321 lines
9.4 KiB
Python
321 lines
9.4 KiB
Python
import numpy as np
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from scipy.optimize import curve_fit
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import matplotlib.pyplot as plt
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plt.rc('text', usetex=True)
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plt.rcParams.update({
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'axes.labelsize': 26,
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'xtick.labelsize': 32,
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'ytick.labelsize': 32,
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'legend.fontsize': 23,
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})
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from .io import load_spectrum
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from .utils import OptimizeResult
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from .analysis import finds_peak
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def thickness_scheludko_at_order(wavelengths,
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intensities,
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interference_order,
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refractive_index,
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Imin=None):
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"""
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Compute the film thickness for a given interference order.
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Parameters
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----------
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wavelengths : array
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Wavelength values in nm.
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intensities : array
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Intensity values.
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interference_order: TYPE
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DESCRIPTION.
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refractive_index : TYPE
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DESCRIPTION.
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Imin : TYPE, optional
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DESCRIPTION. The default is None.
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Returns
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-------
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thickness : TYPE
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DESCRIPTION.
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"""
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if Imin is None:
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Imin = np.min(intensities)
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n = refractive_index
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m = interference_order
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I = (np.asarray(intensities) - Imin) / (np.max(intensities) - Imin)
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prefactor = wavelengths / (2 * np.pi * n)
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argument = np.sqrt(I / (1 + (1 - I) * (n**2 - 1)**2 / (4 * n**2)))
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if m % 2 == 0:
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term1 = (m / 2) * np.pi
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else:
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term1 = ((m+1) / 2) * np.pi
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term2 = (-1)**m * np.arcsin(argument)
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return prefactor * (term1 + term2)
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def Delta(wavelengths, thickness, interference_order, refractive_index):
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"""
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Compute the Delta values.
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Parameters
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----------
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wavelengths : array
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Wavelength values in nm.
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thickness : array_like (or float)
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Film thickness.
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interference_order : int
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Interference order.
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refractive_index : array_like (or float)
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Refractive index.
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Returns
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-------
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ndarray
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Delta values.
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"""
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# ensure that the entries are numpy arrays
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wavelengths = np.asarray(wavelengths)
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h = np.asarray(thickness)
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n = np.asarray(refractive_index)
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m = interference_order
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# Calculation of p as a function of the parity of m
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if m % 2 == 0:
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p = m / 2
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else:
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p = (m + 1) / 2
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# Calculation of alpha
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alpha = ((n**2 - 1)**2) / (4 * n**2)
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# Argument of sinus
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angle = (2 * np.pi * n * h / wavelengths) - p * np.pi
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# A = sin²(argument)
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A = np.sin(angle)**2
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# Final calcuation of Delta
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return (A * (1 + alpha)) / (1 + A * alpha)
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def Delta_fit(xdata, thickness, interference_order):
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"""
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Wrapper on Delta() for curve_fit.
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Parameters
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----------
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xdata : tuple
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(wavelengths, refractive_index)
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thickness : array_like (or float)
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Film thickness.
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interference_order : int
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Interference order.
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Returns
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-------
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ndarray
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Delta values.
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"""
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lambdas, r_index = xdata
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return Delta(lambdas, thickness, interference_order, r_index)
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def thickness_from_scheludko(wavelengths,
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intensities,
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refractive_index,
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min_peak_prominence,
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plot=None):
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"""
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Parameters
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----------
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wavelengths : array
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Wavelength values in nm.
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intensities : array
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Intensity values.
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refractive_index : scalar, optional
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Value of the refractive index of the medium.
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plot : bool, optional
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Display a curve, useful for checking or debuging. The default is None.
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Returns
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-------
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thickness : TYPE
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DESCRIPTION.
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"""
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max_tested_order = 12
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r_index = refractive_index
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peaks_min, peaks_max = finds_peak(wavelengths, intensities,
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min_peak_prominence=min_peak_prominence,
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plot=False)
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# Get the last oscillation peaks
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lambda_min = wavelengths[peaks_min[-1]]
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lambda_max = wavelengths[peaks_max[-1]]
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# Order them
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lambda_start = min(lambda_min, lambda_max)
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lambda_stop = max(lambda_min, lambda_max)
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# mask input data
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mask = (wavelengths >= lambda_start) & (wavelengths <= lambda_stop)
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wavelengths_masked = wavelengths[mask]
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r_index_masked = r_index[mask]
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intensities_masked = intensities[mask]
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min_ecart = np.inf
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best_m = None
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best_h = None
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if plot:
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plt.figure(figsize=(10, 6), dpi=300)
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plt.ylabel(r'$h$ ($\mathrm{{nm}}$)')
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plt.xlabel(r'$\lambda$ ($ \mathrm{nm} $)')
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for m in range(0, max_tested_order+1):
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h_values = thickness_scheludko_at_order(wavelengths_masked,
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intensities_masked,
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m, r_index_masked)
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ecart = np.max(h_values) - np.min(h_values)
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print(f"Écart pour m={m} : {ecart:.3f} nm")
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if ecart < min_ecart:
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min_ecart = ecart
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best_m = m
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best_h = h_values
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if plot:
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plt.plot(wavelengths_masked, h_values,'.', markersize=3, label=f"Épaisseur du film (Scheludko, m={m})")
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# Delta
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num = intensities_masked - np.min(intensities_masked)
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denom = np.max(intensities_masked) - np.min(intensities_masked)
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DeltaVrai = num / denom
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# DeltaVrai = (intensities_masked -np.min(intensities_masked))/(np.max(intensities_masked) -np.min(intensities_masked))
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# DeltaVrai = (intensities_raw_masked -np.min(intensities_raw_masked))/(np.max(intensities_raw_masked) -np.min(intensities_raw_masked))
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DeltaScheludko = Delta(wavelengths_masked,
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np.mean(best_h),
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best_m,
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r_index_masked)
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xdata = (wavelengths_masked, r_index_masked)
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popt, pcov = curve_fit(lambda x, h: Delta_fit(x, h, m), xdata, DeltaVrai, p0=[np.mean(best_h)])
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fitted_h = popt[0]
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if plot:
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Delta_values = Delta(wavelengths_masked, fitted_h, best_m, r_index_masked)
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plt.figure(figsize=(10, 6), dpi=300)
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plt.plot(wavelengths_masked, DeltaVrai,
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'bo-', markersize=2, label=r'$\mathrm{{Smoothed}}\ \mathrm{{Data}}$')
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plt.plot(wavelengths_masked, DeltaScheludko,
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'go-', markersize=2, label = rf'$\mathrm{{Scheludko}}\ (h = {np.mean(best_h):.1f} \pm {np.std(best_h):.1f}\ \mathrm{{nm}})$')
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plt.plot(wavelengths_masked, Delta_values, 'ro-',markersize=2, label=rf'$\mathrm{{Fit}}\ (h = {fitted_h:.1f}\pm {np.sqrt(pcov[0][0]):.1f} \ \mathrm{{nm}})$')
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plt.legend()
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plt.ylabel(r'$\Delta$')
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plt.xlabel(r'$\lambda$ ($ \mathrm{nm} $)')
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return OptimizeResult(thickness=fitted_h ,)
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def thickness_for_order0(wavelengths,
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intensities,
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refractive_index,
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min_peak_prominence,
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plot=None):
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# TODO :
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# Load "trou"
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File_I_min = 'tests/spectre_trou/000043641.xy'
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wavelengths_I_min, intensities_I_min = load_spectrum(File_I_min, lambda_min=450)
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r_index = refractive_index
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peaks_min, peaks_max = finds_peak(wavelengths, intensities,
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min_peak_prominence=min_peak_prominence,
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plot=False)
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lambda_unique = wavelengths[peaks_max[0]]
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# On crée le masque pour ne garder que les wavelengths superieures a wavelengths unique
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mask = wavelengths >= lambda_unique
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wavelengths_masked = wavelengths[mask]
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r_index_masked = r_index[mask]
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intensities_masked = intensities[mask]
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intensities_I_min_masked =intensities_I_min[mask]
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# best_m = None
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# best_h = None
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m = 0
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h_values = thickness_scheludko_at_order(wavelengths_masked,
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intensities_masked,
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0,
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r_index_masked,
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Imin=intensities_I_min_masked)
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if plot:
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plt.figure(figsize=(10, 6), dpi=300)
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plt.plot(wavelengths_masked, h_values, label=r"Épaisseur du film (Scheludko, m=0)")
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best_m = m
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best_h = h_values
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# Delta
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num = intensities_masked - np.min(intensities_I_min_masked)
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denom = np.max(intensities_masked) - np.min(intensities_I_min_masked)
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DeltaVrai = num / denom
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DeltaScheludko = Delta(wavelengths_masked, np.mean(best_h), best_m, r_index_masked)
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#print(np.mean(best_h),np.std(best_h))
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if plot:
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plt.figure(figsize=(10, 6), dpi=300)
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plt.plot(wavelengths_masked,DeltaVrai,'bo-', markersize=2,label=r'$\mathrm{{Raw}}\ \mathrm{{Data}}$')
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plt.plot(wavelengths_masked,DeltaScheludko,'ro-', markersize=2,label = rf'$\mathrm{{Scheludko}}\ (h = {np.mean(best_h):.1f} \pm {np.std(best_h):.1f}\ \mathrm{{nm}})$')
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xdata = (wavelengths_masked, r_index_masked)
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popt, pcov = curve_fit(lambda x, h: Delta_fit(x, h, m), xdata, DeltaVrai, p0=[np.mean(best_h)])
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fitted_h = popt[0]
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if plot:
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Delta_values = Delta(wavelengths_masked, fitted_h, best_m, r_index_masked)
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plt.plot(wavelengths_masked, Delta_values,
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'go-', markersize=2,
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label=rf'$\mathrm{{Fit}}\ (h = {fitted_h:.1f}\pm {np.sqrt(pcov[0][0]):.1f} \ \mathrm{{nm}})$')
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plt.legend()
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plt.ylabel(r'$\Delta$')
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plt.xlabel(r'$\lambda$ (nm)')
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return OptimizeResult(thickness=fitted_h,)
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