{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Analyse de spectres de l'hydrogène\n", "\n", "Les données que nous allons analyser sont des données de spectroscopie de l'atome de deutérieum (l'isotope de l'hydrogène de masse atomique 2). Dans le modèle simple de Bohr, les niveaux d'énergies sont donnés par : \n", "\n", "$$\n", "E_n = -hc\\frac{R_D}{n^2}\n", "$$\n", "\n", "où $h$ et la constante de Planck, $c$ la célérité de la lumière et $R_D$ la constante de Rydberg du deutérium qui est reliée à la constante de Rydberg $R_\\infty$ par : \n", "\n", "$$ \n", "R_D = \\frac{R_\\infty}{1+\\frac{m_e}{m_D}}\n", "$$\n", "\n", "où $m_e$ est la masse de l'électron et $m_D$ celle du Deuteron (Noyau de l'atome de deutérium : un proton et un neutron). La constante $R_\\infty$ correspond à la constante de Rydberg pour un noyau de masse infinie.\n", "\n", "La transition que l'on étudie est la transition entre les niveau $n=1$ et $n=3$. Sa fréquence vaut : \n", "\n", "$$\n", "\\nu_\\mathrm{Bohr} = \\frac{E_3 - E_1}{h}\n", "$$\n", "\n", "* Constante de rydberg : $R_\\infty = 10973731.56816$ m$^{-1}$\n", "* Rapport de masse : $\\frac{m_D}{m_e} = 3670.4829679$\n", "* Vitesse de la lumière dans le vide: $c = 299792458$ m/s\n", "\n", "\n", "1. Calculer la fréquence de la transition dans le modèle de Bohr et donner sa valeur en MHz. On formatera la valeur pour avoir trois chiffres après la virgule (précision au kHz)." ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "from matplotlib.pyplot import figure\n", "import matplotlib.pyplot as plt" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Nu Bohr : 2923507473.443 MHz\n" ] } ], "source": [ "R_infty = 10973731.56816\n", "mD_sur_me = 3670.4829679\n", "me_sur_mD = 1/mD_sur_me\n", "c = 299792458\n", "\n", "RD = R_infty/(1+me_sur_mD)\n", "\n", "freq_transition_bohr = RD*(1 - 1/9)*c\n", "print(f'Nu Bohr : {freq_transition_bohr/1E6:.3f} MHz')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Le principe de la spectroscopie consiste a illuminer un jet d'atomes à l'aide d'un laser dont on connait la fréquence et à mesurer la fluorescence des atomes. Cette fluorescence étant très faible, on utilise un compteur de photon pour la mesurer.\n", "\n", "Les données sont dans le fichier {download}`data/data_hydrogene_simple.txt`. Il s'agit d'un fichier texte simple. Il comprend une colonne qui correspond à la fréquence (mesurée) du laser de spectroscopie et une colonne qui correspond au nombre de photons détectés sur une seconde de mesure. Ce nombre est proportionnel au nombre de photons absorbés par les atomes d'hydrogènes. \n", "\n", "2. Lire et afficher les données." ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [], "source": [ "freq, counts = np.loadtxt('data/data_hydrogene_simple.txt', unpack=True)" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "Text(0, 0.5, 'Counts [/s]')" ] }, "execution_count": 4, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "fig = figure()\n", "ax = fig.subplots(1, 1)\n", "\n", "ax.plot(freq, counts, '.')\n", "ax.set_xlabel('Relative frequency [MHz]')\n", "ax.set_ylabel('Counts [/s]')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "On va ajuster le profile par une fonction lorentzienne : \n", "\n", "$$ \n", "a + \\frac{b}{1+ \\left(\\frac{f-f_0}{\\Delta f}\\right)^2}\n", "$$\n", "\n", "où $a$ est un offset, $b$ une amplitude, $f_0$ la fréquence centrale et $\\Delta f$ la largeur en fréquence. \n", "\n", "3. Faire un ajustement des données par une lorentzienne (que l'on représentera graphiquement)." ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "from scipy.optimize import curve_fit\n", "\n", "def fonction(x, offset, amplitude, centre, largeur):\n", " return offset + amplitude/(1 + ((x-centre)/largeur)**2)\n", "\n", "p0 = 100, 300, 0, 1\n", "popt, pcov = curve_fit(fonction, freq, counts, p0)\n", "\n", "x = np.linspace(-2, 2, 201)\n", "fig = figure()\n", "ax = fig.subplots(1, 1)\n", "\n", "ax.plot(freq, counts, '.', label='Data')\n", "ax.plot(x, fonction(x, *popt),label='Fit')\n", "ax.set_xlabel('Relative frequency [MHz]')\n", "ax.set_ylabel('Counts [/s]')\n", "ax.legend()\n", "ax.grid()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Les données sont prises par rapport à une fréquence de référence, c'est à dire que la fréquence du laser est la somme entre la fréquence de référence ($f_\\mathrm{ref} = 2923538429.3$ MHz) et la fréquence des données. \n", "\n", "4. Donner la valeur de la fréquence absolue $\\nu$ ainsi que l'incertitude absolue $\\sigma_\\nu$ et relative $\\sigma \\nu / \\nu$) de la mesure du pic. La différence par rapport à la valeur du modèle de Bohr est dûe a des corrections supplémentaires (effet du spin de l'électron, de la taille fini du noyau, effets relativistes, ou encore de la polarization du vide qui peuvent être calculés à l'aide de l'Electrodynamique Quantique). Calculer cet écart." ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Frequence : 2923538429.2486176 MHz\n", "Incertitude : 10.226763342276545 kHz\n", "Incertitude relative : 3.4980772751138214e-12\n", "Différence avec la valeur du modèle : -30955.805622577667 MHz\n" ] } ], "source": [ "freq_ref = 2923538429.3\n", "\n", "freq_abs = freq_ref + popt[2]\n", "sigma_abs = np.sqrt(pcov[2, 2])\n", "\n", "print(f'Frequence : {freq_abs} MHz')\n", "print(f'Incertitude : {sigma_abs*1e3} kHz')\n", "print(f'Incertitude relative : {sigma_abs/freq_abs}')\n", "print(f'Différence avec la valeur du modèle : {freq_transition_bohr*1e-6-freq_abs} MHz')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "5. Les données correspondent en réalité à 6 spectres de N points qui ont été enregistrés à la suite. Ajuster chacun des 6 spectres pour en déduire leurs fréquences absolues et leurs incertitudes que l'on affichera. \n", "\n", "6. Tracer avec des barres d'erreurs les points sur un graphique ayant comme axe des abscisses le numéro du spectre (1, 2, .., 6). Représenter sur ce même graphique la valeur moyenne des fréquences $\\bar{\\nu}$ et son écart type $\\sigma_{\\nu}$ (on utilisera une ligne continue rouge pour la moyenne et des lignes discontinues noires pour $\\bar{\\nu}\\pm\\sigma_{\\nu}$). Est-ce que l'écart type des 6 fréquences est en accord avec l'incertitude obtenue à partir de l'ajustement de l'ensemble des données (à la question 4)." ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "L'écart type des fréquence est de 10.0 kHz et correspond bien à celui obtenu à la question 4: 10.2 kHz\n" ] }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "N = len(counts)//6\n", "centers = np.zeros(6)\n", "sigma_centers = np.zeros(6)\n", "\n", "for i in range(6):\n", " popt, pcov = curve_fit(fonction, freq[i*N:(i+1)*N], counts[i*N:(i+1)*N], p0)\n", " centers[i] = popt[2]\n", " sigma_centers[i] = np.sqrt(pcov[2,2])\n", " #plt.plot(freq[i*N:(i+1)*N],counts[i*N:(i+1)*N],'.')\n", " #plt.plot(x, fonction(x,*popt))\n", " \n", "freq_abs_6 = freq_ref + centers\n", "\n", "plt.errorbar(np.arange(6)+1, freq_abs_6, yerr=sigma_centers, fmt='o')\n", "\n", "mean = np.mean(freq_abs_6)\n", "std = np.std(freq_abs_6)\n", "plt.plot([1,6],[mean, mean],'r')\n", "plt.plot([1,6],[mean, mean]+std,'k--')\n", "plt.plot([1,6],[mean, mean]-std,'k--')\n", "plt.xlabel('Numéro du spectre')\n", "plt.ylabel('Fréquence Absolue')\n", "print(f\"L'écart type des fréquence est de {std*1e3:.1f} kHz et correspond bien à celui obtenu à la question 4: {sigma_abs*1e3:.1f} kHz\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Les données du fichier `data_hydrogene_simple.txt` sont en fait le centre d'un spectre plus large. Le fichier {download}`data/data_complete.dat ` contient tous les points de mesures. Ce fichier est formaté légèrement différement (il contient un en-tête et un ';' comme séparateur). \n", "\n", "7. En utilsant les options de `np.loadtxt` lire le fichier et tracer les points. " ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [], "source": [ "freq_2, counts_2 = np.loadtxt('data/data_complete.dat', skiprows=1, delimiter=';', unpack=True)" ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "Text(0, 0.5, 'Counts [/s]')" ] }, "execution_count": 9, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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/8f9le4CInOHtEBCRccCngdeBjfTuMr4EPObdftw7xrv/N6pqk75REDJN4kPBiteMUiHX7KOHgB8D9wOpHB9TA/zMiyvEgAdVdb2IvAasEZG/A34H/MS7/ifA/xaRHcAR4KYcX8cwhp0lc6tJxF0xu3h86JN4VAfJNzK2WzCKjVyNQlJVfzSYJ/a0kT6a4Xwz0Kevs9cL+vrBvIZh5BV/ozqMG9Y9R49z9zNvkky5Etp3XV1Le1e31S4YRUOuRuEJEfm/cYPFJ/yTqnokL6MyjAKzqbmNnpTbFCfppaEOZdL2U1zf73GCc91Jh+8+1oiqWu2CUTTkahR8X/+3QucUmDu8wzGM4qBqfHmQjup4x0PBT3GNknI78JhyqlE05GQUVPWsfA/EMIqJ9q5uvARSxDseCn6gubvHwTcNcYF4PEYq5Vjw2SgacjIKIvIHmc6r6s+HdziGURyEdwrK0HcKfqD5kYZWHvJkM+JxiykYxUeu7qMLQ7dPAS7H7atgRsEYlbR3dRMTcBRiMvSdAriGYVNzGylHg1TX9q5ubr9s3tAHbBjDRK7uoz8JH3v1B2vyMSDDKAai/ZWHy7Uz3KmuhjHcnGyP5vcAizMYo5aFs6tYvqw26M08rK6dUKrr9v2dJqdtFBW5xhSegMDFGgc+CDyYr0EZxkgT7XVQv6udFeub6E46bNl5hPOmVg7LpL2puY2k5z5KOsryxxpxLCXVKCJy3Sl8P3Q7CexS1dY8jMcwRpxwr4NETLh+0UwU+khdD8eEHXYfiUgQX7CUVKNYyDWm8JyITKE34Jy165phlBLhXgfdKWVVXQtliRiJmDtpD3u6qOc+EnGluFOOm4m05+hx6ne1m2EwCkqu7qMbgH8AnsVN2/5XEfmWqj6c9YGGUQL4QeUTPa4Anp8ZdNNFs5g2adyw+vvD7iN1lOsvcuXfH9q6mzWbW1jX0GpuJKOg5Oo++g5woaoeBFcBFXiG3g5qhlGyhGsI1m7ZTcpRYjHh2qH0TuiHaFZT7bSJbGjcR9LRYXdVGcbJkKtRiPkGwaON3GW3DaPoWTi7iu37O1nltABu283t+zuHfXKOqqWuWN8U7FBiJqttFAG5TuxPisivRORWEbkV+A9gQ/6GZRgjz4bGfVmPh4uFs6u4/bJ5tHd1By0/Y8DH500215FRcHIyCqr6LeBe4MPev5Wq+hf5HJhhjDRL59dkPR5u/JafAiTiwh1XnGsGwSg4Wd1HIjIPmKKqv1XVdcA67/wlInK2qr49EoM0jJHglsVu0NcvWPOP80qGvs1+zUTV+HLTRTJGnIFiCncDf5nhfId339XDPB7DKAir6loCY/C/v7I4r6/lT/p7jx4PWn4mQy0/b175UtDLQYCKMitsM0aOgYzCFFXdFj2pqttEZE5+hmQYI4M/OXce7+HHzzcD8MJbhwHytksIF8rFYoLXTgFHXSXWRxpa6U71dnpToLvHMpKMkWMgozApy33jhnEchjGihCfnaLPNtVta8mYUwoVyGpr8Y/T2cIgyHE1+DCNXBgo0bxWRr0VPishXgfr8DMkw8k/a5ByxClMmnJK31/XrFNwGO0Jc3C9heZmbinrtghmUJ9K/lsMl3W0YuTDQTuEO4FER+SK9RmARUA58Po/jMoy8Ub+rnZd3Hw1cN0DQZS0mMLmyIm9yE+FCuYfrW0niFsotX1YbvN7qry1hXUMra7e0kHIgEROrXTBGjKxGQVUPAB8TkcuA+d7p/1DV3+R9ZIaRB3y30Yme3n7JgmsMUur69lfXtfDw1t2svu3ivBmGTc1tJFPuTkXQPjsBBSRDZpJh5JtcBfE2AhvzPBbDyDu+2yjsMYrFBMeJBHdTyiMNrXkL7kblLqrGl3PPxh1UjS/nrscb04LNqZTDuoZW67tgjAgn22THMEoSfzLu7nFwcHcJvlqpnwbqk8/1eSa5i+6kg+DuWMJjiMdjbl9nx/ouGPnH9IuMMYU/GX/8nMnEhF610kUzuXnxLMriboVxeSLGtQtm5H0sYbkLx3NfhfnwjIl8YeGMPoJ54LrC7tm4g/pd7XkdpzG2sJ2CMaqJdlTzmXX6eOpC/RJ8RdT5nmrpsLfgzEJ632bXKCVT7riWX10LwLqG1rR+0eGUWts9GMOJGQVj1JJp4gR6u6zFY9x40Uyu8wxCvlpw5oLjeHEOVf7mmg/R3tVN1fjywKD5ribfuN2zcUdeOsMZhhkFY9QSrkUIu13C53Yf6cp6/UhMtI80tJL0kqGSDjTu7eC6BTP6GLTbL5sXPCYaqLaUVWO4MKNgjFrCE6ff7nJCRSLw2yvw4luH2bLzCMuX1bL36PH8teDMwuHOE32O01qEZjBQ4UC1ZSQZw4kZBWPUsnB2FcuX1bJ2SwtNeztYs7mFWCTn39cWWv5YI45qH5dSoagaX95HFynKwtlVZgyMYceMgjHqCEtPhzubATgRTQvBq1NQN7snlXKYPmnciE62kysr+hz7Okh+Ax6TuTBGCjMKxqihfld7r3xEyiEmQjKa40mvpIUAs6vH85naqTzw0s6C+eevWzCDh7fupielxGOu++hQ5wnKEjFSKYsZGCOLaFQNrIRYtGiRbt26tdDDMIqAsHzFQJ/omOdBciUm3H4Fy5fVFrShjW/QHvKMA0AiBjdeOCuol7DGO8ZwISL1qroo03152ymIyEzg58AU3IXZSlX9gYicDqwF5gA7gRtUtV1coZcfAFcBXcCtqtqQr/EZo4tM8hX9MfeM06iZeAovvnUYxc00au/qTsvuGWl69ZBC8hYOTJvkKtSHDV5MsNoEI2/ks6I5CfwPVT0fWALcLiLnA3cCv1bVc4Bfe8cAS4FzvH+3AT/K49iMEiRbBW+43/FAH+ovf/ws7rjiXCrKXAnrYnHPLJlbTVlINrss7qqjRg1eNMXWMIaTvO0UVHUfsM+73SkirwPTgWuAT3qX/Qx4Fvi2d/7n6vqzNonIJBGp8Z7HGOPkUsGr+OqiEMftkxCLwZzJp9F88F0cXJcMuDuLQruMoiycXRXIZiukZUCF9ZoAJCZ0Hu/h939SN3L9pI0xwYgEmr3WnR8F6nBbfPoT/X5c9xK4BmN36GGt3rk0oyAit+HuJJg1y74IY4WBCsvWNbQGvng/tuxrG+04+G5wneMQpJ8WowsmnGbq74z8iuZ7n3ubp147ALgyGOEWohu3H+SPLj077bH91TCE7wOs1sFII+9GQUROAx4B7lDVYxLKE1dVFZFBRbpVdSWwEtxA83CO1SheBqrgPRQpAAPPOEQUR8Ppp8UsD5FpZ3S8J9Xv9U+/doDnth/k+kUzqZ02MZDriBq+8PMmYgIiJFOmn2T0klejICJluAbhF6q6zjt9wHcLiUgNcNA7vweYGXr4DO+cYQxYwZvL6uDDMyZy44WzWLG+qejlITLtjGprJvDCW4f7fUx3SvlFXYu7Q1KCIHrY8KU9b8q1mpmuM8Yu+cw+EuAnwOuq+k+hux4HvgR8z/v5WOj8N0RkDbAY6LB4ghEmUwWv7wrpr/dBXNwdQzwG86dP5LyplSUhD5GpCU80sOzXW0QJu8+ihi9N+sPbKVgthBEmb3UKInIJ8AKwDYL42F/hxhUeBGYBu3BTUo94RuTfgM/gpqT+oapmLUKwOoXSJpvfO9fH37zypaDoS0SCuAK4k+LNF81CIShoKyU3SbbKbHANXcrJ/FgBLjlnMndcca7FFIw+FKROQVVfpP/mVZdnuF6B2/M1HqO4GEw/gPDk6EtKN+7tYPM7R4K2lUkHLpoziRNJh9f2HcMJ9UkI90MuJTeJvzPyZbKjXeGcDAYh5m0fEnFh1unjsz5v+BhyD06Xwt/OOHlM5sIYEaKTykDZRAOtkjOxZWc7IpCICTddNCtonANk7IdcKhNc0ELU+3vFgEQiBqppvZwBLpk3mRmnj+fh+lZWb27hkYZWbr14Dk37jmVNXc1mpK2hz9jCjIKRdzJNKv1lE2XSL3JUcwokK26ANeUo0zxRO9+4+DUJ4X7IpTLBLZxdxa0Xz+HJpv1cMHMS50ypZMncarbv72TF+ibe7+ndMrQc6WLx3OpgZ3Six0lLXX12+0G+Hkpd9clmpAvVZ8IoDNaj2cg7ab0BehzufuZNAJYvq+Vj8yazfFltMIHffN8mVtW19PYsdhSR/ryQ6cSFtApl3xj941PbWbG+iSVzq9P6IZdKVfCquhZ+/HwzO9u6+OXLewMZ7ahBAPhM7dS06u6oMX3qtQPcfN+mPlXhvpHOVOGd7T5j9GE7BSPvBO4PryL3tzsOU/fOEVAl6WjQ+nJdQyvdyd5JTnDdJI7jpCmbxmPwqQ9M4cCx93mltSO49qaLZjFt0risLStLsWPZhsb0JLyVz7/Nx+ZNTvtbgRtP6DyRZPv+ThChv/1Vd9JhXUNrn7jC8mW1GftTW0OfsYUZBWPYicYP/Enl7mfe5Lc7DgeTNKTn0h+MFKCdfeZpXHTW6azZ3BIIwX18Xm9Gjb8T8Cf4ayONcTIZgFKc4KL1Cbvautjb0Uoi5mZbhTWRwnUK2TjYeYJ7Nu7grQOdvLz7KBfMnMSTTfvpTjrUNbfRtLcj7e9pDX3GDiadbQyJqAHIJWDpt8dElZSjxOMxvrBwBoc7TwQyDgBfXOwGi2++r3fiX/21JRkD0v1N8KWeNROWBIded1Bc3J2Rn27bk6NCrE8iLmmKrJkoz/D3NkYHBUlJNUY/mQzApua2IFOouyc9KBldpYOrWfTQ1t1eq8z05z/UecJ1hfgLlwwLmIFWsKW+wg0rpMYE4iKoatrO6LoFM3ikoZW1W3aTytBUKIoAqQEMAqS7mXKtbSh1I2yYUTCGQKaslKrx5b3uDPr2Fo5O0pua20g6rhZRdM5/+rUD/OaNg0H2UcrRYc18KYUJLOoCy6Ts6v9NJ1QkgkwjcCf/srinb5R04zmCu0sQ6JPOKhncTo17OlhV1xJkbMVignrvV0WZpa6ORswoGCdNJp/9Iw2tadc07u3I+Tl82QXfFaJA0lEvk0aJx4S9R48HmTNDrYYuhQlsMDGQynFlacd+RfP2/Z2s3dJC494OHMc1DF/++Fk82bSfnW1dwfWZPMnb9nTQtLeRlOMaZidkSKI7QUtdHR2YUTBOmkwT1rqIUWjyVpr+6hZ6J/Pt+zvZ0LiPz9ROpe29bpbOr+G8qZX8/YbX2byzN2Vy2YdrGF+R4MGtu1lV18Larbu9eATE48INi2am9R7IZQdQShNYri6w6K7slLJ4UMsQLv5LppT7X3wHx7MCMdxdQnjjMHVCBQc7T3g7OM24i3CAp5r2UzW+nFsWzyrJzC6jL2YUjCERnbCuXTCDh0KBz1daO3ildVsgWy3i1h7ExJWmCPPS222suGY+JyJ3vHP4PWqnTwwCo+EAaTKlrKprYV1DK7/46hKAnHYAo3ECa+/qJia9gnjPvHaAjW8cDFb50Fc+3M/oqq2ZwH0vNOOo63L608vP5a4nmoJ4Rn/5KP77C3DL4lkll9ll9MWMgpEzuQQb/e5hK55oCmoIgCAm4JMpHpp0lOWPNbJg1qS08xWJGE17sruhwoVouewASjE1dSB8Q+fvChRw1HW7qffT77dw1+ON9KRc19zS+TWsWN/kqckKd312PrcsnkXj3g5W17XklNX00xeb2dC4j9qaCX3cWEZpYUbByIm05ixeOmnSydy9bOHsKmqnT0wzCrniqHLOlErqW46S8nYUDbuPpu0OyuLiGhkvRz9GeqVtrjuAUs9MiuIbOj+jK+WJAkaD0/W72gOjobhxn94dgdK4t4N7Nu5gQkWCWMitFBN3l5EplXXHoffYcei9oJ5iMOmspRDwH0uYUShSiu2LEvXBQ+YmLj7zp00c1PP72ajliRi10yYSl92B3np4EvrIjIksv7o2GJOvnBr+O422HcBg8A2drw6b6W8Qbl3ak1I2v3OEREzcmpGYBLpT4d1cPCbceKEbu/FjQdWnltP2Xjf7Ot5Pa3kK7m5txRNNLL+6Nut7UCoB/7GEGYUipBi+KKvqWgLJg2gQMVp4tsfLCAqPMezfFtxAZtRlFI+58s/+ilWAWy+eQ3tXN0nPDx71ZZ854ZRgtQtw3tTKPn+b0bYDGC78hUa0cnzHwXcpT8S4/INncuDY+7za2tHHZeQ4ynRPZBAIxAXbu7rpPN7TxyiAG2/44v2bMqbR+mTSxcrUA8IYOcwoFCEjnRkT3ZWsqmvhrx51g4e+O+CWxbMCpc7P1E7l07VTWdfQytotLayua+HBLS3ceGGvXHXUiDiOg6prHM6srGDJ3Gr+c9s+UqHpR4H7XnyHv71mfvBYRNJiEQePvc+qupbAJ14WF1bfdrFNIiEyLSqAoCFRLIMMZjLl8Js3DpLsp/gtLDJ4832bAt0lP3DdH909Dssfa8TRzK7GTLpYW3YesR1DATGjUISMRGZMtF+BHyv4wsIZfYK6viCbXxj14+ebaT78nldH4F6TdFzdnQe37maNN0n7bpw9R48H+kWqcODYCda/ui9j9a3jKO1d3cFjq8aXc9cTTUE206utHTTu2Rb4ubtTyiMRcbexTqZFxZ6jx4NitWi3NgFiEePrM++MUzm1IsHFc6vZ1NzGK7uPpgnxRRMIwsSEQPq8vwWOL8S38vm32dXWFVy3rqF1zLoAC40ZhSIkn5kx9bva3RX+1t2kUuqmJ3qumu6kw+q6FuLx9JXf0vk1fZQ6wxpFYXpSyt9veJ1LzzuTJXOruf2yedTvaufhrbuDSSmcFeM4SniOCgvX+b/3eVMrufuZN3nxrcPeY9NfMzdh7bFDpkVFtH7Ef4vDGUmZmhntOtJFytEgaSAXrf15Z57GFR84k8pxZcGiI1PfjOiixE8aiMdjPLR1d59EhnzF2YotfldozCgUKYP1i0djAJnw3QphDf6Uo8ToFVpT3MCuL1Udj0HT3o4+Sp3Z2LyznS0720nE3Qln/rSJrt+I3mKp8lBWjN9eU6CP0qn/t7jjinPZsvNIUPnsj9PXADJ66W9R4dePlCVi3HV1Xz+/b3zD73NPJNPIwX3/+mkNTUyg+dC7PNDeleYC8tNVH2lo5d7n3mbj9oMkvUWJejsJAWZVj+ecKZX8+vUDfXpe5CPOVgzxu2LDjMIooL8YgI+/Etp79HgfDX7o24glfC7luM9fURbjjz4xl3+v28W7J1LBdZLl8T0pdXceXrEU9JW/jlK/qz1jq8xMYnq2uuuf6KLCrx/J9jdbOLuKpfNrBjT+V5w/hcmVFTxc30oq5bjVzrjuJ38XF57M/Z1Apuf1M55i6u4YW450sbfj/SAbyt9d5Nq+dbCfh1KqbB8pzCiMAqKunQ2N+wKjkFZfEBMS8digZZb91NPKcWX898Wz00TXrrlgGudMqaTzeA9N+47xfk+KLSGJCt/nHPf0i8oSsawGwQ+GZgogZ5rojNzJZfcZrYr28Xs0lCViQTvP+dMmsqFxH+PK4jzzeq87USDjZN7vuGZNoqIsHvTaSKWcPg2ToP/6k6Gs9pfMrQ6+E/F49vjdWHEzmVEoYfwPadS1s3R+TXA7/KVMOcqNF81EIIgp+IqZyZT26xLwv+RV48vT2lcKcGqF+xH6dCgj6Xct7WkSFgp89ZKzqBxXlvUL9UhDaxB3sAByYQiygbzPTAwoL4tx68VzaNp3LOjKVr+rPcgAi8clrc7h+kUzA5feK7uPZjUIAPOmVHLdghnUvXMkmJyjbsTwTjH8OVw4u2roq/0s0uw+Y8nNZEZhBDmZlUZ/j4l+SP/oE3Np2neM2poJtHd1B3n8e48eT9uK+8Jxtd4qzzcgvs+380SSQ50neHa7q5kjMaG2ZgIXz60O3ADgThaJRG9A0PUNuxWxiXiMj0yrTGuVWTmujNsvm5f1d40GjC2APPJEJ18/5uO/937r1LABT6aUK8+fwkdmTurTbCnaQzpKXNz3eaC+GZkC0/7k7Pek7km5Rmkw2Xq+dPtA0uxjyc1kRmGEOJmVRlRa4gsLZwSTevRDWjmujDuuODdwv/gZRCkvL33+9InceOGs4Avrf7Hqmttcvf2UQ907R/jCwhl8/dKz+fqlZwdyCa588rFAWE2Aj58zmZmnj2fN5hYcTZdUTqYcpkw4BXCNgtKr4JnNMIbF9CyAXDiibqZMva6jBvuMyoog0+yejTvcFNgM8asoKYXVm1uClFh/cvZTUv0kBL/KOpzi2p10i92Wzq/pTWQQ4emm/cH5/pIufHJN/x6uNPFScEGZURgB6ne1c/czbw56pZFW7emli/pqoL4vtNsr8KoaX95n9eaTctzq0u0HmjhvamW6QUm59cThlFT/NaZNGhc0wHFCqzeFQOZ6XUNrnzTGmAhnVFYEvumYEOxeshnGXIKhxsjT34QYNeDRRUwo4SwNPz7h3xXIc3vHEhMe2ro7rf90gKpXLOd+Ll986zAvvd0WNGLqSTpBzCtT0kWUXNO/hyNNvFRcUGYU8ky4x67ifiFyXWlkUr3sSTo80tDqtVR0V2IpR7nriSY+ee4ZWZ8v3B3N9/MqrsBc0vsCKr3NU5bMrXbrGKIdunDdTedNrUwTYPNTDFdcMz9wMYQnkly24CZRUXz0NyFGDXh0RxGd0AW38Y+vyupXMUOv1Am4BqO7n0CEH9/wGwT5O4tYTBDVPulwK59/O6MUSvT3y+UzN9TPZqm4oMwoDDPR7WFaj10GTscMP9av9ly7pYXGPR1uLrcQrKLC9CQdJodW55mIx2PUNbexeeeR4JwA1y+ayeHOE0FBWriNZqZevkq6HMH/+/kPpcUo/N1IJs2b0dbDYKyQaUKMngvvKDLpVlWUpWeebWjcR0tbF7uOdKVd5/TzAf7IDNcF6hfZ+Wjo/xiQCj1mZ1sXN9+3KVBsHch9M1j3TjjW0Z++k0+p9PAwozCMZNoeLplb3etGiUFtzYSM/s5wOmYs5qqMXjy3mgde2pmW0ue6aft+aWIxYceBzqyZHj1Jh+cjueIKTKhIsPtIV7DI8t099z73dr+pq9HCokwxiugWOZ+V2kbhCb+/bx3o5Jcv7w3umz7pFG6/7Jy0mFbU7ejT32euIhFj7ZaWjI/zpTscdaU5jnT1cOS9bsB1i/oV3dlSngfr3glf7xffRftW9/f3KebPvxmFQZJtJdFfI/uwPlDU3+mvql/efTRNm8btaNXRb3FYH1TTWlhmvCTDOQHue6E5TTO/3Es/fbX1aL/P1V8uejhG0Z/WTbF+GYyh47+/92zckfbZ3Xv0fVasT49pDaZWBhjw8433ejsOvddHjqNxTwcHO0+kpTzf+9zbaRlT4fiYH8TOtqu/+5k30wyUAu/3ONz73Nus/INFGcdXCp9/MwohohN+pmM/PhCPSZB7H07di24P737mzX5fb+2WFrYf6MyapeEH67J9gRKhiuHBEm6iAq6C6ecumN5niw6QiAsayUWPuoXiMXGVTVPFvUU28suSudVUlPWNh/nfp3CsrD8GWhD5gelM10TlOLbt6UD2Hku75unXDvD0aweoKHMlVx7aujst+P3CW4epe+dIH0mQ8A7Bz8YLj+Gp1w6wqq4lMIC57AqKKStJ9CQnk2Jg0aJFunXr1mF5rujWcfmy2j750Jua2/j+r7anfQD8D4S/dQz70QHufe7tfsXjTj+1jPb3erJ+8P/oE3PpPJFkzeYWMrj3mXfGqXz5krmB6JhfV3DW5FPTtu+Z+L/OmcyJnlSfFZhf1+C/3Jzq8dz2ibOzfshzadVpjC188cVMXeDCvRia9h2j+tTytM/rledPQXEn7mz4ooqZvkNXnj+F4z2pQEgRyFytjZti7VdUZ3oNDUl/b2pu4x+f2p7W43rf0ePsOPRe8JiPzJgYLPgGEvUrRFaSiNSrasbtzJjfKfhvkp9X7bt+NjTu6+MKWjK3mnhM0jTnw1vHnqRD494Opk8ax9NN+7n/xXc8NVA44zR3BT6r+lR++tt32HHwXY6815N1bIm48OnaqUGx2Xd/ua2PYVg8t5pbFs+ipe29oNfBnVd9kHs27sj4BUjEeuUK7rjiXNY1tPYxCqnIl+y2T5wdxD+ypeyZBIURxv9M+F3gMhWehT8nF51VnSbquKquJc0oXDSnij0d77On/Xhw7twzT6M8EaPRq6PxKYsLX7/0bLbv7+yjuTR1QgX7j/U2Gop5fap9wUVI3z37z+s3AVo6vyatV8jM08dTWzOBHYd65V+mTDiFbV5ySDj2Fo5p3PXZ+bR3dQeaZOHai0I2GsqbURCRnwLLgIOqOt87dzqwFpgD7ARuUNV2ERHgB8BVQBdwq6o25GtsPn7DkJ6kQyJUql+WiKV9SMJyziuumc/yxxr7TJzu70fGVoao20Pgp799h+sXzcx5fBqqsGzv6u7zeuVefviqupa0XgcAx04k3SrjUK53IgYrrvlQnywJP9/cz5CKhXYKMdygs2EMlvCq+PbL5mUsggtPfLcsnpWWfBHt3ldRFqe2ZkKaUXjz4LtuFX1MuPz8KfzmjQOknF7XUuPejrQxOUqaQQBXguWWxbOCupu3DnRmjF+EmwAtX1ZL094OHtq6mzWbW9JUBfwMvOffOpQ2f0RlXL77y20oBJpk/rzx4luFbTSUz53CA8C/AT8PnbsT+LWqfk9E7vSOvw0sBc7x/i0GfuT9zCvrGloDf35PhlL9TO6S8Idn7ZYWUk54tyD9is0p7gdhVV2LGyfIwPk1lRx5r5tD754A7dUbumfjDqrGlwfCXX52kl+hHI1brHyhOa04KBiDul+0sNxEuGAsKmtQ7KlzRvHSXyZeeIWdqY2r/9hHGlo53HmCREwCXa7f7jhMIh4jEZc+vUCSjnK8J+UWwtHb16Mlku4aJYYrweLziBds7g/foDXu7WD3ka6gwK476dC071jaCj/cqdAPZIfxdyPJlHLT4pnsPtLFC56ry68VGlVGQVWfF5E5kdPXAJ/0bv8MeBbXKFwD/FzdAMcmEZkkIjWquo880F+v2sleqb6P/4aExbf8n5ua24IPoE9/vs0wmfK3ff77kjncsnhWML7O4z3BrqQs4bW0xM1O2rant0I5KnecyS8azhaKkikjYjBBMsOIkikT7/bL5qUVO67Z3Fs9H/av37zypWBFXRYXPjRjYuCKCSuodh7vCXbGjrrp3nXvHAkCwANlKwluMVzn8R5+/yd1nFIWzxr8jnuNR+IxCTwC4cB0eIW/fX9n2u59VvWpXLtgBmv9Is+Qa9cBDneeSBO2dICXdx/NaDTzzUjHFKaEJvr9wBTv9nRgd+i6Vu9cH6MgIrcBtwHMmpVd1yQT4RWMiATN48viwvxpE4NVeVQILBHJuAlXBYPf0pCMweBcafK2uv6H4MZ7XwriF91JJ01vxv+yPdLQyvRJ49IE8R54aWdQLRoT+ugm5UIppM4ZxUt/hVr+gsqXT4m6kTY1t6UVZiZTSu10N2jrP1fttIm0d3XTfLg3sCtA075jXHruGTzz2oEBF2cxgbmTT6U8EUuTgs/GWZNPo2biKYFUeHTx5a/wv7fhdbZFWtr+9LfvcGp5nKDoOvLYp1474MnL9y40n3ntAC+8dWjE3UgFCzSrqorIoKdQVV0JrAQ3+2iwj9/U3Na7GlAlLq5LqLIi0SdWENZo8V0/jzS0snxZLRsa96VlHl1yzmTGlcX7zTTK6XeLjDPa+9Y3YP5kH16xhAN3n66dmnOV5VApplQ6o3jIVqiVrbJ3ydxqyuLSu1PwlH2vWzCDdQ2tHOw8wV1PNPWJ2ym97qXw4/vDUdKyhXLhncPv8vbBd4nF+lcNcCCtn4jPjoPvDvj8vvS473Hor9Yn34y0UTjgu4VEpAY46J3fA4QjsDO8c8NO1fjytMk3pW5hS+Oejj6rfD/A5eMXp3zn0W1phiMRE2adPp7aaRPZuP1gHwmKsrjw0ZmTsm5ny+PCdSFV0EyZTjde6G6b/cn+ld1HedpbFYU/PCO1yi8VgS+jMPT3OcxmMBbOrmL1bRcH+l7+ztyPM2Rz74TdS4dCsi0+USG+wSD0Vk2n+g855EzC0xuL8qkPnIkAv37d/V4XIqY30kbhceBLwPe8n4+Fzn9DRNbgBpg78hVPaO/q7lNs4uv+50r4sePL4xzvSbF6cwuJeCxQe/SviQv8zWfnByl2ft+CB17aGQTcoq4df/W97MM1abnbtdMmpnVU+8Ezb/Yap5j0G7jLF6Ui8GUUH9kWLpnui1ZBB5IsuBNsuGDST4H1F0z+Tt4X4osaFgGqTi3jaFdPsAOIx4SzqscHu4kheIX7pIZ/cGolf/f5D7F9f6era7a3I3BhX3bemaxY34TjxS6WL6sdPTEFEVmNG1SeLCKtwF/jGoMHReQrwC7gBu/y/8RNR92Bm5L6h/ka15K51cT7sdKZGOiqcL9i3+8ffYyf0hlOufNdPNma58Sk18fo6xH5+H5ZcD/UjqMZA3f5pFQEvozSJy1zyYvv+bGF/gomK8p6P5vhrKCVz7/NzrberKRYTDja1UMiHuPSc8/gzMoKrl0wg0caWnNyMc2pHs8FMyex/tV9aTt7cItLT61IpC08yxOxYKyPfeOSYLG4dH4NjXs7eqvAVQuSDp7P7KOb+7nr8gzXKnB7vsYSJSoF7TN1QgWJmNB69P3gXC4yE2H8lYm/igmnlYY/sP2tlMKrb7fwzd3zZvK9+l8SCTUoGckVe6kIfBmlTy6ftagbKnp9WIgP3IVWuGlPKuVwwcxJaRmID3uKxP0lkcQEPjZvMtctmMHvXzyH239Rn1YHcWpFgovnVqcZhcY9HWzb09FHOaGuuY1UaK5JKbx1oDPj3yOfsbwxV9G8qbmt317E+4+d6NNRatrEU5g+aVyfeEB/uix+yfzS+TV9Mphy8bv7rQX9QJmIG0sYqGdtoeoKLEvJGCkG+1mLXp9Jxn7p/BrueqIpcOWGvzt+fMOffLfv7+Rffv1mevGbkrZD/9PLz+WvHt0W3F2eiPHMGwcJ4xuXPsoJGZoK/fLlvUydcAp3XvXB4Fy+Y3ljzigsmVtNeSg7ISYwaXxZIDkRXumDq+64L7RzAHdLuHhuNavqWoLrfX2U6FZ1oCrOKAtnV3H9opnBc6ujTJs0rt+VkX/e6goMIztRd+cdV5zr3pGlN3T4O+YXtAYS9+LOE9FaDCDogZIpE0nonTPGlcWDotT+vBFPNu1PMwr5juWNOaMQzm443HmC32w/2EeD6MI5VVSUxYPqwuibdWpFIvA5+h+wsNBXuNhtIL97pm1g9LlzWfnbit0wspPJpXTPxh0kQ72hc1m0+buH/nbotyyeRXtXN69mSWCRmOAAz7x+AJHs7ukLZk5KO853LG/MGQXonUC/8+i2jAHnc6ZUUjttYh8hLR9fXiLsvsnmKurPF9rfNtB89YaRH6KLp5OZYHPZoUfrLRJxV73Yr8xOUz/IYhEEdz6Kvn4+54cxaRR8Mr0X5aGUtmjcwJeQjiqGhrOF/KBVLnUD2baBtvI3jPwz1Ak2Wy1GtN4C3LnCl7gfKAPSb3iVqzTNcDGmjcJ1C2YE2QXxWN+AbtjSlydi/OMNF/SbP+24OWRuA3H6ZgtlwlI6DaPw5GuCzfS8vgHae/Q4qze3BD0Zrvig2/uhtmZCWuOuQngKxnyTnWypXX4VZbiyMtPjfesfji0MtvG3uYkMY+wQnTdGWg0gW5OdMW8UhoNcjIdhGEaYQi4IrfPaCOD3ZnhkBCuKDcMoXYo1bhgr9ABGA5kCxoZhGKWIGYVhwA8Yx6UwqoaGYRjDhbmPhgGrKzAMY7RgRmGYKFb/oGEYxmAw95FhGIYRYEbBMAzDCDCjYBiGYQSYUTAMwzACzCgYhmEYAWYUDMMwjICS1j4SkUPArkKPIwuTgcxNGUY39nuPLez3Lj1mq+oZme4oaaNQ7IjI1v5Ep0Yz9nuPLez3Hl2Y+8gwDMMIMKNgGIZhBJhRyC8rCz2AAmG/99jCfu9RhMUUDMMwjADbKRiGYRgBZhQMwzCMADMKeUBErheRJhFxRGRR5L6/FJEdIrJdRP5bocaYb0TkLhHZIyIve/+uKvSY8omIfMZ7T3eIyJ2FHs9IISI7RWSb9x4XvmF6nhCRn4rIQRFpDJ07XUSeFpG3vJ+jQjvfjEJ+aASuBZ4PnxSR84GbgFrgM8APRSQ+8sMbMf5ZVS/w/v1noQeTL7z38B5gKXA+cLP3Xo8VLvPe41GXsx/iAdzvbJg7gV+r6jnAr73jkseMQh5Q1ddVdXuGu64B1qjqCVV9B9gBXDSyozPywEXADlVtVtVuYA3ue22MElT1eeBI5PQ1wM+82z8DPjeSY8oXZhRGlunA7tBxq3dutPINEXnV23qPiq11P4y19zWMAk+JSL2I3FbowYwwU1R1n3d7PzClkIMZLqwd50kiIs8AUzPc9R1VfWykx1MIsv0NgB8Bf4s7afwt8I/Al0dudMYIcYmq7hGRM4GnReQNb1U9plBVFZFRkd9vRuEkUdUrTuJhe4CZoeMZ3rmSJNe/gYjcB6zP83AKyah6XweDqu7xfh4UkUdxXWljxSgcEJEaVd0nIjXAwUIPaDgw99HI8jhwk4hUiMhZwDnA5gKPKS94XxKfz+MG30crW4BzROQsESnHTSZ4vMBjyjsicqqIVPq3gSsZ3e9zlMeBL3m3vwSMCg+B7RTygIh8HvhX4AzgP0TkZVX9b6raJCIPAq8BSeB2VU0Vcqx55H+JyAW47qOdwNcLOpo8oqpJEfkG8CsgDvxUVZsKPKyRYArwqIiAO5esUtUnCzuk/CAiq4FPApNFpBX4a+B7wIMi8hVcCf8bCjfC4cNkLgzDMIwAcx8ZhmEYAWYUDMMwjAAzCoZhGEaAGQXDMAwjwIyCYRiGEWBGwcg7IpLyVDQbReQJEZk0wPV3icifD3DN58KicyKyQkROpqAw+rwf8Mb6OxE5e6jPVwyIyK0ickhE7veOPykiKiJfDV1zgXfuz73jB0TkC5HneTfLa4zz/m7dIjI5X7+LkX/MKBgjwXFPRXM+rqjY7cPwnJ/DVSQFQFWXq+ozw/S8D6vqR1X1bf+kuJTy92Wtqn41dNxIel79zcArJ/vkqnpcVS8A9p7scxjFQSl/yI3S5CU8sTgROVtEnvTE1F4QkQ9ELxaRr4nIFhF5RUQeEZHxIvIx4LPAP3ir07P9la3X1+Ch0OM/KSLrvdtXishLItIgIg+JyGmR17oKuAP4YxHZKCJzvB4JP8edRGeKyLe88bwqIn8Teux3RORNEXlRRFaHVtzPitdTQ0Qmi8hO73ZcRP4h9FxfD433WRF5WETeEJFfiFcdJiIXish/eX+LzSJSKSLPe0WC/jheFJGP5PA+7AJOEZEp3vN/BtiQw+P8XZnfJ2OPiPz/uTzOKA3MKBgjhrh9By6nVwJiJfAnqroQ+HPghxketk5VL1TVjwCvA19R1f/ynuNb3g7k7dD1zwCLPdkFgBuBNZ5L438CV6jqAmAr8M3wC3k9H36M2wfiMu/0OcAPVbUWOM87vgi4AFgoIp8QkYW40hYXAFcBF+bw5/gK0KGqF3rXf01c6ROAj+Iap/OBucDHPfmMtcCfeX+LK4DjwE+AWwFE5FzgFFXNdcX/MHA98DGgATgRuf8fQpP/y/5Jb1d2AW6F7xHg33J8PaMEMJkLYyQY500q03En9qe9VfrHgIe8hTBARYbHzheRvwMmAafhSkn0iyc58SRwtYg8DPwe8BfApbiT7G+91yvH3bUMxC5V3eTdvtL79zvv+DRcI1EJPKqqXQAikovu0ZXAh0N++4nec3UDm1W11Xuul4E5QAewT1W3eL/nMe/+h4Dvisi3cFVoH8jhtX0exDU0HwBW474fYb6lqg/7B+GYgre7+Hfgn1S1fhCvaRQ5ZhSMkeC4ql4gIuNxJ/XbcSevo96KMxsPAJ9T1VdE5Fbc1elArAG+gbuK3aqqnd4k9rSq3jzIsb8Xui3A/6eq94YvEJE7sjw+Se+O/JTIc/2JqqYZORH5JOkr9hRZvqeq2iUiT+M2fLkBWJhlLNHH7heRHuDTwJ/R1yhk4y6gVVXNdTTKMPeRMWJ4K+k/Bf4H0AW8IyLXQxDIzeQLrwT2iUgZ8MXQ+U7vvkw8BywAvoZrIAA24bph5nmvd6rnbhkMvwK+7MciRGS6uH0Engc+J24GTiVwdegxO+mdqL8Qea4/9n4vROTckMsrE9uBGhG50Lu+UkR8Y3E/8C/AFlVtH+TvtBz49mCEGUXkalz31Z8O8rWMEsCMgjGiqOrvgFdxs12+CHxFRF4BmsjcwvK7QB3wW+CN0Pk1wLckQ+qoN8Gtx+2ZvN47dwjX975aRF7FdR31CWwPMPangFXASyKyDdcnX6mqDbhumFdwg7VbQg/7Pu7k/zsgnKp5P65aboO4zeDvJfuOoBs3PvKv3t/rabydh+e+OQYMetWuqv+lqr8c5MO+iesK3OzFG1YM9nWN4sVUUg1jmBGRu4B3VfX7I/R604BngQ+oqpPh/luBRar6jREYy07vtQ7n+7WM/GA7BcMoYUTkD3B3Ut/JZBA8jgNLxStey9M4/GSCMqC/cRglgO0UDMMwjADbKRiGYRgBZhQMwzCMADMKhmEYRoAZBcMwDCPAjIJhGIYR8H8AS9bxZlSncsIAAAAASUVORK5CYII=\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "fig = figure()\n", "ax = fig.subplots(1, 1)\n", "\n", "ax.plot(freq_2, counts_2, '.')\n", "ax.set_xlabel('Relative frequency [MHz]')\n", "ax.set_ylabel('Counts [/s]')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Ce spectre peut être modélisé par la somme d'une gaussienne (fond large) et d'une lorentzienne (étroite). \n", "\n", "8. Faire l'ajustement. Donner la valeur de la position du centre de la lorentzienne étroite et son écart type. Comparer ces résultats à ceux obtenus à la question 4." ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "Text(0, 0.5, 'Counts [/s]')" ] }, "execution_count": 10, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "def fonction_2(x, amplitude1, centre1, largeur1, amplitude2, centre2, largeur2):\n", " return amplitude1*np.exp(-((x-centre1)/largeur1)**2) + amplitude2/(1 + ((x-centre2)/largeur2)**2)\n", "\n", "p0 = 100, 0, 10, 500, 0, 1\n", "popt_2, pcov_2 = curve_fit(fonction_2, freq_2, counts_2, p0)\n", "\n", "x = np.linspace(-30, 30, 201)\n", "fig = figure()\n", "ax = fig.subplots(1, 1)\n", "\n", "ax.plot(freq_2, counts_2, '.', label='Data')\n", "ax.plot(x, fonction_2(x, *popt_2), label='Fit')\n", "ax.set_xlabel('Relative frequency [MHz]')\n", "ax.set_ylabel('Counts [/s]')" ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Frequence : 2923538429.2489724 MHz\n", "Incertitude : 7.6 kHz\n", "Incertitude relative : 2.6028203411913704e-12\n" ] } ], "source": [ "freq_abs_2 = freq_ref + popt_2[4]\n", "sigma_abs_2 = np.sqrt(pcov_2[4, 4])\n", "\n", "print(f'Frequence : {freq_abs_2} MHz')\n", "print(f'Incertitude : {sigma_abs_2*1E3:.1f} kHz')\n", "print(f'Incertitude relative : {sigma_abs_2/freq_abs_2}')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "8. A l'aide d'un masque, ajuster à l'aide d'une lorentizienne uniquement les points obtenus pour une fréquence laser comprise entre -2 et 2 MHz. Comparez avec la question 4." ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Frequence : 2923538429.2486176 MHz\n", "Incertitude : 10.22676753039575 kHz\n", "Frequence : 2923538429.2486176 MHz\n", "Incertitude : 10.226763342276545 kHz\n" ] }, { "data": { "image/png": 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "mask = (freq_2 < 2) & (freq_2 > -2)\n", "\n", "p0 = 100, 300, 0, 1\n", "popt_tronq, pcov_tronq = curve_fit(fonction, freq_2[mask], counts_2[mask], p0)\n", "\n", "x = np.linspace(-2, 2, 201)\n", "fig = figure()\n", "ax = fig.subplots(1, 1)\n", "\n", "ax.plot(freq_2[mask], counts_2[mask],'.', label='Données tronquées')\n", "#ax.plot(freq, counts,'.', label='Données question 4')\n", "ax.plot(x, fonction(x, *popt),label='Fit')\n", "ax.set_xlabel('Relative frequency [MHz]')\n", "ax.set_ylabel('Counts [/s]')\n", "ax.legend()\n", "ax.grid()\n", "\n", "freq_abs_tronq = freq_ref + popt_tronq[2]\n", "sigma_abs_tronq = np.sqrt(pcov_tronq[2, 2])\n", "\n", "print(f'Frequence : {freq_abs_tronq} MHz')\n", "print(f'Incertitude : {sigma_abs_tronq*1e3} kHz')\n", "print(f'Frequence : {freq_abs} MHz')\n", "print(f'Incertitude : {sigma_abs*1e3} kHz')\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**Fonctions utilisées**" ] }, { "cell_type": "code", "execution_count": 13, "metadata": { "tags": [ "keep" ] }, "outputs": [], "source": [ "from scipy.integrate import solve_ivp\n", "from matplotlib.pyplot import errorbar\n", "# ou ax.errorbar" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] } ], "metadata": { "celltoolbar": "Tags", "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.8.8" }, "varInspector": { "cols": { "lenName": 16, "lenType": 16, "lenVar": 40 }, "kernels_config": { "python": { "delete_cmd_postfix": "", "delete_cmd_prefix": "del ", "library": "var_list.py", "varRefreshCmd": "print(var_dic_list())" }, "r": { "delete_cmd_postfix": ") ", "delete_cmd_prefix": "rm(", "library": "var_list.r", "varRefreshCmd": "cat(var_dic_list()) " } }, "types_to_exclude": [ "module", "function", "builtin_function_or_method", "instance", "_Feature" ], "window_display": false } }, "nbformat": 4, "nbformat_minor": 4 }