{
 "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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\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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N8SuE21Sfvl31G1mqX89wfj79RdXOjrjV73tui5bd8bS2hjoHMeqhs2nTpmSHMKY0NzerqmpnZ6defvnl+pvf/CZuvXj/L8Aa7efzVVX776NQp8/hVuA590P+p6q6UUTudt9kJfAw8AsRqcQ5k7jO3XejiDwBbAIiwC2qGhWRQuBRt5/C4yaWp923fExE8txE8Q7wuRPIe8YMundrDxOJafz+iUgYHr8BKp+H0z8DMy6F7c/B6ofgYDX87RPgPXbkzIKSLGIKG/YcYWnZqXWOm7HnG9/4Bn/+85/p6Ojg4osv5sorrxzw90homnFVfQZ4pkfZXd2edwBxu9tV9R7gnh5l64FFvdS/IJGYjEmWte5lorjTir90j5MkPvqfcNonnbLyD8PEufCHf4AX7oaLv3XMLgtKsgB4Z/chSxTmhCVyB/mpsjuzjTlB7+w+TFnueCaM77GgzZ518JqbILqSRJfTbnTKXv8vqHv7mJdy0wIUT0jl3d1Ngxn2kNJRsHLmaHKq/x+WKIw5QRv2NDFvUo8OQ1V4/i4YlwMXfSv+jhfdDePznJvQevzhLijJ4p3dhwcp4qEVDAZpbGy0ZDFMqCqNjY0Eg8GTbsNWuDPmBBxoCVHf1HF8oqh+CWr+Cpd+F4K9DJkNZsJ5X4Zn/hl2vAJTzzv60sLiLP53fT0NzSHy0gPx9x8hiouLqa2tjTudhUmOYDBIcXHxSe9vicKYE/DeHufy0LziHonitR9AeiGc9qm+G1h0A7zy7/DX+45NFJOdfop3dx/mwxUntgjScOP3+ykrK0t2GGYA2aUnY07AhlonUczpfqPd/i3OGcXpN4EvpZc9Xf4gnPl52PEX2Pf+jKZzizLxeoR3a0fH5SczuliiMOYEvLeniam540kPdhvi+tZPwBvo/2yiy6IbwJsC635xtCg1xcu0vPFsqjsywBEbc+osURhzAjbsaWJu9/6JSBg2PAmzL4fxCa5LMT4HZl0O61dA5/tz/1QUZrCp3hKFGX4sURiToMaWEHU9O7KrXoD2QzD/2hNrbPHfOftte/ZoUUVRBvVNHRxsDQ9QxMYMDEsUxiSoqyP7mDOK9U84Q2KnneB9omUfdIbKbvrd0aI5RU67dvnJDDeWKIxJ0Eb3A3zOJLcjO9QMW/8Icz523LQc/fJ4YfZHYdufIOysmT3bXSlvU/3oufHOjA6WKIxJ0Ja9zRRPSCWjqyO78s8QaYc5V51cgxXLobPVaQfIHp9CYWbQzijMsGOJwpgEbd17hFkF6d0KnoXUCVDScx2vBE0517ls1e3yU0VhxtEzF2OGC0sUxiQgFIlS1dDKrAL3slMsCtv/BOUXg/ck71v1+mDmpc4ZRdRZPW1OUQZVDS10dEYHKHJjTp0lCmMSULW/lWhMmdl1RrF7NbQfhBnLTq3h6RdBRxPsWQM4I59iClv3nvhqa8YMFksUxiRgy17nctDRS0/bngWPD6ZfeGoNTz0fxAvbnwe6d2jb5SczfFiiMCYBW/c2k+L1UJY73imofAEmn+VM9HcqUrOgZKmzhgVQMmEcqX4v2/bZGYUZPhJKFCKyTES2ikiliNwR5/WAiDzuvr5KREq7vXanW75VRC5xy4IislpE3hWRjSLyzW71y9w2trtt9jN5jjGDb8veZqbnp+HzeqC1Efa9B2Xn9b9jIqZ/GOrfhZb9eDzCjIlplijMsNJvonCXK30AuBSoAK4XkYoe1W4CDqnqdOB+4F533wqcZVHnAMuAB932QsAFqroAWAgsE5GuVdDvBe5X1XLgkNu2MUm1Ze8RZhW6l51qXnF+Th3ARAFQ9RIAMyams21fy8C0bcwASOSMYilQqarVqhoGVgDLe9RZDjzqPn8SuFBExC1foaohVd0BVAJL3XW9u/4S/O5D3X0ucNvAbXPgF4A15gQcag2z70jo/f6J6r9ASjoULR6YNyiY51zC2vkq4CSKhuaQTeVhho1EEsUkYHe37Vq3LG4dVY0ATUBOX/uKiFdE3gH2A8+r6ip3n8NuG729lzFDaos7Auno0Ngdr0DpOSc/LLYnjxemnAM1bqJwE5JdfjLDRSKJQuKU9VzjsLc6ve6rqlFVXQgUA0tFZG6C7+W8ocjNIrJGRNbYSlpmMG3tPuKpqRYOVjlzNQ2kKefAwWo4UsfMiZYozPCSSKKoBUq6bRcDdb3VEREfkAkcTGRfVT0MvIzTh3EAyHLb6O29uvZ7SFWXqOqSvLy8BA7DmJOzZW8z2eNTnCVKd7j9EwPVkd2l9FznZ81rTMwIkBH02b0UZthIJFG8BZS7o5FScDqnV/aosxK40X1+NfCiOiurrwSuc0dFlQHlwGoRyRORLAARSQU+DGxx93nJbQO3zd+f/OEZc+q27G1m5sR0RARqXoPUbMjvOZ7jFBXMg0Am1PwVEWFmQbqdUZhho99E4fYX3Ao8B2wGnlDVjSJyt4hc4VZ7GMgRkUrgi8Ad7r4bgSeATcCzwC2qGgUKgZdEZD1OInpeVZ922/oK8EW3rRy3bWOSQlXZvq+52x3ZbzpzO3kG+BYkjxemnAU7XwPeH/nkfHcyJrkS6o1T1WeAZ3qU3dXteQdwTS/73gPc06NsPbCol/rVOCOtjEm6+qYOWsNRpuWnOfdPNFbCok8MzpuVnuvc8d28lxkT02lq38X+5hATM4KD837GJMjuzDamD5X7nVHc5flpsHuVU1hyZh97nIKudnevYobboW39FGY4sERhTB+6EsX0/DTnspPHD0ULB+fNCueDNwVq32LGxDTARj6Z4cEShTF9qGxoIWucn5zxKc6MsUULwZ86OG/mC0DhQtj9FjlpAXLTAnZGYYYFSxTG9KFyXwvT89KQaBj2rDv5RYoSVbIU6t6GSNjmfDLDhiUKY/pQ2dDiXHaqXw/R0OAniuLTnffZ+x7l+WlUNbTayCeTdJYojOnFwdYwB1vD7/dPwNCcUQDUvsW0/DRaQhH2HQkN7nsa0w9LFMb04tiO7NUwoRTSJw7um2YUQUYx1K5mep7ToV3VYDPJmuSyRGFML7bvd/oHpuenOf0Gk04bmjcuOR12O2cU8H7CMiZZLFEY04vK/S2k+r0U+VqgaTcUxb1HdOAVnw5Nu8jnEOkBn51RmKSzRGFMLyr3Ox3Znvp3nIKBWn+iP8VOP4XsWcvU/DQ7ozBJZ4nCmF50JQrq1gHi3BA3FArmgnih/h2m56XZGYVJOksUxsTREopQ39Txfv9E3kwIpA/Nm/tTndlp695men4a+46EONLROTTvbUwcliiMiaPKvdwzLXe8c6PdUPVPdClaAHVvMy13HADVDa1D+/7GdGOJwpg4uvoFZo5vhtb9Q9c/0aVoEbQ1Miu16Zh4jEkGSxTGxLF9fwt+r1DSvsUpGPIzCuf9JrVvxe8V66cwSWWJwpg4Kve3UJozHt/ed8DjczqYh1L+HPD48O59h9Kc8XZGYZIqoUQhIstEZKuIVIrIHXFeD4jI4+7rq0SktNtrd7rlW0XkEresREReEpHNIrJRRG7rVv8bIrJHRN5xHx859cM05sRUdc3xtGcd5M8evBlje+MPHu3QnmYjn0yS9ZsoRMQLPABcClQA14tIzwWDbwIOqep04H7gXnffCpw1tucAy4AH3fYiwO2qOhs4E7ilR5v3q+pC93HMynrGDLZQJMrOxlam5413RjwNdf9El6KF7hDZ8exsbCMciSUnDjPmJXJGsRSoVNVqVQ0DK4DlPeosBx51nz8JXCgi4pavUNWQqu4AKoGlqlqvqusAVLUZZy3uSad+OMacuh0HWokpzE87BB2Hh75/okvRImg/xLy0w0Rjyq6DNvLJJEciiWISsLvbdi3Hf6gfraOqEaAJyElkX/cy1SJgVbfiW0VkvYj8VEQmJBCjMQOmar/zgTwzWukUTErWGYWToGbFqgAb+WSSJ5FEIXHKek6Q31udPvcVkTTgKeAfVfWIW/wjYBqwEKgH7osblMjNIrJGRNY0NDT0fQTGnIBqtz+gsH2bs/Rp3uzkBJJfAR4/hW3OyKsqu5fCJEkiiaIWKOm2XQzU9VZHRHxAJnCwr31FxI+TJB5T1d90VVDVfaoaVdUY8GOcS1/HUdWHVHWJqi7Jy8tL4DCMSUz1gVaKMoP492+EvFngS0lOIL4ATKwgZd+7FGUG7YzCJE0iieItoFxEykQkBadzemWPOiuBG93nVwMvqrMs10rgOndUVBlQDqx2+y8eBjar6ve6NyQihd02PwZsONGDMuZUVDW0MDUvDfZtgIJ5yQ2mYD7s28C0PBsia5Kn30Th9jncCjyH0+n8hKpuFJG7ReQKt9rDQI6IVAJfBO5w990IPAFsAp4FblHVKHAOcANwQZxhsN8VkfdEZD3wIeCfBupgjemPqlLd0Mr8rA5o2Zf8RFG4ANoaWZjVQXVDiy2LapLCl0gld4jqMz3K7ur2vAO4ppd97wHu6VH2KvH7L1DVGxKJyZjBsL85REsowqKUWqdgqG+068lNVItSdtEazmHfkRAFmcHkxmTGHLsz25huum5smx6rcQomJjlRTJwDwPRoNWDLoprksERhTDdds7RObN8OmSUwLju5AQXSIXsq+W3bAUsUJjksURjTTVWDs/xpauOm5J9NdCmYR+DARmdZVOvQNklgicKYbqobWpmZ40Matye/I7tLwTzk0A7m5HrsXgqTFJYojOmmqqGFczIaQGPDKFEsAOCc9Hq79GSSwhKFMa6Ozih7Drez0L/LKRg2icKJY4FvN/VNHbSEIkkOyIw1liiMcdU0tqIK07UGUtIha0qyQ3KkF8C4XKZGnDmfdtjlJzPELFEY4+qaDDC/dZtz/4RnmPx5iEDBPHJbtgE28skMvWHyl2BM8lU3tCDEGHdo8/C57NSlYB6BQ1sJeKKWKMyQs0RhjKuqoYUlGUeQcOvwGRrbpWA+Eg1zTuZBSxRmyFmiMMZVfaCVc9PqnY3hdkZROB+As8fXHb0p0JihYonCGN6fDHChfxeI11knezjJmQ6+VOb5dlF9oJVozCYHNEPHEoUxvD8Z4NToDsgtB39qskM6lscLEyso7awmHImx51B7siMyY4glCmN4fyRRXtswuiO7p4J55DRvAdT6KcyQskRhDM4yo1k0E2yrH9aJwhduoohGSxRmSFmiMAZnaOxCv7sGxXAb8dSlwOnQXjquzhKFGVKWKIzBmQzwnPRhOuKpS34FIJw5bs/RmwONGQoJJQoRWSYiW0WkUkTuiPN6QEQed19fJSKl3V670y3fKiKXuGUlIvKSiGwWkY0iclu3+tki8ryIbHd/Tjj1wzSmb1UNLcz37Ya0AkjLT3Y48QXSIHsqcz277IzCDKl+E4WIeIEHgEuBCuB6EanoUe0m4JCqTgfuB+51960ArgPmAMuAB932IsDtqjobOBO4pVubdwAvqGo58IK7bcyg6ZoMcGqkOvlLn/anYB6Tw1U0toY51BpOdjRmjEjkjGIpUKmq1aoaBlYAy3vUWQ486j5/ErhQRMQtX6GqIVXdAVQCS1W1XlXXAahqM7AZmBSnrUeBK0/u0IxJTE1jKz6NkNNeM3wvO3UpmEdGRy1ptFF9wM4qzNBIJFFMAnZ3267l/Q/14+qoagRoAnIS2de9TLUIWOUWTVTVereteiDudQARuVlE1ojImoaGhgQOw5j4qva3Ui61eLRzBCQKp0N7luyyfgozZBJJFBKnrOdtob3V6XNfEUkDngL+UVWPJBDL+42oPqSqS1R1SV5e3onsaswxqhtaqPDsdDYmDvdE4cQ332f9FGboJJIoaoGSbtvFQF1vdUTEB2QCB/vaV0T8OEniMVX9Tbc6+0Sk0K1TCOxP9GCMORlVDS0sCe4BXyrkTEt2OH1LL4BxOZwe3GOJwgyZRBLFW0C5iJSJSApO5/TKHnVWAje6z68GXlRVdcuvc0dFlQHlwGq3/+JhYLOqfq+Ptm4Efn+iB2XMiag+0OqMeJo4x5kqYzhz16ao8Oy0yQHNkOk3Ubh9DrcCz+F0Oj+hqhtF5G4RucKt9jCQIyKVwBdxRyqp6kbgCWAT8Cxwi6pGgXOAG4ALROQd9/ERt63vABeJyHbgInfbmEHhTAbYQtlIGPHUpWAek8I11B5sJhyJJTsaMwb4Eqmkqs9IpN1gAAAe50lEQVQAz/Qou6vb8w7gml72vQe4p0fZq8Tvv0BVG4ELE4nLmFO1vzlERmgfqdI8/DuyuxTMx6dhpmgduw62Mj0/PdkRmVHO7sw2Y1pV945sd0TRsOdOMVIhNVTayCczBCxRmDGtqqGVCtmJIu4UGSNAbjnqDVDh2Wkd2mZIWKIwY1p1Qwtzfbsge6ozRcZI4PUj+bNZ5N9ticIMCUsUZkyrbmhlnncXMlI6srsUzGOm7KRqvyUKM/gsUZgxbe/+fRTG9o6c/okuBfPIjDXR3LAbZyS6MYPHEoUZszo6o2Qe2eZsjMBEATC5s4qG5lCSgzGjnSUKM2btONDKbOka8TRChsZ2mTgHgArZSaX1U5hBZonCjFnV7oinSDDbmRpjJAlmEsmc4o58siGyZnBZojBj1vb9zVR4apCCec7UGCOMt2g+czy7rEPbDDpLFGbMqt53mBmePXiLRlj/hEsmzmOK7KV2n02zbwaXJQozZoX2biVA58jryO5SMA8PiqdhU7IjMaOcJQozJkWiMdIPb3Y2RlpHdhc37vzWbbSHo0kOxoxmlijMmLT7UDsztIaoJwVyypMdzsnJLCbsz2S27LJlUc2gskRhxqTK/S1USA0d2bPAm9AkysOPCJ15FTbyyQw6SxRmTNq+7wgVnp34J43Q/glXoHgBs2QX1fuakh2KGcUsUZgxqaFuB9nSQsqkhckO5ZT4ihaQKmGa67YmOxQziiWUKERkmYhsFZFKEbkjzusBEXncfX2ViJR2e+1Ot3yriFzSrfynIrJfRDb0aOsbIrInzsp3xgwY2ef+2o3Ujuwubvz+hg39VDTm5PWbKETECzwAXApUANeLSM+J+28CDqnqdOB+4F533wqcNbbnAMuAB932AB5xy+K5X1UXuo9neqljzElRVTK7Rjy5U2GMWLkziYqPCc3biMVsckAzOBI5o1gKVKpqtaqGgRXA8h51lgOPus+fBC4UEXHLV6hqSFV3AJVue6jqK8DBATgGY05IXVMH07WGI+MmQ2CELyPqS+FI2jRmag17DrcnOxozSiWSKCYBu7tt17plceuoagRoAnIS3DeeW0VkvXt5akIC9Y1JmDPiaSedeSP8bMIVyZ9rq92ZQZVIoog3CU7Pc9ze6iSyb08/AqYBC4F64L64QYncLCJrRGRNQ4NNYWASV7NnL2WefaSWjOyO7C7jJi8kXw5TV7sz2aGYUSqRRFELlHTbLgbqeqsjIj4gE+eyUiL7HkNV96lqVFVjwI9xL1XFqfeQqi5R1SV5eXkJHIYxjvbadwEYN3lRkiMZGOMmOwkv5B6XMQMtkUTxFlAuImUikoLTOb2yR52VwI3u86uBF9VZdmslcJ07KqoMKAdW9/VmIlLYbfNjgA3nMAPKt3+j82TiCFv+tBfSNfLpgM35ZAZHv7ekqmpERG4FngO8wE9VdaOI3A2sUdWVwMPAL0SkEudM4jp3340i8gSwCYgAt6hqFEBEfgWcD+SKSC3wdVV9GPiuiCzEuURVA/yfgTxgM7apKrnNm2nxZZGWUZTscAZG6gQO+SeS07wFVUVG4JTpZnhLaO4Cd4jqMz3K7ur2vAO4ppd97wHuiVN+fS/1b0gkJmNOxoGWMDNjlRzOnEPaKPpAbc6azfR922loCZGfHkx2OGaUsTuzzZhSXXeActlDrGBBskMZUFI4j6lSx/ZaG9hhBp4lCjOmNFavxScx0qeenuxQBlRW6SK8ojRUv5PsUMwoZInCjCmR2nUAZE0bXYkivXQxANHat5MciRmNLFGYMWV84waaPJlIZnGyQxlYE0pp9qSTftAGCZqBZ4nCjBmqSkn7VvaPnw2jqCMbABH2pc2mpGOLzflkBpwlCjNm7Gk4yFRqCeWP8BljexHKW0A5u6ltaEx2KGaUsURhxoy6rWvwSYzglCXJDmVQpJYuwScx6re+lexQzChjicKMGe071wJQOPusJEcyOCbOco4rtHNNkiMxo40lCjNmpOxfzyEyGJ87OdmhDIrxuZNpZAKB/TbnkxlYlijMmDGxZRO1qTNHX0d2FxFqU2dS0Lol2ZGYUcYShRkTQu0tTI7upiV7dEwE2JvmnHmURGsJtzYlOxQziliiMGNC3Za38EkMb/HiZIcyqLwlp+ERZe+WN5MdihlFLFGYMaG56g0AcmaeneRIBlfujDMBOFLd52z+xpwQSxRmTPDVrWWP5jJ5ytRkhzKoppRMoVZz8dbbnE9m4FiiMGNCftN7VKbMwu8d3b/yKT4PNSkzyD6yMdmhmFFkdP/VGAPQvJfc6D4OTRhdU4v3pmnCPCZG6tFWu0PbDAxLFGbUO7z9dQC8k0fXjLG98ZQ4d553HbcxpyqhRCEiy0Rkq4hUisgdcV4PiMjj7uurRKS022t3uuVbReSSbuU/FZH9IrKhR1vZIvK8iGx3f044+cMzBpq2v0lYveTPWJrsUIZE3syziaiHpm2vJjsUM0r0myhExAs8AFwKVADXi0hFj2o3AYdUdTpwP3Cvu28FzvrZc4BlwINuewCPuGU93QG8oKrlwAvutjEnzVu3hk06hdmT85MdypCYOXkim3QKvj0255MZGImcUSwFKlW1WlXDwApgeY86y4FH3edPAheKs8L7cmCFqoZUdQdQ6baHqr4CHIzzft3behS48gSOx5hjRSPkHtlIVcpsMoL+ZEczJNKDfranVJB3ZCNEI8kOx4wCiSSKScDubtu1blncOqoaAZqAnAT37Wmiqta7bdUDcb8GisjNIrJGRNY0NNg6waYXDZsJagdHchcmO5Ih1ZS7mIB2wD5byMicukQSRbyJcXqujNJbnUT2PSmq+pCqLlHVJXl5eQPRpBmF2qpXAeCfMjY6srt4p5wBQHv1G0mOxIwGiSSKWqCk23YxUNdbHRHxAZk4l5US2benfSJS6LZVCOxPIEZj4mqpfJ1GTWfy1DnJDmVITSmbQb1m01r5WrJDMaNAIoniLaBcRMpEJAWnc3pljzorgRvd51cDL6qquuXXuaOiyoByoL+5Bbq3dSPw+wRiNCauQP1q1sRmMmdSZrJDGVJzJmWxNlZOYK+tTWFOXb+Jwu1zuBV4DtgMPKGqG0XkbhG5wq32MJAjIpXAF3FHKqnqRuAJYBPwLHCLqkYBRORXwBvATBGpFZGb3La+A1wkItuBi9xtY07ckXoy23ezJWUeOWmBZEczpPLSA2xPqSC9ox6O9HcSb0zffIlUUtVngGd6lN3V7XkHcE0v+94D3BOn/Ppe6jcCFyYSlzF92uXccHZk4tjqn+jSNnEJ1P0Mdq+GOTZ40Jw8uzPbjFrh6ldp0SCZZaN7avHeZE87jQ71E6q2O7TNqbFEYUatzupXWRubwcIpuckOJSnmT8ljXayczqpXkh2KGeEsUZjRqe0g4w9vY3VsFgtKspIdTVLML87kTa1g/OEt0Bbv3lZjEmOJwoxOu5wV3mozFpKZOjbuyO4pPehnV8YSBIWdNkzWnDxLFGZU0p2vEcJPcIzdaNdTcMrptJOC7rDLT+bkWaIwo1Jn1V95JzaNuaUTkx1KUs2dksea6Aw6q/6a7FDMCGaJwow+bQfx71/P69E5LBqj/RNdFpZk8UasgpTGzdB6INnhmBHKEoUZfXa8gqCskvnMLEhPdjRJNasgnXWeuc5Gja1PYU6OJQoz+lS/RJukEis6bdSvkd0fn9cDRYtolyDU2OUnc3LG9l+RGZViVS/xerSCJVNtVmGAxWX5vBmdRazqpWSHYkYoSxRmdDm4A8/hnbwSncvSsuxkRzMsLC3L5uXoAjwHq+BgdbLDMSOQJQozulQ735pf17mcNsWWWwc4bcoEXoktcDa2/zm5wZgRyRKFGV0qX+CAN4/Ugtmkj5GlT/uTHvSTVjSTvd5CqLREYU6cJQozenR2oFUv8qfOhSydmpPsaIaVpWXZPN8537nxrrMj2eGYEcYShRk9av6KdLbxp8gi65/oYWlZNi9G5iOR9qPTrxuTKEsUZvTY+kc6Pam8Eavg9FJLFN2dXprNG7EKIpIC255LdjhmhEkoUYjIMhHZKiKVInJHnNcDIvK4+/oqESnt9tqdbvlWEbmkvzZF5BER2SEi77iPhad2iGZMUIVtz/FOyiJKJ+aQPT4l2RENK9njUygtyOXdwGLY/LTz72VMgvpNFCLiBR4ALgUqgOtFpKJHtZuAQ6o6HbgfuNfdtwJnje05wDLgQRHxJtDml1R1oft455SO0IwNe9+DI7X8pmUeH5wxNtef6M8HZ+TxRMtCOFILdW8nOxwzgiRyRrEUqFTValUNAyuA5T3qLAcedZ8/CVwoIuKWr1DVkKruACrd9hJp05jEbXkaRXg+spAPlNuNdvF8sDyPZyOLiYkXNq9MdjhmBEkkUUwCdnfbrnXL4tZR1QjQBOT0sW9/bd4jIutF5H4RCSQQoxnLVGHDb6hJX0yzb4J1ZPdiSekEQv4MdqQtgk0r7fKTSVgiiULilPX8DeutzomWA9wJzAJOB7KBr8QNSuRmEVkjImsaGhriVTFjxd73oHE7v+s8g6Vl2QT93mRHNCwF/V7OnJrDyvASOFgF+zcnOyQzQiSSKGqBkm7bxUBdb3VExAdkAgf72LfXNlW1Xh0h4Gc4l6mOo6oPqeoSVV2Sl2eXGsa0DU+hHh8/PzyfD9plpz59sDyPXzbNR8UDG55MdjhmhEgkUbwFlItImYik4HRO97zAuRK40X1+NfCiqqpbfp07KqoMKAdW99WmiBS6PwW4EthwKgdoRjn3stOe7DM5RAYXzs5PdkTD2nkz82ggi7qcs+DdxyEWS3ZIZgToN1G4fQ63As8Bm4EnVHWjiNwtIle41R4GckSkEvgicIe770bgCWAT8Cxwi6pGe2vTbesxEXkPeA/IBf5tYA7VjEq7V0PTLp6Onsn0/DSm5qUlO6JhbWrueKbmjud3+kFn9JNNPW4S4Eukkqo+AzzTo+yubs87gGt62fce4J5E2nTLL0gkJmMAWPdz1D+eB/bN4YYPju1lTxMhIlwyt4AHX5nF59PSkXdXwNTzkh2WGebszmwzcnU0wcbfUFN0Kc2xABfPKUh2RCPCsjkFtMb81BRcDJt+D6GWZIdkhjlLFGbkeu/X0NnGLzs/xMSMAPMnZSY7ohFhfnEmRZlBVkTOg85WWP94skMyw5wlCjMyqcKanxHNn8MjOyfw0flFeDzxRl2bnkSEZXML+dmuPCIFC2DV/9g9FaZPlijMyFT9EuzbwKr8a+mMwpWLet4DavrysUWTCEeU1fnXwIGtUP1yskMyw5glCjMyvf5fkDaRH+xfQHl+GnOKMpId0Ygyd1IGMyam8f36eTA+D954INkhmWHMEoUZeerXQ9WLHJr7ad7c1crHFk/Cue3GJEpE+JvFxaze3UrjvJug8nnYszbZYZlhyhKFGXle/DcIZvKTjvPxeZwPPHPiPrZoEl6P8LPOiyB1Arx8b7JDMsOUJQozsux8HbY/R/jM2/j5O01cOq+QiRnBZEc1IuVnBFk2t4BH1zYSXvp52P4c7FqV7LDMMGSJwowcsRj86V8hvZCn/JfR3BHhk2dPSXZUI9qnzymjuSPCr72XQ3oR/PFLEIsmOywzzFiiMCPHmodhzxqiF9zF/7xez7xJmSyePCHZUY1op02ZwMKSLB5atY/oh78J9e/Cukf739GMKZYozMjQtAf+/E2Y+iF+G/0ANY1tfOGC6daJPQA+d940dja28VToTCj9ADz/dThUk+ywzDBiicIMf9FOePJToDFCy/6DH7xYyZyiDC6qsLmdBsIlcyayoCSL+1/YTuiy/3IKf3MzRCPJDcwMG5YozPCmCs99FXavguX/xY83KLsOtnHHpbPsbGKAiAhfWTaT+qYOHt4Yhcvuc/69//hlu2PbAJYozHD3l+/C6v+BM2+hpmAZP3ypkkvnFti62APs7Gm5XDJnIv/55+1UF34EzrnN6RP6633JDs0MA5YozPAUi8KfvgYvfxsW/C2dH76b21a8TYrXw10frUh2dKPSt5bPJcXn4fZfv0v4/Ltg3sfhxW85Z3S2wNGYltB6FMZ0F4pE2dXYRnMoQlsoSiQWY1yKj/EBL0WZqWSN85/aZaHGKvjDbc6iOktuQi/9Lnf9fjPv1jbxwN8upjAzdeAOxhyVnxHkO1fN55ZfruMbT2/mnit/hKRmwRs/hLp3YPkPIbvspNtXVQ62hjnQEuZga5jOaAyPCCk+DzlpKeSlB0gP+OyS4jCUUKIQkWXAfwJe4Ceq+p0erweAnwOnAY3Atapa4752J3ATEAX+QVWf66tNd8nUFUA2sA64QVXDp3aY5mQ1HOlg+65a9uzczuG6atoaa2lvOUwq7aTTjocYUbxE8BDCz2FNp82fRWrmRAonTWZq2TQWzZpGTno/H+6xGOx9F9b8DN79FfiCcMV/oYtu4N5nt/Kr1bv4/PnTuGx+4dAc+Bh12fxC3tszjf/+SxUZQT9fWXYvUrgAnr0Tfng6LPxbWHwjTFoM/XygN7WFeWvbLjZv20bj3l10HKpjfLiRDGkjQCcBwniJEcJPOyl0aIA2Xya+rCLSc4vJLZxC2ZRSKiZlkTUuZYj+BUw8ov10VomIF9gGXATU4qx3fb2qbupW5/PAfFX9nIhcB3xMVa8VkQrgV8BSoAj4MzDD3S1umyLyBPAbVV0hIv8NvKuqP+orxiVLluiaNWtO9NhNl0iYzoM17NuxiYO1Wwntr8LXVENGxx4m6gHSpOO4XRQh6hsHXj8Si0IsgicaQjj+EkVEPTR5JxAZl09wQhEZuZOQcdkQi0BnmzMUc+970NoAvlRYcC2c/y80ebP52u838Id367h+6WS+/bG59m1zCKgq//r7Dfy/N3dx2fxCvv2xeWSG98Or34N1P4doGMblQsE8mFAKwQxQJdbZzqGDB2ht2IW3dS9ZkQOMl1Dc94h6A6g3BRUfEg3jjbTH/d0Jq5d6zeGAL5+OcZPwTCghLb+MiSXTySuejmQWg9/uzD9ZIrJWVZf0Wy+BRHEW8A1VvcTdvhNAVf9vtzrPuXXeEBEfsBfI4/21s/9v93rubse1CXwHaAAKVDXS8717c7KJIhzuBBSvx4PHI4h4+v2WdIxYzPmjiYYg2kkk3EEo1EG426Mz3E5nOEQk1EGkM0Sks4NoZ5hoZwexzhCxSBjt7CAW7SQShXAMInjweLx4fT68Xr/z05eCPyUFv9+PPyVAICXg/AykEEwJEgymEAgESPEHEK8fvH7ngzjcBuEWCLcSaT9C68E9dByqI9q0Fz1ST7C9nqzO/Xi7/ZG2aoC9viLaxhUjWSWMzyslr3gaafllkFEIgQzwjwOP5/h/j47D0NYIrQ10HtnH3j017N2zkyMNtXjb9pPPYSZ6DpNJK+r14/EHkQmlePJmQtkH0ZmXsqs9wNPr6/nZazs41NbJFy+awefPn2ZJYgipKv/zSjXffXYLWeNSuOncMi6bV8iUcWFk2x+h5jV073qiTXVIqImoCu3qp1lT2acTCKUWEMguJq9wCkUlpfgyCyGtANInQjDr+L8zVYiEoO0ANO+F5npaDuzmUP0OQgd24m2uJa1jLzmxg3jk2M+sFl82obRJeLNK8GZPJpg7Bf+EyRBIB38q+ALOFxCvz/kd1SjEokSiEdrDnYRCHYRCYUIdIULhDsLhEOFwmM5wmHA45P7dhol0holGwsQinfiJ4hV1/s68fvCmIN4UPL4UvP4AXr/7MyWI3x/AlxLEH0jFn5JCSiDVfQRJCaYSDAZJSQkiHu+J/R/FYnRGIni9XrzeE9u3S6KJIpFLT5OA3d22a4EzeqvjfsA3ATlu+Zs99u1aOCBemznAYVWNxKk/4N7+n89yRuNvjyuPqaACMTyAoIDicX86v+B+OvH1+Abkcx/jByvgU+QDMgGfBtinE2ggiyb/DNozP4zkTCVz0gyKyioonVzKNN9J/OJ5PDAu23nkluMHSuZBiftyY0uIV7Y38JNtB3it6gD7jjjfNr1HhIkHA/irPBz47Wpaw84UEh+ckceXL5nJXFu5bsiJCJ87bxrnTs/l3me38O/PbeXfn9tKetBH1rgCItGr2N98GdGY86GdMz6F82bm8aGZ+XywPI/Mcf4TfUPnzCCz2HkAae6ju/b2dnZUb6du53aa9lYRbtyJv3kPExsbKDr4NpN2PI9fOhN6Sx+Q7j6Gg0710ik+FA9y9JNG3efuw/1i7yGGV5QU4L3zH2be+VcPamyJJIp4X+N6nob0Vqe38nijrfqqf3xQIjcDNwNMnjw5XpV+jZt3OW/WFKCxGKqKqvszFnW39ZjXcF/3iBDzpoDHj3pTjn6bwBfA0/VNwhfAm+J8k/D5A/hTgs4jEHS+SQSCBNxvFYFg0Nlf9ei3nfd/xohGOgmFQrSHOujo6KAjFKIjFCYUCrmPDsKdzrefznCYzs4QkXAnHVGI+MYhgTQkkIY3mE5aThG52TnkZwSYlzuecSlDN54hJy3AxxYV87FFxagqVQ2trK89zI4DrdQd7qAzGiN7fApT88Zz3ow8puQM15Q7dsydlMkvbjqDnY2tvFbZyOb6I7SEInhEKMgMMDU3jYWTsyjLGT8kKwympqZSMWc+FXPmHy2LxpSdja1UNbTyVnMHbYf3Ejm0G+lsQzo7INqBNxoi4Im5Z+levF4fKX4/KX4fKSkB55u+e6YeCAQIBgIEgkGCKQGCqUFS/O7fuNcPHp/zUzzOzaCxTudnNExnOEQ41EEo1E5nKERnZwedoQ4i4a6Hc1Uh1hki2hkmFulAIyE0EkYjIYiEiUajRBRAEBHE40FE8IgHca98OGVexOujpGTWoP+7J/IpUcv7XwoBioG6XurUupeeMoGD/ewbr/wAkCUiPvesIt57AaCqDwEPgXPpKYHjOI6ThQc3Ew8ELzDOfYwWIsL0/DSm5/f8zmiGoyk544dt4vZ6hKl5aUzN6/pdmsLxFz0GiS9wzKbffQzPf6mTl8h9FG8B5SJSJiIpwHXAyh51VgI3us+vBl5Up/NjJXCdiATc0UzlwOre2nT3eYn3P71vBH5/8odnjDHmVPV7RuH2OdwKPIfz5fanqrpRRO4G1qjqSuBh4BciUolzJnGdu+9GdxTTJiAC3KKqUYB4bbpv+RVghYj8G/C227Yxxpgk6XfU00hgw2ONMebEJTrqyabwMMYY0ydLFMYYY/pkicIYY0yfLFEYY4zpkyUKY4wxfRoVo55EpAHYmew4TkIuzk2GY4kd8+g31o4XRu4xT1HVflcBGxWJYqQSkTWJDE0bTeyYR7+xdrww+o/ZLj0ZY4zpkyUKY4wxfbJEkVwPJTuAJLBjHv3G2vHCKD9m66MwxhjTJzujMMYY0ydLFEkiIv8sIioiue62iMgPRKRSRNaLyOJkxzhQROTfRWSLe1y/FZGsbq/d6R7zVhHpc8nbkUZElrnHVSkidyQ7nsEgIiUi8pKIbBaRjSJym1ueLSLPi8h29+eEZMc60ETEKyJvi8jT7naZiKxyj/lxdwmFUcESRRKISAlwEbCrW/GlOOt1lOOs3PejJIQ2WJ4H5qrqfGAbcCeAiFTgTEk/B1gGPCgiJ7f47zDjHscDOP+vFcD17vGONhHgdlWdDZwJ3OIe5x3AC6paDrzgbo82twGbu23fC9zvHvMh4KakRDUILFEkx/3Alzl2mdflwM/V8SbOSn+FSYlugKnqn7qtg/4mzsqF4BzzClUNqeoOoBJYmowYB8FSoFJVq1U1DKzAOd5RRVXrVXWd+7wZ54NzEs6xPupWexS4MjkRDg4RKQYuA37ibgtwAfCkW2VUHbMliiEmIlcAe1T13R4vTQJ2d9uudctGm08Df3Sfj+ZjHs3HFpeIlAKLgFXARFWtByeZAPnJi2xQfB/ny17M3c4BDnf7QjSq/r8TWTPbnCAR+TNQEOelrwL/Alwcb7c4ZSNmSFpfx6yqv3frfBXnUsVjXbvFqT9ijrkfo/nYjiMiacBTwD+q6hHnC/boJCKXA/tVda2InN9VHKfqqPn/tkQxCFT1w/HKRWQeUAa86/4hFQPrRGQpzjeQkm7Vi4G6QQ51wPR2zF1E5EbgcuBCfX9M9og+5n6M5mM7hoj4cZLEY6r6G7d4n4gUqmq9ewl1f/IiHHDnAFeIyEeAIJCBc4aRJSI+96xiVP1/26WnIaSq76lqvqqWqmopzofJYlXdC6wE/s4d/XQm0NR16j7SicgynLXQr1DVtm4vrQSuE5GAiJThdOSvTkaMg+AtoNwdCZOC02m/MskxDTj32vzDwGZV/V63l1YCN7rPbwR+P9SxDRZVvVNVi92/4euAF1X1/wNeAq52q42qY7YziuHjGeAjOB26bcCnkhvOgPohEACed8+k3lTVz6nqRhF5AtiEc0nqFlWNJjHOAaOqERG5FXgO+P/bt2MTBIIgDKP/YFnWYWhkEcLFBlZhLDbjgVw9a3DGk+mBvBduNNkHy8wuyW2MsWw81jfskxyTvKpq/rxNSa5JHlV1yrrdd9hovl86J7lX1SXJM2tA/4LLbABavp4AaAkFAC2hAKAlFAC0hAKAllAA0BIKAFpCAUDrDcaR1kKuhCtEAAAAAElFTkSuQmCC\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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eGFOIJJyEWa847QFlqsNNY6BRzyw3Gb8smqFT1xNzOJbq4cW54JxKTFm1m7jEFB7t0ZD7ujagWBHvPYqClZdEcMIdpzh1YJqOOA3GufUU8J2IvAwsI/szC2NMYbd5jlMk7tBWiLwberwAxctmucn4ZdEMHBtFbKLzuzTmcBxjFu+kQeVSDLstkgaVS/s87MLCSyJ4HJgINHDvH6iM84veM1WdDcx2pzcD7XMUpTGmcIo9DNOfg6VfOl1B7/gF6l7gadOhU9efSgJpxSUmWxLIoSwTgYiE4Fzf7wI0xmnsXa+qiX6IzRhTmK2bDL88Dsf3wPmPOCUiwrwN9pKQlEL04dgMX4s5HJeXUQaFLBOBqqaIyFuq2glY7aeYjDGF2fF9Tn2g1WOhSjO4YTTUbONp09RxAl6fsi7TdWqEF56Rw/zFyy1100TkarGOt8aYs6EKK8fAR+1h3SS46FnoP9tzEli89SBXf7KA+75ZStEiIfTvXI8SYad/hZUIC2VAz8Z5H3sh57WNoBSQJCJxOJeHVFWzbskxxphUR3Y6ReI2ToVa7ZwicVWaeNp0877jvD5lHVNX76FKmWK8fnULrm5TiyKhITStUe5Ur6Ea4SUY0LMx/VpneI+qyUJ2bQQCNFPV7X6KxxhTmKSkOKOFTR8EmuzcE9C+v6cicfuPx/PejI2MXrSd4kVCePziRvy7cz1KFv3na6tf65r2xZ8HsmsjUBEZB+RslAdjjDnwN0x8CLbNh/pd4fL3oHzdbDeLTUjm89838+mczcQmJnNj+9o80r0RlcsU83XEQcvLpaE/RaSdqv7l82iMMQVfchL88SHMfg1CizmXgVrfkm15iOQU5aclO3lr+nr2HI3nkqZVeapXE+sK6gdeEsFFwD0isg04wT9tBDZCmTHmdLujYMKDsGs5NOkDvd+EstWz3ERVmb1hH0Mmr2P9nmO0qh3OBze2oX294B4jwJ+8JIJePo/CGFOwJcXD3KHw+ztQojxcOxKa9sv2LGBV9BFe+3Ut8zcdoE7Fknx0Uxt6t6hm1UH9zEsisMqfxpjM7VjknAXsXw/n3eiMGlYy61/zOw+d5K1pGxi3LJryJcMYdHlTbu5QxwaJCRAvieAXnGQgOHcZ1wPWA818GJcxJr9LOAEzB8PCT6FcLbj5J2jYI8tNjpxM5OPZmxixYCsC3Ne1Afd1bUDZ4sE5VnB+4WVgmhZp50WkDXCPzyIyxuR/f89yisQd3g7t/gM9BkGxMpmuHp+UzFd/bOPDWZs4EpvIVa1r8X+XNLK7gPMJL2cEp1HVpSLSzhfBGGPyudhDMO1ZWPY1VDwH7vwV6vwr09VVlZ9X7mLo1HXsOBhL54aVeLpXE5rVKOfHoE12vIxQ9nia2RCgDbDPZxEZY/KntT/DL/8HJ/bDBY9Bl6chrHimqy/cfIBXJ69lxc4jNKlWhi/vas+FjSr7MWDjlZczgrTne0k4bQY/+SYcY0y+c3wvTB4Aa8ZDtRbOgDE1WmW6+qa9xxjy6zpmrN1L9XLFefPa87iydU1CQ6wnUH7lpY3gRX8EYozJZ1Rh5fcw5WmnYbjbc0656NCMG3b3Hovjnekb+f6v7ZQsWoQBPRtz9wX1KB5mI4Tld5kmAhH5mSy6jqpqX59EZIwJvMM7YNKjsGkG1O7g3B1cuVGGq56IT2LY3M38b95mEpJSuK1TXR7qdg4VS1tJiIIiqzOCN/0WhTEmf0hJgcWfw4wXnDOCXkOh3b8h5Mz+/UnJKYxZvJN3Zmxg37F4ereoxoCeTahXqZT/4zZnJdNEoKpzUqdFpCjQBOcMYb2qJvghNmOMP+3f6BSJ2/4HNOgGfd6F8nXOWE1Vmbl2L0OmrGPT3uNE1inPp7e0pW2d8gEI2uQFL72GLgM+Bf7Guamsnojco6q/+jo4Y4wfJCfCgg9g9hBnqMh+nzh3CGdQ5mHFjsO8OnktC7ccpH6lUnx6S1t6NqtqJSEKOC+9ht4CLlLVTQAi0gCn55AlAmMKul0rnPIQu1fCuX2dInFlqgIwfln0qUFfqpQtRo1yJVi24zAVSxVl8BXNuKF9BGGhVhKiMPCSCPamJgHXZmCvj+IxxvhDYhzMfQN+fxdKVoTrvoSmV5x6efyyaAaOjSI2MRmAPUfj3dLQVXjrulaUsZIQhUpWvYaucidXi8hkYAxOG8G1gI1NYExBtf1P5yzgwEZodTNc8vIZReKGTl13KgmktTrmmCWBQiirM4LL00zvAbq40/sAaxUypqCJPw4zX4JFw6BcbbhlLJzT/YzVtu4/QfThuAx3EXM41tdRmgDIqtfQnf4MxBjjQ5tmwM+PwZEd0OEe5+awYqeP/JWYnMLweVt4d8YGZ/SpDHZjReIKpxwXnTPGFCAnD8LUZ2DFaKjUCO6aAhEdz1ht5c7DPPVTFGt3HaVns6p0alCR139df9rloRJhoQzo2dif0Rs/sURgTGG1ZgL88gScPACdn4ALB5xRJO5EfBJvT9/AiPlbqFS6GJ/e0pZLm1cDILxE0VO9hmqEl2BAz8b0a10zEJ/E+JglAmMKm2O7YfITTrXQai3hlp+g+plDjM9ev5dnxq0i+nAsN3eI4KleTU4bIKZf65r2xR8ksuo19HhmrwGo6tt5H44xJtdUYflomDrQ6R7a4wXo9BCEnv7ffP/xeAZPWsOE5TE0qFyKH+7tRLu6NlB8MMvqjCC1/HRjoB0w0Z2/HJjry6CMMTl0aBv8/AhsngUR/4K+70Olhqetoqr8uGQnr0xey4n4JB7p3pD7L2pAsSJWHTTYZdVr6EUAEZkGtFHVY+78C8APfonOGJO1lGT4azjMeNEpCdH7TYi8+4wicdsOnOC/46KYv+kAbeuUZ8hVLWhYNfOhJU1w8dJGEAGkLTKXANTNbiMRKY5z5lDMfZ8fVXWQiNQDvgMqAEuBW62InTG5sG+9UyRux0I4p4dTJC689mmrpO0SGhYawuB+zbm5fQQhNkiMScNLIvgKWCQi43C6Fl8JfOlhu3igm6oeF5Ew4HcR+RV4HHhHVb8TkU+Bu4FPche+MUEoORHmvwtz3oCipeDKz6Dl9WcUiUvbJfSSplV56YrmVCuX+dCSJnh5GaHsFfcLvLO76E5VXeZhOwWOu7Nh7kOBbsBN7vJRwAtYIjDGm5jlTnmIPVHQ7Ero9QaUrnLaKicTknhrWtouoW24tHn1AAVsCgKv3UdLAkdVdYSIVBaReqq6JbuNRCQUWAKcA3yEU8r6sKomuavsBDLsnyYi/YH+ABERER7DNKaQSox1ykQv+ABKVYbrv4Fz+5yxWtouoTd1iOCpS5tQroTVBjJZ8zIewSAgEqf30AicX/ZfA+dnt62qJgOtRCQcGAecm9FqmWw7DBgGEBkZmemQmcYUetsWOG0BBzZB61udInElwk9b5cDxeF5K0yV0zD2daF/PuoQab7ycEVwJtMZp2EVVY0QkR90NVPWwiMwGOgLhIlLEPSuoBcTkLGRjgkTcUZj5otMrKLwO3DYB6nc9bRVV5ael0bz8yxpOxCfxcPeGPGBdQk0OeUkECaqqIqIAIuJpQFIRqQwkukmgBNADeB2YBVyD03PodmBCriI3pjDbOB1+fhSORkPH+6Hbs07DcBrbDpzgmXGr+H3TftrWKc9rV7WgkXUJNbngJRGMEZHPcH7J/we4C/ifh+2qA6PcdoIQYIyqThKRNcB3IvIysAz4PJexG1P4nDwIUwbCyu+gchO4ezrUbnfaKknJKQz/3ekSWiQkhMFXNOPmDnWsS6jJNS+9ht4UkYuBozjtBM+r6nQP263EuaSUfvlmoH0uYjWm8FKF1eNg8gCIOwwXPgkXPgFFip22WtTOIzw9diWrY45ycdOqvHRFM6qXs9LQ5ux4aSx+DPjBy5e/MSYXju5yisStmwQ1WkPfCVCt+WmrnExI4p3pG/j89y1ULF2MT25uw6XNq9mg8SZPeLk0VBaYKiIHca7r/6iqe3wbljFBQBWWfQVTn4XkeLh4sNMekK5I3NwN+/jvuCh2HorlxvYRPN3LuoSavOXl0tCLwIsi0hK4HpgjIjtVtYfPozOmsDq4BX5+GLbMhToXOEXiKjY4bZUDx+N5+Ze1jFsWTf3Kpfi+f0c61K8YoIBNYZaT8Qj2AruBA0CVbNY1xmQkJRkWfga/DQYJhT7vQJs7TisSp6qMWxbN4ElrOB6fxMPdzuH+i86heJh1CTW+4aWN4D6cM4HKwI/Af1R1ja8DM6bQ2bvWKQ8RvRga9nSSQLnTb6zffuAkz4yPYt7G/bSJCGfI1S2tS6jxOa/VRx9V1eW+DsaYQikp4Z8iccXKwFXDocU1pxWJS0pO4Yv5W3h7utMl9KUrmnGLdQk1fpJlIhCREOByVR3op3iMKVyil8CEh2Dvamh+DfR6HUpVOm2VVdFOl9BV0UfpcW5VBvezLqHGv7JMBKqaIiIrRCRCVbf7KyhjCryEkzD7VfjjIyhdDW78Dhr3Om2V2IRk3pnhdAmtUKooH9/chl7WJdQEgJdLQ9WB1SKyCDiRulBV+/osKmMKsi3znB5BBzdD2zvg4pegeLnTVpm30ekSuuNgLDe2r83Tl55LuZLWJdQEhpdE8KLPozCmMIg7AtMHwZIRUL4e3P4z1LvwtFUOnkjg5UlrGLssmvqVSvFd/450tC6hJsC83EcwR0TqAA1VdYaIlASsH5sxaW2Y6hSJO74bOj0IFz0DRUueellVGb88msGT1nI0NpGHup3DA9Yl1OQTXrqP/gdngJgKQAOcgWQ+Bbr7NjRjCoAT+2HK0xD1A1RpCtd/DbXanrbKjoMneWb8KuZu2EfriHCGXNWSxtWsS6jJP7xcGnoAp0jcQgBV3SgidkOZCW6qsOon+PVJZ9yArv+FCx6DIkVPrZKUnMKI+Vt5e/oGQgRe7NuMWzrWIdS6hJp8xksiiFfVhNSeDCJShExGFTMmKByJhl8ehw1ToGZb6PshVG162iqroo8wcGwUUdFH6HFuFV66ojk1wq1LqMmfvCSCOSLyX6CEW476fuBn34ZlTD6UkgJLR8H05yE5EXq+Ch3uZfyK3Qwd8Rsxh2OpXq44jauVYe7G/ZQvWZSPbmpD7xbWJdTkb14SwdPA3UAUcA8wGRjuy6CMyXcO/A0/PwJb50Hdzk6RuAr1Gb8smoFjo4hNTAYg5kgcMUfi6FivAp/dGmldQk2B4KXXUArOiGT/E5EKQC1VtUtDJjgkJ8HCT+C3VyA0DC5/H9rcdqo8xNCp608lgbR2HIq1JGAKDC+9hmYDfd11lwP7RGSOqj7u49iMCaw9q50icTFLoVEv6PM2lK1x6uXtB04SfTg2w01jMlluTH7k5dJQOVU9KiL/Bkao6iARWenrwIwJmKR4mPeW8ygeDtd8Ac2uOnUWsPPQST6atYkfFu/MdBfWMGwKEi+JoIiIVAeuA57xcTzGBNbOxc5ZwL610PJ66PkalHLu/N19JI6PZm3iu7+2Iwg3d4igfuVSDPn19MtDJcJCGdCzcaA+gTE55iURvARMBear6l8iUh/Y6NuwjPGzhBNOO8CfHzuXf24aA416ArD3WBwfz/qb0Yu2o6pcF1mbBy4659Sv/nIlijJ06npiDsdSI7wEA3o2pl/rmlm9mzH5ihSEdt/IyEhdvHhxoMMwhdXm2TDxYTi8DSLvhh4vQPGyHDgez6dz/uarP7eRmKxc06YWD3Y7h9oVSmazQ2PyBxFZoqqR2a3npbG4PvAe0BHnRrI/cAaq2XLWURoTSLGHYfpzsPRLqFAf7vgF6l7AoRMJDJuyjlELthKXmEy/1jV5uFtD6lYqFeiIjfEJL5eGRgMfAVe68zcA3wEdfBWUMT637heY9Dic2AvnPwJdB3IksQifT1vPF/O3ciIhictb1uCRHg1pULl0oKM1xqe8JAJR1a/SzH8tIg/6KiBjfOr4Pqc+0OqxUKUZ3PgtRyu2YMScrQz/fTPH4pK4rEV1HunR0MYKNkEj00Tg3jwGMEtEnsY5C1Ccgex/8UNsxuQdVVg5BqY85TQMX/QsJ9o9wMiFMQybO4sjsYlc0rQqj/ZoRNMaZQMdrTF+ldUZwRKcL/7UIin3pHlNgcG+CsqYPHVkJ0x6DDZOg1rtiOv1HqM2FefWQS+oAAAdv0lEQVSzt+Zz8EQC3ZpU4bEejWhRq1z2+zKmEMo0EahqPX8GYkyeS0mBJV84o4ZpCokXv8pXKT35eMRW9h+P58JGlXmsR0NaR5QPdKTGBJSXXkNhwH1A6ph7s4HPVDXRh3EZc3b2b4KJD8H2BaTU68L4Wk/y+pw49hxdz78aVOSTW9rQrm6F7PdjTBDw0lj8CRAGfOzO3+ou+7evgjIm15KT4I8PYfZraGhRFjZ/icc3NCNm7RHa1S3Pu9e3plMDGyPYmLS8JIJ2qnpemvnfRGRFdhuJSG3gS6AakAIMU9X33Ebo74G6wFbgOlU9lNPAjTnD7iiY8ADsWsHOqt144MjNrFhcgtYRJXjj2lacf05FGxfAmAx4SQTJItJAVf+GUzeYnVl390xJwP+p6lIRKQMsEZHpwB3ATFUd4vZGehp4KnfhGwMkxsHcoej8d4kvUo7Xig1g1LZWtKwVzogrG9G1UWVLAMZkwUsiGIDThXQzTg+iOsCd2W2kqruAXe70MRFZizPw/RVAV3e1UThtDpYITO5sX4hOfBDZv4FpRS7iqaM3UL16Tf53RSN6nFvFEoAxHngZmGamiDQEGuMkgnWqGp+TNxGRukBrYCFQ1U0SqOouEamSyTb9gf4AEREROXk7Ewzij6MzX4JFw9grlXgy4Sl2l7uAIf0acknTaoTYAPHGeObljAD3iz9XYxCISGngJ5z6REe9/kJT1WHAMHCKzuXmvU3hpJt+I27sg5Q4Gc2opIv5Ifwu7unXistaVLcEYEwueEoEueV2Pf0J+EZVx7qL94hIdfdsoDqw15cxmIJt/LLoUyWeG5dL4vUy33Pe/l+ISanOuyVfoVvPfkw4ryahlgCMybWsSkycr6rzRaRYTi8FudsL8DmwVlXfTvPSROB2YIj7PCGn+zbBIe3A8D1DFjE4biQV4o7yRUg/yl32HO9E1qdIaEigwzSmwMvqjOB9oC1O2ek2udj3+Tj3HESJyHJ32X9xEsAYEbkb2A5cm4t9myAwdOp6Sice4K2wkfQOXcTqlDrcmTiAQ+XOZUGHcwIdnjGFRlaJIFFERgA1ReT99C+q6sNZ7VhVf+efOkXpdfceoglGSUnJdDw6leeKfUUJ4hmaeB2fJfchiSLI4bhAh2dMoZJVIugD9AC64RSgM8Yv/t64liNj7uetoktZnNKIpxL/w9/6z9CPNjC8MXkrq6Jz+4HvRGStqmZ7J7ExZyshMYn53w6h/d/vU12EX2o9xoBt7TiZps+YDQxvTN7z0mvogIiMw7nmr8DvwCOqutOnkZmgsn7VUpLG3c9FyWtZW7od1W/+lMtqnENiml5DNjC8Mb7hJRGMwBmuMrVR9xZ32cW+CsoEj7i4OBZ+8wIdtw8nToqxqv0Qmve6F9z7Tfq1rmlf/Mb4mJdEUEVVR6SZHykij/oqIBM8Vi+ZR9FfHqJLyhaiynWhzq0f07xyrUCHZUzQ8ZII9onILcC37vyNwAHfhWQKu5Mnj7Nk1NN02v0NR6Qsazp/SIvutwY6LGOClpdEcBfwIfAOThvBAneZMTm2csEUwqc/RmeNYWnFy2h823s0Da8c6LCMCWpeis5tB/r6IRZTiB09cpDVX/4fnQ6MZbdUYV2PUbS5oF+gwzLG4ONaQ8YALJ/1I1XnPEUHPcBf1a6jxW1vUq2UDRRvTH5hicD4zOH9u9n41cO0OzKV7SG1+Lv3D7SLtM5mxuQ3lghM3lNl6ZSR1Fk4iNZ6jIW176L1La9QtHjJQEdmjMlAtolARIoBV+OMMXxqfVV9yXdhmYJq/65t7Pj6ftqc+J1NoQ040u97OrToFOiwjDFZ8HJGMAE4glNvKMflqE1w0JQUlk78iIbLX6OpJvBHg4dpd+NzFAkrGujQjDHZ8JIIaqnqpT6PxBRYe7atY/+399E2bilrwppT+rqP6dTwvECHZYzxyEsiWCAiLVQ1yufRmAJFk5NY8uNQmq55h9IIf5w7kPbXDiA0NDTQoRljcsBLIrgAuENEtuBcGhJAVbWlTyMz+VrMxmUcH3MfkYlrWV48kso3fkKnuo0CHZYxJhe8JIJePo/CFBjJiQks//YFWvz9GSUpzh+tXqXjFfchITZkpDEFlZc7i7eJyHlAZ3fRPBufIDjtWDWf5PEP0DZpC4tKdaHOrR/SqXpEoMMyxpylbH/GicgjwDdAFffxtYg85OvATP6RGHeCpZ8/TI0fLqNk0mEWtn+fdgMmUNWSgDGFgpdLQ3cDHVT1BICIvI4zoP0HvgzM5A9blkyj6C+P0CYlhvnletP41vfoULlKoMMyxuQhL4lAgOQ088lkPii9KSTiTxxi7Zf/R6s9P7GTKizqPILzu18V6LCMMT7gdYSyhe5wlQD9gM99F5IJtL/nj6XMjAG0TDnA7IrX0uq2obQPLx/osIwxPuKlsfhtEZmN041UgDtVdZmvAzP+F3t4L5u+eogWB6awWWqz45Lv6Xp+z0CHZYzxsUwTgYiUVdWjIlIB2Oo+Ul+roKoHfR+e8QtVNv72JZXmPUcTPc7ManfS/taXqV+6dKAjM8b4QVZnBKOBPjg1hjTNcnHn6/swLuMnJ/bvYPuX93Lu0d9ZG3IO8b1H0z3ygkCHZYzxo0wTgar2cZ/r+S8c4zeqbPj1I6oveoV6msj02g9y/i3PUbJ48UBHZozxMy9lqGeqavfslpmC42jMRvZ8059GJ5ayPLQ5Rfp9yMUtWgc6LGNMgGTVRlAcKAlUEpHy/NNltCxQww+xmbyWksy6CUOpu+ItqmkoUxs8TZcbnqB40bBAR2aMCaCszgjuAR7F+dJfmmb5UeAjXwZl8t7hLcs59P29NIlby8KwdpS75kN6Nm4S6LCMMflAVm0E7wHvichDqmp3ERdQmhTP+h9fosG6T0nREkxp8jLdr72fsCJWKtoY48jq0lA3Vf0NiBaRM24pVdWxWe1YRL7A6XW0V1Wbu8sqAN/jDHu5FbhOVQ/lOnqTpQMb/iD2h/tokriFOcW6UuvG97i0bt1Ah2WMyWeyKjrXxX2+PINHHw/7HgmkH9nsaWCmqjYEZrrzJo9pwgnWj3qY8NG9KJJwhGkt3+WCp8bTwJKAMSYDWV0aGuQ+35mbHavqXBGpm27xFUBXd3oUMBt4Kjf7NxnbFzWDlAkP0Tgphukle9Po5re5pGb1QIdljMnHPJWhFpGy4hguIktF5JJcvl9VVd0F4D5nWsZSRPqLyGIRWbxv375cvl3wSDl5mA3D76LyT1cTn5jMtHbD6f7EaOpYEjDGZMPLsFJ3qepR4BKcL+47gSE+jQpQ1WGqGqmqkZUrV/b12xVou/8ax6E329Jgx1gml7mW0AcWcMll1xISYkVijTHZ81qGGqA3MEJVV4hIbr9h9ohIdVXdJSLVgb253I8Bko/tY8vXD3LOnilsIIJlnT+gV/de5P7PY4wJRl7OCJaIyDScRDBVRMoAKbl8v4nA7e707cCEXO4nuKmya96XnHi7DRG7pzOh/O2EPzKfHj16WxIwxuSY1xHKWgGbVfWkiFTEuTyUJRH5FqdhuJKI7AQG4VxSGiMidwPbgWtzG3iwSjy0g51f3Ue9g/OIoiH7e7xF3wsutARgjMk1L+MRpIhILeAm98tmjqr+7GG7GzN5yWoU5UZKCtG/fUL53wdTTZMZW+UButz6LC3Klgx0ZMaYAs5L0bkhQDucAewBHhaRf6nqQJ9GZk6J3+MUiYs4upS/pAXxvd/hqvbtAh2WMaaQ8HJpqDfQSlVTAERkFLAMsETga8lJ7Pz1TSovfotwLcIPNZ/kklsGUK5k0UBHZowpRLwkAoBwIHVEsnI+isWkEbtzBQdH96fWyXXMDWlP0b7vcG2r5oEOyxhTCHlJBK8By0RkFk5X0guxswHfSYpnx4TBVI/6mGJaijH1XuKyG+6nVHErFW2M8Q0vjcXfuoPXp16UfkpVd/s0qiB14u8/OD7mXmrHb2Vaka5Uuvptrju3QaDDMsYUcl4vDXUCLsAZqzgUGOeziILE+GXRDJ26npjDsdQvJ7waPoF2e77niJZnTOO36XvtHRQPs1LRxhjf89Jr6GPgHOBbd9E9ItJDVR/waWSF2Phl0QwcG0VsYjL/ClnFkNj/ERG/jx9DLqXxzW9yXYPagQ7RGBNEvJwRdAGaq6rCqV5DUT6NqpAbOnU9YYlHeb7IaG4sMovNKdW4Lv45dpZtzQJLAsYYP/OSCNYDEcA2d742sNJnEQWBZkfnMbjYF1TkKJ8mXc47SVcTT1HkSFygQzPGBCEviaAisFZEFrnz7YA/RGQigKr29VVwhU3K0T1sH/0gw4pOY01KHe5OfIJVWv/U6zXCSwQwOmNMsPKSCJ73eRSFnSq7fx9Fqd+epXpKLCOL38LQE5dyQv+p+VciLJQBPRsHMEhjTLDy0n10jj8CKaziD2wj5ut7qXdoAStoxL7ub3J75wsJXx5zqtdQjfASDOjZmH6tawY6XGNMEPLafdTkVEoKW6d9QJU/X6WqKmOrPUSXm//LeW6RuH6ta9oXvzEmX7BE4APHY9ay75t7qHdiBYtCziOlz3tc1aZ1oMMyxpgMWSLIS8lJbBj/KnWi3qeChjGx3rP0uPFRShaz8hDGmPzLyw1lfYDBQB13fQFUVcv6OLYC5cDfSzj+/T00StjI/LBOlL/2Pfo2ssZfY0z+5+WM4F3gKiAq9aYy84+UhFjWfP8cjf/+ghQtzdTmQ+l21b8JC/UyCqgxxgSel0SwA1hlSeBMO1fOggkP0Tx5B3NKXky9m96lZ61agQ7LGGNyxEsieBKYLCJzgPjUhar6ts+iyucSTh5l7ddP0CJ6DLulInPaf8aFva63cYONMQWSl0TwCnAcKA4E/dBYG/+YQJlpT9AiZR/zyvej2a1v0aVixUCHZYwxueYlEVRQ1Ut8Hkk+d/zwfjZ++RCtD05mm9Rkafdv6HLhZYEOyxhjzpqXRDBDRC5R1Wk+jyafWjn9S2rMf44WepR51W6j9W2vUadU6UCHZYwxecJLIngAeFJE4oFEgqj76P7d29nx9QO0Pj6XTSH12Xf513Ru3TnQYRljTJ7yUmuojD8CyU80JYVFEz6myYpXaaoJLKj3AJE3DqJosWKBDs0YY/KclxvKLsxouarOzftwAm/n5nUc/P5+OsQvYV1YU0pe+wn/atQq0GEZY4zPeLk0NCDNdHGgPbAE6OaTiAIkMSmJP78bQpuN71NehL+a/pe2Vz9BSKiNG2yMKdy8XBq6PO28iNQG3vBZRAGwftViksY9ROfkNawu1Y6qN31Cu1oNAx2WMcb4RW6Kzu0Emud1IIFwMjaWP78exPk7PydOihPV7nVa9L4H7MYwY0wQ8dJG8AGQWl4iBGgFrPBlUP6w5M9ZlJn6GN10C6vCu1Lnto9pUdHGBzDGBB8vZwSL00wnAd+q6nwfxeNzBw4dZtlXA+l64DuOhJRj00Wf0LzLTYEOyxhjAsZLG8EofwTia6rK3BkTqTP/KXqwi1VVL6fhre9RsYyVhzDGBLeAjEcgIpcC7wGhwHBVHZLbfWVm/LLoU2MC1y2TwmMymr4Jk9kTUpWdvUfTPNLKQxhjDARgPAIRCQU+Ai7GaXj+S0Qmquqas913qvHLohk4NorYxGS6hKzglYTPqcEB5la8hgv6v0tI8aC7R84YYzIViPEI2gObVHUzgIh8B1wB5FkiGDp1PbGJybxaZDg3FfmNjSk1uSZxEHtOnsd8SwLGGHOaQIxHUBMnuaTaCXRIv5KI9Af6A0REROToDWIOxwKwVavyflI/Pky6kgTCEHe5McaYfwRiPIKMOumfcbahqsOAYQCRkZE5OhupEV6C6MOxDEu+/IzlxhhjTheI8Qh2ArXTzNcCYvJw/wzo2fhUG0GqEmGhDOhpg8kbY0x6XkZYnyEieZkI/gIaikg9ESkK3ABMzMP90691TV67qgU1w0sgQM3wErx2VQv6tbYbxowxJj3Jrg1YRI4BpYAE95EX3Ud74/RGCgW+UNVXslo/MjJSFy9enNUqxhhj0hGRJaoamd16ARmPQFUnA5Pzer/GGGNyLttLQ+K4RUSec+dri0h734dmjDHGH7y0EXwMdAJSC/Icx7khzBhjTCHgpddQB1VtIyLLAFT1kNvIa4wxphDwckaQ6JaFUAARqQyk+DQqY4wxfuOl19DNwPVAG2AUcA3wrKr+4PvwTsWwD9iWy80rAfvzMJyCyI6BHQOwYwDBdwzqqGrl7FbKNhEAiEgToDtO19GZqrr27OPzDxFZ7KX7VGFmx8COAdgxADsGmcmyjUBEQoCVqtocWOefkIwxxvhTlm0EqpoCrBCRnFV9M8YYU2B46TVUHVgtIouAE6kLVbWvz6LKW8MCHUA+YMfAjgHYMQA7Bhny0ljcJaPlqjrHJxEZY4zxKy9nBL1V9am0C0TkdcASgTHGFAJe7iO4OINlvfI6EGOMMYGRaSIQkftEJApoIiIr0zy2AFH+CzH3RORSEVkvIptE5OlAx+MPIvKFiOwVkVVpllUQkekistF9Lh/IGH3NrYc1S0TWishqEXnEXR40x0FEiovIIhFZ4R6DF93l9URkoXsMvg+GKgEiEioiy0RkkjsfdMcgO1mdEYwGLgcmuM+pj7aqerMfYjsr7t3QH+GcvTQFbhSRpoGNyi9GApemW/Y0zv0fDYGZ7nxhlgT8n6qeC3QEHnD/9sF0HOKBbqp6HtAKuFREOgKvA++4x+AQcHcAY/SXR4C09z4F4zHIUqaJQFWPqOpW4HNV3ZbmcVBEbvdfiLnWHtikqptVNQH4DrgiwDH5nKrOBQ6mW3wFzl3huM/9/BqUn6nqLlVd6k4fw/kSqEkQHQd1HHdnw9yHAt2AH93lhfoYAIhILeAyYLg7LwTZMfDCSxvB8yLyiYiUEpGqIvIzzplBflcT2JFmfqe7LBhVVdVd4HxJAlUCHI/fiEhdoDWwkCA7Du4lkeXAXmA68DdwWFWT3FWC4f/Eu8CT/FMfrSLBdwyy5SURdMH5B7Qc+B0YrarX+DSqvCEZLMu+noYpNESkNPAT8KiqHg10PP6mqsmq2gpnXPD2wLkZrebfqPxHRPoAe1V1SdrFGaxaaI+BV14SQXmgA04yiAfquKdX+d1OoHaa+VpATIBiCbQ9IlIdwH3eG+B4fE5EwnCSwDeqOtZdHHTHAUBVDwOzcdpLwkUktdt4Yf8/cT7QV0S24lwa7oZzhhBMx8ATL4ngT+BXVb0UaAfUAOb7NKq88RfQ0O0hUBS4AZgY4JgCZSKQ2q5zO04HgELL/aHyObBWVd9O81LQHAcRqSwi4e50CaAHTlvJLJwKwlDIj4GqDlTVWqpaF+f//29uR5egOQZeebmzOEJVt6dbdqHbKJmviUhvnF8AocAXqvpKgEPyORH5FuiKU253DzAIGA+MASKA7cC1qpq+QbnQEJELgHk43ZxTrw3/F6edICiOg4i0xGkIDcX5wTdGVV8Skfo4v44rAMuAW1Q1PnCR+oeIdAWeUNU+wXoMsuIlEQhwM1Df/YcUAVRT1UX+CNAYY4xveUkEn+D8quqmque6N+FMU9V2/gjQGGOMb9mYxcYYE+RszGJjjAlyXhLB+8A4oIqIvIJzL8GrPo3KGGOM3xT6MYuNMcZkzcsZAaq6TlU/UtUPLQkEjoiEi8j9gY7Dn0TkJRHp4U4/KiIl07w2ObWvvI/eu7JbpXKZiHRO91r6WI6fuQffEZG6InJTmvlIEXk/l/uaLSJnPaC7iHzrVih+LN3ykSKyRUTuPdv3yCtuddrjefG5CwNPicDkG+FAhonAbccpdFT1eVWd4c4+CpRM81pv965ZX+kOrFPV1qo6L91rp8XiC2nufs1IXeBUIlDVxar6sC/jyYqIVAP+paotVfWdDFYZoKqf5mB/Xjqy5JqqXgQs9uV7FCSWCAJMRG5x68YvF5HP3EJhddxa6ZVEJERE5onIJcAQoIG77lAR6er+shmNO0ZERvtzlx8XkddFZImIzBCR9u4vwc0i0tdd5w4R+TBNbJPcG3E8bZ/uc3UVkbkiMk5E1ojIpyIS4r52o4hEicgqcUa7Sy2QNtJdFpX6q9Jddo2IPIxzV/ssEZnlvrZVRCq504+7264SkUfdZXXFGZPgf+LU5J/m3mWbPtY6IjLT/TU7U0QiRKQV8AbQ2z2WJdKsf0Ys7vJXxKn//6eIVHWXVRaRn0TkL/dxvru8goiMd9/zT3FuAENEXhCRYSIyDfjSPS5D3W1Xisg97tsNATq7sT3mHu/UevulRWSEexxXisjV7vJPRGSxpBmfIJt/m1vdv/ki93GOu/xa9zivEJHUG0un4bQjLpd0Z08Z7Pdy+edMa0aaY5XRZ38zzed4yF1viPtvaqWIvJnNcc7wWJh0VNUeAXrgFAH7GQhz5z8GbnOn/41TKncA8Jm7rC6wKs32XYETQD0P+1Oglzs9Duc/bhhwHrDcXX4H8GGa/U8CunrdPt1n6wrEAfVx7m6djnNbfw2cu3or43Rf/g2nDHBbYHqa7cPd55HANe70VqBSmnW24txB3RYnEZYCSgOrcSqO1sUZm6CVu/4YnLtI08f6M3C7O30XMD6j45Fum/SxKHC5O/0G8Kw7PRq4wJ2OwCl7AfABMMid7pbmb/ACsAQo4c73T7OvYji/Yuu5x3dSuuM9yZ1+HXg3zWvl3ecK7nMoTu2hlu78bCAyk8/4jDt9W5r9RwE10/2d6pLm32a6/Zz6G6bGwz/tk/8G3srks9+HUy+qSGr87mN9mu1T3z+z45zhscjqcwfjw6enXyZb3XG+xP4Sp45fCdxCaKo6XESuBe7FGVgkM4tUdUt2+wMSgCnudBQQr6qJ4oxCV9dDrLnZfpGqboZTpS8uABKB2aq6z13+DXAhMBioLyIfAL/gJBqvLgDGqeoJd59jgc44tYW2qOpyd70lmcTaCbjKnf4K54s8pxJwEmfq+6QO8doDaCr/1GksKyJl3JivBlDV30SkooiUc9eZqKqx7vQlQEsRSa2NUw5o6L5fZnrg1NbB3f8hd/I6EemPk4Cr4wzYtDKbz/VtmufUSz7zgZEiMgYYm+FWWasFfC9O4b+iwJY0r6X97D2AT9UtGa3OWChFcH5gDBeRX/jnmGd2nDM7FiYNSwSBJcAoVR14xgtOQ2Qtd7Y0cCyTfZzwsj8gUd2fQTj3gcQDqGqK/HM9NonTLxcWz+H26aXvkqZkXAYYdW5UPA/oCTwAXIfz69yLrKrhpq0hk4yTHLOTm7LEaY9PMv/83woBOqX5cgNOlW7J7H3T/00fUtWp6bbvmkUsQrrPICL1gCeAdu6xHsnpf9/MaPppVb1XRDrgDPiy3L2MlhMfAG+r6kT3c7yQ5rX0n/20z6GqSSLSHudHzw3AgzhnVFkd56AvM50dayMIrJnANSJSBU5dN67jvvY68A3wPPA/d9kxoEwu9+fFVqCVOO0StXFq2J+N9uJUfw0Brse5B2Uh0EWc9o9Q4EZgjjjX+kNU9SfgOaBNBvvL7PPPBfqJSEkRKQVciVN0zqsF/POr8WY3zuxk97dINQ3nywqANF+ac933Sv1S368Zj5kwFbhPnLLaiEgj9zNm9f7p37M8UBbnS/aIe02+l4fYwfm7pT7/4e6vgaouVNXngf2cXu7di3JAtDud1WiH04B7U39ouP+eSwPlVHUyToN9qzTrZnScMzoWJh1LBAGkqmuAZ4FpIrIS5zp6dRHpglPy+3VV/QZIEJE7VfUAMN9tqBvqdX85CGk+zml6FPAmsPQsPh44XxxDgFXufsepMzLYQJxSwCuApao6AWeUqNnijKg10l0nvWHAr5KmgRZAnWEpRwKLcBLNcFVdloM4HwbudI/ZrThj3GYnw1gy2Xek21C5BudSHzi/giPd9xxC5l+Iw4E1wFIRWQV8hnO2sRJIchtsH0u3zctA+dQGXeAiVV2BU2lzNfAF3kvJFxORhTjHJPV9hrqNr6twEtoKj/tK9QLwg4jMw0kkmRmO05600v0cN+Ekv0nucZuTJqbMjvMZxyKHsQYFTzeUGZNTkqbsb6BjMbkjzoAukaqa1Ze1l/2MxGlo/jG7df1JRGbj/BsN+m6kdkZgjPG1I8BgyWc3lOH0aEsMdCz5gZ0RGGNMkLMzAmOMCXKWCIwxJshZIjDGmCBnicAYY4KcJQJjjAly/w8Zx7puw07KPwAAAABJRU5ErkJggg==\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": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.image.AxesImage at 0x7f82c9716470>"
      ]
     },
     "execution_count": 3,
     "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('../dmu18_HELP-PACS-maps/data/GAMA-12_PACS160_v0.9.fits')\n",
    "stackhd = fits.open('./data/output_data/GAMA12-160um-psffromstack_20171002.fits')\n",
    "psf = stackhd[0].data\n",
    "hd = stackhd[0].header\n",
    "plt.imshow(psf)"
   ]
  },
  {
   "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": 4,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "resol= np.abs(stackhd[0].header['CDELT1'])/np.abs(stackhd_im[1].header['CDELT1'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.0"
      ]
     },
     "execution_count": 5,
     "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": 6,
   "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": 7,
   "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": 8,
   "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": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-3.0000000726000002"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "hd['CDELT1']*3600."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'Encircled flux')"
      ]
     },
     "execution_count": 10,
     "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": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.001311874482780695\n"
     ]
    }
   ],
   "source": [
    "# This is clearly. \n",
    "print(np.median(psf[0:5,:]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'Encircled flux')"
      ]
     },
     "execution_count": 12,
     "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": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "75"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "len(nbpix)"
   ]
  },
  {
   "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[30:], encircled_flux[30:], 1)\n",
    "bkg = p[0]/resol**2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "193.0"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "nbpix[30]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "2.779736007386497e-13\n"
     ]
    }
   ],
   "source": [
    "print(bkg)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[3.34129795e-13 1.64045243e-12 2.91951046e-12 4.15437045e-12\n",
      " 6.58373785e-12 7.76228148e-12 8.92898472e-12 1.12550195e-11\n",
      " 1.35462389e-11 1.46833691e-11 1.69472372e-11 1.80800793e-11\n",
      " 2.03342050e-11 2.25844182e-11 2.37089897e-11 2.59568912e-11\n",
      " 2.82025829e-11 2.93244345e-11 3.15693880e-11 3.26900479e-11\n",
      " 3.49334087e-11 3.71687883e-11 3.94091945e-11 4.16446309e-11\n",
      " 4.27630726e-11 4.50015353e-11 4.61210560e-11 4.83549935e-11\n",
      " 5.05885996e-11 5.28159585e-11 5.50468055e-11 5.61636659e-11\n",
      " 6.06295407e-11 6.28596184e-11 6.39749408e-11 6.62038749e-11\n",
      " 6.84315830e-11 7.06592407e-11 7.17745154e-11 7.40006783e-11\n",
      " 7.62317077e-11 7.84591559e-11 8.06868161e-11 8.29100225e-11\n",
      " 8.51376377e-11 8.62492748e-11 8.84728562e-11 8.95846473e-11\n",
      " 9.18121408e-11 9.40383421e-11 9.62623271e-11 9.84831578e-11\n",
      " 1.00710132e-10 1.02930636e-10 1.05156176e-10 1.05710948e-10\n",
      " 1.06819425e-10 1.10148789e-10 1.11259859e-10 1.14590388e-10\n",
      " 1.16809721e-10 1.17918437e-10 1.20140440e-10 1.21250513e-10\n",
      " 1.23475190e-10 1.24584437e-10 1.25694478e-10 1.27916474e-10\n",
      " 1.29024523e-10 1.31243683e-10 1.32354704e-10 1.33465404e-10\n",
      " 1.34574473e-10 1.35682927e-10 1.35958794e-10]\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 0x7f82c9583208>"
      ]
     },
     "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(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 0x7f82c94e9860>"
      ]
     },
     "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 0x7f82c9456358>"
      ]
     },
     "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 0x7f82c943e240>"
      ]
     },
     "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 = 1.000, ff = 1.057, residual = 0.008\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 0x7f82c8bf86a0>"
      ]
     },
     "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": [
       "412203844356.9508"
      ]
     },
     "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": "markdown",
   "metadata": {},
   "source": [
    "### As units of map in MJy/sr, divide by 1E6\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [],
   "source": [
    "psfok=psfok/1.0E6"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Validation\n",
    "To check PSF is reasonable, lets look at a 160 micron source, e.g. `----`. We can see from `GAMA-12_PACS160_v0.9.fits` that it has a flux of -- Jy. Maximum value in our normalised PSF gives ---"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from astropy.table import Table"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "ename": "FileNotFoundError",
     "evalue": "[Errno 2] No such file or directory: './data/GAMA12_PACSxID24_v1.fits'",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mFileNotFoundError\u001b[0m                         Traceback (most recent call last)",
      "\u001b[0;32m<ipython-input-31-005699daabf9>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[0;32m----> 1\u001b[0;31m \u001b[0mPACScat\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mTable\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mread\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m'./data/GAMA12_PACSxID24_v1.fits'\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m",
      "\u001b[0;32m~/anaconda3/lib/python3.6/site-packages/astropy/table/table.py\u001b[0m in \u001b[0;36mread\u001b[0;34m(cls, *args, **kwargs)\u001b[0m\n\u001b[1;32m   2548\u001b[0m         \u001b[0;31m# RST table and inserts at the end of the docstring.  DO NOT REMOVE.\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   2549\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m-> 2550\u001b[0;31m         \u001b[0mout\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mio_registry\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mread\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mcls\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m*\u001b[0m\u001b[0margs\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m**\u001b[0m\u001b[0mkwargs\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m   2551\u001b[0m         \u001b[0;31m# For some readers (e.g., ascii.ecsv), the returned `out` class is not\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   2552\u001b[0m         \u001b[0;31m# guaranteed to be the same as the desired output `cls`.  If so,\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m~/anaconda3/lib/python3.6/site-packages/astropy/io/registry.py\u001b[0m in \u001b[0;36mread\u001b[0;34m(cls, format, *args, **kwargs)\u001b[0m\n\u001b[1;32m    500\u001b[0m                     \u001b[0;32mtry\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    501\u001b[0m                         \u001b[0mctx\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mget_readable_fileobj\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0margs\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m0\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mencoding\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;34m'binary'\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 502\u001b[0;31m                         \u001b[0mfileobj\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mctx\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m__enter__\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    503\u001b[0m                     \u001b[0;32mexcept\u001b[0m \u001b[0mOSError\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    504\u001b[0m                         \u001b[0;32mraise\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m~/anaconda3/lib/python3.6/contextlib.py\u001b[0m in \u001b[0;36m__enter__\u001b[0;34m(self)\u001b[0m\n\u001b[1;32m     79\u001b[0m     \u001b[0;32mdef\u001b[0m \u001b[0m__enter__\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     80\u001b[0m         \u001b[0;32mtry\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 81\u001b[0;31m             \u001b[0;32mreturn\u001b[0m \u001b[0mnext\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mgen\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m     82\u001b[0m         \u001b[0;32mexcept\u001b[0m \u001b[0mStopIteration\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     83\u001b[0m             \u001b[0;32mraise\u001b[0m \u001b[0mRuntimeError\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m\"generator didn't yield\"\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;32mfrom\u001b[0m \u001b[0;32mNone\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m~/anaconda3/lib/python3.6/site-packages/astropy/utils/data.py\u001b[0m in \u001b[0;36mget_readable_fileobj\u001b[0;34m(name_or_obj, encoding, cache, show_progress, remote_timeout)\u001b[0m\n\u001b[1;32m    191\u001b[0m                 \u001b[0mname_or_obj\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mcache\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mcache\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mshow_progress\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mshow_progress\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    192\u001b[0m                 timeout=remote_timeout)\n\u001b[0;32m--> 193\u001b[0;31m         \u001b[0mfileobj\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mio\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mFileIO\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mname_or_obj\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m'r'\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    194\u001b[0m         \u001b[0;32mif\u001b[0m \u001b[0mis_url\u001b[0m \u001b[0;32mand\u001b[0m \u001b[0;32mnot\u001b[0m \u001b[0mcache\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    195\u001b[0m             \u001b[0mdelete_fds\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mappend\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mfileobj\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;31mFileNotFoundError\u001b[0m: [Errno 2] No such file or directory: './data/GAMA12_PACSxID24_v1.fits'"
     ]
    }
   ],
   "source": [
    "PACScat=Table.read('./data/GAMA12_PACSxID24_v1.fits')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "ename": "NameError",
     "evalue": "name 'PACScat' is not defined",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mNameError\u001b[0m                                 Traceback (most recent call last)",
      "\u001b[0;32m<ipython-input-32-c5b280bad8ff>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[0;32m----> 1\u001b[0;31m \u001b[0mPACScat\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m'HELP_ID'\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m",
      "\u001b[0;31mNameError\u001b[0m: name 'PACScat' is not defined"
     ]
    }
   ],
   "source": [
    "PACScat['HELP_ID']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "ename": "NameError",
     "evalue": "name 'PACScat' is not defined",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mNameError\u001b[0m                                 Traceback (most recent call last)",
      "\u001b[0;32m<ipython-input-33-6c28fc823ff0>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[0;32m----> 1\u001b[0;31m \u001b[0mPACScat\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mPACScat\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m'HELP_ID'\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m==\u001b[0m\u001b[0;34m'GAMA12-PACSxID24-1-69605'\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m",
      "\u001b[0;31mNameError\u001b[0m: name 'PACScat' is not defined"
     ]
    }
   ],
   "source": [
    "PACScat[PACScat['HELP_ID']=='GAMA12-PACSxID24-1-69605']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Max PSF = 18.0339 Jy/sr, off pixel Max PSF = 15.8760 Jy/sr\n"
     ]
    }
   ],
   "source": [
    "cpix=np.int((hd['NAXIS1']+1)/2.0)\n",
    "\n",
    "print(\"Max PSF = {:.4f} Jy/sr, off pixel Max PSF = {:.4f} Jy/sr\".format(psfok[cpix-1,cpix-1]*0.0185,psfok[cpix-3,cpix-3]*0.0185))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "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, which provide the same functionality instead.\n",
      "  obj_type='module')\n"
     ]
    },
    {
     "ename": "OSError",
     "evalue": "File not found: ./data/input_data/GAMA-12_PACS160_v0.9.fits",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mOSError\u001b[0m                                   Traceback (most recent call last)",
      "\u001b[0;32m<ipython-input-34-8cb47a2ad34b>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[1;32m      3\u001b[0m \u001b[0msns\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mset_style\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m\"white\"\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      4\u001b[0m \u001b[0mcmap\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0msns\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mcubehelix_palette\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m8\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mstart\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;36m.5\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mrot\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;34m-\u001b[0m\u001b[0;36m.75\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mas_cmap\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;32mTrue\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 5\u001b[0;31m \u001b[0mfig\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0maplpy\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mFITSFigure\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m'./data/input_data/GAMA-12_PACS160_v0.9.fits'\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m      6\u001b[0m \u001b[0mfig\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mrecenter\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mPACScat\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mPACScat\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m'HELP_ID'\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m==\u001b[0m\u001b[0;34m'GAMA12-PACSxID24-1-69605'\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m'RA'\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mPACScat\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mPACScat\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m'HELP_ID'\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m==\u001b[0m\u001b[0;34m'GAMA12-PACSxID24-1-69605'\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m'Dec'\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mradius\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;36m0.005\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      7\u001b[0m \u001b[0mfig\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mshow_colorscale\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mvmin\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;34m-\u001b[0m\u001b[0;36m0.001\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mvmax\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;36m0.002\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mcmap\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mcmap\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m~/anaconda3/lib/python3.6/site-packages/aplpy/core.py\u001b[0m in \u001b[0;36m__init__\u001b[0;34m(self, data, hdu, figure, subplot, downsample, north, convention, dimensions, slices, auto_refresh, **kwargs)\u001b[0m\n",
      "\u001b[0;32m~/anaconda3/lib/python3.6/site-packages/aplpy/decorators.py\u001b[0m in \u001b[0;36m_auto_refresh\u001b[0;34m(f, *args, **kwargs)\u001b[0m\n\u001b[1;32m     23\u001b[0m     \u001b[0mmydata\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mnesting\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mgetattr\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mmydata\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m'nesting'\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;36m0\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;34m+\u001b[0m \u001b[0;36m1\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     24\u001b[0m     \u001b[0;32mtry\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 25\u001b[0;31m         \u001b[0;32mreturn\u001b[0m \u001b[0mf\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0margs\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m**\u001b[0m\u001b[0mkwargs\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m     26\u001b[0m     \u001b[0;32mfinally\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     27\u001b[0m         \u001b[0mmydata\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mnesting\u001b[0m \u001b[0;34m-=\u001b[0m \u001b[0;36m1\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m~/anaconda3/lib/python3.6/site-packages/aplpy/core.py\u001b[0m in \u001b[0;36m__init__\u001b[0;34m(self, data, hdu, figure, subplot, downsample, north, convention, dimensions, slices, auto_refresh, **kwargs)\u001b[0m\n\u001b[1;32m    215\u001b[0m         \u001b[0;32melse\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    216\u001b[0m             self._data, self._header, self._wcs = self._get_hdu(data, hdu, north, \\\n\u001b[0;32m--> 217\u001b[0;31m                 convention=convention, dimensions=dimensions, slices=slices)\n\u001b[0m\u001b[1;32m    218\u001b[0m             \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_wcs\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mnx\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_header\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m'NAXIS%i'\u001b[0m \u001b[0;34m%\u001b[0m \u001b[0;34m(\u001b[0m\u001b[0mdimensions\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m0\u001b[0m\u001b[0;34m]\u001b[0m \u001b[0;34m+\u001b[0m \u001b[0;36m1\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    219\u001b[0m             \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_wcs\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mny\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_header\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m'NAXIS%i'\u001b[0m \u001b[0;34m%\u001b[0m \u001b[0;34m(\u001b[0m\u001b[0mdimensions\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m]\u001b[0m \u001b[0;34m+\u001b[0m \u001b[0;36m1\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m~/anaconda3/lib/python3.6/site-packages/aplpy/core.py\u001b[0m in \u001b[0;36m_get_hdu\u001b[0;34m(self, data, hdu, north, convention, dimensions, slices)\u001b[0m\n\u001b[1;32m    297\u001b[0m             \u001b[0;31m# Check file exists\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    298\u001b[0m             \u001b[0;32mif\u001b[0m \u001b[0;32mnot\u001b[0m \u001b[0mos\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mpath\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mexists\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mfilename\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 299\u001b[0;31m                 \u001b[0;32mraise\u001b[0m \u001b[0mIOError\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m\"File not found: \"\u001b[0m \u001b[0;34m+\u001b[0m \u001b[0mfilename\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    300\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    301\u001b[0m             \u001b[0;31m# Read in FITS file\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;31mOSError\u001b[0m: File not found: ./data/input_data/GAMA-12_PACS160_v0.9.fits"
     ]
    }
   ],
   "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/GAMA-12_PACS160_v0.9.fits')\n",
    "fig.recenter(PACScat[PACScat['HELP_ID']=='GAMA12-PACSxID24-1-69605']['RA'],PACScat[PACScat['HELP_ID']=='GAMA12-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": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.colorbar.Colorbar at 0x7fee7352b160>"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "rad=20\n",
    "plt.imshow(psfok[cpix-1-rad:cpix+rad:5,cpix-1-rad:cpix+rad:5]*0.0185,vmin=0,vmax=2,cmap=cmap)\n",
    "plt.colorbar()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In summary, the PSF is within 10% of this source, and given noise and shape of source will add additional uncertianty, as well as non-zero background, this seems reasonable.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [],
   "source": [
    "stackhd[0].data=psfok\n",
    "stackhd.writeto('./data/dmu18_PACS_160_PSF_GAMA12_20190228sr.fits',output_verify='fix+warn', overwrite=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "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": 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(800,900,1));\n",
    "plt.yscale('log')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1013.0244746745424"
      ]
     },
     "execution_count": 39,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.max(psfok)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.0"
      ]
     },
     "execution_count": 40,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.mean(~np.isnan(psf))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
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