Quantized Lippmann.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Fully discretized Lippmann"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 250,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Populating the interactive namespace from numpy and matplotlib\n"
     ]
    }
   ],
   "source": [
    "%pylab inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "import seaborn as sns\n",
    "\n",
    "def get_figure_hd(axes = [0,0,1,1]):\n",
    "    fig = plt.figure(figsize=(1920/300, 1080/300), dpi=300, facecolor='black', frameon = False)\n",
    "    ax = plt.Axes(fig, axes, )\n",
    "    ax.set_axis_off()\n",
    "    fig.add_axes(ax)\n",
    "    \n",
    "    return fig\n",
    "\n",
    "def get_figure_2hd(axes = [0,0,1,1]):\n",
    "    fig = plt.figure(figsize=(3840/300, 1080/300), dpi=300, facecolor='black', frameon = False)\n",
    "    ax = plt.Axes(fig, axes, )\n",
    "    ax.set_axis_off()\n",
    "    fig.add_axes(ax)\n",
    "    \n",
    "    return fig\n",
    "\n",
    "def plot_style():\n",
    "    \n",
    "    plt.gca().xaxis.set_ticklabels([])\n",
    "    plt.gca().yaxis.set_ticklabels([])\n",
    "    plt.gca().set_axis_bgcolor('black')\n",
    "    plt.ylim([-2,2])\n",
    "    plt.yticks([])\n",
    "    plt.xticks([])\n",
    "    \n",
    "def plot_style_color():\n",
    "    \n",
    "    plt.gca().xaxis.set_ticklabels([])\n",
    "    plt.gca().yaxis.set_ticklabels([])\n",
    "    plt.gca().set_axis_bgcolor('black')\n",
    "    plt.yticks([])\n",
    "    plt.xticks([])\n",
    "    \n",
    "def save_figure(idx):\n",
    "    plt.savefig('Frames/' + str(idx).zfill(4) +  '.png', dpi=300, bbox_inches='tight', facecolor=plt.gcf().get_facecolor(), transparent=True)\n",
    "\n",
    "def plot_mono_plane_wave(A0, space, time, idx):\n",
    "    \n",
    "    omega = 2*np.pi\n",
    "    \n",
    "    U_r   = A0 * np.exp(-1j*space)\n",
    "    U_r_t = U_r * np.exp(1j*omega*time)\n",
    "    \n",
    "    fig = get_figure_hd()\n",
    "    \n",
    "    plt.plot(space, np.real(U_r_t), c='#55D7FF', lw=6)\n",
    "    plot_style()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 314,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import scipy as sp\n",
    "from scipy.interpolate import interp1d\n",
    "from skimage.color import rgb2xyz, xyz2rgb\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "\n",
    "def read_cie_data(wavelengths):\n",
    "    \n",
    "    cie_data = np.genfromtxt('cie_cmf.txt', delimiter='\t')\n",
    "    wavelengths_cie = cie_data[:,0]*1E-9     \n",
    "    cmf_cie = cie_data[:,1:4]\n",
    "        \n",
    "    cmf_cie_interp_x = interp1d(wavelengths_cie, cmf_cie[:,0], kind='cubic', bounds_error=False, fill_value=0.0)(wavelengths)     \n",
    "    cmf_cie_interp_y = interp1d(wavelengths_cie, cmf_cie[:,1], kind='cubic', bounds_error=False, fill_value=0.0)(wavelengths)\n",
    "    cmf_cie_interp_z = interp1d(wavelengths_cie, cmf_cie[:,2], kind='cubic', bounds_error=False, fill_value=0.0)(wavelengths)      \n",
    "  \n",
    "    return cmf_cie_interp_x, cmf_cie_interp_y, cmf_cie_interp_z\n",
    "\n",
    "def from_spectrum_to_xyz(wavelengths, spectral_colors, normalize=True):\n",
    "    \n",
    "    c = 299792458    \n",
    "    \n",
    "    cmf_cie_x, cmf_cie_y, cmf_cie_z = read_cie_data(wavelengths=wavelengths)\n",
    "    nu = c/wavelengths\n",
    "        \n",
    "    X = np.trapz(y=spectral_colors*cmf_cie_x, x=nu, axis=spectral_colors.ndim-1)\n",
    "    Y = np.trapz(y=spectral_colors*cmf_cie_y, x=nu, axis=spectral_colors.ndim-1)    \n",
    "    Z = np.trapz(y=spectral_colors*cmf_cie_z, x=nu, axis=spectral_colors.ndim-1)  \n",
    "    \n",
    "    #'normalize'\n",
    "    if normalize:\n",
    "        normalization_cste = np.max(Y)\n",
    "        X = X/normalization_cste\n",
    "        Y = Y/normalization_cste\n",
    "        Z = Z/normalization_cste\n",
    "        \n",
    "    return np.stack([X,Y,Z], axis=-1)\n",
    "    \n",
    "def from_xyz_to_rgb(xyz_colors, normalize=True):\n",
    "    \n",
    "    rgb_colors = xyz2rgb(xyz_colors)\n",
    "    \n",
    "    if normalize:\n",
    "        return rgb_colors/np.max(rgb_colors)\n",
    "    else:\n",
    "        return rgb_colors\n",
    "    \n",
    "def from_rgb_to_xyz(rgb_colors, normalize=True):\n",
    "    \n",
    "    xyz_colors = rgb2xyz(rgb_colors)\n",
    "    \n",
    "    if normalize:\n",
    "        return xyz_colors/np.max(xyz_colors)\n",
    "    else:\n",
    "        return xyz_colors\n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 315,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def plot_spectrum_poly(wavelengths, spectrum, visible=False):\n",
    "    \n",
    "    fig = get_figure_hd()\n",
    "    \n",
    "    if visible:\n",
    "        i = np.where( (wavelengths >= 390E-9) & (wavelengths <= 700E-9) )\n",
    "        wavelengths   = wavelengths[i]\n",
    "        spectrum = spectrum[i] \n",
    "    \n",
    "    colors = plt.cm.Spectral_r(np.linspace(0, 1, len(wavelengths)))\n",
    "    cs = [colors[i] for i in range(len(wavelengths))]\n",
    "    \n",
    "    plt.plot(wavelengths, spectrum, c='black', alpha=0.3, lw=1, zorder=1)\n",
    "    plt.scatter(wavelengths, spectrum, color=cs, s=20, zorder=2)    \n",
    "    \n",
    "    plot_style_color()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 741,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "#functions to plot the plates\n",
    "\n",
    "def plot_intensity_reflected_pulsed_plane_wave(z, wavelengths, spectrum, color, normalization, plot=True):\n",
    "    \n",
    "    #true value of wavelengths\n",
    "    wavelengths = wavelengths*1E-9\n",
    "    \n",
    "    c     = 299792458  #speed of light\n",
    "    \n",
    "    wave = np.zeros(len(z))\n",
    "\n",
    "    for i, wavelength in enumerate(wavelengths):\n",
    "    \n",
    "        nu    = c/wavelength\n",
    "        omega = 2*np.pi*nu\n",
    "        k     = omega/c\n",
    "\n",
    "        space = k*z\n",
    "        \n",
    "        wave += spectrum[i]**4*np.sin(2*pi*nu*z/c)**2\n",
    "\n",
    "    if plot:\n",
    "        fig = get_figure_hd()\n",
    "\n",
    "        plt.plot(z, wave/normalization, c='#55D7FF', lw=6)\n",
    "        plot_style()\n",
    "        plt.ylim([-1.1, 1.1])\n",
    "\n",
    "        save_figure(0)\n",
    "\n",
    "        plt.close(fig)\n",
    "        \n",
    "    return wave/normalization\n",
    "\n",
    "def plot_plate(wavelengths, spectrum, plate, visible=False):\n",
    "    \n",
    "    #plot spectrum\n",
    "    plot_spectrum_poly(wavelengths, spectrum, visible=visible)\n",
    "    \n",
    "    #plot plate\n",
    "    fig = get_figure_hd()\n",
    "    plt.imshow(plate, extent=[0, 1, -1.1, 1.1], aspect='auto', origin='upper', zorder=2, cmap='gray', vmin = np.min(plate), vmax = np.max(plate), interpolation='nearest')\n",
    "    plt.axis('off');\n",
    "    \n",
    "    \n",
    "\n",
    "def plot_plate_mono(mu=450, plate_depth=20, n_freq=1000, n_pixels=1000, n_depth=1000, windowed=False):\n",
    "\n",
    "    wavelengths = np.linspace(390, 700, n_freq)\n",
    "    z           = np.linspace(0, plate_depth*390E-9, n_depth)\n",
    "\n",
    "    spectrum    = zeros(len(wavelengths))\n",
    "    spectrum[np.argmin(np.abs(wavelengths-mu))] = 1\n",
    "    intensity = plot_intensity_reflected_pulsed_plane_wave(z, wavelengths, spectrum=spectrum, color=np.argmin(np.abs(wavelengths-mu)), normalization=np.sum(spectrum)/2, plot=False) \n",
    "    \n",
    "    if windowed:\n",
    "        intensity *= np.cos(np.linspace(0, np.pi/2, n_depth)) \n",
    "    \n",
    "    plate = tile(intensity, [n_pixels, 1])\n",
    "    \n",
    "    plot_plate(wavelengths, spectrum, plate)\n",
    "    \n",
    "    return plate, intensity, z, spectrum\n",
    "    \n",
    "    \n",
    "def plot_plate_gaussian(mu=450, sigma=30, plate_depth=20, n_freq=1000, n_pixels=1000, n_depth=1000, windowed=False):\n",
    "\n",
    "    wavelengths = np.linspace(390, 700, n_freq)\n",
    "    z           = np.linspace(0, plate_depth*390E-9, n_depth)\n",
    "\n",
    "    spectrum    = exp(-(wavelengths-mu)**2/(2*sigma**2))/sqrt(2*pi*sigma**2)\n",
    "    intensity = plot_intensity_reflected_pulsed_plane_wave(z, wavelengths, spectrum=spectrum, color=np.argmin(np.abs(wavelengths-mu)), normalization=np.sum(spectrum)/100, plot=False) \n",
    "\n",
    "    if windowed:\n",
    "        intensity *= np.cos(np.linspace(0, np.pi/2, n_depth))\n",
    "    \n",
    "    plate = tile(intensity, [n_pixels, 1])\n",
    "    \n",
    "    plot_plate(wavelengths, spectrum, plate)\n",
    "    \n",
    "    return plate, intensity, z, spectrum\n",
    "\n",
    "def quantize_plate(intensity, n_pixels=1000):\n",
    "    \n",
    "    plate = np.zeros([n_pixels, len(intensity)])\n",
    "    int_max = np.max(intensity)\n",
    "    \n",
    "    for idx, i in enumerate(intensity):\n",
    "        plate[:, idx] = (np.random.rand(n_pixels) < i/int_max).astype(np.int)\n",
    "        \n",
    "    #plot plate\n",
    "    fig = get_figure_hd()\n",
    "    plt.imshow(plate, extent=[0, 1, -1.1, 1.1], aspect='auto', origin='upper', zorder=2, cmap='gray', vmin = np.min(plate), vmax = np.max(plate), interpolation='nearest')\n",
    "    plt.axis('off');\n",
    "    \n",
    "    return plate\n",
    "    \n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 723,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([  1.00000000e+00,   9.99874128e-01,   9.99496542e-01,\n",
       "         9.98867339e-01,   9.97986676e-01,   9.96854776e-01,\n",
       "         9.95471923e-01,   9.93838464e-01,   9.91954813e-01,\n",
       "         9.89821442e-01,   9.87438889e-01,   9.84807753e-01,\n",
       "         9.81928697e-01,   9.78802446e-01,   9.75429787e-01,\n",
       "         9.71811568e-01,   9.67948701e-01,   9.63842159e-01,\n",
       "         9.59492974e-01,   9.54902241e-01,   9.50071118e-01,\n",
       "         9.45000819e-01,   9.39692621e-01,   9.34147860e-01,\n",
       "         9.28367933e-01,   9.22354294e-01,   9.16108457e-01,\n",
       "         9.09631995e-01,   9.02926538e-01,   8.95993774e-01,\n",
       "         8.88835449e-01,   8.81453363e-01,   8.73849377e-01,\n",
       "         8.66025404e-01,   8.57983413e-01,   8.49725430e-01,\n",
       "         8.41253533e-01,   8.32569855e-01,   8.23676581e-01,\n",
       "         8.14575952e-01,   8.05270258e-01,   7.95761841e-01,\n",
       "         7.86053095e-01,   7.76146464e-01,   7.66044443e-01,\n",
       "         7.55749574e-01,   7.45264450e-01,   7.34591709e-01,\n",
       "         7.23734038e-01,   7.12694171e-01,   7.01474888e-01,\n",
       "         6.90079011e-01,   6.78509412e-01,   6.66769001e-01,\n",
       "         6.54860734e-01,   6.42787610e-01,   6.30552667e-01,\n",
       "         6.18158986e-01,   6.05609687e-01,   5.92907929e-01,\n",
       "         5.80056910e-01,   5.67059864e-01,   5.53920064e-01,\n",
       "         5.40640817e-01,   5.27225468e-01,   5.13677392e-01,\n",
       "         5.00000000e-01,   4.86196736e-01,   4.72271075e-01,\n",
       "         4.58226522e-01,   4.44066613e-01,   4.29794912e-01,\n",
       "         4.15415013e-01,   4.00930535e-01,   3.86345126e-01,\n",
       "         3.71662456e-01,   3.56886222e-01,   3.42020143e-01,\n",
       "         3.27067963e-01,   3.12033446e-01,   2.96920375e-01,\n",
       "         2.81732557e-01,   2.66473814e-01,   2.51147987e-01,\n",
       "         2.35758936e-01,   2.20310533e-01,   2.04806668e-01,\n",
       "         1.89251244e-01,   1.73648178e-01,   1.58001396e-01,\n",
       "         1.42314838e-01,   1.26592454e-01,   1.10838200e-01,\n",
       "         9.50560433e-02,   7.92499569e-02,   6.34239197e-02,\n",
       "         4.75819158e-02,   3.17279335e-02,   1.58659638e-02,\n",
       "         6.12323400e-17])"
      ]
     },
     "execution_count": 723,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.cos(np.linspace(0,np.pi/2,100))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 702,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def floyd_steinberg_dithering(plate, plot=False):\n",
    "    \n",
    "    quantized_plate = plate/np.max(plate)\n",
    "        \n",
    "    for i in range(plate.shape[0]):\n",
    "        for j in range(plate.shape[1]):\n",
    "            pixel = quantized_plate[i,j]\n",
    "            \n",
    "            quantized_pixel = np.rint(pixel)\n",
    "            error = pixel-quantized_pixel\n",
    "            #replace with new pixel\n",
    "            quantized_plate[i,j] = quantized_pixel\n",
    "            \n",
    "            if j+1 < plate.shape[1]:\n",
    "                quantized_plate[i,j+1] += error*7/16\n",
    "                \n",
    "            if i+1 < plate.shape[0] and j-1 < 1:\n",
    "                quantized_plate[i+1,j-1] += error*3/16 \n",
    "                \n",
    "            if i+1 < plate.shape[0]:\n",
    "                quantized_plate[i+1,j] += error*5/16 \n",
    "                \n",
    "            if i+1 < plate.shape[0] and j+1 < plate.shape[1]:\n",
    "                quantized_plate[i+1,j+1] += error*1/16\n",
    "                \n",
    "                \n",
    "    #plot plate\n",
    "    fig = get_figure_hd()\n",
    "    plt.imshow(quantized_plate, extent=[0, 1, -1.1, 1.1], aspect='auto', origin='upper', zorder=2, cmap='gray', interpolation='nearest')\n",
    "    plt.axis('off');\n",
    "            \n",
    "    return quantized_plate"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 759,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "#replay methods\n",
    "\n",
    "import matplotlib.gridspec as gridspec\n",
    "\n",
    "def get_spectrum_from_reflectivity(intensity, z, n_freq, plot=False, root=False):\n",
    "    \n",
    "    #light attenuation coefficient\n",
    "    Kd = 1\n",
    "    \n",
    "    wavelengths = np.linspace(390, 700, n_freq)*1E-9\n",
    "    c     = 299792458  #speed of light\n",
    "    nu    = c/wavelengths\n",
    "    omega = 2*np.pi*nu\n",
    "    k     = omega/c\n",
    "    \n",
    "    #white light\n",
    "    L = np.ones(n_freq)\n",
    "    \n",
    "    matrix_exponentials = np.exp(-2j*np.outer(k,z))*np.tile(np.exp(-Kd*z), [len(k), 1])   \n",
    "    integrals = matrix_exponentials @ intensity\n",
    "    \n",
    "    if root:\n",
    "        spectrum = 4*L*np.abs(integrals)\n",
    "    else:\n",
    "        spectrum = 4*L*np.abs(integrals)**2\n",
    "    \n",
    "    if plot:\n",
    "        plot_spectrum_poly(wavelengths, spectrum)\n",
    "    \n",
    "    return wavelengths, spectrum\n",
    "\n",
    "\n",
    "def get_spectrums_from_plate(plate, z, n_freq, plot=False, title=''):\n",
    "    \n",
    "    spectrums = np.zeros([plate.shape[0], n_freq])\n",
    "    rgb_colors = np.zeros([plate.shape[0], 1, 3])\n",
    "    \n",
    "    for i in range(plate.shape[0]):\n",
    "        \n",
    "        reflectivity = plate[i,:]\n",
    "        \n",
    "        w, s = get_spectrum_from_reflectivity(reflectivity, z, n_freq=n_freq, plot=False)\n",
    "        spectrums[i,:] = s\n",
    "\n",
    "        xyz = from_spectrum_to_xyz(w, s)\n",
    "        rgb = from_xyz_to_rgb(xyz.reshape([1,1,3]))\n",
    "        rgb_colors[i, 0, :] = rgb\n",
    "        \n",
    "    if plot:\n",
    "        plot_spectrums(w, spectrums, rgb_colors, title=title)\n",
    "    \n",
    "    return spectrums, rgb_colors\n",
    "        \n",
    "def plot_spectrums(w, spectrums, rgb_colors, vmax=None, title=''):\n",
    "        \n",
    "    fig = get_figure_hd()\n",
    "    plt.title(title)\n",
    "\n",
    "    gs = gridspec.GridSpec(1, 4, width_ratios=[8,1,1,1])\n",
    "    gs.update(left=0.02, right=0.98, hspace=0.02, wspace=0.02)\n",
    "    ax1 = fig.add_subplot(gs[0])\n",
    "    ax2 = fig.add_subplot(gs[1])\n",
    "    ax3 = fig.add_subplot(gs[2])\n",
    "    ax4 = fig.add_subplot(gs[3])\n",
    "\n",
    "    if vmax is None:\n",
    "        vmax = np.max(spectrums)\n",
    "    \n",
    "    #plot spectrums\n",
    "    ax1.imshow(spectrums, extent=[0, 1, -1.1, 1.1], aspect='auto', origin='upper', zorder=2, cmap='gray', vmin=0, vmax=vmax, interpolation='nearest')\n",
    "    ax1.axis('off');\n",
    "\n",
    "    #plot rgb\n",
    "    ax2.imshow(rgb_colors, extent=[0, 1, -1.1, 1.1], aspect='auto', origin='upper', zorder=2, cmap='gray', interpolation='nearest')\n",
    "    ax2.axis('off');\n",
    "\n",
    "    #plot average\n",
    "    ax3.imshow(np.mean(rgb_colors, axis=0).reshape([1,1,3]), extent=[0, 1, -1.1, 1.1], aspect='auto', origin='upper', zorder=2, cmap='gray', interpolation='nearest')\n",
    "    ax3.axis('off');\n",
    "\n",
    "    av_spectrum = np.mean(spectrums, axis=0)\n",
    "    \n",
    "    av_xyz = from_spectrum_to_xyz(w, av_spectrum)\n",
    "    av_rgb = from_xyz_to_rgb(av_xyz.reshape([1,1,3]))\n",
    "\n",
    "    ax4.imshow(av_rgb.reshape([1,1,3]), extent=[0, 1, -1.1, 1.1], aspect='auto', origin='upper', zorder=2, cmap='gray', interpolation='nearest')\n",
    "    ax4.axis('off');"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 704,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def generate_plots(mu=600, sigma=30, n_freq=100, n_pixels=100, n_depth=100):\n",
    "    #generate plate\n",
    "    gaussian_plate, intensity, z, original_spectrum = plot_plate_gaussian(mu=mu, sigma=sigma, n_freq=n_freq, n_pixels=n_pixels, n_depth=n_depth)\n",
    "    #gaussian_plate, intensity, z, original_spectrum = plot_plate_mono(mu=mu, n_freq=n_freq, n_pixels=n_pixels, n_depth=n_depth)\n",
    "    \n",
    "    #recover spectrum\n",
    "    w, s = get_spectrum_from_reflectivity(intensity, z, n_freq)\n",
    "    \n",
    "    #quantize plate\n",
    "    quantized_plate = quantize_plate(intensity, n_pixels=n_pixels)\n",
    "    \n",
    "    #Floyd-Steinberg dithering\n",
    "    fs_plate = floyd_steinberg_dithering(gaussian_plate, plot=True)\n",
    "    #quantized_plate = fs_plate\n",
    "    \n",
    "    #recover the spectrums for each pixel\n",
    "    spectrums, rgb = get_spectrums_from_plate(gaussian_plate, z, n_freq, plot=True, title='Unquantized')\n",
    "\n",
    "    #recover the quantized spectrums for each pixel\n",
    "    quantized_spectrums, rgb = get_spectrums_from_plate(quantized_plate, z, n_freq=n_freq, plot=False, title='Quantized')\n",
    "    \n",
    "    #compute errors\n",
    "    errors = np.zeros(n_pixels)\n",
    "    \n",
    "    for i in range(n_pixels):\n",
    "        spec_est = quantized_spectrums[i,:]\n",
    "        errors[i] = np.linalg.norm(spec_est-original_spectrum)\n",
    "        \n",
    "    indices = np.argsort(errors)\n",
    "        \n",
    "    sorted_spectrums = quantized_spectrums[indices[::-1], :]\n",
    "    sorted_rgb       = rgb[indices[::-1], :]\n",
    "    \n",
    "    plot_spectrums(w, sorted_spectrums, sorted_rgb, title='Quantized Sorted')\n",
    "    \n",
    "    #plot_spectrums(w, np.abs(spectrums-sorted_spectrums/np.max(sorted_spectrums)*np.max(spectrums)), sorted_rgb, title='Absolute difference', vmax=np.max(spectrums))\n",
    "    \n",
    "    #select the best spectrum\n",
    "    best_spectrum  = sorted_spectrums[0,:]\n",
    "    best_rgb       = sorted_rgb[0,:]\n",
    "    best_spectrums = np.tile(best_spectrum, [n_pixels, 1])\n",
    "    best_rgbs       = np.tile(best_rgb, [n_pixels, 1]).reshape([n_pixels, 1, 3])\n",
    "    \n",
    "    plot_spectrums(w, best_spectrums, best_rgbs, title='Best repeated')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 705,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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b9w438MKvNPajBwAB8Axw/BELJ+vnYyuobCVvzVv3nx2AF4GOAJWVsdnRaLh3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\nAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11a8b96d8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAgIAAAEiCAYAAACLAbpnAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n7C9LXixO6zjh4wAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1196b87f0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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YXL+T2DYR1hZTE8clO3pvE9wk+ydiodP+M6ZJEzo9jU/tpHHcWCdCpRMR2YnY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\ngg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x115bbc240>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x119b41cf8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAfoAAAEvCAYAAACt5gPVAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\noJjQA0AxoQeAYkIPAMWEHgCKCT0AFPs3PXeds6kvTUkAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x114efa2b0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
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zzz9/dn93ngP7Qo2bMfn8fiTzfnKNsw7q7aSeu37PPfdMNvMQdPnp6/q47LLL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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x119654940>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAfoAAAEvCAYAAACt5gPVAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\nAAALEgAACxIB0t1+/AAACuhJREFUeJzt3X+oZGd9x/HP3ZvN7iYhbjBCXPyxGNfvH7UU425V1Ehb\nErSmxYLW5p8WijaQpkqbBhUtBQv+LtpiLKlaLFLQFKJVaUhsmqQFuwQxdoN/PEkDRbAloWtrazc/\ndvfe/jFnx3Mvd3VNstz47esFgWcyc57zzJm79z3nzLC7sr6+HgCgpx3bvQAA4OwRegBoTOgBoDGh\nB4DGhB4AGhN6AGjsnO1eAPx/VVXPT/JgkiNJVpKsJvnfJNePMb72BOfcn+QjY4w3PlXrfCpU1R8k\n+eYY48s/5nb/k+SnxhjfPjsrg/6EHrbXsTHGZaduVNWbknwmyYue4Hz7n8S2Z9PPJ/nWE9jOX/QB\nT5LQw9PLxUn+7dSNqroqyXuS7ExyLMkNY4zDVVVJPp1kVxZXAz6V5M+TfDLJvqq6dYzxuvnEVXVn\nku8mqSR/luSzSf4kyYun+e+Y5l+rquNJPpbk55Kcl+TdY4wvTPP8ZpJrp/0eTfI7Y4xRVQeS3Jjk\n/CT7knwzyZuTvCXJwSQfrqqTSf42yQeTXJ7FVYx7k7xtjPH9qnp1kj9Nspbk6/HxIjxp/hDB9jqv\nqr5RVfdW1b8m+WiS9ydJVb0wyfuSvG6M8dIk1yS5par2JLkhyZfGGIeSvD7J5WOMtSyi+uDmyM98\nd4zx4jHGjdO+vj7NcVmSZyX5velxq0n+Y4xxMItY/0VVPbOqLk/yG0leNa3pw0lumbZ5a5LPjDFe\nmeRAkhckef0Y4xNZRPv3xxh/k+SdSY6PMQ6OMV6S5N+TfKCqdia5OcnvTnPfmWTPEz6yQBJn9LDd\nNl+6f0WSW6vqZ5JckeSSJHdU1cr0kBNJXpjkC0n+sqpeluTvkrztDPf3j7PxVUkOVdVbptu7sziT\nPuXjSTLGuK+qjmRxBv7yJJcm+dpsTXuram+SdyS5oqpuyOLjg2cnuWA236nHX5XkGVV15XR7Z5KH\nkvx0ksfHGHdN+/1cVd10hs8LOA2hh6eRMcY/VdVI8rNZnFXfMca4+tT9VfWcJN+Z4nsgizcDv5Dk\nD6c3CT/K92fjHUneNMYY09zPyMbQn5yNV6fbq0k+O8Z412xN+8YY/1VVn5/mvDnJV5I8Lz+IezbN\n9fYxxm3T9udl8Sbj+Vs8/sQZPCfgh3DpHrbXhrBV1YuyuOx9b5K/T3Ll9Hl8quoXk/xzkt1V9VdJ\nfm2McXOS307yvSTPzSKMO89w37dlulRfVbuSfCnJdbP7f32677IsPte/O8ntSa6uqkum+67N4rP9\nJLkyyXvHGH89Pa+XZRH1bFrXbUmuq6qdVbUji+8avD/JfUlWquq109y/nGTvGT4X4DSc0cP22l1V\n35jGK9N/bx1j/EuSVNVvJfnc1PoTSX5pjPFIVf1Rkk9N959McssY4x+mS+hrVXV4jPHyTfva/A32\ntyf5WFXdl8Xvgq8m+dDs/ldW1TXTmn51jPG9JLdX1QeTfHX6Yt1/J/mV6fHvSvLFqjqaxRcH78ri\nY4Yk+XKSj1TVuUnem+SPs3gzsyOLL+1dP8Y4UVVvSHJTVb1v+v8P/xjHEtjCin+mFtisqtaSPHOM\n8Z/bvRbgyXHpHtjKerb+fB34CeOMHgAac0YPAI0JPQA0JvQA0JjQA0BjQg8AjQk9ADQm9ADQmNAD\nQGNCDwCNCT0ANCb0ANCY0ANAY0IPAI0JPQA0JvQA0JjQA0BjQg8AjQk9ADQm9ADQmNADQGNCDwCN\nCT0ANCb0ANCY0ANAY0IPAI0JPQA0JvQA0JjQA0Bj52z3An6Y1dXV9VPj9fXlcMM4SXbt2rUcn3vu\nuVs+7vjx48vxiRMnTjvX6aysrCzHO3b84P3Rzp07Nzxuft/a2tpy/Pjjjy/HJ0+e3HLec87Z+HLM\n75vPdbrt52vZs2fPhrlOd1wee+yx5fiRRx5ZjufHa/M2p1vjfP3ztcz3nWw8RvP9zNcyP16bzfez\nurq65WPm653vb/6zkiTnn3/+cjw/ZvN552uZH6PN65+v68ILL1yOL7744uX4oosuWo43H5f56zrf\n53wte/fuXY7379+/YftLL710Od63b9+W6zp69Ohy/MADDyzH999//4a5HnrooS23n+/z4MGDy/Gh\nQ4eW4wMHDmyYa/fu3cvxww8/vBwfOXJkOT58+PByfM8992zYfr62+frnr/H8tbvggguW482v9/zn\ndX6Mjx07tuX40Ucf3bD9/DWam/+MzfcxX+P8987m2/Px2traYoK733xmv5y2y2s+v/K0X2Pyk7XO\ns8QZPQA0JvQA0JjQA0BjQg8AjQk9ADQm9ADQmNADQGNCDwCNCT0ANCb0ANCY0ANAY0IPAI0JPQA0\nJvQA0JjQA0BjQg8AjQk9ADQm9ADQmNADQGNCDwCNCT0ANCb0ANCY0ANAY0IPAI0JPQA0JvQA0JjQ\nA0BjQg8AjQk9ADQm9ADQmNADQGNCDwCNCT0ANCb0ANCY0ANAY0IPAI0JPQA0JvQA0JjQA0BjQg8A\njQk9ADQm9ADQmNADQGNCDwCNCT0ANCb0ANCY0ANAY0IPAI0JPQA0JvQA0JjQA0BjQg8AjQk9ADQm\n9ADQmNADQGNCDwCNCT0ANCb0ANCY0ANAY0IPAI0JPQA0JvQA0JjQA0BjQg8AjQk9ADQm9ADQmNAD\nQGNCDwCNCT0ANCb0ANCY0ANAY0IPAI0JPQA0JvQA0JjQA0BjQg8AjQk9ADQm9ADQmNADQGNCDwCN\nCT0ANCb0ANCY0ANAY0IPAI0JPQA0JvQA0JjQA0BjQg8AjQk9ADQm9ADQmNADQGNCDwCNCT0ANCb0\nANCY0ANAY0IPAI0JPQA0JvQA0JjQA0BjQg8AjQk9ADQm9ADQmNADQGNCDwCNCT0ANCb0ANCY0ANA\nY0IPAI0JPQA0JvQA0JjQA0BjQg8AjQk9ADQm9ADQmNADQGNCDwCNCT0ANCb0ANCY0ANAY0IPAI0J\nPQA0JvQA0JjQA0BjQg8AjQk9ADQm9ADQmNADQGNCDwCNCT0ANCb0ANCY0ANAY0IPAI0JPQA0JvQA\n0JjQA0BjQg8AjQk9ADQm9ADQmNADQGNCDwCNCT0ANCb0ANCY0ANAY0IPAI0JPQA0JvQA0JjQA0Bj\nQg8AjQk9ADQm9ADQmNADQGNCDwCNCT0ANCb0ANCY0ANAY0IPAI0JPQA0JvQA0JjQA0BjQg8AjQk9\nADQm9ADQmNADQGNCDwCNCT0ANCb0ANCY0ANAY0IPAI0JPQA0JvQA0JjQA0BjQg8AjQk9ADQm9ADQ\nmNADQGNCDwCNCT0ANCb0ANCY0ANAY0IPAI0JPQA0JvQA0JjQA0BjQg8AjQk9ADQm9ADQmNADQGNC\nDwCNCT0ANCb0ANCY0ANAY0IPAI0JPQA0JvQA0JjQA0BjQg8AjQk9ADQm9ADQmNADQGMr6+vr270G\nAOAscUYPAI0JPQA0JvQA0JjQA0BjQg8AjQk9ADQm9ADQmNADQGNCDwCNCT0ANCb0ANCY0ANAY0IP\nAI0JPQA0JvQA0JjQA0BjQg8AjQk9ADQm9ADQmNADQGNCDwCNCT0ANCb0ANCY0ANAY0IPAI0JPQA0\nJvQA0JjQA0BjQg8AjQk9ADQm9ADQmNADQGNCDwCNCT0ANCb0ANCY0ANAY0IPAI0JPQA0JvQA0JjQ\nA0BjQg8AjQk9ADQm9ADQmNADQGNCDwCNCT0ANCb0ANCY0ANAY0IPAI0JPQA0JvQA0JjQA0BjQg8A\njQk9ADQm9ADQmNADQGP/B4BP3jN/cNr4AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x117df1f28>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "generate_plots(mu=600, sigma=50, n_pixels=50, n_depth=2000)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 699,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "9.75e-10"
      ]
     },
     "execution_count": 699,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "50*390E-9/20000"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Blue"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 706,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAdsAAAERCAYAAAAzCQ3mAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\npTxaZQxHAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11a8b9eb8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAgIAAAEiCAYAAACLAbpnAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nACQmBAAgMSEAAIkJAQBITAgAQGL/Anrgu12rnEebAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x117334128>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "blue, int_blue, z, s = plot_plate_mono(mu=400)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Red"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 760,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAdsAAAERCAYAAAAzCQ3mAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nRK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x117792588>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
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      "text/plain": [
       "<matplotlib.figure.Figure at 0x116520ac8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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kdy67fPj6WopEJQhbAEhg67qhQ0eazU9tHx1/7uK5s6+Q9Mniphb3n7n6R5KOKjW/etnl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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x117792940>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "red, int_red, z, s = plot_plate_mono(mu=650, plate_depth=200, windowed=True)\n",
    "w, s = get_spectrum_from_reflectivity(int_red, z, n_freq=1000, plot=True, root=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Gaussian"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 772,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x11791c7b8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAgIAAAEiCAYAAACLAbpnAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nCABAmBAAgDAhAABhvwAq9npOCPD4oQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11522c0f0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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QYP4ojG5AoD7XwBzJT8OK4VB+4nBt9Khnzs68dyQr+TrX43DFM1IDVeFgw5hJ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/vsZ8KJgTUEHEynfJQibvdNnA5xbPZo53T4tPfYDFrVGF0TwOdtbmNzdULU5QqrM3YezJckRpj4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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1168a5d30>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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VWk+21pvt9zV+Lqmw/bnvOUFfeOlIYf6ndsD9r6lWj8HZlBB60+FoT680CGHw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\nlExhKyIiUjKFrYiISMn+P8SgAz1VXalSAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1168a5198>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "gaussian, int_gaussian, z, s = plot_plate_gaussian(mu=500, sigma=20, plate_depth=500, n_depth=2500, windowed=True)\n",
    "quantize_plate(intensity, n_pixels=1000)\n",
    "w, s = get_spectrum_from_reflectivity(int_gaussian, z, n_freq=1000, plot=True, root=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "hide_input": false,
  "kernelspec": {
   "display_name": "Python [Root]",
   "language": "python",
   "name": "Python [Root]"
  },
  "latex_envs": {
   "bibliofile": "biblio.bib",
   "cite_by": "apalike",
   "current_citInitial": 1,
   "eqLabelWithNumbers": true,
   "eqNumInitial": 0
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}