PSFModel.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Go look at the ones in the EagleSimScripts folder\n",
    "\n",
    "# PSF Modelling"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Define the PSF module"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We base our analysis on the prescription given in Racine (1996). The PSF is specified by its total flux and by its FWHM. Various profiles are then provided as methods of the PSF class. Note that these methods return functions."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Overwriting PSF.py\n"
     ]
    }
   ],
   "source": [
    "%%writefile PSF.py\n",
    "\n",
    "import numpy as np\n",
    "import matplotlib.pylab as plt\n",
    "import warnings\n",
    "\n",
    "class PSF(object):\n",
    "\n",
    "    \"\"\"This class generates representations of various point-spread\n",
    "    functions.\"\"\"\n",
    "\n",
    "    def __init__(self, flux, fwhm):\n",
    "        self.flux = flux\n",
    "        self.fwhm = fwhm\n",
    "\n",
    "    def moffat_profile(self, beta=4.765, flux_fraction=1.0):\n",
    "        \"\"\"Profile with default beta suggested by Trujillo et al. 2001. This\n",
    "            value of beta corresponds to Kolmogorov turbulence.\"\"\"\n",
    "        def moffat(theta):\n",
    "            totalflux = flux_fraction*self.flux\n",
    "            fwhm = self.fwhm\n",
    "            ibeta = 1.0/beta\n",
    "            alpha = fwhm/(2.0*np.sqrt(2.0**ibeta - 1.0))\n",
    "            coefficient = totalflux*(beta-1.0)/(np.pi*(alpha**2))\n",
    "            firstMoffat = coefficient * (1 + (theta/alpha)**2)**(-beta)\n",
    "            return firstMoffat\n",
    "        return moffat\n",
    "\n",
    "    def two_moffat_profile(self, flux_fraction=1.0):\n",
    "        \"\"\"Simple analytical expression given by Racine (1996) to model the\n",
    "        CCD-based PSF. Racine's analysis did not go far enough out to contain\n",
    "        the full aureole component given by King (1971), which was determined\n",
    "        photographically.\"\"\"\n",
    "        def two_moffat(theta):\n",
    "            totalflux = flux_fraction*self.flux\n",
    "            fwhm = self.fwhm\n",
    "\n",
    "            # The first Moffat profile\n",
    "            flux = 0.8*totalflux\n",
    "            beta = 7.0\n",
    "            ibeta = 1.0/beta\n",
    "            alpha = fwhm/(2.0*np.sqrt(2.0**ibeta - 1.0))\n",
    "            coefficient = flux*(beta-1.0)/(np.pi*(alpha**2))\n",
    "            firstMoffat = coefficient * (1 + (theta/alpha)**2)**(-beta)\n",
    "\n",
    "            # The second Moffat profile\n",
    "            flux = 0.2*totalflux\n",
    "            beta = 2.0\n",
    "            ibeta = 1.0/beta\n",
    "            alpha = fwhm/(2.0*np.sqrt(2.0**ibeta - 1.0))\n",
    "            coefficient = flux*(beta-1.0)/(np.pi*(alpha**2))\n",
    "            secondMoffat = coefficient * (1 + (theta/alpha)**2)**(-beta)\n",
    "\n",
    "            # The total profile\n",
    "            return firstMoffat + secondMoffat\n",
    "        return two_moffat\n",
    "\n",
    "    def aureole_profile(self, d0=50, flux_fraction=1.0):\n",
    "        \"\"\"Analytical function suggested by Racine (1996) for modelling the full\n",
    "        PSF aureole. The default value of d0 matches the photographic data of\n",
    "        King (1971). Note that d0 is specified in units of the FWHM. (It is 50\n",
    "        and not 100 as in the Racine paper because it is in units of FWHM and\n",
    "        not HW). Note that constructing a PSF with an Aureole will change the\n",
    "        effective PSF (likely by a very small amount, assuming only a small\n",
    "        fraction of the light is in the aureole) but this will not be correctly\n",
    "        captured by the fwhm property of the PSF.\"\"\"\n",
    "        def aureole(theta):\n",
    "            totalflux = flux_fraction*self.flux\n",
    "            fwhm = self.fwhm\n",
    "            print fwhm\n",
    "            d = d0 * fwhm\n",
    "            coeff = totalflux/(8*np.pi*d**2)\n",
    "            cosfac = np.cos(np.arctan(theta/(2*d)))\n",
    "            return coeff*(cosfac**3.0)\n",
    "        return aureole\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Examples"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "%run PSF.py\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Example 1"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "Try to reproduce Figure 3 in Racine (1996), who show the PSF as a function of radius in units of the Half-Width. We can generate this by setting the FWHM = 2 (i.e. two half-width units). He shows a two-moffat model with a single moffat model for comparison. Note that PSF does not include the very wide-angle power-law aureole that is described by King (1971). To make this clear, I will draw that too, even though it's not in Racine's figure."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
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55x1iY2NRSnHRRRfx/vvv25NkUFAQQ4YM4cknnyQjI4O9e/cybdo0Ro4cWe72R44cyfLl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\nJCmEEGWQJCmEEGX4f3nqSTfLeaQ4AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10ec20350>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "foo=PSF(1.0,2.0);\n",
    "profile1 = foo.moffat_profile(beta=4)\n",
    "profile2 = foo.two_moffat_profile()\n",
    "\n",
    "x = 10.0**np.linspace(-1.0, 2.0, 20)\n",
    "y1 = 2.5*np.log10(profile1(x[0]))-2.5*np.log10(profile1(x))  # One moffat\n",
    "y2 = 2.5*np.log10(profile2(x[0]))-2.5*np.log10(profile2(x))  # Two moffat\n",
    "y3 = 2.5*np.log10(x[0]**(-2.0))-2.5*np.log10(x**(-2.0))      # Power law\n",
    "plt.plot(np.log10(x),y1,'r:', label=\"One Moffat\")\n",
    "plt.plot(np.log10(x),y2,'b', label=\"Two Moffat\", linewidth=3)\n",
    "plt.plot(np.log10(x),y3,'g:', label=\"Power Law\")\n",
    "plt.legend()\n",
    "\n",
    "# Ignore Unicode equal comparison warnings\n",
    "with warnings.catch_warnings():\n",
    "    warnings.simplefilter(\"ignore\")\n",
    "    plt.gca().set_ylim(ymin=-2)\n",
    "    plt.gca().set_ylim(ymax=18)\n",
    "    xl0,xl1 = plt.gca().get_xlim()\n",
    "    yl0,yl1 = plt.gca().get_ylim()\n",
    "    plt.gca().set_aspect(0.83*(xl1-xl0)/(yl1-yl0))\n",
    "    plt.gca().set_xlabel(r'log($\\theta$/HW)')\n",
    "    plt.gca().set_ylabel(r'$\\mu(\\theta) - \\mu(0)$')\n",
    "    plt.gca().invert_yaxis()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "--------"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Example 2"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "Racine (1991) also provides a simple model for the aureole, based on a physical model for a single reflection. His figure is reproduced below, along with a few extra curves (such as a fiducial power law to show how the aureole model approximates this). Note that he thinks the origin of the aureole is unclear. He thinks it is a reflection (perhaps internal to an emuslion) in the photographic data, but for the CCD data (in which only the innermost part of the aureole is seen) he thinks its probably due to light cirrus in Tonry's data (which he uses, in addition to his own CCD data)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "2.0\n",
      "2.0\n",
      "2.0\n",
      "2.0\n"
     ]
    },
    {
     "data": {
      "image/png": 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OpVnFZrxd8+1XPs7x48fx8vIiJSUFgDFjxmTo+GvKZEI0TXJwBynX7EraMav9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\nYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10f197e50>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "foo=PSF(1.0,2.0);\n",
    "profile1 = foo.moffat_profile(beta=4)\n",
    "profile2 = foo.two_moffat_profile()\n",
    "profile3 = foo.aureole_profile()\n",
    "\n",
    "def profile4(x):\n",
    "    p1 = foo.two_moffat_profile(flux_fraction=0.98)\n",
    "    p2 = foo.aureole_profile(flux_fraction=0.02)\n",
    "    return p1(x) + p2(x)\n",
    "\n",
    "x = 10.0**np.linspace(-1.0, 4.0, 50)\n",
    "y1 = 2.5*np.log10(profile1(x[0]))-2.5*np.log10(profile1(x))         # Moffat\n",
    "y2 = 2.5*np.log10(profile2(x[0]))-2.5*np.log10(profile2(x))         # Two Moffat\n",
    "y3 = 16.2 + 2.5*np.log10(profile3(x[0]))-2.5*np.log10(profile3(x))  # Pure Aureole\n",
    "y4 = 2.5*np.log10(profile4(x[0]))-2.5*np.log10(profile4(x))         # Two Moffat + Aureole\n",
    "y5 = 1.4 + 2.5*np.log10(x[0]**(-2.0))-2.5*np.log10(x**(-2.0))       # Power law (alpha = -2)\n",
    "plt.plot(np.log10(x),y1,'r:',label=\"Moffat\")\n",
    "plt.plot(np.log10(x),y2,'b:',label=\"Two Moffat\")\n",
    "plt.plot(np.log10(x),y3,'k:',label=\"Aureole\")\n",
    "plt.plot(np.log10(x),y4,'k', label=\"Final PSF\", linewidth=3)\n",
    "plt.plot(np.log10(x),y5,'g-',label=\"Power law\", linewidth=0.5)\n",
    "\n",
    "# Ignore Unicode equal comparison warnings\n",
    "with warnings.catch_warnings():\n",
    "    warnings.simplefilter(\"ignore\")\n",
    "    plt.gca().set_ylim(ymin=-2)\n",
    "    plt.gca().set_ylim(ymax=28)\n",
    "    xl0,xl1 = plt.gca().get_xlim()\n",
    "    yl0,yl1 = plt.gca().get_ylim()\n",
    "    plt.gca().set_aspect(0.83*(xl1-xl0)/(yl1-yl0))\n",
    "    plt.gca().set_xlabel(r'log($\\theta$/HW)')\n",
    "    plt.gca().set_ylabel(r'$\\mu(\\theta) - \\mu(0)$')\n",
    "    plt.gca().invert_yaxis()\n",
    "    plt.legend()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Example 3"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "Compare with the PSF from the first Dragonfly paper."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def generate_psf_model(fwhm = 3.0, aureole_fraction = 0.02, d0 = 50):\n",
    "    unitFluxPSF = PSF(1.0,fwhm);\n",
    "    def profile(x):\n",
    "        p1 = unitFluxPSF.two_moffat_profile(flux_fraction=(1.0 - aureole_fraction))\n",
    "        p2 = unitFluxPSF.aureole_profile(flux_fraction=aureole_fraction, d0 = d0)\n",
    "        return p1(x) + p2(x)\n",
    "    return profile"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x10faabe10>"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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wM2bMYMyYMfa8Y8eOER8fT2BgINHR0cTFxdl/nNRXQ91wlWvr3r07AQEBtV9+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\n+QAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x109f45590>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "good_seeing_good_cirrus = generate_psf_model(fwhm = 3.0)\n",
    "bad_seeing_good_cirrus = generate_psf_model(fwhm = 6.0)\n",
    "good_seeing_bad_cirrus = generate_psf_model(fwhm = 3.0, aureole_fraction = 0.1)\n",
    "bad_seeing_bad_cirrus = generate_psf_model(fwhm = 6.0, aureole_fraction = 0.1)\n",
    "coeff = 1.0e9;\n",
    "\n",
    "plt.figure(figsize=(11, 5))\n",
    "\n",
    "# Log-linear\n",
    "plt.subplot(1, 2, 1)\n",
    "x = np.linspace(1, 3000, 200)\n",
    "y1 = coeff * good_seeing_good_cirrus(x)\n",
    "y2 = coeff * good_seeing_bad_cirrus(x)\n",
    "y3 = coeff * bad_seeing_good_cirrus(x)\n",
    "y4 = coeff * bad_seeing_bad_cirrus(x)\n",
    "\n",
    "plt.semilogy(x/60,y1,'k',label=\"Good seeing/Good cirrus\")\n",
    "plt.semilogy(x/60,y2,'k:',label=\"Good seeing/Bad cirrus\")\n",
    "plt.semilogy(x/60,y3,'r',label=\"Bad seeing/Good cirrus\")\n",
    "plt.semilogy(x/60,y4,'r:',label=\"Bad seeing/Bad cirrus\")\n",
    "\n",
    "plt.gca().set_xlabel(r'$\\theta$/arcmin')\n",
    "plt.gca().set_ylabel(r'$log(I)$')\n",
    "plt.legend(loc=1)\n",
    "\n",
    "# Log-Log\n",
    "plt.subplot(1, 2, 2)\n",
    "x = 10.0**np.linspace(0.5, 3.5, 50)\n",
    "y1 = coeff * good_seeing_good_cirrus(x)\n",
    "y2 = coeff * good_seeing_bad_cirrus(x)\n",
    "y3 = coeff * bad_seeing_good_cirrus(x)\n",
    "y4 = coeff * bad_seeing_bad_cirrus(x)\n",
    "\n",
    "plt.loglog(x/60,y1,'k',label=\"Good seeing/Good cirrus\")\n",
    "plt.loglog(x/60,y2,'k:',label=\"Good seeing/Bad cirrus\")\n",
    "plt.loglog(x/60,y3,'r',label=\"Bad seeing/Good cirrus\")\n",
    "plt.loglog(x/60,y4,'r:',label=\"Bad seeing/Bad cirrus\")\n",
    "\n",
    "plt.gca().set_xlabel(r'log($\\theta$/arcmin)')\n",
    "plt.gca().set_ylabel(r'$\\log(I)$')\n",
    "plt.legend(loc=3)\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Unit tests "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The following test framework exercises the PSF module. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Overwriting TestPSF.py\n"
     ]
    }
   ],
   "source": [
    "%%writefile TestPSF.py\n",
    "\n",
    "from PSF import PSF\n",
    "import unittest\n",
    "import numpy as np\n",
    "import scipy.integrate as integrate\n",
    "\n",
    "\n",
    "class TestPSFMethods(unittest.TestCase):\n",
    "\n",
    "    def test_moffat_normalization(self):\n",
    "\n",
    "        # Integrals need to be good to 0.1%\n",
    "        tolerance = 0.001\n",
    "        fwhm = 2.0\n",
    "\n",
    "        # Check default\n",
    "        expected_answer = 1.0\n",
    "        star = PSF(expected_answer, fwhm)\n",
    "        profile = star.moffat_profile()\n",
    "        result = integrate.quad(\n",
    "            lambda r: (2.0 * np.pi * r) * profile(r), 0, 10000)\n",
    "        self.assertTrue(\n",
    "            abs(result[0] - expected_answer) <= tolerance*expected_answer)\n",
    "\n",
    "        # Check flux parameter\n",
    "        expected_answer = 1000.0\n",
    "        star = PSF(expected_answer, fwhm)\n",
    "        profile = star.moffat_profile()\n",
    "        result = integrate.quad(\n",
    "            lambda r: (2.0 * np.pi * r) * profile(r), 0, 10000)\n",
    "        self.assertTrue(\n",
    "            abs(result[0] - expected_answer) <= tolerance*expected_answer)\n",
    "\n",
    "        # Check that correct normalization does not depend on beta\n",
    "        expected_answer = 1000.0\n",
    "        star = PSF(expected_answer, fwhm)\n",
    "        profile = star.moffat_profile(beta=3)\n",
    "        result = integrate.quad(\n",
    "            lambda r: (2.0 * np.pi * r) * profile(r), 0, 10000)\n",
    "        self.assertTrue(\n",
    "            abs(result[0] - expected_answer) <= tolerance*expected_answer)\n",
    "\n",
    "    def test_two_moffat_normalization(self):\n",
    "\n",
    "        # Integrals need to be good to 0.1%\n",
    "        tolerance = 0.001\n",
    "        fwhm = 2.0\n",
    "\n",
    "        # Check default case\n",
    "        expected_answer = 1.0\n",
    "        star = PSF(expected_answer, fwhm)\n",
    "        profile = star.two_moffat_profile()\n",
    "        result = integrate.quad(\n",
    "            lambda r: (2.0 * np.pi * r) * profile(r), 0, 10000)\n",
    "        self.assertTrue(\n",
    "            abs(result[0] - expected_answer) <= tolerance*expected_answer)\n",
    "\n",
    "        # Check flux parameter\n",
    "        expected_answer = 1000.0\n",
    "        star = PSF(expected_answer, fwhm)\n",
    "        profile = star.two_moffat_profile()\n",
    "        result = integrate.quad(\n",
    "            lambda r: (2.0 * np.pi * r) * profile(r), 0, 10000)\n",
    "        self.assertTrue(\n",
    "            abs(result[0] - expected_answer) <= tolerance*expected_answer)\n",
    "\n",
    "    def test_aureole_normalization(self):\n",
    "\n",
    "        # Integrals only need to be good to 5%\n",
    "        tolerance = 0.05\n",
    "        fwhm = 1.0\n",
    "\n",
    "        # Check default case\n",
    "        expected_answer = 1.0\n",
    "        star = PSF(expected_answer, fwhm)\n",
    "        profile = star.aureole_profile()\n",
    "        result = integrate.quad(\n",
    "            lambda r: (2.0 * np.pi * r) * profile(r), 0, 10000)\n",
    "        self.assertTrue(\n",
    "            abs(result[0] - expected_answer) <= tolerance*expected_answer)\n",
    "\n",
    "        # Check flux parameter\n",
    "        expected_answer = 1000.0\n",
    "        star = PSF(expected_answer, fwhm)\n",
    "        profile = star.aureole_profile()\n",
    "        result = integrate.quad(\n",
    "            lambda r: (2.0 * np.pi * r) * profile(r), 0, 10000)\n",
    "        self.assertTrue(\n",
    "            abs(result[0] - expected_answer) <= tolerance*expected_answer)\n",
    "\n",
    "    def test_composite_normalization(self):\n",
    "\n",
    "        # Integrals only need to be good to 5%\n",
    "        tolerance = 0.05\n",
    "\n",
    "        # Check default case\n",
    "        fwhm = 2.0\n",
    "        expected_answer = 1000\n",
    "        star = PSF(expected_answer, fwhm)\n",
    "\n",
    "        def profile(x):\n",
    "            p1 = star.two_moffat_profile(flux_fraction=0.9)\n",
    "            p2 = star.aureole_profile(flux_fraction=0.1)\n",
    "            return p1(x) + p2(x)\n",
    "\n",
    "        result = integrate.quad(\n",
    "            lambda r: (2.0 * np.pi * r) * profile(r), 0, 10000)\n",
    "        self.assertTrue(\n",
    "            abs(result[0] - expected_answer) <= tolerance*expected_answer)\n",
    "\n",
    "    def test_fwhm(self):\n",
    "\n",
    "        # Define the star\n",
    "        flux = 1.0\n",
    "        fwhm = 3.0\n",
    "        star = PSF(flux, fwhm)\n",
    "\n",
    "        # The measured FWHM of the star should always be within\n",
    "        # 0.1% of expectation\n",
    "        tolerance = 0.001\n",
    "\n",
    "        # The value at FWHM/2.0 should always be half the central value\n",
    "        expected_answer = 0.5\n",
    "\n",
    "        # Check that the FWHM of a single Moffat PSF profile is correct.\n",
    "        # Remember the default PSF has unity totql _flux_ not unity at x=0\n",
    "        profile = star.moffat_profile()\n",
    "        result = profile(fwhm/2.0)/profile(0.0)\n",
    "        self.assertTrue(\n",
    "            abs(result - expected_answer) <= tolerance*expected_answer)\n",
    "\n",
    "        # Check that the FWHM of the two Moffat PSF profile is correct\n",
    "        profile = star.two_moffat_profile()\n",
    "        result = profile(fwhm/2.0)/profile(0.0)\n",
    "        self.assertTrue(\n",
    "            abs(result - expected_answer) <= tolerance*expected_answer)\n",
    "\n",
    "        # Check that adding a 5% extended aureole to create a composite PSF\n",
    "        # does not change the FWHM by very much.\n",
    "        def cprofile(x):\n",
    "            p1 = star.two_moffat_profile(flux_fraction=0.95)\n",
    "            p2 = star.aureole_profile(flux_fraction=0.05)\n",
    "            return p1(x) + p2(x)\n",
    "        result = cprofile(fwhm/2.0)/cprofile(0.0)\n",
    "        self.assertTrue(\n",
    "            abs(result - expected_answer) <= tolerance*expected_answer)\n",
    "\n",
    "if __name__ == '__main__':\n",
    "    unittest.main()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      ".....\n",
      "----------------------------------------------------------------------\n",
      "Ran 5 tests in 0.039s\n",
      "\n",
      "OK\n"
     ]
    }
   ],
   "source": [
    "%run TestPSF.py"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
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