvenient parametrization as an extremely skewed coordinate basis and show that it induces a large parameter-effects curvature on the manifold. Using coordinates based on geodesic motion, these narrow canyons are transformed in many cases into a single quadratic, isotropic basin. We interpret the modified Gauss-Newton and Levenberg-Marquardt fitting algorithms as an Euler approximation to geodesic motion in these natural coordinates on the model manifold and the model graph respectively. By adding a geodesic acceleration adjustment to these algorithms, we alleviate the difficulties from parameter-effects curvature, improving both efficiency and success rates at finding good fits.Comment: 40 pages, 29 Figure

PIONIER: a visitor instrument for the VLTI

PIONIER is a 4-telescope visitor instrument for the VLTI, planned to see its first fringes in 2010. It combines four ATs or four UTs using a pairwise ABCD integrated optics combiner that can also be used in scanning mode. It provides low spectral resolution in H and K band. PIONIER is designed for imaging with a specific emphasis on fast fringe recording to allow closure-phases and visibilities to be precisely measured. In this work we provide the detailed description of the instrument and present its updated status.Comment: Proceedings of SPIE conference Optical and Infrared Interferometry II (Conference 7734) San Diego 201

First-light LBT nulling interferometric observations: warm exozodiacal dust resolved within a few AU of eta Corvi

We report on the first nulling interferometric observations with the Large Binocular Telescope Interferometer (LBTI), resolving the N' band (9.81 - 12.41 um) emission around the nearby main-sequence star eta Crv (F2V, 1-2 Gyr). The measured source null depth amounts to 4.40% +/- 0.35% over a field-of-view of 140 mas in radius (~2.6\,AU at the distance of eta Corvi) and shows no significant variation over 35{\deg} of sky rotation. This relatively low null is unexpected given the total disk to star flux ratio measured by Spitzer/IRS (~23% across the N' band), suggesting that a significant fraction of the dust lies within the central nulled response of the LBTI (79 mas or 1.4 AU). Modeling of the warm disk shows that it cannot resemble a scaled version of the Solar zodiacal cloud, unless it is almost perpendicular to the outer disk imaged by Herschel. It is more likely that the inner and outer disks are coplanar and the warm dust is located at a distance of 0.5-1.0 AU, significantly closer than previously predicted by models of the IRS spectrum (~3 AU). The predicted disk sizes can be reconciled if the warm disk is not centrosymmetric, or if the dust particles are dominated by very small grains. Both possibilities hint that a recent collision has produced much of the dust. Finally, we discuss the implications for the presence of dust at the distance where the insolation is the same as Earth's (2.3 AU).Comment: 9 pages, 6 figures, accepted for publication in Ap

Silicon-Organic Hybrid MZI Modulator Generating OOK, BPSK and 8-ASK Signals for up to 84 Gbit/s

We report on high-speed multilevel signal generation and arbitrary pulse shaping with silicon-organic hybrid (SOH) Mach-Zehnder interferometer (MZI) modulators. Pure phase modulation exploiting the linear electrooptic effect allows the generation of multiple modulations formats at highest speed such as 40-Gbit/s on-off-keying (OOK) and binary-phase-shift keying (BPSK) and 28-Gbd 4-ASK and 8-ASK with data rates up to 84 Gbit/s. Additionally, beside NRZ pulse shaping, for the first time, Nyquist pulse shaping with silicon modulators is demonstrated to enable multiplexing at highest spectral efficiency