def test_angle_with_directions(self):
(a, b, c) = (1.022, 0.596, 0.481)
olivine = Lattice.orthorhombic(a, b, c)
(h1, k1, l1) = (1., 1., 1.)
(h2, k2, l2) = (3., 3., 2.)
d1 = HklDirection(h1, k1, l1, olivine)
d2 = HklDirection(h2, k2, l2, olivine)
# compare with formula in orthorhombic lattice, angle must be 6.589 degrees
angle = np.arccos(
((h1 * h2 * a**2) + (k1 * k2 * b**2) + (l1 * l2 * c**2)) /
(np.sqrt(a**2 * h1**2 + b**2 * k1**2 + c**2 * l1**2) *
np.sqrt(a**2 * h2**2 + b**2 * k2**2 + c**2 * l2**2)))
self.assertAlmostEqual(d1.angle_with_direction(d2), angle)
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)