def Prominence_from_fft(lambdas, intensities, refractive_index, num_half_space=None, plot=True):
    if num_half_space is None:
        num_half_space = len(lambdas)

    # # # 1. Spectre original
    # if plot:
    #     plt.figure(figsize=(10, 6), dpi=150)
    #     plt.plot(1/lambdas, intensities, label='Spectre original')
    #     plt.xlabel('1/Longueur d\'onde (nm-1)')
    #     plt.ylabel('Intensité')
    #     plt.legend()
    #     plt.show()


    # 2. Conversion lambda → k = n(λ) / λ
    k_vals = refractive_index / lambdas
    f_interp = interp1d(k_vals, intensities, kind='linear', fill_value="extrapolate")

    # 3. Axe k uniforme + interpolation
    k_linspace = np.linspace(k_vals[0], k_vals[-1], 2 * num_half_space)
    intensities_k = f_interp(k_linspace)

    # 4. FFT
    delta_k = (k_vals[-1] - k_vals[0]) / (2 * num_half_space)
    fft_vals = fft(intensities_k)
    freqs = fftfreq(2 * num_half_space, delta_k)

    # 5. Pic FFT
    freqs_pos = freqs[freqs > 0]
    abs_fft_pos = np.abs(fft_vals[freqs > 0])
    idx_max = np.argmax(abs_fft_pos)
    F_max = freqs_pos[idx_max]

    if plot:
        plt.figure(figsize=(10, 6), dpi=150)
        plt.plot(freqs_pos, abs_fft_pos, label='|FFT|')
        plt.axvline(F_max, color='r', linestyle='--', label='Pic principal')
        plt.xlabel('Distance optique [nm]')
        plt.ylabel(r'FFT($I^*$)')
        plt.xscale('log')
        plt.yscale('log')
        plt.legend()
        plt.show()

    # 6. Filtrage (garde hautes fréquences)
    cutoff_HF =  2*F_max
    
    mask_HF = np.abs(freqs) >= cutoff_HF
    fft_filtered_HF = np.zeros_like(fft_vals, dtype=complex)
    fft_filtered_HF[mask_HF] = fft_vals[mask_HF]
    
    # 7. Filtrage (garde basses fréquences)
    cutoff_BF =  10*F_max
    mask_BF = np.abs(freqs) <= cutoff_BF
    fft_filtered_BF = np.zeros_like(fft_vals, dtype=complex)
    fft_filtered_BF[mask_BF] = fft_vals[mask_BF]
    
    
    # 8. Reconstruction
    signal_filtered_HF = np.real(ifft(fft_filtered_HF))
    signal_filtered_BF = np.real(ifft(fft_filtered_BF))
    lambda_reconstructed = np.interp(k_linspace, k_vals[::-1], lambdas[::-1])

    # Masque dans la plage [550, 700] nm
    mask_Cam_Sensitivity = (lambda_reconstructed >= 550) & (lambda_reconstructed <= 700)
    
    # 9. Affichage reconstruction
    if plot:
        plt.figure(figsize=(10, 6), dpi=150)
        plt.plot(lambda_reconstructed, intensities_k, '--', label='Original interpolé')
        plt.plot(lambda_reconstructed, signal_filtered_HF,'--',color='gray')

        plt.plot(lambda_reconstructed[mask_Cam_Sensitivity], signal_filtered_HF[mask_Cam_Sensitivity],color='orange', label='Spectre filtré HF')
        plt.plot(lambda_reconstructed, signal_filtered_BF, label='Spectre filtré BF')

        plt.xlabel('Longueur d\'onde (nm)')
        plt.ylabel('Intensité')
        plt.legend()
        plt.show()

    max_amplitude = np.max(np.abs(signal_filtered_HF[mask_Cam_Sensitivity]))
    
    return max_amplitude,signal_filtered_BF,lambda_reconstructed