def nickel_zone_axes(nickel_kikuchi_band, nickel_rotations, pc1):
bands = nickel_kikuchi_band
hkl = bands.hkl.data
phase = bands.phase
nav_shape = (5, 5)
detector = kp.detectors.EBSDDetector(
shape=(60, 60),
binning=8,
px_size=70,
pc=np.ones(nav_shape + (3, )) * pc1,
sample_tilt=70,
tilt=0,
convention="tsl",
)
nav_dim = detector.navigation_dimension
navigation_axes = (1, 2)[:nav_dim]
n_hkl = bands.size
n_hkl2 = n_hkl**2
uvw = np.cross(hkl[:, np.newaxis, :], hkl).reshape((n_hkl2, 3))
not000 = np.count_nonzero(uvw, axis=1) != 0
uvw = uvw[not000]
with np.errstate(divide="ignore", invalid="ignore"):
uvw = uvw / np.gcd.reduce(uvw, axis=1)[:, np.newaxis]
uvw = np.unique(uvw, axis=0).astype(int)
det2direct = detector2direct_lattice(
sample_tilt=detector.sample_tilt,
detector_tilt=detector.tilt,
lattice=phase.structure.lattice,
rotation=nickel_rotations.reshape(*nav_shape),
)
uvw_detector = np.tensordot(uvw, det2direct, axes=(1, 0))
upper_hemisphere = uvw_detector[..., 2] > 0
is_in_some_pattern = np.sum(upper_hemisphere, axis=navigation_axes) != 0
uvw = uvw[is_in_some_pattern, ...]
uvw_in_pattern = upper_hemisphere[is_in_some_pattern, ...].T
uvw_detector = np.moveaxis(uvw_detector[is_in_some_pattern],
source=0,
destination=nav_dim)
return kp.simulations.features.ZoneAxis(
phase=phase,
uvw=uvw,
uvw_detector=uvw_detector,
in_pattern=uvw_in_pattern,
gnomonic_radius=detector.r_max,
)
def geometrical_simulation(
self,
reciprocal_lattice_point: Optional[ReciprocalLatticePoint] = None
) -> GeometricalEBSDSimulation:
"""Project a set of Kikuchi bands and zone axes onto the
detector, one set for each rotation of the unit cell.
The zone axes are calculated from the Kikuchi bands.
Parameters
----------
reciprocal_lattice_point
Crystal planes to project onto the detector. If None, and
the generator has a phase with a unit cell with a point
group, a set of planes with minimum distance of 1 Å and
their symmetrically equivalent planes are used.
Returns
-------
GeometricalEBSDSimulation
Examples
--------
>>> from diffsims.crystallography import ReciprocalLatticePoint
>>> simgen
EBSDSimulationGenerator (1,)
EBSDDetector (60, 60), px_size 1 um, binning 1, tilt 0, pc
(0.5, 0.5, 0.5)
<name: . space group: None. point group: None. proper point
group: None. color: tab:blue>
Rotation (1,)
>>> sim1 = simgen.geometrical_simulation()
>>> sim1.bands.size
94
>>> rlp = ReciprocalLatticePoint(
... phase=simgen.phase, hkl=[[1, 1, 1], [2, 0, 0]]
... )
>>> sim2 = simgen.geometrical_simulation()
>>> sim2.bands.size
13
"""
rlp = reciprocal_lattice_point
if rlp is None and (hasattr(self.phase.point_group, "name") and
hasattr(self.phase.structure.lattice, "abcABG")):
rlp = ReciprocalLatticePoint.from_min_dspacing(self.phase,
min_dspacing=1)
rlp = rlp[rlp.allowed].symmetrise()
elif rlp is None:
raise ValueError("A ReciprocalLatticePoint object must be passed")
self._rlp_phase_is_compatible(rlp)
# Unit cell parameters (called more than once)
phase = rlp.phase
hkl = rlp._hkldata
# Get number of navigation dimensions and navigation axes
# indices
n_nav_dims = self.navigation_dimension
navigation_axes = (1, 2)[:n_nav_dims]
# Get Kikuchi band coordinates for all bands in all patterns
# U_Kstar, transformation from detector frame D to reciprocal
# crystal lattice frame Kstar.
# Output shape is (3, n, 3) or (3, ny, nx, 3)
det2recip = detector2reciprocal_lattice(
sample_tilt=self.detector.sample_tilt,
detector_tilt=self.detector.tilt,
lattice=phase.structure.lattice,
rotation=self.rotations,
)
# Output shape is (nhkl, n, 3) or (nhkl, ny, nx, 3)
hkl_detector = np.tensordot(hkl, det2recip, axes=(1, 0))
if n_nav_dims == 0:
hkl_detector = hkl_detector.squeeze()
# Get bands that are in some pattern
hkl_is_upper, hkl_in_a_pattern = _get_coordinates_in_upper_hemisphere(
z_coordinates=hkl_detector[..., 2],
navigation_axes=navigation_axes)
hkl = hkl[hkl_in_a_pattern, ...]
hkl_in_pattern = hkl_is_upper[hkl_in_a_pattern, ...].T
# Get coordinates in the proper shape
hkl_detector = np.moveaxis(hkl_detector[hkl_in_a_pattern],
source=0,
destination=n_nav_dims)
# And store it all
bands = KikuchiBand(
phase=phase,
hkl=hkl,
hkl_detector=hkl_detector,
in_pattern=hkl_in_pattern,
gnomonic_radius=self.detector.r_max,
)
# Get zone axes coordinates from Kikuchi bands
uvw = _get_uvw_from_hkl(hkl=hkl)
det2direct = detector2direct_lattice(
sample_tilt=self.detector.sample_tilt,
detector_tilt=self.detector.tilt,
lattice=self.phase.structure.lattice,
rotation=self.rotations,
)
uvw_detector = np.tensordot(uvw, det2direct, axes=(1, 0))
if n_nav_dims == 0:
uvw_detector = uvw_detector.squeeze()
uvw_is_upper, uvw_in_a_pattern = _get_coordinates_in_upper_hemisphere(
z_coordinates=uvw_detector[..., 2],
navigation_axes=navigation_axes)
uvw = uvw[uvw_in_a_pattern, ...]
uvw_in_pattern = uvw_is_upper[uvw_in_a_pattern, ...].T
uvw_detector = np.moveaxis(uvw_detector[uvw_in_a_pattern],
source=0,
destination=n_nav_dims)
zone_axes = ZoneAxis(
phase=phase,
uvw=uvw,
uvw_detector=uvw_detector,
in_pattern=uvw_in_pattern,
gnomonic_radius=self.detector.r_max,
)
return GeometricalEBSDSimulation(
detector=self.detector,
rotations=self.rotations,
bands=bands,
zone_axes=zone_axes,
)
def test_init(
self,
nickel_kikuchi_band,
detector,
nickel_rotations,
hkl_slices,
desired_nav_shape,
desired_nav_dims,
desired_data_shape,
):
bands = nickel_kikuchi_band[hkl_slices]
phase = bands.phase
n_nav_dims = bands.navigation_dimension
navigation_axes = (1, 2)[:n_nav_dims]
rotations = nickel_rotations.reshape(5, 5)[hkl_slices[:2]]
uvw = _get_uvw_from_hkl(bands.hkl.data)
det2direct = detector2direct_lattice(
sample_tilt=detector.sample_tilt,
detector_tilt=detector.tilt,
lattice=phase.structure.lattice,
rotation=rotations,
)
uvw_detector = np.tensordot(uvw, det2direct, axes=(1, 0))
if n_nav_dims == 0:
uvw_detector = uvw_detector.squeeze()
uvw_is_upper, uvw_in_a_pattern = _get_coordinates_in_upper_hemisphere(
z_coordinates=uvw_detector[..., 2],
navigation_axes=navigation_axes)
uvw = uvw[uvw_in_a_pattern, ...]
uvw_in_pattern = uvw_is_upper[uvw_in_a_pattern, ...].T
uvw_detector = np.moveaxis(uvw_detector[uvw_in_a_pattern],
source=0,
destination=n_nav_dims)
za = ZoneAxis(
phase=phase,
uvw=uvw,
uvw_detector=uvw_detector,
in_pattern=uvw_in_pattern,
gnomonic_radius=detector.r_max,
)
assert za.navigation_shape == desired_nav_shape
assert za.navigation_dimension == desired_nav_dims
assert za._data_shape == desired_data_shape
x_detector = uvw_detector[..., 0]
y_detector = uvw_detector[..., 1]
z_detector = uvw_detector[..., 2]
assert np.allclose(za.x_detector, x_detector)
assert np.allclose(za.y_detector, y_detector)
assert np.allclose(za.z_detector, z_detector)
with np.errstate(divide="ignore"):
desired_x_gnomonic = x_detector / z_detector
desired_y_gnomonic = y_detector / z_detector
assert np.allclose(za.x_gnomonic, desired_x_gnomonic)
assert np.allclose(za.y_gnomonic, desired_y_gnomonic)
assert np.allclose(
za.r_gnomonic,
np.sqrt(desired_x_gnomonic**2 + desired_y_gnomonic**2),
)