def build_list(lattice=None, max_miller=3, extinction=None, Laue_extinction=False, max_keV=120.):
hklplanes = []
indices = range(-max_miller, max_miller + 1)
for h in indices:
for k in indices:
for l in indices:
if h == k == l == 0: # skip (0, 0, 0)
continue
if not extinction :
hklplanes.append(HklPlane(h, k, l, lattice))
if extinction == 'FCC':
# take plane if only all odd or all even hkl indices
if (h % 2 == 0 and k % 2 == 0 and l % 2 == 0) or (h % 2 == 1 and k % 2 == 1 and l % 2 == 1):
hklplanes.append(HklPlane(h, k, l, lattice))
if extinction == 'BCC':
# take plane only if the sum indices is even
if ((h**2 + k**2 + l**2) % 2 == 0):
hklplanes.append(HklPlane(h, k, l, lattice))
if Laue_extinction is True:
lam_min = lambda_keV_to_nm(max_keV)
val = 2. * lattice._lengths[0] / lam_min # lattice have to be cubic !
print 'Limit value is %d' % val
for hkl in hklplanes:
(h, k, l) = hkl.miller_indices()
test = h ** 2 + k ** 2 + l ** 2
if val < test: # TODO check the test
hklplanes.remove(HklPlane(h, k, l, lattice))
return hklplanes
def grain_projection_simulation(self, gid=1):
"""Function to compute all the grain projection in DCT geometry and create a composite image.
:param int gid: the id of the grain to project (1 default).
"""
print('forward simulation of grain %d' % gid)
detector = self.exp.get_active_detector()
lambda_keV = self.exp.source.max_energy
lambda_nm = lambda_keV_to_nm(lambda_keV)
X = np.array([1., 0., 0.]) / lambda_nm
lattice = self.exp.get_sample().get_material()
if not hasattr(self, 'grain'):
# load the corresponding grain
self.load_grain(gid=gid)
# compute all the omega values
print('simulating diffraction spot positions on the detector')
omegas = np.zeros(2 * len(self.hkl_planes))
g_uv = np.zeros((2, 2 * len(self.hkl_planes)))
for i, plane in enumerate(self.hkl_planes):
#print(plane.miller_indices())
try:
w1, w2 = self.grain.dct_omega_angles(plane,
lambda_keV,
verbose=False)
except ValueError:
# plane does not fulfil the Bragg condition
continue
omegas[2 * i] = w1
omegas[2 * i + 1] = w2
for j in range(2):
omega = omegas[2 * i + j]
omegar = omega * np.pi / 180
R = np.array([[np.cos(omegar), -np.sin(omegar), 0],
[np.sin(omegar),
np.cos(omegar), 0], [0, 0, 1]])
gt = self.grain.orientation_matrix().transpose()
G = np.dot(R, np.dot(gt, plane.scattering_vector()))
K = X + G
# position of the grain at this rotation angle
g_pos_rot = np.dot(R, self.grain.center)
pg = detector.project_along_direction(K, g_pos_rot)
(up, vp) = detector.lab_to_pixel(pg)[0]
g_uv[:, 2 * i + j] = up, vp
# check detector flips
hor_flip = np.dot(detector.u_dir, [0, -1, 0]) < 0
ver_flip = np.dot(detector.v_dir, [0, 0, -1]) < 0
if self.verbose:
print(detector.u_dir)
print(detector.v_dir)
print('detector horizontal flip: %s' % hor_flip)
print('detector vertical flip: %s' % ver_flip)
# compute the projections
stack_sim = self.grain_projections(omegas,
gid,
hor_flip=hor_flip,
ver_flip=ver_flip)
return self.grain_projection_image(g_uv, stack_sim)
def grain_projection_simulation(self, gid=1, data=None):
"""Function to compute all the grain projection in DCT geometry and create a composite image."""
print('forward simulation of grain %d' % gid)
detector = self.exp.get_active_detector()
lambda_keV = self.exp.source.max_energy
lambda_nm = lambda_keV_to_nm(lambda_keV)
X = np.array([1., 0., 0.]) / lambda_nm
lattice = self.exp.get_sample().get_material()
if not hasattr(self, 'grain'):
# load the corresponding grain
self.load_grain(gid=gid)
from scipy import ndimage
if data is None:
grain_ids = self.exp.get_sample().get_grain_ids()
print('binarizing grain %d' % gid)
data = np.where(
grain_ids[ndimage.find_objects(grain_ids == gid)[0]] == gid, 1,
0)
print('shape of binary grain is {}'.format(data.shape))
# compute all the omega values
print('simulating diffraction spot positions on the detector')
omegas = np.zeros(2 * len(self.hkl_planes))
g_uv = np.zeros((2, 2 * len(self.hkl_planes)))
for i, plane in enumerate(self.hkl_planes):
#print(plane.miller_indices())
try:
w1, w2 = self.grain.dct_omega_angles(plane,
lambda_keV,
verbose=False)
except ValueError:
# plane does not fulfil the Bragg condition
continue
omegas[2 * i] = w1
omegas[2 * i + 1] = w2
for j in range(2):
omega = omegas[2 * i + j]
omegar = omega * np.pi / 180
R = np.array([[np.cos(omegar), -np.sin(omegar), 0],
[np.sin(omegar),
np.cos(omegar), 0], [0, 0, 1]])
gt = self.grain.orientation_matrix().transpose()
G = np.dot(R, np.dot(gt, plane.scattering_vector()))
K = X + G
# position of the grain at this rotation angle
g_pos_rot = np.dot(R, self.grain.center)
pg = detector.project_along_direction(K, g_pos_rot)
(up, vp) = detector.lab_to_pixel(pg)[0]
g_uv[:, 2 * i + j] = up, vp
# build the 3d projection stack at once
print('building grain projections stack')
stack_sim = radiographs(data, omegas)
stack_sim = stack_sim.transpose(
2, 0, 1)[:, :, ::
-1] # (u, v) axes correspond to (Y, -Z) for DCT detector
return self.grain_projection_image(g_uv, stack_sim)
def test_Bragg_condition(self):
al = Lattice.from_symbol('Al')
p = HklPlane(0, 0, 2, lattice=al)
lambda_keV = 42
lambda_nm = lambda_keV_to_nm(lambda_keV)
rod = [0.1449, -0.0281, 0.0616]
o = Orientation.from_rodrigues(rod)
(w1, w2) = o.dct_omega_angles(p, lambda_keV, verbose=False)
# test the two solution of the rotating crystal
for omega in (w1, w2):
alpha = o.compute_XG_angle(p, omega, verbose=True)
theta_bragg = p.bragg_angle(lambda_keV)
self.assertAlmostEqual(alpha, 180 / np.pi * (np.pi / 2 - theta_bragg))
def dct_projection(orientations, data, dif_grains, omega, lambda_keV, detector, lattice, include_direct_beam=True,
att=5, verbose=True):
'''Work in progress, will replace function in the microstructure module.'''
full_proj = np.zeros(detector.size, dtype=np.float)
lambda_nm = lambda_keV_to_nm(lambda_keV)
omegar = omega * np.pi / 180
R = np.array([[np.cos(omegar), -np.sin(omegar), 0], [np.sin(omegar), np.cos(omegar), 0], [0, 0, 1]])
if include_direct_beam:
# add the direct beam part by computing the radiograph of the sample without the diffracting grains
data_abs = np.where(data > 0, 1, 0)
for (gid, (h, k, l)) in dif_grains:
mask_dif = (data == gid)
data_abs[mask_dif] = 0 # remove this grain from the absorption
proj = radiograph(data_abs, omega)
add_to_image(full_proj, proj[::-1, ::-1] / att, np.array(full_proj.shape) // 2)
# add diffraction spots
X = np.array([1., 0., 0.]) / lambda_nm
for (gid, (h, k, l)) in dif_grains:
grain_data = np.where(data == gid, 1, 0)
if np.sum(grain_data) < 1:
print('skipping grain %d' % gid)
continue
local_com = np.array(ndimage.measurements.center_of_mass(grain_data, data))
print('local center of mass (voxel): {0}'.format(local_com))
g_center_mm = detector.pixel_size * (local_com - 0.5 * np.array(data.shape))
print('center of mass (voxel): {0}'.format(local_com - 0.5 * np.array(data.shape)))
print('center of mass (mm): {0}'.format(g_center_mm))
# compute scattering vector
gt = orientations[gid].orientation_matrix().transpose()
# gt = micro.get_grain(gid).orientation_matrix().transpose()
p = HklPlane(h, k, l, lattice)
G = np.dot(R, np.dot(gt, p.scattering_vector()))
K = X + G
# position of the grain at this rotation
g_pos_rot = np.dot(R, g_center_mm)
pg = detector.project_along_direction(K, g_pos_rot)
(up, vp) = detector.lab_to_pixel(pg)
if verbose:
print('\n* gid=%d, (%d,%d,%d) plane, angle=%.1f' % (gid, h, k, l, omega))
print('diffraction vector:', K)
print('postion of the grain at omega=%.1f is ' % omega, g_pos_rot)
print('up=%d, vp=%d for plane (%d,%d,%d)' % (up, vp, h, k, l))
data_dif = grain_data[ndimage.find_objects(data == gid)[0]]
proj_dif = radiograph(data_dif, omega) # (Y, Z) coordinate system
add_to_image(full_proj, proj_dif[::-1, ::-1], (up, vp), verbose) # (u, v) axes correspond to (-Y, -Z)
return full_proj
def compute_Laue_pattern(orientation, detector, hkl_planes=None, Xu=np.array([1., 0., 0.]), use_friedel_pair=False,
spectrum=None, spectrum_thr=0., r_spot=5, color_field='constant', inverted=False,
show_direct_beam=False, verbose=False):
"""
Compute a transmission Laue pattern. The data array of the given
`Detector2d` instance is initialized with the result.
The incident beam is assumed to be along the X axis: (1, 0, 0) but can be changed to any direction.
The crystal can have any orientation using an instance of the `Orientation` class.
The `Detector2d` instance holds all the geometry (detector size and position).
A parameter controls the meaning of the values in the diffraction spots in the image. It can be just a constant
value, the diffracted beam energy (in keV) or the intensity as computed by the :py:meth:`diffracted_intensity`
method.
:param orientation: The crystal orientation.
:param detector: An instance of the Detector2d class.
:param list hkl_planes: A list of the lattice planes to include in the pattern.
:param Xu: The unit vector of the incident X-ray beam (default along the X-axis).
:param bool use_friedel_pair: also consider the Friedel pair of each lattice plane in the list as candidate for diffraction.
:param spectrum: A two columns array of the spectrum to use for the calculation.
:param float spectrum_thr: The threshold to use to determine if a wave length is contributing or not.
:param int r_spot: Size of the spots on the detector in pixel (5 by default)
:param str color_field: a traing describing, must be 'constant', 'energy' or 'intensity'
:param bool inverted: A flag to control if the pattern needs to be inverted.
:param bool show_direct_beam: A flag to control if the direct beam is shown.
:param bool verbose: activate verbose mode (False by default).
:return: the computed pattern as a numpy array.
"""
detector.data = np.zeros(detector.size, dtype=np.float32)
# create a small square image for one spot
spot = np.ones((2 * r_spot + 1, 2 * r_spot + 1), dtype=np.uint8)
max_val = np.iinfo(np.uint8).max # 255 here
direct_beam_lab = detector.project_along_direction(Xu)
direct_beam_pix = detector.lab_to_pixel(direct_beam_lab)[0]
if show_direct_beam:
add_to_image(detector.data, max_val * 3 * spot, (direct_beam_pix[0], direct_beam_pix[1]))
if spectrum is not None:
print('using spectrum')
#indices = np.argwhere(spectrum[:, 1] > spectrum_thr)
E_min = min(spectrum) #float(spectrum[indices[0], 0])
E_max = max(spectrum) #float(spectrum[indices[-1], 0])
lambda_min = lambda_keV_to_nm(E_max)
lambda_max = lambda_keV_to_nm(E_min)
#if verbose:
print('energy bounds: [{0:.1f}, {1:.1f}] keV'.format(E_min, E_max))
for hkl in hkl_planes:
(the_energy, theta) = select_lambda(hkl, orientation, Xu=Xu, verbose=False)
if the_energy < 0:
if use_friedel_pair:
if verbose:
print('switching to Friedel pair')
hkl = hkl.friedel_pair()
(the_energy, theta) = select_lambda(hkl, orientation, Xu=Xu, verbose=False)
else:
continue
assert(the_energy >= 0)
if spectrum is not None:
if the_energy < E_min or the_energy > E_max:
#print('skipping reflection {0:s} which would diffract at {1:.1f}'.format(hkl.miller_indices(), abs(the_energy)))
continue
#print('including reflection {0:s} which will diffract at {1:.1f}'.format(hkl.miller_indices(), abs(the_energy)))
K = diffracted_vector(hkl, orientation, Xu=Xu, use_friedel_pair=False, verbose=verbose)
if K is None or np.dot(Xu, K) == 0:
continue # skip diffraction // to the detector
d = np.dot((detector.ref_pos - np.array([0., 0., 0.])), detector.w_dir) / np.dot(K, detector.w_dir)
if d < 0:
if verbose:
print('skipping diffraction not towards the detector')
continue
R = detector.project_along_direction(K, origin=[0., 0., 0.])
(u, v) = detector.lab_to_pixel(R)[0]
if verbose and u >= 0 and u < detector.size[0] and v >= 0 and v < detector.size[1]:
print('* %d%d%d reflexion' % hkl.miller_indices())
print('diffracted beam will hit the detector at (%.3f, %.3f) mm or (%d, %d) pixels' % (R[1], R[2], u, v))
print('diffracted beam energy is {0:.1f} keV'.format(abs(the_energy)))
print('Bragg angle is {0:.2f} deg'.format(abs(theta * 180 / pi)))
# mark corresponding pixels on the image detector
if color_field == 'constant':
add_to_image(detector.data, max_val * spot, (u, v))
elif color_field == 'energy':
add_to_image(detector.data, abs(the_energy) * spot.astype(float), (u, v))
elif color_field == 'intensity':
I = diffracted_intensity(hkl, I0=max_val, verbose=verbose)
add_to_image(detector.data, I * spot, (u, v))
else:
raise ValueError('unsupported color_field: %s' % color_field)
if inverted:
# np.invert works only with integer types
print('casting to uint8 and inverting image')
# limit maximum to max_val (255) and convert to uint8
over = detector.data > 255
detector.data[over] = 255
detector.data = detector.data.astype(np.uint8)
detector.data = np.invert(detector.data)
return detector.data
def dct_projection(self, omega, include_direct_beam=True, att=5):
"""Function to compute a full DCT projection at a given omega angle.
:param float omega: rotation angle in degrees.
:param bool include_direct_beam: flag to compute the transmission through the sample.
:param float att: an attenuation factor used to limit the gray levels in the direct beam.
:return: the dct projection as a 2D numpy array
"""
if len(self.reflections) == 0:
print(
'empty list of reflections, you should run the setup function first'
)
return None
grain_ids = self.exp.get_sample().get_grain_ids()
detector = self.exp.get_active_detector()
lambda_keV = self.exp.source.max_energy
lattice = self.exp.get_sample().get_material()
index = np.argmax(self.omegas > omega)
dif_grains = self.reflections[
index -
1] # grains diffracting between omegas[index - 1] and omegas[index]
# intialize image result
full_proj = np.zeros(detector.get_size_px(), dtype=np.float)
lambda_nm = lambda_keV_to_nm(lambda_keV)
omegar = omega * np.pi / 180
R = np.array([[np.cos(omegar), -np.sin(omegar), 0],
[np.sin(omegar), np.cos(omegar), 0], [0, 0, 1]])
if include_direct_beam:
# add the direct beam part by computing the radiograph of the sample without the diffracting grains
data_abs = np.where(grain_ids > 0, 1, 0)
for (gid, (h, k, l)) in dif_grains:
mask_dif = (grain_ids == gid)
data_abs[mask_dif] = 0 # remove this grain from the absorption
proj = radiograph(
data_abs, omega
)[:, ::-1] # (u, v) axes correspond to (Y, -Z) for DCT detector
add_to_image(full_proj, proj / att, np.array(full_proj.shape) // 2)
# add diffraction spots
X = np.array([1., 0., 0.]) / lambda_nm
for (gid, (h, k, l)) in dif_grains:
grain_data = np.where(grain_ids == gid, 1, 0)
if np.sum(grain_data) < 1:
print('skipping grain %d' % gid)
continue
local_com = np.array(
ndimage.measurements.center_of_mass(grain_data, grain_ids))
print('local center of mass (voxel): {0}'.format(local_com))
g_center_mm = detector.get_pixel_size() * (
local_com - 0.5 * np.array(grain_ids.shape))
print('center of mass (voxel): {0}'.format(
local_com - 0.5 * np.array(grain_ids.shape)))
print('center of mass (mm): {0}'.format(g_center_mm))
# compute scattering vector
gt = self.exp.get_sample().get_microstructure().get_grain(
gid).orientation_matrix().transpose()
p = HklPlane(h, k, l, lattice)
G = np.dot(R, np.dot(gt, p.scattering_vector()))
K = X + G
# position of the grain at this rotation angle
g_pos_rot = np.dot(R, g_center_mm)
pg = detector.project_along_direction(K, g_pos_rot)
up, vp = detector.lab_to_pixel(pg)[0]
if self.verbose:
print('\n* gid=%d, (%d,%d,%d) plane, angle=%.1f' %
(gid, h, k, l, omega))
print('diffraction vector:', K)
print('postion of the grain at omega=%.1f is ' % omega,
g_pos_rot)
print('up=%d, vp=%d for plane (%d,%d,%d)' % (up, vp, h, k, l))
data_dif = grain_data[ndimage.find_objects(grain_ids == gid)[0]]
proj_dif = radiograph(data_dif, omega) # (Y, Z) coordinate system
add_to_image(full_proj, proj_dif[:, ::-1], (up, vp),
self.verbose) # (u, v) axes correspond to (Y, -Z)
return full_proj
