def test_select_lambda(self):
"""Verify the wavelength diffracted by a given hkl plane."""
orientation = Orientation.cube()
hkl = HklPlane(-1, -1, -1, self.ni)
(the_lambda, theta) = select_lambda(hkl, orientation)
self.assertAlmostEqual(the_lambda, 5.277, 3)
self.assertAlmostEqual(theta * 180 / np.pi, 35.264, 3)
def test_IPF_color(self):
o1 = Orientation.cube() # 001 // Z
o2 = Orientation.from_euler([35.264, 45., 0.]) # 011 // Z
o3 = Orientation.from_euler([0., 54.736, 45.]) # 111 // Z
orientations = [o1, o2, o3]
targets = [np.array([1., 0., 0.]), np.array([0., 1., 0.]), np.array([0., 0., 1.])]
for case in range(2):
o = orientations[case]
print(o)
target = targets[case]
col = o.get_ipf_colour()
print(col)
for i in range(3):
self.assertAlmostEqual(col[i], target[i])
def test_gnomonic_projection_point(self):
"""Verify that the gnomonic projection of two diffracted points on a detector give access to the angle
between the lattice plane normals."""
olivine = Lattice.orthorhombic(
1.022, 0.596, 0.481) # nm Barret & Massalski convention
orientation = Orientation.cube()
p1 = HklPlane(2, 0, -3, olivine)
p2 = HklPlane(3, -1, -3, olivine)
detector = RegArrayDetector2d(size=(512, 512),
u_dir=[0, -1, 0],
v_dir=[0, 0, -1])
detector.pixel_size = 0.200 # mm, 0.1 mm with factor 2 binning
detector.ucen = 235
detector.vcen = 297
detector.ref_pos = np.array([131., 0., 0.]) + \
(detector.size[0] / 2 - detector.ucen) * detector.u_dir * detector.pixel_size + \
(detector.size[1] / 2 - detector.vcen) * detector.v_dir * detector.pixel_size # mm
angle = 180 / np.pi * np.arccos(np.dot(p1.normal(), p2.normal()))
# test the gnomonic projection for normal and not normal X-ray incidence
for ksi in [0.0, 1.0]: # deg
Xu = np.array(
[np.cos(ksi * np.pi / 180), 0.,
np.sin(ksi * np.pi / 180)])
OC = detector.project_along_direction(
Xu
) # C is the intersection of the direct beam with the detector
K1 = diffracted_vector(p1, orientation, Xu=Xu)
K2 = diffracted_vector(p2, orientation, Xu=Xu)
R1 = detector.project_along_direction(K1, origin=[0., 0., 0.])
R2 = detector.project_along_direction(K2, origin=[0., 0., 0.])
OP1 = gnomonic_projection_point(R1, OC=OC)[0]
OP2 = gnomonic_projection_point(R2, OC=OC)[0]
hkl_normal1 = OP1 / np.linalg.norm(OP1)
hkl_normal2 = (OP2 / np.linalg.norm(OP2))
# the projection must give the normal to the diffracting plane
for i in range(3):
self.assertAlmostEqual(hkl_normal1[i], p1.normal()[i], 6)
self.assertAlmostEqual(hkl_normal2[i], p2.normal()[i], 6)
angle_gp = 180 / np.pi * np.arccos(np.dot(hkl_normal1,
hkl_normal2))
self.assertAlmostEqual(angle, angle_gp, 6)
