matrix = 'air'
boundary = 'film'
# indices of refraction
n_particle = ri.n(
'polystyrene',
wavelength) # refractive indices can be specified as pint quantities or
n_matrix = ri.n(
'vacuum',
wavelength) # called from the refractive_index module. n_matrix is the
n_medium = ri.n(
'vacuum',
wavelength) # space within sample. n_medium is outside the sample.
# Calculate the effective refractive index of the sample
n_sample = ri.n_eff(n_particle, n_matrix, volume_fraction)
# Calculate the phase function and scattering and absorption coefficients from the single scattering model
# (this absorption coefficient is of the scatterer, not of an absorber added to the system)
p, mu_scat, mu_abs = mc.calc_scat(particle_radius, n_particle, n_sample,
volume_fraction, wavelength)
lscat = 1 / mu_scat.magnitude # microns
# Initialize the trajectories
r0, k0, W0 = mc.initialize(nevents, ntrajectories, n_medium, n_sample,
boundary)
r0 = sc.Quantity(r0, 'um')
k0 = sc.Quantity(k0, '')
W0 = sc.Quantity(W0, '')
# Generate a matrix of all the randomly sampled angles first
def calc_sphere_mc():
# caculate the effective index of the sample
n_sample = ri.n_eff(n_particle, n_matrix, volume_fraction_particles)
# Calculate the phase function and scattering and absorption coefficients
#from the single scattering model
# (this absorption coefficient is of the scatterer, not of an absorber
#added to the system)
p, mu_scat, mu_abs = mc.calc_scat(particle_radius, n_particle, n_sample,
volume_fraction_particles, wavelength)
# Initialize the trajectories
r0, k0, W0 = mc.initialize(nevents,
ntrajectories,
n_matrix_bulk,
n_sample,
boundary,
sample_diameter=sphere_boundary_diameter)
r0 = sc.Quantity(r0, 'um')
k0 = sc.Quantity(k0, '')
W0 = sc.Quantity(W0, '')
# Create trajectories object
trajectories = mc.Trajectory(r0, k0, W0)
# Generate a matrix of all the randomly sampled angles first
sintheta, costheta, sinphi, cosphi, _, _ = mc.sample_angles(
nevents, ntrajectories, p)
# Create step size distribution
step = mc.sample_step(nevents, ntrajectories, mu_scat)
# Run photons
trajectories.absorb(mu_abs, step)
trajectories.scatter(sintheta, costheta, sinphi, cosphi)
trajectories.move(step)
# Calculate reflection and transmition
(refl_indices, trans_indices, _, _, _, refl_per_traj, trans_per_traj, _, _,
_, _, reflectance_sphere, _, _, norm_refl,
norm_trans) = det.calc_refl_trans(trajectories,
sphere_boundary_diameter,
n_matrix_bulk,
n_sample,
boundary,
p=p,
mu_abs=mu_abs,
mu_scat=mu_scat,
run_fresnel_traj=False,
return_extra=True)
return (refl_indices, trans_indices, refl_per_traj, trans_per_traj,
reflectance_sphere, norm_refl, norm_trans)
### Calculate phase function and lscat ###
# use output of calc_refl_trans to calculate phase function, mu_scat,
# and mu_abs for the bulk
p_bulk, mu_scat_bulk, mu_abs_bulk = pfs.calc_scat_bulk(
refl_per_traj, trans_per_traj, trans_indices, norm_refl, norm_trans,
volume_fraction_bulk, sphere_boundary_diameter, n_matrix_bulk,
wavelength)
return p_bulk, mu_scat_bulk, mu_abs_bulk
def calc_refl_trans(volume_fraction, radius, thickness, Sample, ntrajectories,
nevents, seed):
"""
Calculates a reflection spectrum using the structcol package.
Parameters
----------
volume_fraction : float
volume fraction of scatterer in the system
radius : float (in nm)
radius of scatterer
thickness : float (in um)
film thickness of sample
Sample : Sample object
contains information about the sample that produced data
ntrajectories : int
number of trajectories for the multiple scattering calculations
nevents : int
number of scattering events for the multiple scattering calculations
seed : int or None
If seed is int, the simulation results will be reproducible. If seed is
None, the simulation results are random.
Returns
----------
reflectance : ndarray
fraction of reflected trajectories over the wavelength range
transmittance : ndarray
fraction of transmitted trajectories over the wavelength range
"""
# Read in system parameters from the Sample object
particle_radius = sc.Quantity(radius, 'nm')
thickness = sc.Quantity(thickness, 'um')
particle_index = sc.Quantity(Sample.particle_index, '')
matrix_index = sc.Quantity(Sample.matrix_index, '')
medium_index = sc.Quantity(Sample.medium_index, '')
front_index = sc.Quantity(Sample.front_index, '')
back_index = sc.Quantity(Sample.back_index, '')
incident_angle = Sample.incident_angle
wavelength = sc.Quantity(Sample.wavelength, 'nm')
reflectance = np.zeros(len(wavelength))
transmittance = np.zeros(len(wavelength))
for i in np.arange(len(wavelength)):
# Calculate the effective index of the sample
sample_index = ri.n_eff(particle_index[i],
matrix_index[i],
volume_fraction,
maxwell_garnett=True)
# Calculate the phase function and scattering and absorption lengths
# from the single scattering model
p, mu_scat, mu_abs = mc.calc_scat(particle_radius, particle_index[i],
sample_index, volume_fraction,
wavelength[i])
# Initialize the trajectories
r0, k0, W0 = mc.initialize(nevents,
ntrajectories,
medium_index[i],
sample_index,
seed=seed,
incidence_angle=incident_angle)
r0 = sc.Quantity(r0, 'um')
k0 = sc.Quantity(k0, '')
W0 = sc.Quantity(W0, '')
# Generate a matrix of all the randomly sampled angles first
sintheta, costheta, sinphi, cosphi, _, _ = mc.sample_angles(
nevents, ntrajectories, p)
# Create step size distribution
step = mc.sample_step(nevents, ntrajectories, mu_abs, mu_scat)
# Create trajectories object
trajectories = mc.Trajectory(r0, k0, W0)
# Run photons
trajectories.absorb(mu_abs, step)
trajectories.scatter(sintheta, costheta, sinphi, cosphi)
trajectories.move(step)
# Calculate the reflection fraction
reflectance[i], transmittance[i] = mc.calc_refl_trans(
trajectories,
sc.Quantity('0.0 um'),
thickness,
medium_index[i],
sample_index,
n_front=front_index[i],
n_back=back_index[i],
detection_angle=np.pi / 2)
return (reflectance, transmittance)
def calc_refl_trans(volume_fraction,
Sample,
ntrajectories=300,
nevents=200,
seed=None):
"""
Calculates a reflection spectrum using the structcol package.
Parameters
----------
volume_fraction : float
volume fraction of scatterer in the system
Sample : Sample object
contains information about the sample that produced data
ntrajectories : int
number of trajectories
nevents : int
number of scattering events
seed : int or None
If seed is int, the simulation results will be reproducible. If seed is
None, the simulation results are random.
Returns
----------
reflection : ndarray
fraction of reflected trajectories
transmission : ndarray
fraction of transmitted trajectories
"""
# Read in system parameters from the Sample object
particle_radius = sc.Quantity(Sample.particle_radius, 'nm')
thickness = sc.Quantity(Sample.thickness, 'um')
particle_index = sc.Quantity(Sample.particle_index, '')
matrix_index = sc.Quantity(Sample.matrix_index, '')
medium_index = sc.Quantity(Sample.medium_index, '')
incident_angle = Sample.incident_angle
wavelength = sc.Quantity(Sample.wavelength, 'nm')
# Calculate the effective index of the sample
sample_index = ri.n_eff(particle_index, matrix_index, volume_fraction)
reflectance = []
transmittance = []
for i in np.arange(len(wavelength)):
# Calculate the phase function and scattering and absorption lengths
# from the single scattering model
p, mu_scat, mu_abs = mc.calc_scat(particle_radius,
particle_index[i],
sample_index[i],
volume_fraction,
wavelength[i],
phase_mie=False,
mu_scat_mie=False)
# Initialize the trajectories
r0, k0, W0 = mc.initialize(nevents,
ntrajectories,
medium_index[i],
sample_index[i],
seed=seed,
incidence_angle=incident_angle)
r0 = sc.Quantity(r0, 'um')
k0 = sc.Quantity(k0, '')
W0 = sc.Quantity(W0, '')
# Generate a matrix of all the randomly sampled angles first
sintheta, costheta, sinphi, cosphi, _, _ = mc.sample_angles(
nevents, ntrajectories, p)
# Create step size distribution
step = mc.sample_step(nevents, ntrajectories, mu_abs, mu_scat)
# Create trajectories object
trajectories = mc.Trajectory(r0, k0, W0)
# Run photons
trajectories.absorb(mu_abs, step)
trajectories.scatter(sintheta, costheta, sinphi, cosphi)
trajectories.move(step)
# Calculate the reflection fraction
R_fraction, T_fraction = mc.calc_refl_trans(trajectories,
sc.Quantity('0.0 um'),
thickness,
medium_index[i],
sample_index[i],
detection_angle=np.pi / 2)
reflectance.append(R_fraction)
transmittance.append(T_fraction)
# Define an array for the visible wavelengths
wavelength_sigma = sc.Quantity(np.arange(400, 1000, 61), 'nm')
# The uncertainty for the reflection fraction is taken to be 1 standard
# deviation from the mean, and was calculated using the results of 100 identical runs.
sigma_measured = np.array([
1.578339786806479475e-02, 1.814049675099610806e-02,
2.263508305348480368e-02, 2.280651893165159400e-02,
2.289441072296988580e-02, 2.475289930703982594e-02,
2.591244161256863951e-02, 2.432751507610093206e-02,
2.840212103614853448e-02, 2.464656608869982696e-02,
2.535837658100221007e-02, 2.352910256218017013e-02,
2.264365724262535837e-02, 2.574192164180175851e-02,
2.546192844771695551e-02, 2.767992948024671981e-02,
2.399941085043348632e-02, 2.767133759422578734e-02,
2.759793344858079908e-02, 2.581248267951743655e-02,
2.664000919072649631e-02, 2.914272756298553688e-02,
2.549173729396642454e-02, 2.722649681737301583e-02,
2.322297011391676741e-02, 2.409138186086920430e-02,
2.807311239866464025e-02, 3.018509924866123045e-02,
2.929772336148638717e-02, 2.866675231142475078e-02,
2.377896176281297722e-02, 2.532538972626817778e-02,
2.408458082494839558e-02, 2.823887112376391451e-02,
2.285680624758363796e-02, 2.834624619602043455e-02,
2.342167374818072967e-02, 2.896504983742856365e-02,
2.835463183413225105e-02, 2.981124596936481769e-02,
2.499991827718371987e-02, 2.697080309787770400e-02,
2.788310424558666095e-02, 2.819362357263776805e-02,
2.852537757990830647e-02, 2.651641629976883227e-02,
3.022850005391930842e-02, 2.772006618991802729e-02,
2.971671988748269405e-02, 3.219841220549832933e-02,
2.570752641741474998e-02, 2.352680291863861600e-02,
2.709648629442167056e-02, 2.524674214046034038e-02,
2.758045644043585765e-02, 2.607698592177773098e-02,
2.738258841523178236e-02, 2.868487596917410412e-02,
3.176931078488830218e-02, 2.729837088883461590e-02,
2.513728413028934808e-02
])
# Find the uncertainties corresponding to each wavelength
wavelength_ind = main.find_close_indices(wavelength_sigma, wavelength)
sigma = sigma_measured[np.array(wavelength_ind)]
return main.Spectrum(wavelength.magnitude,
reflectance=np.array(reflectance),
transmittance=np.array(transmittance),
sigma_r=sigma,
sigma_t=sigma)