DoubleSlit.ipynb

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      "name": "DoubleSlit",
      "version": "0.3.2",
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        "id": "view-in-github",
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        "<a href=\"https://colab.research.google.com/github/jrstevenjlab/ColaboratoryAtomicLab/blob/master/DoubleSlit.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
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      "source": [
        "The goal of the excercise is to fit the function \n",
        "\n",
        "$$I(x)= B + 4 I_0 \\cos^2\\left(\\frac{\\pi d}{\\lambda}\\frac{x-x_0}{\\ell} \\right)\\left[\\frac{\\sin (\\frac{\\pi\n",
        "a}{\\lambda}\\frac{x-x_0}{\\ell})}{\\frac{\\pi a}{\\lambda}\\frac{x-x_0}{\\ell}} \\right]^2$$\n",
        "\n",
        "to your data for intensity as a function of position of the slit that you recorded in lab.  The parameters of the function are:\n",
        "\n",
        "*   $\\lambda$: wavelength of light source (670 nm for laser and 546 nm for bulb)\n",
        "*   $\\ell$: distance between double slit and viewing screen (you should have measured this)\n",
        "*   B: background \"pedestal\" for laser data or \"dark rate\" for bulb data,\n",
        "*   $I_0$: Intensity magnitude \n",
        "*   d: slit separation distance\n",
        "*   a: slit width distance\n",
        "*   $x_0$: position of maximum intensity\n",
        "\n",
        "By \"fitting\" the data we mean that the parameters of the model are allowed to vary until the curve defined by this function best match the data you've measured.  This is done by minimizing the $\\chi^2$ which is a metric for comparing the model function to the observed data.  The $\\chi^2$ is defined as\n",
        "\n",
        "$$\\chi^{2} = \\sum_{i=0} \\frac{(I_i - I_{model}(x_i))^2}{\\sigma_{I_{i}}^2}$$\n",
        "\n",
        "where the sum of $i$ is over all the data points\n",
        "*  $I_i$ are the individual intensity datapoints for a given position (y-axis value), \n",
        "*  $\\sigma_{I_{i}}$ are the errors on the individual datapoints,\n",
        "*  and $I_{model}(x_i)$ is the value of your model function for slit position $x_i$\n",
        "\n",
        "The steps below describe the process that you should follow:\n",
        "\n",
        "1.   Save your data to Google Drive in a file named DoubleSlitAll.  See example at [DoubleSlitAll](https://docs.google.com/spreadsheets/d/1Vj3S7WAFMn4c7h2KipQQj63Ob5xlXL5MeTSI55f64AI/edit?usp=sharing)\n",
        "2.   Run the fit code by pressing the \"Play\" button, which will cause a few things to happen:\n",
        "> * You will be prompted to enter an authorization code, which appears in a new browser window (be sure to allow pop-ups).  This gives the Python code access to the files in your Google Drive.\n",
        "> * The datapoints will be plotted vs position in the figure below the code \n",
        "> * The `curve_fit` command in the code will find the \"best fit\" values for the paremeters of the model which gives the smallest value for the $\\chi^2$ possible (ie. it \"minimizes\" the $\\chi^2$).\n",
        "> * The function $I_{model}(x)$ with these \"best fit\" parameters will be plotted in red overlayed with your data points\n",
        "> * The values for the parameters are output as text below the figure, along with the uncertainties on those parameters\n",
        "> * The $\\chi^2$ and # DOF will also be output to determine the quality of the fit\n",
        "3.   To switch between the laser (Photodiode) data and the bulb (PMT) data you need to make a few modifications:\n",
        "> * Set the wavelength ($\\lambda$) to the appropriate value for your data by commenting/ucommenting a line\n",
        "> * Set y = ybulb and ey = eybulb (or vice versa) to use a given dataset under 'CHOOSE YOUR DATA HERE!'\n",
        "> * Set the initial parameters of your fit for B and $I_0$ (the first 2 parameters in the list) to match the scale of the y-axis for your datapoints, and the parameter $x_0$ to match the position of the intensity maximum\n",
        "> * Change axes labels appropriately\n",
        "\n",
        "Finally, we need evaluate the \"quality\" of our fit by looking at the $\\chi^{2}/DOF$, where DOF is the **Degrees Of Freedom** of the fit, defined as:\n",
        "\n",
        "$$DOF = # data points - # parameters$$\n",
        "\n",
        "In our case the # parameters = 5 (B, $I_0$, a, d, $x_0$). and the # data points is given by the number of points you observed in lab.   In general, a \"good\" fit will have a $\\chi^{2}/DOF$ close to 1.  \n",
        "*  If $\\chi^{2}/DOF$ >> 1, then the errors were likely **underestimated** meaning the model function does not describe the data.\n",
        "*  If $\\chi^{2}/DOF$ << 1, then the errors were likely **overestimated** meaning the model describes the data better than it should (statistically).\n",
        "\n"
      ]
    },
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        "outputId": "d884c0e7-960f-4e25-8a7a-7fbcb8fe2523",
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      "source": [
        "# import modules needed for data analysis\n",
        "import numpy as np\n",
        "import matplotlib.pyplot as plt\n",
        "from scipy.optimize import curve_fit\n",
        "\n",
        "# import modules for reading data from Google Sheets\n",
        "!pip install --upgrade -q gspread\n",
        "import gspread\n",
        "from google.colab import auth\n",
        "auth.authenticate_user()\n",
        "from oauth2client.client import GoogleCredentials\n",
        "gc = gspread.authorize(GoogleCredentials.get_application_default())\n",
        "\n",
        "# function for detected intensity vs position\n",
        "def IntensityModel(x, B, I0, D, A, x0):\n",
        "  L=500 # distance between slits in (mm)\n",
        "  #l=546e-6 # green bulb wavelength (mm)\n",
        "  l=670e-6 # laser wavelength (mm)\n",
        "  C=np.pi/(l*L)\n",
        "  return B + 4*I0 * np.power(np.cos(C*D*(x-x0)),2.0) * np.power(np.sin(C*A*(x-x0))+1e-9,2.0) / np.power((C*A*(x-x0))+1e-9,2.0)\n",
        "\n",
        "########################\n",
        "# LOAD YOUR DATA HERE! #\n",
        "########################\n",
        "\n",
        "# Open our new sheet and read some data.  Upload the file to Google Drive main folder for access\n",
        "worksheet = gc.open(\"DoubleSlitAll\").sheet1\n",
        "\n",
        "# Wednesday afternoon data\n",
        "x=worksheet.col_values(1,'UNFORMATTED_VALUE')[1:] # first column is position (x-axis variable)\n",
        "ylaser=worksheet.col_values(2,'UNFORMATTED_VALUE')[1:] # second column is laser data (y-axis variable)\n",
        "ybulb=worksheet.col_values(3,'UNFORMATTED_VALUE')[1:] # thrid column is bulb data (y-axis variable)\n",
        "\n",
        "# check that data from spreadsheet is in the right format\n",
        "print(x)\n",
        "print(ylaser)\n",
        "print(ybulb)\n",
        "\n",
        "eylaser_value = 0.03 # set this value to what you determined for errors in lab\n",
        "eylaser = np.repeat(eylaser_value, len(ylaser)) \n",
        "eybulb = np.sqrt(ybulb)\n",
        "\n",
        "##########################\n",
        "# CHOOSE YOUR DATA HERE! #\n",
        "##########################\n",
        "y = ylaser\n",
        "ey = eylaser\n",
        "\n",
        "# plot the data on a new figure\n",
        "plt.figure() # create new figure for plotting\n",
        "plt.errorbar(x, y, ey, fmt='or', label=\"Laser\") # plot intensity vs position\n",
        "plt.axis([1.5, 7.5, 0, 2.0])  # set axes [xmin, xmax, ymin, ymax]\n",
        "plt.xlabel('Slit position (mm)') # set x-axis label\n",
        "plt.ylabel('Photodiode intensity (mV)') # set y-axis label \n",
        "\n",
        "################################\n",
        "# SET INITIAL PARAMETERS HERE! #\n",
        "################################\n",
        "initialParameters = [0.01,1.200,0.356,0.085,4.78] # start with initial guess for fit parameters (B, I0, D, A, x0)\n",
        "\n",
        "# fit the data\n",
        "finalParameters, finalParameterErrors = curve_fit(IntensityModel, x, y, initialParameters, ey, True)\n",
        "\n",
        "# show red curve for fit results and plot on top of the data\n",
        "plt.plot(x, IntensityModel(x, *finalParameters), 'r--', label='fit: B=%5.3f, I0=%5.3f, D=%5.3f, A=%5.3f, x0=%5.3f' % tuple(finalParameters)) #\n",
        "plt.legend()\n",
        "plt.show()\n",
        "\n",
        "# output fit parameter values and errors\n",
        "print(\"Model parameters:\")\n",
        "print(\"B   =\", finalParameters[0], \" +/- \",np.sqrt(finalParameterErrors[0,0]))\n",
        "print(\"I0  =\", finalParameters[1], \" +/- \",np.sqrt(finalParameterErrors[1,1]))\n",
        "print(\"D   =\", finalParameters[2], \" +/- \",np.sqrt(finalParameterErrors[2,2]))\n",
        "print(\"A   =\", finalParameters[3], \" +/- \",np.sqrt(finalParameterErrors[3,3]))\n",
        "print(\"x0  =\", finalParameters[4], \" +/- \",np.sqrt(finalParameterErrors[4,4]))\n",
        "\n",
        "# compare model function with obtained parameters to data to determine fit quality\n",
        "IntensityModel_i = IntensityModel(x, *finalParameters)\n",
        "deltaIntensity = y - IntensityModel_i # calculate difference between data and model\n",
        "chisq = np.sum((deltaIntensity/ey)**2) # calculate chi^2 by summing over difference for all data points\n",
        "dof = len(x) - len(finalParameters) # Degrees of Freedom = # data points - # parameters\n",
        "print(\"\\nFit quality:\")\n",
        "print(\"chisq =\",chisq,\"dof =\",dof)"
      ],
      "execution_count": 9,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "[1.92, 2.02, 2.12, 2.22, 2.32, 2.42, 2.52, 2.62, 2.72, 2.82, 2.92, 3.02, 3.12, 3.22, 3.32, 3.42, 3.52, 3.62, 3.72, 3.82, 3.92, 4.02, 4.12, 4.22, 4.32, 4.42, 4.52, 4.62, 4.72, 4.72, 4.82, 4.82, 4.92, 5.02, 5.12, 5.22, 5.32, 5.42, 5.52, 5.62, 5.72, 5.82, 5.92, 6.02, 6.12, 6.22, 6.32, 6.42, 6.52, 6.62, 6.72, 6.82, 6.92, 7.02, 7.12, 7.22, 7.32, 7.42, 7.52, 7.62, 7.72, 7.82, 7.92, 8.02]\n",
            "[0.06, 0.08, 0.1, 0.1, 0.07, 0.05, 0.03, 0.05, 0.15, 0.3, 0.39, 0.44, 0.38, 0.24, 0.15, 0.02, 0.1, 0.3, 0.57, 0.82, 0.9, 0.78, 0.5, 0.19, 0.02, 0.07, 0.34, 0.69, 1.18, 1, 1.12, 1.13, 0.86, 0.47, 0.15, 0.02, 0.12, 0.42, 0.74, 0.95, 0.95, 0.75, 0.45, 0.18, 0.04, 0.06, 0.2, 0.36, 0.46, 0.46, 0.36, 0.23, 0.11, 0.04, 0.03, 0.05, 0.08, 0.09, 0.09, 0.06, 0.04, 0.02, 0.01, 0.01]\n",
            "[79.6, 81, 83.5, 91.6, 100.6, 130.4, 127.8, 122.2, 93.5, 91.9, 155.2, 281.4, 401.7, 424.7, 338.8, 203.9, 73, 103.7, 317, 657, 870, 808, 522, 211, 72.2, 232, 596, 1006, 1154, 1160, 1049, 1069, 751.5, 331, 117, 197, 505, 842, 984, 844, 528, 255, 131, 211, 387, 540, 526, 407, 257, 142, 113, 143, 164, 182, 158, 119, 92, 87.8, 69.4, 61, 50.5, 44.3, 44.2, 48.9]\n"
          ],
          "name": "stdout"
        },
        {
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++uorTp06xZo1awDo3bs3Dz/8MJMmTWLz5s3odDpef/31ErvehRBCCHGDYjQa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\nIBAIBIJKwv8D4Ibm7Ak6DxQAAAAASUVORK5CYII=\n",
            "text/plain": [
              "<matplotlib.figure.Figure at 0x7f55d90adf98>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "stream",
          "text": [
            "Model parameters:\n",
            "B   = 0.01725841505407293  +/-  0.0063295399583370646\n",
            "I0  = 0.2795263762128382  +/-  0.0031466706503749456\n",
            "D   = 0.37021047120466094  +/-  0.0009178183687938539\n",
            "A   = 0.09426043627964316  +/-  0.0012954698353500411\n",
            "x0  = 4.789732035479556  +/-  0.002203557420085344\n",
            "\n",
            "Fit quality:\n",
            "chisq = 88.98974541809363 dof = 59\n"
          ],
          "name": "stdout"
        }
      ]
    }
  ]
}