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Coordinate Systems for Solar Image Data A&A 449, 791–803 (2006) Astronomy DOI: 10.1051/0004-6361:20054262 & c ESO 2006 Astrophysics Coordinate systems for solar image data W. T. Thompson L-3 Communications GSI, NASA Goddard Space Flight Center, Code 612.1, Greenbelt, MD 20771, USA e-mail: [email protected] Received 27 September 2005 / Accepted 11 December 2005 ABSTRACT A set of formal systems for describing the coordinates of solar image data is proposed. These systems build on current practice in applying coordinates to solar image data. Both heliographic and heliocentric coordinates are discussed. A distinction is also drawn between heliocentric and helioprojective coordinates, where the latter takes the observer’s exact geometry into account. The extension of these coordinate systems to observations made from non-terrestial viewpoints is discussed, such as from the upcoming STEREO mission. A formal system for incorporation of these coordinates into FITS files, based on the FITS World Coordinate System, is described, together with examples. Key words. standards – Sun: general – techniques: image processing – astronomical data bases: miscellaneous – methods: data analysis 1. Introduction longitude and latitude – only need to worry about two spatial dimensions. The same can be said for normal cartography of Solar research is becoming increasingly more sophisticated. a planet such as Earth. However, to properly treat the complete Advances in solar instrumentation have led to increases in spa- range of solar phenomena, from the interior out into the corona, tial resolution, and will continue to do so. Future space mis- a complete three-dimensional coordinate system is required. sions will view the Sun from different perspectives than the Unfortunately, not all the information necessary to determine current view from ground-based observatories, or satellites in the full three-dimensional position of a solar feature is usually Earth orbit. Both of these advances will require more careful at- available. Therefore, in developing coordinate systems for so- tention to the coordinate systems used for solar image data. In lar data, one must take into account that one of the axes of the fact, some taste of this has already occured with the Solar and coordinate system may be missing. Heliospheric Observatory (SOHO) satellite (Domingo et al. Also, since the Sun is a gaseous body, there are no fixed 1995), which views the Sun from the inner Lagrange point be- points of reference on the Sun. What’s more, different parts tween Earth and the Sun. The Sun appears approximately 1% of the Sun rotate at different rates. The rotation rate depends bigger from SOHO than it does from Earth, requiring adjust- not only on latitude, but also on how deeply the magnetic field ment whenever SOHO images are compared with data from lines of a given feature are anchored in the photosphere. Thus, ground-based observatories, or satellites in low Earth orbit. for example, active regions follow different differential rotation Although there is widespread agreement on the coordi- laws than smaller-scale magnetic features at the same latitudes. nate systems to be used for interplanetary space (Russell 1971; For the above reasons, attention will be given to coordi- Hapgood 1992; Fränz & Harper 2002) no formal structure ex- nate systems which take the observer’s viewing geometry into ists for solar image coordinates, except for the well-established consideration. Some coordinate systems will be rotating with heliographic coordinate systems. In particular, there is no respect to other coordinate systems, and in all the coordinate agreement on how these coordinates should appear in FITS systems, at least some part of the Sun will be moving rela- headers, with potential confusion when data from one observa- tive to that coordinate system. For those reasons, the coordinate tory is compared to data from another. This document outlines system should not really be considered complete without also the various possible coordinate systems which may be used for taking time into account. In the discussion which follows, all solar image data, and to show how these coordinate systems re- coordinates will assume a given observation time t. late to the World Coordinate System (WCS) formalism used in With solar imaging instrumentation now planned for space- FITS files. In devising the coordinate systems outlined below, craft which will operate at large distances away from the attention is given to current practice within the solar imaging Earth-Sun line, such as STEREO (Socker et al. 1996), con- community. sideration must also be given as to how the viewpoint of the Normal coordinate systems used for extra-solar observa- instrument should be taken into account in the coordinate sys- tions – such as right ascension and declination, or galactic tem. This is discussed in Sect. 9.1. Article published by EDP Sciences and available at http://www.edpsciences.org/aa or http://dx.doi.org/10.1051/0004-6361:20054262 792 W. T. Thompson: Coordinate systems for solar image data 1.1. Coordinate systems within FITS files matrix replaces the older CROTAn keyword, which is deprecated in the WCS formalism. As well as ro- Two different styles of including coordinate information within tations, the PC matrix can also encode other trans- FITS files will be considered here. The first is the coordinate formations, such as skew. (There is also an optional system from the original FITS specification, while the second is form of the WCS formalism in which both the PCi_ j the more modern World Coordinate System. The latter allows and CDELTi keywords are combined into a single for much more flexibility in the types of coordinate systems CDi_ j matrix.) which can be expressed, as well as in describing how the in- CTYPEi: For spherical coordinates, the first four char- strument coordinate axes map into real-world coordinates. For acters express the coordinate type, while the second those reasons, we will concentrate on the World Coordinate four characters express the map projection used. System implementations of the coordinate systems. However, PVi_m: Additional parameters required in some coor- the older system will also be considered where appropriate. dinate systems. CUNITi: The units of the coordinates along axis i. 1.1.1. The original FITS coordinate system LONPOLE, LATPOLE: Angles used for spherical coordi- nate transformations. These keywords have default In the original FITS paper (Wells et al. 1981), the coordinates values which depend on the map projection used. of a data array were specified with the following keywords in the FITS header: For spherical coordinates, some care must be taken in the selec- CRPIXn: Reference pixel to subtract from the pixel co- tion of the reference pixel, depending on the projection being ordinates along axis n. Note that CRPIXn follows the used. Fortran convention of counting from 1 to N, instead It is a requirement in FITS files, and in WCS in particular, of from 0 to N − 1 as is done in some programming that all angles must be in degrees. (However, see Sect. 9.2.) languages. For simplicity, in the following, all trigonometric functions are CRVALn: Coordinate value of the reference pixel along assumed to have their arguments in degrees, while the inverse axis n. functions are assumed to return values in degrees. CDELTn: Pixel spacing along axis n. It is possible in WCS to have more than one coordinate CROTAn: Rotation angle, in degrees, to apply to axis n. system for any given data set. An alternate coordinate system The exact method of applying the rotation angle would be expressed using all the above keywords followed by was not specified in the original paper, but com- one of the letters “A” to “Z”, e.g. CRPIX1A, PC1_1A,etc.The monly used conventions have developed over the keywords WCSNAMEa can be used to label each alternative years, as discussed in Sect. 8. coordinate system – see Figs. 4 and 5. CTYPEn: A string value labeling each coordinate axis. Modified versions of the above keywords for use in binary A common system, used by the SOHO spacecraft, tables and pixel lists are listed in Greisen & Calabretta (2002) labels the westward axis as SOLARX and the north- and in Calabretta & Greisen (2002). ward axis as SOLARY. In the simple case of linear coordinates with no rotation, the 2. Heliographic coordinates transformation from pixel to real world coordinates is then 2 x = CRVALn + CDELTn × (i − CRPIXn). The well-known heliographic coordinate system expresses the latitude Θ and longitude Φ of a feature on the solar surface, and (The case where CROTAn 0 is discussed in Sect. 8.) Later, we can be extended to three dimensions by adding the radial dis- will show that this older system can be considered a special tance r from the center of the Sun. The rotational axis used to case of the coordinate systems described below. define the coordinate system is based on the original work of Carrington (1863). Seidelmann et al. (2002) lists the right as- α = ◦. 1.1.2. The World Coordinate System cension and declination of the solar north pole as 0 286 13, ◦ δ0 = 63.87. There are two basic variations on the heliographic The World Coordinate System (WCS) (Greisen & Calabretta system, which we will refer to as Stonyhurst and Carrington 2002; Calabretta & Greisen 2002) is a system for describing heliographic. Both use the same solar rotational axis, and differ the coordinates of a FITS array, and includes a system of de- only in the definition of longitude. 1 scribing various map projections for spherical coordinates .In There are several limitations to the use of heliographic simplified form, the keywords CRPIXn, CRVALn, CDELTn are coordinates when used with two-dimensional image data: retained from the original specification, combined with the following additional or modified keywords: – Without the r axis, coordinates can only be expressed for PCi_ j: A coordinate transformation matrix, describing pixels on the solar disk.
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