/** Get the scaling when it is described as a matrix */
private boolean extractScaler2(double crpix1, double crpix2) throws TransformationException {
// Look for the CD matrix...
//
double m11 = h.getDoubleValue("CD" + lonAxis + "_" + lonAxis, NaN);
double m12 = h.getDoubleValue("CD" + lonAxis + "_" + latAxis, NaN);
double m21 = h.getDoubleValue("CD" + latAxis + "_" + lonAxis, NaN);
double m22 = h.getDoubleValue("CD" + latAxis + "_" + latAxis, NaN);
boolean matrix = !isNaN(m11 + m12 + m21 + m22);
if (!matrix) {
return false;
}
wcsKeys.put("CD1_1", m11);
wcsKeys.put("CD1_2", m12);
wcsKeys.put("CD2_1", m21);
wcsKeys.put("CD2_2", m22);
m11 = toRadians(m11);
m12 = toRadians(m12);
m21 = toRadians(m21);
m22 = toRadians(m22);
// we have
// t = a11 (x-x0) + a12 (y-y0); u = a21(x-x0) + a22(y-y0)
// t = a11x + a12y - a11 x0 - a12 y0;
//
Scaler s =
new Scaler(-m11 * crpix1 - m12 * crpix2, -m21 * crpix1 - m22 * crpix2, m11, m12, m21, m22);
s = s.inverse();
// Are longitude and latitude in unusual order?
if (lonAxis > latAxis) {
s.interchangeAxes();
}
this.scale = s;
add(s);
setWCSScale(s);
return true;
}
/**
* Write FITS WCS keywords given key values. Only relatively simple WCSs are handled here. We
* assume we are dealing with axes 1 and 2.
*
* @param h The header to be updated.
* @param s A Scaler giving the transformation between standard projection coordinates and
* pixel/device coordinates.
* @param projString A three character string giving the projection used. Supported projections
* are: "Tan", "Sin", "Ait", "Car", "Zea".
* @param coordString A string giving the coordinate system used. The first character gives the
* general frame. For most frames the remainder of the string gives the equinox of the
* coordinate system. E.g., J2000, B1950, Galactic, "E2000", "H2020.10375".
*/
public void updateHeader(
Header h, Scaler s, double[] crval, String projString, String coordString) throws Exception {
if (proj.isFixedProjection()) {
h.addValue("CRVAL1", toDegrees(proj.getReferencePoint()[0]), "Fixed reference center");
h.addValue("CRVAL2", toDegrees(proj.getReferencePoint()[1]), "Fixed reference center");
} else {
h.addValue("CRVAL1", crval[0], "Reference longitude");
h.addValue("CRVAL2", crval[1], "Reference latitude");
}
coordString = coordString.toUpperCase();
String[] prefixes = new String[2];
char c = coordString.charAt(0);
if (c == 'J' || c == 'I') {
h.addValue("RADESYS", "FK5", "Coordinate system");
prefixes[0] = "RA--";
prefixes[1] = "DEC-";
} else if (c == 'B') {
h.addValue("RADESYS", "FK4", "Coordinate system");
prefixes[0] = "RA--";
prefixes[1] = "DEC-";
} else {
prefixes[0] = c + "LON";
prefixes[1] = c + "LAT";
}
if (c != 'G' && c != 'I') {
try {
double equinox = Double.parseDouble(coordString.substring(1));
h.addValue("EQUINOX", equinox, "Epoch of the equinox");
} catch (Exception e) {
// Couldn't parse out the equinox
}
}
if (c == 'I') {
h.addValue("EQUINOX", 2000, "ICRS coordinates");
}
String upProj = projString.toUpperCase();
h.addValue("CTYPE1", prefixes[0] + "-" + upProj, "Coordinates -- projection");
h.addValue("CTYPE2", prefixes[1] + "-" + upProj, "Coordinates -- projection");
// Note that the scaler transforms from the standard projection
// coordinates to the pixel coordinates.
// P = P0 + M X where X is the standard coordinates and P is the
// pixel coordinates. So the reference pixels are just the constants
// in the scaler.
// Remember that FITS pixels are offset by 0.5 from 0 offset pixels.
h.addValue("CRPIX1", s.x0 + 0.5, "X reference pixel");
h.addValue("CRPIX2", s.y0 + 0.5, "Y reference pixel");
// Remember that the FITS values are of the form
// X = M(P-P0)
// so we'll need to invert the scaler.
//
// Do we need a matrix?
if (abs(s.a01) < 1.e-14 && abs(s.a10) < 1.e-14) {
// No cross terms, so we'll just use CDELTs
h.addValue("CDELT1", toDegrees(1 / s.a00), "X scale");
h.addValue("CDELT2", toDegrees(1 / s.a11), "Y scale");
} else {
// We have cross terms. It's simplest
// just to use the CD matrix and not worry about
// normalization. First invert the matrix to get
// the transformation in the direction that FITS uses.
Scaler rev = s.inverse();
h.addValue("CD1_1", toDegrees(rev.a00), "Matrix element");
h.addValue("CD1_2", toDegrees(rev.a01), "Matrix element");
h.addValue("CD2_1", toDegrees(rev.a10), "Matrix element");
h.addValue("CD2_2", toDegrees(rev.a11), "Matrix element");
}
}
/** Handle the NEAT special projection */
private void doNeatWCS() throws TransformationException {
// The NEAT transformation from the standard spherical system
// includes:
// Transformation to J2000 spherical coordinates (a null operation)
// A tangent plane projection to the standard plane
// A scaler transformation to corrected pixel coordinates.
// A distorter to distorted pixel coordinates
// A scaler transformation of distorted coordinates to actual pixels
CoordinateSystem csys = CoordinateSystem.factory("J2000");
this.csys = csys;
// The RA0/DEC0 pair are the actual center of the projection.
double cv1 = toRadians(h.getDoubleValue("RA0"));
double cv2 = toRadians(h.getDoubleValue("DEC0"));
wcsKeys.put("CRVAL1", toDegrees(cv1));
wcsKeys.put("CRVAL2", toDegrees(cv2));
Projection proj = new Projection("Tan", new double[] {cv1, cv2});
this.proj = proj;
double cd1 = toRadians(h.getDoubleValue("CDELT1"));
double cd2 = toRadians(h.getDoubleValue("CDELT2"));
wcsKeys.put("CDELT1", toDegrees(cd1));
wcsKeys.put("CDELT2", toDegrees(cd2));
wcsScale = abs(cd1);
double cp1 = h.getDoubleValue("CRPIX1");
double cp2 = h.getDoubleValue("CRPIX2");
wcsKeys.put("CPRIX1", cp1);
wcsKeys.put("CRPIX2", cp2);
wcsKeys.put("CTYPE1", "RA---XTN");
wcsKeys.put("CTYPE2", "DEC--XTN");
Scaler s1 = new Scaler(0., 0., -1 / cd1, 0, 0, -1 / cd2);
// Note that the the A0,A1,A2, B0,B1,B2 rotation
// is relative to the original pixel values, so
// we need to put this in the secondary scaler.
//
double x0 = h.getDoubleValue("X0");
double y0 = h.getDoubleValue("Y0");
Distorter dis =
new skyview.geometry.distorter.Neat(
h.getDoubleValue("RADIAL"), h.getDoubleValue("XRADIAL"), h.getDoubleValue("YRADIAL"));
double a0 = h.getDoubleValue("A0");
double a1 = h.getDoubleValue("A1");
double a2 = h.getDoubleValue("A2");
double b0 = h.getDoubleValue("B0");
double b1 = h.getDoubleValue("B1");
double b2 = h.getDoubleValue("B2");
// The reference pixel is to be computed in the distorted frame.
double[] cpix = new double[] {cp1, cp2};
double[] cout = new double[2];
dis.transform(cpix, cout);
Scaler s2 =
new Scaler(
cout[0] - a0 - a1 * x0 - a2 * y0,
cout[1] - b0 - b2 * x0 - b1 * y0,
-(1 + a1),
-a2,
-b2,
-(1 + b1));
wcsKeys.put("A0", a0);
wcsKeys.put("A1", a1);
wcsKeys.put("A2", a2);
wcsKeys.put("B0", b0);
wcsKeys.put("B1", b1);
wcsKeys.put("B2", b2);
this.distort = dis;
add(csys.getSphereDistorter());
add(csys.getRotater());
add(proj.getRotater());
add(proj.getProjecter());
this.scale = s1;
// Note that s1 is defined from the projection plane to the pixels coordinates,
// so we don't need to invert it.
//
// But the second scaler, s2, used in the NEAT correction
// is defined in the direction from pixels to sphere, so we
// need to take its inverse.
this.scale = this.scale.add(s2.inverse());
add(this.scale);
add(dis);
}
/**
* Return a new WCS from the existing WCS where we add a scale. This allows us to return a WCS for
* a subset of an image easily.
*/
public WCS addScaler(Scaler shift) throws TransformationException {
return new WCS(csys, proj, scale.add(shift));
}
/** Handle a DSS projection */
private void doDSSWCS() throws TransformationException {
double plateRA =
h.getDoubleValue("PLTRAH")
+ h.getDoubleValue("PLTRAM") / 60
+ h.getDoubleValue("PLTRAS") / 3600;
plateRA = toRadians(15 * plateRA);
wcsKeys.put("PLTRAH", h.getDoubleValue("PLTRAH"));
wcsKeys.put("PLTRAM", h.getDoubleValue("PLTRAM"));
wcsKeys.put("PLTRAS", h.getDoubleValue("PLTRAS"));
double plateDec =
h.getDoubleValue("PLTDECD")
+ h.getDoubleValue("PLTDECM") / 60
+ h.getDoubleValue("PLTDECS") / 3600;
plateDec = toRadians(plateDec);
if (h.getStringValue("PLTDECSN").substring(0, 1).equals("-")) {
plateDec = -plateDec;
}
wcsKeys.put("PLTDECD", h.getDoubleValue("PLTDECD"));
wcsKeys.put("PLTDECM", h.getDoubleValue("PLTDECM"));
wcsKeys.put("PLTDECS", h.getDoubleValue("PLTDECS"));
wcsKeys.put("PLTDECSN", h.getStringValue("PLTDECSN"));
double plateScale = h.getDoubleValue("PLTSCALE");
double xPixelSize = h.getDoubleValue("XPIXELSZ");
double yPixelSize = h.getDoubleValue("YPIXELSZ");
wcsKeys.put("PLTSCALE", plateScale);
wcsKeys.put("XPIXELSZ", xPixelSize);
wcsKeys.put("YPIXELSZ", yPixelSize);
double[] xCoeff = new double[20];
double[] yCoeff = new double[20];
for (int i = 1; i <= 20; i += 1) {
xCoeff[i - 1] = h.getDoubleValue("AMDX" + i);
yCoeff[i - 1] = h.getDoubleValue("AMDY" + i);
wcsKeys.put("AMDX" + i, xCoeff[i - 1]);
wcsKeys.put("AMDY" + i, yCoeff[i - 1]);
}
double[] ppo = new double[6];
for (int i = 1; i <= 6; i += 1) {
ppo[i - 1] = h.getDoubleValue("PPO" + i);
wcsKeys.put("PPO" + i, ppo[i - 1]);
}
double plateCenterX = ppo[2];
double plateCenterY = ppo[5];
double cdelt1 = -plateScale / 1000 * xPixelSize / 3600;
double cdelt2 = plateScale / 1000 * yPixelSize / 3600;
wcsScale = abs(cdelt1);
// This gives cdelts in degrees per pixel.
// CNPIX pixels use a have the first pixel going from 1 - 2 so they are
// off by 0.5 from FITS (which in turn is offset by 0.5 from the internal
// scaling, but we handle that elsewhere).
double crpix1 = plateCenterX / xPixelSize - h.getDoubleValue("CNPIX1", 0) - 0.5;
double crpix2 = plateCenterY / yPixelSize - h.getDoubleValue("CNPIX2", 0) - 0.5;
wcsKeys.put("CNPIX1", h.getDoubleValue("CNPIX1", 0));
wcsKeys.put("CNPIX2", h.getDoubleValue("CNPIX2", 0));
Projection proj = new Projection("Tan", new double[] {plateRA, plateDec});
this.proj = proj;
CoordinateSystem coords = CoordinateSystem.factory("J2000");
this.csys = coords;
cdelt1 = toRadians(cdelt1);
cdelt2 = toRadians(cdelt2);
Scaler s = new Scaler(-cdelt1 * crpix1, -cdelt2 * crpix2, cdelt1, 0, 0, cdelt2);
// Got the transformers ready. Add them in properly.
add(coords.getSphereDistorter());
add(coords.getRotater());
add(proj.getRotater());
add(proj.getProjecter());
this.distort =
new skyview.geometry.distorter.DSS(
plateRA, plateDec, xPixelSize, yPixelSize, plateScale, ppo, xCoeff, yCoeff);
add(this.distort);
this.scale = s.inverse();
add(this.scale);
}
private void extractProjection() throws TransformationException {
Projection proj = null;
Scaler ncpScale = null;
String lonType = h.getStringValue("CTYPE" + lonAxis).substring(5, 8);
String latType = h.getStringValue("CTYPE" + latAxis).substring(5, 8);
if (!lonType.equals(latType)) {
throw new TransformationException(
"Inconsistent projection in FITS header: " + lonType + "," + latType);
}
if (lonType.equals("AIT")) {
proj = new Projection("Ait");
} else if (lonType.equals("CAR")) {
proj = new Projection("Car");
// Allow non-central latitudes for the Cartesian projection.
try {
double lon = h.getDoubleValue("CRVAL" + lonAxis);
if (lon != 0) {
proj.setReference(toRadians(lon), 0);
}
} catch (Exception e) {
System.err.println("Unable to read reference longitude in Cartesian projection");
}
} else if (lonType.equals("CSC")) {
proj = new Projection("Csc");
} else if (lonType.equals("SFL") || lonType.equals("GLS")) {
proj = new Projection("Sfl");
} else if (lonType.equals("TOA")) {
proj = new Projection("Toa");
} else {
double crval1 = h.getDoubleValue("CRVAL" + lonAxis, NaN);
double crval2 = h.getDoubleValue("CRVAL" + latAxis, NaN);
if (isNaN(crval1 + crval2)) {
throw new TransformationException("Unable to find reference coordinates in FITS header");
}
wcsKeys.put("CRVAL1", crval1);
wcsKeys.put("CRVAL2", crval2);
if (lonType.equals("TAN")
|| lonType.equals("SIN")
|| lonType.equals("ZEA")
|| lonType.equals("ARC")
|| lonType.equals("STG")) {
String type = lonType.substring(0, 1) + lonType.substring(1, 3).toLowerCase();
proj = new Projection(type, new double[] {toRadians(crval1), toRadians(crval2)});
double lonpole = h.getDoubleValue("LONPOLE", NaN);
if (!isNaN(lonpole)) {
wcsKeys.put("LONPOLE", lonpole);
}
// ---- Following is probably erroneous -----
// The WCS standard indicates that the default LONPOLE for
// a projection is 180 when the CRVAL latitude is less than
// the native latitude of the projection (90 degrees for the projections
// handled here) and 0 otherwise. This means that for a projection
// around the pole the default lonpole is 0. Some data (the SFD surveys)
// seem to require that we do a rotation of 180 degrees to accommodate
// this. However we do not implement this unless the LONPOLE is
// explicitly given since this seems non-intuitive to me and I suspect
// that a user who is not careful enough to specify a LONPOLE in this
// situation probably doesn't understand what is going on anyway.
// ----- We now assume that our standard processing of
// ----- zenithal projections handles lonpole of 180 and that
// ----- this is the default for all zenithal images.
// ----- Previously we assumed that we were using lonPole=0 at
// ----- at the poles, but we weren't....
//
if (!isNaN(lonpole)) {
double lonDefault = 180;
if (lonpole != lonDefault) {
Rotater r = proj.getRotater();
Rotater lon = new Rotater("Z", toRadians(lonpole - lonDefault), 0, 0);
if (r != null) {
proj.setRotater(r.add(lon));
} else {
proj.setRotater(lon);
}
}
}
} else if (lonType.equals("NCP")) {
// Sin projection with projection centered at pole.
double[] xproj = new double[] {toRadians(crval1), PI / 2};
if (crval2 < 0) {
xproj[1] = -xproj[1];
}
double poleOffset = sin(xproj[1] - toRadians(crval2));
// Have we handled South pole here?
proj = new Projection("Sin", xproj);
// NCP scales the Y-axis to accommodate the distortion of the SIN projection away
// from the pole.
ncpScale = new Scaler(0, poleOffset, 1, 0, 0, 1);
ncpScale = ncpScale.add(new Scaler(0., 0., 1, 0, 0, 1 / sin(toRadians(crval2))));
} else {
throw new TransformationException("Unsupported projection type:" + lonType);
}
}
this.proj = proj;
if (ncpScale != null) {
this.scale = ncpScale;
}
add(proj.getRotater());
add(proj.getProjecter());
add(ncpScale); // Ignored if null
}
/** Get the scaling when CDELT is specified */
private boolean extractScaler1(double crpix1, double crpix2) throws TransformationException {
boolean matrix = false;
double cdelt1 = h.getDoubleValue("CDELT" + lonAxis, NaN);
double cdelt2 = h.getDoubleValue("CDELT" + latAxis, NaN);
wcsKeys.put("CDELT1", cdelt1);
wcsKeys.put("CDELT2", cdelt2);
if (isNaN(cdelt1) || isNaN(cdelt2)) {
return false;
}
// We use 1 indexing to match better with the FITS files.
double m11, m12, m21, m22;
// We've got minimal information... We might have more.
double crota = h.getDoubleValue("CROTA" + latAxis, NaN);
if (!isNaN(crota) && crota != 0) {
wcsKeys.put("CROTA2", crota);
crota = toRadians(crota);
m11 = cos(crota);
m12 = sin(crota);
m21 = -sin(crota);
m22 = cos(crota);
matrix = true;
} else {
m11 = h.getDoubleValue("PC" + lonAxis + "_" + lonAxis, NaN);
m12 = h.getDoubleValue("PC" + lonAxis + "_" + latAxis, NaN);
m21 = h.getDoubleValue("PC" + latAxis + "_" + lonAxis, NaN);
m22 = h.getDoubleValue("PC" + latAxis + "_" + latAxis, NaN);
matrix = !isNaN(m11 + m12 + m21 + m22);
if (matrix) {
wcsKeys.put("PC1_1", m11);
wcsKeys.put("PC1_2", m12);
wcsKeys.put("PC2_1", m21);
wcsKeys.put("PC2_2", m22);
}
}
// Note that Scaler is defined with parameters t = x0 + a00 x + a01 y; u = y0 + a10 x + a11 y
// which is different from what we have here...
// t = scalex (x-x0), u = scaley (y-y0)
// t = scalex x - scalex x0; u = scaley y - scaley y0
// or
// t = scalex [a11 (x-x0) + a12 (y-y0)], u = scaley [a21 (x-x0) + a22 (y-y0)] ->
// t = scalex a11 x - scalex a11 x0 + scalex a12 y + scalex a12 y0 ->
// t = - scalex (a11 x0 + a12 y0) + scalex a11 x + scalex a12 y (and similarly for u)
Scaler s;
cdelt1 = toRadians(cdelt1);
cdelt2 = toRadians(cdelt2);
if (!matrix) {
s = new Scaler(-cdelt1 * crpix1, -cdelt2 * crpix2, cdelt1, 0, 0, cdelt2);
} else {
s =
new Scaler(
-cdelt1 * (m11 * crpix1 + m12 * crpix2),
-cdelt2 * (m21 * crpix1 + m22 * crpix2),
cdelt1 * m11,
cdelt1 * m12,
cdelt2 * m21,
cdelt2 * m22);
}
// Note that this scaler transforms from pixel coordinates to standard projection
// plane coordinates. We want the inverse transformation as the scaler.
s = s.inverse();
// Are lon and lat in unusual order?
if (lonAxis > latAxis) {
s.interchangeAxes();
}
this.scale = s;
add(s);
setWCSScale(s);
return true;
}
/** Set the scale of the transformation */
private void setWCSScale(Scaler s) {
// Use the determinant of the transformation matrix to get the scale
double[] p = s.getParams();
double det = p[2] * p[5] - p[3] * p[4];
wcsScale = 1 / sqrt(abs(det));
}