data = np.array([[[1, 2, 3, 4], [2, 4, 5, 3], [0, 1, 2, 3]],
[[2, 4, 5, 1], [10, 5, 2, 2], [10, 3, 3, 0]]])
data_2D = np.array([[1, 2, 3, 4], [2, 4, 5, 3]])
data_1D = np.array([1, 2])
data_4D = np.array([[[[1, 2, 3, 4], [2, 4, 5, 3], [0, 1, 2, 3]],
[[2, 4, 5, 1], [10, 5, 2, 2], [10, 3, 3, 0]]],
[[[1, 2, 3, 4], [2, 4, 5, 3], [0, 1, 2, 3]],
[[2, 4, 5, 1], [10, 5, 2, 2], [10, 3, 3, 0]]]])
header = {'CTYPE1': 'HPLN-TAN', 'CUNIT1': 'arcsec', 'CDELT1': 0.4,
'CRPIX1': 0, 'CRVAL1': 0, 'NAXIS1': 4,
'CTYPE2': 'HPLT-TAN', 'CUNIT2': 'arcsec', 'CDELT2': 0.5,
'CRPIX2': 0, 'CRVAL2': 0, 'NAXIS2': 3,
'CTYPE3': 'Time ', 'CUNIT3': 'seconds', 'CDELT3': 0.3,
'CRPIX3': 0, 'CRVAL3': 0, 'NAXIS3': 2}
wcs = WCS(header=header, naxis=3)
header_2D = {'CTYPE1': 'Time ', 'CUNIT1': 'seconds', 'CDELT1': 0.4,
'CRPIX1': 0, 'CRVAL1': 0, 'NAXIS1': 4,
'CTYPE2': 'HPLT-TAN', 'CUNIT2': 'arcsec', 'CDELT2': 0.5,
'CRPIX2': 0, 'CRVAL2': 0, 'NAXIS2': 2}
wcs_2D = WCS(header=header_2D, naxis=2)
header_4D = {'CTYPE1': 'Time ', 'CUNIT1': 'seconds', 'CDELT1': 0.4,
'CRPIX1': 0, 'CRVAL1': 0, 'NAXIS1': 4,
'CTYPE2': 'HPLT-TAN', 'CUNIT2': 'arcsec', 'CDELT2': 0.5,
'CRPIX2': 0, 'CRVAL2': 0, 'NAXIS2': 3,
'CTYPE3': 'Time ', 'CUNIT3': 'seconds', 'CDELT3': 0.4,
'CRPIX3': 0, 'CRVAL3': 0, 'NAXIS3': 2,
'CTYPE4': 'HPLN-TAN', 'CUNIT4': 'arcsec', 'CDELT4': 0.5,
'CRPIX4': 0, 'CRVAL4': 0, 'NAXIS4': 2}
wcs_4D = WCS(header=header_4D, naxis=4)
header_1D = {'CTYPE1': 'Time ', 'CUNIT1': 'seconds', 'CDELT1': 0.4,
[[2.252, 4.528, -5.372], [-2.876, 5.764, 6.264]]])
SOURCE_UNCERTAINTY_PHOTONS_NUV = np.sqrt(SOURCE_DATA_PHOTONS_NUV)
SOURCE_UNCERTAINTY_PHOTONS_FUV = np.sqrt(SOURCE_DATA_PHOTONS_FUV)
time_dim_len = SOURCE_DATA_DN.shape[0]
single_exposure_time = 2.
EXPOSURE_TIME = u.Quantity(np.zeros(time_dim_len)+single_exposure_time, unit=u.s)
# Define an sample wcs object
h0 = {
'CTYPE1': 'WAVE ', 'CUNIT1': 'Angstrom', 'CDELT1': 0.2, 'CRPIX1': 0, 'CRVAL1': 10,
'NAXIS1': 3,
'CTYPE2': 'HPLT-TAN', 'CUNIT2': 'deg', 'CDELT2': 0.5, 'CRPIX2': 2, 'CRVAL2': 0.5, 'NAXIS2': 2,
'CTYPE3': 'HPLN-TAN', 'CUNIT3': 'deg', 'CDELT3': 0.4, 'CRPIX3': 2, 'CRVAL3': 1, 'NAXIS3': 2,
}
wcs0 = WCS(header=h0, naxis=3)
# Define sample meta
meta0 = {"detector type": "FUV", "OBSID": 1, "spectral window": "C II 1336"}
# Define sample extra coords
extra_coords0 = [("time", 0,
np.array([datetime.datetime(2017, 1, 1)+datetime.timedelta(seconds=i)
for i in range(time_dim_len)])),
("exposure time", 0, EXPOSURE_TIME)]
extra_coords1 = [("time", 0,
np.array([datetime.datetime(2017, 1, 1)+datetime.timedelta(seconds=i)
for i in range(time_dim_len, time_dim_len*2)])),
("exposure time", 0, EXPOSURE_TIME)]
# Define IRISSpectrogramCubes in various units.
def read_iris_spectrograph_level2_fits(filenames, spectral_windows=None):
"""
Reads IRIS level 2 spectrograph FITS from an OBS into an IRISSpectrograph instance.
Parameters
----------
filenames: `list` of `str` or `str`
Filename of filenames to be read. They must all be associated with the same
OBS number.
spectral_windows: iterable of `str` or `str`
Spectral windows to extract from files. Default=None, implies, extract all
spectral windows.
Returns
-------
result: `irispy.spectrograph.IRISSpectrograph`
"""
if type(filenames) is str:
filenames = [filenames]
for f, filename in enumerate(filenames):
hdulist = fits.open(filename)
hdulist.verify('fix')
if f == 0:
# Determine number of raster positions in a scan
raster_positions_per_scan = int(hdulist[0].header["NRASTERP"])
# Collecting the window observations.
windows_in_obs = np.array([
hdulist[0].header["TDESC{0}".format(i)]
for i in range(1, hdulist[0].header["NWIN"] + 1)
])
# If spectral_window is not set then get every window.
# Else take the appropriate windows
if not spectral_windows:
spectral_windows_req = windows_in_obs
window_fits_indices = range(1, len(hdulist) - 2)
else:
if type(spectral_windows) is str:
spectral_windows_req = [spectral_windows]
spectral_windows_req = np.asarray(spectral_windows_req,
dtype="U")
window_is_in_obs = np.asarray([
window in windows_in_obs for window in spectral_windows_req
])
if not all(window_is_in_obs):
missing_windows = window_is_in_obs == False
raise ValueError(
"Spectral windows {0} not in file {1}".format(
spectral_windows[missing_windows], filenames[0]))
window_fits_indices = np.nonzero(
np.in1d(windows_in_obs, spectral_windows))[0] + 1
# Generate top level meta dictionary from first file
# main header.
top_meta = {
"TELESCOP": hdulist[0].header["TELESCOP"],
"INSTRUME": hdulist[0].header["INSTRUME"],
"DATA_LEV": hdulist[0].header["DATA_LEV"],
"OBSID": hdulist[0].header["OBSID"],
"OBS_DESC": hdulist[0].header["OBS_DESC"],
"STARTOBS": parse_time(hdulist[0].header["STARTOBS"]),
"ENDOBS": parse_time(hdulist[0].header["ENDOBS"]),
"SAT_ROT": hdulist[0].header["SAT_ROT"] * u.deg,
"AECNOBS": int(hdulist[0].header["AECNOBS"]),
"FOVX": hdulist[0].header["FOVX"] * u.arcsec,
"FOVY": hdulist[0].header["FOVY"] * u.arcsec,
"SUMSPTRN": hdulist[0].header["SUMSPTRN"],
"SUMSPTRF": hdulist[0].header["SUMSPTRF"],
"SUMSPAT": hdulist[0].header["SUMSPAT"],
"NEXPOBS": hdulist[0].header["NEXPOBS"],
"NRASTERP": hdulist[0].header["NRASTERP"],
"KEYWDDOC": hdulist[0].header["KEYWDDOC"]
}
# Initialize meta dictionary for each spectral_window
window_metas = {}
for i, window_name in enumerate(spectral_windows_req):
if "FUV" in hdulist[0].header["TDET{0}".format(
window_fits_indices[i])]:
spectral_summing = hdulist[0].header["SUMSPTRF"]
else:
spectral_summing = hdulist[0].header["SUMSPTRN"]
window_metas[window_name] = {
"detector type":
hdulist[0].header["TDET{0}".format(
window_fits_indices[i])],
"spectral window":
hdulist[0].header["TDESC{0}".format(
window_fits_indices[i])],
"brightest wavelength":
hdulist[0].header["TWAVE{0}".format(
window_fits_indices[i])],
"min wavelength":
hdulist[0].header["TWMIN{0}".format(
window_fits_indices[i])],
"max wavelength":
hdulist[0].header["TWMAX{0}".format(
window_fits_indices[i])],
"SAT_ROT":
hdulist[0].header["SAT_ROT"],
"spatial summing":
hdulist[0].header["SUMSPAT"],
"spectral summing":
spectral_summing
}
# Create a empty list for every spectral window and each
# spectral window is a key for the dictionary.
data_dict = dict([(window_name, list())
for window_name in spectral_windows_req])
# Determine extra coords for this raster.
times = np.array([
parse_time(hdulist[0].header["STARTOBS"]) +
datetime.timedelta(seconds=s)
for s in hdulist[-2].data[:, hdulist[-2].header["TIME"]]
])
raster_positions = np.arange(int(hdulist[0].header["NRASTERP"]))
pztx = hdulist[-2].data[:, hdulist[-2].header["PZTX"]] * u.arcsec
pzty = hdulist[-2].data[:, hdulist[-2].header["PZTY"]] * u.arcsec
xcenix = hdulist[-2].data[:, hdulist[-2].header["XCENIX"]] * u.arcsec
ycenix = hdulist[-2].data[:, hdulist[-2].header["YCENIX"]] * u.arcsec
obs_vrix = hdulist[-2].data[:,
hdulist[-2].header["OBS_VRIX"]] * u.m / u.s
ophaseix = hdulist[-2].data[:, hdulist[-2].header["OPHASEIX"]]
exposure_times_fuv = hdulist[-2].data[:, hdulist[-2].
header["EXPTIMEF"]] * u.s
exposure_times_nuv = hdulist[-2].data[:, hdulist[-2].
header["EXPTIMEN"]] * u.s
# If OBS is raster, include raster positions. Otherwise don't.
if top_meta["NRASTERP"] > 1:
general_extra_coords = [("time", 0, times),
("raster position", 0,
np.arange(top_meta["NRASTERP"])),
("pztx", 0, pztx), ("pzty", 0, pzty),
("xcenix", 0, xcenix),
("ycenix", 0, ycenix),
("obs_vrix", 0, obs_vrix),
("ophaseix", 0, ophaseix)]
else:
general_extra_coords = [("time", 0, times), ("pztx", 0, pztx),
("pzty", 0, pzty), ("xcenix", 0, xcenix),
("ycenix", 0, ycenix),
("obs_vrix", 0, obs_vrix),
("ophaseix", 0, ophaseix)]
for i, window_name in enumerate(spectral_windows_req):
# Determine values of properties dependent on detector type.
if "FUV" in hdulist[0].header["TDET{0}".format(
window_fits_indices[i])]:
exposure_times = exposure_times_fuv
DN_unit = iris_tools.DN_UNIT["FUV"]
readout_noise = iris_tools.READOUT_NOISE["FUV"]
elif "NUV" in hdulist[0].header["TDET{0}".format(
window_fits_indices[i])]:
exposure_times = exposure_times_nuv
DN_unit = iris_tools.DN_UNIT["NUV"]
readout_noise = iris_tools.READOUT_NOISE["NUV"]
else:
raise ValueError(
"Detector type in FITS header not recognized.")
# Derive WCS, data and mask for NDCube from file.
# Sit-and-stare have a CDELT of 0 which causes issues in astropy WCS.
# In this case, set CDELT to a tiny non-zero number.
if hdulist[window_fits_indices[i]].header["CDELT3"] == 0:
hdulist[window_fits_indices[i]].header["CDELT3"] = 1e-10
wcs_ = WCS(hdulist[window_fits_indices[i]].header)
data_mask = hdulist[window_fits_indices[i]].data == -200.
# Derive extra coords for this spectral window.
window_extra_coords = copy.deepcopy(general_extra_coords)
window_extra_coords.append(("exposure time", 0, exposure_times))
# Collect metadata relevant to single files.
try:
date_obs = parse_time(hdulist[0].header["DATE_OBS"])
except ValueError:
date_obs = None
try:
date_end = parse_time(hdulist[0].header["DATE_END"])
except ValueError:
date_end = None
single_file_meta = {
"SAT_ROT":
hdulist[0].header["SAT_ROT"] * u.deg,
"DATE_OBS":
date_obs,
"DATE_END":
date_end,
"HLZ":
bool(int(hdulist[0].header["HLZ"])),
"SAA":
bool(int(hdulist[0].header["SAA"])),
"DSUN_OBS":
hdulist[0].header["DSUN_OBS"] * u.m,
"IAECEVFL":
hdulist[0].header["IAECEVFL"],
"IAECFLAG":
hdulist[0].header["IAECFLAG"],
"IAECFLFL":
hdulist[0].header["IAECFLFL"],
"KEYWDDOC":
hdulist[0].header["KEYWDDOC"],
"detector type":
hdulist[0].header["TDET{0}".format(window_fits_indices[i])],
"spectral window":
window_name,
"OBSID":
hdulist[0].header["OBSID"],
"OBS_DESC":
hdulist[0].header["OBS_DESC"],
"STARTOBS":
parse_time(hdulist[0].header["STARTOBS"]),
"ENDOBS":
parse_time(hdulist[0].header["ENDOBS"])
}
# Derive uncertainty of data
uncertainty = u.Quantity(
np.sqrt((hdulist[window_fits_indices[i]].data *
DN_unit).to(u.photon).value +
readout_noise.to(u.photon).value**2),
unit=u.photon).to(DN_unit).value
# Appending NDCube instance to the corresponding window key in dictionary's list.
data_dict[window_name].append(
IRISSpectrogramCube(hdulist[window_fits_indices[i]].data,
wcs_,
uncertainty,
DN_unit,
single_file_meta,
window_extra_coords,
mask=data_mask))
hdulist.close()
# Construct dictionary of IRISSpectrogramCubeSequences for spectral windows
data = dict([(window_name,
IRISSpectrogramCubeSequence(data_dict[window_name],
window_metas[window_name],
common_axis=0))
for window_name in spectral_windows_req])
# Initialize an IRISSpectrograph object.
return IRISSpectrograph(data, meta=top_meta)
'NAXIS1': 4,
'CTYPE2': 'HPLT-TAN',
'CUNIT2': 'deg',
'CDELT2': 0.5,
'CRPIX2': 2,
'CRVAL2': 0.5,
'NAXIS2': 3,
'CTYPE3': 'HPLN-TAN',
'CUNIT3': 'deg',
'CDELT3': 0.4,
'CRPIX3': 2,
'CRVAL3': 1,
'NAXIS3': 2,
}
wt = WCS(header=ht, naxis=3)
wm = WCS(header=hm, naxis=3)
cube1 = NDCube(data,
wt,
missing_axes=[False, False, False, True],
extra_coords=[
('pix', 0, u.Quantity(range(data.shape[0]), unit=u.pix)),
('distance', None, u.Quantity(0, unit=u.cm)),
('time', None, datetime.datetime(2000, 1, 1, 0, 0))
])
cube2 = NDCube(data,
wm,
extra_coords=[
('pix', 0,
'CRVAL1': 10,
'NAXIS1': 3,
'CTYPE2': 'HPLT-TAN',
'CUNIT2': 'deg',
'CDELT2': 0.5,
'CRPIX2': 2,
'CRVAL2': 0.5,
'NAXIS2': 2,
'CTYPE3': 'HPLN-TAN',
'CUNIT3': 'deg',
'CDELT3': 0.4,
'CRPIX3': 2,
'CRVAL3': 1,
'NAXIS3': 2,
}
WCS0 = WCS(header=H0, naxis=3)
H_NO_COORDS = {
'CTYPE1': 'PIX ',
'CUNIT1': '',
'CDELT1': 1,
'CRPIX1': 0,
'CRVAL1': 0,
'NAXIS1': 3,
'CTYPE2': 'PIX ',
'CUNIT2': '',
'CDELT2': 1,
'CRPIX2': 0,
'CRVAL2': 0,
'NAXIS2': 3,
'CTYPE3': 'PIX ',
import pytest
import sunpy.map
import numpy as np
import astropy.units as u
from ndcube import NDCube, NDCubeOrdered
from ndcube.utils.wcs import WCS, _wcs_slicer
from ndcube.tests import helpers
# sample data for tests
# TODO: use a fixture reading from a test file. file TBD.
ht = {'CTYPE3': 'HPLT-TAN', 'CUNIT3': 'deg', 'CDELT3': 0.5, 'CRPIX3': 0, 'CRVAL3': 0, 'NAXIS3': 2,
'CTYPE2': 'WAVE ', 'CUNIT2': 'Angstrom', 'CDELT2': 0.2, 'CRPIX2': 0, 'CRVAL2': 0,
'NAXIS2': 3,
'CTYPE1': 'TIME ', 'CUNIT1': 'min', 'CDELT1': 0.4, 'CRPIX1': 0, 'CRVAL1': 0, 'NAXIS1': 4}
wt = WCS(header=ht, naxis=3)
data = np.array([[[1, 2, 3, 4], [2, 4, 5, 3], [0, -1, 2, 3]],
[[2, 4, 5, 1], [10, 5, 2, 2], [10, 3, 3, 0]]])
hm = {'CTYPE1': 'WAVE ', 'CUNIT1': 'Angstrom', 'CDELT1': 0.2, 'CRPIX1': 0, 'CRVAL1': 10,
'NAXIS1': 4,
'CTYPE2': 'HPLT-TAN', 'CUNIT2': 'deg', 'CDELT2': 0.5, 'CRPIX2': 2, 'CRVAL2': 0.5,
'NAXIS2': 3,
'CTYPE3': 'HPLN-TAN', 'CUNIT3': 'deg', 'CDELT3': 0.4, 'CRPIX3': 2, 'CRVAL3': 1, 'NAXIS3': 2}
wm = WCS(header=hm, naxis=3)
h_disordered = {
'CTYPE1': 'TIME ', 'CUNIT1': 'min', 'CDELT1': 0.4, 'CRPIX1': 0, 'CRVAL1': 0, 'NAXIS1': 2,
'CTYPE2': 'WAVE ', 'CUNIT2': 'Angstrom', 'CDELT2': 0.2, 'CRPIX2': 0, 'CRVAL2': 10,
'NAXIS2': 4,
'NAXIS3': 2,
'CTYPE2': 'WAVE ',
'CUNIT2': 'Angstrom',
'CDELT2': 0.2,
'CRPIX2': 0,
'CRVAL2': 0,
'NAXIS2': 3,
'CTYPE1': 'TIME ',
'CUNIT1': 'min',
'CDELT1': 0.4,
'CRPIX1': 0,
'CRVAL1': 0,
'NAXIS1': 4
}
wt = WCS(header=ht, naxis=3)
cube1 = NDCube(data,
wt,
missing_axis=[False, False, False, True],
extra_coords=[
('pix', 0, u.Quantity(range(data.shape[0]), unit=u.pix)),
('hi', 1, u.Quantity(range(data.shape[1]), unit=u.s)),
('distance', None, u.Quantity(0, unit=u.cm)),
('time', None, datetime.datetime(2000, 1, 1, 0, 0))
])
cube1_with_unit = NDCube(
data,
wt,
missing_axis=[False, False, False, True],
import pytest
import numpy as np
import astropy.units as u
from ndcube import NDCube, NDCubeOrdered
from ndcube.utils.wcs import WCS, _wcs_slicer
from ndcube.tests import helpers
from ndcube.ndcube_sequence import NDCubeSequence
# sample data for tests
# TODO: use a fixture reading from a test file. file TBD.
ht = {'CTYPE3': 'HPLT-TAN', 'CUNIT3': 'deg', 'CDELT3': 0.5, 'CRPIX3': 0, 'CRVAL3': 0, 'NAXIS3': 2,
'CTYPE2': 'WAVE ', 'CUNIT2': 'Angstrom', 'CDELT2': 0.2, 'CRPIX2': 0, 'CRVAL2': 0,
'NAXIS2': 3,
'CTYPE1': 'TIME ', 'CUNIT1': 'min', 'CDELT1': 0.4, 'CRPIX1': 0, 'CRVAL1': 0, 'NAXIS1': 4}
wt = WCS(header=ht, naxis=3)
data = np.array([[[1, 2, 3, 4], [2, 4, 5, 3], [0, -1, 2, 3]],
[[2, 4, 5, 1], [10, 5, 2, 2], [10, 3, 3, 0]]])
hm = {'CTYPE1': 'WAVE ', 'CUNIT1': 'Angstrom', 'CDELT1': 0.2, 'CRPIX1': 0, 'CRVAL1': 10,
'NAXIS1': 4,
'CTYPE2': 'HPLT-TAN', 'CUNIT2': 'deg', 'CDELT2': 0.5, 'CRPIX2': 2, 'CRVAL2': 0.5,
'NAXIS2': 3,
'CTYPE3': 'HPLN-TAN', 'CUNIT3': 'deg', 'CDELT3': 0.4, 'CRPIX3': 2, 'CRVAL3': 1, 'NAXIS3': 2}
wm = WCS(header=hm, naxis=3)
h_disordered = {
'CTYPE1': 'TIME ', 'CUNIT1': 'min', 'CDELT1': 0.4, 'CRPIX1': 0, 'CRVAL1': 0, 'NAXIS1': 2,
'CTYPE2': 'WAVE ', 'CUNIT2': 'Angstrom', 'CDELT2': 0.2, 'CRPIX2': 0, 'CRVAL2': 10,
'NAXIS2': 4,
import pytest
from ndcube.tests.helpers import assert_cubesequences_equal
from ndcube.utils.wcs import WCS
import astropy.units as u
from astropy.time import Time, TimeDelta
from sunraster import RasterSequence, SpectrogramCube, SpectrogramSequence
# Define an sample wcs objects.
H0 = {
'CTYPE1': 'WAVE ', 'CUNIT1': 'Angstrom', 'CDELT1': 0.2, 'CRPIX1': 0, 'CRVAL1': 10,
'NAXIS1': 3,
'CTYPE2': 'HPLT-TAN', 'CUNIT2': 'deg', 'CDELT2': 0.5, 'CRPIX2': 2, 'CRVAL2': 0.5, 'NAXIS2': 2,
'CTYPE3': 'HPLN-TAN', 'CUNIT3': 'deg', 'CDELT3': 0.4, 'CRPIX3': 2, 'CRVAL3': 1, 'NAXIS3': 2}
WCS0 = WCS(header=H0, naxis=3)
h2 = {
'CTYPE1': 'HPLN-TAN',
'CUNIT1': 'deg',
'CDELT1': 0.2,
'CRPIX1': 0,
'CRVAL1': 10,
'NAXIS1': 3,
'CTYPE2': 'HPLT-TAN',
'CUNIT2': 'deg',
'CDELT2': 0.5,
'CRPIX2': 2,
'CRVAL2': 0.5,
'NAXIS2': 2,
'CTYPE3': 'WAVE ',
from sunpy.visualization.animator import ImageAnimatorWCS, LineAnimator
except ImportError:
from sunpy.visualization.imageanimator import ImageAnimatorWCS, LineAnimator
from ndcube import NDCube
from ndcube.utils.wcs import WCS
from ndcube.mixins import plotting
# sample data for tests
# TODO: use a fixture reading from a test file. file TBD.
ht = {'CTYPE3': 'HPLT-TAN', 'CUNIT3': 'deg', 'CDELT3': 0.5, 'CRPIX3': 0, 'CRVAL3': 0, 'NAXIS3': 2,
'CTYPE2': 'WAVE ', 'CUNIT2': 'Angstrom', 'CDELT2': 0.2, 'CRPIX2': 0, 'CRVAL2': 0,
'NAXIS2': 3,
'CTYPE1': 'TIME ', 'CUNIT1': 'min', 'CDELT1': 0.4, 'CRPIX1': 0, 'CRVAL1': 0, 'NAXIS1': 4}
wt = WCS(header=ht, naxis=3)
hm = {'CTYPE1': 'WAVE ', 'CUNIT1': 'Angstrom', 'CDELT1': 0.2, 'CRPIX1': 0, 'CRVAL1': 10,
'NAXIS1': 4,
'CTYPE2': 'HPLT-TAN', 'CUNIT2': 'deg', 'CDELT2': 0.5, 'CRPIX2': 2, 'CRVAL2': 0.5,
'NAXIS2': 3,
'CTYPE3': 'HPLN-TAN', 'CUNIT3': 'deg', 'CDELT3': 0.4, 'CRPIX3': 2, 'CRVAL3': 1, 'NAXIS3': 2}
wm = WCS(header=hm, naxis=3)
spatial = {
'CTYPE1': 'HPLT-TAN', 'CUNIT1': 'deg', 'CDELT1': 0.5, 'CRPIX1': 2, 'CRVAL1': 0.5,
'NAXIS1': 3,
'CTYPE2': 'HPLN-TAN', 'CUNIT2': 'deg', 'CDELT2': 0.4, 'CRPIX2': 2, 'CRVAL2': 1,
'NAXIS2': 2
}
spatial = WCS(header=spatial, naxis=2)