SURVEY FOOTPRINTS Tamás Budavári / The Johns Hopkins University 7/7/2009
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SURVEY FOOTPRINTS 7/7/2009 Tamás Budavári / The Johns Hopkins University What is it? 2 Tamás Budavári Window fn of observations: Call it “mask” in large-scale structure Angular selection function Means different things to everyone: A figure, image, rectangle, wcs, layers, fractals No Footprint – Rare! 3 Tamás Budavári Approaches to Consider 4 Tamás Budavári Pixel maps Sensitivity, Equations of shapes Spherical etc… “vector graphics” And beyond… An Observation 5 Tamás Budavári FITS header with WCS Image dimensions map to the geometry More exposures? No common pixel coordinate-system Overlapping areas Common Pixels 6 Tamás Budavári Pre-defined pages of an atlas Standard in cartography Image pyramids of hierarchical pixels Including HTM, Igloo, HEALPix, SDSSPix, etc… Always approximate! Practical Implementation 7 Tamás Budavári Looking at Terapixels We know how to work with images Now have commodity Internet We have cheap hard-drives A service like Ggle Earth! Integrated catalogs for efficiency How about more surveys? Drawing with Equations 8 Tamás Budavári Many ways of describing shapes on the sphere Useful 3D concepts Circle/Cap Convex Simple shapes Halfspace We use 3D but solve geometry on surface Patch and Region Drawing with Equations 9 Tamás Budavári Many ways of describing shapes on the sphere Useful 3D concepts Circle/Cap Convex Simple shapes Halfspace We use 3D but solve geometry on surface Patch/Polygon and Region Drawing with Equations 10 Tamás Budavári Working with 3D normal vectors Benefits include No wraparound No projections No singularities Point in Region Test 11 Tamás Budavári Halfspace: one side of a plane (n, c) Inside, when n x c Convex: a collection of halfspaces Inside, when inside all halfspaces Region: a collection of convexes Inside, when inside any convex Shape Operations 12 Tamás Budavári Intersection Concat halfspace lists Union Concat convex lists Unique coverage Analytic area Boolean algebra GALEX and SDSS 13 Tamás Budavári 7/7/2009 Closer to GALEX 14 Tamás Budavári r = 0.6 r = 0.5 15 Sky coverage of the Sloan Digital Sky Survey’s 5th Data Release and the Galaxy Evolution Explorer’s 2nd7/7/2009 Public Release Footprints and Masks 16 Tamás Budavári Simple algorithmic negation of a region But potential combinatoric explosion Instead inclusive footprint and exclusive masks Simpler footprint that covers it all Many small masks to censor artifacts, etc. SDSS photometry is a dozen rectangles But has 16 million masks 17 Hybrid Solutions Indexing the Sky 18 Tamás Budavári Hierarchical Triangular Mesh Region approximation Fast filtering using HTM ID ranges Heuristic Simplification 19 Tamás Budavári The FIRST footprint as a union of 50k circles Each overlapping with 12 other – Ouch! Heuristic Simplification 20 Tamás Budavári The FIRST footprint as a union of 50k circles Each But overlapping with 12 other – Ouch! Heuristic Simplification 21 Tamás Budavári Divide and Conquer Pixels with simple region equations – not HEALPix Pixels that can be merged – not HTM A good example is the Igloo scheme: Pixel can be empty, full or partial Not only discard or keep… But solve for shape or keep and define mask For example, limiting on fractional area FIRST North 22 Tamás Budavári FIRST North 23 Tamás Budavári Summary 24 Tamás Budavári Pixel maps can represent continuous functions Large amount of data on the same system Spherical geometry of homogeneous regions Lightweight Survey-specific challenges ahead Hybrid solutions Work TBD but can get fragmented Basic Tools Exist
