The Footprint Database and Web Services of the Herschel Space Observatory

Data from the Herschel Space Observatory is freely available to the public but no uniformly processed catalogue of the observations has been published so far. To date, the Herschel Science Archive does not contain the exact sky coverage (footprint) of individual observations and supports search for measurements based on bounding circles only. Drawing on previous experience in implementing footprint databases, we built the Herschel Footprint Database and Web Services for the Herschel Space Observatory to provide efficient search capabilities for typical astronomical queries. The database was designed with the following main goals in mind: (a) provide a unified data model for meta-data of all instruments and observational modes, (b) quickly find observations covering a selected object and its neighbourhood, (c) quickly find every observation in a larger area of the sky, (d) allow for finding solar system objects crossing observation fields. As a first step, we developed a unified data model of observations of all three Herschel instruments for all pointing and instrument modes. Then, using telescope pointing information and observational meta-data, we compiled a database of footprints. As opposed to methods using pixellation of the sphere, we represent sky coverage in an exact geometric form allowing for precise area calculations. For easier handling of Herschel observation footprints with rather complex shapes, two algorithms were implemented to reduce the outline. Furthermore, a new visualisation tool to plot footprints with various spherical projections was developed. Indexing of the footprints using Hierarchical Triangular Mesh makes it possible to quickly find observations based on sky coverage, time and meta-data. The database is accessible via a web site (http://herschel.vo.elte.hu) and also as a set of REST web service functions.Comment: Accepted for publication in Experimental Astronom

Scale-discretised ridgelet transform on the sphere

We revisit the spherical Radon transform, also called the Funk-Radon transform, viewing it as an axisymmetric convolution on the sphere. Viewing the spherical Radon transform in this manner leads to a straightforward derivation of its spherical harmonic representation, from which we show the spherical Radon transform can be inverted exactly for signals exhibiting antipodal symmetry. We then construct a spherical ridgelet transform by composing the spherical Radon and scale-discretised wavelet transforms on the sphere. The resulting spherical ridgelet transform also admits exact inversion for antipodal signals. The restriction to antipodal signals is expected since the spherical Radon and ridgelet transforms themselves result in signals that exhibit antipodal symmetry. Our ridgelet transform is defined natively on the sphere, probes signal content globally along great circles, does not exhibit blocking artefacts, supports spin signals and exhibits an exact and explicit inverse transform. No alternative ridgelet construction on the sphere satisfies all of these properties. Our implementation of the spherical Radon and ridgelet transforms is made publicly available. Finally, we illustrate the effectiveness of spherical ridgelets for diffusion magnetic resonance imaging of white matter fibers in the brain.Comment: 5 pages, 4 figures, matches version accepted by EUSIPCO, code available at http://www.s2let.or

Searchable Sky Coverage of Astronomical Observations: Footprints and Exposures

Sky coverage is one of the most important pieces of information about astronomical observations. We discuss possible representations, and present algorithms to create and manipulate shapes consisting of generalized spherical polygons with arbitrary complexity and size on the celestial sphere. This shape specification integrates well with our Hierarchical Triangular Mesh indexing toolbox, whose performance and capabilities are enhanced by the advanced features presented here. Our portable implementation of the relevant spherical geometry routines comes with wrapper functions for database queries, which are currently being used within several scientific catalog archives including the Sloan Digital Sky Survey, the Galaxy Evolution Explorer and the Hubble Legacy Archive projects as well as the Footprint Service of the Virtual Observatory.Comment: 11 pages, 7 figures, submitted to PAS

Approximation and Reconstruction from Attenuated Radon Projections

Attenuated Radon projections with respect to the weight function $W_\mu(x,y) = (1-x^2-y^2)^{\mu-1/2}$ are shown to be closely related to the orthogonal expansion in two variables with respect to $W_\mu$. This leads to an algorithm for reconstructing two dimensional functions (images) from attenuated Radon projections. Similar results are established for reconstructing functions on the sphere from projections described by integrals over circles on the sphere, and for reconstructing functions on the three-dimensional ball and cylinder domains.Comment: 25 pages, 3 figure