def arc_model_to_rgb(thickness, porosity, aoi=8):
# Wavelength axis
wavelength = np.arange(360, 801, 5).astype('float')
# Choice of illuminant makes a very small change to the calculated RGB color.
illuminant = 'LED-B3'
# # Scan thickness and porosity.
# thickness = np.arange(0, 196, 5).astype('float')
# porosity = np.arange(0, 0.51, 0.1).astype('float')
# col = np.zeros((3, len(thickness), len(porosity)))
# col_hex = np.empty((len(thickness), len(porosity)), dtype='object')
# xyY = np.zeros((3, len(thickness), len(porosity)))
index_film = refractive_index_porous_silica(wavelength, porosity)
index_substrate = refractive_index_glass(wavelength)
# Calculate reflectance
reflectance = thin_film_reflectance(index_film=index_film,
index_substrate=index_substrate,
film_thickness=thickness,
aoi=aoi,
wavelength=wavelength)
reflectance_ref = thin_film_reflectance(index_film=index_film,
index_substrate=index_substrate,
film_thickness=0,
aoi=aoi,
wavelength=wavelength)
rgb = spectrum_to_rgb(wavelength, reflectance, illuminant=illuminant)
rgb_ref = spectrum_to_rgb(wavelength,
reflectance_ref,
illuminant=illuminant)
# White balance
rgb_wb = rgb / rgb_ref
# Clamp
rgb_wb[rgb_wb >= 1] = 1
rgb_wb[rgb_wb < 0] = 0
return rgb_wb
def arc_model_c(wavelength, thickness, fraction_abraded, fraction_dust,
porosity):
index_film = refractive_index_porous_silica(wavelength=wavelength,
porosity=porosity)
index_substrate = refractive_index_glass(wavelength=wavelength)
thin_film_R = thin_film_reflectance(
index_film=index_film,
index_substrate=index_substrate,
film_thickness=thickness,
wavelength=wavelength,
aoi=aoi
)
#
# thin_film_R = thin_film_reflection_fast(
# wavelength=wavelength,
# thickness=thickness,
# aoi=aoi,
# porosity=porosity)
#
# index_film = index_porous_silica(wavelength=wavelength,
# porosity=porosity)
# thin_film_reflectance = thin_film_reflection(
# polarization='mixed',
# wavelength=wavelength,
# d_list=[np.inf, thickness, np.inf],
# index_film=index_film,
# index_substrate=index_glass,
# aoi=aoi)
glass_reflectance = np.interp(wavelength, wavelength_calc,
glass_reflectance_calc)
reflectance = (1 - fraction_dust) * (
fraction_abraded * glass_reflectance + (
1 - fraction_abraded) * thin_film_R) + fraction_dust
return 100 * reflectance
"""Example test comparing fast explicit method and tmm method for thin film
reflectance.
toddkarin
09/10/2020
"""
import numpy as np
from time import time
from pvarc.materials import refractive_index_glass, refractive_index_porous_silica
from pvarc.tmm import thin_film_reflectance_tmm
from pvarc import thin_film_reflectance
wavelength = np.linspace(200, 1250, 2000)
index_substrate = refractive_index_glass(wavelength)
index_film = refractive_index_porous_silica(wavelength)
aoi = 8
film_thickness = 120
polarization = 'mixed'
start_time = time()
R_tmm = thin_film_reflectance_tmm(index_film=index_film,
index_substrate=index_substrate,
film_thickness=film_thickness,
aoi=aoi,
wavelength=wavelength,
polarization=polarization)
time_tmm = time() - start_time
print('Elapsed time for TMM method: {:.5f} s'.format(time_tmm))
start_time = time()
def arc_reflection_model(wavelength,
thickness=125,
fraction_abraded=0,
porosity=0.3,
fraction_dust=0,
aoi=8,
n0=1.0003):
"""
Return the reflection values for a model of an aged ARC. The reflection
is a linear combination of reflection from a thin film of a variable
thickness and the reflection from BK7 glass.
Parameters
----------
wavelength : ndarray
wavelength in nm
thickness
thickness of ARC in nm.
fraction_abraded
fraction of coating loss. 1 corresponds to 100% of the coating area
removed and only underlying glass is present, 0 corresponds to the
coating covering the entire sample.
fraction_dust
fraction of module area covered by dust with reflectivity of 1. A
value of 0 corresponds to no dust (clean sample), 1 to full dust
coverage (reflectivity of 1).
aoi
angle of incidence in degrees.
Returns
-------
reflectance : ndarray
Reflectance of sample at the values of wavelength specified.
"""
index_substrate = refractive_index_glass(wavelength)
index_film = refractive_index_porous_silica(wavelength, porosity=porosity)
glass_reflectance = single_interface_reflectance(
n0=n0,
n1=index_substrate,
polarization='mixed',
aoi=aoi)
thin_film_R = thin_film_reflectance(index_film=index_film,
index_substrate=index_substrate,
film_thickness=thickness,
aoi=aoi,
wavelength=wavelength)
reflectance = (1 - fraction_dust) * (
fraction_abraded * glass_reflectance + (
1 - fraction_abraded) * thin_film_R) + fraction_dust
return reflectance
def fit_arc_reflection_spectrum(wavelength,
reflectance,
x0=None,
aoi=8,
model='d',
fixed=None,
verbose=False,
method='basinhopping',
niter=20,
wavelength_min=450,
wavelength_max=1000):
"""
This function fits an ARC model to the reflection spectrum. The ARC model
is described in the function arc_reflection_model.
Parameters
----------
wavelength : ndarray
Wavelength in nm
reflectance : ndarray
Fractional reflection between 0 and 1, unitless.
x0 : dict
Startpoint for fitting algorithm.
aoi : float
Angle of incidence of light
model : str
Different variation of the same model are available. The model is
described under the function `arc_reflection_model`. The fixed values
are specified in the input 'fixed'.
'TP' - thickness and poristy are fit, fraction_abraded and fraction_dust
set to fixed values.
'TPA' - thickness, porosity and fraction_abraded are fit,
fraction_dust is fixed.
'TPAD' - thickness, porosity, fraction_abraded and fraction_dust are
fit.
'TAD' - thickness, fraction_abraded, fraction_dust are fit, porosity
is a fixed value.
fixed : dict
Dictionary of parameters to be fixed. Default is:
fixed = {'thickness': 125, 'fraction_abraded': 0, 'fraction_dust': 0,
'porosity': 0.3}
verbose : bool
Whether to print output at each iteration.
method : str
Optimization method, can be 'minimize' or 'basinhopping'
niter : int
Number of basinhopping steps if method == 'basinhopping'
wavelength_min : float
Lower bound for wavelength values used in fit.
wavelength_max : float
Upper bound for wavelength values used in fit.
Returns
-------
result : dict
Dictionary of best fit values.
ret
Output of optimizer.
"""
if np.mean(reflectance) > 1:
print(
'Warning: check that reflectance is a fractional value between 0 and 1.')
if x0 == None:
x0 = estimate_arc_reflection_model_params(wavelength, reflectance)
fixed_default = {'thickness': 125,
'fraction_abraded': 0,
'fraction_dust': 0,
'porosity': 0.3}
if fixed == None:
fixed = fixed_default
else:
for p in fixed_default:
if p not in fixed:
fixed[p] = fixed_default[p]
# print('x0: ', x0)
scale = {'thickness': 0.01,
'fraction_abraded': 1,
'fraction_dust': 1000,
'porosity': 1}
if model == 'TPA':
x0_list = [x0['thickness'] * scale['thickness'],
x0['fraction_abraded'] * scale['fraction_abraded'],
x0['porosity'] * scale['porosity']
]
elif model == 'TAD':
x0_list = [x0['thickness'] * scale['thickness'],
x0['fraction_abraded'] * scale['fraction_abraded'],
x0['fraction_dust'] * scale['fraction_dust']
]
elif model == 'TPAD':
x0_list = [x0['thickness'] * scale['thickness'],
x0['fraction_abraded'] * scale['fraction_abraded'],
x0['fraction_dust'] * scale['fraction_dust'],
x0['porosity'] * scale['porosity'],
]
elif model == 'TP':
x0_list = [x0['thickness'] * scale['thickness'],
x0['porosity'] * scale['porosity'],
]
else:
raise Exception('model options are "TP", "TPA", "TPAD" or "TAD"')
# Increase by a factor of 100 to improve numeric accuracy.
reflectance = reflectance * 100
reflectance[reflectance < 0] = 0
reflectance[reflectance > 100] = 100
cax = np.logical_and(wavelength > wavelength_min,
wavelength < wavelength_max)
wavelength_calc = wavelength.copy()
index_substrate = refractive_index_glass(wavelength)
glass_reflectance_calc = single_interface_reflectance(n0=1.0003,
n1=index_substrate,
aoi=aoi,
polarization='mixed',
)
# # Get interpolator for correct
# if not aoi == 8:
# raise Exception('aoi must be 8 degrees.')
thickness_min = 50
thickness_max = 200
porosity_max = 0.499
if model == 'TPA':
bounds = [(thickness_min * scale['thickness'],
thickness_max * scale['thickness']),
(0, 1 * scale['fraction_abraded']),
(0, porosity_max * scale['porosity']),
]
elif model == 'TAD':
bounds = [(thickness_min * scale['thickness'],
thickness_max * scale['thickness']),
(0, 1 * scale['fraction_abraded']),
(0, 1 * scale['fraction_dust']),
]
elif model == 'TPAD':
bounds = [(thickness_min * scale['thickness'],
thickness_max * scale['thickness']),
(0, 1 * scale['fraction_abraded']),
(0, 1 * scale['fraction_dust']),
(0, porosity_max * scale['porosity']),
]
elif model == 'TP':
bounds = [(thickness_min * scale['thickness'],
thickness_max * scale['thickness']),
(0, porosity_max * scale['porosity']),
]
def arc_model_c(wavelength, thickness, fraction_abraded, fraction_dust,
porosity):
index_film = refractive_index_porous_silica(wavelength=wavelength,
porosity=porosity)
index_substrate = refractive_index_glass(wavelength=wavelength)
thin_film_R = thin_film_reflectance(
index_film=index_film,
index_substrate=index_substrate,
film_thickness=thickness,
wavelength=wavelength,
aoi=aoi
)
#
# thin_film_R = thin_film_reflection_fast(
# wavelength=wavelength,
# thickness=thickness,
# aoi=aoi,
# porosity=porosity)
#
# index_film = index_porous_silica(wavelength=wavelength,
# porosity=porosity)
# thin_film_reflectance = thin_film_reflection(
# polarization='mixed',
# wavelength=wavelength,
# d_list=[np.inf, thickness, np.inf],
# index_film=index_film,
# index_substrate=index_glass,
# aoi=aoi)
glass_reflectance = np.interp(wavelength, wavelength_calc,
glass_reflectance_calc)
reflectance = (1 - fraction_dust) * (
fraction_abraded * glass_reflectance + (
1 - fraction_abraded) * thin_film_R) + fraction_dust
return 100 * reflectance
def arc_coating_error_function(x):
# print('x: ',x)
if model == 'TPA':
thickness = x[0] / scale['thickness']
fraction_abraded = x[1] / scale['fraction_abraded']
porosity = x[2] / scale['porosity']
reflectance_model = arc_model_c(wavelength, thickness,
fraction_abraded=fraction_abraded,
fraction_dust=fixed[
'fraction_dust'],
porosity=porosity)
elif model == 'TAD':
thickness = x[0] / scale['thickness']
fraction_abraded = x[1] / scale['fraction_abraded']
fraction_dust = x[2] / scale['fraction_dust']
reflectance_model = arc_model_c(wavelength, thickness,
fraction_abraded, fraction_dust,
porosity=fixed['porosity'])
# if verbose:
# print(
# 'Thickness: {:03.2f}, Fraction Abraded: {:.1%}, Fraction dust: {:.1%}'.format(
# thickness,
# fraction_abraded,
# fraction_dust))
elif model == 'TPAD':
thickness = x[0] / scale['thickness']
fraction_abraded = x[1] / scale['fraction_abraded']
fraction_dust = x[2] / scale['fraction_dust']
porosity = x[3] / scale['porosity']
reflectance_model = arc_model_c(wavelength, thickness,
fraction_abraded, fraction_dust,
porosity)
elif model == 'TP':
thickness = x[0] / scale['thickness']
porosity = x[1] / scale['porosity']
reflectance_model = arc_model_c(wavelength, thickness,
fraction_abraded=fixed[
'fraction_abraded'],
fraction_dust=fixed[
'fraction_dust'],
porosity=porosity)
else:
raise Exception('model type unknown')
residual = np.mean(
np.sqrt(np.abs(reflectance_model - reflectance) ** 2))
return residual
if method == 'minimize':
res = minimize(arc_coating_error_function,
x0=x0_list,
options=dict(
# maxiter=100,
disp=verbose
),
bounds=bounds
)
elif method == 'basinhopping':
def basinhopping_callback(x, f, accept):
if model == 'TPA' and verbose:
# print('x:', x)
print(
'--\nThickness: {:03.2f}, Fraction Abraded: {:.1%}, Porosity: {:.1%}'.format(
x[0] / scale['thickness'],
x[1] / scale['fraction_abraded'],
x[2] / scale['porosity']
)
)
res = basinhopping(arc_coating_error_function,
x0=x0_list,
niter=niter,
minimizer_kwargs={'bounds': bounds},
disp=verbose,
callback=basinhopping_callback
)
if model == 'TPA':
result = {'thickness': res['x'][0] / scale['thickness'],
'fraction_abraded': res['x'][1] / scale['fraction_abraded'],
'fraction_dust': fixed['fraction_dust'],
'porosity': res['x'][2] / scale['porosity']}
elif model == 'TAD':
result = {'thickness': res['x'][0] / scale['thickness'],
'fraction_abraded': res['x'][1] / scale['fraction_abraded'],
'fraction_dust': res['x'][2] / scale['fraction_dust'],
'porosity': fixed['porosity']}
elif model == 'TPAD':
result = {'thickness': res['x'][0] / scale['thickness'],
'fraction_abraded': res['x'][1] / scale['fraction_abraded'],
'fraction_dust': res['x'][2] / scale['fraction_dust'],
'porosity': res['x'][3] / scale['porosity'],
}
elif model == 'TP':
result = {'thickness': res['x'][0] / scale['thickness'],
'fraction_abraded': fixed['fraction_abraded'],
'fraction_dust': fixed['fraction_dust'],
'porosity': res['x'][1] / scale['porosity'],
}
return result, res
x, ret = fit_arc_reflection_spectrum(wavelength,
reflection,
model='TPA',
aoi=8,
wavelength_min=450,
wavelength_max=1000,
method='basinhopping',
verbose=True)
wavelength_extend = np.linspace(300, 1250, 1000)
reflection_fit = arc_reflection_model(wavelength_extend, **x)
# Calculate solar weighted photon reflection (SWPR) using fit
swpr = solar_weighted_photon_reflectance(wavelength_extend, reflection_fit)
# Calculate SWPR for glass reference
index_glass = refractive_index_glass(wavelength_extend)
reflection_BK7 = single_interface_reflectance(n0=1.0003,
n1=index_glass,
aoi=8)
swpr_bk7 = solar_weighted_photon_reflectance(wavelength_extend, reflection_BK7)
# Calculate power enhancement due to coating.
power_enchancement = swpr_bk7 - swpr
# Compare fit vs simulated value.
print('--\nComparison of true values vs. best fit')
for p in ['thickness', 'porosity', 'fraction_abraded']:
print('{}.\t True: {:.2f}, Fit: {:.2f}, '.format(p, param_true[p], x[p]))
# Plot theory.
plt.plot(wavelength_extend,
def calculate_rgb_vs_thickness_porosity(
camera='Ximea-MC050cg_combined_labeled.csv',
light_source='LEDW7E_A01_intensity.csv',
optical_system='MVL23M23.csv',
thickness_max=186,
thickness_step=0.4,
porosity_max=0.5,
porosity_step=0.01,
aoi=0):
# Wavelength axis
wavelength = np.arange(300, 755, 5).astype('float')
dwavelength = wavelength[1] - wavelength[0]
# Scan thickness and porosity.
thickness = np.arange(0, thickness_max, thickness_step).astype('float')
porosity = np.arange(0, porosity_max, porosity_step).astype('float')
# Initialize arrays.
swpr = np.zeros((len(thickness), len(porosity)))
rgb_wb = np.zeros((len(thickness), len(porosity), 3))
# Load Camera QE
qe_fpath = os.path.join(os.path.dirname(__file__), 'cameras',
camera)
df = pd.read_csv(qe_fpath, skiprows=2)
dfi = pd.DataFrame({'Wavelength': wavelength})
for k in ['Red', 'Green', 'Blue']:
dfi[k] = np.interp(wavelength, df['Wavelength'], df[k],
left=0, right=0)
# Load Illuminant spectrum
illum_fpath = os.path.join(os.path.dirname(__file__), 'sources',
light_source)
df_illum = pd.read_csv(illum_fpath, skiprows=2)
# illuminant_sd = ILLUMINANTS_SDS[sources[s]]
# illuminant_conv = ILLUMINANTS['CIE 1931 2 Degree Standard Observer'][illuminant_name]
illuminant_spectrum = np.interp(wavelength, df_illum['Wavelength'],
df_illum['Intensity'], left=0, right=0)
illuminant_spectrum_photon = illuminant_spectrum * wavelength
# Load optical system
optical_system_fpath = os.path.join(os.path.dirname(__file__), 'cameras',
optical_system)
df_optical_system = pd.read_csv(optical_system_fpath, skiprows=2)
optical_system_transmission = 0.01 * np.interp(
wavelength,
df_optical_system['Wavelength'],
df_optical_system['Transmission'],
left=0, right=0)
# Calculate RGB colors
for k in tqdm(range(len(porosity))):
index_film = refractive_index_porous_silica(wavelength, porosity[k])
index_substrate = refractive_index_glass(wavelength)
for j in range(len(thickness)):
# Calculate reflectance
reflectance = thin_film_reflectance(index_film=index_film,
index_substrate=index_substrate,
film_thickness=thickness[j],
aoi=aoi,
wavelength=wavelength)
# for c in ['Blue', 'Green', 'Red']:
# np.sum(reflectance * illuminant_spectrum_photon * dfi[c] / 100) * dwavelength
rgb = np.sum(
reflectance[:, np.newaxis] * \
optical_system_transmission[:, np.newaxis] * \
illuminant_spectrum_photon[:, np.newaxis] * \
np.array(dfi.iloc[:, 1:]) / 100,
axis=0) * dwavelength
swpr[j, k] = solar_weighted_photon_reflectance(wavelength,
reflectance)
# Use first run through, with 0 nm thickness, (i.e. low-iron glass)
# as a reference for white balance.
if thickness[j] == 0:
rgb_ref = rgb.copy()
# White balance
rgb_wb[j, k, :] = rgb / rgb_ref
# x = rgb_wb[0, :, :] / np.sum(rgb_wb, axis=0)
# y = rgb_wb[1, :, :] / np.sum(rgb_wb, axis=0)
# z = rgb_wb[2, :, :] / np.sum(rgb_wb, axis=0)
# t_grid, P_grid = np.meshgrid(thickness, porosity, indexing='ij')
return thickness, porosity, rgb_wb, swpr
"""Example for printing a list of the refractive index of BK7 glass, useful
for performing a light reference in the spectrometer software.
"""
import numpy as np
from pvarc.materials import refractive_index_glass
from pvarc import single_interface_reflectance
wavelength = np.arange(190, 1125, 10)
index_glass = refractive_index_glass(wavelength, type='BK7')
reflectance = single_interface_reflectance(n0=1.0003,
n1=index_glass,
aoi=8.0,
polarization='mixed')
print('Glass reflectance')
for k in range(len(wavelength)):
print('{}\t{:.5f}'.format(wavelength[k], reflectance[k]))
# aoi_scan = np.arange(70,-1,-10)
# aoi_scan = np.array([0,10,20,30,40,50,60,70])
for porosity in [0.15, 0.3]:
plt.figure(0, figsize=(3.7, 3))
plt.clf()
ax = plt.axes()
rect = ax.patch
rect.set_facecolor('k')
Rmat = np.zeros((len(wavelength), len(thickness_scan)))
index_film = refractive_index_porous_silica(wavelength, porosity)
index_film_smooth = refractive_index_porous_silica(wavelength_smooth,
porosity)
index_substrate = refractive_index_glass(wavelength)
index_substrate_smooth = refractive_index_glass(wavelength_smooth)
def smoothit(y, N=10):
return np.convolve(y, np.ones((N, )) / N, mode='valid')
plt.plot(smoothit(source['wavelength'][1:-200]),
smoothit(source['value'][1:-200]) / source['value'][1:-5].max() *
5,
'w--',
label='LED')
for j in range(len(thickness_scan)):
# Calculate reflectance at rough.
Rmat[:, j] = thin_film_reflectance(index_film=index_film,
index_substrate=index_substrate,