HEALPix is an acronym for Hierarchical Equal Area isoLatitude Pixelation of a sphere. As suggested in the name, this pixelation produces a subdivision of a spherical surface in which each pixel covers the same surface area as every other pixel.
The original motivation for devising HEALPix was one of necessity.
Satellite missions to measure the cosmic microwave background (CMB)
anisotropy -- NASA's
Anisotropy Probe (WMAP),
operating ESA's mission
-- have been producing multi-frequency data
sets sufficient for the construction of full-sky maps of the
microwave sky at an angular resolution of a few arcminutes. The
principal requirements in the development of HEALPix were to
create a mathematical structure which supports a suitable
discretization of functions on a sphere at sufficiently high
resolution, and to facilitate fast and accurate statistical and
astrophysical analysis of massive full-sky data sets.
HEALPix satisfies these requirements because it possesses the following three essential properties:
- The sphere is hierarchically tessellated into curvilinear quadrilaterals. The lowest resolution partition is comprised of 12 base pixels. Resolution of the tessellation increases by division of each pixel into four new ones. The figure below illustrates (clockwise from upper-left to bottom-left) the resolution increase by three steps from the base level (i.e., the sphere is partitioned, respectively, into 12, 48, 192, and 768 pixels).
- Areas of all pixels at a given resolution are identical.
- Pixels are distributed on lines of constant latitude. This property is essential for all harmonic analysis applications involving spherical harmonics. Due to the iso-latitude distribution of sampling points the speed of computation of integrals over individual spherical harmonics scales as ~N1/2 with the total number of pixels, as opposed to the ~N scaling for the non-iso-latitude sampling distributions (examples of which are the Quadrilateralized Spherical Cube used for the NASA's COBE data, and any distribution based on the symmetries of the icosahedron).
Main Features of HEALPix Software
The HEALPix package
contains a suite of programs which allow all of the following (and more):
- Programs for fast simulation and analysis of full-sky maps of CMB temperature and polarization anisotropy (sky maps preview) up to sub-arcminute angular resolution
- C, C++, Fortan 90, IDL, Java, Python implementation of most routines and facilities (for third party implementation in other languages, see this HEALPix wiki page)
- Most critical routines are parallelized
- Forward and backward scalar and spin-weighted Spherical Harmonics Transforms
- Highly optimised Spherical Harmonics Transforms library (libsharp) used by all implementations for better performance
- Routines to read and write the FITS formatted map data sets, and allowing the IDL, Java or Python display and processing of your results
- Fortran 90 and C++ visualization facilities
- Comprehensive documentation (PDF and HTML)
- Automated installation and build scripts
- Programs to search the maps for pixel neighbours and extrema of a random field
- Pixel queries in discs, triangles, polygons and strips
- Programs to manage, modify and rotate spherical harmonic coefficients of arbitrary maps
- Programs to perform median filtering of sky maps
- Constrained and non-Gaussian realization facilities.
- Mask processing facilities
- An IDL toolkit for pixel manipulation and FITS file manipulation.
- Facilities to output HEALPix maps into Google Earth/Google Sky compliant images and into DomeMaster format used in planetariums.
For a detailed list of the new features added in the latest HEALPix release, see the Getting HEALPix page.