Two-Mirror Apodization for High-Contrast Imaging

Direct detection of extrasolar planets will require imaging systems capable of unprecedented contrast. Apodized pupils provide an attractive way to achieve such contrast but they are difficult, perhaps impossible, to manufacture to the required tolerance and they absorb about 90% of the light in order to create the apodization, which of course lengthens the exposure times needed for planet detection. A recently proposed alternative is to use two mirrors to accomplish the apodization. With such a system, no light is lost. In this paper, we provide a careful mathematical analysis, using one dimensional mirrors, of the on-axis and off-axis performance of such a two-mirror apodization system. There appear to be advantages and disadvantages to this approach. In addition to not losing any light, we show that the nonuniformity of the apodization implies an extra magnification of off-axis sources and thereby makes it possible to build a real system with about half the aperture that one would otherwise require or, equivalently, resolve planets at about half the angular separation as one can achieve with standard apodization. More specifically, ignoring pointing error and stellar disk size, a planet at $1.7 \lambda/D$ ought to be at the edge of detectability. However, we show that the non-zero size of a stellar disk pushes the threshold for high-contrast so that a planet must be at least $2.5 \lambda/D$ from its star to be detectable. The off-axis analysis of two-dimensional mirrors is left for future study.Comment: 21 pages, 7 figures. For author's webpage version see http://www.orfe.princeton.edu/~rvdb/tex/piaa/ms.pdf This version has improved figures and addresses comments of a refere

Qubit Complexity of Continuous Problems

The number of qubits used by a quantum algorithm will be a crucial computational resource for the foreseeable future. We show how to obtain the classical query complexity for continuous problems. We then establish a simple formula for a lower bound on the qubit complexity in terms of the classical query complexityComment: 6 pages, 2 figure

GABA-enhanced collective behavior in neuronal axons underlies persistent gamma-frequency oscillations

Gamma (30–80 Hz) oscillations occur in mammalian electroencephalogram in a manner that indicates cognitive relevance. In vitro models of gamma oscillations demonstrate two forms of oscillation: one occurring transiently and driven by discrete afferent input and the second occurring persistently in response to activation of excitatory metabotropic receptors. The mechanism underlying persistent gamma oscillations has been suggested to involve gap-junctional communication between axons of principal neurons, but the precise relationship between this neuronal activity and the gamma oscillation has remained elusive. Here we demonstrate that gamma oscillations coexist with high-frequency oscillations (>90 Hz). High-frequency oscillations can be generated in the axonal plexus even when it is physically isolated from pyramidal cell bodies. They were enhanced in networks by nonsomatic -aminobutyric acid type A (GABAA) receptor activation, were modulated by perisomatic GABAA receptor-mediated synaptic input to principal cells, and provided the phasic input to interneurons required to generate persistent gamma-frequency oscillations. The data suggest that high-frequency oscillations occurred as a consequence of random activity within the axonal plexus. Interneurons provide a mechanism by which this random activity is both amplified and organized into a coherent network rhythm

On the Completeness of Reflex Astrometry on Extrasolar Planets near the Sensitivity Limit

We provide a preliminary estimate of the performance of reflex astrometry on Earth-like planets in the habitable zones of nearby stars. In Monte Carlo experiments, we analyze large samples of astrometric data sets with low to moderate signal-to-noise ratios. We treat the idealized case of a single planet orbiting a single star, and assume there are no non-Keplerian complications or uncertainties. The real case can only be more difficult. We use periodograms for discovery and least-squares fits for estimating the Keplerian parameters. We find a completeness for detection compatible with estimates in the literature. We find mass estimation by least squares to be biased, as has been found for noisy radial-velocity data sets; this bias degrades the completeness of accurate mass estimation. When we compare the true planetary position with the position predicted from the fitted orbital parameters, at future times, we find low completeness for an accuracy goal of 0.3 times the semimajor axis of the planet, even with no delay following the end of astrometric observations. Our findings suggest that the recommendation of the ExoPlanet Task Force (Lunine et al. 2008) for "the capability to measure convincingly wobble semi-amplitudes down to 0.2 $\mu$as integrated over the mission lifetime," may not be satisfied by an instrument characterized by the noise floor of the Space Interferometry Mission, $\sigma_\mathrm{floor}\approx0.035\mu$as. An important, unsolved, strategic challenge for the exoplanetary science program is figuring out how to predict the future position of an Earth-like planet with accuracy sufficient to ensure the efficiency and success of the science operations for follow-on spectroscopy, which would search for biologically significant molecules in the atmosphere.Comment: v2: 16 pages, 4 figures; ApJ accepte