ComptonScattering.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt\n",
    "import scipy.optimize as optimize\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "calib_path = \"C:\\Users\\Jason\\Desktop\\ComptonScattering\\calibration_data.xlsx\"\n",
    "correction_data_path = \"C:\\Users\\Jason\\Desktop\\ComptonScattering\\plot_hack_data.csv\"\n",
    "data_path = \"C:\\Users\\Jason\\Desktop\\ComptonScattering\\\\run_data1.xlsx\""
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x165b8fd0>]"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
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      ],
      "text/plain": [
       "<matplotlib.figure.Figure at 0xd07dac8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "calib_data = pd.read_excel(calib_path,sheetname=0).ix[:-2]\n",
    "calib = lambda x,a,b,c: np.array(a*x**2 + b*x + c, dtype=np.float)\n",
    "a0,pcov = optimize.curve_fit(calib,calib_data.Centroid.values,calib_data.Energy.values)\n",
    "plt.scatter(calib_data.Centroid,calib_data.Energy)\n",
    "x = np.arange(calib_data.Centroid.min(),calib_data.Centroid.max(),0.1)\n",
    "plt.plot(x,calib(x,a0[0],a0[1],a0[2]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x16833828>]"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
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       "jp/8HabTeQ7eS/ZaoC55PRz4LeFcsJf8EP68HJ68biRk95QfwkSOF2etu8k/kzCqo4lwgaAU3QM8\n",
       "D+wmXDO4hDCqYD65hyldR/g+y4F3DWrS3E4jnOJYQudwqxn4+Q5HE86fLiEM1/tU8r6X/B2m0zmK\n",
       "xkv2Qwi/70sIQ2w7/o56yQ9wDOEIfinwY8KFV0/5hwMv0fkPLfjKLyIiIiIiIiIiIiIiIiIiIiIi\n",
       "IiIiIiIiIiLSs/8HJmDgC5JM91IAAAAASUVORK5CYII=\n"
      ],
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1689b518>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "correction_data = pd.DataFrame.from_csv(correction_data_path)\n",
    "correction_data['x']= correction_data.index\n",
    "correction_data.index = np.arange(len(correction_data))\n",
    "\n",
    "detector_correction = lambda x,a,b,c,d,e: np.array(a*x**4 + b*x**3 + c*x**2 + d*x + e,dtype=np.float)\n",
    "\n",
    "a1,pcov = optimize.curve_fit(detector_correction,correction_data.x.values,correction_data.y.values)\n",
    "plt.scatter(correction_data.x,correction_data.y)\n",
    "x = np.arange(correction_data.x.min(),correction_data.x.max(),0.1)\n",
    "plt.plot(x,detector_correction(x,a1[0],a1[1],a1[2],a1[3],a1[4]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "data = pd.read_excel(data_path)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x16cb44a8>]"
      ]
     },
     "execution_count": 41,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
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       "SCj9p8nfZ/E64BfAb4A/ADcThn7z+FkUVfs3MbRL58Z1VTW77O8DDid8c3cBH6C0c67dFQjXENoK\n",
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       "PH4WRdX+TdxC+LdTPHn1cODepqcbwULCTpjthJ0MeVHp5LS/JOyUup32P6ysmrdQ+sLP62dxFGHL\n",
       "fjNha3Ya+f0szqN06OVqwm/Defks1hD2VfyesAHwUYb/u/vkVTMzMzMzMzMzMzMzMzMzMzMzMzMz\n",
       "MzMzMzOzav4/h0R09e8jtYYAAAAASUVORK5CYII=\n"
      ],
      "text/plain": [
       "<matplotlib.figure.Figure at 0x168abf98>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "energies = calib(data.Centroid.values,a0[0],a0[1],a0[2])\n",
    "plt.plot(data.theta.values,energies)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div style=\"max-height:1000px;max-width:1500px;overflow:auto;\">\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>theta</th>\n",
       "      <th>Centroid</th>\n",
       "      <th>FWHM</th>\n",
       "      <th>Net Area</th>\n",
       "      <th>Uncertainty</th>\n",
       "      <th>Net Rate</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>   0</td>\n",
       "      <td> 163.50</td>\n",
       "      <td> 11.829</td>\n",
       "      <td> 79866</td>\n",
       "      <td> 0.39</td>\n",
       "      <td> 4371.91</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>  30</td>\n",
       "      <td> 142.78</td>\n",
       "      <td> 11.457</td>\n",
       "      <td>  1559</td>\n",
       "      <td> 5.38</td>\n",
       "      <td>    7.68</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>  40</td>\n",
       "      <td> 129.10</td>\n",
       "      <td> 14.065</td>\n",
       "      <td>  6926</td>\n",
       "      <td> 2.33</td>\n",
       "      <td>   14.76</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>  60</td>\n",
       "      <td> 103.53</td>\n",
       "      <td>  9.371</td>\n",
       "      <td>  2566</td>\n",
       "      <td> 4.53</td>\n",
       "      <td>    2.32</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>  80</td>\n",
       "      <td>  82.27</td>\n",
       "      <td>  7.486</td>\n",
       "      <td>  2451</td>\n",
       "      <td> 4.97</td>\n",
       "      <td>    1.46</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>  90</td>\n",
       "      <td>  74.46</td>\n",
       "      <td>  5.811</td>\n",
       "      <td>  3584</td>\n",
       "      <td> 4.82</td>\n",
       "      <td>    1.38</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td> 100</td>\n",
       "      <td>  67.81</td>\n",
       "      <td>  6.637</td>\n",
       "      <td>  2720</td>\n",
       "      <td> 4.85</td>\n",
       "      <td>    1.81</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   theta  Centroid    FWHM  Net Area  Uncertainty  Net Rate\n",
       "0      0    163.50  11.829     79866         0.39   4371.91\n",
       "1     30    142.78  11.457      1559         5.38      7.68\n",
       "2     40    129.10  14.065      6926         2.33     14.76\n",
       "3     60    103.53   9.371      2566         4.53      2.32\n",
       "4     80     82.27   7.486      2451         4.97      1.46\n",
       "5     90     74.46   5.811      3584         4.82      1.38\n",
       "6    100     67.81   6.637      2720         4.85      1.81"
      ]
     },
     "execution_count": 40,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 84,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "401649.5812793253"
      ]
     },
     "execution_count": 84,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "rest_E = 0.511e6\n",
    "E_0 = 661.7e3\n",
    "inv_E = lambda theta: 1/E_0 + 1/rest_E*(1-np.cos(theta*np.pi/180))\n",
    "1/inv_E(60)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 83,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "407315.65089702629"
      ]
     },
     "execution_count": 83,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "calib(102.36,a0[0],a0[1],a0[2])*1e3 #eV\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "corr_fac = #gaussian\n",
    "photon_E = calib(theta)*corr_fac"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "ename": "SyntaxError",
     "evalue": "invalid token (<ipython-input-10-bdf75a26e38e>, line 3)",
     "output_type": "error",
     "traceback": [
      "\u001b[1;36m  File \u001b[1;32m\"<ipython-input-10-bdf75a26e38e>\"\u001b[1;36m, line \u001b[1;32m3\u001b[0m\n\u001b[1;33m    h = 4.135667516e−15\u001b[0m\n\u001b[1;37m                   ^\u001b[0m\n\u001b[1;31mSyntaxError\u001b[0m\u001b[1;31m:\u001b[0m invalid token\n"
     ]
    }
   ],
   "source": [
    "c = 1\n",
    "r0 = 2.82e-15\n",
    "gamma = photon_E/rest_E #hf = calib'd energy\n",
    "dN_classical = lambda theta: c*r0**2*((1+cos(theta)**2)/2)\n",
    "dN_KN = dN_classical*1.0/(1+gamma*(1-cos(theta)))**2*(1+gamma**2*(1-cos(theta))**2/((1+cos(theta)**2)(1+gamma*(1-cos(theta)))))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": []
  }
 ],
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