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

A Possible Aeronomy of Extrasolar Terrestrial Planets

Terrestrial planetary systems may exist around nearby stars as the Earth-sized counterparts to the many giant planets already discovered within the solar neighborhood. In this chapter we first discuss the numerous techniques which have been suggested to search for extrasolar terrestrial planets. We then focus on the expected results from that technique in which an orbiting telescope or interferometer is used to obtain a visible or infrared spectrum of a planet, without contamination from the parent star. We show examples of such spectra for selected cases: the present Earth, the Neoproterozoic (snowball) Earth, a methane-rich Earth, and the present Mars and Venus. We conclude by discussing the implications of such spectra for the detection of life on an extrasolar terrestrial planet.Comment: This will appear in the upcoming AGU Monograph 130 "Atmospheres in the Solar System: Comparative Aeronomy". It will be on page 36

Measurement of HO2 and other trace gases in the stratosphere using a high resolution far-infrared spectrometer at 28 KM

The major events and results to date of the ongoing program of measuring stratospheric composition by the technique of far-infrared Fourier-transform spectroscopy from a balloon-borne platform are reviewed. The highlights of this period were the two balloon flight campaigns which were performed at Palestine, Texas, both of which produced large amounts of scientifically useful data

Measurement of H2O and other trace gases in the stratosphere using a high resolution far-infrared spectrometer at 28 km

Data analysis results from the 1983 BIC 1 and 2 balloon flights are presented, with emphasis on H2O2, OH, HCL, O3, O2, and H2O. A 2 sigma limit on H2O2 abundance was set, as a function of altitude. This is comparable to or less than the theoretically predicted winter abundances from the 2-D models of Dupont, with a large enough summer maximum to facilitate concentration profile measurements. There is a definite drop in OH concentration from day to night following two model profiles. There was general agreement between HF measurements. The dominant role of the far wings of H2O lines in low altitude spectra was recognized. The strength of these wings exceeds that of many molecular line cores, including O3 and O2, especially near the long wavelength end of the spectra (100 cm (-1)). Newly measured positions for O3 and H2O were obtained

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

Measurement of H2O and other trace gases in the stratosphere using a high resolution far-infrared spectrometer at 28 KM

The highlights of the stratospheric program were reviewed for the past 2.5 years. The major efforts were analysis of the data from the BIC-2 campaign, and the building or new instrumentation to replace that lost at the end of BIC-2. For clarity, the review will be done by topic, rather than chronologically: construction of the initial far-infrared spectrometer, balloon slight program, laboratory measurement, data analysis, and duplicate stabilized platform

High-contrast Imaging from Space: Speckle Nulling in a Low Aberration Regime

High-contrast imaging from space must overcome two major noise sources to successfully detect a terrestrial planet angularly close to its parent star: photon noise from diffracted star light, and speckle noise from star light scattered by instrumentally-generated wavefront perturbation. Coronagraphs tackle only the photon noise contribution by reducing diffracted star light at the location of a planet. Speckle noise should be addressed with adaptative-optics systems. Following the tracks of Malbet, Yu and Shao (1995), we develop in this paper two analytical methods for wavefront sensing and control that aims at creating dark holes, i.e. areas of the image plane cleared out of speckles, assuming an ideal coronagraph and small aberrations. The first method, speckle field nulling, is a fast FFT-based algorithm that requires the deformable-mirror influence functions to have identical shapes. The second method, speckle energy minimization, is more general and provides the optimal deformable mirror shape via matrix inversion. With a NxN deformable mirror, the size of matrix to be inverted is either N^2xN^2 in the general case, or only NxN if influence functions can be written as the tensor product of two one-dimensional functions. Moreover, speckle energy minimization makes it possible to trade off some of the dark hole area against an improved contrast. For both methods, complex wavefront aberrations (amplitude and phase) are measured using just three images taken with the science camera (no dedicated wavefront sensing channel is used), therefore there are no non-common path errors. We assess the theoretical performance of both methods with numerical simulations, and find that these speckle nulling techniques should be able to improve the contrast by several orders of magnitude.Comment: 31 pages, 8 figures, 1 table. Accepted for publication in ApJ (should appear in February 2006