def test_eval_child_ray(self):
ray_in = Ray(origin=(-1.0, -2.0, -3.0),
direction=(1.0, 2.0, 3.0),
E_vector=(1.0, -2.0, 0.0),
E1_amp=(1.0 + 1.0j),
E2_amp=(2.0 + 0.0j),
refractive_index=1.5)
mat = FullDielectricMaterial(n_inside=1.0,
n_outside=1.5,
reflection_threshold=-0.01,
transmission_threshold=-0.01)
out = RayCollection(8)
ray_idx = 123
point = (0.0, 0.0, 0.0)
normal = (0.0, 0.0, -1.0)
tangent = (0.0, -1.0, 0.0)
mat.eval_child_ray(ray_in, ray_idx, point, normal, tangent, out)
self.assertEqual(len(out), 2)
aspect_in = dotprod(norm(ray_in.direction), norm(normal))
P_in = (P(ray_in.E1_amp) +
P(ray_in.E2_amp)) * (ray_in.refractive_index.real)
print("D_in:", norm((1.0, 2.0, 3.0)), "P_in:", P_in * aspect_in)
for item in out:
E1 = item.E1_amp
E2 = item.E2_amp
aspect_out = dotprod(norm(item.direction), norm(normal))
print((P(E1) + P(E2)) * (item.refractive_index.real) * aspect_out,
item.refractive_index)
def test_brewster_angle(self):
n_out = 1.2
n_in = 2.0
theta_B = numpy.arctan2(n_in, n_out)
print("Brewsters angle:", theta_B * 180 / numpy.pi)
y = numpy.sin(theta_B)
z = numpy.cos(theta_B)
#angle inside dielectric (for transmitted ray)
theta_inside = numpy.arcsin(n_out * numpy.sin(theta_B) / n_in)
trans_direction = norm(
(0.0, numpy.sin(theta_inside), numpy.cos(theta_inside)))
###input ray is directed into object
ray_in = Ray(origin=(0.0, -y, -z),
direction=(0.0, y, z),
E_vector=(0.0, 1.0, 0.0),
E1_amp=(1.0 + 1.0j),
E2_amp=(0.0 + 0.0j),
refractive_index=n_out)
mat = FullDielectricMaterial(n_inside=n_in,
n_outside=n_out,
reflection_threshold=-0.01,
transmission_threshold=-0.01)
out = RayCollection(8)
ray_idx = 123
point = (0.0, 0.0, 0.0)
normal = (0.0, 0.0, -1.0)
tangent = (0.0, -1.0, 0.0)
P_in = ray_power(ray_in)
mat.eval_child_ray(ray_in, ray_idx, point, normal, tangent, out)
self.assertEqual(len(out), 2)
refl_pow = ray_power(out[0])
trans_pow = ray_power(out[1])
self.assertAlmostEqual(0.0, refl_pow)
self.assertAlmostEqual(refl_pow, out[0].power)
self.assertAlmostEqual(P_in, trans_pow)
###check relfected ray direction
self.assertAlmostEqual(
abs(
dotprod(norm(subvv(ray_in.direction, out[0].direction)),
normal)), 1)
###check transmitted ray direction
self.assertAlmostEqual(abs(dotprod(out[1].direction, trans_direction)),
1)
def test_convert_to_sp(self):
ray_in = Ray(origin=(-1.0, -2.0, -3.0),
direction=(1.0, 2.0, 3.0),
E_vector=(1.0, -2.0, 0.0),
E1_amp=(1.0 + 2.0j),
E2_amp=(3.0 + 4.0j))
ray_in.project_E(1.5, -2.0, 0.0)
E_vector = ray_in.E_vector
E1_amp = ray_in.E1_amp
E2_amp = ray_in.E2_amp
normal = (1.0, -1.0, 0.0)
ray_out = Convert_to_SP(ray_in, normal)
ray_out.project_E(1.5, -2.0, 0.0)
self.assertEqual(E_vector, ray_out.E_vector)
self.assertAlmostEqual(E1_amp, ray_out.E1_amp)
self.assertAlmostEqual(E2_amp, ray_out.E2_amp)
def test_preserve_polariasation(self):
m = TransparentMaterial
ray_idx = 123
ray_in = Ray(origin=(0.0, 0.0, 0.0),
direction=(0.0, 0.0, 1.0),
E_vector=(1.0, 0.0, 0.0),
E1_amp=(1.0 + 2.0j),
E2_amp=(3.0 + 4.0j))
out = RayCollection(1)
point = (0.0, 0.0, 0.0)
normal = (0.0, 0.0, -1.0)
def test_apply_half_wave_retardance(self):
ray_in = Ray(origin=(-1.0, -2.0, -3.0),
direction=(0.0, 0.0, 3.0),
E_vector=(1.0, 0.0, 0.3),
E1_amp=(1.0 + 1.0j),
E2_amp=(-1.0 - 1.0j),
refractive_index=1.5)
m = WaveplateMaterial(retardance=0.5)
ray_out = m.apply_retardance(ray_in)
self.assertAlmostEqual(0.0, ray_out.ellipticity)
ray_out.project_E(1.0, 1.0, 0.0)
ray_in.project_E(1.0, 1.0, 0.0)
print(ray_in.E_vector, ray_in.E1_amp, ray_in.E2_amp)
print(ray_out.E_vector, ray_out.E1_amp, ray_out.E2_amp)
self.assertAlmostEqual(ray_in.E1_amp, ray_out.E2_amp)
self.assertAlmostEqual(ray_in.E2_amp, ray_out.E1_amp)
ray_in = Ray(origin=(-1.0, -2.0, -3.0),
direction=(1.0, 2.0, 3.0),
E_vector=(1.0, -2.0, 0.3),
E1_amp=(1.0 + 1.0j),
E2_amp=(2.0 + -3.0j),
refractive_index=1.5)
m = WaveplateMaterial(retardance=0.5)
ray_out = m.apply_retardance(ray_in)
self.assertAlmostEqual(abs(ray_in.ellipticity),
abs(ray_out.ellipticity))
def test_apply_quarter_wave_retardance(self):
ray_in = Ray(origin=(-1.0, -2.0, -3.0),
direction=(1.0, 2.0, 3.0),
E_vector=(1.0, -2.0, 0.3),
E1_amp=(2.0 + 2.0j),
E2_amp=(2.0 + 2.0j),
refractive_index=1.5)
m = WaveplateMaterial(retardance=0.25)
ray_out = m.apply_retardance(ray_in)
self.assertEqual(ray_in.ellipticity, 0.0)
self.assertEqual(abs(ray_out.ellipticity), 1.0)
def test_apply_zero_retardance(self):
ray_in = Ray(origin=(-1.0, -2.0, -3.0),
direction=(1.0, 2.0, 3.0),
E_vector=(1.0, -2.0, 0.3),
E1_amp=(1.0 + 1.0j),
E2_amp=(2.0 + -3.0j),
refractive_index=1.5)
m = WaveplateMaterial(retardance=0.0)
ray_out = m.apply_retardance(ray_in)
self.assertEqual(ray_in.E1_amp, ray_out.E1_amp)
self.assertEqual(ray_in.E2_amp, ray_out.E2_amp)
def test_normal_incidence(self):
ray_in = Ray(origin=(-1.0, -2.0, -3.0),
direction=(1.0, 2.0, 3.0),
E_vector=(1.0, -2.0, 0.0),
E1_amp=(1.0 + 2.0j),
E2_amp=(3.0 + 4.0j))
P_in = P(ray_in.E1_amp) + P(ray_in.E2_amp)
normal = (1.0, 2.0, 3.0)
ray_out = Convert_to_SP(ray_in, normal)
P_out = P(ray_out.E1_amp) + P(ray_out.E2_amp)
self.assertAlmostEqual(P_in, P_out)
ray_in.project_E(1.0, -2.0, 0.0)
ray_out.project_E(1.0, -2.0, 0.0)
self.assertEqual(ray_out.E_vector, ray_in.E_vector)
self.assertAlmostEqual(ray_out.E1_amp, ray_in.E1_amp)
self.assertAlmostEqual(ray_out.E2_amp, ray_in.E2_amp)
def test_project_E(self):
ray_in = Ray(origin=(-1.0, -2.0, -3.0),
direction=(1.0, 2.0, 3.0),
E_vector=(1.0, -2.0, 0.0),
E1_amp=(1.0 + 2.0j),
E2_amp=(3.0 + 4.0j))
ray_in.project_E(1.0, -2.0, 0.0)
E_vector = ray_in.E_vector
E1_amp = ray_in.E1_amp
E2_amp = ray_in.E2_amp
ray_in.project_E(0.3, .7, 0)
ray_in.project_E(-0.8, 0.235, 0)
ray_in.project_E(1.0, -2.0, 0.0)
self.assertEqual(E_vector, ray_in.E_vector)
self.assertAlmostEqual(E1_amp, ray_in.E1_amp)
self.assertAlmostEqual(E2_amp, ray_in.E2_amp)
def test_normal_incidence(self):
n_out = 1.3
n_in = 2.0
ray_in = Ray(origin=(0.0, 0.0, -1.0),
direction=(0.0, 0.0, 3.0),
E_vector=(5.0, 0.0, 0.0),
E1_amp=(1.0 + 1.0j),
E2_amp=(2.0 + 0.0j),
refractive_index=n_out)
mat = FullDielectricMaterial(n_inside=n_in,
n_outside=n_out,
reflection_threshold=-0.01,
transmission_threshold=-0.01)
out = RayCollection(8)
ray_idx = 123
point = (0.0, 0.0, 0.0)
normal = (0.0, 0.0, -1.0)
tangent = (0.0, -1.0, 0.0)
P_in = ray_power(ray_in)
mat.eval_child_ray(ray_in, ray_idx, point, normal, tangent, out)
self.assertEqual(len(out), 2)
#textbook reflection and transmission coefficients
R = ((n_in - n_out) / (n_in + n_out))**2
T = (n_in / n_out) * ((2 * n_out / (n_out + n_in))**2)
self.assertAlmostEqual(1, T + R)
refl_pow = ray_power(out[0])
self.assertAlmostEqual(R, refl_pow / P_in)
trans_pow = ray_power(out[1])
self.assertAlmostEqual(T, trans_pow / P_in)
self.assertAlmostEqual(P_in, refl_pow + trans_pow)
print(ray_in.E_left, ray_in.E_right)
def test_conserve_power(self):
ray_in = Ray(origin=(-1.0, -2.0, -3.0),
direction=(1.0, 2.0, 3.0),
E_vector=(1.0, -2.0, 0.0),
E1_amp=(1.0 + 2.0j),
E2_amp=(3.0 + 4.0j))
P_in = P(ray_in.E1_amp) + P(ray_in.E2_amp)
normal = (0.2, 0.3, -1.1)
ray_out = Convert_to_SP(ray_in, normal)
P_out = P(ray_out.E1_amp) + P(ray_out.E2_amp)
self.assertAlmostEqual(P_in, P_out)
ray_out.project_E(1.0, -2.0, 0.0)
self.assertAlmostEqual(ray_out.E1_amp, ray_in.E1_amp)
def test_snells_law(self):
n_out = 1.2
n_in = 2.0
d_out = NondispersiveCurve(n_out)
d_in = NondispersiveCurve(n_in)
d_coating = NondispersiveCurve(1.4)
theta_B = numpy.arctan2(n_in, n_out)
print("Brewsters angle:", theta_B * 180 / numpy.pi)
y = numpy.sin(theta_B)
z = numpy.cos(theta_B)
#angle inside dielectric (for transmitted ray)
theta_inside = numpy.arcsin(n_out * numpy.sin(theta_B) / n_in)
trans_direction = norm(
(0.0, numpy.sin(theta_inside), numpy.cos(theta_inside)))
###input ray is directed into object
ray_in = Ray(origin=(0.0, -y, -z),
direction=(0.0, y, z),
E_vector=(0.0, 1.0, 0.0),
E1_amp=(1.0 + 1.0j),
E2_amp=(0.0 + 0.0j),
refractive_index=n_out)
print(ray_in.wavelength_idx)
mat = CoatedDispersiveMaterial(dispersion_inside=d_in,
dispersion_outside=d_out,
coating_thickness=0.1,
dispersion_coating=d_coating,
reflection_threshold=0.01,
transmission_threshold=0.01)
wavelens = numpy.array([0.78], 'd')
mat.wavelengths = wavelens
out = RayCollection(8)
ray_idx = 123
point = (0.0, 0.0, 0.0)
normal = (0.0, 0.0, -1.0)
tangent = (0.0, -1.0, 0.0)
P_in = ray_power(ray_in)
mat.eval_child_ray(ray_in, ray_idx, point, normal, tangent, out)
self.assertEqual(len(out), 2)
refl_pow = ray_power(out[0])
trans_pow = ray_power(out[1])
#self.assertAlmostEquals(0.0, refl_pow)
#self.assertAlmostEquals(refl_pow, out[0].power)
#self.assertAlmostEquals(P_in, trans_pow)
###check relfected ray direction
self.assertAlmostEqual(
abs(
dotprod(norm(subvv(ray_in.direction, out[0].direction)),
normal)), 1)
###check transmitted ray direction
self.assertAlmostEqual(abs(dotprod(out[1].direction, trans_direction)),
1)
def test_brewster_angle(self):
n_out = 1.2
n_in = 2.0
theta_B = numpy.arctan2(n_in, n_out)
print("Brewsters angle:", theta_B * 180 / numpy.pi)
y = numpy.sin(theta_B)
z = numpy.cos(theta_B)
#angle inside dielectric (for transmitted ray)
theta_inside = numpy.arcsin(n_out * numpy.sin(theta_B) / n_in)
print("Internal angle:", theta_inside * 180 / numpy.pi)
trans_direction = norm(
(0.0, numpy.sin(theta_inside), numpy.cos(theta_inside)))
###input ray is directed into object
ray_in = Ray(origin=(0.0, -y, -z),
direction=(0.0, y, z),
E_vector=(0.0, 1.0, 0.0),
E1_amp=(1.0 + 1.0j),
E2_amp=(0.0 + 0.0j),
refractive_index=n_out)
mat = SingleLayerCoatedMaterial(thickness=0.1,
n_coating=1.5,
n_inside=n_in,
n_outside=n_out,
reflection_threshold=-0.01,
transmission_threshold=-0.01)
mat.wavelengths = numpy.array([0.78])
out = RayCollection(8)
ray_idx = 123
point = (0.0, 0.0, 0.0)
normal = (0.0, 0.0, -1.0)
tangent = (0.0, -1.0, 0.0)
P_in = ray_power(ray_in)
mat.eval_child_ray(ray_in, ray_idx, point, normal, tangent, out)
self.assertEqual(len(out), 2)
refl_pow = ray_power(out[0])
trans_pow = ray_power(out[1])
#self.assertAlmostEquals(0.0, refl_pow)
#self.assertAlmostEquals(refl_pow, out[0].power)
#self.assertAlmostEquals(P_in, trans_pow)
###check relfected ray direction
self.assertAlmostEqual(
abs(
dotprod(norm(subvv(ray_in.direction, out[0].direction)),
normal)), 1)
dir_out = out[1].direction
theta_trans = 180 * numpy.arctan2(dir_out[2], dir_out[1]) / numpy.pi
print("Transmitted angle:", theta_trans)
###check transmitted ray direction
self.assertAlmostEqual(abs(dotprod(out[1].direction, trans_direction)),
1)
def test_circular_polarisation(self):
n_out = 1.3
n_in = 2.0
ray_in = Ray(origin=(0.0, 0.0, -1.0),
direction=(0.0, 0.0, 3.0),
E_vector=(5.0, 0.0, 0.0),
E1_amp=(2.0 + 2.0j),
E2_amp=(2.0 - 2.0j),
refractive_index=n_out)
mat = FullDielectricMaterial(n_inside=n_in,
n_outside=n_out,
reflection_threshold=-0.01,
transmission_threshold=-0.01)
out = RayCollection(8)
ray_idx = 123
point = (0.0, 0.0, 0.0)
normal = (0.0, 0.0, -1.0)
tangent = (0.0, -1.0, 0.0)
P_in = ray_power(ray_in)
mat.eval_child_ray(ray_in, ray_idx, point, normal, tangent, out)
self.assertEqual(len(out), 2)
#textbook reflection and transmission coefficients
R = ((n_in - n_out) / (n_in + n_out))**2
T = (n_in / n_out) * ((2 * n_out / (n_out + n_in))**2)
self.assertAlmostEqual(1, T + R)
refl_pow = ray_power(out[0])
self.assertAlmostEqual(R, refl_pow / P_in)
trans_pow = ray_power(out[1])
self.assertAlmostEqual(T, trans_pow / P_in)
self.assertAlmostEqual(P_in, refl_pow + trans_pow)
refl = out[0]
trans = out[1]
pwr = lambda x: (x * x.conjugate()).real
P_left_in = pwr(ray_in.E_left) * ray_in.refractive_index
P_right_in = pwr(ray_in.E_right) * ray_in.refractive_index
P_left_refl = pwr(refl.E_left) * refl.refractive_index
P_right_refl = pwr(refl.E_right) * refl.refractive_index
P_left_trans = pwr(trans.E_left) * trans.refractive_index
P_right_trans = pwr(trans.E_right)
self.assertEqual(P_right_in, 0)
self.assertEqual(P_left_refl, 0)
self.assertEqual(P_right_trans, 0)
#check for conservation of total power
self.assertEqual(P_left_in, P_left_trans + P_right_refl)