def scatcoeffs(m, x, nstop): # see B/H eqn 4.88
# implement criterion used by BHMIE plus a couple more orders to
# be safe
nmx = int(array([nstop, np.round_(np.absolute(m*x))]).max()) + 20
Dnmx = mie_specfuncs.log_der_1(m*x, nmx, nstop)
n = np.arange(nstop+1)
psi, xi = mie_specfuncs.riccati_psi_xi(x, nstop)
psishift = np.concatenate((np.zeros(1), psi))[0:nstop+1]
xishift = np.concatenate((np.zeros(1), xi))[0:nstop+1]
an = ( (Dnmx/m + n/x)*psi - psishift ) / ( (Dnmx/m + n/x)*xi - xishift )
bn = ( (Dnmx*m + n/x)*psi - psishift ) / ( (Dnmx*m + n/x)*xi - xishift )
return array([an[1:nstop+1], bn[1:nstop+1]]) # output begins at n=1
def scatcoeffs(m, x, nstop): # see B/H eqn 4.88
# implement criterion used by BHMIE plus a couple more orders to
# be safe
nmx = int(array([nstop, np.round_(np.absolute(m * x))]).max()) + 20
Dnmx = mie_specfuncs.log_der_1(m * x, nmx, nstop)
n = np.arange(nstop + 1)
psi, xi = mie_specfuncs.riccati_psi_xi(x, nstop)
psishift = np.concatenate((np.zeros(1), psi))[0:nstop + 1]
xishift = np.concatenate((np.zeros(1), xi))[0:nstop + 1]
an = ((Dnmx / m + n / x) * psi - psishift) / (
(Dnmx / m + n / x) * xi - xishift)
bn = ((Dnmx * m + n / x) * psi - psishift) / (
(Dnmx * m + n / x) * xi - xishift)
return array([an[1:nstop + 1], bn[1:nstop + 1]]) # output begins at n=1
def scatcoeffs_multi(marray, xarray):
'''
Calculate scattered field expansion coefficients (in the Mie formalism)
for a particle with an arbitrary number of layers.
Inputs:
marray: numpy array of layer indices, innermost first
xarray: numpy array of layer size parameters (k * radius), innermost first
'''
# ensure correct data types
marray = np.array(marray, dtype = 'complex128')
xarray = np.array(xarray, dtype = 'float64')
# sanity check: marray and xarray must be same size
if marray.size != xarray.size:
raise ModelInputError('Arrays of layer indices and size parameters must be the same length!')
# need number of layers L
nlayers = marray.size
# calculate nstop based on outermost radius
nstop = miescatlib.nstop(xarray.max())
# initialize H_n^a and H_n^b in the core, see eqns. 12a and 13a
intl = log_der_13(marray[0]*xarray[0], nstop)[0]
hans = intl
hbns = intl
for lay in np.arange(1, nlayers): # lay is l-1 (index on layers used by Yang)
z1 = marray[lay]*xarray[lay-1] # m_l x_{l-1}
z2 = marray[lay]*xarray[lay] # m_l x_l
# calculate logarithmic derivatives D_n^1 and D_n^3
derz1s = log_der_13(z1, nstop)
derz2s = log_der_13(z2, nstop)
# calculate G1, G2, Gtilde1, Gtilde2 according to
# eqns 26-29
# using H^a_n and H^b_n from previous layer
G1 = marray[lay]*hans - marray[lay-1]*derz1s[0]
G2 = marray[lay]*hans - marray[lay-1]*derz1s[1]
Gt1 = marray[lay-1]*hbns - marray[lay]*derz1s[0]
Gt2 = marray[lay-1]*hbns - marray[lay]*derz1s[1]
# calculate ratio Q_n^l for this layer
Qnl = Qratio(z1, z2, nstop, dns1 = derz1s, dns2 = derz2s)
# now calculate H^a_n and H^b_n in current layer
# see eqns 24 and 25
hans = (G2*derz2s[0] - Qnl*G1*derz2s[1]) / (G2 - Qnl*G1)
hbns = (Gt2*derz2s[0] - Qnl*Gt1*derz2s[1]) / (Gt2 - Qnl*Gt1)
# repeat for next layer
# Relate H^a and H^b in the outer layer to the Mie scat coeffs
# see Yang eqns 14 and 15
psiandxi = riccati_psi_xi(xarray.max(), nstop) # n = 0 to nstop
n = np.arange(nstop+1)
psi = psiandxi[0]
xi = psiandxi[1]
# this doesn't bother to calculate psi/xi_{-1} correctly,
# but OK since we're throwing out a_0, b_0 where it appears
psishift = np.concatenate((np.zeros(1), psi))[0:nstop+1]
xishift = np.concatenate((np.zeros(1), xi))[0:nstop+1]
an = ((hans/marray[nlayers-1] + n/xarray[nlayers-1])*psi - psishift) / (
(hans/marray[nlayers-1] + n/xarray[nlayers-1])*xi - xishift)
bn = ((hbns*marray[nlayers-1] + n/xarray[nlayers-1])*psi - psishift) / (
(hbns*marray[nlayers-1] + n/xarray[nlayers-1])*xi - xishift)
return np.array([an[1:nstop+1], bn[1:nstop+1]]) # output begins at n=1
def scatcoeffs_multi(marray, xarray, eps1 = 1e-3, eps2 = 1e-16):
'''
Calculate scattered field expansion coefficients (in the Mie formalism)
for a particle with an arbitrary number of layers.
Inputs:
marray: numpy array of layer indices, innermost first
xarray: numpy array of layer size parameters (k * radius), innermost first
'''
# ensure correct data types
marray = np.array(marray, dtype = 'complex128')
xarray = np.array(xarray, dtype = 'float64')
# sanity check: marray and xarray must be same size
if marray.size != xarray.size:
raise ModelInputError('Arrays of layer indices and size parameters must be the same length!')
# need number of layers L
nlayers = marray.size
# calculate nstop based on outermost radius
nstop = miescatlib.nstop(xarray.max())
# initialize H_n^a and H_n^b in the core, see eqns. 12a and 13a
intl = log_der_13(marray[0]*xarray[0], nstop, eps1, eps2)[0]
hans = intl
hbns = intl
for lay in np.arange(1, nlayers): # lay is l-1 (index on layers used by Yang)
z1 = marray[lay]*xarray[lay-1] # m_l x_{l-1}
z2 = marray[lay]*xarray[lay] # m_l x_l
# calculate logarithmic derivatives D_n^1 and D_n^3
derz1s = log_der_13(z1, nstop, eps1, eps2)
derz2s = log_der_13(z2, nstop, eps1, eps2)
# calculate G1, G2, Gtilde1, Gtilde2 according to
# eqns 26-29
# using H^a_n and H^b_n from previous layer
G1 = marray[lay]*hans - marray[lay-1]*derz1s[0]
G2 = marray[lay]*hans - marray[lay-1]*derz1s[1]
Gt1 = marray[lay-1]*hbns - marray[lay]*derz1s[0]
Gt2 = marray[lay-1]*hbns - marray[lay]*derz1s[1]
# calculate ratio Q_n^l for this layer
Qnl = Qratio(z1, z2, nstop, dns1 = derz1s, dns2 = derz2s, eps1 = eps1,
eps2 = eps2)
# now calculate H^a_n and H^b_n in current layer
# see eqns 24 and 25
hans = (G2*derz2s[0] - Qnl*G1*derz2s[1]) / (G2 - Qnl*G1)
hbns = (Gt2*derz2s[0] - Qnl*Gt1*derz2s[1]) / (Gt2 - Qnl*Gt1)
# repeat for next layer
# Relate H^a and H^b in the outer layer to the Mie scat coeffs
# see Yang eqns 14 and 15
psiandxi = riccati_psi_xi(xarray.max(), nstop) # n = 0 to nstop
n = np.arange(nstop+1)
psi = psiandxi[0]
xi = psiandxi[1]
# this doesn't bother to calculate psi/xi_{-1} correctly,
# but OK since we're throwing out a_0, b_0 where it appears
psishift = np.concatenate((np.zeros(1), psi))[0:nstop+1]
xishift = np.concatenate((np.zeros(1), xi))[0:nstop+1]
an = ((hans/marray[nlayers-1] + n/xarray[nlayers-1])*psi - psishift) / (
(hans/marray[nlayers-1] + n/xarray[nlayers-1])*xi - xishift)
bn = ((hbns*marray[nlayers-1] + n/xarray[nlayers-1])*psi - psishift) / (
(hbns*marray[nlayers-1] + n/xarray[nlayers-1])*xi - xishift)
return np.array([an[1:nstop+1], bn[1:nstop+1]]) # output begins at n=1
