330 lines
9.5 KiB
Python
330 lines
9.5 KiB
Python
import numpy as np
|
|
from scipy.optimize import curve_fit
|
|
|
|
import matplotlib.pyplot as plt
|
|
plt.rc('text', usetex=True)
|
|
plt.rcParams.update({
|
|
'axes.labelsize': 26,
|
|
'xtick.labelsize': 32,
|
|
'ytick.labelsize': 32,
|
|
'legend.fontsize': 23,
|
|
})
|
|
|
|
from .io import load_spectrum
|
|
from .utils import OptimizeResult
|
|
from .analysis import finds_peak
|
|
|
|
|
|
def thickness_scheludko_at_order(wavelengths,
|
|
intensities,
|
|
interference_order,
|
|
refractive_index,
|
|
Imin=None):
|
|
"""
|
|
Compute the film thickness for a given interference order.
|
|
|
|
Parameters
|
|
----------
|
|
wavelengths : array
|
|
Wavelength values in nm.
|
|
intensities : array
|
|
Intensity values.
|
|
interference_order: TYPE
|
|
DESCRIPTION.
|
|
refractive_index : TYPE
|
|
DESCRIPTION.
|
|
Imin : TYPE, optional
|
|
DESCRIPTION. The default is None.
|
|
|
|
Returns
|
|
-------
|
|
thickness : TYPE
|
|
DESCRIPTION.
|
|
|
|
"""
|
|
if Imin is None:
|
|
Imin = np.min(intensities)
|
|
|
|
n = refractive_index
|
|
m = interference_order
|
|
I = (np.asarray(intensities) - Imin) / (np.max(intensities) - Imin)
|
|
|
|
|
|
prefactor = wavelengths / (2 * np.pi * n)
|
|
argument = np.sqrt(I / (1 + (1 - I) * (n**2 - 1)**2 / (4 * n**2)))
|
|
|
|
if m % 2 == 0:
|
|
term1 = (m / 2) * np.pi
|
|
else:
|
|
term1 = ((m+1) / 2) * np.pi
|
|
|
|
term2 = (-1)**m * np.arcsin(argument)
|
|
|
|
return prefactor * (term1 + term2)
|
|
|
|
|
|
|
|
"""
|
|
Calculates the Delta value for arrays of wavelengths, thicknesses h and r_indexs n.
|
|
|
|
Parameters:
|
|
- wavelengths: array_like (or float), wavelengths λ
|
|
- thickness : array_like (or float), thicknesses h
|
|
- interference_order : int, interference order
|
|
- refractive_index : array_like (or float), refractive r_indexs n
|
|
|
|
Returns:
|
|
- delta: ndarray of corresponding Δ values
|
|
"""
|
|
|
|
|
|
def Delta(wavelengths, thickness, interference_order, refractive_index):
|
|
"""
|
|
|
|
|
|
Parameters
|
|
----------
|
|
wavelengths : array
|
|
Wavelength values in nm.
|
|
thickness : array_like (or float)
|
|
Film thickness.
|
|
interference_order : int
|
|
Interference order.
|
|
refractive_index : array_like (or float)
|
|
Refractive index.
|
|
|
|
Returns
|
|
-------
|
|
TYPE
|
|
DESCRIPTION.
|
|
|
|
"""
|
|
|
|
# ensure that the entries are numpy arrays
|
|
wavelengths = np.asarray(wavelengths)
|
|
h = np.asarray(thickness)
|
|
n = np.asarray(refractive_index)
|
|
m = interference_order
|
|
|
|
# Calculation of p as a function of the parity of m
|
|
if m % 2 == 0:
|
|
p = m / 2
|
|
else:
|
|
p = (m + 1) / 2
|
|
|
|
# Calculation of alpha
|
|
alpha = ((n**2 - 1)**2) / (4 * n**2)
|
|
|
|
# Argument of sinus
|
|
angle = (2 * np.pi * n * h / wavelengths) - p * np.pi
|
|
|
|
# A = sin²(argument)
|
|
A = np.sin(angle)**2
|
|
|
|
# Final calcuation of Delta
|
|
return (A * (1 + alpha)) / (1 + A * alpha)
|
|
|
|
|
|
|
|
def Delta_fit(xdata, thickness, interference_order):
|
|
"""
|
|
Wrapper on Delta() for curve_fit.
|
|
|
|
Parameters
|
|
----------
|
|
xdata : tuple
|
|
(wavelengths, n)
|
|
thickness : array_like (or float)
|
|
Film thickness.
|
|
interference_order : int
|
|
Interference order.
|
|
|
|
Returns
|
|
-------
|
|
ndarray
|
|
Delta values.
|
|
|
|
"""
|
|
lambdas, n = xdata
|
|
return Delta(lambdas, thickness, interference_order, n)
|
|
|
|
|
|
|
|
|
|
def thickness_from_scheludko(wavelengths,
|
|
intensities,
|
|
refractive_index,
|
|
min_peak_prominence,
|
|
plot=None):
|
|
"""
|
|
|
|
|
|
Parameters
|
|
----------
|
|
wavelengths : array
|
|
Wavelength values in nm.
|
|
intensities : array
|
|
Intensity values.
|
|
refractive_index : scalar, optional
|
|
Value of the refractive index of the medium.
|
|
plot : bool, optional
|
|
Display a curve, useful for checking or debuging. The default is None.
|
|
|
|
Returns
|
|
-------
|
|
thickness : TYPE
|
|
DESCRIPTION.
|
|
|
|
"""
|
|
max_tested_order = 12
|
|
r_index = refractive_index
|
|
|
|
peaks_min, peaks_max = finds_peak(wavelengths, intensities,
|
|
min_peak_prominence=min_peak_prominence,
|
|
plot=False)
|
|
|
|
# Get the last oscillation peaks
|
|
lambda_min = wavelengths[peaks_min[-1]]
|
|
lambda_max = wavelengths[peaks_max[-1]]
|
|
|
|
# Order them
|
|
lambda_start = min(lambda_min, lambda_max)
|
|
lambda_stop = max(lambda_min, lambda_max)
|
|
|
|
# mask input data
|
|
mask = (wavelengths >= lambda_start) & (wavelengths <= lambda_stop)
|
|
wavelengths_masked = wavelengths[mask]
|
|
r_index_masked = r_index[mask]
|
|
intensities_masked = intensities[mask]
|
|
|
|
|
|
min_ecart = np.inf
|
|
best_m = None
|
|
meilleure_h = None
|
|
|
|
if plot:
|
|
plt.figure(figsize=(10, 6),dpi =600)
|
|
plt.ylabel(r'$h$ ($\mathrm{{nm}}$)')
|
|
plt.xlabel(r'$\lambda$ ($ \mathrm{nm} $)')
|
|
|
|
|
|
for m in range(0, max_tested_order+1):
|
|
h_values = thickness_scheludko_at_order(wavelengths_masked, intensities_masked, m, r_index_masked)
|
|
|
|
if plot:
|
|
plt.plot(wavelengths_masked, h_values,'.', markersize=3, label=f"Épaisseur du film (Scheludko, m={m})")
|
|
ecart = np.max(h_values)-np.min(h_values)
|
|
|
|
print(f"Écart pour m={m} : {ecart:.3f} nm")
|
|
|
|
if ecart < min_ecart:
|
|
min_ecart = ecart
|
|
best_m = m
|
|
meilleure_h = h_values
|
|
|
|
|
|
DeltaVrai = (intensities_masked -np.min(intensities_masked))/(np.max(intensities_masked) -np.min(intensities_masked))
|
|
#DeltaVrai = (intensities_raw_masked -np.min(intensities_raw_masked))/(np.max(intensities_raw_masked) -np.min(intensities_raw_masked))
|
|
|
|
DeltaScheludko = Delta(wavelengths_masked, np.mean(meilleure_h), best_m, r_index_masked)
|
|
#print(np.mean(meilleure_h),np.std(meilleure_h))
|
|
|
|
if plot:
|
|
plt.figure(figsize=(10, 6), dpi=600)
|
|
plt.plot(wavelengths_masked, DeltaVrai,
|
|
'bo-', markersize=2, label=r'$\mathrm{{Smoothed}}\ \mathrm{{Data}}$')
|
|
plt.plot(wavelengths_masked, DeltaScheludko,
|
|
'go-', markersize=2, label = rf'$\mathrm{{Scheludko}}\ (h = {np.mean(meilleure_h):.1f} \pm {np.std(meilleure_h):.1f}\ \mathrm{{nm}})$')
|
|
|
|
|
|
xdata = (wavelengths_masked, r_index_masked)
|
|
popt, pcov = curve_fit(lambda x, h: Delta_fit(x, h, m), xdata, DeltaVrai, p0=[np.mean(meilleure_h)])
|
|
fitted_h = popt[0]
|
|
|
|
|
|
if plot:
|
|
plt.plot(wavelengths_masked, Delta(wavelengths_masked, fitted_h, best_m, r_index_masked ), 'ro-',markersize=2, label=rf'$\mathrm{{Fit}}\ (h = {fitted_h:.1f}\pm {np.sqrt(pcov[0][0]):.1f} \ \mathrm{{nm}})$')
|
|
plt.legend()
|
|
plt.ylabel(r'$\Delta$')
|
|
plt.xlabel(r'$\lambda$ ($ \mathrm{nm} $)')
|
|
|
|
|
|
return OptimizeResult(thickness=fitted_h ,)
|
|
|
|
|
|
def thickness_for_order0(wavelengths,
|
|
intensities,
|
|
refractive_index,
|
|
min_peak_prominence,
|
|
plot=None):
|
|
|
|
|
|
File_I_min = 'tests/spectre_trou/000043641.xy'
|
|
r_index = refractive_index
|
|
|
|
peaks_min, peaks_max = finds_peak(wavelengths, intensities,
|
|
min_peak_prominence=min_peak_prominence,
|
|
plot=False)
|
|
|
|
|
|
|
|
|
|
wavelengths_I_min, intensities_I_min = load_spectrum(File_I_min, lambda_min=450)
|
|
|
|
lambda_unique = wavelengths[peaks_max[0]]
|
|
|
|
|
|
# On crée le masque pour ne garder que les wavelengths superieures a wavelengths unique
|
|
mask = wavelengths >= lambda_unique
|
|
wavelengths_masked = wavelengths[mask]
|
|
r_index_masked = r_index[mask]
|
|
intensities_masked = intensities[mask]
|
|
intensities_I_min_masked =intensities_I_min[mask]
|
|
|
|
min_ecart = np.inf
|
|
best_m = None
|
|
meilleure_h = None
|
|
|
|
|
|
m = 0
|
|
h_values = thickness_scheludko_at_order(wavelengths_masked,
|
|
intensities_masked,
|
|
0,
|
|
r_index_masked,
|
|
Imin=intensities_I_min_masked)
|
|
|
|
if plot:
|
|
plt.figure(figsize=(10, 6), dpi=600)
|
|
plt.plot(wavelengths_masked, h_values, label=r"Épaisseur du film (Scheludko, m=0)")
|
|
|
|
ecart = np.max(h_values) - np.min(h_values)
|
|
best_m = m
|
|
meilleure_h = h_values
|
|
|
|
|
|
|
|
DeltaVrai = (intensities_masked -np.min(intensities_I_min_masked))/(np.max(intensities_masked) -np.min(intensities_I_min_masked))
|
|
|
|
#DeltaVrai = (intensities_masked -np.min(intensities_masked))/(np.max(intensities_masked) -np.min(intensities_masked))
|
|
|
|
DeltaScheludko = Delta(wavelengths_masked, np.mean(meilleure_h), best_m, r_index_masked)
|
|
#print(np.mean(meilleure_h),np.std(meilleure_h))
|
|
|
|
|
|
if plot:
|
|
plt.figure(figsize=(10, 6), dpi=600)
|
|
plt.plot(wavelengths_masked,DeltaVrai,'bo-', markersize=2,label=r'$\mathrm{{Raw}}\ \mathrm{{Data}}$')
|
|
plt.plot(wavelengths_masked,DeltaScheludko,'ro-', markersize=2,label = rf'$\mathrm{{Scheludko}}\ (h = {np.mean(meilleure_h):.1f} \pm {np.std(meilleure_h):.1f}\ \mathrm{{nm}})$')
|
|
|
|
|
|
xdata = (wavelengths_masked, r_index_masked)
|
|
popt, pcov = curve_fit(lambda x, h: Delta_fit(x, h, m), xdata, DeltaVrai, p0=[np.mean(meilleure_h)])
|
|
fitted_h = popt[0]
|
|
|
|
if plot:
|
|
plt.plot(wavelengths_masked, Delta(wavelengths_masked, fitted_h, best_m, r_index_masked ), 'go-',markersize=2, label=rf'$\mathrm{{Fit}}\ (h = {fitted_h:.1f}\pm {np.sqrt(pcov[0][0]):.1f} \ \mathrm{{nm}})$')
|
|
plt.legend()
|
|
plt.ylabel(r'$\Delta$')
|
|
plt.xlabel(r'$\lambda$ (nm)')
|
|
|
|
return OptimizeResult(thickness=fitted_h ,)
|