def diffraction_pattern_for_radial(self):
"""
Two diffraction patterns with easy to see radial profiles, wrapped
in ElectronDiffraction <2|8,8>
"""
dp = ElectronDiffraction(np.zeros((2, 8, 8)))
dp.data[0] = np.array([[0., 0., 2., 2., 2., 2., 0., 0.],
[0., 2., 3., 3., 3., 3., 2., 0.],
[2., 3., 3., 4., 4., 3., 3., 2.],
[2., 3., 4., 5., 5., 4., 3., 2.],
[2., 3., 4., 5., 5., 4., 3., 2.],
[2., 3., 3., 4., 4., 3., 3., 2.],
[0., 2., 3., 3., 3., 3., 2., 0.],
[0., 0., 2., 2., 2., 2., 0., 0.]])
dp.data[1] = np.array([[0., 0., 0., 0., 0., 0., 0., 0.],
[0., 0., 0., 0., 0., 0., 0., 0.],
[0., 0., 0., 0., 0., 0., 0., 0.],
[1., 1., 1., 1., 1., 1., 1., 1.],
[1., 1., 1., 1., 1., 1., 1., 1.],
[0., 0., 0., 0., 0., 0., 0., 0.],
[0., 0., 0., 0., 0., 0., 0., 0.],
[0., 0., 0., 0., 0., 0., 0., 0.]])
return dp
def test_reproject_as_polar(diffraction_pattern: ElectronDiffraction):
shape_cartesian = diffraction_pattern.axes_manager.signal_shape
diffraction_pattern.reproject_as_polar()
assert isinstance(diffraction_pattern, Signal2D)
shape_polar = diffraction_pattern.axes_manager.signal_shape
assert shape_polar[0] == max(shape_cartesian)
assert shape_polar[1] > np.sqrt(2) * shape_cartesian[0] / 2
def plot_calibrated_data(self, data_to_plot, *args, **kwargs):
""" Plot calibrated data for visual inspection.
Parameters
----------
data_to_plot : string
Specify the calibrated data to be plotted. Valid options are:
{'au_x_grating_dp', 'au_x_grating_im', 'moo3_dp', 'moo3_im'}
"""
# Construct object containing user defined data to plot and set the
# calibration checking that it is defined.
if data_to_plot == 'au_x_grating_dp':
dpeg = self.calibration_data.au_x_grating_dp
size = dpeg.data.shape[0]
dpegs = stack_method([dpeg, dpeg, dpeg, dpeg])
dpegs = ElectronDiffraction(dpegs.data.reshape((2, 2, size, size)))
dpegs.apply_affine_transformation(self.affine_matrix,
preserve_range=True,
inplace=True)
data = dpegs.mean((0, 1))
data.set_diffraction_calibration(self.diffraction_calibration)
elif data_to_plot == 'au_x_grating_im':
data = self.calibration_data.au_x_grating_im
#Plot the data
data.plot(*args, **kwargs)
def pattern_for_fit_ring(self, input_parameters):
dp = ElectronDiffraction(np.zeros((256, 256)))
x0 = input_parameters
dp.data = dp.generate_ring_pattern(mask=True,
mask_radius=10,
scale=x0[0],
amplitude=x0[1],
spread=x0[2],
direct_beam_amplitude=x0[3],
asymmetry=x0[4],
rotation=x0[5])
return dp
def ragged_peak(self):
"""
A small selection of peaks in an ElectronDiffraction, to allow flexibilty
of test building here.
"""
pattern = np.zeros((2, 2, 128, 128))
pattern[:, :, 40:42, 45] = 1
pattern[:, :, 110, 30:32] = 1
pattern[1, 0, 71:73, 21:23] = 1
dp = ElectronDiffraction(pattern)
dp.set_diffraction_calibration(1)
return dp
def test_plot_best_matching_results_on_signal_vector(structure, rot_list, edc):
# Just test that the code runs
library, match_results = get_vector_match_results(structure, rot_list, edc)
# Hyperspy can only add markers to square signals
match_results.data = np.vstack((match_results.data, match_results.data))
dp = ElectronDiffraction(2 * [2 * [np.zeros((144, 144))]])
match_results.plot_best_matching_results_on_signal(dp, library=library)
def test_bad_vectors_numpy():
""" tests that putting bad vectors in causes an error to be thrown when
you initiate the geneartor
"""
v = np.array([[1, -100]])
dp = ElectronDiffraction(np.ones((20, 20)))
sprg = SubpixelrefinementGenerator(dp, v)
def as_signal(self, size, sigma, max_r):
"""Returns the diffraction data as an ElectronDiffraction signal with
two-dimensional Gaussians representing each diffracted peak. Should only
be used for qualitative work.
Parameters
----------
size : int
Side length (in pixels) for the signal to be simulated.
sigma : float
Standard deviation of the Gaussian function to be plotted.
max_r : float
Half the side length in reciprocal Angstroms. Defines the signal's
calibration
Returns
-------
dp : ElectronDiffraction
Simulated electron diffraction pattern.
"""
from skimage.filters import gaussian as point_spread
l, delta_l = np.linspace(-max_r, max_r, size, retstep=True)
mask_for_max_r = np.logical_and(
np.abs(self.coordinates[:, 0]) < max_r,
np.abs(self.coordinates[:, 1]) < max_r)
coords = self.coordinates[mask_for_max_r]
inten = self.intensities[mask_for_max_r]
dp_dat = np.zeros([size, size])
x, y = (coords)[:, 0], (coords)[:, 1]
if len(x) > 0: # avoiding problems in the peakless case
num = np.digitize(x, l, right=True), np.digitize(y, l, right=True)
dp_dat[num] = inten
# sigma in terms of pixels. transpose for Hyperspy
dp_dat = point_spread(dp_dat, sigma=sigma / delta_l).T
dp_dat = dp_dat / np.max(dp_dat)
dp = ElectronDiffraction(dp_dat)
dp.set_diffraction_calibration(2 * max_r / size)
return dp
def test_apply_affine_transformation_with_casting(self,
diffraction_pattern):
diffraction_pattern.change_dtype('uint8')
transformed_dp = ElectronDiffraction(
diffraction_pattern).apply_affine_transformation(D=np.array(
[[1., 0., 0.], [0., 1., 0.], [0., 0., 1.2]]),
order=2,
keep_dtype=True,
inplace=False)
assert transformed_dp.data.dtype == 'uint8'
def get_distortion_residuals(self, mask_radius, spread):
"""Obtain residuals for experimental data and distortion corrected data
with respect to a simulated symmetric ring pattern.
Parameters
----------
mask_radius : int
Radius, in pixels, for a mask over the direct beam disc.
spread : float
Gaussian spread of each ring in the simulated pattern.
Returns
-------
diff_init : ElectronDiffraction
Difference between experimental data and simulated symmetric ring
pattern.
diff_end : ElectronDiffraction
Difference between distortion corrected data and simulated symmetric
ring pattern.
"""
# Check all required parameters are defined as attributes
if self.calibration_data.au_x_grating_dp is None:
raise ValueError(
"This method requires an Au X-grating diffraction "
"pattern to be provided. Please update the "
"CalibrationDataLibrary.")
if self.affine_matrix is None:
raise ValueError(
"This method requires a distortion matrix to have "
"been determined. Use get_elliptical_distortion "
"to determine this matrix.")
# Set name for experimental data pattern
dpeg = self.calibration_data.au_x_grating_dp
ringP = self.ring_params
size = dpeg.data.shape[0]
dpref = generate_ring_pattern(image_size=size,
mask=True,
mask_radius=mask_radius,
scale=ringP[0],
amplitude=ringP[1],
spread=spread,
direct_beam_amplitude=ringP[3],
asymmetry=1,
rotation=ringP[5])
# Apply distortion corrections to experimental data
dpegs = stack_method([dpeg, dpeg, dpeg, dpeg])
dpegs = ElectronDiffraction(dpegs.data.reshape((2, 2, size, size)))
dpegs.apply_affine_transformation(self.affine_matrix,
preserve_range=True,
inplace=True)
# Calculate residuals to be returned
diff_init = ElectronDiffraction(dpeg.data - dpref.data)
diff_end = ElectronDiffraction(dpegs.inav[0, 0].data - dpref.data)
residuals = stack_method([diff_init, diff_end])
return ElectronDiffraction(residuals)
def diffraction_pattern(self):
dp = ElectronDiffraction(np.zeros((2, 8, 8)))
dp.data[0] = np.array([[0., 0., 2., 2., 2., 2., 0., 0.],
[0., 2., 3., 3., 3., 3., 2., 0.],
[2., 3., 3., 4., 4., 3., 3., 2.],
[2., 3., 4., 5., 5., 4., 3., 2.],
[2., 3., 4., 5., 5., 4., 3., 2.],
[2., 3., 3., 4., 4., 3., 3., 2.],
[0., 2., 3., 3., 3., 3., 2., 0.],
[0., 0., 2., 2., 2., 2., 0., 0.]])
dp.data[1] = np.array([[0., 0., 0., 0., 0., 0., 0., 0.],
[0., 0., 0., 0., 0., 0., 0., 0.],
[0., 0., 0., 0., 0., 0., 0., 0.],
[0., 0., 0., 1., 1., 0., 0., 0.],
[0., 0., 0., 1., 1., 0., 0., 0.],
[0., 0., 0., 0., 0., 0., 0., 0.],
[0., 0., 0., 0., 0., 0., 0., 0.],
[0., 0., 0., 0., 0., 0., 0., 0.]])
return dp
def ring_pattern(input_parameters):
x0 = input_parameters
ring_data = generate_ring_pattern(image_size=256,
mask=True,
mask_radius=10,
scale=x0[0],
amplitude=x0[1],
spread=x0[2],
direct_beam_amplitude=x0[3],
asymmetry=x0[4],
rotation=x0[5])
return ElectronDiffraction(ring_data)
def plot_corrected_diffraction_pattern(self, reference_circle=True):
"""Plot the distortion corrected diffraction pattern with an optional
reference circle.
Parameters
----------
reference_circle : bool
If True a CircleROI widget is added to the plot for reference.
"""
# Check all required parameters are defined as attributes
if self.calibration_data.au_x_grating_dp is None:
raise ValueError(
"This method requires an Au X-grating diffraction "
"pattern to be provided. Please update the "
"CalibrationDataLibrary.")
if self.affine_matrix is None:
raise ValueError(
"This method requires a distortion matrix to have "
"been determined. Use get_elliptical_distortion "
"to determine this matrix.")
# Set name for experimental data pattern
dpeg = self.calibration_data.au_x_grating_dp
# Apply distortion corrections to experimental data
size = dpeg.data.shape[0]
dpegs = stack_method([dpeg, dpeg, dpeg, dpeg])
dpegs = ElectronDiffraction(dpegs.data.reshape((2, 2, size, size)))
dpegs.apply_affine_transformation(self.affine_matrix,
preserve_range=True,
inplace=True)
dpegm = dpegs.mean((0, 1))
# Plot distortion corrected data
dpegm.plot(cmap='magma', vmax=0.1)
# add reference circle if specified
if reference_circle is True:
circ = CircleROI(cx=128, cy=128, r=53.5, r_inner=0)
circ.add_widget(dpegm)
def test_strain_mapping_affine_transform():
latt = diffpy.structure.lattice.Lattice(3, 3, 3, 90, 90, 90)
atom = diffpy.structure.atom.Atom(atype='Zn', xyz=[0, 0, 0], lattice=latt)
structure = diffpy.structure.Structure(atoms=[atom], lattice=latt)
ediff = DiffractionGenerator(300., 0.025)
affines = [[[1, 0, 0], [0, 1, 0], [0, 0, 1]],
[[1.04, 0, 0], [0, 1, 0], [0, 0, 1]],
[[1.08, 0, 0], [0, 1, 0], [0, 0, 1]],
[[1.12, 0, 0], [0, 1, 0], [0, 0, 1]]]
data = []
for affine in affines:
# same coords as used for latt above
latt_rot = diffpy.structure.lattice.Lattice(3,
3,
3,
90,
90,
90,
baserot=affine)
structure.placeInLattice(latt_rot)
diff_dat = ediff.calculate_ed_data(structure, 2.5)
dpi = diff_dat.as_signal(64, 0.02, 2.5)
data.append(dpi.data)
data = np.array(data)
dp = ElectronDiffraction(data.reshape((2, 2, 64, 64)))
m = dp.create_model()
ref = ScalableReferencePattern(dp.inav[0, 0])
m.append(ref)
m.multifit()
disp_grad = ref.construct_displacement_gradient()
assert disp_grad.data.shape == np.asarray(affines).reshape(2, 2, 3,
3).shape
def create_spot():
z1 = np.zeros((128, 128))
z2 = np.zeros((128, 128))
for r in [4, 3, 2]:
c = 1 / r
rr, cc = draw.circle(30, 90, radius=r, shape=z1.shape) #30 is y!
z1[rr, cc] = c
z2[rr, cc] = c
rr2, cc2 = draw.circle(100, 60, radius=r, shape=z2.shape)
z2[rr2, cc2] = c
dp = ElectronDiffraction(np.asarray([[z1, z1],
[z2, z2]])) # this needs to be in 2x2
print(dp.axes_manager)
return dp
def single_peak(self):
pattern = np.zeros((2, 2, 128, 128))
pattern[:, :, 40, 45] = 1 #single point peak
return ElectronDiffraction(pattern)
def test_remove_background(self, diffraction_pattern: ElectronDiffraction,
method, kwargs):
bgr = diffraction_pattern.remove_background(method=method, **kwargs)
assert bgr.data.shape == diffraction_pattern.data.shape
assert bgr.max() <= diffraction_pattern.max()
def test_get_background_model(self,
diffraction_pattern: ElectronDiffraction,
saturation_radius):
bgm = diffraction_pattern.get_background_model(saturation_radius)
assert bgm.axes_manager.signal_shape == diffraction_pattern.axes_manager.signal_shape
def test_get_diffraction_variance(diffraction_pattern: ElectronDiffraction):
dv = diffraction_pattern.get_diffraction_variance()
assert dv.axes_manager.navigation_shape == (3, )
assert dv.axes_manager.signal_shape == diffraction_pattern.axes_manager.signal_shape
def test_init():
z = np.zeros((2, 2, 2, 2))
dp = ElectronDiffraction(
z, metadata={'Acquisition_instrument': {
'SEM': 'Expensive-SEM'
}})
def test_apply_gain_normalisation(diffraction_pattern: ElectronDiffraction,
dark_reference, bright_reference):
diffraction_pattern.apply_gain_normalisation(
dark_reference=dark_reference, bright_reference=bright_reference)
assert diffraction_pattern.max() == bright_reference
assert diffraction_pattern.min() == dark_reference
def get_diffraction_calibration(self, mask_length, linewidth):
"""Determine the diffraction pattern pixel size calibration in units of
reciprocal Angsstroms per pixel.
Parameters
----------
mask_length : float
Halfwidth of the region excluded from peak finding around the
diffraction pattern center.
linewidth : float
Width of Line2DROI used to obtain line trace from distortion
corrected diffraction pattern.
Returns
-------
diff_cal : float
Diffraction calibration in reciprocal Angstroms per pixel.
"""
# Check that necessary calibration data is provided
if self.calibration_data.au_x_grating_dp is None:
raise ValueError(
"This method requires an Au X-grating diffraction "
"pattern to be provided. Please update the "
"CalibrationDataLibrary.")
if self.affine_matrix is None:
raise ValueError(
"This method requires a distortion matrix to have "
"been determined. Use get_elliptical_distortion "
"to determine this matrix.")
dpeg = self.calibration_data.au_x_grating_dp
size = dpeg.data.shape[0]
dpegs = stack_method([dpeg, dpeg, dpeg, dpeg])
dpegs = ElectronDiffraction(dpegs.data.reshape((2, 2, size, size)))
dpegs.apply_affine_transformation(self.affine_matrix,
preserve_range=True,
inplace=True)
dpegm = dpegs.mean((0, 1))
# Define line roi along which to take trace for calibration
line = Line2DROI(x1=5, y1=5, x2=250, y2=250, linewidth=linewidth)
# Obtain line trace
trace = line(dpegm)
trace = trace.as_signal1D(0)
# Find peaks in line trace either side of direct beam
db = (np.sqrt(2) * 128) - (5 * np.sqrt(2))
pka = trace.isig[db +
mask_length:].find_peaks1D_ohaver()[0]['position']
pkb = trace.isig[:db -
mask_length].find_peaks1D_ohaver()[0]['position']
# Determine predicted position of 022 peak of Au pattern d022=1.437
au_pre = db - (self.ring_params[0] / 1.437)
au_post = db + (self.ring_params[0] / 1.437)
# Calculate differences between predicted and measured positions
prediff = np.abs(pkb - au_pre)
postdiff = np.abs(pka - au_post)
# Calculate new calibration value based on most accurate peak positions
dc = (2 / 1.437) / (pka[postdiff == min(postdiff)] -
pkb[prediff == min(prediff)])
# Store diffraction calibration value as attribute
self.diffraction_calibration = dc[0]
return dc[0]
def simulate_kinematic_scattering(atomic_coordinates,
element,
accelerating_voltage,
simulation_size=256,
max_k=1.5,
illumination='plane_wave',
sigma=20,
scattering_params='lobato'):
"""Simulate electron scattering from arrangement of atoms comprising one
elemental species.
Parameters
----------
atomic_coordinates : array
Array specifying atomic coordinates in structure.
element : string
Element symbol, e.g. "C".
accelerating_voltage : float
Accelerating voltage in keV.
simulation_size : int
Simulation size, n, specifies the n x n array size for
the simulation calculation.
max_k : float
Maximum scattering vector magnitude in reciprocal angstroms.
illumination : string
Either 'plane_wave' or 'gaussian_probe' illumination
sigma : float
Gaussian probe standard deviation, used when illumination == 'gaussian_probe'
scattering_params : string
Type of scattering factor calculation to use. One of 'lobato', 'xtables'.
Returns
-------
simulation : ElectronDiffraction
ElectronDiffraction simulation.
"""
# Delayed loading to prevent circular dependencies.
from pyxem.signals.electron_diffraction import ElectronDiffraction
# Get atomic scattering parameters for specified element.
coeffs = np.array(get_scattering_params_dict(scattering_params)[element])
# Calculate electron wavelength for given keV.
wavelength = get_electron_wavelength(accelerating_voltage)
# Define a 2D array of k-vectors at which to evaluate scattering.
l = np.linspace(-max_k, max_k, simulation_size)
kx, ky = np.meshgrid(l, l)
# Convert 2D k-vectors into 3D k-vectors accounting for Ewald sphere.
k = np.array((kx, ky, (wavelength / 2) * (kx**2 + ky**2)))
# Calculate scattering vector squared for each k-vector.
gs_sq = np.linalg.norm(k, axis=0)**2
# Get the scattering factors for this element.
fs = get_atomic_scattering_factors(gs_sq, coeffs[np.newaxis, :],
scattering_params)
# Evaluate scattering from all atoms
scattering = np.zeros_like(gs_sq)
if illumination == 'plane_wave':
for r in atomic_coordinates:
scattering = scattering + (fs *
np.exp(np.dot(k.T, r) * np.pi * 2j))
elif illumination == 'gaussian_probe':
for r in atomic_coordinates:
probe = (1 / (np.sqrt(2 * np.pi) * sigma)) * \
np.exp((-np.abs(((r[0]**2) - (r[1]**2)))) / (4 * sigma**2))
scattering = scattering + (probe * fs *
np.exp(np.dot(k.T, r) * np.pi * 2j))
else:
raise ValueError(
"User specified illumination '{}' not defined.".format(
illumination))
# Calculate intensity
intensity = (scattering * scattering.conjugate()).real
return ElectronDiffraction(intensity)
def ragged_peak(self):
pattern = np.zeros((2, 2, 128, 128))
pattern[:, :, 40, 45] = 1
pattern[1, 0, 71, 21] = 1
return ElectronDiffraction(pattern)
def diffraction_pattern(request):
return ElectronDiffraction(request.param)
def axes_test_dp(self):
dp_data = np.random.randint(0, 10, (2, 2, 10, 10))
dp = ElectronDiffraction(dp_data)
return dp
def diffraction_pattern(request):
"""
A boring, multiuse dp, with signature: ElectronDiffraction <2,2|8,8>
"""
return ElectronDiffraction(request.param)
def diffraction_pattern_one_dimension(request):
"""
1D (in navigation space) diffraction pattern <1|8,8>
"""
return ElectronDiffraction(request.param)
def simulate_kinematic_scattering(atomic_coordinates,
element,
accelerating_voltage,
simulation_size=256,
max_k=1.5,
illumination='plane_wave',
sigma=20,
scattering_params='lobato'):
"""Simulate electron scattering from arrangement of atoms comprising one
elemental species.
Parameters
----------
atomic_coordinates : array
Array specifying atomic coordinates in structure.
element : string
Element symbol, e.g. "C".
accelerating_voltage : float
Accelerating voltage in keV.
simulation_size : int
Simulation size, n, specifies the n x n array size for
the simulation calculation.
max_k : float
Maximum scattering vector magnitude in reciprocal angstroms.
illumination = string
Either 'plane_wave' or 'gaussian_probe' illumination
Returns
-------
simulation : ElectronDiffraction
ElectronDiffraction simulation.
"""
# Delayed loading to prevent circular dependencies.
from pyxem.signals.electron_diffraction import ElectronDiffraction
# Get atomic scattering parameters for specified element.
if scattering_params == 'lobato':
c = np.array(ATOMIC_SCATTERING_PARAMS_LOBATO[element])
elif scattering_params == 'xtables':
c = np.array(ATOMIC_SCATTERING_PARAMS[element])
else:
raise NotImplementedError(
"The scattering parameters `{}` are not implemented. "
"See documentation for available "
"implementations.".format(scattering_params))
# Calculate electron wavelength for given keV.
wavelength = get_electron_wavelength(accelerating_voltage)
# Define a 2D array of k-vectors at which to evaluate scattering.
l = np.linspace(-max_k, max_k, simulation_size)
kx, ky = np.meshgrid(l, l)
# Convert 2D k-vectors into 3D k-vectors accounting for Ewald sphere.
k = np.array((kx, ky, (wavelength / 2) * (kx**2 + ky**2)))
# Calculate scatering angle squared for each k-vector.
s2s = (np.linalg.norm(k, axis=0) / 2)**2
gs = (np.linalg.norm(k, axis=0))
# Evaluate atomic scattering factor.
if scattering_params == 'lobato':
fs = np.zeros_like(s2s)
for i in np.arange(5):
fs = (fs + c[i, 0] * (2 + c[i, 1] * gs**2) *
np.divide(1, np.square(1 + c[i, 1] * gs**2)))
elif scattering_params == 'xtables':
fs = np.zeros_like(s2s)
for i in np.arange(5):
fs = fs + (c[i][0] * np.exp(-c[i][1] * s2s))
# Evaluate scattering from all atoms
scattering = np.zeros_like(s2s)
if illumination == 'plane_wave':
for r in atomic_coordinates:
scattering = scattering + (fs *
np.exp(np.dot(k.T, r) * np.pi * 2j))
elif illumination == 'gaussian_probe':
for r in atomic_coordinates:
probe = (1 / (np.sqrt(2 * np.pi) * sigma)) * \
np.exp((-np.abs(((r[0]**2) - (r[1]**2)))) / (4 * sigma**2))
scattering = scattering + (probe * fs *
np.exp(np.dot(k.T, r) * np.pi * 2j))
else:
raise ValueError("User specified illumination not defined.")
# Calculate intensity
intensity = (scattering * scattering.conjugate()).real
return ElectronDiffraction(intensity)
def diffraction_pattern(request):
"""A simple, multiuse dp, with dimensions: ElectronDiffraction <2,2|8,8>
"""
return ElectronDiffraction(request.param)
