{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# PSF normalization\n",
    "\n",
    "Let us assume that we have reduced an observation, for which we have determined the PSF by stacking the flux of point-like sources. The PSF we obtain will not be as high S/N as the instrumental PSF that has been determined by the instrument team. Moreover, it is likely to be fattened due to the some small pointing errors. We need to find out what fraction of a point-like flux the PSF we have determined represent. In order to do this, we use the growth curve of the theoretical PSF that has been determine by the instrument team, and compare it to the growth curve we determine from our PSF.\n",
    "\n",
    "We will first look at a theoretical case, then go practical with an example drawn from the PACS observation of the the XMM-LSS.\n",
    "\n",
    "## 1) Theoretical example. \n",
    "\n",
    "Let us suppose we have a perfect telescope, without any central obscuration and spider to support the secondary. Diffraction theory gives us the shape of a PSF in this case, an Airy function. Let's compute it, and assume the resolution is 10\".\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# import what we will need. \n",
    "%matplotlib inline\n",
    "import numpy as np\n",
    "from astropy.io import fits\n",
    "from astropy.table import Table\n",
    "from astropy.io import ascii as asciiread\n",
    "from matplotlib import pyplot as plt\n",
    "from scipy import interpolate \n",
    "from scipy import special\n",
    "from scipy import signal\n",
    "from scipy import fftpack"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# Let us perform our computation with a 0.1\" resolution on a 5' field of view\n",
    "resol = 0.1\n",
    "size = 300.\n",
    "# wavelength\n",
    "wavelength = 250e-6\n",
    "# primary aperture = 3.6 m diameter\n",
    "aperture = 3.6 / 2."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# Ensure we have an odd number of points \n",
    "nbpix = np.ceil(size/resol) // 2 * 2 + 1\n",
    "xcen = int((nbpix - 1) / 2)\n",
    "ycen = int((nbpix - 1) / 2)\n",
    "x = y = (np.arange(nbpix) - xcen)*resol\n",
    "xv, yv = np.meshgrid(x, y, sparse=False, indexing='xy')\n",
    "r = np.sqrt(xv**2+yv**2)\n",
    "# avoid division by 0 problems in the center\n",
    "r[xcen,ycen] = 1e-6\n",
    "# coordinates in fourier\n",
    "q = 2 * np.pi / wavelength * aperture * np.sin(r/3600.*np.pi/180.)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "psf = (2*special.jn(1, q)/q)**2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# put back the correct value at center\n",
    "psf[xcen, ycen] = 1.\n",
    "# and normalize the PSF\n",
    "psf = psf/(np.sum(psf)*resol**2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "$\\int\\int$ psf dx dy = 1.0000000000000018\n"
     ]
    },
    {
     "data": {
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uYZ3YmF314A0j9IMqE9QW4ugWbglIahvjLrxBjNOz2dY22sKbfUCyKR290Wc92I/WOD5e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\nfpNFYHPcK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JQFWVoKmY6txySGxsAVHpmLZUuhU+SZhGqkUgEV4N23n/Htp4e8deeC1F2A\nBTZxxVErv7+MVgyNKg3KnbmD95ZMI5cPrg6wzYSD1kxoLPlkUn0a0simPvU2LU4uh5ywaiQQ5x3S\nVoklfCHzNmFscLc35sfe+1i0BdBjHD2q0Bv5faAKVjK6kGsXX/tNvvPs4FYwKY4VYXaTYHKxbOFa\nMQNX9C+RWR01OokVnWcZ21wvG+wdj0VmsOZRUX0nUmuZ+i6NViDot3GbdpK3NJh7dFurW6MTKcau\nIgurHQhqVG9roGR3klzofZXjtXbKym5XVpaIzEmd9mjCjNZu+kzmLi2nFGc3OWdtI6FphwwnTZY5\nAJl6emuU0m+siP/XAxZ/LSifOop7VoKRjDoG3pLPrnYYWvLJsIX6IAxvqRlx2JrxZNTnUmsXTxKd\nrKA/6g1hkaAb5dov799/zmejgejl0tBpmwGpoZHqWqkRqBQIcmBJiRAU0UkjPCOkbfnsuXMWsc00\ndPn2zT5hbHLQmdG2RDmCrcdFJ3jpldhGf9R1kdJMJ8if5n4sxMuLqTCX7bfmPOjdFFkyOfHNPFOl\nakPFtmuRjrTTz2KHi2Wb4aLB+/ef07FXhQArQXAto5OLsLPI4XLZZhnY3O+PaJjRZgNbjeoMVw3m\nS5cHezfC9Kakfje5YheRjfWPBng/c/ES0YnJMrKIY4OmHRZLmG52xgoxdjJ3aTf9sl3CBrpTtFYI\nbF7leL0BJRYI6hh6KbjWxFlDT2naEaObtuglIUM8I6s4Z0UXtRjHMBh0F4xmDRpWVIDEtiilZQdc\n/fSQxaIhIiBDZEJE6J+uUZ+WFXA8mPDFHx3hvR+VDXX0WNTN1PQUEBf4bm/M58NBhe96sBFUdCX7\nY2kp5k7C2aLDJ6NdTtoT+s6S2IgKCpRm2ppgCxSZnUTTcTIxkdNMo2369O0lR41p0f9jkdvmr572\n6RzOaLsBnpXb72vZhqJGJW8QtYosZr7D9LzN3t0RfXdF115xcDArqJUaPajURh5zcU8owmuCXlAc\nKaI+n3WxzZjHO1fCZ6JQN3He18FklVjMYofrVYvx0uONwZCWWZYX1MEkyie6n9vxzz7Y594PnNGy\ngi1UR89bV+j4icVw0cD+6SG9XDu5LTpZxRajWYNBd1F8F7N2PPJch3l0EvsWzf5sq9Vebbq0uGrw\nKsdrDSiakbEMbFwzFktRZNVQ1dRT7Ew0U+r2F0yXruCYRrKWQpZRimvERZSykGnhDVGKFE9dI6Lj\n+jy5HDB1XaHcm9kGgbakPl3b5/DdS84mHax+2R7QMLJKKtnMHbGeIVo03uuP+PRqR6yZIvS9CqiI\n/VTpT6Ep6Skjv8Ef//OHPPiRp+y4CyLTKDrSJ+TekToNggoVSjMNMxeB00wjMkVflcjVudM0iAYX\nRWm+rIuJU30tWyBF4Lbl03eWmO0U8+C5AEDlqb+JRt0GJKpWUoivsdBePvvaXR78yFP67rJwwKou\nXSidoXUwuVq1OB+3ebh3U1A9WatUHEMxeUVEM48cziYdDt+9pGv7W6mOFGL92GIauCyWDrv7w4Jy\n19srqNHJIrSL6MRVWitsShUHicl06dLtC1v+xjV9lPqqZWBjdcLtE/B7GK81oOh6xmLp0HaDvFK4\nzPhIxJVP+oYTMvu4x+rd8qmkppBBRClprqUMuotCS5Fl5XX3rKkn2Gh4pmhXcDVp0bRCYcevCbR1\n6tN1fOa+w8j3ckdsVmSFNom0AKmt8cbukA+fHGLeK28ECSpqf1aZUi6fQuI7OD/2GU/HolfLYXNK\nbOl4RoRNTKpVaZDcf1nTJMRbi6SgEw5xRf8of19vQlUfRhFRZcWTUqUd6vfZJvJWnLk1IXeV+z7O\nFx0Wgc07P/YZHcvfqpdUBFgFTEZBg8+f7fL2/XM6tn+rCKvqJiPfw9BTunlWZxvVUS32V5MWe/1Z\nEe2aerVSvp7ZGc+9Ijox88xkcTxKqlhGJ+GTFv33LiuRVQFWSnQSJQaLpUOzEWy8dt/reK0BRdMy\nopldWOZj3cAkLUTXujjrPZwyWzk07ZAwNcXfSCtaivSZNO2Q8bTBIrQFAG3I+KBR9D/p2AFz2ylu\norpAu4n6HLZnfHK+lzsVyyeX0GAU+3mmY+oJTUJw4O3753z45JA37lwXkYqDhq3HlexPPVoxLNGC\nwN2JuPGb/P4HDyqZG8+IiPSkkrmhdtPVwUVuv8jSyDoUqqLrplERbRXwgJqDdkOmaBuQSCBQM0IP\nH15w3JqIqGSDgCyPUYKJzCrJyESCSc9Z0TTCQvRcozqpUaaIA4+rYYc3D69upTpSiJUAZNsxHTso\nohO1ZmeT7yRN9CI6UTM78jvJSCZKDWYrB+/hdKsYC0JMTvJWk9HMxu3NN16773W81oCia5nwmfg2\nTTvE0FPivGsaVFPIlp7QcgPOP99hmRdO2bp4KleqkKVj1YwYdBdcDdu4+3EZRajZpPymkua1neaS\nLz44xH0nLkxLGPFG6pPqCU0r4O7+kM8/PsB4fC4urhkWomxdpDWMfGLloPL59YAs00g9jTbiSWJq\nyZr5DUQtkJ5lxTmx9YT22wHXqyZ/OD7i/mBULNGh6gq3UY1qGYMoYpStE+QxwItredau65ZUcx1E\nZDSkppalR+TJsE+/ueJLb39RtFNQKY48P1D1mRSNkiKhmZyP2xUwkZHJJt0kyM1rk9DjySf7vPHo\nIm9dsZ3qBIkQoeehw/XHO9x797w0va35aORaOybLyOZq2GZvMMtp+WaHroxOlpHF8rLJ4Rs3lbYS\n6mfifNXNIDFZ+MKn4prxxmvxvY7XGlA0MppOyOr/3sf/SUFltqWQRWvGiM7RjOnSxTXjXBGP1jI+\n0pfStENmXshk5SrpOAPDKE+yEFSTQqDdf3zN+bCDs6/UgeRZHzl0TUQKqaHRtX1OHlzz5GIH81BO\n3M0iLZle0B8ceLh3wxejvugr25iRWKKjW11TUSMVSYEsXaSEG2ZIz11xMW8Xa850bL+YPOrTXJ2I\nmyKIbUCgb2iQ/DJDrSNRF6xX+85KbWCRiMzT2bSDaaQ82BnemtYu9rHBtDbPsznjpSc0E+V8bAOT\nQoQNXZ5c7HDy4Jqu7eMa8dp6P3K/Ub6e8SK2OR922H98XZrY8houdcR5F/5VbDFZubheKDI7Nd+J\n+r0k0E6XLp2jmUg01Gp36qliPzaxfqeD95OXleVlXsV4zQEFbCNh8tUZaS7OWkY1hbwpSjn7eA+/\n4W/N+KhRSq+5YvQ7hyx+PBTeET0lSo1awR3YekJqRHQdn6UnCsCKDEdOl1RbPuiFntJzV8R9ndNp\nB6OnNBTOe75uoz+6naEPMp6OeySZxkFjTmrppIZOKp/Gt0QrppYU/puWFTANXS7mLc7SDgftmZhI\nRU1LSqQnaxqHrmUkbI42XmRqk2NTAZpKoeoaTZwaxSSWKeyLWRtdTwtA9IyoyA7VwVBuF0rxNaj5\nTJaBzRuDEpS20pys1FvmkcPptMNuf0bPXVV0k21ZnWVsM1x6uF4otBZDRCd1qiOXSxEmOZvgawP6\nP35+a3QiMzV+bLI6a3H06GprdFI0XEpMFoFN/NUZXSMp6sde1Xi9AUXLcMyYlhdw/axH815Yza1v\niFJcM6Z9Z8pk4RVRyiZfisgQxbSskNWP3jBaeMJJmwNQsgZaVerz5GynaCpUz/qoeorM4NCAKNE5\nn7XRO+JilxmcW+gPcL8/4nze5tPRgDvdCT17RWpoOGiF0Co+W41WUjR0I8PKU+aeEdGxfdG1fdXg\no9N97h0M6dp+4Z+Q4KJmYOS26zrId/tsU/UX+buMHtRIQLRbFJ3ivrgYsL8z5aQ7KaiNPEazBoDq\nfjYZ6Mahx7NJF9eKud8fFanh2yITFUzOZ8I3s9tYFMeySTeRWZ1lbDMNXEajFvePbjZSHVCFWCHc\njhYe7o/e0MoLBrdFJ/K7TRYe7TtTJSpfj07i1BAVyLHJ/KLF7p1x8QB9leO1BhQQXgnPinAGK+a+\nI7wP2fYoxTFi2m7A89MBC0/W7FSjFLUS2THFshjP5n0mvls2kNaqXd1U6tO2A473xzw/HWDdVVKL\nip6ybs3XiuVGL+ZtaImL3STcGqmoHdjNdsLQb/LBJ8c8enBB31mSomHrWpE+rkcrQhMSVcwmegEs\nTSOkY/kcNadMQo9PRwPSVF8zsBWTNj+3haBac8nKfaqjLtTK6EP+HmdG3u29jEZUw5uup+y1Fnzp\n3jNcIy6iiBcBCZSUSTpnF7Go6fn4swPu37tm4C5omFHpM7kFTBaJLaKaeZss0zhsz26x1iu6SWIy\nCx2enw44OR6KJTc2UB21GZKfWEx8lzCw2O/Miwm/zeMTxCKtvJq6DI6Ht9vs833MfQdnsCo8RC8b\nZb7seO0BRU76diNg9OGA1btlYd+mKEX2ke3vzhjPvIImSa1DppFlBsjWYzxTZ7c/4/y0j3unfCJA\nvdcIBefsOD7B/pTLaQu7p7gXcz2lbHMgRFrySOWgPeN02uFy0SoWLd8GKjoUNnpZCe08iHly02fZ\nsdjzxJMyNXThm1GiFfGZzcCS6mIh8yg1aFkBe968mMxPxn0mkwYHexM6dpCnN/PucoX4WN7gampY\nHfWUcrGeTD5Rpfi4ii2mocPFVZdud8mgueTRznXFlVvvXbsNSNSoRO1je7VqcjNt8taDc7qO6MSn\nbrdy3BvA5HLRIogNjjuin65cPkMVYYv9S90kcricttjdn4piwVuoTpg7iOehw9V5l8PjUVFGojpd\n1Zqdogn2zKO/OxPR9RabvYxOVpGF/1mb/tvDEqy2COff63itAUW4SIRA6Jgx1j1RWfyiKMXSdVpO\nyHTWYB7YRV2NWolcF2hbdkh7Z8F45RYrsUlvSj3rI2z5olvbKhTWa62YvCmkVPwFpp4IWcWISC2N\no/aMZ+MulwhQ2UZ/QGR1ZJpZFg5a+wkX8zafjQalyGqG2LpGqunFE1x8z6z6U1IhGdHpOlEWiajF\nXglw6VmsYot5ZPN01MNf2uwM5jRtQYtkf41NTZ3VofYXkevrBol4qt4MW7iNkH5rSccOOLj/fC0y\nkpNWBRL1u6j72Ka9nE072GbCo/3rNcpUn0ybaM7losXCt7nTm1TApO4fKfdtMI+c/J6AnrcqUsSb\nsjqqI3a8cmnvLGhtEWLl5wpjXWCTJgYtJ3yhdhLmFcjWPWF6kwWW267d9zpea0BBTuA86mg3fG4+\n2mH1Vrg1SpHuWc+M6HcXXJ91adzNXY+p8GuYKJEAwmIfZzqDxoqnF30m+QprhTipPMUK6oNGMwvZ\na895ejkovCl6nsHZBiquEYPtc6cHZ7N2hf54RGvZH1B1lUgIylqK3YkZBQ2+88Uhx4cjdr0FDVN4\nTRw0cXORYWRqm8ByQoqFw8idsSJqERMqom2KZt5RanC3PS6eiEGcZxRCBz+0WAUWwcxBn5qkvQjd\nysPySEcfW6SdGKcd4DkRrh3hGIKSdto+97tDTD0tnKJywr0MiEAVSFQ9YZVYolhv1eT0vM/9k2v6\nzjKvy4k36iVie6WGU4i38zZBbHCnN6GdZ3RuBxOh/Yx9j9Gkyd39oQD63MBWz+oUfV9jm4nvspi5\n3D0QFcKy8Zb63tKdLKKN0UWH3aOy94oaWW+KTpZPOuw8vlGimc1Nl/7/jNccUMifpCmxJsxrzp05\nc98pqUyql0guzWh6gmUIQ9BqZynSwkWIF+XhuNLeAGFeSy2NvZ0Zl5/uYD9KXkB9RH+SFI3j3TFP\nv9jFvJu/3wT0uJL5STKteiPaPlon42LW5nTa4bA9E0teGMLDUuf2dV1FdN5PaL4Rcr1s8u2Lfe7u\njGlbfkUfqAOLPKe3gQvICVst7lMXkpf9NOTE3nbt5HVRMyGq9qC6aIEXgoj8qQKJpDfLWNTWPL3p\n0Wut+HNvnFbE0216SemAzbuo5QJslmkKzYkLnwuwltFRweTieZ+7966L9Z1s2TZyA9URXdscrj8b\nsP/whoYVKhGNONaKIzYXrScrl+bOkqYd5t3bqtFJpZ1BYgrt5M4c15TLkb56MIE/I4Cia6KZUpLF\ndBo+wz/YY/l+WdUpHK611QA1sRpgt7Hi9IsdPFuZYIZqN69Sn7YTEN0fcTNrVlrn1Q1vFReto3Fy\n94bTD/fR37lAdwWo1Ot9oIxaiqKtTsbFvMXTcY/jzpTU1sAU9RWWnlTbSOa6iq5nIlWdRytuns4+\nnXa41Foctme088yNpaWlWEd1/Zw1OiTBBQqAgXpWprro/DbbvRx1jaX8LutZo/rvcmwDkiAxifLU\n7Cx0OZ+1STON+zujIqIozW6bKY4KJnI7p9MOthlz2J5tpTkqyEpBeex7nH64z8nbl4VusskNqxrY\nFpHNzaxJ//6Itmz8tZXqiDTxLHCYXzU5vndTLNZeoYGUWaAoN72FH3YYfOlK1PgUzu3vQ0CB8kYX\n3dFinHcmTBfCvGboaVHjo1YiyzqchhUxOJownDRxTaW4qtKEqaQ+KRo9T2MV2IyXXjXNpycVUClW\ngjNDcCF564pnF32MI8Vxmmd+KrqIoqkA6O2M62WTT873uH9wI55G+QJmwmuyjQKVS4XIlPYscnhy\n06fdCNjJ05tuuj6xdG09alF/yt/TTEMnKQot69FItTJpfdQXAHtRdkiOTSCiahxBKjIp88jhZtlk\ntnQ4GUxoW0ElBb6txUJ9W8vYEg7Yix12+zN2G4JCbtNM6k7YSejy7KLPwVtX9NxVngmq9rstwCRv\nY7CKLcZLD03L6Hl+IYCveU7yaMNPLJaRzXDSZHA0KUxsanRSryhexRbThYvzzkRE9UWU9urBBF57\nQCkbLQstRSu7tF32Wcn1RvJq4W0CbdOOmBspM9+prO9qIquQS+pj6zGpqTFoLXn+xQ6uHRWCq9h4\nUttPKdJ2HZ94YHA26kBf+RoKqFToTw4qupZBQ2S0Pv3okPtvXpI6K1JTeE3EusRaJSNRRCvoGHLd\nXF20o2wehIx9j+88PWBnZ14CS95lX040NWqRRZfl9jfTjjLjkF+bl3SjvOgGVoGqHhnJFLOsWVGB\n5OamxZ3DEUcH0yKd6+jrlFEd6vak52UcCDv9yYNreu6qqM9RwWRTelj6Zc5GHXYG88K8tmkp0QJM\npEcldBhftDm5d7OW1VGpjoyCgsRk5jsYhmjZcbsQm2tKkUUwcundHVUWEatfx1c1XmtAyaC40QUA\nJMS6jmdFdA7mjKcN7DrqbhNo20sWv73P4ifKBba2Up9M2OwP7ow4P+1jpTI9/wAAIABJREFUnAzL\nMLS26qClpUVqt2UF0IA0g9NhF31HmUS1mh+gaHwtaYGppViPEp5eDggGBv38xk4MDUdX2xVUo5WC\nBuWiplgDKKL3xopZ6PDkZoBtxey2FjStsJh4qs+kXhFcBxixr9upycuOTR4VYK2Sue5TWcY2i8jm\net4kjEwOe1OO3hCLlquRxCZ6I/azWS8Z+aLQ741HF8JOn2tQZm07m8BkFjmcDru0Gn4B3IK2iOMo\n9q0U/knd5Py0z8GdkbDjbzCwyc+pnpP4dwf0f+LyhUKsdNCOpw06B3M8K8qj+fXG3K9yvNaAog55\nEuSSoS03YLF0mPlO2Yh3i0DrmCIjE3x1yPWojb2bFP06qt4UYUTDgDSLaTsB4d6Mi2EHc7fKOdVQ\nVmZ+ABpmyG5DuHKfD7ucDCbll9hAf+Q+vTyDo2sp9mHC+azNbOVy1J3StvwKBTKKaustNCgTi7S7\nRkTDDOnaPovcAv7pJwcc3hvSdYTGYhuJkkbNqk/2rDzvEmTUa/HdDvXmVU1u4mc52aVfJUxNUfgW\n20wCl/MvBgyOJ+y35zTNcKMBbxu9UQFKUpxZ5HI26WDoKW8eXtGU4qvSRa2+nTqYPB926TR9Bt6y\noDmbzGt1EfZi2KG/N6PtiH2qa/IUx6xQnVVscT1q0/7qUKTvzZgXCbEz3yEDWm6gRCd1D8+f4kJf\nf9IjQ1u7iU0tIdU1XDOm214y/+YOix9Sq4U3CbR5P1nPJ4hMRkuvkuatUp+qntJvrEhSnatZU4CQ\njITS9cwPeoKbH7uWH++zmx7HOaikeQsCS9MqYbR01Oo5/TF10YluErh8+s0Tjt69LG/YrAzpVcFW\nfFeVBglgcXTR5V4Ay4qj9ox56PBs3CMMTPb6M1qWuEFdhTqpBjZVVJRAo16TF40qnVGbVZcZI9Xw\n5icWQWwyj2yuRm1sR0RX7739rDCIqZP+tlaU9ahERjrDVYOzD/ZFcyTHLyILWRuk0lNgzdE7CV1O\nczDZKfSWuAJs8ntGipFvEdlczZo0GgH9xup23SQrDWyjpYftRHQ9v+KILT5TE2IXoU3wrR7d92+K\ndgbVZlHlguqvcrzegJIJvmvXlumUKcCmHRG8O2W2fJFAK6hPYsT0W0tOn4qsT7UFwXY9pd9YcT5u\nM1p66E1xDK4Zbcz8qKCSeRppRlVTyVPK0qeSZFq1oLBYgkO0ILB/4IzTYZdVZLLbWNK0AlIzIs70\nvE/q5mhFAguaKF40tRQn03HzQsGes2IVWywim2fjLv7KZqc/p+0EuaCZFA7ZOrCU+kp1Asuncj3z\nU4BInmpWgUROtFD2dQ0cbkYtXC+k31zxYF/oCzKbUfesbDoOuU+5L6m9LGOLReRwvRQ9YO/9wFlB\ncdQo7WXA5GzUodUoI5NtYCIzOn5siRKApUeS6Oy1Fy/WTRKzoDrz6ybHd2+Ka6NG4puE2NnSxXp3\nqmgt69FJnHe+e5Xj9QaUnD/qGBVXpppGbns+Fxc95o5dWuy1qCKcqtQnRWP3aMLVRRfrOMkF13Sr\nnuISgQ37XY3nVz0MPUP3ygls6/GtoKI1hRX/ydkOdw5G9NxVBVT0HEyKxcPyVozyxjT1BGcvZrhq\n8J1Pjzi5e1NkERJDU2pbNgMLgJPfqFYeIaWZ6OLWsgz6rs5+YyaigtzFerro4s8cejtzGk5YZAek\nEU1Xbs7KeVaGTCvLG11qI9KcFaWC4y8Dm/FNC7cd0G2uaDsBuyd5t3kjWQOR76YxtgQCPze7jX2P\n50932Dse82DvpoxKahSn0iBJoV9yG88u+uwM5i+MTCSYFRmdlcdk2uBkbyzWfTKiW3UTIT7bXF10\n2c2zOpuojjzPUridBzbBwubgYLwxTVy4l/PeKK9yvN6AkpEvo1EVCaVAa+k6DSuiN5gzumrjHKu1\nD0phVaV4UKPlBASDBTfTJlZPQW7FRVvoKTqFSHu4O+H0ix20E3khg43pZBVUigyOkfDs2wekb1+S\nuhoNszSw1cVauW89L4iTi5q1HwRczlpMVi777XlZyJfFtwKL3KYatajgEhs6rSwQN5mrE7cmhHtm\nxSq/DC2WC5dkYmHv+DhOhGUkWEZaZMFkXCLF9CzTiJLcch9YhDcuRjei0fRp2BFu3vH+pDspRElJ\nuTYZ4OT32DS2CbmyRuly1gLg4YOLNWG6PqFV8TVSsjLSZ3Lw1lWFJm2NTIou90L4vT7tcnzvpiLC\n1nUTCbh+YuHHFjfTJu3BQqzosKH4r/CnpGbhORldtenvid4oaiaoPFd5pPj9toxGkiOooafoekaa\nVZ+Ktp6vwueE+F2fycLD0DJxg2/J+oCgMT3P5yIQNEZEERku0VaRFiC1NQ7vDjl/soN+Lyt0Ehe2\nggqI7I+ppxhvX/L86Q7xyYieq4vCvkxbE2u3RSt2bh2fBi6fn+3Q6y0YNFalQPmSwAKsgUuSCYCr\n05JYcWnGfYP0jriB06xcxkKChzrK2qasKGMwD9Mi6ioyd2uRxxbdZsu4DUikED0eNznam9CRQvQt\nUYncphQ2ZW2OdMCevH0peqEY0QvBxJdp5cDl6mmfw/s3wj2rRF+3ibCjpUeWaaVHRckEyX2lFeCy\nmSw8vK5f1Peo/YzFfsrF16WD9lWO1xpQ0iTvLiWpTG01vbqD9uK0x8KKS69JnvXZpKd4ZsSgs+D8\nyQ7miRrObxNpE9IsJrMDsntDrr+1h/YDl1Veeguo6FomVvy7d83pdY+kq5N5Gk1LtHZM9ARLk1FY\nyeE3Rit6QvM4ZLhq8Nm/OmHvvatq1mYDsMjzpY5N4LKtSlh9XdVEoKQ39aEK43J/1cbVGVUQ5aVB\nRO63DiRqVujqW3v03xny6Piq0GE2RSWbKI4EhEVe6DeaNLl777oAJTWS2hiZyHYEgcv1t/Y4eO8q\n7yWbU5AtIqws/Jvmy44c3r9ZSxGruoma1VkENquxy8FxleqU+ymFWEk5p6Pvp2U09IzZyhFPdy1F\n1wzM2ho1JoLGxJZOf3/G+IsezkMlRVYzvKl6SguN3TtjZr+/i/Ujl+VF3iDSkoGttIbkvSsuPtlF\nf3QFQGpEGyMVSaX0LMv7yWYY+ylXsxbPgi77nTltW7g7U6kXiC2KQ9kQrcj1lx0zpvflFeOVx4ff\nOeHw/k3RcsA1I8y0pj9siVqgCi4AppZPXPkEVUBDFV1flHZU96WmUtUJdRt4qGNTbZHMoPixVbRC\nOH+yw+6dMQ++/FycizyaUM+FPJ4k27w9YcMXLQg0De7uD8voIndP130mamQiweTik132c8BXMzrb\nRNhVbDELHBZf32X3h69pbUkRi/NRNbBNnnbp3xuL/kEqPVK1E7lca2QxWzlYXvRS5/5lx2sNKIae\n4j9ps3xU7WlSpz5yBcGWExKdzBhOmpj9tLIGrqqnFNTH0Oi4PulXrrm87GIcpgWN0c0oT49WMz8o\noJI+GHL28R7pm9d0HTHJ7FybKKIihPktVfQfnQyzmzJeeXz+dI+T4yGxowtQySmQnt0SrehZEc66\nRiRaWT4WwPLxH96h9+aQnufny2LGqEar74ZSVARe5fUCbKAAnBeNlwUNdbwoxSz7iCwim/HKZfzJ\ngMGjIY8en60ByaaIqF7oKCmO7LT2/HTA7v6UnlfSyvo6Ourx1SOki0922X0wrIDJxqI/xLIZUoS9\nvOzS/8o1HbdcEkZtvSF1k8LCH1kMJ02aJzNaTrWr4Taqswwt/CdtBm/durz4dz1eCCiapt0FfgU4\nRDw2fznLsl/SNO2/Bv5T4Cp/689lWfbr+Wf+DvDXEF0C//Msy34jf/0vAb+EUCX+lyzLfuH2fWc0\nHkyZTBs4lhp1lNRHzfpkWUTiaVz5oslvdUFprTLJRVpWgkpA3DO4GrXR+oBd0ikdtR9tDVRc0B/e\ncPVH+2TvXZE5GhTd6as3nqz90bMUzNyIpic4xzGnlz1W/Xmhh0i/ikG2NVpJM30NWJpmyOAHl0xD\nhyeXAzwvpN9Y5RWsoiRefboW4CJLHF6CbsjxvQDEi8amwkMVRGS5v5x8y0ikYVcrm73+jEc/+KyY\nuC8CknoFdV13GY1anBwPy+ZIRlmyUAeT0mciBFhJc+qRSR1M5OfDJC8nCB2uRm3avSUdNyjAZJPf\nRGR1xOJhk5XIKXaKeqD1rE6d6kymDRoPpnjWn3yEEgN/K8uyr2ua1gZ+X9O038z/9j9mWfbfq2/W\nNO3PAf8B8B5wDPyWpmlv5X/+n4B/C3gGfE3TtF/LsuyPt+1Y1zJaboC/spmt3IpwJ6mPfJ9JQmpo\nNIjodZZcPe1jn8RKHU68UU9xESe031gRJzrDeQO9regiRr5A2DZQAUF/vhiQ3h0BkGaCcqjmNyj3\nKxffNnNznXWUcLNo8ORywOFgSiunQLaerGkr8AJgMSOaVkDfXbGMbCYrl2cf7tN/MKLjBgUfV7uw\nrQmiNYApr8erAZE6TdoEICqFUL0qq9hi6juMPuvTvT9hp7mk0RuvpZlfBCT1SGcZ28IOP+zgeiH3\nj0oBdZNeIo+7TrlGvsfV0z4HLwEmEoSKor95A8uOC8NbJa1c002k4W0W2MwvWuzdHYmsjrE5qyMN\nb4LquOi6mFvOn/QyGlmWnQFn+e8zTdM+AE5u+chPAb+aZVkAfKZp2sfAj+Z/+zjLsk8BNE371fy9\nWwEFEE2nWytWX99h+RVBfYx0c9ZHrgzYtEOioynDqw7GweQFeooQaVMzot9ccTluMVw0lOgnTydL\njWELqGj3bzh/OiA71uh5K6DUXCpZDEWsla0CdFuY2Ca2y7NvH7D76Ia+qxdaiNRWVBoEW4AFLddY\nRNTSsgN231swD21Oh12SRGfQXdC0Q0Xsq3pMthnYDKriax1wto26aKsKvuLnemapCOlzEFmEosrW\nMFIGnQVvvndaPMG/WyDZBgTXH++w//i6AgQyotskvqoR0yK2Ga9EaljVsupgIoe6lOsyshkuGsSx\nzn5vnovHVRG2OJeKbrIIbYZXHXpHU9EXZYOBTaU6YWqwDC2Sb3Zpf+Wm6I3yKsd3paFomvYG8GXg\nXwJfBf6Gpmn/MfD/IqKYEQJs/oXysWeUAPS09vqfv31/IjXcsCPC9yeMx01sM9lKfaSdPTU02m5A\n1DMYTURfE50M3VzXU6RI6wLYkPXgatRmqHtKWjha86jUQUXTMvR7N5xfd0lSjbSh0cwnkqlpG8Xa\nNL/JCru7keC+G3OzaDCZe+x150rIrVdokK6lxcSsA4tppIWTNk5jYlMXawy7K8GfI4vLaYvlVZPO\n4YyWG4i2EEZp0VZvZlV3gbqgejuoVGz3WyKRMltRmq38WKQ0p+dtGnsLOg2f+/uiEbN8ctc9K8BG\nIBHHUaU3MjKYBi5Xkxa2HXPv3fPCcLYpJSy/gxo5+YlwG4+WwrR2fE9GNvFGMKl7TRaRoFhFGUT+\n2bU6HUU3CWJxDUeTJs3eirYbKA7a9eI/SXVWkcV43KTx/oSGXYLWqxwvDSiaprWAfwr8zSzLppqm\n/T3g5xHS5c8D/wPwn0DtcSSGMHdsfr2+n58FfhbAO2hhGQkeQhsJQ4Pp0i0BIac6sJ5KzjLRXOkm\n1hnNGxht4RuRDtZ1kVYIqi0rhP6Mi5uu+CJ5I2kVVOR+JKjoZlRwVmMv43LSIohM9toLUlu0NhAf\nSqo6jhqtKL4Mx4hFtmLYYdZwGDSXNK0Q19DXaNAmYAGw89DaylPBSabh5q0uu7bOjrck6k1YxRar\nSBiogqFH62COl5vOZO/RouapljVQwWSbUxbUAsCy3kSCSJKJSlo/NlmFFvOLFs5gRbsR0PV8Dh/P\nsHL9og4i9WhEnoM6kNTpTTGRFw0WS4e9/qwSUWyKSuR3qqeF56HD1axJkugVB6zU3zbRnAqYLBos\nFy4HOxOxbIZRRoybwMTPM0GjeQPDTOgW9UDbUsQl1ZkuXUxbuMu9gh79KQCKpmkWAkz+cZZl/wwg\ny7IL5e//M/B/5f99BtxVPn4HOM1/3/Z6MbIs+2XglwF67+xnulY2Vuq2fK5Pu8zyKEXTMjBYr/VR\n9JS0veTypsPYdNcngxIxyMyPPCPpYMrldQfpdAUFVGqaikgp58DmZOi9jNHS4/l1j4PBlJYtMjh2\nTkdkY6YXRSsNK2LquwR//4j5Tw/puOuZG0PTlZui6umoRC0aFXBJM1EP1M5v1LilE+3kmZPEYB7Y\nXE5ahGdNtJ0ArxHiWBGWUQKMrNhWz70clQZJaWnaihKdILJYLW2yGwf7aEHDDfHsiGYr5LgzrTTB\nfikqlv9fpTZAEZHUM0JT38X6RwPsnx6yuz+sZIS2RSVARXyVmsvFsEOjEbDXXhQO2JcFk/HSYz5z\n2d+dFgWamzI6qQpieTPrwLfY35mu6SbqdYgzcS1l5fFq6LF7rDRaqoHxqxgvk+XRgL8PfJBl2S8q\nrx/l+grAvwv8Uf77rwH/m6Zpv4gQZR8Dv4d4Fj/WNO0B8Bwh3P5HL9q/vDC2Ltbn6ezPmV43cY7i\nsgVBrdYHSj2lYUUMeguGHw+w3hS1OzLLUhFpoQIqLTSynRkX5z1xIC8AFVFkmE8sW6S8R3rK8+cD\nDo9HYo3iLKroKrdFK8LAJmjI/GciZkuP4WiH/d0pHTuoVAcnchLUNBaoRi0quKRZ7pDVFfphlS7Y\n2DOI2zrJzkhMzFQnSoWNfhlaIrpIdOLYIEl0skQjS8XE0/QMzcgwjBTTTMRPPcU0Ulwrpu2EGJ0Z\n5lFaVH3LCaFGny8qSNwWjWyiJUEsmmtfXndotAK8n7mgt8G1ui0qUfWSwu9y2qe/N1sTUVX6dRuY\njG9aHByOC6+JBBN136UIaxQi7OLzLoNHQ8Vav66byFqdKBV2/Ol1k86+6Iti1+jUqxwvE6F8FfjL\nwB9qmvaN/LWfA/5DTdN+CEFbPgf+M4Asy76lado/QYitMfDXsyxLADRN+xvAbyDSxv8gy7JvvWjn\nqv09RaOVayPjmVcCyi16CkDLCUgejhg96aO/MVJOfjXzI5eXkA2oATgcc3UjepVK+mNnsQAPSpt+\ncTJ1ATq6lqE3M2wz4fzpAP9gRq+xommFpPnTMNWytSxQEa1kaRE52XpCwwpZNkSIfDVq53w7LCzZ\n8iZRxdt1OgQquIAURkvLPcZmjUO8tyzyU4v/1J/ldau5ZHNDXT1K3KbRbAIQ9XtsAxLZT0VGJKvY\nYh6KNgiuG3GyP66k0bdlcMSZqm6vAgYXbQ7uiD6wqi1+k51epoZlhDRcNJjPXA4Ox5XPq+eqntER\nRX8Ooyd9eg9HRW3Pi3STZSTW7vF6fpHVsYyqwe9VjpfJ8vwOm3WRX7/lM38X+LsbXv/12z63bYjC\nNi2nPhqdhs/1qL0xlSzer/hTdAqvSXJnyvVpF+1EDQ3X08kSbOTZ0XYzroYdMiBraDSs3MRmJBXz\nm2o8k5PF0FLMeynDeYPzcYed9qKgQPJptGY0y4/DMGL01Cicsa4R07BC5qHDeOlxedMpWg4UwGLo\nytNWVybn5om5CWBMDSTIiHdU7fjyfeXvW6z3qsai1aOmdWt+/X3qe+W+t0UjRcPoxFBSqqIVgtcI\ni3R8XSxV6WfxfWpRSZzqBcW5mTXRtIyTvMjvNvFVBZMiNbz0WC5ymqM8EIp7YQuYzAKH69MunTtT\nxaOyzW9STRGniUGns/zXSnXkeK2dsuqQT+s0E9Sn21kw+qKPcSJOqNRT6qACaaFvdD2NbB+ub9ro\nuxk4+c2cshapqPRHJ0PfmXA1anOd6gyagh6kWX4zKTb9TWKtXP1wvHI5/XiP3QdDkjwtnGZaJVqR\n37Vw2eqiZ4pY/LwElpYdsGwKn8nwgx06bwmfiWtGRZagqj/olSf/iwBGnMPy7yXQyJFn1LaASbmN\nzWH1thv6NgCR+9uWYvbzhtFT32H6nT7NRxNO9tYjkjqdKr6jopXUo5yJ73L92YD+/VGlWK+ul8hj\nVe300oQ3XDQIA7MQYOs0Z71Gp+wRc33Tpr0/p+vl/Vu2mtfKBtgz32F51qJ/b1QsParqM+p5fVXj\ntQYU0bFNmaiZKPbLMtFcKTqZMnvWwbxfbemoa9XMj0kCBmRZROpqJIkuPA39/OSaVJaP2Ep/+jOu\nxi2u0yaDlgZ2/voWUFF1FfnPephyddPGb5v0PJ+WHQgKZCSkSd7JraatSBokgUVSOtsQVMh/f8XU\nd3jy6T7N/QXdxkr0zlBs22sTKVPbQaSV6AOqdTdibLPnf2/Xtr79OoDAdhApC+mUxdUji8nSY3HZ\npH884c7758XEq9ORbfRG6i5qVDEPHcYrsQjX/sObjRRHnIftYDIPHYZz4TNRO+RtozmF1yRPDw8n\nTbxmUBoTt4iwqrV+EVrMnnVo3RFNlmwFTOop7Fc5Xm9AycSFll+5rqe03YD0eM543MQYVE/umkib\nZ36ahGRNGKZNrict6M7zD+TNkmAr/dG0DK0Ho4XH5ahN1ocspz+pjAiUY803W6FAlp7gHsQMlx5P\nn+2wdzih6/p4mbhJ0zwTtIkGqfqKqYkUcmzoBRXqP1oJzrzwOB0N6O/PaNiRUiy2OXNCpm+gHy8O\niddBZ/PYtHbPbV3dxN6rnhU1EpHVtavIYhlajC7bNPorOg2fg0ezF3acq+x3Q7SjRiVX513aOwvu\nHoxoWOHG7arHrx6nXM71atTGsmP2e3ORCVJADtbBRK7SOI9srictDDOl1xT626aMjpoFkoa38bhJ\n43guPCpbdBOZjn6V4/UGFPmFdYp+mBJU0lxPST2fONbXRFpBY6onXgJGixDacDMVi2jTyXe4AVRU\n+qMjMjimnjJaepyd99nfn5AilveQGSBVrK1TIDPNxVMjoemEXI/aLHybfn7DlO5KrUglbwMWlQq5\n+blqWiZdx8dvL1hGFtfTJsFcdF9rOuLJ+FIGNgVkxHnfBB4vXyW8/tr3ZngLYlGmP75p4bQCOk2f\n+/eu16KRTZmi6pFvbkUp22KOFh5hYHF4PBJZGMVQt43ilJ3WrIKqXF52afeW9BurNToqr+c2MLmZ\nCr1m0F7QysFERjVrGZ2aCGs5wm9SdNurgYk8p1H6fdRgSXZs07WMVMmmCF1CQySRIGutuB63mCy8\n8sY34rXMD5SA0SCCzoLrSYurcQt6ZaQiJ9p6SpmiC5vWzDCNhPHX9om+ck3HFc2SitThFgokoxXp\nR3H3YqGD/M4hix8Z0vX82pPwxcACYjKqUUvDDGnZpnDH9oRxbLTwCD/qYD2a0fKCinlNagGVVptK\n1LKxDUENKFTvxKZRpzNqNFL2RC0ph2p6m68coo/b2I+ntL2A+3eui4Xbt9E69ZiK/W4BkjA1itqn\n4GsD3B+9Yb8zX6t9qmef6hRMNkea+qIFQT+/N+plDus+E72gOfPI5mos2ibsdueF12QTmMh9F7Rv\n4ZGmOoPOvKC9ci2e+rlP8uU5XuV4rQElzURJuaZl6EZWXZazJtL2O0uuz7oYhridt2V+IK/Lyf0g\ng86C4YZIpS7Uyv2pk0v3MvQfvub6WY/4UPgR0tyRquoqYv/yglajFZkWnv94xHjh8fSyz95gJmpt\ncvu8KZtvbwEWQGSFtLqAK8DFSw1iW6fr+IQ/PMePTfzQYjhukQQGzd4Kz46K0NjWk2pKfkvKl+Ib\nbaY+t7llZepZ/j/JvRZRIibVKrRYjD0MJ6HdWtFtrnB/eCaqiGvGtxeVB8hj2abByFqhq2FbNMf+\n8fONRrNNFKeul/h5p7XpeZvdHy5bENQL/eQxbQITEZmIe7Oh0NXNYKI4YVcuq5EnFlC/RYQt1vpJ\nTFbR9xGgJInOMrKKmhqRpl0XaSEmszWSgymj5130I0VPMdczP+WqfbFoVdDNuJmWmoqgMCICqoOK\nWqWsaxm6l2HeTxhOm5z/f+2da4wk13Xff7ceXdXv7tnZ9y7JpSiSFgFKZijCgAxHdgI/FAPKhwAm\nDBhCYsBArCAv5IMMA4kC5IsdBAnygAUFNmAZQWRZThAjgJDIjh9xEoumZYoWrRe5Ii3ucnd2d/r9\nrqqbD/fe6lvV1T0zq9mdSdgHGFR1TXfVqVv3/uuc/zn33LnHmcYI6Yu0BMHygW6yVvQ8Hi9iVFaT\n4LpumVZtYk3iOxywFFktiROrzuvpzltStWPP1YZpZux0oSyYcT+EyCFsTQlLC3xP6eYKuQIymRUV\n14gpD5kHj1gKFrHLInKZzn2m3RC8hEpDXbdZmXC2PkzB7ahzjNLrHwJIusMySewsgXwlr6TYKrHr\nudpgIKXgwqP3Ulcps4hXAZjYxPLdXg0hZGqZ2NxXEZjMIi+N6Axv1Whf7ql1e1wbCC29tfWXWjT9\n6tEG5QFyqgEFoD8KMx1ZNZKSlKR10AWWBPJSn9kf7zD44D5OeX04OQMqAI0R+4Mqdzp1dpojSEtt\nrgcVU13fQeK3EhUWvrnD2fM93TGdFRfI6K3vQFkr7tINCtyIsr9gNC9xt1uj68W062MralPsCqmz\nbQYXgMRxSGSU6dCJdFRx6sQhbumtzoydRy7TRcB87rGYecj9AFlKENUIz49xXDXzWwiJ0AaJlCgQ\nSQRJ7BAtXOTIQ8wdxM4MP4golZQ1FJYW1MMZbquPqcxnk8ZFAAKruSy2FHEy+eU6xgufzqBCFLlr\nZ18fZJXYLs5orqrT13dGaVjZjuQcBCaDWaAij17CTn10KDCx0+oXL7dpfXB/WWApl2RnrmuvONAf\nhXBIYv2wcqoBxXUTZv2AgZc194pIWlNImhCS5zv0r7cQ7+mQzgY8AFQcJNShOyqzd7dBckat6pa4\ngpLMdbJcBMjx1NvbdRICL+bOzRaT3ZFaJMxzCuZoLK0Vu/SA5yR4SZwWUa6W5qqjdup4XkyrNqHs\nLzZ2/I3ggsDV7WYGmyn0bVsQRS5Jamlcyn2Wy0zavJh2tgtW25bNOpfKBhDzjNeVjzSyjtjNl0GY\nLHy6w3IGSAKd27MOSGC9VWKKSQ/vVtm92KMWrPIlts55new8k3IN6KVEAAAb7klEQVR1Rqs6SQnY\ng8Akzbm53qL2fIe65mqKIjo2CTuNPAaTkFk/YOd8f83ouz851YDiCEljd0T0UpvhC7rL+GZw5Eha\nWFanDwXyWo/OzSZc6h0IKoa8rTFHVBWQ3bnRQl5SHcRupXwHsXkVY0GVrkZ0hhVu3m2x2x5QlXMd\n3l1GCezwct4NUoWX4nRZTAMsnUGFOwuXnZYaCKGVk5B3h2LEWnAx959Yg7QogQyWAzWfYp+J0qzJ\nZbA7dJ57cfK65dyKgwDE1i2fPZuGbq2BN5qX2O9W8fyYpnYl1wGJrYcdDjZWhb2G0d1OnVKw4NLV\neyu5P3mrBFgBuKHOgK2fG9IIZ2loeD0BmwWTzs0m9Wu9jWCSzrjWJQyG0wD5cpPGCx3K/kMusHSS\nIoRal7X3fI/+vSruWeshucv6JOitg8B1Esr+Agkk5xw6txuIC/b6wkXZtMvoTxVVSFqcg3tvtkke\n7SADQeItUlxyhCx0gSBaukCNhN4kZPR755h9aF/lzPgiDW0Wh5dhhV/RCWwGWCaayb97p077zHBt\nnomD3AguK/um4+ZM4IMKUt9PpmxhxKhApyLZVJV/bZ7KvRphbc7ZnUHaViVr0BbxJEXnTmvGLkoM\npgHR/9qh/qH9dHnQwItWeB6jsx3FMuTtYFai81abxpU+Te0mHRZMBrMSndsNqudGCkz0YuhFllUk\nnZTsHs99+veqVJ/vnUzFtpMUgVq+ohbOiBsO3U4V98zSjMbJgoonYkNTUPGBikpG299rwDnLtNsA\nKraJ7j6S0H1jh8VjPVplZeIHnlgJK2d4FSkzLtDowxGdQYXBKGSnOaIezIh0XZN08MvlZD4bWEpC\nuSOOUBm7oRtR9hZUS3OmdeU73/iLM4TtKfXKNH1D5s1lT9hFsje7Dyufre/mweZ+5SDQsCVfbT/P\nY2TyMCyycTAOmXZC6ueGXLrYSQtI2ZPpDgskeffEVI5rf3gvtXTs8x4UyZnoEgSjN5u0Hl9OmSjK\ngF0HJvt7DWq7Ixrl6XLWsZNfv3iZrGcAttupEjZm1EKVYGemexyXnG5AEYpsBUgqiuTr9CuIpllk\nKzoYVADZFocGFZOmDyDKEveJffa7VaLIpV0bZyJAxsUBOy9kCQ6GGCu5MaO5z50bLSZnR+ptZN6U\n0mLjDwAWm2Mpewtq/pydisqOHU4C7l7foXJ5mKnAZpvA6s3pFJr2h3ExjgIE9yNFS3Xk0+8zRLIF\nIqbC2/hGjfDiiHplyvnmYAVg17k25lr56xjSdLJQxaCHd6rsXOxRLS1S4nWdVQKk5SDsSE5nWGE2\n9dl5Yn85a/iIYFJtT44EJuOFT6dfwQ8j6pVl/zuxim0nIULnfkgZI/0F1KDTq9IblnHqpnNHKzkq\nay2VW03k+f5GTgXUMRN5cYTEOxPTGVTY22/Q1kRe4qlJfea3B1krgRcRPhLRG6v1ddvn+9SC+Wqn\n3AAsNseSSEHkKMK34s9phlNm9VFKOs5vVahcWa5NbFdfywOMOnvxIFuXXn9UcDlsspvaigx3YwNI\nvsrbeFZi/HaN0oUx9cqMnSf3VD6NNcjykaL8Pa7LzjXWxNC4F2fGXHrkXjqID7JK7JR4Ewnq9Kq4\nXpwWR8rPGj6QM7l9OMskm2vi0xuWEUCzpuZ52TVrj1NONaCAGqyuk+ATE0pBoz6mc69O3w3TJUQh\nm6MCy8Q3sCyVMyJD1EopCvNUlKjSB+nxhqQ3LnPndpP4bD/lVVQVtmIXaBm1SNKQqO8klEsLOr0q\nw3FAq74kCDN+fS7MnAeWBIHjSjyZkDiq4wZ6Tk8jnDJrjJgsVGhw9Kd1kucGVMIZoa/fhk6STmVf\nXQB9CTIRqzyI4WWOKivV7guIXzvKFFlkYqTX4Z0uPMbTAOfLdeLvHVAtz2g9eScHIsnKQF8HJOa6\n5lqGJ0nnxAzKJLHL7sVeIRGeJ5fzoJSxLO40qLYm6eTN5VKh68FkFnnpSoKdm02q51bBpChxbR67\ny/DwOGQx8WmfGahUfDfOVNs7Tjn1gALLyIrRVu4M6dxu6HWIFWCk7kdh4tvSUnEuJPTeaCMf71IP\n1Ro6iStWO6FQVfWBtFO6VTUHZ/9Gi/n5oeW6CBK5NKkhm8GaWisa5EyuyXCmcheGjanKBPUiAtfN\nAIsj5MrMYLXVA0KQukP2W7HsLaiVHHYqE2YfHqop7XOfvUGF+G5A6cKYSjin5CnS1ySPpesQWx3V\nniavtq61f7BkI0I2eCzXprHXSzZ5MPPYZR65jKcl5rcquLszKpUZzeqE0oeHK1bXUUEkP4dmbrlP\nvVGZST+kvTtILck8N7UpimMTw71JyPB2jdbF/ko0xg4LG71sTsgkrfWvt9JoTh5M8olrdqW2gc6e\nbZ9Xs45t4M3002OSUw8o6dtY6Hohns6+PDeg93YTLtodO1oBFUedBFCgIgBxrcfsj3dInu+QhIIy\nC5XgpicUwmpY2ZC1rpPgX43p9ivsTX12miMi31EWBktuxbZWbG7Fkwq8jBtUKS0YTANuv7FL+eKQ\nhiZX546bfRMay2eD1VIELokUlD31ho8Dh6g2UrVjY5fZQg2caT8ACUFjRlCK1MoCOjvW0+SynUNi\n2sferpN8mNnOmo0T48IIIg0es7nHrB+AgLAxIywtaNUmlJ4apoMwXzayCERMGy31KOZijBWRlkoc\nh0zeqVG/0mfn0n6awr7OvQHWApNZ0Q/g7NVOxhIt4kuAFTAySWtpnskh3RyTazJ+p0briqpyH1gF\nluyxdZxyqgFFInT5ApnWjPOdGLQLk1zu079Vh3NAZaJ/lQUVyHIqjq8e4uCD+3RvNkguiLRrJM4y\nWU5ti3kVz0nw3Zj+JGTv+hmaV3tUg7ku7yiy1oXp6GvcIN+JCbyI2hMzhtOAW2+eoXJuRL08y4Q4\n8zVX0xsiO3Dy4JIgKJkSj5YpbQZULB2iVjYzdha5DMYB84lP+esh4/fO8cIIvxSl9WEVuK4CjBEb\nQOJERchMHdrF3COaelS+VWLy9JRSeZFmzlbqc/zmMGMxGdciDyDqbg8GEaOPbQnZmaZmnd/xXpXG\nxQEXn7izdlkRc03IAokBk0XsMlqUGM1K9L7TpHp5kHFRNrk4pkJcCm6TkOGtGq0P7qeWjQ2m9n3m\nwcTUhmlc7lMN5ikQ2X3SLu95XHK6AUXqjmnVJwFwhXq7yxC4AOOvtxg8nSzJ1g2gkna+EMTlHp3b\nDeK2Q1JVfi2A54hCXsUu3OSgFi73H4np7NWZtabEVUHFXygXyuqIRu8iN8gTIgWW0IuoPDZnOA24\n+7VdSo8qi8UUFvbdGC8pMrmLrBZ1xYxJLtTWk8ZEzmbFmsEmLU4hvuDQktYcnESQaMtiHjnqGSVq\na4sQ4DhJunWFpORFuCWJW50obuzycn6QJ5I0XG+b8tn2X1oG60BE3VexW2O7EvNkubTE/K0a5cf7\nXHjMIlxzVkSRe2NbOXY0pTcqM+mGtB/pFrpLtv42yK+co1OmfbmXOYcBVvteVyyTacDsmw0aT3fT\nXBPXaksbTN6V9VAypQREjlMJQT7dZfZaC57pHggqCU4aFnaExL3Yo9OvcC+qEtcnJCVV22RtBKjA\nBSpdiumPw7QKuukAicWtrHODEmlmB8dE0sXXlfqnz0wZz9TC2V64oFnTfE0ugmEPwES6Gd4gm6mq\nU/wt68UATFo/1l12cFh2VrVvH1egY2Sd2Wy7BSIPDBkLY9UizFsDmwDE6Gp0MzrZ1ojhFWaRiXqE\nRFOfZntE+5m9tG7IJiAx5y0CqDQadKdOuTnl/KVuoYWZ50vy1lJKBCdOSgTnw//2PReCyWstys90\n0/SBlG8pAJN3Xz0U6ayUZywCFZ7pMvl6i+TJfur+JDJejf5YafrCgEIroTssc2+/RtwaUS05qlyk\nRdaq3666QJ42QUtuzLC0oLtfY1KdU69Mlz6zjgQVuUHrgEVFbNTEudFcDYC7gyb1s6pQUuhFGasl\nDQObAWgRuea+1wKMblsDMrAEGtWOq6Tqus95WY0QrWbnQnHWrq17XorcGbOfz1OZ62jHaFZicKeG\nX59Rr06ptgeFAH0QkBSBwGAcMhuV0hdKWsgqF0Gz2ywPSKO5WtnPDyJ2GsNMrsg6MLGjOb1xmdk3\nG5SfUQGHTWBiCPB3Xz2UyAOPZUbfBlART3dTTiUpT9NwsZrtyyqoOGBIVFGXDLyQzlttoiv9lKw1\nU/89kQUVEwUy1oorFK8S+BGDSUjvlV2m1oPN++O2G1QMLCrPxddJbPVgzrShBsWt7+zgN9SgMGFg\nu05I0UQ723oxbZAfqHbl+wz7b2HGd+tzbyJxi4Bjed3VKvtFExptEDFh5sEoZNEPqJ0dcf7yMmvW\ndZIVTqMISMw1i5ZLNRaB/z19zp/vrnWZbN3zVpMhXwdvN1TZxpUck1UwMTk5djRntFdN3ZyDwMRY\na+O5f/SHuEFONaDEscPI3PAhQYULMLjRgIvqcOjpym65jFoDKoZoVcckzpWEwY0G8cUhcVlzIjJe\ncYHsbT4RzncSRs8u6A0qTMYBrcY4nSVc5AZBMbCA6kiJ4+h6KWreTqM8ZTL3GQzLdO6FlC8OqQTK\nHQpyHSnz1rUmCeYBxrSJvS2S7Ho+h5dN58zLUfJVbILZDJJZ5DGe+UzeqeGdmVKrTim3humcqHxy\nn9JvPZAUuTeThU+3X0ECzWfvZUKyRcRr5ly5yJKJxtSu9FdeQLZLaNrGzoC1ozmNy/0jgclo7tMf\nlo/0HA+SUw0oAINhGaeuPxwCVEQIzpUe3b06SVsgK1P942JQsYs0KUtDEa29fpX53CWuK7JWSpG6\nQPk3mjpXnHZQY62EfqQI1htNgvaURtWeb+Nk8xCKgAU1mTCRCZ4UJI76HCUOFX9BI5wxaw2Zzn16\ngzKLTkB4drKSwJbPkE31llmuIpGb80uyLtP9p2yvA6OMa1Uwy9m2QtIIVS7hbXqnjN+eUa3MaLzn\nLoGrLLd1bo2596Lr5oHEEKb9UcisE9I4P8wMYNsqUW20GsXJn8skzrUf6azkiRwEJoZUnnTKtK70\n0prBhwGTyUK9kHg3RXlcNyGOHHrDEGr64AGg4vjqIYrzfbr7NeLYIalNkP6SbHUyLozKVckszuUk\n+G5Cfxxy550mjV09o1O7QOuiQEq9JbdiOln56kIVVn51l/FT6i2yjNxsBpb0PoVccYci16EiBYvS\nnGZ5yqylcktGk4DuGzs456aUK0tw8S2AKYqmmPuxgcboAqSAkx7f4L7Yss5NWlci0mzz0ScDIIt4\n6c5MxgHJXoh/Sa2R3Lo2zoCIiSAVvgQOCSQmIjScBsy/0SB4ukfraqeQ4ziKi9O/W6XcmtLQFmze\nbbXFWGI2GPWGZZUBe76fzjq3w+ybwKQ3DIkjh2ZzfKhneFg51YDiCEmzOabbrR4aVBwp05op4syA\n/qDCfq+KbIzV4lyoFQhx8hGGLFnr6AiO78X092osdtxMCHedtZLlVpRbUdIh4en75wqkvrlL5dFl\nfoANLMbKMcl8kI10JMJ0fG21yCy4xCWHeXnKojFalnbsVQm+UmH+gRFBuCD0Izw3xneSlQzZFffI\nisDYzwXgqEmWxRmzy2xZ25WxM2YXiUOk72U29Sm9UmX2/jHlyox2c0Rpp79SC/eoIAIUkrmThc9o\nVmL8VoPgypCd99/JcDB5q8e+vyJeJ7Uq9ss0zg1XXJRNkRwbEDr9CgJonxlkLJui0HARmERzj1Zr\nRKW0ONpDPEBONaAIgbrh1ohup0pPluEA9wdIM2oB3OaI3rDMvXs1Wu2R6jwWWVsUAbL5EFdISpdi\nesOQvbuN9CGss1bsbUmoUo2R42qrR1ks0/fOGIxD7l7fJbw2yMwOdp0ET+Y66QarBbLgkjgOAdHy\nrR46LCoTFj/YV2+3hcdgHKhs1ERQas4olSJKXoTvKoBZVz+26B7z+7YUA8hqxmya46K3i9hhHnnM\n5x7zXgCOTLN4W40x/g8O8HV7rrO28gN8kzViWxCxxU0MpwHTb9fxHxlx5r330kmWefcp3wbrrJKx\njuJ4pYjdS72VNIAiF8cGk/QcnSp+GNGsTTI6HQpMBmWiuUurPUqzZ49TTjegIFUCGyBbY3rdyqEs\nFViCiiMk1GDghHTu1InPjJAosnZdWNnwKrYL5Lmxmhfx5TPMn+0Rl0UKAomznltRasbpLGGTlFdy\nY2ZPzRiMA27/xQ6188twcOBGRI6z+vazPId8FMYGl0QKPG3JmBC0GbRJqMzmqDHS7oN6ew71BLLw\njYDpe2Z44QLfj/EMyDiqHYz1JtgMKnkwkWZrJcjFiUMUOywWLtF0eW2/vCAIFtQqU/z6OA3N+3qp\nj0yN4YLoW1Eb5d2rTUAympUY3q4R7ExoP7VP4EWpO7FcenS9e7OOOI1fbVJ5tpeul2NcHNPPDgoL\nD6cB/Xuqnompf2O7doezTFyarXG6yoEn7p8LK5IDAUUIEQJ/gCrb7AGfl1L+EyHENeCzwA7wZeCn\npJRzIUQAfAb4S8A94CeklG/qc/0c8NOoBIe/K6X8bxuvjVryItQoKtry0O6PbeKmLoybEL3Upvd8\nj6Q81REg7SoV8ComCW7pFkjGz0UMhmUm4xLNxjj1XY214ki5krdi3KBEqhnCkXRwhaosV/YXTCoz\nhpOAye+fo//9faqhTpXOkIk5H/1Q4CLwWM7rUYlrDom3TGwylkJUVYMquSDSuTVxopOmFh5R5Co+\nau4ipy5+10U6ENVi8CS4lk4SiAVEAm/oIhJYtGJEGOOUYpW+76lt4EdUggVec4R7Yelqmje2MNZH\nbtBlCfGjgUg+7GqWoRhNS/h/2CD60IDdK93UglhLalvnBtI1hfIWRa9fwXEk9efupf0lz+/YYkeu\nbECSLzfTSmvGVTZtZe79QDenPaJcWhBqMHGdhwwowAz4ISnlUAjhA38ohPgC8A+Bfyml/KwQ4lMo\noPglve1IKZ8QQrwI/ALwE0KI9wEvAs8Al4DfFkI8KaVcXzJKqMFMAqEXqe7RGtHrVegNyiQWqJiH\nbkAlQaQd0ZjrrpMwfCGhf7dK1HBoVKcpWes6yVpeJS2ahExzTYbTgN7rbWaPDojKTsZlsfNW1HlW\n+RVPOCmfY96A8x+ekMxK3L3ZxK/PqVZmVIJ5mmdiD7RMCvcacDGRIhtg0AADkDjZjNiibFj7uJRZ\nVwGWNEqeeDXXFNbn9FiOqynKos2DR9E2f79QDCKQHexmDaB57DKelRiNAxaDErWzI8o/vEfTjQtd\nkXVAss7SGUwCpm/VqVxbhnMPY5XY50mjSv2AxgudtNLacgEvK0pnZcCapLWRTi+IIyd11wMLTA5L\nrB9WDgQUKaUE9LJ6+PpPAj8E/KQ+/qvAJ1GA8lG9D/B54N8KIYQ+/lkp5Qz4thDideAF4P9sur4j\nJGhQwfh7zTH9QYXeoIKsqcW1jC+YBxXjX6cJbCF452N6g4pa6KqhZwt7EYlcrk+crVW7tFbMG9N3\nEsInI3rDkNv9Jo32OPOwbTcovQ/IAEsiReoK+U5MnDiU/QW1cMZ07jMaB3Rv1ameHafAsuwMbnFn\nz4HLJoCBJcgs91cJU1glMPP7Bz7D3H5Wr2LgyO/nf5fXzehkWyL2AI30IEuB5E4Fv6GAO2wN0wFv\nA3cRkGSvk3Vv5rGrXJNOBb+8YOfJ/bWWTvZ8WatJWRaeWjdHSHbO9yn7q3lGpk3y6fRp/VgdGm42\nxw8cTOCQHIoQwgX+BHgC+HfAG0BXSmkYnbeBy3r/MvAdACllJIToAWf08T+yTmv/xr7WzwA/oz/O\nvvCX/81Xj3JDD0F2gbsnrYQlW302y2nTB06fTk8d14kOBSjaLfmAEKIF/Gfge4q+prdFry254Xj+\nWp8GPg0ghHhZSvn8YXR8WHLadNrqs1lOmz5w+nQSQrx8XOc6Uv60lLIL/B7wfUBLCGEA6QpwU++/\nDVwF0P9vAvv28YLfbGUrW/n/QA4EFCHEWW2ZIIQoA38V+Brwu8Df0F/7GPBf9P5v6c/o//8PzcP8\nFvCiECLQEaL3Ai8d141sZStbOXk5jMtzEfhVzaM4wOeklP9VCPHnwGeFEP8M+FPgl/X3fxn4NU26\n7qMiO0gpXxNCfA74cyACPr4xwqPk00e+owcvp02nrT6b5bTpA6dPp2PTR8h8qa2tbGUrW7lPOd76\nb1vZylbe1bIFlK1sZSvHJqcWUIQQPyqE+IYQ4nUhxCce4nXfFEL8mRDiFRNOE0LsCCG+KIT4lt62\n9XEhhPjXWsdXhRDPHZMOvyKE2BNCfNU6dmQdhBAf09//lhDiY0XX+i70+aQQ4oZup1eEEB+x/vdz\nWp9vCCF+xDp+LM9UCHFVCPG7QoivCSFeE0L8PX38RNpogz4n0kZCiFAI8ZIQ4itan3+qj18TQnxJ\n3+uvCyFK+nigP7+u///YQXquFSnlqftDlZF+A3gcKAFfAd73kK79JrCbO/aLwCf0/ieAX9D7HwG+\ngMqx+T7gS8ekww8AzwFfvV8dUHOsruttW++3j1GfTwL/qOC779PPKwCu6efoHuczRQUKntP7deCb\n+ron0kYb9DmRNtL3WdP7PvAlfd+fA17Uxz8F/G29/7PAp/T+i8Cvb9Jz07VPq4XyAvC6lPK6lHKO\nmoT40RPU56Oo6QXo7V+3jn9GKvkjVG7Oxe/2YlLKP0BFyL4bHX4E+KKUcl9K2QG+CPzoMeqzTtIp\nFlLKbwNmisWxPVMp5TtSyi/r/QEqjeEyJ9RGG/RZJw+0jfR9rpsu83l9PN8+pt0+D/wVIbLTZXJ6\nrpXTCihp+r6WwjT9ByQS+O9CiD8RahoAwHkp5TugOg9qabGHredRdXgYuv0d7UL8inEvHrY+2jz/\nXtRb+MTbKKcPnFAbCSFcIcQrwB4KKA89XQawp8scSZ/TCiiHStN/QPIhKeVzwI8BHxdC/MCG756k\nngfp8KB1+yXgPcAHgHeAf/Gw9RFC1IDfBP6+lLK/6asPQ6cCfU6sjaSUsZTyA6iM9Bd4gNNlbDmt\ngHJiafpSypt6u4eat/QCcNu4Mnq7dwJ6HlWHB6qblPK27rQJ8O9ZmsIPRR+hSmn8JvAfpJT/SR8+\nsTYq0uek20jr8HCny9wPKfag/1AZvNdRRJAhp555CNetAnVr/3+jfOp/Tpbs+0W9/9fIkn0vHaMu\nj5ElQY+kA4po/DaKbGzr/Z1j1Oeitf8PUL42qHo3NpF3HUU2Htsz1ff6GeBf5Y6fSBtt0OdE2gg4\nC7T0fhn4n8CPA79BlpT9Wb3/cbKk7Oc26bnx2g9qcB7DgPoIii1/A/j5h3TNx3UDfgV4zVwX5U/+\nDvAtvd2xOpIp5/BnwPPHpMd/RJnIC9Rb4qfvRwfgb6GItNeBv3nM+vyavt6rqHla9uD5ea3PN4Af\nO+5nCnw/yvR+FXhF/33kpNpogz4n0kbAs6jpMK8CXwX+sdW/X9L3+htAoI+H+vPr+v+PH6Tnur9t\n6v1WtrKVY5PTyqFsZStb+X9QtoCyla1s5dhkCyhb2cpWjk22gLKVrWzl2GQLKFvZylaOTbaAspWt\nbOXYZAsoW9nKVo5N/i8Y+dfQSqsaLgAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x105c90f28>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.imshow(np.log10(psf))\n",
    "print(r'$\\int\\int$ psf dx dy = {}'.format(np.sum(psf)*resol**2))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x1295daa90>"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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NmJqZysRkFwfrrUZhhpcFCjNu1dS3UzB5AhOSXbEuyqCIiK12Z0aEBQozbtXU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\nVGCKMACnAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1295daac8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(y[ycen-500:ycen+500], psf[ycen-500:ycen+500, xcen], label='Without obscuration')\n",
    "plt.legend()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let us now suppose that we observe a point source, and our image reconstruction has a ...This will shows a a blurring of the image, with a gaussian of 10\" FWHM. Let's generate this blurring"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "fwhm = 10.\n",
    "sigma = fwhm / 2. / np.sqrt(2. * np.log(fwhm))\n",
    "sigmasq = sigma**2\n",
    "kernel_blur = 1./ 2./ np.pi / sigmasq * np.exp(-(r**2/2./sigmasq))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.99999999999999956"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Check our kernel is properly normalized\n",
    "np.sum(kernel_blur*resol**2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# apply the blur\n",
    "psfblur = signal.convolve(psf, kernel_blur, mode='same')*resol**2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x12dc58e80>"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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btgE28skMvWHyl2BM8lU3tCDEGHdo8/C57NSlYB6BQ1sJeKKWKMyQs0RhjKuq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\nDcaR1kKuhCtEAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1296df7b8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(y[ycen-500:ycen+500], psf[ycen-500:ycen+500, xcen], label='Original')\n",
    "plt.plot(y[ycen-500:ycen+500], psfblur[ycen-500:ycen+500, xcen], label='With blurring')\n",
    "plt.legend()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "We see the effect of blurring, the, observed PSF is wider, and we have lost some flux in the central core. Suppose now that we observed this psf with sources of unknown fluxes, so that we re unsure of its scaling, and that a background remain in our observation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "psfobs = psfblur * 2. + 1e-4"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The question is now how to recover the PSF that serve for our observation. For this, we will use the PSFs curve of growth. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.0 212.1\n",
      "10.0 212.1\n",
      "20.0 212.1\n",
      "30.0 212.1\n",
      "40.0 212.1\n",
      "50.0 212.1\n",
      "60.0 212.1\n",
      "70.0 212.1\n",
      "80.0 212.1\n",
      "90.0 212.1\n",
      "100.0 212.1\n",
      "110.0 212.1\n",
      "120.0 212.1\n",
      "130.0 212.1\n",
      "140.0 212.1\n",
      "150.0 212.1\n",
      "160.0 212.1\n",
      "170.0 212.1\n",
      "180.0 212.1\n",
      "190.0 212.1\n",
      "200.0 212.1\n",
      "210.0 212.1\n"
     ]
    }
   ],
   "source": [
    "radii = np.arange(0, np.max(r), resol)\n",
    "growth_psf = np.zeros(radii.shape)\n",
    "growth_psfobs = np.zeros(radii.shape)\n",
    "nbpix_psfobs = np.zeros(radii.shape)\n",
    "for i, radius in enumerate(radii):\n",
    "    if ((i % 100) == 0):\n",
    "        print(radius, np.max(radii))\n",
    "    if i == 0:\n",
    "        idj, idi = np.where(r <= radius)\n",
    "        growth_psf[i] = np.sum(psf[idj, idi])*resol**2\n",
    "        growth_psfobs[i] = np.sum(psfobs[idj, idi])*resol**2\n",
    "        nbpix_psfobs[i] =len(idi)\n",
    "    else:\n",
    "        idj, idi = np.where((r > radii[i-1]) & (r <= radius))\n",
    "        growth_psf[i] = growth_psf[i-1]+np.sum(psf[idj, idi])*resol**2\n",
    "        growth_psfobs[i] = growth_psfobs[i-1]+np.sum(psfobs[idj, idi])*resol**2\n",
    "        nbpix_psfobs[i] = nbpix_psfobs[i-1]+len(idi)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x12dd3cf98>"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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xKneDd8nnl+/A6g8hb4d36Kd1Hzh1ADQ9R71/iUiZiHohMLOGwPPACUAIGOmc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\nTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1296dffd0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(radii, growth_psf, label='PSF')\n",
    "plt.plot(radii, growth_psfobs, label='Observed PSF')\n",
    "plt.xlabel('Radius [arcsec]')\n",
    "plt.ylabel('Encircled flux')\n",
    "plt.legend()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This strongly rising shape of the observed PSF is a sure sign of an non zero background. Let's determine it. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0x1296c6c50>"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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FjAJIS0ur1Ir6pTWlW35RpV4rIpIsggiC9UCHUvfbAxvLLuTuE4AJAJmZmf8V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\nAhGRJKcgEBFJcgoCEZEk9/8BGBd4JKX73oUAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1295dacf8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(nbpix_psfobs, growth_psfobs)\n",
    "plt.xlabel('Number of pixels')\n",
    "plt.ylabel('Encircled flux')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "When plotted as a function of the intergated area, there is a clear linear relation, that we will fit:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "idx, = np.where(radii > 50)\n",
    "p = np.polyfit(nbpix_psfobs[idx], growth_psfobs[idx], 1)\n",
    "bkg = p[0]/resol**2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# Correct PSF and curve of growth\n",
    "psfcor = psfobs-bkg\n",
    "growth_psfcor = growth_psfobs - bkg*nbpix_psfobs*resol**2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x12de25588>"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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9kLtf12Hf4cDtQDnByLjLwn13pCvepNovSQV3Sa2rquOY0kG6Q0pEsk46Wxgz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\nrkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x12dd8c080>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(radii, growth_psf, label='PSF')\n",
    "plt.plot(radii, growth_psfcor, label='Observed PSF')\n",
    "plt.xlabel('Radius [arcsec]')\n",
    "plt.ylabel('Encircled flux')\n",
    "plt.legend()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<a id='direct_ratio'></a> Let's have a look at the ratio of the two:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0x12dddea90>"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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EcYJUFkREksWwCSOoUouZvX/kwhlb+vudg+3dlOSpS0pEEl+kFsY7zCwN+MJI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\nxQLTGZNdnwAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x132306e10>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(radii[1:], growth_psfcor[1:]/growth_psf[1:])\n",
    "plt.xlabel('Radius [arcsec]')\n",
    "plt.ylabel('Ratio of encircled flux')\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Due to the different resolution, the ratio is not constant. Let's note the calibration $C(r)$. Let us assume that our observed PSF encirled energy is of the form:\n",
    "\n",
    "$E(r) = \\alpha C(r \\times \\beta)$\n",
    "\n",
    "Where $\\beta$ is the fattening of the PSF. If we differentiate as a function of $r$:\n",
    "\n",
    "$E'(r) = \\alpha \\beta C'(r \\times \\beta)$\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# compute the derivatives\n",
    "deriv_growth_psf = (growth_psf[2:]-growth_psf[0:-2])/(radii[2:]-radii[0:-2])\n",
    "deriv_growth_psfcor  = (growth_psfcor[2:]-growth_psfcor[0:-2])/(radii[2:]-radii[0:-2])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(0, 60)"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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/Y7v3KqXUCAwbHETEDTwEXAMsAm4VkUUDLrsbaDTGzAEeBL7t995hY8xy5/VJ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\nc2LZjTAAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x12dde97f0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(radii[1:-1], deriv_growth_psf)\n",
    "plt.plot(radii[1:-1], deriv_growth_psfcor)\n",
    "plt.xlim([0,60])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Compared with the growth curve plot, the derivative show clear maxima and minima that are out of phase. Findind the positions of the these will tell us if our assumption of homothetical variation is correct."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[  0.           6.18161082  17.48546882  23.79928199  32.07353102\n",
      "  38.40607579  46.76238796] [  0.           6.52203326  18.7589197   24.07489413  32.78748297\n",
      "  38.5386345   47.21468159]\n"
     ]
    },
    {
     "data": {
      "image/png": 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GPC0ieUA1gaQBMA+4S0S8gA+4zhhTbS37PvB3IBJ4y3oppZQKkaCeqWyMWQYs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\nC6xi3+h9YIz5mTEmyxiTQ+DZ7B8YYy4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      "text/plain": [
       "<matplotlib.figure.Figure at 0x1324932e8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Find the local minima and maxima of the two curves.\n",
    "# To find a local extremum, we will fit the portion of curve with a degree 3 polynomial, \n",
    "# extract the roots of its derivative and only retain the one that are between the bounds.\n",
    "# This is what the following function does.\n",
    "def local_max(xvalues, yvalues, lower_bound, upper_bound, check_plot=False):\n",
    "    idx,=np.where((xvalues > lower_bound) & (xvalues < upper_bound))\n",
    "    p = np.polyfit(xvalues[idx], yvalues[idx], 3)\n",
    "    delta = (2.*p[1])**2 - 4.*3.*p[0]*p[2]\n",
    "    r1 = (-2*p[1]+np.sqrt(delta))/(2*3*p[0])\n",
    "    r2 = (-2*p[1]-np.sqrt(delta))/(2*3*p[0])\n",
    "    result = r1 if ((r1 > lower_bound) and (r1 < upper_bound)) else r2\n",
    "    if check_plot:\n",
    "        plt.plot(xvalues[idx], yvalues[idx])\n",
    "        plt.plot(xvalues[idx], p[0]*xvalues[idx]**3+p[1]*xvalues[idx]**2+\n",
    "                 p[2]*xvalues[idx]+p[3], '--')\n",
    "        plt.plot(np.array([result, result]), np.array([np.min(yvalues), np.max(yvalues)]), '-')\n",
    "    return result\n",
    "    \n",
    "    \n",
    "max_dpsf_1 = local_max(radii[1:-1], deriv_growth_psf, 3, 10, check_plot=True)\n",
    "max_dpsfcor_1 = local_max(radii[1:-1], deriv_growth_psfcor, 3, 10, check_plot=True)\n",
    "\n",
    "max_dpsf_2 = local_max(radii[1:-1], deriv_growth_psf, 14, 21, check_plot=True)\n",
    "max_dpsfcor_2 = local_max(radii[1:-1], deriv_growth_psfcor, 14, 21, check_plot=True)\n",
    "\n",
    "max_dpsf_3 = local_max(radii[1:-1], deriv_growth_psf, 21, 28, check_plot=True)\n",
    "max_dpsfcor_3 = local_max(radii[1:-1], deriv_growth_psfcor, 21, 28, check_plot=True)\n",
    "\n",
    "max_dpsf_4 = local_max(radii[1:-1], deriv_growth_psf, 28, 35, check_plot=True)\n",
    "max_dpsfcor_4 = local_max(radii[1:-1], deriv_growth_psfcor, 28, 35, check_plot=True)\n",
    "\n",
    "max_dpsf_5 = local_max(radii[1:-1], deriv_growth_psf, 35, 45, check_plot=True)\n",
    "max_dpsfcor_5 = local_max(radii[1:-1], deriv_growth_psfcor, 35, 45, check_plot=True)\n",
    "\n",
    "max_dpsf_6 = local_max(radii[1:-1], deriv_growth_psf, 40, 50, check_plot=True)\n",
    "max_dpsfcor_6 = local_max(radii[1:-1], deriv_growth_psfcor, 40, 50, check_plot=True)\n",
    "\n",
    "plt.xlabel('Radius [arcsec]')\n",
    "\n",
    "# Lets pack all of them, adding the r=0 point. \n",
    "max_dpsf = np.array([0, max_dpsf_1, max_dpsf_2, max_dpsf_3, max_dpsf_4, max_dpsf_5, max_dpsf_6])\n",
    "max_dpsfcor = np.array([0, max_dpsfcor_1, max_dpsfcor_2, max_dpsfcor_3, max_dpsfcor_4, \n",
    "                        max_dpsfcor_5, max_dpsfcor_6])\n",
    "\n",
    "print(max_dpsf,max_dpsfcor)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "From the plot, we can deduce that our homothetical assumption is not perfect: the spacing increases for the first three (don't forget the point at 0, 0, not shown), is very small for the 4th and 6th, and gets narrower for the 5th and 7th...\n",
    "Let's plot the situation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[ 1.07402112 -0.04599678]\n",
      "1.05507018262\n",
      "1.07282909576\n"
     ]
    },
    {
     "data": {
      "image/png": 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o6joRsRvKTHBTheU/wC+POOMGdHsczn4QSpQ8sUpKahqjZm/mtWlrCRH4X5+W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\nrkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x12dded7b8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(max_dpsf, max_dpsfcor, 'o-')\n",
    "p = np.polyfit(max_dpsf[0:3], max_dpsfcor[0:3], 1)\n",
    "plt.plot(max_dpsf, p[0]*max_dpsf+p[1])\n",
    "plt.xlabel('extremum position of theoretical psf [arcsec]')\n",
    "plt.ylabel('extremum position of observed blurred psf [arcsec]')\n",
    "\n",
    "\n",
    "print(p)\n",
    "print((max_dpsfcor[1]-max_dpsfcor[0])/(max_dpsf[1]-max_dpsf[0]))\n",
    "print((max_dpsfcor[2]-max_dpsfcor[0])/(max_dpsf[2]-max_dpsf[0]))\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0x1325f4e48>"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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2+3cYY8y+WMf5Nli//jPme4KcUTi23fcdCjtc+8+5vLt0K78/93BLDsaYpLEE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\ncKQAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x12ddc16d8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Lets use the data before 20\", corresponding to the central core\n",
    "beta = (max_dpsfcor[2]-max_dpsfcor[0])/(max_dpsf[2]-max_dpsf[0])\n",
    "\n",
    "# lets interpolate at the scaled radius\n",
    "tckpsfcor = interpolate.splrep(radii, growth_psfcor, s=0)\n",
    "interp_growth_psfcor = interpolate.splev(radii*beta, tckpsfcor, der=0)\n",
    "\n",
    "# check interpolation\n",
    "plt.plot(radii*beta, growth_psf)\n",
    "plt.plot(radii, growth_psfcor)\n",
    "plt.plot(radii*beta, interp_growth_psfcor)\n",
    "plt.xlim([0,60])\n",
    "plt.xlabel('radius [arcsec]')\n",
    "plt.ylabel('Encircled flux')\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let us check the ratio, using the psf with a corrected radius"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "alpha = 2.005\n"
     ]
    },
    {
     "data": {
      "image/png": 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JrXHczDoCxwSb09096gWZzSwT+AC41d1frHLsVeBPVRLHL4BTgPQqiaPY3f+3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\niIhITJQ4REQkJv8fYSyUO2glbEQAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1326ed208>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(radii[1:]*beta, interp_growth_psfcor[1:]/growth_psf[1:])\n",
    "plt.xlabel('radius [arcsec]')\n",
    "plt.ylabel('Ratio of encircled flux')\n",
    "plt.xlim([0,60])\n",
    "idx, = np.where(((radii*p[0]) > 0) & ((radii*p[0]) < 60))\n",
    "scale_factor = np.median(interp_growth_psfcor[idx]/growth_psf[idx])\n",
    "print(\"alpha = {:.3f}\".format(scale_factor))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We now have a much better looking ratio [compared with the cell where we computed the direct ratio](#the_ratio), and we have a decent determination of the psf scaling. The normalized PSF to use for our observations is then:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "psf_obs_norm = psfcor / scale_factor"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\\int \\int psf_obs_norm dx dy = 0.9664739715532878\n"
     ]
    }
   ],
   "source": [
    "print('\\int \\int psf_obs_norm dx dy = {}'.format(np.sum(psf_obs_norm)*resol**2))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Indeed, let's look at the encircled energy in the core of our psf:\n",
    "In this example, we have used the derivative of the scale factor"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "central core for observation: 0.8526738059811085\n",
      "central core for theoretical: 0.8526789463354869\n"
     ]
    }
   ],
   "source": [
    "idj, idi = np.where(r<max_dpsfcor_2)\n",
    "print('central core for observation: {}'.format(np.sum(psf_obs_norm[idj, idi])*resol**2))\n",
    "idj, idi = np.where(r<max_dpsf_2)\n",
    "print('central core for theoretical: {}'.format(np.sum(psf[idj, idi])*resol**2))\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The two agree extremely well. \n",
    "\n",
    "Unfortunately, with real data, it is not always possible as we will see to use the derivative of the curve of growth to derive the factor beta of PSF fattening. For real observation, one can use a brute force approach to try all the reasonable couples alpha, beta and try to match the theoretical psf to the observed one. This is how we will proceed next on real data."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 2) Real data: PACS observations\n",
    "\n",
    "We will look at a real stack of point sources in the PACS ELAIS-N1 observations, and try to find its normalization factor. \n",
    "\n",
    "Let's load the stacked PSF:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 121,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.image.AxesImage at 0x13b149ba8>"
      ]
     },
     "execution_count": 121,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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/n1UxVSpzVAaNpJJ8CptXdPoCNCKo3fL3GeOP4kcVNXlVG1HL721lSY38aq/R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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11ad14080>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "stackhd = fits.open('../data/ELAIS-N1/PACS_PSF/ELAIS-N1-160um_psf_hires.fits')\n",
    "psf = stackhd[1].data\n",
    "hd = stackhd[1].header\n",
    "plt.imshow(psf)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Set the resolution of the psf. Because the map is in units of Jy/pixel, this turns out to be:\n",
    "* =1 if psf at same resolution of map\n",
    "* otherwise, should be in factor of map pixel size"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 122,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "resol= np.abs(stackhd[1].header['CDELT1'])/np.abs(stackhd[0].header['CDELT1'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 123,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.20000000000000001"
      ]
     },
     "execution_count": 123,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "resol"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now let's build the growthcurve for our PSF."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 124,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# find the brightest pixel, it will be our center.\n",
    "jmax, imax = np.unravel_index(np.argmax(psf), psf.shape)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 125,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# build the array of coordinates\n",
    "x = np.arange(hd['NAXIS1'])\n",
    "y = np.arange(hd['NAXIS2'])\n",
    "xv, yv = np.meshgrid(x, y, sparse=False, indexing='xy')\n",
    "xp = (xv-imax)*np.abs(hd['CDELT1'])*3600.\n",
    "yp = (yv-jmax)*np.abs(hd['CDELT2'])*3600.\n",
    "r = np.sqrt(xp**2 + yp**2)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 126,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# build the growth curve\n",
    "radii = np.unique(r)\n",
    "encircled_flux = np.zeros(radii.shape)\n",
    "nbpix = np.zeros(radii.shape)\n",
    "for i, radius in enumerate(radii):\n",
    "    idj, idi = np.where(r <= radius)\n",
    "    nbpix[i] =len(idi)\n",
    "    encircled_flux[i] = np.sum(psf[idj, idi])*resol**2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 127,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-0.6000000145200001"
      ]
     },
     "execution_count": 127,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "hd['CDELT1']*3600."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 128,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0x12b9833c8>"
      ]
     },
     "execution_count": 128,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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rhPo6kojfKLXU27Rpw1dffUXHjh0JDg72vN64sR6uICK/z6HjeUz/YD2GAZMn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\nqYuIiPiJ/w8ub/CoMYcOpwAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x12ccedcc0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(radii, encircled_flux)\n",
    "plt.xlabel('Radius [arcsec]')\n",
    "plt.ylabel('Encircled flux')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Looking at the shape of the encircled flux, it looks like the background level of our PSF is not zero. Let's check"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 129,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "8.81614e-05\n"
     ]
    }
   ],
   "source": [
    "# This is clearly. \n",
    "print(np.median(psf[0:5,:]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 130,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0x12d3aa5f8>"
      ]
     },
     "execution_count": 130,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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HTk4Ob731Flu3bmXs2LFFUZ+IFIG8fBcLVqWy/Ou9+mS7SAlW6G/shg0b+Oyz\nzwCoVq0a77//Pv369VOoi/iI1IOX1mw/mmmnRuWyjBscpUVkREqoQkPd6XSSm5tb8EG5/Px8jxcl\nIp6X63Dy8apUPkvYB0DvTvUZ0bMpgerORUqsQn97Y2Nj6d+/P126dAEgISGBYcOGebwwEfGcHftP\nMzMuieOnsqhZJZjxMVE0r1/4hZpEpHgrNNR/vuzq1q1bsVgsvPHGGzRr1qwoahOROyw3z8l/V+5i\nxcb9APTt3IBhPZoQGKDuXMQXFPqbPGzYMFauXElERERR1CMiHrJ93ylmxSVx4nQ2tataGR8TRdN6\nlbxdlojcQYWGepMmTVi+fDkREREEBgYWPF6rVi2PFiYid0ZOnpMP/7eT/206gJ8J+t/XkKE9mlDG\n3+zt0kTkDis01JOTk0lOTr7iMZPJxLp16zxWlIjcGcl7Mpm1yMbJM9ncVf1Sd944TN25iK8qNNTX\nr19fFHWIyB2UnZvP+yt2suq7g/iZYFDXRsR2a0yAunMRn3bNUJ89ezZjx45l8uTJvzp++YpzIlJ8\nJKWdZPZiG5lncwirEcL42Cga3VXR22WJSBG4Zqg3b94cgDZt2hRZMSJy67Jy8nkvfgdrthzCz89E\nzG/DiekWjr9F3blIaeF3rYGfv5ferVs3srOz6devH+3bt+fw4cP06NGjyAoUkcJt3ZXBmDfWs2bL\nIerWLMeb4+/lkZ5NFegipcw1Q/1nzz77LCdPngQuXX7V7Xbzpz/9yeOFiUjh7Dn5zFyYxF/e3czZ\ni3kM7d6Yf0zoTMPQCt4uTUS8oNAPyh07doy3334bAKvVyjPPPMPDDz/s8cJE5Pq+33mCuYuTOXMh\nl/q1yzMhNop6tcp7uywR8aJCQ91kMpGWlkbjxo0B2LdvHxaLVp8S8ZaL2Q7+vXw7GxLTsZhNPNKj\nCQO6NMJiLvTAm4j4uELT+fnnn2fkyJFUr14dgLNnz/K3v/3N44WJyNU2pxznrSXJnL2YR8PQ8oyP\njaZuzXLeLktEiolCQ719+/Zs2LCB3bt3Y7FYqF+/PgEBAUVRm4j85Lw9j3eWbych6SgWsx8jHmxK\n//saYlZ3LiKXKTTUjx49ykcffcT58+cxDKPgcX1PXaRofLvtGPOWbuOcPY/wOhUYHxNFnRrqzkXk\naoWG+oQJE2jdujWtW7fGZDIVRU0iwqXu/O1l29iYfAx/ix+/79WMh+9toO5cRK6p0FB3Op08//zz\nRVGLiPyyEFUqAAAesklEQVRkY/JR5i3dxoUsB03CKjIuJoq7qod4uywRKeYKDfVWrVqxfv16Onbs\nqHPpIh529mIuby/bxrfbjhNg8WNUn+b07tQAs5+OkolI4QoN9VWrVvHRRx8VHHo3DAOTycSuXbs8\nXpxIaWEYBglJR/nXp9u5mO2gWb1KjI+JolZVq7dLE5ESpNBQ37hx4y1t2O12M2XKFNLS0ggICGDq\n1KmEhYVd8ZycnBx+//vf8+qrr9KgQQMA+vXrh9V66Q9ZaGioPpAnPu/MhVzeWpLMlh0nKBNg5vG+\nLejVoT5+6s5F5CZdM9QXLFjA0KFDAdizZw+NGjUqGHv11Vf585//fN0Nr127FofDQVxcHDabjenT\npzNv3ryC8e3bt/Pyyy+TkZFR8FheXh6GYTB//vxbfkMiJYVhGGxITOffy7djz8mnRYPKjBscRc0q\nwd4uTURKqGt+jHbx4sUFt3+51vvWrVsL3XBiYiKdOnUCIDIykpSUlCvGHQ4Hc+fOpX79+gWPpaam\nkpOTw8iRIxkxYgQ2m+3G3oVICXP6fA5/fW8L//zkR5wuN0/1j+DVpzoo0EXktlyzU7/8O+mX375R\ndru94DA6gNlsxul0Fiwx26pVq6vmBAYGMmrUKAYNGsTBgwd5/PHHWbVqlZalFZ9hGAbrfjjCu59t\nJyvXSUTDKowdHEmNygpzEbl9N5SWt/L9dKvVSlZWVsF9t9tdaDjXq1ePsLAwTCYT9erVo0KFCmRm\nZlKzZs2bfn2R4ibzbA5zl9hITD1JUBkzTw9sSY+2YVr/QUTumGsefr/dPzTR0dEkJCQAYLPZCA8P\nL3TOkiVLmD59OgAZGRnY7XaqVq16W3WIeJthGKzZcogxf19PYupJIsOrMufZLvRsV1eBLiJ31DVb\n5z179tC1a1fgUsD+fNswDDIzMwvdcLdu3di0aROxsbEYhsG0adOIj48nOzubmJiYX50zcOBAJk+e\nzJAhQzCZTEybNk2H3qVEO3k2mzmLbCTtzqRsoIWxgyPp1qaOwlxEPMJkXOOE+dGjR687sXbt2h4p\n6Gakp6fTtWtX1q1bR2hoqLfLESlgGAarNh/i/fgUcvJctGpSjdEDI6laMcjbpYlICVZY7l2zDS4O\noS1SEp04ncXsRTa27T1FcKCF8TFRdL3nLnXnIuJxOrYtcoe43QYrvz3AB//bSa7DxT3NqjN6YEsq\nl1d3LiJFQ6EucgccP5XFrEVJpOw7jTXIn4lDW3JfdKi6cxEpUgp1kdvgdhus2LSf/36xizyHi980\nr8HTA1tSqVygt0sTkVJIoS5yi45l2pkZl8TOA2cIKRvA2EGR3BtVW925iHiNQl3kJrncBvHf7Gf+\nFztxON20j6jJU/0jqBii7lxEvEuhLnIT0k9eZObCJFIPnaVccADPDI2gY0t9U0REigeFusgNcLkN\nPvt6Lx+tSiXf6aZjy1o81T+C8tYy3i5NRKSAQl2kEIdPXGBmXBK7D5+jgrUMfxgQQfuIWt4uS0Tk\nKgp1kWtwudws+2ovC1an4XS56RwVyhP97qZccIC3SxMR+VUKdZFfcej4BWbEJbH3yDkqhpTh6YEt\nadtCVwsUkeJNoS5yGafLzdL1e1j4ZRpOl0GX1nfx2MMtCCmr7lxEij+FushPDhw7z4yFSew/ep5K\n5QIZPaglbZrV8HZZIiI3TKEupV6+082SdbuJW7sbl9vgt/fUYdTDLbAG+Xu7NBGRm6JQl1JtX/o5\nZixM4uDxC1QpH8iYwZG0alLd22WJiNwShbqUSvlOF3Ff7mbx+j243QbdfxPGyN7NCVZ3LiIlmEJd\nSp09R84yc2ESh05cpGrFIMYOiiSqcTVvlyUictsU6lJqOPJdLPwyjaUb9uJ2G/RsV5ff9WpG2UB1\n5yLiGxTqUiqkHTrDzLgkjmTYqVapLOMGR9KyUVVvlyUickcp1MWn5eW7WLAqleVf78VtQK8O9Rjx\nUDOCyuhHX0R8j/6yic/adeBSd340006NymUZFxPF3Q2qeLssERGPUaiLz8l1OPl4VSqfJewDoE+n\n+gzv2ZRAdeci4uP0V058yo79p5kZl8TxU1nUqhLMuJgomtev7O2yRESKhEJdfEJunpP/rtzFio37\nAejbuQHDejQhMEA/4iJSeugvnpR42/edYlZcEidOZ1O7qpUJsVE0qVvJ22WJiBQ5hbqUWDl5Tj78\n307+t+kAfiYYcH9DhjzQhDL+Zm+XJiLiFQp1KZGSd2cya7GNk2eyuat6CONjImkcpu5cREo3hbqU\nKNm5+by/YiervjuIn5+JQV0bMaR7Y/wt6s5FRPw8tWG3281LL71ETEwMw4cP59ChQ1c9Jycnh9jY\nWPbt23fDc6T0+jHtJGP+voFV3x0krEYIb467lxEPNlOgi4j8xGOd+tq1a3E4HMTFxWGz2Zg+fTrz\n5s0rGN++fTsvv/wyGRkZNzxHSqesnHzei9/Bmi2HMPuZiOkWTsxvwxXmIiK/4LFQT0xMpFOnTgBE\nRkaSkpJyxbjD4WDu3Ln86U9/uuE5Uvps3ZXB3MU2Tp3PpV6tcoyPiaJBaAVvlyUiUix5LNTtdjtW\nq7Xgvtlsxul0YrFceslWrVrd9BwpPezZDt79PIV1PxzB7GdiaPfGDOwajr/FY2eMRERKPI+lpdVq\nJSsrq+C+2+0uNJxvZY74nu93nmDu4mTOXMilfu3yTIiNol6t8t4uS0Sk2PNY2xMdHU1CQgIANpuN\n8PBwj8wR33Ex28E/FiTy1/9s4UJWHo/0bMKb4+9VoIuI3CCPtcHdunVj06ZNxMbGYhgG06ZNIz4+\nnuzsbGJiYm54jpQO320/zrylyZy9mEfDuyowISaKsJrlvF2WiEiJYjIMw/B2EbcqPT2drl27sm7d\nOkJDQ71djtyC8/Y83lm+nYSko1jMfgx9oDH972uI2axz5yIiv1RY7umEtXjNpm3HeHvpNs7Z82hc\npyLjYiKpU0PduYjIrVKoS5E7b8/j7WXb2Jh8DH+LH7/v1ZyHOzfA7GfydmkiIiWaQl2KjGEYbEw+\nxtvLtnEhy0HTupUYFxNJaLUQb5cmIuITFOpSJM5ezGXe0m18t/04Af5mHnu4Bb061ld3LiJyBynU\nxaMMwyAh6Sj/+nQbF7PzaV6/MuMGR1KrqrXwySIiclMU6uIxZy7k8taSZLbsOEGZADNP9L2bhzrU\nw0/duYiIRyjU5Y4zDIMNien8e/l27Dn53N2gCmMHR1KzSrC3SxMR8WkKdbmjTp/PYc7iZLbuyiAw\nwMxT/SPo2a6uunMRkSKgUJc7wjAM1v1wmHc/SyEr10lEwyqMi4mieqWy3i5NRKTUUKjLbcs8m8Oc\nJTZ+TD1JUBkLowe25IG2YZhM6s5FRIqSQl1umWEYrNlymPfiU8jOdRIVXpUxgyOpVlHduYiINyjU\n5ZacPJPN7MU2bLszKRtoYdzgSH7bpo66cxERL1Koy00xDINVmw/xfnwKOXkuWjWpxphBkVSpEOTt\n0kRESj2FutywjDPZzIpLYtveUwQH+TMhNoIure9Sdy4iUkwo1KVQbrfBqs0HeT9+B7kOF/c0q87o\ngS2pXF7duYhIcaJQl+s6eSabWYuSSN5zqTt/ZkhL7m8Vqu5cRKQYUqjLr/rluXN15yIixZ9CXa5y\n8mw2sxdd+mR7cKCFCbFROncuIlICKNSlwKXvnR/iP5/vICfPSeum1RkzSN25iEhJoVAX4NKqcLMX\nJZH0U3c+PiaKrveoOxcRKUkU6qWcYRh8+f1h/vP5pVXh9L1zEZGSS6Feip06l8PsxZfWbNeqcCIi\nJZ9CvRQyDIO13x/m3Z+68+jGl7rzqhXVnYuIlGQK9VLm1Lkc5iy2kfjTFdXGDIqk+2/UnYuI+AKF\neilx6XrnR3j3s+1k5TqJDK/KWF1RTUTEpyjUS4HT53OYsziZrbsyfurOW9L9N7reuYiIr1Go+zDD\nMFi/9Qj//iyFrJx8Ihv91J1XUncuIuKLPBbqbrebKVOmkJaWRkBAAFOnTiUsLKxgfP369cydOxeL\nxcKAAQMYPHgwAP369cNqtQIQGhrKa6+95qkSfdrp8znMXZLMDzszCCpj5umBLenRVt25iIgv81io\nr127FofDQVxcHDabjenTpzNv3jwA8vPzee2111iyZAlBQUEMGTKELl26EBISgmEYzJ8/31Nl+TzD\nMNiQmM47y7eTlZNPy0ZVGDs4iurqzkVEfJ7HQj0xMZFOnToBEBkZSUpKSsHYvn37qFOnDuXLlweg\nVatW/PDDD9SqVYucnBxGjhyJ0+lk4sSJREZGeqpEn3PmQi5vLUlmy44TBAaYeXpABD3a1VV3LiJS\nSngs1O12e8FhdACz2YzT6cRisWC32wkJCSkYCw4Oxm63ExgYyKhRoxg0aBAHDx7k8ccfZ9WqVVgs\nOvVfmISkdOYt3YY9J5+IhlUYOziSGpWDvV2WiIgUIY+lpdVqJSsrq+C+2+0uCOdfjmVlZRESEkK9\nevUIC7t03rdevXpUqFCBzMxMatas6akyS7yL2Q7mLd3GN7ajlAkw81S/u+nZvh5+furORURKGz9P\nbTg6OpqEhAQAbDYb4eHhBWMNGjTg0KFDnDt3DofDwdatW4mKimLJkiVMnz4dgIyMDOx2O1WrVvVU\niSXe1l0ZjHljPd/YjtIkrCKz/ngfD3Wsr0AXESmlPNapd+vWjU2bNhEbG4thGEybNo34+Hiys7OJ\niYlh0qRJjBo1CsMwGDBgANWrV2fgwIFMnjyZIUOGYDKZmDZtmg69/4qcPCfvxe9g1XcHsZhNjHiw\nKf3vb4RZYS4iUqqZDMMwvF3ErUpPT6dr166sW7eO0NBQb5dTJHYeOM0/P/mRE6ezqVuzHBOHRlOv\nVnlvlyUiIkWgsNxTG1xC5DtdfLwqlWVf7QVgwP0NGdajCf4Ws5crExGR4kKhXgIcOHaefyz4kYPH\nL1CjclkmxEbTvH5lb5clIiLFjEK9GHO53Cz7ai8LVqfidBn0aFeXkb2bE1RG/2wiInI1pUMxdeyU\nnX8u+JHUQ2epVK4MYwdH0bppdW+XJSIixZhCvZgxDIOV3x3kvfgd5DlcdIqszR8GRBBSNsDbpYmI\nSDGnUC9GTp/PYVacjR/TTmIN8mfcI5HcG1U6PtUvIiK3T6FeDBiGQULSUeYt20ZWTj7RTaoxbnAk\nlcsHebs0EREpQRTqXnYhy8G8pclsTD5GmQBdIlVERG6dQt2Ltu7KYFZcEmcv5tG0biUmDImiVhVr\n4RNFRER+hULdC7Jz83kvfgerNx/CYjbx6EPN6HdfQy3zKiIit0WhXsR27L+0zGvGGS3zKiIid5ZC\nvYg48i8t8/rp13sxAQO7NGLoA421zKuIiNwxCvUisP/oef6xIJFDJy5Ss3IwE4ZE0ayelnkVEZE7\nS6HuQS6Xm6Ub9vLJmkvLvPZsV5ffa5lXERHxEKWLhxzLtPOPT34k7adlXsfFRNGqiZZ5FRERz1Go\n32GGYfDFtwd5f8WlZV7vjarNU/21zKuIiHieQv0OOnUuh5lxSdh2Z2IN8mf8I1F0iqrt7bJERKSU\nUKjfAYZh8PWP6bz96XaycvJp1aQaY7XMq4iIFDGF+m06b89j3tJtbNp2jMAAM6MHtuQBLfMqIiJe\noFC/Dd/vPMHsRTbO/bTM6zNDoqlZJdjbZYmISCmlUL8F2bn5/OfzHazZcgiL2Y/fPdSMvlrmVURE\nvEyhfpNS9p3inwuTOKllXkVEpJhRqN8gR76Lj1alsvynZV4HdW3EkO5a5lVERIoPhfoN2Jd+jn98\n8iOHf1rm9Zkh0TStV8nbZYmIiFxBoX4dbrfBsq/28tHKXbjcBj3b12Vkr+YEaplXEREphpRO13D2\nYi7/WPAjtt2ZVCpXhvEx0UQ3qebtskRERK5Jof4rDp24wJR/b+bUuRxaN63OhNgoylvLeLssERGR\n6/JYqLvdbqZMmUJaWhoBAQFMnTqVsLCwgvH169czd+5cLBYLAwYMYPDgwYXOKQrHTtmZPHcTF7Md\nDO/ZlEFdG2khGRERKRE8Fupr167F4XAQFxeHzWZj+vTpzJs3D4D8/Hxee+01lixZQlBQEEOGDKFL\nly78+OOP15xTFPKdLqa+9z0Xsx08PSCCnu3rFdlri4iI3C6PhXpiYiKdOnUCIDIykpSUlIKxffv2\nUadOHcqXv/T97latWvHDDz9gs9muOacofJawnyMZF+nZrq4CXUREShw/T23YbrdjtVoL7pvNZpxO\nZ8FYSEhIwVhwcDB2u/26c4pCxplsalQuy6MPNSuy1xQREblTPNapW61WsrKyCu673W4sFsuvjmVl\nZRESEnLdOUXh6QERuN0GZrPH/q8jIiLiMR5Lr+joaBISEgCw2WyEh4cXjDVo0IBDhw5x7tw5HA4H\nW7duJSoq6rpzioLJZFKgi4hIieWxNrhbt25s2rSJ2NhYDMNg2rRpxMfHk52dTUxMDJMmTWLUqFEY\nhsGAAQOoXr36r84RERGRG2MyDMPwdhG3Kj09na5du7Ju3TpCQ0O9XY6IiIhHFZZ7OtYsIiLiIxTq\nIiIiPkKhLiIi4iMU6iIiIj5CoS4iIuIjFOoiIiI+QqEuIiLiIxTqIiIiPqLoFlb3AJfLBcCJEye8\nXImIiIjn/Zx3P+ffL5XoUM/MzARg2LBhXq5ERESk6GRmZhIWFnbV4yV6mdjc3FxSUlKoWrUqZrPZ\n2+WIiIh4lMvlIjMzkxYtWhAYGHjVeIkOdREREfk/+qCciIiIj1Coi4iI+AiFuoiIiI9QqIuIiPiI\nEv2VtjvJ7XYzZcoU0tLSCAgIYOrUqb/6dQFfkp+fzwsvvMDRo0dxOBz84Q9/oGHDhkyaNAmTyUSj\nRo14+eWX8fPzY9GiRSxcuBCLxcIf/vAH7r//fnJzc3nuuec4ffo0wcHBvP7661SqVAmbzcarr76K\n2WymY8eOjBkzxttv9bacPn2a/v37895772GxWLR/LvOvf/2L9evXk5+fz5AhQ2jTpo32z2Xy8/OZ\nNGkSR48exc/Pj7/+9a/6GfpJcnIyf//735k/fz6HDh3y2D6ZM2cOX331FRaLhRdeeIGIiAgvv3MP\nM8QwDMNYvXq18fzzzxuGYRhJSUnGU0895eWKPG/JkiXG1KlTDcMwjLNnzxqdO3c2nnzySWPz5s2G\nYRjGiy++aKxZs8Y4efKk0atXLyMvL8+4cOFCwe333nvPmDVrlmEYhrFixQrjr3/9q2EYhtGnTx/j\n0KFDhtvtNh577DFjx44d3nmDd4DD4TCefvppo3v37sbevXu1fy6zefNm48knnzRcLpdht9uNWbNm\naf/8wpdffmmMGzfOMAzD2LhxozFmzBjtI8Mw3nnnHaNXr17GoEGDDMMwPLZPUlJSjOHDhxtut9s4\nevSo0b9/f++84SKkw+8/SUxMpFOnTgBERkaSkpLi5Yo8r0ePHowfPx4AwzAwm83s2LGDNm3aAHDv\nvffy7bffsm3bNqKioggICCAkJIQ6deqQmpp6xT679957+e6777Db7TgcDurUqYPJZKJjx458++23\nXnuPt+v1118nNjaWatWqAWj/XGbjxo2Eh4czevRonnrqKe677z7tn1+oV68eLpcLt9uN3W7HYrFo\nHwF16tRh9uzZBfc9tU8SExPp2LEjJpOJWrVq4XK5OHPmjFfec1FRqP/EbrdjtVoL7pvNZpxOpxcr\n8rzg4GCsVit2u51x48YxYcIEDMPAZDIVjF+8eBG73U5ISMgV8+x2+xWPX/7cy/fjz4+XRMuWLaNS\npUoFf0AA7Z/LnD17lpSUFGbOnMlf/vIXnn32We2fXyhbtixHjx6lZ8+evPjiiwwfPlz7CHjggQew\nWP7v7K+n9okv7KubpXPqP7FarWRlZRXcd7vdV/zQ+arjx48zevRohg4dSu/evXnjjTcKxrKysihX\nrtxV+yYrK4uQkJArHr/ec8uVK1d0b+gOWrp0KSaTie+++45du3bx/PPPX/G//NK+fypUqED9+vUJ\nCAigfv36lClT5orrMJT2/QPwwQcf0LFjR/74xz9y/PhxHn30UfLz8wvGtY8u8fP7v/7yTu4Tf3//\nX92GL1On/pPo6GgSEhIAsNlshIeHe7kizzt16hQjR47kueeeY+DAgQA0a9aMLVu2AJCQkEDr1q2J\niIggMTGRvLw8Ll68yL59+wgPDyc6Opqvv/664LmtWrXCarXi7+/P4cOHMQyDjRs30rp1a6+9x9vx\n8ccf89FHHzF//nyaNm3K66+/zr333qv985NWrVrxzTffYBgGGRkZ5OTk0K5dO+2fy5QrV64gRMqX\nL4/T6dTv2K/w1D6Jjo5m48aNuN1ujh07htvtplKlSt58qx6nZWJ/8vOn33fv3o1hGEybNo0GDRp4\nuyyPmjp1KitXrqR+/foFj/35z39m6tSp5OfnU79+faZOnYrZbGbRokXExcVhGAZPPvkkDzzwADk5\nOTz//PNkZmbi7+/Pm2++SdWqVbHZbEybNg2Xy0XHjh155plnvPgu74zhw4czZcoU/Pz8ePHFF7V/\nfvK3v/2NLVu2YBgGzzzzDKGhodo/l8nKyuKFF14gMzOT/Px8RowYQYsWLbSPgPT0dCZOnMiiRYs4\ncOCAx/bJ7NmzSUhIwO12M3ny5BL/H6DCKNRFRER8hA6/i4iI+AiFuoiIiI9QqIuIiPgIhbqIiIiP\nUKiLiIj4CIW6SDGUnp5O48aN2bRp0xWPd+nShfT09Nve/p3azvUcO3aMHj160L9/f+x2e6HPX7du\nHTNnzrzp19myZQvDhw+/lRJFfI5CXaSY8vf358UXX7yhQCyOvv/+e5o3b86yZcuuWKrzWrp27Vpw\nLQIRuTUKdZFiqlq1arRv357XX3/9qrFfdqeTJk1i2bJlpKen8/DDDzNmzBi6d+/OxIkTWbhwITEx\nMfTo0YN9+/YVzJkzZw59+/YlJiaG1NRU4NIqg08//TT9+/dnwIABBRcKmT17NqNGjeLBBx/k448/\nvqKWAwcOMHz4cHr37k1MTAzbtm1j165dzJgxg2+++YaXXnrpiufPnj2bP/7xjwwaNIhu3brx7rvv\nApfW2p80aRLHjx+nXbt27Nu3D4fDQe/evfnqq69wuVy89tpr9OvXjz59+vDBBx9ctV/ef/99+vTp\nQ9++fa96XZHSwPcXNxcpwSZNmkTv3r3ZtGkTHTp0uKE5aWlpvPbaazRp0oQHHniA2rVrExcXx5w5\nc4iLi+OFF14AICwsjOnTp/P1118zadIkli9fzquvvsqAAQPo2rUrJ0+eZOjQoSxfvhwAh8PBF198\ncdXrPffcczzxxBN0794dm83G+PHjWb16NePGjeP777/nlVdeuWrO7t27WbhwIW63m/79+9OuXbuC\nsZo1a/Lss88yZcoUoqOjiYqK4r777uOTTz4B4NNPP8XhcDBq1ChatGhRMM/pdPKvf/2Lb775BrPZ\nzF/+8hcyMjKoXr36je9wkRJOoS5SjFmtVv7617/y4osv8vnnn9/QnCpVqtCsWTMAatSoURCYtWrV\nuuI8+qBBgwDo3Lkzzz33HBcuXODbb79l//79zJo1C7gUlEeOHAEgIiLiqtfKysri8OHDdO/eHbh0\n2eLy5cuzf//+69bYq1cvgoODgUvn9zdv3kzFihULxgcMGMDKlSuJj49nxYoVAAUX1tm8eTMA2dnZ\npKWl0bBhQwAsFgtRUVEMHDiQrl27MmzYMAW6lDoKdZFirmPHjlcdhjeZTFy+wvPlV/4KCAi4Yr7Z\nbP7V7f7ycX9/f9xuNx9++CEVKlQAICMjgypVqrB27VoCAwOv2oZhGPxypWnDMHC5XNd9T5e/ttvt\nvqqWvLw8Tpw4gcvl4sSJE9SvXx+Xy8Vzzz1X8B+IM2fOULZsWZKTkwvmvfXWW9hsNhISEnjsscf4\n+9//XnCdbpHSQOfURUqASZMmsXHjRk6ePAlAxYoVOXLkCHl5eZw7d47ExMSb3mZ8fDwAX375JfXr\n1ycoKIi2bduyYMECAPbu3UufPn3Iycm55jasVit33XUXa9asAS5d4fDUqVM0atTouq+9du1aHA4H\n58+fZ8OGDXTs2PGK8RkzZtC2bVsmT57MCy+8gNvtpm3btixatIj8/HyysrIYOnToFYF+5swZevbs\nSXh4OOPHj6dDhw6kpaXd9H4RKcnUqYuUAD8fhh81ahQAjRo1onPnzjz00EPUrl2bVq1a3fQ2Dx48\nyMMPP0xwcDDTp08H4P/9v//HSy+9RO/evYFLV2Er7JPrb7zxBlOmTGH27Nn4+/sze/bsq44W/FKZ\nMmUYOnQodrudJ598koYNG7Jt2zYAkpKSWL16NZ9//jlWq5VPP/2U//znP/zud7/j0KFD9OvXD6fT\nSf/+/fnNb35TcMnOSpUqERsby8CBAwkKCqJmzZr069fvpveLSEmmq7SJSJGaPXs2AGPHjvVyJSK+\nR4ffRUREfIQ6dRERER+hTl1ERMRHKNRFRER8hEJdRETERyjURUREfIRCXURExEco1EX+/0bBKBgF\no2CYAABJ7hQ51InoxgAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11b722a90>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(nbpix, encircled_flux)\n",
    "plt.xlabel('Number of pixels')\n",
    "plt.ylabel('Encircled flux')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 131,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Lets do a linear fit to the outer part of the curve to determine the backgound\n",
    "p = np.polyfit(nbpix[1000:], encircled_flux[1000:], 1)\n",
    "bkg = p[0]/resol**2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 132,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "9425.0"
      ]
     },
     "execution_count": 132,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "nbpix[1000]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 133,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "8.46783062542e-05\n"
     ]
    }
   ],
   "source": [
    "print(bkg)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 134,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# Lets correct the psf and encircled flux\n",
    "psf = psf - bkg\n",
    "encircled_flux = encircled_flux - bkg * nbpix*resol**2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 135,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0x11b1732b0>"
      ]
     },
     "execution_count": 135,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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Dt/UnPNRqciIREWmMaiz7Z599Fqgue8MwTlpmsVh47bXXAptM+Oq7o5Q7XVw3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\nSJBT2YuIiAQ5lb2IiEiQ+/9FautgHiPFawAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11b01f9b0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(radii, encircled_flux)\n",
    "plt.xlabel('Radius [arcsec]')\n",
    "plt.ylabel('Encircled flux')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Our PSF does now behaves correctly.\n",
    "\n",
    "Now let us compare our growth curve with the encircled energy curve provided by the instrument team. We use the standard growth curve for 160 µm PACS, taken with 20\"/s scan speed. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 136,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "f = open('../data/PACS/EEF_red_20.txt', 'r')\n",
    "lines = f.readlines()\n",
    "f.close()\n",
    "radiuseff = np.zeros(len(lines)-3)\n",
    "valeff = np.zeros(len(lines)-3)\n",
    "i = 0\n",
    "for line in lines:\n",
    "    if line[0] != '#':\n",
    "        bits = line.split()\n",
    "        radiuseff[i] = float(bits[0])\n",
    "        valeff[i] = float(bits[1])\n",
    "        i = i+1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 137,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x12c9a6518>"
      ]
     },
     "execution_count": 137,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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QysZdRWz4pqj90TVLkI4FU5KZOTaBMUOi/d7Fa0bZfv667e84PS5uHLdIwl0I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\nJAD9H3Mavqx93Yr+AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11b0ad4a8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(radiuseff, valeff, label='Calibration')\n",
    "plt.plot(radii, encircled_flux/np.max(encircled_flux), label='Our PSF')\n",
    "plt.xlim([0, 100])\n",
    "plt.xlabel('Radius [arcsec]')\n",
    "plt.ylabel('Encircled flux')\n",
    "plt.legend()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We will work below 30\" where our PSF is well behaved"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 138,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x12c368f98>"
      ]
     },
     "execution_count": 138,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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OITLzajAa4OJZSdxw8RhCAhUoZ8tis5BVncPO0v3k1uZT1lKF/fiiL3B8f/Gw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\nRETEQ/wfEBZ8cdt7vHUAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x12d60c438>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(radiuseff, valeff, label='Calibration')\n",
    "plt.plot(radii, encircled_flux/np.max(encircled_flux), label='Our PSF')\n",
    "plt.xlim([0, 30])\n",
    "plt.xlabel('Radius [arcsec]')\n",
    "plt.ylabel('Encircled flux')\n",
    "plt.legend()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We see that while the calibration curve still rises beyond 30\", our PSF has reached a plateau. Let's note the calibration $C(r)$. Our PSF encirled energy is of the form:\n",
    "\n",
    "$E(r) = \\alpha C(r \\times \\beta)$\n",
    "\n",
    "Where $\\beta$ is the fattening of the PSF.\n",
    "\n",
    "We could take the derivative, but this too noisy. Instead we do a brute force approach"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 139,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x11e581e10>"
      ]
     },
     "execution_count": 139,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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OITLzajAa4OJZSdxw8RhCAhUoZ8tis5BVncPO0v3k1uZT1lKF/fiiL3B8f/Gw\nFC4dvZApMePx0mYoIqdNoS4CNLV28fx7h1m3qxiHA6aMieSmy9JJigl0dWlD1ufXxcubK9lQuJUd\nJfvosPaMUPcxeTMyNJnE4DiSguJIDolnZGiyRqmLnCWFugxrdruDf+8s5rl3D9HaYSEpOoCbrhjP\nlNGRri5tSHE4HNS215Ndk09ObT75DUWUNlXQZevufYzBYGBx2gJmxmcwOiwVo9HowopF3JNCXYat\nwvImnl6zn+yiBny9Tdy8ZDyXzhmBh4fCpj8Oh4OmrhbKmivZV5HFO9n/7tPuYfQgPiCaCHM44X4h\nxAVEc+GI2dpfXMTJFOoy7HR0WXn14xz+tTkfu93B+ZNi+dF/jNdc85Ow2+2Ut1RR3VZHdVsta3PW\n0WHppPVLS6+avfy5atwljA5PZURwAiYPfbyIDDT9XyfDyt7sap58PZPaxg6iw/y45aqJTB0T5eqy\nBpX27g4qW6upaK2mrLmK93M39M4P/6JpcZOID4wmPjCGkaFJxAZGu6BaEfmifkO9qqqKqKi+H3oH\nDhxg4sSJTitK5Fzr7LLy7LuH+GDrMUweBpZdlMbVF6XhPcw3W2nubGFn2X4O1+RR1VpDZWsNLV2t\nfR5jwEC0OYL5I+YQ4R9GpH8YKaFJmicuMgj1G+rXXHMNd999N9/+9rexWCz8+c9/5oMPPmDDhg3f\n+Dy73c4DDzxATk4OXl5ePPTQQyQlJfW2HzhwgBUrVuBwOIiIiODxxx/H21urc8m5d7iwjj+/uo+K\nujaSogP41fVTSYkbPiuQ2R126tsbqWitpqKlmsqWnl54fXsjJc0VWO1WADwMRiL9w0kNSSTaHEl0\nQASxAVEkBscR6hvs4nchIqei31B/4YUXuOeee/joo48oKChgxowZvPPOO/0eeN26dXR3d7N69Woy\nMzNZsWIFK1euBHoG2dx333088cQTJCUl8frrr1NWVkZKSsrZvyOR4yxWGy9/mM1bm47iAJbOH8kN\nl4zB0+TePczmrlaONZSwoXArxY1lVLXVYrFZvvI4b5M3YX4hXJg8i4nRY0kJSdSUMpEhrt9Qj4mJ\nYcaMGaxZswYPDw9mzZqF2Wzu98B79uxh7ty5AGRkZJCVldXbVlhYSHBwMM899xx5eXnMmzdPgS7n\nVElVC4+9uJtjFc3EhPnzn9dNZtyIMFeXdc5YbVaya/M5UpNHVWst1W21VLfV0dDR1GejE+jZOzw1\nNInogEiQ4EOuAAAgAElEQVRizJHEBPT8BHj3//+xiAwt/Yb65ZdfzpQpU3j//fepqanhnnvu4e23\n3+avf/3rNz6vtbW1T/h7eHhgtVoxmUw0NDSwb98+7r//fhITE7nlllsYP348s2fPPvt3JMPe1gPl\n/HnVPjq6rFwyO5mbLk/H13tojgm12CzUtNdT3VpLVWstVW21VLZUc6Qmj7YvDF4zGAyE+YYwMjQJ\nD6MHkeZwxoSnMiVmAqF+OnUuMlz0+0l31113sWDBAgACAgJ45ZVXePbZZ/s9sNlspq3txJQXu92O\nydTzcsHBwSQlJZGamgrA3LlzycrKUqjLWbHZ7Lz4wRHe2HgUby8P7vzuVC6YHO/qsk6LxWbhYFU2\nW4v3cLgmj7r2hq/0vAECvPz5VuoFTIkdT2xgNOF+oRq4JiL9h3pzczNvv/12n/vCw8P7PfCUKVPY\nuHEjixcvJjMzk7S0tN62hIQE2traKCoqIikpid27d/Od73znDMoX6dHY0sXjL+3mwNFaYsP9uecH\nM0iKHrxLvDZ1NpNTW0Btez0lTRVk1x6l09pFfUcjDkdPiHsaTYyJSCXKHEGUfzhR5nAij/830DsA\ng8Hg4nchIoNNv6G+Y8eO3tsWi4U9e/Ywbdo0lixZ8o3PW7RoEVu2bOHaa6/F4XDwyCOPsHbtWtrb\n21m2bBkPP/wwd9xxBw6Hg8mTJ3PhhRee9ZuR4Sm3uIE/PLeT2qZOZqZHc/t1Uwblbmrt3R3sLMtk\nW8leDlQdwWa39WmP8A8jLSyFKP9wFqTMYXR4qgauichp6TfU//CHP/T5vbGxkdtvv73fAxuNRh58\n8ME+931+uh1g9uzZrFmz5lTrFPlam/aU8MRrmdhsdm5cPJal80dhNLq2B2u32zlaf4ys6hwqW2uo\naq2luLG0zzXwuMBoZsZPJik4jgAvf5JDEjB7+buwahFxB6c9esjPz4+ysjJn1CJyyux2By9/lM1r\n63Lx9zHxmx/MZMoY127C0tDRxLr8T1lX8BkNHU192qLMEaSEJjEqbARzk2YQp9XXRMQJ+g315cuX\n9167czgclJaWcsEFFzi9MJGT6eyy8v9W7WXrgQpiwvy574czSYgKGNAarDYr9Z1NFDeWcaQmj7y6\nQnLrCnv3B58SO4H5I2aTEBRLuF8oXh6D73KAiLiffkP9tttu671tMBgICQlh5MiRTi1K5GTqmjr4\n72d3kF/axPjUMH77vRkE+g/Mzl+fby+aU5vP85lv0NTZ3NtmMBhIDIpj/ojZzIqfomlkIuISJw31\nXbt2AXxlhG1DQwO7du1i+vTpzq1M5EsKy5t44O/bqG/uYtGMRH66dBKepoHZJnVbyR5e2PcGdR0N\nABgNRs5LnEa0OZL0yDRGhibh4+kzILWIiJzMSUP9iSeeAHpC/fMpNp8zGAy88MILzq1M5AuOFNbz\nX/+3jbZOKzddns6SealOndLVYemkrLmS3eX7ya0tJKs6B4AZ8RmMDE0mIzqd5JChNQdeRNzfSUM9\nOjqaxx9/nNdff52rr756IGsS6WNfTjUPP7cTi9XOr66fwvypCU55nW6bhayqHP6V/THZNUf7LPoS\nFxDN5WMWsSBljlNeW0TkXDhpqO/Zs4fXX3+dlStX4un51UE+/c1TFzkXth0s57EX92AwwD3fm87M\n8THn/DXsDjvv5Wzg3dx1fUatL0g5j5SQBM5LnI6/l985f10RkXPtpKH++9//no8++oi2trY+C9B8\nTqEuzrZhdzF/WZ2Jl8nI734wk0lpEU55nRcz3+S93PV4e3hxycgLGRc5itHhqYT4Dp/tWUXEPZw0\n1OfNm8e8efN0+l1c4oOthTz9xgHMvp48cPMsRieFnrNjt3d3sLloB+sLtlDZUk2XrZtwv1D+e+Gv\nCfMLOWevIyIy0Pqd0qZAl4H20fYinn7jAMFmb/77ljkkx5z9Gu52h52DVdlsL9nHZ8W76LJ24WH0\nIDEoFrOXP1eOvUSBLiJD3tDcj1Lc1vpdxTy1JpMAPy8eumUOSecg0Bs6mnhi+7Mcqs4FINwvlKvG\nXsKClDkE+QzeTV9ERE6XQl0GjU/2lvLE6n34+3ies0Bv7W7jd+seo6a9nikx47l8zCLGho/EaByY\n+e0iIgPppKH+29/+9huf+OWNXkTOxpb95fzPq3vx9Tbx3z+ZQ0rcmQ9SszvsbCrczsbCreTWFeBw\nOIg2R/CbuT/FaFCYi4j7Ommoz5gxA4CNGzfS1tbGFVdcgclk4v333ycgYGDX2Rb3tiOrgsdf2o23\npwf/9ePZjEw48yVWu63drPj0abKqczAajET4hTI1diLfnXSlAl1E3N5JQ/3KK68E4JVXXmH16tW9\npyu//e1vc8011wxMdeL2Dhyt4dEXd2MyGfn9j858lHtmxSF2lu1nf+VhatrqmBA1hltn3KjBbyIy\nrPR7Tb2lpYXGxkZCQ3s+bGtra2lvb3d6YeL+8koaeOjZHTgcDu79/kzSU8LO6Dh7y7NY8elTAHh5\neHLJqAv57sQr8TINzEYvIiKDRb+hfsstt3DFFVcwZcoU7HY7+/fv57777huI2sSNlVS18PtnttPV\nbeM3y6czefTp74XeYenkxcw3WF+4BYPBwN1zb2VC1FhMRg8nVCwiMvj1G+pLlixhzpw57Nu3D4PB\nwH/9138RFnZmPSoRgOr6du7/21Za2ru57ZoMzpsUe9rHaO5s4Ynt/+RA1RHiAqO5acoyJkSNcUK1\nIiJDR78jh7q7u3nzzTdZv349s2fP5tVXX6W7u3sgahM31NjSxX1/20ptUyc/uCydb81MOu1j1Lc3\ncte//8CBqiOMjRjFY9+6R4EuIsIp9NQffPBBQkNDOXz4MCaTieLiYu69914ef/zxgahP3Ei3xcbD\n/9xBeW0b31kwiqvmjzzl5zocDo7U5LHp2Hb2lB2gpbuNq8ZdwjXpl2vOuYjIcf2G+qFDh3jrrbfY\nvHkzvr6+PProo1x++eUDUZu4EYfDwV9W7yO7qIELp8Rz4+Kxp/zcypZq/rb75d4V4YJ8Arlm/GUs\nHbfYqXuqi4gMNf2GusFgoLu7u/fDs6GhQR+kctpe/TiHzfvKGJscym3XZJzyvyGr3cbDnzxJVVst\nGdHjuHLcJYwOT9WccxGRr9FvqN9444384Ac/oKamhocffph169bxs5/9bCBqEzexaW8pr36cQ1So\nH/f+YAZenqc2Or3T0smKT5+mqq2W1JAk7pl3m5MrFREZ2k5p9Pv48ePZsWMHNpuNlStXMmaMBiXJ\nqTlSWM9fVu3Dz8fE/T+cSZDZ+5Se13V8ZbjDNXlMj5vErTNudHKlIiJD30lD/e233+7zu7+/PwDZ\n2dlkZ2ezZMkS51YmQ15NQwcPP7cDu8PB3TdOJzH61DZosdvt/H3PKxyuyWNm/GR+OfuHmnsuInIK\nThrqO3bs+MYnKtTlm1isNh59YRdNrd385MoJp7S4TJe1myM1R/kgbwP7Kg4R7hfKrTNuVKCLiJyi\nk4b6F3dhO3z4MOPGjaOlpYWsrCxmz549IMXJ0PX3f2WRU9zA/KnxXHreiH4ff7g6l0c/XUmHtROA\nMN8Q/nvhr/H19HF2qSIibqPfa+p/+tOfOHToEM8++ywdHR08/fTT7N69m9tu06Al+XrrdxXzwdZj\nJMcEcut3JvU70r20qYLHPvtfuu0WrhiziIlRYxkTnqq120VETlO/84I2btzI3//+dwAiIyP55z//\nyccff+z0wmRoKihr4uk1+/H3MXHP92fg4/XN3xvtDjvP7l1Nu6WDn05fzncnXcXE6LEKdBGRM9Bv\nT91qtdLZ2dk7UM5isTi9KBmaWtu7+cPzO+m22rnre9OJCff/xsdn1+TzxuH3yKrOYVL0OC5InjlA\nlYqIuKd+Q/3aa6/lqquuYsGCBQBs3ryZG264wemFydBitzv40yt7qaxrZ9lFacwYF33SxzocDl45\n8Db/yu4545MemcZts34wUKWKiLitfkP9821Xd+/ejclk4vHHH2fcuHEDUZsMIa+tz2X3kSomp0Vw\n3cXfvI5Bfn0R/8r+mCCfQO6YczNjIk59DXgRETm5fkP9hhtu4IMPPmDixIkDUY8MQXuyq3jlo2wi\nQ3z59Xen4WH85oFxBQ1FAFwxepECXUTkHOo31MeMGcPbb7/NxIkT8fE5Mb0oNvb098AW91NV384f\nX9qDycPI3d+bTqD/yQe42ew2PszbxPOZawCYHJs+UGWKiAwL/Yb6/v372b9/f5/7DAYD69evd1pR\nMjR0W2z84fmdtHZY+PnVGYxKCDnpY+32nlHu/87/FB+TN5ePvoi4gJNfdxcRkdPXb6hv2LBhIOqQ\nIehvbx0kv7SJRTMSuXhW0kkf19rdxp+2PMOh6lwSAmP4/YJfEehtHsBKRUSGh5OG+pNPPsltt93G\nb3/7269t/+KKczL8fLK3lI93FJESF8QtV518vEV2zVGe2vkCVa01TIudyC3Tv6tAFxFxkpOGenp6\nz/XOGTNmDFgxMjSU17by1Jr9+Hp7cNfyaV+7lWq3tZtVB9/hvdyeMz1Lxl7MteOvwGjUPugiIs5y\n0k/Yz+elL1q0iPb2dq688krmzJlDcXExl1xyyYAVKIOLxWrj8Rd309Fl5dalk4iN+Ppe9zO7X+Hd\n3PVEmyN4cOEdXD9xiQJdRMTJ+v2U/fWvf011dTXQs/2q3W7nN7/5jdMLk8HpufcOc7S0iYumJ3Lh\n1ISvfUxFSzVbS/YQFxDNYxffy+jw1AGuUkRkeOo31MvLy7n99tsBMJvN3H777RQXFzu9MBl8dh6q\n5J3NBSREmfnJlRNO+rj/2/MqVruVq8dfhrfWcBcRGTD9hrrBYCAnJ6f39/z8fEymfgfNi5tpaOnk\nL6v34WUy8pvl0/Hx/vp/A40dTRysymZsxEjmJE4d4CpFRIa3ftP5rrvu4qabbiIqKgqAhoYGHnvs\nMacXJoOHw+Hg6TX7aW7r5ub/GE9yTOBJH9vY2QJAQpAWJxIRGWj9hvqcOXPYuHEjubm5mEwmUlJS\n8PLSKdXhZNPeUrZnVTI+NYzLzk/5SrvD4WBbyR6yqnM5Up0HQKJCXURkwPUb6mVlZbz00ks0NTXh\ncDh679c89eGhrqmDv711EF9vD365bDLGr1nXPae2gD9v+wcAnkYT6ZFpnJc4faBLFREZ9voN9f/8\nz/9k2rRpTJs2DYPhmzfqEPficDh44rVM2jos/Ow7k4gO67s/ent3B+/nbeT943PRfz7z+8xJmIrJ\nQ2MuRERcod9PX6vVyl133TUQtcgg8/GOYvZmVzNldOTXLgP7yOa/kltXgNnLn+9OupK5STP0xU9E\nxIX6Hf0+depUNmzYQHd392kd2G63c//997Ns2TKWL19OUVHR1z7uvvvu449//ONpHVucr6q+nX+8\ncxB/HxO3XZPxlbC2O+xUtdYQ5BPIU5c9xBVjvqVAFxFxsX576h9++CEvvfRS7we2w+HAYDBw5MiR\nb3zeunXr6O7uZvXq1WRmZrJixQpWrlzZ5zGrVq0iNzeX6dN1/XUwsdsdPLF6Hx1dNm6/bjLhwb59\n2tu621mdtZamrhbOT5yOr6fPSY4kIiIDqd9Q/+yzz87owHv27GHu3LkAZGRkkJWV1ad979697N+/\nn2XLllFQUHBGryHO8d6WQg4crWVmejTzv7RqnN1h54GN/4+ixlLC/EK4cfJ3XFSliIh82UlPv7/y\nyiu9t/Py8vq0Pfzww/0euLW1FbP5xLrgHh4eWK1WAKqrq3nqqae4//77T7tgca7ymlaee+8wAX5e\n/Ow7k75ySn1naSZFjaXMiM/g/3379wT7nHzOuoiIDKyThvrrr7/ee/vLa73v3r273wObzWba2tp6\nf7fb7b0r0X344Yc0NDTw4x//mGeeeYZ3332XN99887SLl3PLZnfw51X76LbY+OnSiYQE9j2t7nA4\neOvwhxgMBq6fuAQfk7eLKhURka9z0tPvX5yT/sXbp2rKlCls3LiRxYsXk5mZSVpaWm/bjTfeyI03\n3gjAm2++SUFBAVddddVpv4acW//6JJ8jx+qZmxHH3Iy4r7QXNBRT2FjCjPgMYgOiXFChiIh8k1Oa\nUHwmo5oXLVrEli1buPbaa3E4HDzyyCOsXbuW9vZ2li1bdtrHE+cqq2nl5Q+PEGz2/spmLXaHnef2\nvs66gp7xFedrYRkRkUHppKF+ttOTjEYjDz74YJ/7UlO/ugWneuiuZ7M7+MuqfXRb7fxq6USCzH1P\nq2fX5PPh0U1E+odx2eiLmBk/2UWViojINzlpqOfl5bFw4UIAqqqqem87HA5qamoGpjoZEO99VsCR\nY/WcNymW8yb2XbO909LJy/t7xjvcPO16JkWPc0WJIiJyCk4a6h999NFA1iEuUlHbxvPvHyHAz4tb\nrpzYp62ps5k/bXmGvPpjzE2awcSosS6qUkRETsVJQz0u7qsDpcS92O0OnnitZ7T7L67JIDjgxGn3\n4sYy/vDpU9S1NzA7YSo/nXGjVowTERnktPPGMPbBtmNk5dcxMz2aCyaf+BJX21bPw5ufpKGjiWsn\nXMGVYy9RoIuIDAEK9WGqqr6d5949hNnXk1u/sMiM3W7nT1ufoaGjiRszlnLZ6ItcXKmIiJyqfjd0\nEffjcDj46+uZdHbbuHnJeEK/sMjMx/mbya8v4rzEaQp0EZEhRqE+DH28o5jM3BqmjY3qs7b7gcoj\nPL/vdfy9/FiesdSFFYqIyJlQqA8ztY0dPLs2Cz8fU5+13W12G09u/ycGg5HfnH8Lob7BLq5URERO\nl0J9GHE4HKx84wDtnVZuunx8ny1V8+oKaepqYf6I2YyNGOXCKkVE5Ewp1IeR7VmV7DxcyYTUcL41\nM7FP22fFuwCYGjvx654qIiJDgEJ9mOjosvLM2wcxeRj46dKJfaaodVm7+axoFyG+QUyK1gIzIiJD\nlUJ9mHj14xxqGztYOn8UCVEBvfdbbBZWHXyHdksHFybPxsPo4cIqRUTkbGie+jBQWN7EvzbnEx3m\nx9UX9WyB223tZn3BFv6V/TH1HY0EeQdw6eiFLq5URETOhkLdzdntDp5esx+73cEtV03E29MDu8PO\nfev/SGFjCd4eXlw2+iKuGH0Rgd5mV5crIiJnQaHu5v69s4jsogbOmxjL1DFRABxrKKGwsYQJUWP4\n5aybCPQJ6OcoIiIyFOiauhtrbOniuXcP4+tt4uYl44Gendf+vudVABamnK9AFxFxI+qpu7F/vnuI\n1g4LNy8ZT1iQL/Udjfx+/Z+oaqvlguSZzIqf7OoSRUTkHFKou6mDR2vZsLuE1PggLp0zAoB3sv9N\nVVst/zHmW1w/cYl2XhMRcTM6/e6GLFY7T7+xH4MBbl06CQ8PI52WTjYVbiPEJ4hl4y9XoIuIuCGF\nuht6a9NRSqtbWTxnBGmJIQB8WrSLdksHC1PPx+ShEzQiIu5Ioe5mKuvaWP3vHEICvFn+7ROrw60v\n+AwPg5GLUs93YXUiIuJMCnU34nA4WPnmAbqtdn70H+Px9/UEoLGzmYKGYsZFpmn3NRERN6ZQdyNb\nD1SwN7uajLQI5mbE9d6/qXAbgNZ1FxFxc7q46ibaOy088/ZBPE1GfnpVz4YttW31PJ+5hh2l+/D3\n9GX+iDmuLlNERJxIoe4mXv4wm/rmTq7/1mhiI8xsKNjCs3tX022zkBaWws3TriNAy8CKiLg1hbob\nOFrayLufFRAb7s/SBaOw2Cz8c+9reBpN/GjqdVyQPBOjQVdaRETcnT7phzjb5xu2OOCnSyfi5elB\nbl0hXbZuLkiexYUjZivQRUSGCX3aD3EfbjtGXkkj8ybHk5EWCcD+ysOABsaJiAw3Ov0+hDU0d/LC\n+4fx9zHxwyvScTgcZNceZWvxbjyMHoyLGOXqEkVEZAAp1Iew/3sni/ZOKz9dOhEfX3hw0585VJ0L\nwEWpc/Hx9HFxhSIiMpAU6kNUZm41m/eVkZYYzKKZifx52985VJ3LxKixfCd9MaPDU11dooiIDDCF\n+hDUbbGx8o0DGI9v2PLR0Y3sKttPemQad1/wM0xGD1eXKCIiLqCBckPQGxvyKK9t47K5KaTGB/ee\ncv/5zO8r0EVEhjGF+hBTXtPKa+vzCAvy4YaLx/Rp89U1dBGRYU2hPoQ4HA5WvnEAq83OzUsm4OfT\ns2FLVWstXh6eeHl4ubhCERFxJYX6ELJ5XxmZeTVMHRPJnAkxAOTXF1HaXMG4iFE69S4iMsxpoNwQ\n0dph4f/eycLLZOSWqyYC8FrWu7x5+AMAzk+a4cryRERkEFCoDxEvvn+YxpYuln97LNFh/ryfu4E1\nh94jwj+MH065limx411dooiIuJhCfQjILW7gg23HSIgyc+WFI9lbnsULmW8Q5BPIgwvuIMwvxNUl\niojIIKBQH+RsNjtPrdmPwwE/uWo8bxx5l7cOf4iH0YM7z/uJAl1ERHop1Ae597YUUlDWxHnTQlhz\n7AVy6gqI9A/jF7NuIi08xdXliYjIIKJQH8Tqmjp46cNszL6e2GIOklNVwJzEafx46vX4efm6ujwR\nERlkNKVtkPp8TnpHl5Xll44muzaXuIBofjnrJgW6iIh8LYX6ILXlQDk7DlUyPjWMqMR2umzdTIwe\ni8FgcHVpIiIySCnUB6GW9m7+9uZBvExGfvadibx2aC0A85JnubgyEREZzBTqg9Cz7xyisbWL6y4e\nQ3FnLoUNJZyfOJ2U0ERXlyYiIoOY0wbK2e12HnjgAXJycvDy8uKhhx4iKSmpt/3dd9/l+eefx8PD\ng7S0NB544AGMRn3HyMytZt2uYlJig1gyL5WVu54HYMnYi11cmYiIDHZOS9F169bR3d3N6tWrueOO\nO1ixYkVvW2dnJ3/+85954YUXWLVqFa2trWzcuNFZpQwZnd1W/vr6foxGA7cty8DkYaSosQxvDy/i\ng2JcXZ6IiAxyTgv1PXv2MHfuXAAyMjLIysrqbfPy8mLVqlX4+vaM4rZarXh7ezurlCHj5Q+zqapv\nZ8kFqYyMD8Zqs1LWXEFiUCxGg85iiIjIN3Pa6ffW1lbMZnPv7x4eHlitVkwmE0ajkfDwcABefPFF\n2tvbOe+885xVypCQW9zAO5vziQnzZ+lFKazL/4z3ctZjc9hJCU3q/wAiIjLsOS3UzWYzbW1tvb/b\n7XZMJlOf3x9//HEKCwt58sknh/VULavNzpOvZWJ3wPIlyfzXpscpaa7Aw+jBvORZXD3+MleXKCIi\nQ4DTQn3KlCls3LiRxYsXk5mZSVpaWp/2+++/Hy8vL55++ulhP0DuzY1HOVbRzJwZ/rx09P9o6Ghi\nYcr5XD3+UkJ9g11dnoiIDBFOC/VFixaxZcsWrr32WhwOB4888ghr166lvb2d8ePHs2bNGqZNm8b3\nvvc9AG688UYWLVrkrHIGrdLqFlb9O4egiA6yTZvo6Ohk+aSlXD7mIleXJiIiQ4zTQt1oNPLggw/2\nuS81NbX3dnZ2trNeesiw2x389fX9WKx2UibVk93cya0zbuTCEbNdXZqIiAxBw/u8t4t9tP0Yhwrq\nmDUhmvKuQoJ9ArVqnIiInDGFuovUNXXwz3cP4+9jYvLMbpq7WsmITh/WAwZFROTsKNRd4Is7sC1e\nFMTLWa/h6+nDFWOH35gCERE5dxTqLvDZ/p4d2MaO8uWTxn9hc9i5ffbNxAdq1TgRETlzCvUB1tLe\nzTNv9ezANmZKGy1drXx30pVkxIxzdWkiIjLEKdQH2D/eyerdga2g+ShGg5H5I+a4uiwREXEDCvUB\ntOtwJet3lZASF0TK6C7y6gsZFTYCfy8/V5cmIiJuQKE+QFrau/nr65mYPAwsvMjEY1tWYjJ4sHTc\nYleXJiIibsJpi89IX8+8fZD65i6WXTyCf+W/gJeHJ/fOu43R4an9P1lEROQUqKc+ALYdrGDTnlJG\nJQTTFXaYlu42vpO+WIEuIiLnlHrqTtbU2sXTa/bj6WMhaVoxH+dvIyYgksWjFri6NBERcTMKdSdy\nOBysfPMALV7H8E8/wpaybqLNEdw28weYPPRHLyIi55aSxYnW7yphW1Em3qMOYPLw5rsTrmFR6lwF\nuoiIOIXSxUnKa1r528cb8R6Z2TsoLi08xdVliYiIG9NAOSewWO2seHULjNiN0Qi/Pv8nCnQREXE6\nhboTvPJRNsXteRhMVpZNuFxLwIqIyIBQqJ9j+/NqeGNjHn6RtQDMSZzq4opERGS40DX1c6i+uZM/\nvrwHj+AaHOZaEgPjiDJHuLosEREZJhTq54jNZufxl3bT4p2Pd8ohPIwmbsxY6uqyRERkGFGonyMv\nfXiE7PZdeKXk4uflx91zb9WKcSIiMqAU6ufArsMV/OvoWjwTigjxCea+C39BfFCMq8sSEZFhRqF+\nlirr2vjjphcwRRcR6RvJAxf9knC/UFeXJSIiw5BC/Sx0dlu5f9VbOMKPEeoZwYqLf4PZ29/VZYmI\nyDClKW1nyOFw8D+vbaMhaCcGPPjdwp8q0EVExKUU6mfo7U+Osqf13xg8LXx34pW6hi4iIi6nUD8D\n+/NqeGH7R3iE1DAmbBSXjpnv6pJEREQU6qerqr6dFS/uxBSfi4+HD7+Y832MBv0xioiI6ymNTkNb\nh4UH/7Gdds9yDJ4WFqTM1kh3EREZNBTqp8hqs7PihV0UVzYTP7oBgAuSZ7q4KhERkRM0pe0UOBwO\n/rpmDwcbdxM0rYwaRzMJgTGMCEl0dWkiIiK9FOqnYMXaN9hr/QSvZCt2o4l5ibP4TvpiDAaDq0sT\nERHppVD/Bhabhd+//38c7TiAweDJZSMv5or0BQT7BLq6NBERka9QqJ9EfUcjv//or1R1lWHoDOK+\nBbcyPkGn20VEZPBSqH+N0uYKfvfxn2i3tUFDLA9eegujE7QvuoiIDG4K9a/xxCf/v717D6qy3vc4\n/l6wcC0DERQvtRFDvKHoQYq001a3pEexMUrUdDxeOZZNlpyGDDUVhS001OTkBZtSh8wZNVPR6ZjH\nS/al3iAAAA1ZSURBVEq73N4SDRhRCy0iAW87F8ptref80biOFzTNzV7Lxef1F896Fr/ny29+w2c9\nv/U8z28tV+yVmH4JZ8Hz/0mXdrptTURE3J9C/Saf/S2P4soTmK42Jy1+HJ3aBbq6JBERkbui+9Sv\nk5P7PWu+3YbJBKN7xSrQRUTkgaIzdcDhMFi5tYCt332NpeOPBFoCebbnn11dloiIyD1p9KFeWVXF\nXzf8D8cvHsfSsQSr2cIbfV/E7OXt6tJERETuSaMM9eq6Gg7+nMffTn/LkdICDJ86zK3B39KM1//9\nv+jY8lFXlygiInLPGl2oOwwHGV8tpaD8xG/bNQ/xJ0s4Cf2fJqJNJ7y8dJmBiIg8mBpdqO/+/hsK\nyk/g+EcQdT91YeLAPsT1C9MjX0VE5IHXqEK9uLycjw5+imF4Yy2P4o1xf+bfOuuhMiIi4hkaRahf\nunqZVbm72Ve6Dx6q4eGqJ1gwfSgBzSyuLk1EROSfxmND/R9Vv7K/JI+///Qt+WUnwGTAQxDStCNv\njxiPt7eubhcREc/icaFe+utZthzfwd4z+7E77AB4VwfyiE9HXowZRJe27VxcoYiISMN44EPdMAwu\nXL3EDxd/ZO/pv3Ow5CgGBg83a82gsL70Du5FK9+Wri5TRESkwTVYqDscDlJSUigqKqJJkyakpaXR\nvn175/7du3ezdOlSzGYz8fHxjBo16nfbNAyDMlsFxRd/4oeLP1J88SeKL/7Ir9U253vCAtsTF/4f\nPPGnSN2eJiIijUqDhfrOnTupqalh3bp15OXlkZGRQVZWFgC1tbWkp6ezYcMGmjZtypgxY4iJiSEo\nKOiObc74379i97vx1rPWvi0Jb9WJ0MB2hLfqSNegjro9TUREGqUGC/XDhw/Tt29fACIjI8nPz3fu\n+/777wkJCaF58+YAPPbYYxw8eJDY2Ng7tuln8aV7SDc6BLYjNDCE0IB2+Fl8G+pPEBEReaA0WKjb\nbDb8/Pyc297e3tTV1WE2m7HZbDRr1sy5z9fXF5vNVl8zN5j3l/8mODi4QeoVERF50DXYl85+fn5U\nVlY6tx0OB2azud59lZWVN4S8iIiI3LsGC/WoqChyc3MByMvLo3Pnzs59YWFhnDlzhkuXLlFTU8Oh\nQ4fo1atXQ5UiIiLSKDTY9PugQYP4+uuvGT16NIZhsHDhQrZu3cqVK1d44YUXSE5OJiEhAcMwiI+P\np02bNg1VioiISKPQYKHu5eXFggULbngtLCzM+XNMTAwxMTENdXgREZFGRzdyi4iIeAiFuoiIiIdQ\nqIuIiHgIhbqIiIiHUKiLiIh4CIW6iIiIh1Coi4iIeIgHYj11u90OwNmzZ11ciYiIyL/Gtcy7loF3\n44EI9YqKCgDGjh3r4kpERET+tSoqKmjfvv1dvddkGIbRwPXct6qqKvLz82nVqhXe3t6uLkdERKTB\n2e12KioqiIiIwGq13tXvPBChLiIiIr9PF8qJiIh4CIW6iIiIh1Coi4iIeAiFuoiIiIdw+1vaHA4H\nKSkpFBUV0aRJE9LS0u760v7G5vnnn8fPzw+A4OBg0tPTXVyRezl69CjvvPMOq1ev5syZMyQnJ2My\nmejUqRPz5s3Dy0ufca+5vq8KCwt56aWXePTRRwEYM2YMQ4cOdW2BLlZbW8usWbP4+eefqamp4eWX\nX6Zjx44aU/Wor68efvhhjamb2O123nrrLYqLizGZTMyfPx+LxXLPY8rtQ33nzp3U1NSwbt068vLy\nyMjIICsry9VluZ3q6moMw2D16tWuLsUtffjhh2zZsoWmTZsCkJ6eTmJiIr1792bu3Lns2rWLQYMG\nubhK93BzXxUUFDBp0iQmT57s4srcx5YtWwgICCAzM5NLly7x3HPP0bVrV42petTXV6+88orG1E2+\n/PJLANauXcv+/ft57733MAzjnseU23+MPHz4MH379gUgMjKS/Px8F1fkno4fP87Vq1eZPHky48eP\nJy8vz9UluZWQkBAWL17s3C4oKOCJJ54AoF+/fnzzzTeuKs3t3NxX+fn57Nmzh7FjxzJr1ixsNpsL\nq3MPQ4YMYfr06QAYhoG3t7fG1G3U11caU7caOHAgqampAJSWluLv7/+HxpTbh7rNZnNOKQN4e3tT\nV1fnworck9VqJSEhgRUrVjB//nySkpLUT9cZPHgwZvP/T0wZhoHJZALA19eXy5cvu6o0t3NzX/Xs\n2ZMZM2awZs0a2rVrx9KlS11YnXvw9fXFz88Pm83Ga6+9RmJiosbUbdTXVxpT9TObzbz55pukpqYy\nbNiwPzSm3D7U/fz8qKysdG47HI4b/uHIb0JDQ3n22WcxmUyEhoYSEBDgfLyu3Or676UqKyvx9/d3\nYTXubdCgQURERDh/LiwsdHFF7uGXX35h/PjxxMXFMWzYMI2pO7i5rzSmbu/tt99m+/btzJkzh+rq\naufrdzum3D7Uo6KiyM3NBSAvL4/OnTu7uCL3tGHDBjIyMgAoKyvDZrPRqlUrF1flvrp168b+/fsB\nyM3N5fHHH3dxRe4rISGBY8eOAbBv3z66d+/u4opc79y5c0yePJk33niDESNGABpTt1NfX2lM3Wrz\n5s188MEHADRt2hSTyURERMQ9jym3f0zstavfT5w4gWEYLFy4kLCwMFeX5XZqamqYOXMmpaWlmEwm\nkpKSiIqKcnVZbqWkpITXX3+d9evXU1xczJw5c6itraVDhw6kpaVpXYHrXN9XBQUFpKam4uPjQ1BQ\nEKmpqTd8JdYYpaWlsW3bNjp06OB8bfbs2aSlpWlM3aS+vkpMTCQzM1Nj6jpXrlxh5syZnDt3jrq6\nOqZMmUJYWNg9/59y+1AXERGRu+P20+8iIiJydxTqIiIiHkKhLiIi4iEU6iIiIh5CoS4iIuIhFOoi\nbqKkpISIiAji4uKcD+mIiYnh/fffv6d2Fi9e7HzMa1xc3H3X1aVLF+Li4igpKbnvtu5HVVUVcXFx\nREREuLwWEXelR7OJuJHWrVuTk5Pj3C4rK2Pw4ME888wzf+j5DNe3dT/+We3cD6vVSk5ODjExMa4u\nRcRtKdRF3FhFRQWGYeDr60tdXR0pKSmcPHmSc+fOERoaypIlS7BarXz00UesX7+ewMBA/P396dmz\nJ/DbWXZRUZHzzP3VV18FICYmho8//hibzcbcuXOpq6vDYrGQnp7uXA6zPtu2bWPVqlVUVVVRXV1N\nWloa0dHRjBs3jubNm3Py5EkWLVrEqVOnyMrKwmQy0aNHD1JTUzl06BCZmZkANG/enHfffZcWLVqw\nefNmsrOzcTgcdO/enXnz5mGxWNi6destbfj4+DRsh4s84DT9LuJGysvLiYuLY8iQIfTu3ZtFixax\nZMkS2rZty5EjR/Dx8WHdunXs2LGD6upq9u7dy3fffcdnn33Gpk2bWLVqFWfPnr3r42VnZzNp0iQ2\nbtzIuHHj7ri6n8PhYO3atSxfvpwtW7YwZcoUVqxY4dzfpUsXtm/fTosWLUhPT2flypV8/vnn2O12\n9u7dy7Jly0hJSWHjxo0MGDCAwsJCTp48yfr161m7di05OTm0bNmSFStWUFZWVm8bInJnOlMXcSPX\npt8dDgcZGRkUFRXRp08fAKKjowkICGDNmjX88MMPnD59mitXrnDgwAH69++Pr68v8NtSlw6H466O\n179/fxYsWMBXX33FgAEDGDx48G3f6+XlxdKlS9m9ezfFxcUcOHDghkVMrs0OHDlyhKioKNq2bQvg\nPDsvKSlh2rRpDBw4kKeffpqnnnqKTz75hDNnzjBq1CgAamtr6dat223bEJE705m6iBvy8vJixowZ\nnD9/npUrVwKwa9cukpKSsFqtDB8+nOjoaOfSjNeHeH2rGJpMJq5/InRtbS3w2weATZs20bNnT7Kz\ns5k3b95ta6qsrCQ+Pp6SkhLnlPv1rFZrvce/cOECFy5cYOLEiaxevZqQkBAyMzPJysrCbrcTGxtL\nTk4OOTk5fPrpp8ydO/e2bYjInSnURdyU2WxmxowZLF++nIqKCvbt20dsbCzx8fEEBQVx8OBB7HY7\nTz75JHv27OHy5ctUV1ezY8eOW9oKDAzk1KlTABw7dsy5LG9iYiLHjh1j9OjRTJ8+/Y5LYJ4+fRov\nLy+mTp1Knz59yM3NxW633/K+Hj16cPToUecxFi5cyK5duxg5ciSVlZVMnDiRiRMnUlhYSO/evdmx\nYwfnz5/HMAxSUlLIzs6+bRsicmeafhdxY/369SMyMpJFixYxfvx4kpKS+OKLL2jSpAmRkZGUlJQw\ncuRIJkyYwIgRI/D39+eRRx65pZ2hQ4eyfft2hg4dSvfu3enWrRsAU6dOZfbs2Sxbtgxvb2+Sk5Nv\nW0vXrl0JDw8nNjYWq9VKdHQ0paWlt7yvTZs2zJ49m4SEBBwOB5GRkQwfPpzg4GCSk5Mxm81YLBbm\nz59P586dmTZtGhMmTMDhcBAeHs6LL76IxWKptw0RuTOt0iYid3TtCnp3ce3K/eDgYFeXIuJ2NP0u\nIr/LnR4+U15e7tI6RNyZztRFREQ8hM7URUREPIRCXURExEMo1EVERDyEQl1ERMRDKNRFREQ8hEJd\nRETEQ/wfEBZ8cdt7vHUAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11b0b1d30>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(radiuseff, valeff, label='Calibration')\n",
    "plt.plot(radii, encircled_flux/np.max(encircled_flux), label='Our PSF')\n",
    "plt.xlim([0, 30])\n",
    "plt.xlabel('Radius [arcsec]')\n",
    "plt.ylabel('Encircled flux')\n",
    "plt.legend()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 140,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0 1.0\n",
      "1 1.001\n",
      "2 1.002\n",
      "3 1.003\n",
      "4 1.004\n",
      "5 1.005\n",
      "6 1.006\n",
      "7 1.007\n",
      "8 1.008\n",
      "9 1.009\n",
      "10 1.01\n",
      "11 1.011\n",
      "12 1.012\n",
      "13 1.013\n",
      "14 1.014\n",
      "15 1.015\n",
      "16 1.016\n",
      "17 1.017\n",
      "18 1.018\n",
      "19 1.019\n",
      "20 1.02\n",
      "21 1.021\n",
      "22 1.022\n",
      "23 1.023\n",
      "24 1.024\n",
      "25 1.025\n",
      "26 1.026\n",
      "27 1.027\n",
      "28 1.028\n",
      "29 1.029\n",
      "30 1.03\n",
      "31 1.031\n",
      "32 1.032\n",
      "33 1.033\n",
      "34 1.034\n",
      "35 1.035\n",
      "36 1.036\n",
      "37 1.037\n",
      "38 1.038\n",
      "39 1.039\n",
      "40 1.04\n",
      "41 1.041\n",
      "42 1.042\n",
      "43 1.043\n",
      "44 1.044\n",
      "45 1.045\n",
      "46 1.046\n",
      "47 1.047\n",
      "48 1.048\n",
      "49 1.049\n",
      "50 1.05\n",
      "51 1.051\n",
      "52 1.052\n",
      "53 1.053\n",
      "54 1.054\n",
      "55 1.055\n",
      "56 1.056\n",
      "57 1.057\n",
      "58 1.058\n",
      "59 1.059\n",
      "60 1.06\n",
      "61 1.061\n",
      "62 1.062\n",
      "63 1.063\n",
      "64 1.064\n",
      "65 1.065\n",
      "66 1.066\n",
      "67 1.067\n",
      "68 1.068\n",
      "69 1.069\n",
      "70 1.07\n",
      "71 1.071\n",
      "72 1.072\n",
      "73 1.073\n",
      "74 1.074\n",
      "75 1.075\n",
      "76 1.076\n",
      "77 1.077\n",
      "78 1.078\n",
      "79 1.079\n",
      "80 1.08\n",
      "81 1.081\n",
      "82 1.082\n",
      "83 1.083\n",
      "84 1.084\n",
      "85 1.085\n",
      "86 1.086\n",
      "87 1.087\n",
      "88 1.088\n",
      "89 1.089\n",
      "90 1.09\n",
      "91 1.091\n",
      "92 1.092\n",
      "93 1.093\n",
      "94 1.094\n",
      "95 1.095\n",
      "96 1.096\n",
      "97 1.097\n",
      "98 1.098\n",
      "99 1.099\n",
      "100 1.1\n",
      "101 1.101\n",
      "102 1.102\n",
      "103 1.103\n",
      "104 1.104\n",
      "105 1.105\n",
      "106 1.106\n",
      "107 1.107\n",
      "108 1.108\n",
      "109 1.109\n",
      "110 1.11\n",
      "111 1.111\n",
      "112 1.112\n",
      "113 1.113\n",
      "114 1.114\n",
      "115 1.115\n",
      "116 1.116\n",
      "117 1.117\n",
      "118 1.118\n",
      "119 1.119\n",
      "120 1.12\n",
      "121 1.121\n",
      "122 1.122\n",
      "123 1.123\n",
      "124 1.124\n",
      "125 1.125\n",
      "126 1.126\n",
      "127 1.127\n",
      "128 1.128\n",
      "129 1.129\n",
      "130 1.13\n",
      "131 1.131\n",
      "132 1.132\n",
      "133 1.133\n",
      "134 1.134\n",
      "135 1.135\n",
      "136 1.136\n",
      "137 1.137\n",
      "138 1.138\n",
      "139 1.139\n",
      "140 1.14\n",
      "141 1.141\n",
      "142 1.142\n",
      "143 1.143\n",
      "144 1.144\n",
      "145 1.145\n",
      "146 1.146\n",
      "147 1.147\n",
      "148 1.148\n",
      "149 1.149\n",
      "150 1.15\n",
      "151 1.151\n",
      "152 1.152\n",
      "153 1.153\n",
      "154 1.154\n",
      "155 1.155\n",
      "156 1.156\n",
      "157 1.157\n",
      "158 1.158\n",
      "159 1.159\n",
      "160 1.16\n",
      "161 1.161\n",
      "162 1.162\n",
      "163 1.163\n",
      "164 1.164\n",
      "165 1.165\n",
      "166 1.166\n",
      "167 1.167\n",
      "168 1.168\n",
      "169 1.169\n",
      "170 1.17\n",
      "171 1.171\n",
      "172 1.172\n",
      "173 1.173\n",
      "174 1.174\n",
      "175 1.175\n",
      "176 1.176\n",
      "177 1.177\n",
      "178 1.178\n",
      "179 1.179\n",
      "180 1.18\n",
      "181 1.181\n",
      "182 1.182\n",
      "183 1.183\n",
      "184 1.184\n",
      "185 1.185\n",
      "186 1.186\n",
      "187 1.187\n",
      "188 1.188\n",
      "189 1.189\n",
      "190 1.19\n",
      "191 1.191\n",
      "192 1.192\n",
      "193 1.193\n",
      "194 1.194\n",
      "195 1.195\n",
      "196 1.196\n",
      "197 1.197\n",
      "198 1.198\n",
      "199 1.199\n",
      "200 1.2\n",
      "201 1.201\n",
      "202 1.202\n",
      "203 1.203\n",
      "204 1.204\n",
      "205 1.205\n",
      "206 1.206\n",
      "207 1.207\n",
      "208 1.208\n",
      "209 1.209\n",
      "210 1.21\n",
      "211 1.211\n",
      "212 1.212\n",
      "213 1.213\n",
      "214 1.214\n",
      "215 1.215\n",
      "216 1.216\n",
      "217 1.217\n",
      "218 1.218\n",
      "219 1.219\n",
      "220 1.22\n",
      "221 1.221\n",
      "222 1.222\n",
      "223 1.223\n",
      "224 1.224\n",
      "225 1.225\n",
      "226 1.226\n",
      "227 1.227\n",
      "228 1.228\n",
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      "947 1.947\n",
      "948 1.948\n",
      "949 1.949\n",
      "950 1.95\n",
      "951 1.951\n",
      "952 1.952\n",
      "953 1.953\n",
      "954 1.954\n",
      "955 1.955\n",
      "956 1.956\n",
      "957 1.957\n",
      "958 1.958\n",
      "959 1.959\n",
      "960 1.96\n",
      "961 1.961\n",
      "962 1.962\n",
      "963 1.963\n",
      "964 1.964\n",
      "965 1.965\n",
      "966 1.966\n",
      "967 1.967\n",
      "968 1.968\n",
      "969 1.969\n",
      "970 1.97\n",
      "971 1.971\n",
      "972 1.972\n",
      "973 1.973\n",
      "974 1.974\n",
      "975 1.975\n",
      "976 1.976\n",
      "977 1.977\n",
      "978 1.978\n",
      "979 1.979\n",
      "980 1.98\n",
      "981 1.981\n",
      "982 1.982\n",
      "983 1.983\n",
      "984 1.984\n",
      "985 1.985\n",
      "986 1.986\n",
      "987 1.987\n",
      "988 1.988\n",
      "989 1.989\n",
      "990 1.99\n",
      "991 1.991\n",
      "992 1.992\n",
      "993 1.993\n",
      "994 1.994\n",
      "995 1.995\n",
      "996 1.996\n",
      "997 1.997\n",
      "998 1.998\n",
      "999 1.999\n"
     ]
    }
   ],
   "source": [
    "rfactor = np.arange(1.,2., 1e-3)\n",
    "ffactor = np.arange(1.,2., 1e-3)\n",
    "# work with the data points between 3 and 25\"\n",
    "idx, = np.where((radii > 2) & (radii < 12))\n",
    "xv = radii[idx]\n",
    "yv = encircled_flux[idx]/np.max(encircled_flux)\n",
    "resid = np.zeros((len(rfactor), len(ffactor)))\n",
    "for i, rf in enumerate(rfactor):\n",
    "    print(i, rf)\n",
    "    tck = interpolate.splrep(radiuseff*rf, valeff, s=0)\n",
    "    yfit = interpolate.splev(xv, tck, der=0)\n",
    "    for j, ff in enumerate(ffactor):\n",
    "        resid[i, j] = np.sum((yv-yfit*ff)**2)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 141,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.image.AxesImage at 0x11b0124e0>"
      ]
     },
     "execution_count": 141,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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Nv2eLAMQD1uyWjUfPJ7KxMWRLGpHfVYNxZBP1k7HL2lbbKCHI2Gf8Vew8WRTnCNoxpQnN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\nMdgvGlVr2JfvQoYAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x128b94cc0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.imshow(np.log(resid))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This shows a minimum, with some degeneracy. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 142,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "rf = 1.141, ff = 1.000, residual = 0.098\n"
     ]
    }
   ],
   "source": [
    "imin = np.argmin(resid)\n",
    "rmin, fmin = np.unravel_index(imin, resid.shape)\n",
    "print(\"rf = {:.3f}, ff = {:.3f}, residual = {:.3f}\".format(rfactor[rmin], ffactor[fmin], resid[rmin, fmin]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 143,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x10d937c18>"
      ]
     },
     "execution_count": 143,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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N5WzK386Oor202bo7AXq6eZAcNIK4gGji/aMZERhDctAI9VIXOU0KdREnyCtp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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11b044a20>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(radiuseff*rfactor[rmin], valeff, label='Calibration')\n",
    "plt.plot(radii, encircled_flux/np.max(encircled_flux)/ffactor[fmin], label='Our PSF')\n",
    "plt.xlim([0, 30])\n",
    "plt.xlabel('Radius [arcsec]')\n",
    "plt.ylabel('Encircled flux')\n",
    "plt.legend()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 144,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "23.660456"
      ]
     },
     "execution_count": 144,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# The two curve overlap\n",
    "psfok = psf/np.max(encircled_flux)/ffactor[fmin]\n",
    "np.sum(psfok)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "psfok is the PSF that a source of flux 1 Jy has in our data, and is to be used for source extraction"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Validation\n",
    "To check PSF is reasonable, lets look at a 100 micron source, e.g. `EN1-PACSxID24-ELAIS-N1-HerMES-1-29844`. We can see from `WP4-ELAIS-N1-HerMES-PACSxID24-v1.fits.gz` that it has a flux of 5 Jy. Maximum value in our normalised PSF gives a peak below. Since PSF is double resolution of map, it could also be off centre. Map has value of 0.96 MJy/sr but does appear to be off centre.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 145,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from astropy.table import Table"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 146,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "WARNING: UnitsWarning: 'Degrees' did not parse as fits unit: At col 0, Unit 'Degrees' not supported by the FITS standard.  [astropy.units.core]\n"
     ]
    }
   ],
   "source": [
    "PACScat=Table.read('../data/ELAIS-N1/WP4-ELAIS-N1-HerMES-PACSxID24-v1.fits.gz')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 147,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "&lt;Table length=1&gt;\n",
       "<table id=\"table4748472448\" class=\"table-striped table-bordered table-condensed\">\n",
       "<thead><tr><th>XID</th><th>RA</th><th>Dec</th><th>F_PACS_100__A4</th><th>F_PACS_100__A5</th><th>F_PACS_100__A6</th><th>F_PACS_100__A7</th><th>F_PACS_100__A8</th><th>F_PACS_100__A10</th><th>F_PACS_100</th><th>Ferr_PACS_100__A4</th><th>Ferr_PACS_100__A5</th><th>Ferr_PACS_100__A6</th><th>Ferr_PACS_100__A7</th><th>Ferr_PACS_100__A8</th><th>Ferr_PACS_100__A10</th><th>Ferr_PACS_100</th><th>F_PACS_100__SKY</th><th>F_PACS_160__A4</th><th>F_PACS_160__A5</th><th>F_PACS_160__A6</th><th>F_PACS_160__A7</th><th>F_PACS_160__A8</th><th>F_PACS_160__A10</th><th>F_PACS_160</th><th>Ferr_PACS_160__A4</th><th>Ferr_PACS_160__A5</th><th>Ferr_PACS_160__A6</th><th>Ferr_PACS_160__A7</th><th>Ferr_PACS_160__A8</th><th>Ferr_PACS_160__A10</th><th>Ferr_PACS_160</th><th>F_PACS_160__SKY</th><th>HELP_ID</th></tr></thead>\n",
       "<thead><tr><th></th><th>Degrees</th><th>Degrees</th><th>mJy</th><th>mJy</th><th>mJy</th><th>mJy</th><th>mJy</th><th>mJy</th><th>mJy</th><th>mJy</th><th>mJy</th><th>mJy</th><th>mJy</th><th>mJy</th><th>mJy</th><th>mJy</th><th>mJy / pix</th><th>mJy</th><th>mJy</th><th>mJy</th><th>mJy</th><th>mJy</th><th>mJy</th><th>mJy</th><th>mJy</th><th>mJy</th><th>mJy</th><th>mJy</th><th>mJy</th><th>mJy</th><th>mJy</th><th>mJy / pix</th><th></th></tr></thead>\n",
       "<thead><tr><th>int32</th><th>float32</th><th>float32</th><th>float32</th><th>float32</th><th>float32</th><th>float32</th><th>float32</th><th>float32</th><th>float32</th><th>float32</th><th>float32</th><th>float32</th><th>float32</th><th>float32</th><th>float32</th><th>float32</th><th>float32</th><th>float32</th><th>float32</th><th>float32</th><th>float32</th><th>float32</th><th>float32</th><th>float32</th><th>float32</th><th>float32</th><th>float32</th><th>float32</th><th>float32</th><th>float32</th><th>float32</th><th>float32</th><th>str37</th></tr></thead>\n",
       "<tr><td>296</td><td>243.654</td><td>54.2762</td><td>258.29</td><td>260.645</td><td>269.865</td><td>276.597</td><td>288.702</td><td>301.248</td><td>234.857</td><td>11.4039</td><td>10.6031</td><td>10.6056</td><td>10.908</td><td>11.5442</td><td>13.2409</td><td>8.20634</td><td>0.0</td><td>356.648</td><td>351.387</td><td>356.532</td><td>357.341</td><td>354.393</td><td>350.794</td><td>358.058</td><td>19.3761</td><td>16.3005</td><td>15.1362</td><td>14.3959</td><td>14.0672</td><td>14.637</td><td>11.4608</td><td>0.0</td><td>EN1-PACSxID24-ELAIS-N1-HerMES-1-30011</td></tr>\n",
       "</table>"
      ],
      "text/plain": [
       "<Table length=1>\n",
       " XID     RA     Dec   ... F_PACS_160__SKY                HELP_ID               \n",
       "      Degrees Degrees ...    mJy / pix                                         \n",
       "int32 float32 float32 ...     float32                     str37                \n",
       "----- ------- ------- ... --------------- -------------------------------------\n",
       "  296 243.654 54.2762 ...             0.0 EN1-PACSxID24-ELAIS-N1-HerMES-1-30011"
      ]
     },
     "execution_count": 147,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "PACScat[PACScat['HELP_ID']=='EN1-PACSxID24-ELAIS-N1-HerMES-1-30011']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 151,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Max PSF = 0.0144 Jy/pixel, off pixel Max PSF = 0.0139 Jy/pixel\n"
     ]
    }
   ],
   "source": [
    "cpix=np.int((hd['NAXIS1']+1)/2.0)\n",
    "\n",
    "print(\"Max PSF = {:.4f} Jy/pixel, off pixel Max PSF = {:.4f} Jy/pixel\".format(psfok[cpix-1,cpix-1]*0.358,psfok[cpix-,cpix-3]*0.358))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 149,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "WARNING: Cannot determine equinox. Assuming J2000. [aplpy.wcs_util]\n",
      "WARNING: Cannot determine equinox. Assuming J2000. [aplpy.wcs_util]\n",
      "/Users/pdh21/anaconda3/envs/new/lib/python3.6/site-packages/aplpy/normalize.py:115: RuntimeWarning: invalid value encountered in less\n",
      "  negative = result < 0.\n"
     ]
    },
    {
     "data": {
      "image/png": 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invnKycnRX//6V5199tlKSUlRcnKyzj77bM2cOVO9e/d22ccamT9/vp555hlJ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\nRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x12c9df3c8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import aplpy\n",
    "import seaborn as sns\n",
    "sns.set_style(\"white\")\n",
    "cmap=sns.cubehelix_palette(8, start=.5, rot=-.75,as_cmap=True)\n",
    "fig=aplpy.FITSFigure('../../dmu26/data/ELAIS_N1/PACS/ELAIS-N1-160um-img_wgls.fits')\n",
    "fig.recenter(PACScat[PACScat['HELP_ID']=='EN1-PACSxID24-ELAIS-N1-HerMES-1-30011']['RA'],PACScat[PACScat['HELP_ID']=='EN1-PACSxID24-ELAIS-N1-HerMES-1-30011']['Dec'], radius=0.008)\n",
    "fig.show_colorscale(vmin=-0.001,vmax=0.02,cmap=cmap)\n",
    "fig.add_colorbar()\n",
    "fig.colorbar.set_location('top')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 150,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.colorbar.Colorbar at 0x11232c588>"
      ]
     },
     "execution_count": 150,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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givcaL1eKn3oV8WdpnVJ02mGTI5vScgf9PsNpn3nk9g5+Yjyv97pxVNnjNP4L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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10dd9e0f0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "rad=100\n",
    "plt.imshow(psfok[cpix-1-rad:cpix+rad:5,cpix-1-rad:cpix+rad:5]*0.358,vmin=-0.001,vmax=0.02,cmap=cmap)\n",
    "plt.colorbar()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In summary, the PSF is within 10% of this source, and given noise and shape of source will add additional uncertianty, as well as non-zero background, this seems reasonable.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 117,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "WARNING: VerifyWarning: Verification reported errors: [astropy.io.fits.verify]\n",
      "WARNING: VerifyWarning: HDU 1: [astropy.io.fits.verify]\n",
      "WARNING: VerifyWarning:     'NAXIS1' card at the wrong place (card 4).  Fixed by moving it to the right place (card 3). [astropy.io.fits.verify]\n",
      "WARNING: VerifyWarning:     'NAXIS2' card at the wrong place (card 5).  Fixed by moving it to the right place (card 4). [astropy.io.fits.verify]\n",
      "WARNING: VerifyWarning:     'PCOUNT' card at the wrong place (card 31).  Fixed by moving it to the right place (card 5). [astropy.io.fits.verify]\n",
      "WARNING: VerifyWarning:     'GCOUNT' card at the wrong place (card 32).  Fixed by moving it to the right place (card 6). [astropy.io.fits.verify]\n",
      "WARNING: VerifyWarning: HDU 2: [astropy.io.fits.verify]\n",
      "WARNING: VerifyWarning:     'BITPIX' card at the wrong place (card 2).  Fixed by moving it to the right place (card 1). [astropy.io.fits.verify]\n",
      "WARNING: VerifyWarning:     'NAXIS' card at the wrong place (card 3).  Fixed by moving it to the right place (card 2). [astropy.io.fits.verify]\n",
      "WARNING: VerifyWarning: Note: astropy.io.fits uses zero-based indexing.\n",
      " [astropy.io.fits.verify]\n"
     ]
    }
   ],
   "source": [
    "stackhd[1].data=psfok\n",
    "stackhd.writeto('dmu18_PACS_160_PSF_ELAIS-N1_20170720.fits',output_verify='fix+warn')"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python [default]",
   "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": "3.6.0"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}