Astrometry and Photometry with Coronagraphs

We propose a solution to the problem of astrometric and photometric calibration of coronagraphic images with a simple optical device which, in theory, is easy to use. Our design uses the Fraunhofer approximation of Fourier optics. Placing a periodic grid of wires (we use a square grid) with known width and spacing in a pupil plane in front of the occulting coronagraphic focal plane mask produces fiducial images of the obscured star at known locations relative to the star. We also derive the intensity of these fiducial images in the coronagraphic image. These calibrator images can be used for precise relative astrometry, to establish companionship of other objects in the field of view through measurement of common proper motion or common parallax, to determine orbits, and to observe disk structure around the star quantitatively. The calibrator spots also have known brightness, selectable by the coronagraph designer, permitting accurate relative photometry in the coronagraphic image. This technique, which enables precision exoplanetary science, is relevant to future coronagraphic instruments, and is particularly useful for `extreme' adaptive optics and space-based coronagraphy.Comment: To appear in ApJ August 2006, 27 preprint style pages 4 figure

Nucleophilic substitutions on 3-chloro-4- fluoronitrobenzene

Nucleophilic substitutions on 3-chloro-4- fluoronitrobenzene 5 with piperazines occur on the fluorine rather than on the chlorine atom as reported, to yield 3-chloro-4-piperazinylnitrobenzenes 8 and 9

Robustness of Planar Fourier Capture Arrays to Colour Changes and Lost Pixels

Planar Fourier capture arrays (PFCAs) are optical sensors built entirely in standard microchip manufacturing flows. PFCAs are composed of ensembles of angle sensitive pixels (ASPs) that each report a single coefficient of the Fourier transform of the far-away scene. Here we characterize the performance of PFCAs under the following three non-optimal conditions. First, we show that PFCAs can operate while sensing light of a wavelength other than the design point. Second, if only a randomly-selected subset of 10% of the ASPs are functional, we can nonetheless reconstruct the entire far-away scene using compressed sensing. Third, if the wavelength of the imaged light is unknown, it can be inferred by demanding self-consistency of the outputs.Comment: 15 pages including cover page, 12 figures, associated with the 9th International Conference on Position Sensitive Detector

The Structure of High Strehl Ratio Point-Spread Functions

We describe the symmetries present in the point-spread function (PSF) of an optical system either located in space or corrected by an adaptive o to Strehl ratios of about 70% and higher. We present a formalism for expanding the PSF to arbitrary order in terms of powers of the Fourier transform of the residual phase error, over an arbitrarily shaped and apodized entrance aperture. For traditional unapodized apertures at high Strehl ratios, bright speckles pinned to the bright Airy rings are part of an antisymmetric perturbation of the perfect PSF, arising from the term that is first order in the residual phase error. There are two symmetric second degree terms. One is negative at the center, and, like the first order term, is modulated by the perfect image's field strength -- it reduces to the Marechal approximation at the center of the PSF. The other is non-negative everywhere, zero at the image center, and can be responsible for an extended halo -- which limits the dynamic range of faint companion detection in the darkest portions of the image. In regimes where one or the other term dominates the speckles in an image, the symmetry of the dominant term can be exploited to reduce the effect of those speckles, potentially by an order of magnitude or more. We demonstrate the effects of both secondary obscuration and pupil apodization on the structure of residual speckles, and discuss how these symmetries can be exploited by appropriate telescope and instrument design, observing strategies, and filter bandwidths to improve the dynamic range of high dynamic range AO and space-based observations. Finally, we show that our analysis is relevant to high dynamic range coronagraphy.Comment: Accepted for publication in ApJ; 20 pages, 4 figure

On the influence of spatial heterogeneity on an internal boundary layer at a short fetch

Surface layer meteorological data collected at a coastal site, at Vasco-Da-Gama (15°21′N, 73°51′E, 58.5m MSL) (13–18 July, 2002) with prevailing southwesterly surface winds are analyzed to study the characteristics of internal boundary layer at a short fetch using an instrumented tower (9 m). The spectral and turbulence characteristics of wind are compared with earlier measurements made at a comparatively homogeneous terrain and the standards available in literature. The study show the smaller eddies in the vertical velocity spectrum attains equilibrium with the underlying surface at a short fetch itself and follows spectral similarity. However, this is not followed by longitudinal and transverse velocity spectra under unstable as well as stable condition

Knapsack Cover Subject to a Matroid Constraint

We consider the Knapsack Covering problem subject to a matroid constraint. In this problem, we are given an universe U of n items where item i has attributes: a cost c(i) and a size s(i). We also have a demand D. We are also given a matroid M = (U, I) on the set U. A feasible solution S to the problem is one such that (i) the cumulative size of the items chosen is at least D, and (ii) the set S is independent in the matroid M (i.e. S is in I). The objective is to minimize the total cost of the items selected, sum_{i in S}c(i). Our main result proves a 2-factor approximation for this problem. The problem described above falls in the realm of mixed packing covering problems. We also consider packing extensions of certain other covering problems and prove that in such cases it is not possible to derive any constant factor pproximations

Reactions of tetrahalogeno-o-benzoquinones-Part VII. Reaction of alkyl-2-naphthols with tetrachloro-o-benzoquinone

Reaction of 8-methyl-2-naphthol (4a) with the quinone3 gave a mixture of 8-methyl-2,2-(tetrachloro-o-phenylenedioxy)naphthalen-1(2H)-one (1b) and 8-methyl-1,1-(tetrachloro-o-phenylenedioxy)naphthalen-2(1H)-one (2b) in almost equal amounts. Similarly, reaction of the naphthols (4b), (4d) and (4e) with3 gave the corresponding dienones (1c &2c), (1e &2e) and (1f &2f) in almost equal amounts. Reaction of 8-t-butyl-2-naphthol (4c) with3 gave exclusively 8-t-butyl-2,2-(tetrachloro-o-phenylenedioxy)-naphthalen-1(2H)-one (1d). Oxidation of 3-t-butyl-2-naphthol (4f) with3 gave a mixture of 3-t-butyl-2,2-(tetrachloro-o-phenylendioxy) nephthalene-1(2H)-one(1g) and 3-t-butyl-1,1-(tetrachloro-o-phenylenedioxy)naphthelen-2 (1H)-one (2g) in the ratio 1:6. Thus, onlyt-butyl group exherts pronounced steric influence on the rearrangement observed in the reaction of β-naphthol with the quinone3. Structures of all the compounds have been established by spectral data

The Solar-System-Scale Disk Around AB Aurigae

The young star AB Aurigae is surrounded by a complex combination of gas-rich and dust dominated structures. The inner disk which has not been studied previously at sufficient resolution and imaging dynamic range seems to contain very little gas inside a radius of least 130 astronomical units (AU) from the star. Using adaptive-optics coronagraphy and polarimetry we have imaged the dust in an annulus between 43 and 302 AU from the star, a region never seen before. An azimuthal gap in an annulus of dust at a radius of 102 AU, along with a clearing at closer radii inside this annulus, suggests the formation of at least one small body at an orbital distance of about 100 AU. This structure seems consistent with crude models of mean motion resonances, or accumulation of material at two of the Lagrange points relative to the putative object and the star. We also report a low significance detection of a point source in this outer annulus of dust. This source may be an overdensity in the disk due to dust accreting onto an unseen companion. An alternate interpretation suggests that the object's mass is between 5 and 37 times the mass of Jupiter. The results have implications for circumstellar disk dynamics and planet formation.Comment: 11 pages, 5 figures, accepted for publication in Astrophysical Journal, V. 680, June 10, 200