astro
Class WcsProjection

java.lang.Object
  util.PropertyContainer
      util.PropertyResources
          util.PropertyBundles
              astro.WcsProjection

All Implemented Interfaces:

Cloneable, Initializable, LocalizedSupplying, PropertySupplying, ResourceSupplying, VectorFunction

Direct Known Subclasses:

WcsProjection.EulerRotation, WcsProjection.Gnomonic, WcsProjection.LinearPixelProjection, WcsProjection.ThreeStepWcs

public abstract class WcsProjection
extends PropertyBundles
implements VectorFunction

A wcs projection normally converts pixel on the CCD to ra/de. Because this is a 2D to 2D mapping, one could in principle also use an inversion to get from ra de to pixels, but main use is with the forward approach to solve for a WCS in an image.

According to Calabretta and Greisen A&A 395, 1077 (2002), the transformation to get from pixel coordinates to celestial coordinates is split into three steps:

• Transform the pixel coordinates p into projection plane coordinates or intermediate world coordinates x with a linear transformation, either as

     x_i = s_i*Σm_ij(pj-rj) or
  
     x_i = cij*(pj-rj)
     

  The latter form is implemented in LinearIntermediate, where generally the r_i is fixed. Distortions of the image are generally introduced in this transformation, there is no final definition yet, only DSS and Spitzer have a polynomial distortion correction on pixel coorinates, before the transformation to x_i commences:

     (pi-ri)'=(pi-ri)+poly(pi-ri)
     

  This transformation is accessible as PolynomialDistortion.
• Convert the intermediate world coordinates x_i into native spherical projection coordinates φ and θ. An implementation example would be WcsProjection.Gnomonic.
• From the native spherical coordinates one gets to the celestial spherical coordinates via a rotation of the spherical system. This is simple in case of zenithal projections, where the native pole has right ascension α_p and declination δ_p and the transformation follows from spherical trigonometry.

     cos(de)cos(ra-α_p)=sin(θ)cos(δ_p)+cos(θ)sin(δ_p)cos(&phi)
  
     cos(de)sin(ra-α_p)=cos(θ)sin(&phi)
     

  This rotation is available as WcsProjection.EulerRotation

The most common case, LinearWcs is a concatination of a LinearIntermediate, followed by a Gnomonic projection, followed by an EulerRotation. It has in the minimal case two parameter for scaling the pixel axis to intermediate world coordinates and two parameters as the native pole coordiantes in the euler rotation, at maximum two parameters more describing the rotation of the coordinate system. Note that generally the parameters, which are often supplied by a solver routine, should reflect the concatination of transformation, LinearWcs, if constructed with distortion and shear interprets the parameters as c00,c11,c01,c10,α_p and δ_p. If constructed with scaling only, c00=c11=scale and c01=c10=0. thus scale,α_p and δ_p. If constructed with distortion, c01=c10=0, thus c00,c11,α_p and δ_p. If constructed with rotation, c00=c11=scale*cos(rot) and c01=-scale*sin(rot), c10=scale*sin(rot), thus scale,rot,α_p and δ_p. If constructed with distortion and rotation, c00=scale1*cos(rot), c11=scale2*cos(rot), c01=-scale2*sin(rot), c10=scale1*sin(rot), thus scale1, scale2, rot,α_p and δ_p.

An essential part of a WCS projection is also parsing a fits headers via special fits header keys. These names might be different for different fits sources, thus all projection support a properties look-up table that links unique key names to the key names used in this special fits file. For standard fits headers, this is an key=value mapping, as returned by getStandardKeys().

Nested Class Summary

static class	WcsProjection.EulerRotation A Euler rotation, defined by the coordinates of the native pole.
static class	WcsProjection.Gnomonic The gnomic projection is the oldest known azimuthal projection.
static class	WcsProjection.LinearGnomonicRaDe A combination from a full-linear projection from pixel space to intermediate world coordinates, followed by a gnomic projection and a euler rotation to get to ra and dec.
static class	WcsProjection.LinearPixelProjection The linear transformation from pixel space to intermediate world coordinates.
static class	WcsProjection.PolynomialGnomonicRaDe A combination from a full-polynomial projection from pixel space to intermediate world coordinates .
static class	WcsProjection.PolynomialPixelProjection This now fits intermediate world coordinates from pixel coordinates with Legendre polynomials such that the pixel coordinates are slightly distorted before calculating the intermediate coordinates.
static class	WcsProjection.ReadWcs A test for reading and interpreting header cards that describe a pure linear pixel-to-intermediate transformation, a gnomic projection and finally a rotation to yield ra and dec.
static class	WcsProjection.ThreeStepWcs A combination put together from three individual WcsProjections, a pixel projection that transfers CCD-pixel into intermediate world coordinates, a true geometric projection (like Gnomonic) and a final rotation to yield coordinates in a known space.
static class	WcsProjection.VariableGnomonicRaDe A combination from a full-linear projection from pixel space to intermediate world coordinates with varying projection center.
static class	WcsProjection.VariablePixelProjection It turned out, that the quality of the WCS solution is highly dependant on the correct position of the native pole, rj.

Nested classes/interfaces inherited from class util.PropertyResources

PropertyResources.URLResource

Field Summary

private static double	DEFPARAMETERSCALE Default property value.
static String	KEY_PARAMETERSCALE The parameters length scale as a multiple of the length.
private VectorG	parameters The parameters of the projection we depend on.

Fields inherited from class util.PropertyBundles

KEY_LOCALECOUNTRY, KEY_LOCALELANGUAGE, KEY_RESOURCEBUNDLES

Fields inherited from class util.PropertyResources

KEY_NOINITONCREATE, localurl, locate, POSTFIX_DIR, POSTFIX_EXT, POSTFIX_FILE, POSTFIX_LIST, POSTFIX_URL, urlset

Fields inherited from class util.PropertyContainer

KEY_LISTSEPARATOR, KEY_MAPKEYVALUECHAR, KEY_MAPSEPARATOR

Fields inherited from interface util.ResourceSupplying

KEY_URLRESOURCES, KEY_URLUSECONFIG, KEY_URLUSECURRENT, KEY_URLUSEHOME

Fields inherited from interface util.PropertySupplying

CONFIG, KEY_CLASS

Constructor Summary

protected	WcsProjection() Constructs a new WCS projection.
protected	WcsProjection(Map<String,String> u2f) Constructs a new WCS projection specifying individual fits key names for our unique names.

Method Summary

int	argumentDimension() We have a two-dimensional pixel space.
abstract VectorG	estimateParameters(nom.tam.fits.Header h) Estimates (starting) parameters from a fits header.
VectorG	estimateParameterScales(VectorG start) Length scales of the parameters.
int	functionDimension() The dimension of the projection is two.
abstract Collection<nom.tam.fits.HeaderCard>	getCards() Converts the parameters into a collection of header cards.
VectorG	getParameters() Gets the parameters of this projection.
abstract double	getPixelArea(VectorG pxpy) This is the pixel size, which is determined out of the Jacobian determinant of the projection.
static Map<String,String>	getStandardKeys() Returns a standard mapping of keys.
abstract boolean	parseHeader(nom.tam.fits.Header h) Parses parameters from a fits header.
void	setParameters(VectorG p) Sets the parameters of the projection.

Methods inherited from class util.PropertyBundles

clone, getLocalized, getLocalized, getLocalizedString, getLocalizedString, loadResource

Methods inherited from class util.PropertyResources

createFrom, createFrom, createFrom, getApplet, getAsResources, getLocalClassLoader, getPropertiesToKey, getPropertiesToKey, getResource, getResourceAsStream, getResourceFromKey, getResources, init, keyCreate, keyCreate, reload, setApplet

Methods inherited from class util.PropertyContainer

augment, augment, augment, defaultBoolean, defaultChar, defaultDouble, defaultFloat, defaultInt, defaultLong, defaultObject, defaultObject, defaultProperties, defaultProperty, getAsBoolean, getAsChar, getAsDouble, getAsEnums, getAsFloat, getAsInt, getAsList, getAsLong, getAsMap, getAsMap, getAsObject, getAsObject, getProperties, getProperty, has, isNew, parseObject, reload, removeProperty, rescanned, setObject, setProperties, setProperty, stringProperties, toString

Methods inherited from class java.lang.Object

equals, finalize, getClass, hashCode, notify, notifyAll, wait, wait, wait

Methods inherited from interface vec_math.VectorFunction

evaluate

Methods inherited from interface util.ResourceSupplying

getResource, getResourceAsStream, getResources

Methods inherited from interface util.PropertySupplying

defaultBoolean, defaultChar, defaultDouble, defaultFloat, defaultInt, defaultLong, defaultObject, defaultObject, defaultProperties, defaultProperty, getAsBoolean, getAsChar, getAsDouble, getAsFloat, getAsInt, getAsList, getAsLong, getAsMap, getAsObject, getAsObject, getProperties, getProperty, has, parseObject, removeProperty, setObject, setProperty, stringProperties

Methods inherited from interface util.Initializable

init

Field Detail

KEY_PARAMETERSCALE

public static final String KEY_PARAMETERSCALE

The parameters length scale as a multiple of the length.

See Also:

Constant Field Values

DEFPARAMETERSCALE

private static final double DEFPARAMETERSCALE

Default property value.

See Also:

Constant Field Values

parameters

private VectorG parameters

The parameters of the projection we depend on.

Constructor Detail

WcsProjection

protected WcsProjection()

Constructs a new WCS projection.

WcsProjection

protected WcsProjection(Map<String,String> u2f)

Constructs a new WCS projection specifying individual fits key names for our unique names.

Method Detail

getStandardKeys

public static Map<String,String> getStandardKeys()

Returns a standard mapping of keys.

getParameters

public VectorG getParameters()

Gets the parameters of this projection.

setParameters

public void setParameters(VectorG p)

Sets the parameters of the projection.

functionDimension

public int functionDimension()

The dimension of the projection is two.

Specified by:

functionDimension in interface VectorFunction

argumentDimension

public int argumentDimension()

We have a two-dimensional pixel space.

Specified by:

argumentDimension in interface VectorFunction

getPixelArea

public abstract double getPixelArea(VectorG pxpy)

This is the pixel size, which is determined out of the Jacobian determinant of the projection. Note that due to det(A*B)=det (A)*det (B) this also holds for composed projections.

parseHeader

public abstract boolean parseHeader(nom.tam.fits.Header h)
                             throws nom.tam.fits.HeaderCardException

Parses parameters from a fits header.

Throws:

nom.tam.fits.HeaderCardException

estimateParameters

public abstract VectorG estimateParameters(nom.tam.fits.Header h)
                                    throws nom.tam.fits.HeaderCardException

Estimates (starting) parameters from a fits header.

Throws:

nom.tam.fits.HeaderCardException

estimateParameterScales

public VectorG estimateParameterScales(VectorG start)

Length scales of the parameters. In the default implementation we simply take the length of the vector and multiply it with KEY_PARAMETERSCALE.

getCards

public abstract Collection<nom.tam.fits.HeaderCard> getCards()
                                                      throws nom.tam.fits.HeaderCardException

Converts the parameters into a collection of header cards.

Throws:

nom.tam.fits.HeaderCardException