{
 "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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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "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 0x7fd0841abf98>"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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WOKOiioFSYJuI5IrIJAARmQB8Btjr7E9zvgtwA7BrKDdoTLSd7fZSffzMkJudAhYXTmL/qTY6u6O7Kpkx0TLgqCdV9YjIPcArgAt4WlWrReQhoEpVNwFPAb8QkRr8NYk1zrXVIrIR2A14gLtV1esEg2edEVUJwEZVDSxP9ZyI5OJvttoO3BXNGzZmqD6sa8Hj06gFiosLJ+FT2HXsDEuKh9Y5bsxwiGgKD1XdDGwOObYuaLsLuLmPa9cD60OO7QAW95H+qkjKZEysvOc0E0U6rfhALi6cBMD2o80WKMyoZE9mG3OBth9toXhKGpPTkqOS35T0FAomT+DDo61Ryc+YaLNAYcwF2nWslYUzsqKa58WFk9h+tCWqeRoTLRYojLkAje1uTrR2RT1QVBRM4ljLWRra3FHN15hosEBhzAXYeczfPLSwIMqBYqa/n+JDq1WYUcgChTEXYFedP1AsGOKDdqHKp2fhShA+rLNAYUYfCxTGXICdx1qZPSWNjNSkqOY7IdlFSW4au4+fiWq+xkSDBQpjLsCuY62UR7l/IqBsWia7T1igMKOPBQpjItTU7ub4MHRkB5RNz+REaxenO7qHJX9jBssChTERCnRkD1eNYsF0f77W/GRGGwsUxkSo2nkDXzAjuh3ZAfOdlfJ2n7AH78zoYoHCmAjtPdlGweQJZEa5IzsgOy2ZaVmpVqMwo44FCmMitO/kGS6amjGsr1E2LbO35mLMaGGBwpgIuD1eDjZ0cNHU4Wl2ClgwPZODDe109XiH9XWMuRAWKIyJwMH6Drw+Zd5w1yimZ+JT2HeybVhfx5gLYYHCmAjsPelvDhrupqdzHdrW/GRGDwsUxkRg38k2kl0JFE9JG9bXKZw8kQlJLvafshqFGT0iChQiskpE9olIjYisDXM+RUSed85vFZGioHMPOMf3ichK51iqiGwTkQ9FpFpEvhOUvtjJ44CTZ3Qm/TdmCPaebGNOXjqJQ1wjeyAJCcLc/HQLFGZUGfCv3lmu9HHgGqAMuEVEykKS3QE0q+oc4DHgEefaMvzLoi4AVgFPOPm5gatU9WKgAlglIkudvB4BHlPVUqDZyduYmNp78gwXTRveZqeAufkZ7D/VPiKvZUwkIvl4tASoUdVaVe0GNgCrQ9KsBp51tl8AVoiIOMc3qKpbVQ8BNcAS9Qv8JyQ5X+pcc5WTB06eNwzy3oyJiuaObk6dcQ97/0TA3PwMGtrcNpWHGTUiCRQzgKNB+3XOsbBpVNUDtAI5/V0rIi4R2Q7UA39Q1a3ONS1OHn29ljEjaq8zAmm4h8YGzHUCkjU/mdEikkAhYY5phGn6vFZVvapaARQAS0SkPMLX8r+gyJ0iUiUiVQ0NDX0W3pih2jdCI54C5uVboDCjSySBog4oDNovAI73lUZEEoEs4HQk16pqC/An/H0YjcAkJ4++Xitw3ZOqWqmqlbm5uRHchjGDs/dkG9lpyeRmpIzI6+VnppCZmmjPUphRI5JA8S5Q6oxGSsbfOb0pJM0m4DZn+ybgNVVV5/gaZ1RUMVAKbBORXBGZBCAiE4DPAHuda7Y4eeDk+eLgb8+Yodt7so15+Rn4u9CGn4gwb2qG1SjMqDFgoHD6C+4BXgH2ABtVtVpEHhKR651kTwE5IlID3Ausda6tBjYCu4GXgbtV1QtMA7aIyA78gegPqvqSk9f9wL1OXjlO3sbEhKpy4FTbsD+RHSow8sn/2cmY2EocOAmo6mZgc8ixdUHbXcDNfVy7HlgfcmwHsLiP9LX4R1oZE3MnWrvo6PZSkpc+oq87Nz+D1rNHqG9zk5+ZOqKvbUwoezLbmH7U1PtHcZfGIFCAzflkRgcLFMb0IxAo5ox4oPC/nvVTmNHAAoUx/ahpaGfSxCRy0kZ2Jpmc9BSmpKdYjcKMChYojOlHzal25uSmj9iIp2A255MZLSxQGNOPmob2EW92CijNS+dgQ4eNfDIxZ4HCmD6c7ujmdEd3zAJFSV467W4Pp864Y/L6xgRYoDCmD7HqyA6Yk+t/3YMNNpOsiS0LFMb04UC9v38gljUKOBewjIkVCxTG9KGmvp0JSS6mZ02IyevnZaSQkZJoNQoTcxYojOlDTb2/IzshYeRHPIF/zqfZeelWozAxZ4HCmD4EAkUszclNtxqFiTkLFMaE0e72cKK1K/aBIi+dU2fcnOnqiWk5zPhmgcKYMA46zT0lubENFCW5aQDUNnTEtBxmfLNAYUwYsR4aGzDHRj6ZUcAChTFhHKhvJ8klzMqZGNNyzMyeSJJLrJ/CxJQFCmPCqKlvpygnjSRXbP9FEl0JFOWkWY3CxFRE/wUiskpE9olIjYisDXM+RUSed85vFZGioHMPOMf3ichK51ihiGwRkT0iUi0iXw9K/6CIHBOR7c7X54Z+m8ZcmIMxnOMpVImNfDIxNmCgEBEX8DhwDVAG3CIiZSHJ7gCaVXUO8BjwiHNtGf41thcAq4AnnPw8wDdVdT6wFLg7JM/HVLXC+frYynrGDDe3x8vhpo5REyjm5KVzuKmTbo8v1kUx41QkNYolQI2q1qpqN7ABWB2SZjXwrLP9ArBC/PMyrwY2qKpbVQ8BNcASVT2hqu8DqGob/rW4Zwz9dowZukONHfg09h3ZASV5aXh9ypHTNvLJxEYkgWIGcDRov47z39R706iqB2gFciK51mmmWgxsDTp8j4jsEJGnRWRyBGU0JmoO1vvfkGM9NDZgTq5/WVTrpzCxEkmgCDd/QegE+X2l6fdaEUkH/gP4e1U94xz+CVACVAAngO+HLZTInSJSJSJVDQ0N/d+BMReg1ukPmO08wxBrgXIctGcpTIxEEijqgMKg/QLgeF9pRCQRyAJO93etiCThDxLPqeqvAwlU9ZSqelXVB/wb/qav86jqk6paqaqVubm5EdyGMZGpbexgelYqE5MTY10UANJSEpmelWo1ChMzkQSKd4FSESkWkWT8ndObQtJsAm5ztm8CXlP/slybgDXOqKhioBTY5vRfPAXsUdUfBGckItOCdm8Edl3oTRkzFAcb2pk9SpqdAkpsckATQwMGCqfP4R7gFfydzhtVtVpEHhKR651kTwE5IlID3Ausda6tBjYCu4GXgbtV1QssA24FrgozDPZ7IrJTRHYAnwa+Ea2bNWYgqkptQ8eoaXYKKMlNp7ah3ZZFNTERUd3aGaK6OeTYuqDtLuDmPq5dD6wPOfYm4fsvUNVbIymTMcOhvs1Nu9szajqyA0ry0uno9nLqjJupWamxLo4ZZ+zJbGOCHBxlHdkBJb0d2tb8ZEaeBQpjggRmaR1tNQpbP9vEkgUKY4IcbPAvfzo1c3Q17+QGlkW1Dm0TAxYojAlS29BB8ZS0mC1/2pfAsqj2LIWJBQsUxgQ52NBOySiZuiNUSW6aNT2ZmLBAYYyjq8fLsZazzJ4yujqyA0py0znR2kW72xProphxxgKFMY6PmjpQZVTXKAAOWfOTGWEWKIxxBCYDHM01CrCRT2bkWaAwxjHaJgMMNTNnIq4EWxbVjDwLFMY4Dja0j6rJAEOlJLqYmT3RAoUZcRYojHHUNnaMuskAQ5XkpvU+FGjMSLFAYQznJgMsGaXNTgEluenUNnbg9dnkgGbkWKAwhnOTAY7+GkU63R4fx5rPxrooZhyxQGEMo3cywFAleTY5oBl5FiiM4dwyo6NtMsBQs6fYEFkz8ixQGIN/aOxonAww1OS0ZHLSki1QmBFlgcIY6F3VbrRNBhjO7Ny03ocDjRkJEQUKEVklIvtEpEZE1oY5nyIizzvnt4pIUdC5B5zj+0RkpXOsUES2iMgeEakWka8Hpc8WkT+IyAHn++Sh36Yx/RuN62T3pSQ33WoUZkQNGChExAU8DlwDlAG3iEhZSLI7gGZVnQM8BjziXFsGrAEWAKuAJ5z8PMA3VXU+sBS4OyjPtcAfVbUU+KOzb8ywGe2TAYYqyU2nqaOb5o7uWBfFjBOR1CiWADWqWquq3cAGYHVImtXAs872C8AKERHn+AZVdavqIaAGWKKqJ1T1fQBVbQP2ADPC5PUscMPgbs2YyIz2yQBDBUY+1TZarcKMjEgCxQzgaNB+Hefe1M9Lo6oeoBXIieRap5lqMbDVOZSvqiecvE4AeeEKJSJ3ikiViFQ1NDREcBvGhDfaJwMM1Ts5oPVTmBESSaAI17sX+lhoX2n6vVZE0oH/AP5eVc9EUJZzmag+qaqVqlqZm5t7IZca8zGjfTLAUAWTJ5LsSrB+CjNiIgkUdUBh0H4BcLyvNCKSCGQBp/u7VkSS8AeJ51T110FpTonINCfNNKA+0psxZjBG+2SAoVwJQvEUW+3OjJxIAsW7QKmIFItIMv7O6U0haTYBtznbNwGvqao6x9c4o6KKgVJgm9N/8RSwR1V/0E9etwEvXuhNGXMhxsJkgKFK8mxyQDNyBgwUTp/DPcAr+DudN6pqtYg8JCLXO8meAnJEpAa4F2ekkqpWAxuB3cDLwN2q6gWWAbcCV4nIdufrc05eDwNXi8gB4Gpn35hhMVYmAwxVkpvO4dOddHt8sS6KGQciqmur6mZgc8ixdUHbXcDNfVy7HlgfcuxNwvdfoKpNwIpIymXMUI2VyQBDleSm4/UpR053MCcvI9bFMXHOnsw249pYmQwwVGDkU42NfDIjwAKFGdfGymSAoYpzbRZZM3IsUJhxbaxMBhgqPSWRqZmpFijMiLBAYca1sTQZYKiSvLTeGpExw8kChRnXxtJkgKFKctOprW/HPxLdmOFjgcKMW2NtMsBQJbnptLk9NLS5Y10UE+csUJhx61Dj2JoMMFTvyCfrpzDDzAKFGbcCTzaP2RpF7/rZ1k9hhpcFCjNuHahvQ2TsDY0NmJqZysRkFwfrrUZhhpcFCjNu1dS3UzB5AhOSXbEuyqCIiK12Z0aEBQozbtXUt1M6xqe/KMm1yQHN8LNAYcYlj9dHbWMHc8ZoR3ZASW46x1rOcrbbG+uimDhmgcKMS0ebz9Lt8Y39QOGU35ZFNcPJAoUZl2qcDuDSMR4oZufayCcz/CxQmHHpQH0bMHafoQgoyklDBBv5ZIaVBQozLtXUtzM1M5XM1KRYF2VIUpNcFE6eaCOfzLCKKFCIyCoR2SciNSKyNsz5FBF53jm/VUSKgs494BzfJyIrg44/LSL1IrIrJK8HReRYmJXvjImamvr2Md8/EVCSa5MDmuE1YKAQERfwOHANUAbcIiJlIcnuAJpVdQ7wGPCIc20Z/jW2FwCrgCec/ACecY6F85iqVjhfm/tIY8ygqGqcBYp0ahva8flsckAzPCKpUSwBalS1VlW7gQ3A6pA0q4Fnne0XgBUiIs7xDarqVtVDQI2TH6r6OnA6CvdgzAU53tpFZ7c3fgJFXjpuj49jLWdjXRQTpyIJFDOAo0H7dc6xsGlU1QO0AjkRXhvOPSKyw2memhxBemMiFi8jngICU5BYP4UZLpEEinAruoTWcftKE8m1oX4ClAAVwAng+2ELJXKniFSJSFVDQ8MAWRpzzoFT/hFPpflj+6nsgBIbImuGWSSBog4oDNovAI73lUZEEoEs/M1KkVz7Map6SlW9quoD/g2nqSpMuidVtVJVK3NzcyO4DWP8Dja0k52WTHZacqyLEhXZaclMmphkNQozbCIJFO8CpSJSLCLJ+DunN4Wk2QTc5mzfBLym/mW3NgFrnFFRxUApsK2/FxORaUG7NwK7+kprzGAcOBU/HdlwbnLAGnuWwgyTAQOF0+dwD/AKsAfYqKrVIvKQiFzvJHsKyBGRGuBeYK1zbTWwEdgNvAzcrapeABH5FfA2ME9E6kTkDiev74nIThHZAXwa+EaU7tUYVJUDcTTiKWBufjoHTrXZsqhmWCRGksgZoro55Ni6oO0u4OY+rl0PrA9z/JY+0t8aSZmMGYzG9m5az/bETUd2wNz8DH617SgN7W7yMlJjXRwTZ+zJbDOuBJpn4q1GMW+qv2N+38m2GJfExCMLFGZcCczxNNbXoQg1L98ChRk+FijMuLL3ZBtZE5LIz0yJdVGiKic9hSnpyRYozLCwQGHGlb0nzjBvagb+iQPiy7ypGew/ZYHCRJ8FCjNuqCr7T7Vz0dT4anYKmJufwf5TNueTiT4LFGbcqGs+S7vb09vxG2/m5WdwtsfL0ebwBHRMAAAWNUlEQVTOWBfFxBkLFGbcCLTfXzQ1M8YlGR428skMFwsUZtzY57Tfx2uNIjB3lfVTmGizQGHGjb0n2yiYPIH0lIieMx1z0lMSKcyewF6rUZgos0Bhxo29J87EbUd2wLx8G/lkos8ChRkX3B4vtY0dcdvsFDA3P4Pahg66Pb5YF8XEEQsUZlw4WN+B16fMi9OO7IB5UzPw+JTaRptJ1kSPBQozLuw7dQYg/puebOSTGQYWKMy4sPdkG0kuoXhKWqyLMqxmT0knMUGsQ9tElQUKMy7sO9lGSW46Sa74/pNPTkygND+D6uNnYl0UE0fi+7/GGMfu42eYPy2++ycCFkzPZPfxVlvEyESNBQoT9+rbuqhvc1M+IyvWRRkRC6Zn0tjeTX2bO9ZFMXEiokAhIqtEZJ+I1IjI2jDnU0Tkeef8VhEpCjr3gHN8n4isDDr+tIjUi8iukLyyReQPInLA+T558LdnDL3NMAumj5cahT8gVh9vjXFJTLwYMFCIiAt4HLgGKANuEZGykGR3AM2qOgd4DHjEubYMWAMsAFYBTzj5ATzjHAu1FvijqpYCf3T2jRm06mP+N8yycRIo5k/zj3yqPmb9FCY6IqlRLAFqVLVWVbuBDcDqkDSrgWed7ReAFeKf8H81sEFV3ap6CKhx8kNVXwdOh3m94LyeBW64gPsx5jy7jp2hKGcimalJsS7KiMhITaIoZ6J1aJuoiSRQzACOBu3XOcfCplFVD9AK5ER4bah8VT3h5HUCyAuXSETuFJEqEalqaGiI4DbMeFV9opUF46R/ImDB9CyqT1jTk4mOSAJFuKXAQodT9JUmkmsHRVWfVNVKVa3Mzc2NRpYmDrV29nD09Nlx0z8RUDY9k6Onz9J6tifWRTFxIJJAUQcUBu0XAMf7SiMiiUAW/malSK4NdUpEpjl5TQPqIyijMWEFOnTLp4+3GoU/MO625icTBZEEineBUhEpFpFk/J3Tm0LSbAJuc7ZvAl5T/yDuTcAaZ1RUMVAKbBvg9YLzug14MYIyGhPWeBvxFGAjn0w0DRgonD6He4BXgD3ARlWtFpGHROR6J9lTQI6I1AD34oxUUtVqYCOwG3gZuFtVvQAi8ivgbWCeiNSJyB1OXg8DV4vIAeBqZ9+YQdl1vJXpWankpKfEuigjKjcjhfzMFOvQNlER0QouqroZ2BxybF3Qdhdwcx/XrgfWhzl+Sx/pm4AVkZTLmIHsOtZK2ThrdgpYVDCJD4+2xLoYJg7Yk9kmbrV19VDb2MHCcTbiKaCicBK1jR20dlqHthkaCxQmbu2oa0UVFs+cFOuixERFof++P6yzWoUZGgsUJm5td5pdLi4cn4FiUUEWIud+DsYMlgUKE7c+ONLM7Nw0siaMjyeyQ2WkJjEnN90ChRkyCxQmLqkq24+2sLhwfM8pWVE4ie1HW2zKcTMkFihMXKprPktjezcV47R/IuDiwkmc7uimrvlsrItixjALFCYuBZpbFo/T/omAQIf2B9b8ZIbAAoWJSx8caSElMYF5UzNiXZSYumhqBqlJCWw/YoHCDJ4FChOXPjjazMIZWXG/RvZAEl0JLJyRxQdHm2NdFDOGje//IhOXznZ72VnXypLi7FgXZVT4ZFE2O+taOdvtjXVRzBhlgcLEnfePNOPxqQUKx5LibDw+5f0jVqswg2OBwsSdrYdOkyDwiVnje2hswCdmTSZB/D8XYwbDAoWJO9sONbFgehYZ42Tp04FkpCaxYHoW2w41xbooZoyyQGHiitvj5YMjLdbsFGJJcTYfHGnB7bF+CnPhLFCYuLKzrhW3x2eBIsSS4mzcHh8762whI3PhLFCYuBJoh/9kkQWKYIGfh/VTmMGIKFCIyCoR2SciNSKyNsz5FBF53jm/VUSKgs494BzfJyIrB8pTRJ4RkUMist35qhjaLZrx5K2DjczLzyA7LTnWRRlVstOSuWhqBn+paYx1UcwYNGCgEBEX8DhwDVAG3CIiZSHJ7gCaVXUO8BjwiHNtGf41thcAq4AnRMQVQZ73qWqF87V9SHdoxo3Obg/vHmpm+dwpsS7KqLR8bi5VHzXT4fbEuihmjImkRrEEqFHVWlXtBjYAq0PSrAaedbZfAFaIiDjHN6iqW1UPATVOfpHkacwF2XroNN1eH58qzY11UUal5aW5dHt9vFNro5/MhYkkUMwAjgbt1znHwqZRVQ/QCuT0c+1Aea4XkR0i8piIpERQRmN4Y38jKYkJ1pHdh8qiyaQmJfD6/oZYF8WMMZEECglzLHRy+77SXOhxgAeAi4BPAtnA/WELJXKniFSJSFVDg/3hG3jjQANLirNJTXLFuiijUmqSi6Wzc3j9gPVTmAsTSaCoAwqD9guA432lEZFEIAs43c+1feapqifUzw38DH8z1XlU9UlVrVTVytxca2oY7461nOVAfTvLrdmpX8tLcznU2MHR052xLooZQyIJFO8CpSJSLCLJ+DunN4Wk2QTc5mzfBLym/iW1NgFrnFFRxUApsK2/PEVkmvNdgBuAXUO5QTM+vLr7FAAr5ufFuCSj2xXz/IH0T/vqY1wSM5YMGCicPod7gFeAPcBGVa0WkYdE5Hon2VNAjojUAPcCa51rq4GNwG7gZeBuVfX2laeT13MishPYCUwBvhudWzXx7L92n2ROXjqzc9NjXZRRbfaUNGZPSeO/nMBqTCQSI0mkqpuBzSHH1gVtdwE393HtemB9JHk6x6+KpEzGBLR29vBO7Wn+2/LZsS7KqCcirCyfyr+9XktLZzeTJtrzJmZg9mS2GfNe23cKr0/57IKpsS7KmLBqwVQ8PuWPe6z5yUTGAoUZ8zbvPEl+ZgqLZmTFuihjwqKCLKZnpfJy9clYF8WMERYozJjW0tnNn/bV8/lF00lICDfq2oQSEVaVT+PP+xtoPdsT6+KYMcAChRnTXtpxgh6vcsPi0GdATX9uXDyDbo+Pl3aEjnQ35nwWKMyY9tsPjlGal86C6ZmxLsqYUj4jk7n56fzHe3WxLooZAyxQmDHro8YOqg43c+MlM/A/dmMiJSL8H5cU8P6RFg42tMe6OGaUs0BhxqxfvHOYxAT/G565cDcunoErQXj+3aMDJzbjmgUKMyZ1uD1srDrKNQunkZ+ZGuvijEl5mamsKp/Kr7YdsanHTb8sUJgx6TcfHKOty8OXL58V66KMabcvK6aty8ML1ldh+mGBwow5Hq+Pn75Ry8IZWVwyc3KsizOmfWLWZCoKJ/H0Xw7h8fpiXRwzSlmgMGPOb7cf56OmTv72qjnWiR0Fd11RwuGmTn79/rFYF8WMUhYozJjS1ePlR388wILpmVxdlh/r4sSFlQvyubhwEo+9up+uHm+si2NGIQsUZkz56Ru1HDndydprLrLaRJSICPevmseJ1i6e/suhWBfHjEIWKMyY8VFjBz/eUsM15VNtXewou7xkCisX5PMvrx6g1p6rMCEsUJgxocfr4+sbPiDZlcC6z5fFujhx6Z9Wl5OcmMA3//1Duj3WsW3OiWg9CmOCuT1ejjR10ub20On24vH5mJicSFqKi+lZE5g0MSmqzUKqyroXq/mwrpXH/89LmJY1IWp5m3PyMlN5+AuLuPv/e58Hf1fN+hvKo/57PN3RTWN7N6c7uunx+kgQITkxgZz0ZHIzUshISbQmxVEookAhIquAfwFcwE9V9eGQ8ynAz4FPAE3AF1X1I+fcA8AdgBf4O1V9pb88nSVTNwDZwPvAraraPbTbNIPV0OZmz4kzQV9tHGxox+PTPq/JSE2kNC+dS2ZO5pJZk7m0OJuc9JRBvb6q8sjL+/jVtiN87coSrl00bbC3YiJw7aJp7DxWwv/+80EyU5O4f9W8Qb9xt57t4Z3aJt4+2MTuE2fYf6qNls7+Z6vNSElkTn46c/MyKM1Pp2xaJmXTM22BpRgT/9LW/SQQcQH7gauBOvzrXd+iqruD0nwNWKSqd4nIGuBGVf2iiJQBvwKWANOBV4G5zmVh8xSRjcCvVXWDiPxv4ENV/Ul/ZaysrNSqqqoLvXcTpMfro7ahozcg7HaCQmO7uzfN1MxU5k/LYP60TOZNzSBzQhJpyYm4EoSz3V7auno41nKWw02d7Dlxhh3HWun2+BCBRQWT+PS8XD49L4+FM7IimhK8tbOH//HiLn734XFuWTKT/3ljdD/hmvBUlX98cRe/fOcI1y6axv+8cSFZE5IGvM7rU7YfbeFP++p5/UAjO+ta8ClMSHJRNj2TufkZlOalk5eZQvbEZFKSEvD6/DXUxnY3DW1ujp4+y4H6Ng6caqep49znwxmTJjDfCRpl0zJZMD2TgskT7O9hiETkPVWtHDBdBIHiMuBBVV3p7D8AoKr/KyjNK06at0UkETgJ5HJu7ez/FZzOuey8PIGHgQZgqqp6Ql+7L4MNFIF2WFeCkCAM+Y/O4/XR5fHR1eN1vsJsez5+3B0mvcenpCQmkJrkcr4SmJDkYmJKImnJrt5mnsD3tORE0lISmZjsIiUxoc/76PH6qG9zc+pMFydaujjY0M6B+nYOnGqjtqGDbueBq2RXAnPy0pk/LZP50zIom5bJ/GmZTE67sE913R4f1cdbeeNAI1v21bP9aAuqkJ2WzGUlOSwrmcIniyYzKyeN5ER/d5mqcuR0Jy/tOMHP/nKI5s4e7r16Ll+7ssTeFEaQqvL/vl7L917ey6SJydzxV8Vcu3Aas3Im9v4evD6lpr6d7UebeetgE3/e30BLZw8JAotnTmbZnCksK8lh8czJvb/fC9HY7q/N7j7u/+Cy+/gZDja0E6jMZqQkMt8JHIFAlJuRQk5aMqlJrgHz93h9dHR76ez20NntpdPtpaPbE2bfn6bD7f9+tsdHYoKQ5BISXQkkuxJIcvmb0FITz/3PpgT+f0P+l/3HgtP487jQv29VpceruBIE1yDXYok0UETS9DQDCJ41rA64tK80zht8K5DjHH8n5NrAwgHh8swBWlTVEyZ91P3TS7v5xTuHe/cTnR9473dXAgkSvC+4RPD4lB6vjx6vD7fH52wr3n6aYwYS/AeU6JLeAOLu8fW+gUfClSBMTPYHjwnJLrqdfM72eOnsPn+MfMHkCZTmpbN8bm5vbaEkN50k19DHOSQnJrB45mQWz5zM360opandzesHGnhjfyN/OdjIf+440Vvm/IwUkhITaGxz0+GUc/ncXL69ch7ltnLdiBMR7rqihL+aM4VHXt7LP7+yj39+ZR8ZqYlMmpiEx6vUt7l7/+Zz0pK56qI8Pj0vj+WluWRNHLgGMpAp6Sl8qjT3YyPcznZ72XeqzQkerew+fobn3z3K2ZDnP9JTEklN8n9wSnIJCeL/n/J/De7/Ki3ZRZqTrzfoPaDHq3R7/PkN9j1AhN7gEQgq4P9w538txevz4fEqPb5zxwB+fvsSls8d3lGAkQSKcKEq9KfRV5q+jod7F+ov/fmFErkTuBNg5syZ4ZIM6DNl+UzNSsXjVbzq/CJ8iter/u8+/3efL7DvP5/kfILwf09w/hgT/J8ogt7wU4J+6X19qkhJSui3FgD+T25dzht98Cebjm4vnW4P7W7/p56Obs+5T0FuL509XpJc/sAxIcn/R56fmcrUzFTyMlMonpLGxOSRG8+Qk57CjYsLuHFxAarKwYYOdtS1cKixg+MtXfR4fWSnJTM7N40r5uYyKydtxMpmwiufkcUv7riUw00d/KWmiT0nztDu9pAgwtSsFGZPSadi5iSKc9JGZIXBCckuKgonUVE4qfeY16ccburgYEMHTe1umjq6aWx3+z/EBb2BpwT9vyUnJpCW7K+FB2rjE5OdGnvKue8Tk1xMTHFF/Im/x+v7WOuA+2MtCJG3KnR5fAj+D6+JLsGV4H/PcSX433dcCUJSgr8WMytn4jD+xP0ieZeoAwqD9guA0GWxAmnqnKanLOD0ANeGO94ITBKRRKdWEe61AFDVJ4Enwd/0FMF9nOeKublcMcyROBpcCUJair95CQbXKTzaiAhz8tKZk5ce66KYCMzKSRu1gduVIMzOTWd2buz/lgIfHjPibELjSNoX3gVKRaRYRJKBNcCmkDSbgNuc7ZuA19Tf+bEJWCMiKc5oplJgW195OtdscfLAyfPFwd+eMcaYoRqwRuH0OdwDvIJ/KOvTqlotIg8BVaq6CXgK+IWI1OCvSaxxrq12RjHtBjzA3arqBQiXp/OS9wMbROS7wAdO3sYYY2JkwFFPY4ENjzXGmAsX6agnm8LDGGNMvyxQGGOM6ZcFCmOMMf2yQGGMMaZfFiiMMcb0Ky5GPYlIA3B4wISjzxT8DxmOJ3bP8W+83S+M3XuepaoDPnUcF4FirBKRqkiGpsUTu+f4N97uF+L/nq3pyRhjTL8sUBhjjOmXBYrYejLWBYgBu+f4N97uF+L8nq2PwhhjTL+sRmGMMaZfFihiRES+JSIqIlOcfRGRH4lIjYjsEJFLYl3GaBGRfxaRvc59/UZEJgWde8C5530i0u+St2ONiKxy7qtGRNbGujzDQUQKRWSLiOwRkWoR+bpzPFtE/iAiB5zvk2Nd1mgTEZeIfCAiLzn7xSKy1bnn550lFOKCBYoYEJFC4GrgSNDha/Cv11GKf+W+n8SgaMPlD0C5qi4C9gMPAIhIGf4p6RcAq4AnRGTgxY7HAOc+Hsf/ey0DbnHuN954gG+q6nxgKXC3c59rgT+qainwR2c/3nwd2BO0/wjwmHPPzcAdMSnVMLBAERuPAd/m48u8rgZ+rn7v4F/pb1pMShdlqvpfQeugv4N/5ULw3/MGVXWr6iGgBlgSizIOgyVAjarWqmo3sAH//cYVVT2hqu8722343zhn4L/XZ51kzwI3xKaEw0NECoBrgZ86+wJcBbzgJImre7ZAMcJE5HrgmKp+GHJqBnA0aL/OORZvbgd+72zH8z3H872FJSJFwGJgK5CvqifAH0yAvNiVbFj8EP+HPZ+znwO0BH0giqvfdyRrZpsLJCKvAlPDnPrvwD8Anw13WZhjY2ZIWn/3rKovOmn+O/6miucCl4VJP2bueQDxfG/nEZF04D+Av1fVM/4P2PFJRK4D6lX1PRG5MnA4TNK4+X1boBgGqvqZcMdFZCFQDHzo/CMVAO+LyBL8n0AKg5IXAMeHuahR09c9B4jIbcB1wAo9NyZ7TN/zAOL53j5GRJLwB4nnVPXXzuFTIjJNVU84Taj1sSth1C0DrheRzwGpQCb+GsYkEUl0ahVx9fu2pqcRpKo7VTVPVYtUtQj/m8klqnoS2AT8tTP6aSnQGqi6j3Uisgr/WujXq2pn0KlNwBoRSRGRYvwd+dtiUcZh8C5Q6oyEScbfab8pxmWKOqdt/ilgj6r+IOjUJuA2Z/s24MWRLttwUdUHVLXA+R9eA7ymql8CtgA3Ocni6p6tRjF6bAY+h79DtxP4SmyLE1U/BlKAPzg1qXdU9S5VrRaRjcBu/E1Sd6uqN4bljBpV9YjIPcArgAt4WlWrY1ys4bAMuBXYKSLbnWP/ADwMbBSRO/CP7rs5RuUbSfcDG0Tku8AH+ANoXLAns40xxvTLmp6MMcb0ywKFMcaYflmgMMYY0y8LFMYYY/plgcIYY0y/LFAYY4zplwUKY4wx/bJAYYwxpl//PxtoVGCKMACnAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "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": [
       "0.9999999999999996"
      ]
     },
     "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 0x7fd08292c908>"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "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": {},
   "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": [
      "0.0 212.10000000000002\n",
      "10.0 212.10000000000002\n",
      "20.0 212.10000000000002\n",
      "30.0 212.10000000000002\n",
      "40.0 212.10000000000002\n",
      "50.0 212.10000000000002\n",
      "60.0 212.10000000000002\n",
      "70.0 212.10000000000002\n",
      "80.0 212.10000000000002\n",
      "90.0 212.10000000000002\n",
      "100.0 212.10000000000002\n",
      "110.0 212.10000000000002\n",
      "120.0 212.10000000000002\n",
      "130.0 212.10000000000002\n",
      "140.0 212.10000000000002\n",
      "150.0 212.10000000000002\n",
      "160.0 212.10000000000002\n",
      "170.0 212.10000000000002\n",
      "180.0 212.10000000000002\n",
      "190.0 212.10000000000002\n",
      "200.0 212.10000000000002\n",
      "210.0 212.10000000000002\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 0x7fd0828a2e10>"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "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": [
       "Text(0, 0.5, 'Encircled flux')"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "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 0x7fd0827ea278>"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "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": [
       "Text(0, 0.5, 'Ratio of encircled flux')"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "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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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "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.          6.18050404 17.4854638  23.79928199 32.07353691 38.40607579\n",
      " 46.76238796] [ 0.          6.5206172  18.75895207 24.07489413 32.78746844 38.5386345\n",
      " 47.21468159]\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "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": [
      "[ 1.07402639 -0.04610159]\n",
      "1.0550300032613567\n",
      "1.072831254463463\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "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": [
       "Text(0, 0.5, 'Encircled flux')"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "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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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "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 = 0.966450534666256\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: 0.8526531289184243\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": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.image.AxesImage at 0x7f1c10250080>"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "stackhd_im = fits.open('./data/input_data/XMM-LSS_PACS160_v0.9.fits')\n",
    "im=stackhd_im[1].data\n",
    "stackhd = fits.open('./data/output_data/160um/psf_native.fits')\n",
    "psf = stackhd[1].data\n",
    "hd = stackhd[1].header\n",
    "plt.imshow(psf)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Convert units MJy/sr to mJy/pixel: http://coolwiki.ipac.caltech.edu/index.php/Units\n",
    "#psf=psf*2.35045e-2*(np.abs(stackhd[1].header['CDELT1'])*3600)**2\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "#plt.hist(psf.flatten(),bins=np.arange(-0.1,1.,0.005));\n",
    "#plt.yscale('log')"
   ]
  },
  {
   "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": 5,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "resol= np.abs(stackhd[1].header['CDELT1'])/np.abs(stackhd_im[1].header['CDELT1'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.3333333333333333"
      ]
     },
     "execution_count": 6,
     "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": 7,
   "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": 8,
   "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": 9,
   "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\n",
    "    #multiply by ((np.abs(hd['CDELT1'])*3600.)**2)/4.25E10 as map is in units of MJy/sr\n",
    "    encircled_flux[i] = np.sum(psf[idj, idi])*((np.abs(hd['CDELT1'])*3600.)**2)/4.25E10"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-1.0000000242"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "hd['CDELT1']*3600."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'Encircled flux')"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "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": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.003649331\n"
     ]
    }
   ],
   "source": [
    "# This is clearly. \n",
    "print(np.median(psf[0:5,:]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'Encircled flux')"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "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": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "#Lets do a linear fit to the outer part of the curve to determine the backgound\n",
    "p = np.polyfit(nbpix[250:], encircled_flux[250:], 1)\n",
    "bkg = p[0]/resol**2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2069.0"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "nbpix[250]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "4.1303692677650503e-13\n"
     ]
    }
   ],
   "source": [
    "print(bkg)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[2.47154472e-11 1.21376290e-10 2.15928256e-10 ... 6.72163765e-09\n",
      " 6.72138992e-09 6.72138561e-09]\n"
     ]
    }
   ],
   "source": [
    "print(encircled_flux)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "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": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'Encircled flux')"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "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": 20,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "f = open('./data/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": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x7f1c0f43ab70>"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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T2qDkGPIyk5kxeiDDByQyYkAiuenxWktQqo/RZBFuFj9qO7ITBsJ3noO8i3rs1FUNLazeWcXKokq+LqpiVVEVOysb2vZnp8YxenASV0wcwujByeRlJpGeECQzpSkV5jRZhAuv104H+cE9dnazWa9BVPwRn66+uZXVO6tZVVTJqqIqvt5Zxda9dW377f0HKVx9ylDGDE5hVGYSybHunngnSikHaLIIBw0V8Nr1sPnfMPJCmPnoYSWKxhYP63fXtCWGVUWVbC7Z38cwKDmGMYOTuWxCFmMGJ3NCVjIpcQGcLlIp1es0WYS6+nL4x6VQ/KW9Czv/um77J3ZXNbJsWzkF28pZvqOCDbtraPHYzJAaH8UJWclMHz2IE3yJoX9STG+8E6WUgzRZhLKGCnj8FKjZZQf+G/vdQw7xeg2bS2t9yaGCZdvKKaqw/Qyxbhdjh6Tww1OP4cSsZMZkJTM4JVZvXFMqDGmyCFV7N8Hcq22iOOu/DkgUe2ub+HRTKQs3lLJo81721jYDkJ4QzcScflw7JZeJOf0YOShJL1VVSgGaLELT9s/hufMhwg3fnQsjzqWwvJ731uzmvTW7KdhegTG2Sem04emcemw6J+Wmkp0ap7UGpVSHNFmEmpYGePWHkDCQ2qvm8VZRHK89/jkF2ysAGDkoidumDWfa8QPIy0zSITCUUn7RZBFKdi73NT0V8+TQB3jgsa00tXo5tn8C/zH9ON+YSUd+uaxSKnwFNFmIyHTgz4ALeMoYc/9B+7OBvwEpvmN+ZYxZEMiYQpXZshD+fhEV0o/fNt/KR1uGcMn4wVwxcQgnZiVr85JS6qgELFmIiAt4FPgWUAQsE5H5xpi17Q77LTDXGPO4iIwCFgA5gYopVC1bvZ6Rr32XOm8SN0Tfx4xz87l34hC910Ep1WMCWbM4CdhsjNkCICIvATOB9snCAEm+5WSgOIDxhJyte+uYP/cZrtrzAAlSy2eTnuWVc2YSHdk356BQSgWvQCaLwUBhu/UiYNJBx9wN/EtEfgLEA8E3JZsDGpo9PPLhJnYumsMfXY8RLa00X/kK5x5/jtOhKaVCVCAvou+okfzgKe2vAp4zxmQBM4C/i8ghMYnIbBEpEJGC0tLSAIQaPJZvL2fGI5+y6pM3eCTyYaKSBxBx/b+J0kShlAqgQCaLImBIu/UsDm1m+iEwF8AYsxiIAdIPPpEx5gljTL4xJj8jo2/M4Nbbmlu93LdgHZf9ZTGDm7fxXOJfIeN4XDcuhKwJToenlApxgWyGWgYMF5FcYCdwJXDweBM7gGnAcyIyEpsswrvq0IHC8np+MucrVhRW8nzWW5y+dw644+2ERfFpToenlAoDAUsWxphWEbkFeA97Wewzxpg1InIPUGCMmQ/8HHhSRG7HNlFdY4w5uKkqrH20voTbXvoKY+DVMyvIXzwHhkyCS5+ClGynw1NKhQkJtrI5Pz/fFBQUOB1GwBljeHzhN/zpvQ2MGpTE02d5GLjgh5A0CK7/ECL1slillP9EZLkxJv9In693cPdBTa0e/uPVVby5opgLThjEwylziXz1cUjOhkuf1kShlOp1miz6mKr6Fmb/vYAlW8v55TkjuCnuA+Tdx+GEK+H8ByA60ekQlVJhSJNFH7KrqoEfPL2UbWV1/PnKscxsehve+U8YMhnOu18ThVLKMZos+ohte+v43lNLqGpo4W/XncQpFfPh3V9DbKqdLzs6wekQlVJhTJNFH7Bhdw2znl5Cq8fLnBsmM2bTY7DwfttHMftjTRRKKcfpNGgOW1VUyRVPLEaAuTeezJjy92yiyD0dfrxI76NQSvUJWrNw0NKt5Vz33DJS4ty8eP1ksss/h3k3QuoxMGseuPSfRynVN2jNwiHLtpVzzbNLGZAUzas/OoXsbXPhxe9AylCYdqcmCqVUn6IlkgOWb6/gmmeWMjA5hjmzJ9N/29vw1m0w7Cw7hEeUzmanlOpbNFn0sq92VHD1M0vpnxTDnBsm03/XJzD/VsgcD999RWsUSqk+SUumXrSqqJIfPLOU1PgoXrxhEgN2L4QXL7c7ZzygiUIp1Wdp6dRLVu+sYtZTS0iOdTNn9mQGbXkd3rzJ9lFc9y4kZTodolJKdUqTRS9YW1zNrKeXkBjjZs4Nkxlc+hm8/VMYOAau+SfEJDsdolJKdUmvhgqw7WV1/OCZpcS6Xcy5YTJDalbCa9dBZCx8/01NFEqpoKDJIoBKa5r4wTNLafV6+fsPJ5H9zQvw7HQQF1ypExcppYKHNkMFSE1jC9c8u5SS6iZevGESxzaugXd/BcPPgcufB3es0yEqpZTftGYRAE2tHm78+3I27K7h8VnjGdewBOZcCYmZcMmTmiiUUkFHaxYBcPf8NXz+TRkPXn4iU+v/BW/ebHdc8XeITXE2OKWUOgKaLHrYi0t2MGdpITefOYxLWhbAv34L6cfB9e9rZ7ZSKmhpM1QPWr69grvmr+aMERn8bIIb3vklDDkJrn5LE4VSKqhpsughJdWN/PgfyxmUHMujZxhcT51ld5z2c0gc4GxwSil1lLpNFiIyqoNtUwMSTZAyxvCzuSupaWxl7rhVJPzjPIhKgKvfhmFnOh2eUkodNX9qFnNF5D/FihWR/wPuC3RgweSlZYUs2ryX/56WysAv/tuOHvvjzyD3NKdDU0qpHuFPspgEDAE+B5YBxcCUQAYVTIorG/jDP9cxLSeaS3bcB55mOPsuvepJKRVS/LkaqgVoAGKBGGCrMcYb0KiChDGGO+Z9TY63kL/WP4zsLoTh50L/Q1rulFIqqPlTs1iGTRYTgVOBq0Tk1YBGFSTmfbWThRv28ET6S0Q2VcNVL8P35kKEy+nQlFKqR/lTs/ihMabAt7wbmCki3w9gTEGhtqmVexes5/aMAjIrlsEZ/wnHTXc6LKWUCgh/kkWJiGQftG1hIIIJJk8s/Ibo2iJ+FPk8ZIyEqb92OiSllAoYf5LFPwEDCLbPIhfYAOQFMK4+raSmkSc/3cLLaS/jriuHy54EEafDUkqpgOk2WRhjxrRfF5HxwI0BiygI/OXjLdzMy5xQ9zmc9V9w7NlOh6SUUgF12GNDGWO+FJGJgQgmGJRUN7JyyYe8FjkPxn3f3qGtlFIhrttkISI/a7caAYwHSv05uYhMB/4MuICnjDH3d3DM5cDd2KaulcaY7/pzbqc8+ck3/CrieTzRKbim36fNT0qpsOBPzSKx3XIrtg/jte6eJCIu4FHgW0ARsExE5htj1rY7Zjjwa2CKMaZCRPofTvC9rbqxhcXLlnJHxAaYeh9EJ3b/JKWUCgH+9Fn87gjPfRKw2RizBUBEXgJmAmvbHXMD8KgxpsL3WiVH+Fq94uWlhYxp/Rrc2BnvlFIqTHSaLETkLWzTUIeMMRd2c+7BQGG79SLs0CHtjfC91mfYpqq7jTHvdnNeR3i9huWL3uG+6NchKRvShjkdklJK9ZquahYPHOW5O2rMPzj5RALDgalAFvCpiIw2xlQecCKR2cBsgOzsg2/56B2fb97L75vuJyo+yc6hrX0VSqkw0tVwH3caYxYCM4wxCw9++HHuIuwAhPtkYQchPPiYN40xLcaYrdj7N4YffCJjzBPGmHxjTH5GRoYfL93z1nzyKhlSTdTUX0DmOEdiUEopp3SVLAaJyBnAhSIyTkTGt3/4ce5lwHARyRWRKOBKYP5Bx7wBnAkgIunYZqkth/82AquqoYUzCh+jNHoo7vF9+mItpZQKiK6aoe4EfoWtEfwvBzYrGeCsrk5sjGkVkVuA97D9Ec8YY9aIyD1AgTFmvm/fOSKyFvAAvzTGlB3xuwmQ95at5XLZwe7Rv4TIaKfDUUqpXtdpsjDGvAq8KiL/ZYz5/ZGc3BizAFhw0LY72y0b4Ge+R5+1oeADAAaMmepsIEop5ZBuhyg/0kQRKjbuqSGqbAMAMuhEh6NRSiln+DOfRVh798stXOBajCclR2/CU0qFrcMeGyrc5H15JyMjdhBxzvNOh6KUUo7p6qa81K6eaIwp7/lw+pZtpbVMav6CjVkXc/yo7u5BVEqp0NVVzWI5++exyAYqfMspwA7svBYh7ZOV6/mBNDJgmN5XoZQKb532WRhjco0xx2Avb/22MSbdGJMGXAC83lsBOqlw9WcA9Bs8wuFIlFLKWf50cE/0XQILgDHmHeCMwIXUN+wtLeHmij9SFZ0J2QcPaaWUUuHFn2SxV0R+KyI5IjJURO4A+tyNcz1ty8J/kCJ1lM/4C8T2czocpZRylD/J4iogA5jne2T4toU015YP2CkDyBlzmtOhKKWU4/yZz6IcuE1EEowxtb0Qk+OaW7146sppThiEROitKEop1W1JKCKn+MZuWutbP1FEHgt4ZA76ckcFcaae+CRtflJKKfCvGeoh4Fx8/RTGmJXA6YEMymmfbiwhRWpJSU1zOhSllOoT/LqD2xhTKAdO9uMJTDh9Q+ua+WTJXhiS73QoSinVJ/hTsygUkVMAIyJRIvILYF2A43JMeV0zp1XNpzImCybe4HQ4SinVJ/iTLH4E3IydU7sIGOtbD0nL1mxgsqylccSF4NKhs5RSCvy7Gmov8L1eiKVPiF3yCCKG9ClXOx2KUkr1GV0NJPh/2LGhOmSMuTUgETmpaieTy15nceK5nDrgeKejUUqpPqOrmkVBr0XRR1SuX0gKrZSOutbpUJRSqk/palrVv/VmIH3BzsJtpADDR4x0OhSllOpT/Lkp730RSWm33k9E3gtsWM6o3rOFehPN8UOznA5FKaX6FH+uhsowxlTuWzHGVAD9AxeScxIq1rEz+hgiI11Oh6KUUn2KP8nCIyLZ+1ZEZChddHwHq6r6ZnJavqEhNc/pUJRSqs/x50aCO4BFIrLQt346MDtwITlj5ZadnC4NJA06xulQlFKqz+kyWYgd42MNMB6YjJ1W9XbfvRchZfWWQk4HBg0c6HQoSinV53SZLIwxRkTeMMZMAN7upZgcsXn7TgCiE1IdjkQppfoef/osvhCRiQGPxEFNrR5MyRq7orPiKaXUIfzpszgTuFFEtgN12KYoY4w5IaCR9aJ1m7fwXxHPUp0ykqTsk50ORyml+hx/ksV5AY/CYXXL/kGq1FI58zGIjHY6HKWU6nO6GhsqyRhTDdT0YjyOyC6cz7qI4YzMHe90KEop1Sd1VbN4EbgAWI69r6L97EcGCIlrTE3JeoY0b+H1Abehg3wopVTHuhob6gLf39zeC6f3VRRtIBVwDz3J6VCUUqrP8mdsqItFJLndeoqIXOTPyUVkuohsEJHNIvKrLo67TESMiPT6PKY7d+4AICcnp7dfWimlgoY/l87eZYyp2rfiGyfqru6eJCIu4FFsB/ko4CoRGdXBcYnArcASf4PuSRUlRQAM12ShlFKd8idZdHSMP1dRnQRsNsZsMcY0Ay8BMzs47vfA/wCNfpyzx8WXrqQ4YhAxcQlOvLxSSgUFf5JFgYg8KCLDROQYEXkI2+ndncFAYbv1It+2NiIyDhhijOny7nARmS0iBSJSUFpa6sdL+8d4WhjRuILClJC+51AppY6aP8niJ0Az8DLwCrYGcLMfz5MOtrWNVisiEcBDwM+7O5Ex5gljTL4xJj8jI8OPl/bPrvVLSaSB1uzTeuycSikVirptTjLG1AGddk53oQgY0m49Cyhut54IjAY+tuMVMhCYLyIXGmN6ZUrXXVtWkQn0HzGhN15OKaWCVrfJQkRGAL8Actofb4w5q5unLgOGi0gusBO4Evhuu+dXAentXudj4Be9lSgAyvbY3JWTndNbL6mUUkHJn47qV4C/AE8BHn9PbIxpFZFbgPcAF/CMMWaNiNwDFBhj5h9JwD2ptmIPHiJwx+nggUop1RV/kkWrMebxIzm5MWYBsOCgbXd2cuzUI3mNI9Xq8ZJQu5Wa6AxSIvzpulFKqfDlTyn5lojcJCKDRCR13yPgkQXYluK9nMpKyjOnOh2KUkr1ef7ULK72/f1lu21BPzZU4bovGCFNxIyc7nQoSinV5/lzNVRIjg1VXbgagIHHjnM4EqWU6vs6bYYSkf9ot/ydg/bdG8igeoOUbqRJoonol+10KEop1ed11WdxZbvlXx+0L6jbbppbvWTVr6UidihEuJwORyml+ryukoV0stzRelApWv1aIUAEAAAVmklEQVQJ+REbKM/9ttOhKKVUUOgqWZhOljtaDyquZU9QaeKJOWW206EopVRQ6KqD+0QRqcbWImJ9y/jWYwIeWaAYQ7+SpXzKiUwfNMDpaJRSKih0NVNeaDbmV24nqaWUnYnfwRUR1K1pSinVa8Lu1mXvts8BaB482eFIlFIqePhzU15Iqd3yBZhY0o850elQlFIqaIRdsqgvK6bKpJE3WAcPVEopf4VdM1RLzV4qSGT4AJ1GVSml/BV2ySKisZyW6H7EuEOz/14ppQIh7JJFbEsFkfFpToehlFJBJaySxd6ijaRSDf1HOh2KUkoFlbBKFmUr3wMg9vizHY5EKaWCS1gli4htC9lt+pF7vA5LrpRShyN8koXXy6CyJXwVOZbkuCino1FKqaASPsli90oSvNXsSjvZ6UiUUirohE2yaNr4AQCe3DMcjkQppYJP2NzB3bDpU7Z5szgmJyRniVVKqYAKm5qFq2wj60w2eZnJToeilFJBJzySRXM98Y272BU5hAFJ0U5Ho5RSQSc8kkX5N0RgaE0djojOYaGUUocrLJJF654NAMRmHu9wJEopFZzCIlmUb/8arxEG5o52OhSllApKYZEsGnetp9BkkJfd3+lQlFIqKIVFsnBXbma7DGZoapzToSilVFAKi2QR11hCY3wmERHaua2UUkcioMlCRKaLyAYR2Swiv+pg/89EZK2IrBKRD0RkaE/H0NrSQoK3hphkbYJSSqkjFbBkISIu4FHgPGAUcJWIjDrosK+AfGPMCcCrwP/0dBzbinfhEkNy2sCePrVSSoWNQNYsTgI2G2O2GGOagZeAme0PMMZ8ZIyp961+AWT1dBBbtm8HYMCAzJ4+tVJKhY1AJovBQGG79SLfts78EHinp4PYubMIgIyBXb20UkqprgRyIMGOepNNhweKzALygQ6HhBWR2cBsgOzs7MMKInHnJwC40o45rOcppZTaL5A1iyJgSLv1LKD44INE5GzgDuBCY0xTRycyxjxhjMk3xuRnZGT4HYC3voJza+axJmUqpOpos0opdaQCmSyWAcNFJFdEooArgfntDxCRccBfsYmipKcDqPzkryRKAztH39LTp1ZKqbASsGRhjGkFbgHeA9YBc40xa0TkHhG50HfYn4AE4BURWSEi8zs53RGRDf9kuXc4g0ed1JOnVUqpsBPQyY+MMQuABQdtu7Pd8tkBe/HGKpIrVrPYXMTs/okBexmllAoHoXsH9/bFROBlZ7+JREWG7ttUSqneELLTqpotC2nCjXuoNkEppdTRCtmf3M2bP6bAM4LR2QOcDkUppYJeaCaLhkqiy9ay2JvHCUN0zm2llDpaoZksanYBsMs1iGMzEhwORimlgl9oJotae8tGYlomka7QfItKKdWbQrKDu7VmD5HAwMwh3R6rlOo9LS0tFBUV0djY6HQoISsmJoasrCzcbnePnjckk0Xp7iIGATlDc5wORSnVTlFREYmJieTk5CCik5H1NGMMZWVlFBUVkZvbs0MchWQbTfmenbSaCEYdc3iDDiqlAquxsZG0tDRNFAEiIqSlpQWk5haSyaK+vJhySSY7TTu3leprNFEEVqA+35BMFnHV31ARM0S/lEqpQ+zevZsrr7ySYcOGMWrUKGbMmMHGjRs7PT4hwf7oLC4u5rLLLgPgueee45Zbjm6A0ocffpj6+vq29RkzZlBZWXlU5wykkEsWe2sayPFsoznt4BlclVLhzhjDxRdfzNSpU/nmm29Yu3Yt9957L3v27On2uZmZmbz66quH9Vper7fT/QcniwULFpCSkuL3+XtbyCWLdV8XEC9NJOaMczoUpVQf89FHH+F2u/nRj37Utm3s2LGMGzeOadOmMX78eMaMGcObb755yHO3bdvG6NGj29YLCwuZPn06xx13HL/73e/ajhk5ciQ33XQT48ePp7CwkB//+Mfk5+eTl5fHXXfdBcAjjzxCcXExZ555JmeeeSYAOTk57N27F4AHH3yQ0aNHM3r0aB5++OEDzn3DDTeQl5fHOeecQ0NDQ2A+qA6E3NVQGUv/hwYTReb4GU6HopTqwu/eWsPa4uoePeeozCTu+nZep/tXr17NhAkTDtkeExPDvHnzSEpKYu/evUyePJkLL7ywy6bspUuXsnr1auLi4pg4cSLnn38+6enpbNiwgWeffZbHHnsMgD/84Q+kpqbi8XiYNm0aq1at4tZbb+XBBx/ko48+Ij09/YDzLl++nGeffZYlS5ZgjGHSpEmcccYZ9OvXj02bNjFnzhyefPJJLr/8cl577TVmzZp1hJ/W4QmtmsX6BRxf+QmvJ80iKk2vhFJK+ccYw29+8xtOOOEEzj77bHbu3Nlt09S3vvUt0tLSiI2N5ZJLLmHRokUADB06lMmTJ7cdN3fuXMaPH8+4ceNYs2YNa9eu7fK8ixYt4uKLLyY+Pp6EhAQuueQSPv30UwByc3MZO3YsABMmTGDbtm1H8a4PT+jULFoa8C74JZu9WewZdb3T0SilutFVDSBQ8vLyOux3eOGFFygtLWX58uW43W5ycnK6vfz04FrHvvX4+Pi2bVu3buWBBx5g2bJl9OvXj2uuuabb8xpjOt0XHR3dtuxyuXq1GSp0ahbFK4ioLuJ/Wy9j/DH+z9OtlAofZ511Fk1NTTz55JNt25YtW8b27dvp378/brebjz76iO3bt3d7rvfff5/y8nIaGhp44403mDJlyiHHVFdXEx8fT3JyMnv27OGdd95p25eYmEhNTc0hzzn99NN54403qK+vp66ujnnz5nHaaacd4TvuOaGTLKqKANjCYMYP7edwMEqpvkhEmDdvHu+//z7Dhg0jLy+Pu+++mxkzZlBQUEB+fj4vvPACxx9/fLfnOvXUU/n+97/P2LFjufTSS8nPzz/kmBNPPJFx48aRl5fHddddd0BCmT17Nuedd15bB/c+48eP55prruGkk05i0qRJXH/99Ywb5/wFO9JVlacvys/PNwUFBYfuWPQQ/Pturkp/jTm3BG62VqXUkVu3bh0jR450OoyQ19HnLCLLjTGHZjQ/hUyfRXP5DupNPBOG6+CBSinV00ImWVTt3sZek8aUY9O7P1gppdRhCZk+C09FIbslnfFD++4dkEopFaxCIlkYr4f4hmK8iYOJjnQ5HY5SSoWckEgWuxY9TyJ1xBzr/OVlSikVioI/WTTXk7joPlZ6j2H4Wd93OhqllApJwZ8svniUxOY9vJr2I/onxTkdjVKqjysqKmLmzJkMHz6cYcOGcdttt9Hc3HxU57zmmmvahuIYP348ixcvBuCLL75g0qRJjB07lpEjR3L33XcDdojzjIwMxo4dy9ixY/nBD35wtG8r4II7WTTX4Vn0Z/7lmUD2uG85HY1Sqo8zxnDJJZdw0UUXsWnTJjZu3EhtbS133HHHYZ3H4/Ecsu1Pf/oTK1as4P777+fGG28E4Oqrr+aJJ55gxYoVrF69mssvv7zt+CuuuIIVK1awYsUKnn/++aN7Y70guJPF2vm4mmt4xns+M8dmOh2NUqqP+/DDD4mJieHaa68F7PhKDz30EM888wz19fWHTGp0wQUX8PHHHwN2EqQ777yTSZMmtdUcOnL66aezefNmAEpKShg0aFDba40aFbzz7AT1fRbmq3+wk4HEDjuV/kkxToejlDoc7/wKdn/ds+ccOAbOu7/T3WvWrDlkiPKkpCSys7PbCvjO1NXVMXr0aO65554uj3vrrbcYM2YMALfffjvHHXccU6dOZfr06Vx99dXExNiy6uWXX24bqfa2225rS2B9VfDWLMq+QbYv4qWW07gsX4cjV0p1zxjT4RwVnW1vz+Vycemll3a6/5e//CVjx47liSee4OmnnwbgzjvvpKCggHPOOYcXX3yR6dOntx3fvhmqrycKCNaaRUMl5uVZNEosixLO4ba8AU5HpJQ6XF3UAAIlLy+P11577YBt1dXVFBYWMmzYMFauXHnAVKjthxOPiYnB5er8Pq4//elPbXN0tzds2DB+/OMfc8MNN5CRkUFZWVkPvJPeF9CahYhMF5ENIrJZRH7Vwf5oEXnZt3+JiOR0e1Jj4OVZmNKN3ND0Uy6ZehJuV/BWkJRSvWfatGnU19e3dSh7PB5+/vOfc8011xAXF0dOTg4rVqzA6/VSWFjI0qVLj+r1/vnPf7bNT7Fp0yZcLlefnme7KwGrWYiIC3gU+BZQBCwTkfnGmPbTRP0QqDDGHCsiVwJ/BK7o8sSV22HbZrwX/ZXLzGmcmzcwQO9AKRVq9g1RftNNN/H73/8er9fLjBkzuPfeewGYMmUKubm5jBkzhtGjRzN+/Pijer2///3v3H777cTFxREZGckLL7zQZe2kLwvYEOUicjJwtzHmXN/6rwGMMfe1O+Y93zGLRSQS2A1kmC6Cys90mYJXHoIptwYkbqVU4OgQ5b0jEEOUB7L9ZjBQ2G69yLetw2OMMa1AFZDW5VkT+sMpP+m5KJVSSnUrkMmio0sLDq4x+HMMIjJbRApEpKC0KQq6uWpBKaVUzwpksigC2s9ElAUUd3aMrxkqGSg/+ETGmCeMMfnGmPyMDJ1fWymlelsgk8UyYLiI5IpIFHAlMP+gY+YDV/uWLwM+7Kq/QikV/PS/eGAF6vMNWLLw9UHcArwHrAPmGmPWiMg9InKh77CngTQR2Qz8DDjk8lqlVOiIiYmhrKxME0aAGGMoKytru0u8JwXsaqhAyc/PNwUFBU6HoZQ6Ai0tLRQVFR1ws5vqWTExMWRlZeF2uw/YfrRXQwXnHdxKqaDkdrvJzc11Ogx1BPTWZ6WUUt3SZKGUUqpbmiyUUkp1K+g6uEWkBtjgdBx9RDqw1+kg+gj9LPbTz2I//Sz2O84Yk3ikTw7GDu4NR9OjH0pEpEA/C0s/i/30s9hPP4v9ROSoLiPVZiillFLd0mShlFKqW8GYLJ5wOoA+RD+L/fSz2E8/i/30s9jvqD6LoOvgVkop1fuCsWahlFKqlwVVsuhuTu9QJSJDROQjEVknImtE5Dbf9lQReV9ENvn+9nM61t4iIi4R+UpE3vat5/rmcd/km9c9yukYe4OIpIjIqyKy3vf9ODlcvxcicrvv/8dqEZkjIjHh9L0QkWdEpEREVrfb1uF3QaxHfGXpKhHpdv7YoEkW7eb0Pg8YBVwlIqOcjarXtAI/N8aMBCYDN/ve+6+AD4wxw4EPCK9Re2/Djma8zx+Bh3yfRQV2fvdw8GfgXWPM8cCJ2M8k7L4XIjIYuBXIN8aMBlzYaRHC6XvxHDD9oG2dfRfOA4b7HrOBx7s7edAkC+AkYLMxZosxphl4CZjpcEy9whizyxjzpW+5BlsgDMa+/7/5DvsbcJEzEfYuEckCzgee8q0LcBbwqu+QsPgsRCQJOB071D/GmGZjTCVh+r3A3jcW65tILQ7YRRh9L4wxn3Do5HGdfRdmAs8b6wsgRUQGdXX+YEoW/szpHfJEJAcYBywBBhhjdoFNKEB/5yLrVQ8D/wF4fetpQKVvDhUIn+/GMUAp8KyvSe4pEYknDL8XxpidwAPADmySqAKWE57fi/Y6+y4cdnkaTMnCr/m6Q5mIJACvAT81xlQ7HY8TROQCoMQYs7z95g4ODYfvRiQwHnjcGDMOqCMMmpw64muLnwnkAplAPLap5WDh8L3wx2H/nwmmZOHPnN4hS0Tc2ETxgjHmdd/mPfuqjr6/JU7F14umABeKyDZsU+RZ2JpGiq/5AcLnu1EEFBljlvjWX8Umj3D8XpwNbDXGlBpjWoDXgVMIz+9Fe519Fw67PA2mZOHPnN4hydcm/zSwzhjzYLtd7ecwvxp4s7dj623GmF8bY7KMMTnY78CHxpjvAR9h53GH8PksdgOFInKcb9M0YC1h+L3ANj9NFpE43/+XfZ9F2H0vDtLZd2E+8APfVVGTgap9zVWdCaqb8kRkBvZXpAt4xhjzB4dD6hUicirwKfA1+9vpf4Ptt5gLZGP/s3zHGHNwB1fIEpGpwC+MMReIyDHYmkYq8BUwyxjT5GR8vUFExmI7+qOALcC12B+BYfe9EJHfAVdgrx78Crge2w4fFt8LEZkDTMWOtLsHuAt4gw6+C76E+v+wV0/VA9caY7ocaDCokoVSSilnBFMzlFJKKYdoslBKKdUtTRZKKaW6pclCKaVUtzRZKKWU6pYmC6WUUt3SZKGCkoh4RGSFbzjqt0Qk5TCff7eI/MK3fI+InH2U8eSISIOIrDia8/QkEbnCNwT1207HooKfJgsVrBqMMWN9w1GXAzcf6YmMMXcaY/7dAzF9Y4wZezhP8A29HxDGmJexN6YpddQ0WahQsBjfiJkikiAiH4jIlyLytYi0DWMvIneInTzr38Bx7bY/JyKX+Za3iUi6bzlfRD72LZ/hq8ms8I3wmthdUCLyhogs903IM7vd9lpfbWYJcLKITBSRz0VkpYgsFZFEEcnzLa/wTU4z3PfcWe22/3VfshE7MdiXvnN8cPQfqVIHiuz+EKX6Ll9hOQ3fnA5AI3CxMabaV+h/ISLzsQPsXYkd3j0S+BI7hLW/fgHcbIz5zDf6b6Mfz7nON7RCLLBMRF4zxpRhR0RdbYy50zfO2XrgCmPMMt8cFQ3Aj4A/G2Ne8B3jEpGR2OEsphhjWkTkMeB7IvIO8CRwujFmq4ikHsb7UsovmixUsIr19Q/kYAv9933bBbhXRE7HjqM1GBgAnAbMM8bUA/gSyOH4DHhQRF4AXjfGFPnxnFtF5GLf8hDsrGRlgAc7gjDYGs4uY8wygH1Dz4vIYuAO30RPrxtjNonINGACNvEAxGJHEZ0MfGKM2eo7R8iPA6V6nzZDqWDV4OsfGIodRG9fn8X3gAxggm//HiDGt8+fgdBa2f//Yt/zMMbcj23/j8XWVo7v6iS+QQ7PBk42xpyIHcRu3/kajTGefYd2FJcx5kXgQmwt4z0ROct37N98fTVjjTHHGWPu7uwcSvUkTRYqqBljqrBzL//CN+dHMnZypBYRORObTAA+AS4WkVhff8O3OznlNuyvd4BL920UkWHGmK+NMX8ECoAuk4UvjgpjTL0vsUzu5Lj1QKaITPS9TqKIRPpG0d1ijHkEO5z0Cdg5lC8Tkf6+Y1NFZCi2z+YMEcndt72b2JQ6bNoMpYKeMeYrEVmJ7ZN4AXhLRAqAFdjCGGPMlyLysm/bduyQ7x35HfC0iOwbAn6fn/qSjwc7T8I73YT1LvAjEVkFbAC+6CT2ZhG5Avg/X99GA7ZGcgUwS0RagN3APb7+j98C/xKRCKAF24/yha8D/XXf9hLgW93Ep9Rh0SHKleoBYudGf9t3KW+f0X7OD6djUcFNm6GU6hkeILmv3ZQHPAZUOB2LCn5as1BKKdUtrVkopZTqliYLpZRS3dJkoZRSqluaLJRSSnVLk4VSSqlu/X9++bGj/LQTiwAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "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": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x7f1c0f3af4a8>"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "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": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x7f1c0f391f60>"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "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, 60])\n",
    "plt.xlabel('Radius [arcsec]')\n",
    "plt.ylabel('Encircled flux')\n",
    "plt.legend()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [],
   "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 10\"\n",
    "idx, = np.where((radii > 2) & (radii < 10))\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": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.image.AxesImage at 0x7f1c0f2feda0>"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "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": 26,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "rf = 1.005, ff = 1.000, residual = 0.003\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": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x7f1c0eabb3c8>"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "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, 80])\n",
    "plt.xlabel('Radius [arcsec]')\n",
    "plt.ylabel('Encircled flux')\n",
    "plt.legend()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "55713284000.0"
      ]
     },
     "execution_count": 28,
     "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": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [],
   "source": [
    "### As units of map in MJy/sr, divide by 1E6"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [],
   "source": [
    "psfok=psfok/1.0E6\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "55713.285"
      ]
     },
     "execution_count": 44,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.sum(psfok)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Validation\n",
    "To check PSF is reasonable, lets look at a 100 micron source, e.g. `XMM-PACSxID24-1-69605`. We can see from `XMM-LSS_PACS160_v0.9.fits` that it has a flux of 17 Jy. Maximum value in our normalised PSF gives a peak below. Since PSF is double resolution of map, it could also be off centre."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from astropy.table import Table"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {},
   "outputs": [],
   "source": [
    "PACScat=Table.read('./data/XMM-LSS_PACSxID24_v1.fits')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "&lt;Column name=&apos;HELP_ID&apos; dtype=&apos;bytes21&apos; length=69614&gt;\n",
       "<table>\n",
       "<tr><td>XMM-PACSxID24-1-00001</td></tr>\n",
       "<tr><td>XMM-PACSxID24-1-00002</td></tr>\n",
       "<tr><td>XMM-PACSxID24-1-00003</td></tr>\n",
       "<tr><td>XMM-PACSxID24-1-00004</td></tr>\n",
       "<tr><td>XMM-PACSxID24-1-00005</td></tr>\n",
       "<tr><td>XMM-PACSxID24-1-00006</td></tr>\n",
       "<tr><td>XMM-PACSxID24-1-00007</td></tr>\n",
       "<tr><td>XMM-PACSxID24-1-00008</td></tr>\n",
       "<tr><td>XMM-PACSxID24-1-00009</td></tr>\n",
       "<tr><td>XMM-PACSxID24-1-00010</td></tr>\n",
       "<tr><td>XMM-PACSxID24-1-00011</td></tr>\n",
       "<tr><td>XMM-PACSxID24-1-00012</td></tr>\n",
       "<tr><td>...</td></tr>\n",
       "<tr><td>XMM-PACSxID24-1-69603</td></tr>\n",
       "<tr><td>XMM-PACSxID24-1-69604</td></tr>\n",
       "<tr><td>XMM-PACSxID24-1-69605</td></tr>\n",
       "<tr><td>XMM-PACSxID24-1-69606</td></tr>\n",
       "<tr><td>XMM-PACSxID24-1-69607</td></tr>\n",
       "<tr><td>XMM-PACSxID24-1-69608</td></tr>\n",
       "<tr><td>XMM-PACSxID24-1-69609</td></tr>\n",
       "<tr><td>XMM-PACSxID24-1-69610</td></tr>\n",
       "<tr><td>XMM-PACSxID24-1-69611</td></tr>\n",
       "<tr><td>XMM-PACSxID24-1-69612</td></tr>\n",
       "<tr><td>XMM-PACSxID24-1-69613</td></tr>\n",
       "<tr><td>XMM-PACSxID24-1-69614</td></tr>\n",
       "</table>"
      ],
      "text/plain": [
       "<Column name='HELP_ID' dtype='bytes21' length=69614>\n",
       "XMM-PACSxID24-1-00001\n",
       "XMM-PACSxID24-1-00002\n",
       "XMM-PACSxID24-1-00003\n",
       "XMM-PACSxID24-1-00004\n",
       "XMM-PACSxID24-1-00005\n",
       "XMM-PACSxID24-1-00006\n",
       "XMM-PACSxID24-1-00007\n",
       "XMM-PACSxID24-1-00008\n",
       "XMM-PACSxID24-1-00009\n",
       "XMM-PACSxID24-1-00010\n",
       "XMM-PACSxID24-1-00011\n",
       "XMM-PACSxID24-1-00012\n",
       "                  ...\n",
       "XMM-PACSxID24-1-69603\n",
       "XMM-PACSxID24-1-69604\n",
       "XMM-PACSxID24-1-69605\n",
       "XMM-PACSxID24-1-69606\n",
       "XMM-PACSxID24-1-69607\n",
       "XMM-PACSxID24-1-69608\n",
       "XMM-PACSxID24-1-69609\n",
       "XMM-PACSxID24-1-69610\n",
       "XMM-PACSxID24-1-69611\n",
       "XMM-PACSxID24-1-69612\n",
       "XMM-PACSxID24-1-69613\n",
       "XMM-PACSxID24-1-69614"
      ]
     },
     "execution_count": 57,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "PACScat['HELP_ID']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<i>Table length=1</i>\n",
       "<table id=\"table139758482157016\" 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>deg</th><th>deg</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>float64</th><th>float64</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>bytes21</th></tr></thead>\n",
       "<tr><td>35346</td><td>37.189607</td><td>-5.359364</td><td>24.75368</td><td>33.91122</td><td>39.201374</td><td>42.93285</td><td>50.577137</td><td>53.45504</td><td>27.005695</td><td>25.116787</td><td>22.750774</td><td>22.183317</td><td>22.005985</td><td>22.450182</td><td>24.190016</td><td>15.973581</td><td>0.0</td><td>8.490818</td><td>19.619059</td><td>26.27224</td><td>31.353258</td><td>32.08416</td><td>37.23328</td><td>18.46733</td><td>33.844845</td><td>28.466045</td><td>26.428268</td><td>24.746319</td><td>23.908075</td><td>24.301949</td><td>17.06235</td><td>0.0</td><td>XMM-PACSxID24-1-69605</td></tr>\n",
       "</table>"
      ],
      "text/plain": [
       "<Table length=1>\n",
       " XID      RA       Dec    ... F_PACS_160__SKY        HELP_ID       \n",
       "         deg       deg    ...    mJy / pix                         \n",
       "int32  float64   float64  ...     float32            bytes21       \n",
       "----- --------- --------- ... --------------- ---------------------\n",
       "35346 37.189607 -5.359364 ...             0.0 XMM-PACSxID24-1-69605"
      ]
     },
     "execution_count": 58,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "PACScat[PACScat['HELP_ID']=='XMM-PACSxID24-1-69605']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Max PSF = 3.7900 Jy/pix, off pixel Max PSF = 3.0811 Jy/pix\n"
     ]
    }
   ],
   "source": [
    "cpix=np.int((hd['NAXIS1']+1)/2.0)\n",
    "\n",
    "print(\"Max PSF = {:.4f} Jy/pix, off pixel Max PSF = {:.4f} Jy/pix\".format(psfok[cpix-1,cpix-1]*0.0185,psfok[cpix-3,cpix-3]*0.0185))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/mc741/anaconda3/lib/python3.6/site-packages/mpl_toolkits/axes_grid/__init__.py:12: MatplotlibDeprecationWarning: \n",
      "The mpl_toolkits.axes_grid module was deprecated in Matplotlib 2.1 and will be removed two minor releases later. Use mpl_toolkits.axes_grid1 and mpl_toolkits.axisartist provies the same functionality instead.\n",
      "  obj_type='module')\n",
      "WARNING: hdu=0 does not contain any data, using hdu=1 instead [aplpy.core]\n",
      "WARNING: Cannot determine equinox. Assuming J2000. [aplpy.wcs_util]\n",
      "WARNING: Cannot determine equinox. Assuming J2000. [aplpy.wcs_util]\n"
     ]
    },
    {
     "data": {
      "image/png": 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/r5OxAQAALpTP7hkbOHCgBg4cKEn67rvvZIyRw+FQdna2ysvL1bJlS699Z82apcLCQk2dOrXO6gkPD9eBAwd07NgxhYaG6qOPPlLr1q3rbHwAAIAL4Zcb+NesWaMlS5aocePG+slPfqJXXnlFDofD4755eXl644031KpVK6WkpEiSBg0apLS0NGVnZ2v48OGue8lef/11ZWRkuI0RHR2twsJClZSUaP369Zo/f75uuOEGDRs2TAMHDlRQUJCuueYaTZ8+XZK0ZMkSSdK9997roxkAAADwzGEq3s4ISdI9feM08/WnK7VVTFG5TJX28rPt/9xuVO7adq6tcp+K9nJTXqm9Yr9z26scS+VubTUe45/tVZ/iqtsrjVV13yp1ed+uyu3GuJ2Te93ufTzu/88/jTEej3N2rKrHqLy9QsXDcrlvN176nH98T8fw1O9cW+V6Kx6em8+q5yMv7e77V923tmO51rM5v636sbyeTzX7VxynylKv8Rhet5fX3MetvdzzPMu1veaxqu5bdR24Hno6zyp1uPXxcI6eijjX7n58lXvs4r7YXc2V2yuN5+345xZulcEq6jOVHp8bz7jXW3Ust3P1MpaHRWiqtnn5IXCvwcOCrvo7zttid3suqzn2P5849+esmkVeixrM+QvXNVaVf1NM5faqa1DGvV/VPufayysdy3j5ofbUXrXNmPJq+1Td7movP9t+4x1Xavny5Qo0fAI/AACARYQxAAAAiwhjAAAAFhHGAAAALCKMAQAAWEQYAwAAsIgwBgAAYBFhDAAAwCLCGAAAgEWEMQAAAIsIYwAAABYRxgAAACwijAEAAFhEGAMAALCIMAYAAGARYQwAAMAiwhgAAIBFhDEAAACLCGMAAAAWEcYAAAAsIowBAABYRBgDAACwiDAGAABgEWEMAADAIsIYAACARYQxAAAAiwhjAAAAFhHGAAAALCKMAQAAWEQYAwAAsIgwBgAAYBFhDAAAwCLCGAAAgEWEMQAAAIsIYwAAABYRxgAAACwijAEAAFhEGAMAALCIMAYAAGARYQwAAMAiwhgAAIBFhDEAAACLCGMAAAAWEcYAAAAsIowBAABYRBgDAACwiDAGAABgEWEMAADAIsIYAACARYQxAAAAiwhjAAAAFhHGAAAALCKMAQAAWEQYAwAAsIgwBgAAYBFhDAAAwCLCGAAAgEWEMQAAAIsIYwAAABYRxgAAACwijAEAAFhEGAMAALCIMAYAAGARYQwAAMAiwhgAAIBFhDEAAACLAjKMHT58WIMHD1afPn2UkJCghQsXVtr+pz/9SW3atNGxY8csVQgAAHBWkO0CfKFx48YaN26c2rdvr8LCQvXv319du3bVDTfcoMOHD+vjjz/W1VdfbbtMAACAwLwyFhYWpvbt20uSmjVrplatWsnpdEqSpk+frrFjx8rhcNgsEQAAQFKAhrHzHTp0SHv37lWnTp20YcMGhYWFqW3btrbLAgAAkBSgL1NWOHXqlEaMGKHx48ercePGeuONNzR//nzbZQEAALgE7JWxkpISjRgxQomJiYqLi1NOTo4OHTqkpKQkRUdHKy8vT6mpqfruu+9slwoAABqwgLwyZozRM888o1atWumBBx6QJLVp00bbt2937RMdHa1ly5YpNDTUVpkAAACBeWXss88+08qVK5WVlaWkpCQlJSVp8+bNXvffvXu3nnnmGT9WCAAAcFZAXhnr3Lmz9u3bV+0+mZmZrr937NhRHTt29HVZAAAAbgLyyhgAAEB9QRgDAACwiDAGAABgEWEMAADAIsIYAACARYQxAAAAiwhjAAAAFhHGAAAALCKMAQAAWEQYAwAAsIgwBgAAYBFhDAAAwCLCGAAAgEWEMQAAAIsIYwAAABYRxgAAACwijAEAAFhEGAMAALCIMAYAAGARYQwAAMAiwhgAAIBFhDEAAACLCGMAAAAWEcYAAAAsIowBAABYRBgDAACwiDAGAABgEWEMAADAIsIYAACARYQxAAAAiwhjAAAAFhHGAAAALCKMAQAAWEQYAwAAsIgwBgAAYBFhDAAAwCLCGAAAgEWEMQAAAIsIYwAAABYRxgAAACwijAEAAFhEGAMAALCIMAYAAGARYQwAAMAiwhgAAIBFhDEAAACLCGMAAAAWEcYAAAAsIowBAABYRBgDAACwiDAGAABgEWEMAADAIsIYAACARYQxAAAAiwhjAAAAFhHGAAAALCKMAQAAWEQYAwAAsIgwBgAAYBFhDAAAwCLCGAAAgEWEMQAAAIsIYwAAABYRxgAAACwijAEAAFhEGAMAALCIMAYAAGBRkO0CfKGoqEgDBw5UcXGxysrKFB8frxEjRig3N1ejRo3S8ePH1a5dO82YMUPBwcG2ywUAAA1YQF4ZCw4O1sKFC/Xee+8pPT1dW7du1a5duzRz5kwNGTJEa9euVUhIiJYtW2a7VAAA0MAFZBhzOBxq2rSpJKm0tFSlpaVyOBzKyspSfHy8JCklJUUbNmywWSYAAEBghjFJKisrU1JSku666y7dddddioyMVEhIiIKCzr4yGxERIafTablKAADQ0AVsGGvcuLFWrlypzZs3Kzs7W//4xz/c9nE4HBYqAwAAOCdgw1iFkJAQRUVFadeuXTpx4oRKS0slSXl5eQoLC7NcHQAAaOgCMowdO3ZMJ06ckCSdOXNGH3/8sVq3bq2oqCitWbNGkrRixQpFR0fbLBMAACAwP9riyJEjGjdunMrKymSM0d13361evXrphhtu0JNPPqlXX31VN998s9LS0iRJGzZs0J49e/TEE09YrhwAADQ0ARnG2rZtq/T0dLf2yMhIjx9nERMTo5iYGH+UBgAAUElAvkwJAABQXxDGAAAALCKMAQAAWEQYAwAAsIgwBgAAYBFhDAAAwCLCGAAAgEWEMQAAAIsIYwAAABYRxgAAACwijAEAAFhEGAMAALCIMAYAAGBRUE07HD16VDt37tSRI0fUpEkT3XTTTerQoYMaNSLHAQAAXCyvYSwrK0v//d//rYKCArVr106hoaEqLi7W+vXrlZubq/j4eD344INq1qyZP+sFAAAIKF7D2ObNm/XCCy/o6quvdttWWlqqTZs26aOPPlJ8fLxPCwQAAAhkXsPYU0895b1TUJB69+7tk4IAAAAakmrvGdu6davWr18vp9Mph8OhsLAwxcTEqEePHv6qDwAAIKB5DWNTp07VwYMHlZycrPDwcEmS0+nUn//8Z23ZskUTJkzwW5EAAACBymsY27Jli9asWePWfs8993CfGAAAQB3x+vkUwcHBys7OdmvfvXu3mjRp4tOiAAAAGgqvV8Z+97vf6fnnn9epU6cUEREhSTp8+LCaNWum6dOn+61AAACAQOY1jLVv315Lly7Vd999J6fTKWOMIiIi9NOf/tSf9QEAAAS0at9NefLkSe3YsaPSuym7deumkJAQf9UHAAAQ0LzeM5aenq6UlBR98sknOn36tH744QdlZWUpNTVV6enp/qwRAAAgYHm9MvaHP/xBy5cvd7sKdvz4cf3yl79UcnKyz4sDAAAIdNV+27fD4XDv0KiRjDE+KwgAAKAh8Xpl7NFHH1VKSoq6du2qq666SpL07bff6uOPP9Zjjz3mtwIBAAACmdcwlpKSoujoaG3bts31bsqoqCiNHj1azZs392eNAAAAAavad1M2b95cUVFRld5NSRADAACoO17D2N69e/Xcc8/p5MmTioiIkDFGeXl5CgkJ0XPPPaf27dv7s04AAICA5DWMjRs3TpMnT1anTp0qte/atUtPP/203nvvPZ8XBwAAEOi8vpvy9OnTbkFMkm699VadPn3ap0UBAAA0FF6vjPXo0UNDhw5VcnKy67sp8/LylJ6eru7du/utQAAAgEDmNYxNmDBBmzdv1oYNG3TkyBEZYxQeHq6BAweqZ8+e/qwRAAAgYFX7bsqePXsSvAAAAHzI6z1jZWVleuedd/Tqq69q586dlbbNmTPH54UBAAA0BF7D2LPPPqsdO3aoRYsWmjJliqZPn+7atm7dOr8UBwAAEOi8hrHs7Gy9/PLLGjJkiN5991398MMPGj58uIqLi/luSgAAgDriNYyVlJS4/h4UFKQXXnhBbdu21f33368ffvjBL8UBAAAEOq9hrEOHDtqyZUultuHDh6t///765ptvfF4YAABAQ+D13ZQzZ8702J6Wlqa0tDSfFQQAANCQeA1ja9eu9dopODhYkZGRat26tU+KAgAAaCi8hrGNGzd67VRaWqoDBw7o9ttv14QJE3xSGAAAQEPgNYyd/1EWnpSXlysxMbHOCwIAAGhIvN7Av3LlSpWXl3vteOjQIU2aNMknRQEAADQUXq+MFRQUKDk5We3bt1eHDh3UsmVLFRcX6+uvv9aOHTvUsmVLjR492p+1AgAABByvYezXv/61Bg0apKysLO3cuVP79u1TkyZN1Lp1a82YMUNXX321P+sEAAAISNV+UXjjxo3VtWtXde3a1V/1AAAANChe7xkDAACA7xHGAAAALCKMAQAAWFRjGHvllVd04sQJ1+Pjx49r1qxZPi0KAACgoagxjG3ZskUhISGux82bN3f7AnEAAABcmBrDWFlZmYqLi12Pz5w5U+kxAAAALly1H20hSf369dOvf/1rpaamyuFw6K9//auSk5P9URsAAEDAqzGM/eY3v1GbNm20fft2GWP02GOPqXv37v6oDQAAIODVGMYkqXXr1goKCtJdd92l06dPq7CwUM2aNfN1bQAAAAGvxnvG3n33XY0YMULPPvusJMnpdGrYsGE+LwwAAKAhqDGMLV68WEuWLHFdCbv++ut17NgxnxcGAADQENQYxoKDgxUcHOx6XFpa6tOCAAAAGpIa7xn7+c9/rjfeeENnzpzRRx99pLffflvR0dH+qA0AACDg1XhlbMyYMQoNDdVNN92kv/zlL+rZs6dGjhzpj9oAAAACXo1Xxho1aqTevXurd+/eCg0N9UdNAAAADYbXMGaM0ezZs7Vo0SLX40aNGmnQoEEaPny43woEAAAIZF5fply4cKF27typZcuW6ZNPPtGnn36qpUuX6vPPP9eCBQv8WCIAAEDg8hrG0tPT9fLLLysyMtLVFhkZqZdeeknp6el+Ke5CFRUVacCAAerXr58SEhL02muvSTp7dW/WrFmKj49Xnz599NZbb1muFAAANHReX6YsLS31eI9YaGjoJf/xFsHBwVq4cKGaNm2qkpIS3XffferRo4cOHDigw4cP68MPP1SjRo109OhR26UCAIAGzuuVscsuu8xrp+q2XQocDoeaNm0q6WyoLC0tlcPh0JIlSzRs2DA1anT2tK+88kqbZQIAAHi/Mvbll1/q9ttvd2s3xqi4uNinRdWFsrIypaamKicnR/fdd586deqk3NxcffDBB1q3bp1CQ0M1YcIEXX/99bZLBQAADZjXMLZ3715/1lHnGjdurJUrV+rEiRMaNmyY/u///k/FxcVq0qSJli9frrVr12r8+PF6++23bZcKAAAasBo/9LW+CwkJUVRUlLZu3arw8HDFxcVJkmJjY7Vv3z7L1QEAgIYuIMPYsWPHdOLECUnSmTNn9PHHH6tVq1bq3bu3srKyJEmffvopL1ECAADravwE/vroyJEjGjdunMrKymSM0d13361evXrpjjvu0JgxY7Rw4UJdfvnlmjp1qiRp9+7deuedd1yPAQAA/CUgw1jbtm09fhZaSEiI5s2b59besWNHdezY0R+lAQAAVBKQL1MCAADUF4QxAAAAiwhjAAAAFhHGAAAALCKMAQAAWEQYAwAAsIgwBgAAYBFhDAAAwCLCGAAAgEWEMQAAAIsIYwAAABYRxgAAACwijAEAAFhEGAMAALCIMAYAAGARYQwAAMAiwhgAAIBFhDEAAACLCGMAAAAWEcYAAAAsIowBAABYRBgDAACwiDAGAABgEWEMAADAIsIYAACARYQxAAAAiwhjAAAAFhHGAAAALCKMAQAAWEQYAwAAsIgwBgAAYBFhDAAAwCLCGAAAgEWEMQAAAIsIYwAAABYRxgAAACwijAEAAFhEGAMAALCIMAYAAGARYQwAAMAiwhgAAIBFhDEAAACLCGMAAAAWEcYAAAAsIowBAABYRBgDAACwiDAGAABgEWEMAADAIsIty2ftAAAT0UlEQVQYAACARYQxAAAAiwhjAAAAFhHGAAAALCKMAQAAWEQYAwAAsIgwBgAAYBFhDAAAwCLCGAAAgEWEMQAAAIsIYwAAABYRxgAAACwijAEAAFhEGAMAALCIMAYAAGARYQwAAMAiwhgAAIBFhDEAAACLCGMAAAAWBdkuwFfKysrUv39/hYeHa+7cuRo9erT27Nmjyy67TB07dtTkyZN12WWX2S4TAAA0cAF7Zeytt95S69atXY/79eun1atX6/3331dRUZGWLl3q1qegoMCfJQIAAARmGMvLy9OmTZs0YMAAV1vPnj3lcDjkcDh0yy23yOl0uvXbtm2bP8sEAAAIzDA2bdo0jR07Vo0auZ9eSUmJVq5cqe7du7tt8xTQAAAAfCngwtjGjRsVGhqqDh06eNw+adIkde7cWZ07d3bbZozxdXkAAACVBNwN/Dt37lRmZqa2bNmioqIiFRYWasyYMZo5c6Zmz56tY8eOafbs2R77RkRE+LlaAADQ0AXclbHRo0dry5YtyszM1CuvvKIuXbpo5syZWrp0qbZt26ZXXnnF48uXktStWzc/VwsAABq6gAtj3jz33HP6/vvv9R//8R9KSkpyXR3bvXu3nnnmGUlSixYtbJYIAAAaoIB7mfJ8UVFRioqKkiR98cUXHvfp2LGjOnbs6M+yAAAAXBrMlTEAAIBLEWEMAADAIsIYAACARYQxAAAAiwhjAAAAFhHGAAAALCKMAQAAWEQYAwAAsIgwBgAAYBFhDAAAwCLCGAAAgEWEMQAAAIsIYwAAABYRxgAAACwijAEAAFhEGAMAALCIMAYAAGARYQwAAMAiwhgAAIBFhDEAAACLCGMAAAAWEcYAAAAsIowBAABYRBgDAACwiDAGAABgEWEMAADAIsIYAACARYQxAAAAiwhjAAAAFhHGAAAALCKMAQAAWEQYAwAAsIgwBgAAYBFhDAAAwCLCGAAAgEWEMQAAAIsIYwAAABYRxgAAACwijAEAAFhEGAMAALCIMAYAAGARYQwAAMAiwhgAAIBFhDEAAACLCGMAAAAWEcYAAAAsIowBAABYRBgDAACwiDAGAABgEWEMAADAIsIYAACARYQxAAAAiwhjAAAAFhHGAAAALCKMAQAAWEQYAwAAsIgwBgAAYBFhDAAAwCLCGAAAgEWEMQAAAIsIYwAAABYRxgAAACwijAEAAFhEGAMAALCIMAYAAGARYQwAAMCigA5jZWVlSk5O1iOPPCJJ2r59u1JSUpSUlKR7771XX3/9teUKAQBAQxfQYeytt95S69atXY+ff/55zZw5UytXrlTfvn31hz/8wWJ1AAAAARzG8vLytGnTJg0YMKBSe2FhoevPsLAwG6UBAAC4BNkuwFemTZumsWPH6tSpU662qVOnaujQoWrSpImaNWumd99912KFAAAAAXplbOPGjQoNDVWHDh0qtS9YsEDz5s3Tli1blJqaqunTp1uqEAAA4KyAvDK2c+dOZWZmasuWLSoqKlJhYaGGDh2qf/zjH+rUqZMk6Z577tHDDz9suVIAANDQBeSVsdGjR2vLli3KzMzUK6+8oi5dumjOnDk6efKkvvrqK0nSRx99VOnmfgAAABsC8sqYJ0FBQZoyZYpGjBghh8Oh5s2ba9q0aZKkDRs2aM+ePXriiScsVwkAABqagA9jUVFRioqKkiTFxsYqNjbWbZ+YmBjFxMT4uzQAAIDAfJkSAACgviCMAQAAWEQYAwAAsIgwBgAAYBFhDAAAwCLCGAAAgEWEMQAAAIsIYwAAABYRxgAAACwijAEAAFhEGAMAALCIMAYAAGARYQwAAMAiwhgAAIBFhDEAAACLCGMAAAAWEcYAAAAsIowBAABYRBgDAACwiDAGAABgEWEMAADAIsIYAACARYQxAAAAiwhjAAAAFhHGAAAALCKMAQAAWEQYAwAAsIgwBgAAYBFhDAAAwCLCGAAAgEWEMQAAAIsIYwAAABYRxgAAACwijAEAAFhEGAMAALCIMAYAAGARYQwAAMAiwhgAAIBFhDEAAACLCGMAAAAWEcYAAAAsCrJdwKXGYS7ThNGvX/Q4n332WR1UUz81btxYZWVltsuo95jHi8cc1g3msW409Hm84447LnqMoqKiOqjk0kMYq6JJkyZavny57TLqtdTUVOawDjCPF485rBvMY91gHi9eamqq7RJ8gpcpAQAALCKMAQAAWNT4+eeff952EZeaDh062C6h3mMO6wbzePGYw7rBPNYN5vHiBeIcOowxxnYRAAAADRUvUwIAAFhEGKvHysrKlJycrEceeUSSZIzRrFmzFB8frz59+uitt97y2O/mm29WUlKSkpKS9Oijj7rac3NzlZaWpri4OI0cOVLFxcV+OY/66ELnfsWKFYqLi1NcXJxWrFjhat+zZ48SExMVGxurKVOmiAvWnlWd93Hjxik6Otq1nvfu3euxH2v+4lzovDfE9X748GENHjxYffr0UUJCghYuXChJGjx4sHbv3u22/0cffaTU1FQlJiYqNTVV27dvd21btWqVEhMTlZiYqIceekjHjh370fVUfe7O98ILL+i2227z2O/QoUO65ZZbXM/xs88+69oWyM+fNQb11vz5882oUaPM0KFDjTHGLFu2zIwdO9aUlZUZY4z5/vvvPfa79dZbPbaPGDHCrFq1yhhjzMSJE83ixYt9UHVguJC5z8/PN9HR0SY/P98UFBSY6OhoU1BQYIwxpn///mbnzp2mvLzcPPTQQ2bTpk3+O5l6pOq8P/XUU+bDDz+ssR9r/uJcyLw31PXudDrNnj17jDHGnDx50sTFxZn9+/ebQYMGmezsbLf9//a3v5m8vDxjjDH79u0z3bp1M8YYU1JSYrp06WKOHj1qjDHmxRdfNK+99tqPrqfqc1chOzvbjBkzxuvPRm5urklISPC4LZCfP1u4MlZP5eXladOmTRowYICrbcmSJRo2bJgaNTr7tF555ZW1Hs8Yo6ysLMXHx0uSUlJStGHDBknShx9+qL59+6pfv34aOHBgHZ5F/XShc79t2zZ17dpVLVq0UPPmzdW1a1dt3bpVR44cUWFhoW677TY5HA4lJye75v6tt97SPffco8TERD355JP+OcFLlKd5vxis+dq50HlvqOs9LCxM7du3lyQ1a9ZMrVq1ktPplCStXr1aAwYMUHx8vP7nf/5HktSuXTuFh4dLkm688UYVFxeruLhYxhgZY3T69GkZY1RYWKiwsDBJZ6+yTZs2TQMHDlSfPn2UnZ2t4cOHKy4uTrNmzXLV4u25Kysr04wZMzR27NgffX6B/vzZwoe+1lPTpk3T2LFjderUKVdbbm6uPvjgA61bt06hoaGaMGGCrr/+ere+RUVFSk1NVVBQkIYOHarevXsrPz9fISEhCgo6uyQiIiJcv0DmzJmjP/3pTwoPD9eJEyf8cn6Xsgude6fTqYiICNfj8PBwOZ1Ot/bz537evHnKzMxUcHBwg597T/MuSbNmzdLvf/973XnnnRozZoyCg4Pd+rLmL9yFzjvr/exLfXv37lWnTp0knQ1By5Yt0+bNmzV79mwtWLCg0v5r1qzRzTff7JrL559/XomJibr88st13XXX6bnnnnPte9lll2nx4sVauHChHnvsMS1fvlwtWrRQ7969NWTIELVs2dLrc7do0SLFxMS4wl119ScnJ6tZs2YaOXKkOnfu3KCeP3/iylg9tHHjRoWGhrq9vbe4uNj1DQK//OUvNX78eK/9ly9frpdfflnTpk1TTk6Ox/0cDock6bbbbtO4ceP07rvvNuiv8pAubu6Nh/sqHA6H13ZJatOmjcaMGaOVK1eqcePGdXQW9Y+3eR81apRWr16tv/71rzp+/LjmzZvntT9r/se7mHlv6Ov91KlTGjFihMaPH69mzZpJkmJjYyVJ7du31zfffFNp//3792vmzJmaPHmyJKmkpERLlixRenq6tm7dqjZt2mju3Lmu/aOjoyVJN910k2688UaFhYUpODhYkZGRysvL8/rcOZ1OrV69WoMGDaq2/rCwMG3cuFHp6ekaN26cRo8ercLCwgbz/PkbYawe2rlzpzIzMxUdHa1Ro0YpKytLY8aMUXh4uOLi4iSd/aHft2+fx/4Vl8QjIyP1i1/8Ql988YVatmypEydOqLS0VNLZy9sV/2uaPHmyRo4cqcOHDys5OVn5+fl+OMtL08XMfUREhPLy8lyPnU6nwsLC3NrPn/t58+bpvvvu09/+9jelpqa6np+Gxtu8h4WFyeFwKDg4WKmpqR5vkJZY8xfqYua9Ia/3kpISjRgxQomJia7fC5JcV7waNWpUKeTn5eVp+PDhevHFF3XttddKkutNEddee60cDof69Omjzz//3ONY51+VbNSokUpLS70+d3v37lVOTo7i4uIUHR2t06dPu0Li+YKDg9WyZUtJZz/X69prr9VXX33VIJ4/K2zdrIa6kZWV5box86WXXjJLly51taemprrtX1BQYIqKiowxxhw9etTExsaa/fv3G2OMefzxxyvdzLxo0SJjjDFff/21q39SUpL54osvfHdC9ciPnfv8/HzTq1cvU1BQYAoKCkyvXr1Mfn6+McaY1NRU8/nnn1e6IbasrMzk5uYaY4wpLi42d955pzl+/Lifzu7Sdf68O51OY4wx5eXlZsqUKeall15y2581Xzd+7Lw31PVeXl5uxo4da6ZMmVKp/fwb+I8ePWp69epljDHm+PHjJjEx0axevbrS/nl5eaZr166uG/hnzZplpk+f7jbW+c9L1W0Vqu5zPm838B89etSUlpYaY4zJyckx3bp1axDPny3cMxZAhg4dqjFjxmjhwoW6/PLLNXXqVEnS7t279c4772jq1Kk6cOCAnnvuOdfLBb/5zW90ww03SJLGjh2rJ598Uq+++qpuvvlmpaWlSZJmzJihr7/+WsYYdenSRW3btrV2jpeq2sx9ixYt9Nhjj7luph02bJhatGgh6ey9IU8//bTOnDmjHj16qEePHiotLdXYsWNdLw0MGTJEISEh1s7xUjRmzBjl5+fLGKO2bdtq0qRJkljzvlabeW+o6/2zzz7TypUrddNNNykpKUnS2Zd1vVm0aJFycnI0Z84czZkzR5I0f/58hYeHa9iwYRo4cKCCgoJ0zTXXaPr06T6tfcOGDdqzZ4+eeOIJ7dixQ6+99poaN26sxo0ba9KkSQ3i+bOFT+AHAACwiHvGAAAALCKMAQAAWEQYAwAAsIgwBgAAYBFhDAAAwCLCGAArbr75ZiUlJalv37569NFH3b4+ZcGCBerYsaNOnjzpdYwjR47okUcekSR98sknrr+/9957SkxMVGJion71q1/pyy+/dPXZsmWL4uPjFRsbW+mT43Nzc5WWlqa4uDiNHDlSxcXFks5+u8LIkSMVGxurtLQ0HTp0SJK0b98+jRs3rm4mA0CDRhgDYMVPfvITrVy5UqtWrVLz5s21ePHiSttXrVqljh07at26dV7HePPNN12fDXa+n/3sZ1q0aJHef/99/ed//qcmTpwo6ex3A06ePFl//OMflZGRoVWrVunvf/+7JGnmzJkaMmSI1q5dq5CQEC1btkyStHTpUoWEhGjdunUaMmSIZs6cKensV7/k5eXp22+/rZP5ANBwEcYAWHfrrbe6vmxYknJycvTDDz9o5MiRysjI8Npv7dq16tGjh1v77bffrubNm7vGrvj6luzsbF133XWKjIxUcHCwEhIStGHDBhljlJWVpfj4eElSSkqKNmzYIEnKzMxUSkqKJCk+Pl7bt293fT9fr169qq0PAGqDMAbAqrKyMm3fvt31xcfS2atiCQkJ6ty5s7766isdPXrUrV9ubq6aN29e6Xv5PFm2bJkrsDmdTkVERLi2hYeHy+l0Kj8/XyEhIQoKOvulJBEREa5w6HQ6ddVVV0mSgoKCdMUVV7i+q7JDhw767LPPLuLsAYAwBsCSM2fOKCkpSVFRUTp+/Li6du3q2vbBBx8oISFBjRo1UmxsrFavXu3W/7vvvnN9kbE3WVlZWrZsmcaMGSNJ8vSFIw6Hw2Pfivbq+lx55ZU6cuRItTUAQE0IYwCsqLhnbOPGjSopKXHdM/bll1/q4MGDevDBBxUdHe26t8tT/4qb7D358ssvNWHCBM2ZM8cV2iIiIlwvWUpnr3qFhYWpZcuWOnHihEpLSyVJeXl5CgsLc/U5fPiwJKm0tFQnT550fUdfUVGRmjRpUgezAaAhI4wBsOqKK67QhAkTNH/+fJWUlCgjI0OPP/64MjMzlZmZqW3btsnpdOqbb76p1O/66693a6vw7bff6vHHH9eMGTP0b//2b672jh076uDBg8rNzVVxcbEyMjIUHR0th8OhqKgorVmzRpK0YsUK18um0dHRWrFihSRpzZo16tKli+vK2MGDB3XjjTfW+ZwAaFgIYwCsa9eundq2bauMjAxlZGSod+/elbbHxsa63Sh/+eWXKzIyUl9//bWks/eeVdw/9vvf/14FBQWaNGmSkpKSlJqaKunsPV/PPvusHn74Yd1zzz3q06ePK0yNHTtWb775pmJjY1VQUOB6l+aAAQNUUFCg2NhYvfnmm66XPKWzH6fx7//+7z6ZEwANh8N4uiECAOqBdevWac+ePXryySe1cOFCOZ1O/fa3v/XLsYuLizVo0CC9/fbbrhv/AeBCEMYA1GtLly7V559/rv379+vVV1/VNddc45fjHjx4UE6nU1FRUX45HoDARRgDAACwiHvGAAAALCKMAQAAWEQYAwAAsIgwBgAAYBFhDAAAwCLCGAAAgEX/D8CeanxcAW0OAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 720x648 with 2 Axes>"
      ]
     },
     "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('./data/input_data/XMM-LSS_PACS160_v0.9.fits')\n",
    "fig.recenter(PACScat[PACScat['HELP_ID']=='XMM-PACSxID24-1-69605']['RA'],PACScat[PACScat['HELP_ID']=='XMM-PACSxID24-1-69605']['Dec'], radius=0.005)\n",
    "fig.show_colorscale(vmin=-0.001,vmax=0.002,cmap=cmap)\n",
    "fig.add_colorbar()\n",
    "fig.colorbar.set_location('top')"
   ]
  },
  {
   "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": 61,
   "metadata": {},
   "outputs": [],
   "source": [
    "stackhd[1].data=psfok\n",
    "stackhd.writeto('dmu18_PACS_160_PSF_XMM-LSS_20190125_sr.fits',output_verify='fix+warn', overwrite=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.hist(psfok.flatten(),bins=np.arange(-0.01,0.05,0.0005));\n",
    "plt.yscale('log')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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uEWtN4a6uLq1cuVKStHLlSu3bty8VpcUtLy9P8+fPlyRNnz5dc+fOVTgcduX+ZGVl6dprr5UkDQ8Pa3h4WFlZWfrmm29UU1MjSbrjjjtcc6z19/frwIEDWr16taSLq9y5dV+uJFnHmWuD/kqutJZtOnNjzRMZGBgYWXEsLy9Pp06dSnFF8fv999/1888/6+abb3bt/kSjUa1YsUILFy7UwoULVVBQoBkzZig7+2KHco/H45pjbfv27XrkkUd01VUXY2twcNC1+3LJfffdp7q6Or377ruSkvfvxlY/+lS599579ccff1w2vnnzZi1evDjm71hXWMs2nbmxZtP99ddfamxs1JYtWzR9+vRUl5OwadOm6cMPP9SZM2e0ceNG/frrr5e9xw3H2meffaaZM2fqpptuGveRfzfsyyVvv/228vPzNTAwoPr6+phXKJyS1kH/2muvxf07blzL1o01T2TWrFk6efKk8vLydPLkSc2cOTPVJdn2zz//qLGxUcuWLVN1dbUkd++PJM2YMUOlpaX64YcfdObMGQ0PDys7O1v9/f2uONa+++477d+/X93d3RoaGtK5c+f01FNPuXJfLsnPz5d08diqqqpSMBhM2nFm3KWbiooKBQIBRSIRhUIh9fX1acGCBakua1wmrr9bUVGh3bt3S5J2796tysrKFFdkj2VZeuyxxzR37lzV19ePjLtxf06dOqUzZ85Ikv7++2999dVXmjdvnkpLS/Xpp59Kkj744ANXHGsPP/ywuru7tX//frW1tenWW2/Viy++6Mp9kaTz58/r3LlzI3//8ssvVVRUlLTjzLVNzfbu3asnn3xSp06d0owZM3TjjTfq1VdflSTt2LFD7733nqZNm6YtW7a4YrnDzz//XNu3bx9Zf3fDhg2pLsm20WsKz5o1S5s2bdLixYu1efNmnThxQrNnz9bLL7+s6667LtWlTujbb7/VunXrdP31149cC25qatKCBQtctz+//PKLHn30UUWjUVmWpdtvv10PPvigQqGQHnroIZ0+fVo33nijXnjhBeXk5KS6XNt6enq0c+dOtbe3u3ZfQqGQNm7cKOnifZTa2lpt2LBBg4ODSTnOXBv0AAB7jLt0AwAYi6AHAMMR9ABgOIIeAAxH0AOA4Qh6ADAcQQ8AhiPoAcBw/weu7Hoj4IqUdAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.hist(psfok.flatten(),bins=np.arange(-10,50,0.5));\n",
    "plt.yscale('log')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "204.86528"
      ]
     },
     "execution_count": 63,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.max(psfok)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.004794918232074034"
      ]
     },
     "execution_count": 66,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "204*(2.35045e-5*(np.abs(stackhd[1].header['CDELT1'])*3600)**2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.0"
      ]
     },
     "execution_count": 65,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.mean(~np.isnan(psfok))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python (herschelhelp_internal)",
   "language": "python",
   "name": "helpint"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.6"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}
