Optimization of starshades: focal plane versus pupil plane

We search for the best possible transmission for an external occulter coronagraph that is dedicated to the direct observation of terrestrial exoplanets. We show that better observation conditions are obtained when the flux in the focal plane is minimized in the zone in which the exoplanet is observed, instead of the total flux received by the telescope. We describe the transmission of the occulter as a sum of basis functions. For each element of the basis, we numerically computed the Fresnel diffraction at the aperture of the telescope and the complex amplitude at its focus. The basis functions are circular disks that are linearly apodized over a few centimeters (truncated cones). We complemented the numerical calculation of the Fresnel diffraction for these functions by a comparison with pure circular discs (cylinder) for which an analytical expression, based on a decomposition in Lommel series, is available. The technique of deriving the optimal transmission for a given spectral bandwidth is a classical regularized quadratic minimization of intensities, but linear optimizations can be used as well. Minimizing the integrated intensity on the aperture of the telescope or for selected regions of the focal plane leads to slightly different transmissions for the occulter. For the focal plane optimization, the resulting residual intensity is concentrated behind the geometrical image of the occulter, in a blind region for the observation of an exoplanet, and the level of background residual starlight becomes very low outside this image. Finally, we provide a tolerance analysis for the alignment of the occulter to the telescope which also favors the focal plane optimization.This means that telescope offsets of a few decimeters do not strongly reduce the efficiency of the occulter

Introduction to stellar coronagraphy

This paper gives a simple and original presentation of various coronagraphs inherited from the Lyot coronagraph. We first present the Lyot and Roddier phase mask coronagraphs and study their properties as a function of the focal mask size. We show that the Roddier phase mask can be used to produce an apodization for the star. Optimal coronagraphy can be obtained from two main approaches, using prolate spheroidal pupil apodization and a finite-size focal mask, or using a clear aperture and an infinite mask of variable transmission

Critères de choix du mode de financement par crédit-bail dans les Petites et Moyennes Entreprises (PME) au Cameroun

Les PME constituent une composante principale du tissu économique camerounais. Cependant, le phénomène de rationnement dont elles sont victimes sur le marché du crédit à cause de leur vulnérabilité les obligent à se tourner vers des financements alternatifs. Cet article vise à déterminer les critères expliquant le choix du financement par crédit-bail par les PME camerounaises. Pour y parvenir, nous avons collecté les données à partir d’un questionnaire auprès de 61 PMEs relevant de quatre secteurs d’activité (service, commerce, industrie et agricole) et segmenté en deux groupes : celles qui recourent au crédit-bail et celles qui n’y recourent pas. L’analyse des données a conduit à deux séries de résultats. On constate d’une part une association forte entre l’âge de l’entreprise et le recours au crédit-bail. D’autre part, à l’aide d’une analyse en composante multiple, les facteurs tels que l’âge, la qualité de l’information diffusée par le bailleur, le domaine d’activité, la nature de l’actif et de l’investissement, la performance, les contraintes et l’accessibilité expliquent le recours au crédit-bail.&nbsp

Speckle noise and dynamic range in coronagraphic images

This paper is concerned with the theoretical properties of high contrast coronagraphic images in the context of exoplanet searches. We derive and analyze the statistical properties of the residual starlight in coronagraphic images, and describe the effect of a coronagraph on the speckle and photon noise. Current observations with coronagraphic instruments have shown that the main limitations to high contrast imaging are due to residual quasi-static speckles. We tackle this problem in this paper, and propose a generalization of our statistical model to include the description of static, quasi-static and fast residual atmospheric speckles. The results provide insight into the effects on the dynamic range of wavefront control, coronagraphy, active speckle reduction, and differential speckle calibration. The study is focused on ground-based imaging with extreme adaptive optics, but the approach is general enough to be applicable to space, with different parameters.Comment: 31 pages, 18 figure

Luciola Hypertelescope Space Observatory

Luciola is a large (one kilometer) "multi-aperture densified-pupil imaging interferometer", or "hypertelescope" employing many small apertures, rather than a few large ones, for obtaining direct snapshot images with a high information content. A diluted collector mirror, deployed in space as a flotilla of small mirrors, focuses a sky image which is exploited by several beam-combiner spaceships. Each contains a pupil densifier micro-lens array to avoid the diffractive spread and image attenuation caused by the small sub-apertures. The elucidation of hypertelescope imaging properties during the last decade has shown that many small apertures tend to be far more efficient, regarding the science yield, than a few large ones providing a comparable collecting area. For similar underlying physical reasons, radio-astronomy has also evolved in the direction of many-antenna systems such as the proposed Low Frequency Array having hundreds of thousands of individual receivers . With its high limiting magnitude, reaching the mv=30 limit of HST when 100 collectors of 25cm will match its collecting area, high-resolution direct imaging in multiple channels, broad spectral coverage from the 1200 Angstrom ultra-violet to the 20 micron infra-red, apodization, coronagraphic and spectroscopic capabilities, the proposed hypertelescope observatory addresses very broad and innovative science covering different areas of ESA s Cosmic Vision program. In the initial phase, a focal spacecraft covering the UV to near IR spectral range of EMCCD photon-counting cameras ( currently 200 to 1000nm), will image details on the surface of many stars, as well as their environment, including multiple stars and clusters. Spectra will be obtained for each resel. It will also image neutron star, black-hole and micro-quasar candidates, as well as active galactic nuclei, quasars, gravitational lenses, and other Cosmic Vision targets observable with the initial modest crowding limit. With subsequent upgrade missions, the spectral coverage can be extended from 120nm to 20 microns, using four detectors carried by two to four focal spacecraft. The number of collector mirrors in the flotilla can also be increased from 12 to 100 and possibly 1,000. The imaging and spectroscopy of habitable exoplanets in the mid infra-red then becomes feasible once the collecting area reaches 6m2 , using a specialized mid infra-red focal spacecraft. Calculations ( Boccaletti et al., 2000) have shown that hypertelescope coronagraphy has unequalled sensitivity for detecting, at mid infra-red wavelengths, faint exoplanets within the exo-zodiacal glare. Later upgrades will enable the more difficult imaging and spectroscopy of these faint objects at visible wavelengths, using refined techniques of adaptive coronagraphy (Labeyrie. & Le Coroller, 2004). Together, the infra-red and visible spectral data carry rich information on the possible presence of life. The close environment of the central black-hole in the Milky Way will be imageable with unprecedented detail in the near infra-red . Cosmological imaging of remote galaxies at the limit of the known universe is also expected, from the ultra-violet to the near infra-red, following the first upgrade, and with greatly increasing sensitivity through successive upgrades. These areas will indeed greatly benefit from the upgrades, in terms of dynamic range, limiting complexity of the objects to be imaged, size of the elementary Direct Imaging Field , and limiting magnitude, approaching that of an 8-meter space telescope when 1000 apertures of 25cm are installed. Similar gains will occur for addressing fundamental problems in physics and cosmology, particularly when observing neutron stars and black holes, single or binary, including the giant black holes, with accretion disks and jets, in active galactic nuclei beyond the Milky Way. Gravitational lensing and micro-lensing patterns, including time-variable patterns and perhaps millisecond lensing flasheshich may be beamed by diffraction from sub-stellar masses at sub-parsec distances (Labeyrie, 1994) , will also be observable initially in the favourable cases, and upgrades will greatly improve the number of observable objects. The observability of gravitational waves emitted by binary lensing masses, in the form of modulated lensing patterns, is a debated issue ( Ragazzoni et al., 2003) but will also become addressable observationally. The technology readiness of Luciola approaches levels where low-orbit testing and stepwise implementation will become feasible in the 2015-2025 time frame. For the following decades beyond 2020, once accurate formation flying techniques will be mastered, much larger hypertelescopes such as the proposed 100km Exo-Earth Imager and the 100,000 km Neutron Star Imager should also become feasible. Luciola is therefore also seen as a precursor toward such very powerful instruments

Tetra­kis(μ-3-aza­niumylbenzoato)-κ3 O:O,O′;κ3 O,O′:O;κ4 O:O′-bis­[triaqua­chloridolanthanum(III)] tetra­chloride dihydrate

The tiltle complex, [La2(C7H7NO2)4Cl2(H2O)6]Cl4·2H2O, is a centrosymmetric dimer formed by edge-sharing LaO5(H2O)3Cl polyhedra linked together by a carboxyl­ate ligand. The two LaIII metal ions are linked by two bidentate bridging carboxyl­ate groups with a κ2 O:O′ coordination mode and two bidentate chelating bridging carboxyl­ate groups with a κ3 O:O,O′ coordination mode. The coordination sphere of lanthanum, completed by a terminal chloride and three water mol­ecules, adopts a distorted tricapped trigonal–prismatic arrangement. N—H⋯Cl, N—H⋯O and O—Hwater⋯Cl hydrogen bonds, and slipped π–π inter­actions between parallel benzene rings [centroid–centroid distance of 3.647 (3) Å] are observed in the structure. These combine to stabilize a three-dimensional network