def _calc_scat_matrix(self, scatterer, schema):
if isinstance(scatterer, Sphere):
scat_coeffs = self._scat_coeffs(scatterer, schema.optics)
# TODO: actually use (rather than ignore) the phi
scat_matrs = [mieangfuncs.asm_mie_far(scat_coeffs, theta) for
theta, phi in schema.positions_theta_phi()]
return np.array(scat_matrs)
else:
raise TheoryNotCompatibleError(self, scatterer)
def massage_into_bh_form(asm):
S2, S3, S4, S1 = np.ravel(asm)
S11 = 0.5 * (abs(asm)**2).sum()
S12 = 0.5 * (abs(S2)**2 - abs(S1)**2)
S33 = real(S1 * conj(S2))
S34 = imag(S2 * conj(S1))
deg_of_pol = -S12/S11
# normalization factors: see comment lines 40-44 on p. 479
asm_fwd = mieangfuncs.asm_mie_far(asbs, 0.)
S11_fwd = 0.5 * (abs(asm_fwd)**2).sum()
results = np.array([S11/S11_fwd, deg_of_pol, S33 / S11, S34 / S11])
return results
def _calc_scat_matrix(self, scatterer, schema):
if isinstance(scatterer, Sphere):
scat_coeffs = self._scat_coeffs(scatterer, schema.optics)
# TODO: actually use (rather than ignore) the phi
scat_matrs = [
mieangfuncs.asm_mie_far(scat_coeffs, theta)
for theta, phi in schema.positions_theta_phi()
]
return np.array(scat_matrs)
else:
raise TheoryNotCompatibleError(self, scatterer)
def _raw_scat_matrs(self, scatterer, pos, medium_wavevec, medium_index):
'''
Returns far-field amplitude scattering matrices (with theta and phi
dependence only) -- assume spherical wave asymptotic r dependence
'''
if self._can_handle(scatterer):
scat_coeffs = self._scat_coeffs(
scatterer, medium_wavevec, medium_index)
# In the mie solution the amplitude scattering matrix is
# independent of phi
return [mieangfuncs.asm_mie_far(scat_coeffs, theta)
for r, theta, phi in pos.T]
else:
raise TheoryNotCompatibleError(self, scatterer)
def test_mie_amplitude_scattering_matrices():
'''
Test calculation of Mie amplitude scattering matrix elements.
We will check the following:
far-field matrix elements (direct comparison with [Bohren1983]_)
near-field matrix for kr ~ 10 differs from far-field result
near-field matrix for kr ~ 10^4 is close to far-field result
While radiometric quantities (such as cross sections) implicitly test
the Mie scattering coefficients, they do not involve any angular
quantities.
'''
# scattering units
m = 1.55
x = 2. * pi * 0.525 / 0.6328
asbs = miescatlib.scatcoeffs(m, x, miescatlib.nstop(x))
amp_scat_mat = mieangfuncs.asm_mie_far(asbs, theta)
amp_scat_mat_asym = mieangfuncs.asm_mie_fullradial(asbs, np.array([kr_asym,
theta,
phi]))
amp_scat_mat_near = mieangfuncs.asm_mie_fullradial(asbs, np.array([kr,
theta,
phi]))
# gold results directly from B/H p.482.
location = os.path.split(os.path.abspath(__file__))[0]
gold_name = os.path.join(location, 'gold',
'gold_mie_scat_matrix')
with open(gold_name + '.yaml') as gold_file:
gold_dict = yaml.safe_load(gold_file)
gold = np.array([gold_dict['S11'], gold_dict['pol'],
gold_dict['S33'], gold_dict['S34']])
# B/H gives real scattering matrix elements, which are related
# to the amplitude scatering elements. See p. 65.
def massage_into_bh_form(asm):
S2, S3, S4, S1 = np.ravel(asm)
S11 = 0.5 * (abs(asm)**2).sum()
S12 = 0.5 * (abs(S2)**2 - abs(S1)**2)
S33 = real(S1 * conj(S2))
S34 = imag(S2 * conj(S1))
deg_of_pol = -S12/S11
# normalization factors: see comment lines 40-44 on p. 479
asm_fwd = mieangfuncs.asm_mie_far(asbs, 0.)
S11_fwd = 0.5 * (abs(asm_fwd)**2).sum()
results = np.array([S11/S11_fwd, deg_of_pol, S33 / S11, S34 / S11])
return results
# off-diagonal elements should be zero
assert_allclose(np.ravel(amp_scat_mat)[1:3], np.zeros(2))
# check far-field computation
assert_allclose(massage_into_bh_form(amp_scat_mat), gold,
rtol = 1e-5)
# check asymptotic behavior of near field matrix
asym = massage_into_bh_form(amp_scat_mat_asym)
assert_allclose(asym, gold, rtol = 1e-4, atol = 5e-5)
# check that the near field is different
try:
assert_allclose(amp_scat_mat, amp_scat_mat_near)
except AssertionError:
pass
else:
raise AssertionError("Near-field amplitude scattering matrix " +
"suspiciously close to far-field result.")