def test_scattering_vector(self):
Fe_fcc = Lattice.face_centered_cubic(0.287) # FCC iron
hkl = HklPlane(2, 0, 0, Fe_fcc)
Gc = hkl.scattering_vector()
self.assertAlmostEqual(np.linalg.norm(Gc),
1 / hkl.interplanar_spacing())
Al_fcc = Lattice.face_centered_cubic(0.405)
hkl = HklPlane(0, 0, 2, lattice=Al_fcc)
Gc = hkl.scattering_vector()
self.assertAlmostEqual(np.linalg.norm(Gc),
1 / hkl.interplanar_spacing())
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 test_110_normal_monoclinic(self):
"""Testing (110) plane normal in monoclinic crystal structure.
This test comes from
http://www.mse.mtu.edu/~drjohn/my3200/stereo/sg5.html
corrected for a few errors in the html page.
In this test, the lattice is defined with the c-axis aligned with the Z direction of the Cartesian frame.
"""
Mg2Si = Lattice.from_parameters(1.534,
0.405,
0.683,
90.,
106.,
90.,
x_aligned_with_a=False)
a = Mg2Si.matrix[0]
b = Mg2Si.matrix[1]
c = Mg2Si.matrix[2]
self.assertAlmostEqual(a[0], 1.475, 3)
self.assertAlmostEqual(a[1], 0., 3)
self.assertAlmostEqual(a[2], -0.423, 3)
self.assertAlmostEqual(b[0], 0., 3)
self.assertAlmostEqual(b[1], 0.405, 3)
self.assertAlmostEqual(b[2], 0., 3)
self.assertAlmostEqual(c[0], 0., 3)
self.assertAlmostEqual(c[1], 0., 3)
self.assertAlmostEqual(c[2], 0.683, 3)
p = HklPlane(1, 1, 1, Mg2Si)
Gc = p.scattering_vector()
self.assertAlmostEqual(Gc[0], 1.098, 3)
self.assertAlmostEqual(Gc[1], 2.469, 3)
self.assertAlmostEqual(Gc[2], 1.464, 3)
self.assertAlmostEqual(p.interplanar_spacing(), 0.325, 3)
Ghkl = np.dot(Mg2Si.matrix, Gc)
self.assertEqual(Ghkl[0], 1.) # h
self.assertEqual(Ghkl[1], 1.) # k
self.assertEqual(Ghkl[2], 1.) # l
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