{ "cells": [ { "cell_type": "markdown", "id": "16465f2d", "metadata": {}, "source": [ "# Fit de franges d’interférence" ] }, { "cell_type": "markdown", "id": "cfd3abf1", "metadata": { "mystnb": { "image": { "width": "200px" } } }, "source": [ "\n", "\n", "On souhaite ajuster les franges d’un interféromètre atomique. Les données sont dans le fichier {download}`data/fit_sinus.dat `. La première colonne du fichiers (axe x) représente une fréquence en Hz. La seconde colonne représente la population mesurée pour une fréquence donnée. L’objectif est de trouver la position de la frange centrale.\n", "\n", "Voici à quoi ressemblent les données : \n", "\n", "```{image} data_interfero.png\n", ":alt: Interferometre atomique\n", ":width: 70%\n", ":align: center\n", "```\n", "\n", "\n", "On ajustera par une fonction cosinus avec une amplitude, une moyenne, une position de la frange centrale et une largeur ajustable (interfrange), soit en tout quatre paramètres.\n", "\n", "\n", "1. Lire le fichier et tracer les données.\n", "\n", "2. Écrire la fonction de fit qui dépend des paramètres ci dessus. On appellera frange(x, ...). Tracez la courbe pour x entre ±220 Hz avec des paramètres raisonables. On prendra un inter-frange de 200 Hz.\n", "\n", "3. Calculer les paramètres optimaux. Quelle est la position la frange centrale ? Représentez les points et la courbe.\n", "\n", "4. Quelle est l’incertitude sur la position de la frange centrale ?" ] }, { "cell_type": "markdown", "id": "501f2f54", "metadata": { "tags": [ "sol" ] }, "source": [ "--------------------------------------------------------------------------------------\n", "\n", "## Solution" ] }, { "cell_type": "code", "execution_count": 1, "id": "76a47f59", "metadata": {}, "outputs": [], "source": [ "import matplotlib.pyplot as plt\n", "from scipy.optimize import curve_fit\n", "import numpy as np" ] }, { "cell_type": "code", "execution_count": 2, "id": "be722b88", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "Text(0, 0.5, 'Amplitude')" ] }, "execution_count": 2, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "freq, amp = np.loadtxt('data/fit_sinus.dat', unpack=True)\n", "\n", "fig = plt.figure()\n", "ax = fig.subplots(1, 1)\n", "\n", "ax.plot(freq, amp, 'o')\n", "ax.set_xlabel('Fréquence (Hz)')\n", "ax.set_ylabel('Amplitude')" ] }, { "cell_type": "code", "execution_count": 3, "id": "a2c66d7b", "metadata": { "scrolled": true }, "outputs": [ { "data": { "text/plain": [ "Text(0.5, 0, 'Fréquence (Hz)')" ] }, "execution_count": 3, "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 frange(x, a, b, f_0, Delta_f):\n", " return a + b*np.cos(2*np.pi*(x-f_0)/Delta_f)\n", "\n", "p0 = (0.2, 0.1, 0, 200)\n", "\n", "f_plot = np.linspace(-220, 220)\n", "\n", "fig = plt.figure()\n", "ax = fig.subplots(1, 1)\n", "\n", "ax.plot(freq, amp, 'o')\n", "ax.plot(f_plot, frange(f_plot, *p0))\n", "ax.set_xlabel('Fréquence (Hz)')" ] }, { "cell_type": "code", "execution_count": 4, "id": "e60571c8", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "Text(0.5, 0, 'Fréquence (Hz)')" ] }, "execution_count": 4, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "p_opt, p_cov = curve_fit(frange, freq, amp, p0=p0)\n", "\n", "fig = plt.figure()\n", "ax = fig.subplots(1, 1)\n", "\n", "ax.plot(freq, amp, 'o')\n", "ax.plot(f_plot, frange(f_plot, *p_opt))\n", "ax.set_xlabel('Fréquence (Hz)')" ] }, { "cell_type": "code", "execution_count": 5, "id": "2b1e884a", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Position de la frange :2.37\n", "Incertitude de la frange :0.32\n" ] } ], "source": [ "a, b, f_0, Delta_f = p_opt\n", "incertitude = np.sqrt(p_cov[2, 2])\n", "\n", "print(f\"Position de la frange :{f_0:.2f}\")\n", "print(f\"Incertitude de la frange :{incertitude:.2f}\")" ] }, { "cell_type": "code", "execution_count": null, "id": "6cb9e169", "metadata": {}, "outputs": [], "source": [] } ], "metadata": { "celltoolbar": "Éditer les Méta-Données", "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": 5 }