Using the WCS object¶
This section uses the imaging_wcs_wdist.asdf created in Adding distortion to the imaging example
to read in a WCS object and demo its methods.
>>> import asdf
>>> asdf_file = asdf.open("imaging_wcs_wdist.asdf")
>>> wcsobj = asdf_file.tree["wcs"]
>>> print(wcsobj)
From Transform
----------------- ----------------
detector distortion
undistorted_frame linear_transform
icrs None
Inspecting Available Coordinate Frames¶
To see what frames are defined:
>>> print(wcsobj.available_frames)
['detector', 'undistorted_frame', 'icrs']
>>> wcsobj.input_frame
<Frame2D(name="detector", unit=(Unit("pix"), Unit("pix")), axes_names=('x', 'y'), axes_order=(0, 1))>
>>> wcsobj.output_frame
<CelestialFrame(name="icrs", unit=(Unit("deg"), Unit("deg")), axes_names=('lon', 'lat'), axes_order=(0, 1), reference_frame=<ICRS Frame>)>
Because the output_frame is a CoordinateFrame object we can get
the result of the WCS transform as an SkyCoord object and transform
them to other standard coordinate frames supported by astropy.coordinates.
>>> skycoord = wcsobj(1, 2, with_units=True)
>>> print(skycoord)
<SkyCoord (ICRS): (ra, dec) in deg
(5.50090023, -72.04553535)>
>>> print(skycoord.transform_to("galactic"))
<SkyCoord (Galactic): (l, b) in deg
(306.12713109, -44.8996588)>
Using Bounding Box¶
The WCS object has an attribute bounding_box
(default value of None) which describes the range of
acceptable values for each input axis.
>>> wcsobj.bounding_box = ((0, 2048), (0, 1000))
>>> wcsobj((2,3), (1020, 980))
[array([ nan, 5.54527989]), array([ nan, -72.06454341])]
The WCS object accepts a boolean flag called with_bounding_box with default value of
True. Output values which are outside the bounding_box are set to NaN.
There are cases when this is not desirable and with_bounding_box=False should be passes.
Calling the footprint() returns the footprint on the sky.
>>> wcsobj.footprint()
array([[ 5.5264392 , -72.05149213],
... [ 5.54580408, -72.06422321],
... [ 5.63010439, -72.05426843],
... [ 5.610708 , -72.04173847]])
Warning
GWCS and astropy default to different tuple ordering conventions for representing multi-dimensional bounding boxes.
GWCS uses the
"F"ordering convention, where the tuples are ordered((x0min, x0max), (x1min, x1max), ..., (xnmin, xnmax))(x,y,z ordering).While astropy uses the
"C"ordering convention, where tuples are ordered((xnmin, xnmax), ..., (x1min, x1max), (x0min, x0max))(z, y, x ordering).
This means that given the same tuple of tuples, say ((a, b), (c, d)), setting
the bounding box on the transform prior to creating the GWCS will result in a
different bounding box than if one sets the same tuple of tuples on the GWCS object
itself. Indeed, in this case the former will assume (c, d) is the bounding box
for x while the latter will assume (a, b) is the bounding box for x.
It is recommended that when working on GWCS objects that one sets the bounding box on the GWCS object itself, rather than on the transform prior to creating the GWCS object.
Note if one wants to set the bounding box on the transform itself
rather than the GWCS object then it should be done with
bind_bounding_box with the order argument properly set.
Note
The GWCS will always convert or assume the bounding box to the "F" ordering
convention when setting the bounding box on the GWCS object itself and will
perform this conversion on the first access to the bounding box through the GWCS
object. If conversion occurs on first access, GWCS will issue a warning to alert
the user that the bounding box has been converted.
Manipulating Transforms¶
Some methods allow managing the transforms in a more detailed manner.
Transforms between frames can be retrieved and evaluated separately.
>>> dist = wcsobj.get_transform('detector', 'undistorted_frame')
>>> dist(1, 2)
(41.62325692108675, -12.68101006210054)
Transforms in the pipeline can be replaced by new transforms.
>>> new_transform = models.Shift(1) & models.Shift(1.5) | distortion
>>> wcsobj.set_transform('detector', 'undistorted_frame', new_transform)
>>> wcsobj(1, 2)
(5.501064280097802, -72.04557376712566)
A transform can be inserted before or after a frame in the pipeline.
>>> scale = models.Scale(2) & models.Scale(1)
>>> wcsobj.insert_transform('icrs', scale, after=False)
>>> wcsobj(1, 2)
(11.002128560195604, -72.04557376712566)
Inverse Transformations¶
Often, it is useful to be able to compute inverse transformation that converts coordinates from the output frame back to the coordinates in the input frame.
Note. the backward_transform attribute is equivalent to
forward_transform.inverse.
In this section, for illustration purpose, we will be using the same 2D imaging
WCS from imaging_wcs_wdist.asdf created in Adding distortion to the imaging example whose
forward transformation converts image coordinates to world coordinates and
inverse transformation converts world coordinates back to image coordinates.
>>> import asdf
>>> from astropy.utils.data import get_pkg_data_filename
>>> wcsobj = asdf.open(get_pkg_data_filename('imaging_wcs_wdist.asdf')).tree['wcs']
The most general method available for computing inverse coordinate
transformation is the WCS.invert()
method. This method uses automatic or user-supplied analytical inverses whenever
available to convert coordinates from the output frame to the input frame.
When analytical inverse is not available as is the case for the wcsobj above,
a numerical solution will be attempted using
WCS.numerical_inverse().
Default parameters used by WCS.numerical_inverse()
or WCS.invert() methods should be acceptable in
most situations:
>>> world = wcsobj(350, 200)
>>> print(wcsobj.invert(*world)) # convert a single point
(349.9999994163172, 200.00000017679295)
>>> world = wcsobj([2, 350, -5000], [2, 200, 6000])
>>> print(wcsobj.invert(*world)) # convert multiple points at once
(array([ 1.99999752, 3.49999999e+02, -5.00000000e+03]), array([1.99999972e+00, 2.00000002e+02, 6.00000000e+03])
By default, parameter quiet is set to True in WCS.numerical_inverse()
and so it will return results “as is” without warning us about possible loss
of accuracy or about divergence of the iterative process.
In order to catch these kind of errors that can occur during numerical
inversion, we need to turn off quiet mode and be prepared to catch
gwcs.wcs.NoConvergence exceptions. In the next example, let’s also add a
point far away from the image for which numerical inverse fails.
>>> from gwcs import NoConvergence
>>> world = wcsobj([-85000, 2, 350, 3333, -5000], [-55000, 2, 200, 1111, 6000],
... with_bounding_box=False)
>>> try:
... x, y = wcsobj.invert(*world, quiet=False, maxiter=40,
... detect_divergence=True, with_bounding_box=False)
... except NoConvergence as e:
... print(f"Indices of diverging points: {e.divergent}")
... print(f"Indices of poorly converging points: {e.slow_conv}")
... print(f"Best solution:\n{e.best_solution}")
... print(f"Achieved accuracy:\n{e.accuracy}")
Indices of diverging points: [0]
Indices of poorly converging points: [4]
Best solution:
[[ 1.38600585e+11 6.77595594e+11]
[ 2.00000000e+00 1.99999972e+00]
[ 3.49999999e+02 2.00000002e+02]
[ 3.33300000e+03 1.11100000e+03]
[-4.99999985e+03 5.99999985e+03]]
Achieved accuracy:
[[8.56497375e+02 5.09216089e+03]
[6.57962988e-06 3.70445289e-07]
[5.31656943e-06 2.72052603e-10]
[6.81557583e-06 1.06560533e-06]
[3.96365344e-04 6.41822468e-05]]