{
 "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": [
    {
     "ename": "KeyboardInterrupt",
     "evalue": "",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mKeyboardInterrupt\u001b[0m                         Traceback (most recent call last)",
      "\u001b[0;32m<ipython-input-4-a1b9ad373641>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[0;32m----> 1\u001b[0;31m \u001b[0mpsf\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;34m(\u001b[0m\u001b[0;36m2\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0mspecial\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mjn\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mq\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m/\u001b[0m\u001b[0mq\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m**\u001b[0m\u001b[0;36m2\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m",
      "\u001b[0;31mKeyboardInterrupt\u001b[0m: "
     ]
    }
   ],
   "source": [
    "psf = (2*special.jn(1, q)/q)**2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "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 0x7f2a2b921fd0>"
      ]
     },
     "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 0x7f2a2a0a3828>"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(y[ycen-500:ycen+500], psf[ycen-500:ycen+500, xcen], label='Original')\n",
    "plt.plot(y[ycen-500:ycen+500], psfblur[ycen-500:ycen+500, xcen], label='With blurring')\n",
    "plt.legend()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We see the effect of blurring, the, observed PSF is wider, and we have lost some flux in the central core. Suppose now that we observed this psf with sources of unknown fluxes, so that we re unsure of its scaling, and that a background remain in our observation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "psfobs = psfblur * 2. + 1e-4"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The question is now how to recover the PSF that serve for our observation. For this, we will use the PSFs curve of growth. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.0 212.10000000000002\n",
      "10.0 212.10000000000002\n",
      "20.0 212.10000000000002\n",
      "30.0 212.10000000000002\n",
      "40.0 212.10000000000002\n",
      "50.0 212.10000000000002\n",
      "60.0 212.10000000000002\n",
      "70.0 212.10000000000002\n",
      "80.0 212.10000000000002\n",
      "90.0 212.10000000000002\n",
      "100.0 212.10000000000002\n",
      "110.0 212.10000000000002\n",
      "120.0 212.10000000000002\n",
      "130.0 212.10000000000002\n",
      "140.0 212.10000000000002\n",
      "150.0 212.10000000000002\n",
      "160.0 212.10000000000002\n",
      "170.0 212.10000000000002\n",
      "180.0 212.10000000000002\n",
      "190.0 212.10000000000002\n",
      "200.0 212.10000000000002\n",
      "210.0 212.10000000000002\n"
     ]
    }
   ],
   "source": [
    "radii = np.arange(0, np.max(r), resol)\n",
    "growth_psf = np.zeros(radii.shape)\n",
    "growth_psfobs = np.zeros(radii.shape)\n",
    "nbpix_psfobs = np.zeros(radii.shape)\n",
    "for i, radius in enumerate(radii):\n",
    "    if ((i % 100) == 0):\n",
    "        print(radius, np.max(radii))\n",
    "    if i == 0:\n",
    "        idj, idi = np.where(r <= radius)\n",
    "        growth_psf[i] = np.sum(psf[idj, idi])*resol**2\n",
    "        growth_psfobs[i] = np.sum(psfobs[idj, idi])*resol**2\n",
    "        nbpix_psfobs[i] =len(idi)\n",
    "    else:\n",
    "        idj, idi = np.where((r > radii[i-1]) & (r <= radius))\n",
    "        growth_psf[i] = growth_psf[i-1]+np.sum(psf[idj, idi])*resol**2\n",
    "        growth_psfobs[i] = growth_psfobs[i-1]+np.sum(psfobs[idj, idi])*resol**2\n",
    "        nbpix_psfobs[i] = nbpix_psfobs[i-1]+len(idi)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x7f2a29f59eb8>"
      ]
     },
     "execution_count": 16,
     "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": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'Encircled flux')"
      ]
     },
     "execution_count": 17,
     "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": 18,
   "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": 19,
   "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": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x7f2a29e95e48>"
      ]
     },
     "execution_count": 20,
     "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": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'Ratio of encircled flux')"
      ]
     },
     "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:], 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": 22,
   "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": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(0, 60)"
      ]
     },
     "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(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": 24,
   "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": 25,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[ 1.07402639 -0.04610159]\n",
      "1.0550300032613567\n",
      "1.072831254463463\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(max_dpsf, max_dpsfcor, 'o-')\n",
    "p = np.polyfit(max_dpsf[0:3], max_dpsfcor[0:3], 1)\n",
    "plt.plot(max_dpsf, p[0]*max_dpsf+p[1])\n",
    "plt.xlabel('extremum position of theoretical psf [arcsec]')\n",
    "plt.ylabel('extremum position of observed blurred psf [arcsec]')\n",
    "\n",
    "\n",
    "print(p)\n",
    "print((max_dpsfcor[1]-max_dpsfcor[0])/(max_dpsf[1]-max_dpsf[0]))\n",
    "print((max_dpsfcor[2]-max_dpsfcor[0])/(max_dpsf[2]-max_dpsf[0]))\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'Encircled flux')"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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ycvslOxxjTA90wAShqkdHz4vIBMCuliaQOg4PLn2QQke5/BS79mCMSY52346rqkuIXLA2CfLB4kdZIi1c0+9kApkFyQ7HGNNDHfAMQkS+HzXrASYA9lCGBFFVfr/yjxQ7yoUn2/2IxpjkiecMIifqlU7kmsR5iQyqJ1v8yV9YKi18p/gk/OnZyQ7HGNODxXMN4uedEYiJ+MPHj1EQdrjgpLuTHYoxpofbb4IQkZeI9F6KSVXPTUhEPdjKtS/zT63jlt4TyMjsnexwjDE9XFtnEPd3WhQGgCcX3UeO43DptP9JdijGGNNmgrhTVU8VkXtV9T87LaIeakPp+7wR3Mn3co4gO29gssMxxpg2E0SxiJwEnCsis4jcKLeb293VdJAnP/gF6ap848T/TnYoxhgDHOAMArgNGAD8L3snCAVOSWBcPcr28k+Z37iZSzP6U9BnTLLDMcYYoI0Eoaqzgdkicoeq2mFtAs18/79wgG8e97Nkh2KMMbsd8D4ISw6J1diwk9lVKznVk0f/IScmOxxjjNmt3UNtmI710rt3UeMRrjjm2mSHYowxe7EEkUTqODyz9R2OVB8TxlyR7HCMMWYvbd0o1+Yocaq6q+PD6Vn+tXQGG7zwP4OmIyIH/oAxxnSitnoxLWbPcyAGAZXudD7wOZHnQphD8LdVf6Ug7PDV4+w2E2NM17PfJiZVHaqqw4DXgHNUtVBVewNnA893VoCpqqJ8Fe+EqzgvdwRpGbnJDscYY74gnmsQx6rq/NYZVX0FOClxIfUML/7rV4REuODY7x94Y2OMSYJ4HjlaISI/A/5KpMnpG8DOhEaV4jQU5PmKJUzwBhg62Lq2GmO6pnjOIC4HioA57qvIXWYOUsmS3/O5V7ho6NnJDsUYY/YrnudB7AJuFpFsVa3rhJhS3nOr/48cRzltyq3JDsUYY/brgGcQInK8iKwCVrnz40Tk0YRHlqKqt3/CgnAN03OPIJBuF6eNMV1XPE1MvwW+invdQVWXAdZwfpDmfXgvLR7hokm3JDsUY4xpU1x3Uqtq6T6LwgmIJeVpsInnKpYwWgKMsovTxpguLp4EUSoixwMqImki8kPg0wTHlZJWljzOWr+XC+3itDGmG4gnQfwHcD3QH9gMjHfnTTs9t3oWAYXpx1rzkjGm64unF1MFYCPJHaKGbcuYTy1fyR1Jtt05bYzpBtoarO93RG6Mi0lVb0pIRCnqtUUP0ODxcOGE65IdijHGxKWtM4iSTosi1TkOz5WVMMyfxvjBpyY7GmOMiUtbjxz986HsWESeIjKwX5mqfuFByxIZ3/pBYDrQAFypqksO5Tu7qvWrn2eZH37Y70Qb1tsY023Ec6PcAhHJj5rvJSKvxbHvPwFntLH+TGCE+7oaeCyOfXZLzy1/Ep8q50z5QbJDMcaYuMXTi6lIVataZ1S1EuhzoA+p6rtAWw8VOg94WiM+BPJFpDiOeLqVlqYaXmr8nFP8hRTkDkh2OMYYE7d4EkRYRAa1zojIYNq4eN0O/YHoG/A2u8u+QESuFpESESkpLy/vgK/uPG8teohqj4cLR16S7FCMMaZd4hnu+6fA+yLyjjt/IpEmoUMVqzE+ZuJR1RnADIBJkyZ1RHLqNM9tnEe/sDJ1/PeSHYoxxrRLmwnCvZC8EpgATCVSqd/q3htxqDYDA6PmBwBbO2C/XUZp2Qo+1DquzxuFx5eW7HCMMd2QqtISdmgJua+wQ3PQ2b2sOeTQHArvtb51efSyg9FmglBVFZEXVHUi8PJBfcP+zQVuEJFZwBSgWlW3dfB3JNWcRb/Fo8r5du+DMe0WdnR3xdda2TWHwjS5lWMorIQdxdHIq3U67EQ+q6qE3eWquNtFKtzWeWXPctx3J3q9grL3ct29n9Zle+9nzzat+4GQ4+xTjtaKfO/y7ZUIQg7N7nyyxNPE9KGIHKuqi9qzYxGZCUwDCkVkM3AX4AdQ1ceB+US6uK4n0s31O+3Zf1cXdsK8WF7CCWEfhw05OdnhGJNwjqPUt4Soaw5R1+S+u9O1Ucvqm/ee32vb5hBNwUilGXK6T2uyR8AjggiICB4BwX0XwecV0rwe0v0e0rwe0nxe0nwe0n0estJ99Mr0kObz7F6W5vOQ5vXutWzP8tZle9bvWRa1XdTyNJ+HjHvbX654EsTJwDUi8hlQT6SZSVV1bFsfUtU2nzqnqkoKj+m0eP3LlInDj/qdBHbvg+liWo/Om4MOTe57c8ihKRimoSXsVtZB6prDbgUepL45TG30dHOIuqagW+lHPhOPDL+H7HRf5JURee+XHyA73UtWuo+A3+tWpJH3dLcyTN+nAvV7PXjcytjrETwewSsSWeaJLPOK7K6wvR5BiFTiHo8gsPvzSOv0nuXiIWqb1sqfvbdxE0CqiidBnJnwKFLQvE/+RKbjcNJkG5gv1TUFw1TUNVPTGKLWrTDrmkPUNIV2V65NwUhTQTC8pymhdToY3tMcAZEmjUjTBqD7zMOeJg1nT9NHdDNKOKqJpHV52FGC4T1JoL1H516P7KnU3Yo9P+BnQH6ArHQvORn+L1T62Rk+ctJ9ZLnLczIi035vXE8ZMF1AW2Mx5apqDVDbifGkhOZQEwtq13Oa5BDofXiywzEHKewo5bXNbKlqYHNlI1urmtha1UhZbRMVdS1U1DVTUdtMfUvbj0fxeoSA34vfK/i9e5/6+70e/N6oI9TWzn0SOXqNHMV6dh+9tq5vPZL1evY0Y3jdI+fd07ubPQSvh93NEq1H5BmtR+f+yLIMv5c0r4fMdC856X6yM3yRyj/dT4bfk9JHyia2ts4g/o/IUBmLiRy8RP86FBiWwLi6tfeW/5lagbOGTE92KOYAWkIOpZUNbCivZ2NFHRsr6tlYUc+Wqka2VzcRDO99pJ0X8NMnJ53C7HTGDsinMDuNwux0CrPTyAv49xxJZ0SOmK1yNd1ZW2Mxne2+D+28cFLDvDV/p3c4zORjU/YSS7eiqmyvaWJjeT0bKur3SgallY2Eo5pbCrLSGNI7k2MG9qL/2AD9891Xr4DbTh5Pq6wxqeGAv3YRuQB4S1Wr3fl8YJqqvpDo4LqjmsZdvNO8nUvTi/Fl9k52OD1KZX0LG3fWs7G8fveZwIaKejZV1NMY3NMMlOH3MLQwm6P65XHOuH4MLcza/crPtPtVjGkVz+HQXao6p3VGVatE5C7AEkQMb5Q8TFCEs0ZdmuxQUk5dc4gtlY1sqWpgS2Ujmysb2VzVyJbKRjbtrKeqIbh7W69HGFSQyZDemRw3rDdDi7IYXpjF0KIs+uZk4PFYk48xBxJPgojV5cDOs/dj3qZXGRxyOGrclckOpVM4jhL6ws1KkWad6GlHIayK4/aqCTkOjVFdKhuaw9S3RPrI76pvYWd9C7vqWthZ38zO+hYqapupadq7G2Wa10O//Az69wow/ehihkWdCQwsyLTeMsYcongq+hIR+Q3wCJGL0zcSuXBt9rFj13oWhWu4NncE0s2G1qhtCrKhvJ5/l9exrbqJspomymqb2VnXEunn3hLp697QEorcweomgEQQgYLMNAqyIq8jD8ul9+FpFOdFrgUM6BVgQH6Awux0OxMwJoHiSRA3AncAzxLpyfQ6KXyD26F4peRBVITpY7v2wHxNwTBLP69iyeeVLPmskhVbq9lR07zXNjkZPvrkpNM7O51++RlkpkX6sGelefF5PXg94BXB64lMezyRrpqRrpZ7uljuNR11M5LXIwTSvGSl+chMd9/TIjdK5QX8eK3iNybpDpggVLUeuK0TYun25m37gDEhGHzEWckO5Qt21bfw1uoyFqzaznvrKmhw++4PL8rihOGFHN43m+FFkVf//ACBNG+SIzbGJFs8vZiOAH4IDIneXlVPSVxY3c+/Sz9gNS38Z9HELjO0Rijs8Paacp4tKeWt1WWEHeWw3Ay+NqE/J4/sw8TBvazXjjFmv+JpYvo78DjwB6DtW0Z7sHlLHsWjyhmTbkx2KDQFw8xevJkZ727g810NFGan870vD+Wcsf04ql+u3bRljIlLPAkipKop+7zojqCOw/xdy5lKOoX9JiYtjpaQw18//IxH3/43FXXNjBuYz21njuL00X2tR48xpt3iSRAvich1wBxg95VMVW3redM9yrI1c9jiUa7rNy0p36+qLFi1g3teWc3GinqOG9abhy4fz3HDetvZgjHmoMWTIL7tvv8oapmNxRTl5RV/IsNRTp18a6d/9/bqJm5/fjn/WFPO8KIs/njlsUwbWWSJwRhzyOLpxWRjMbUhGGri9bqNTPPlk5U3oNO+V1WZvXgzd7+8imDY4Y6zR/Ot4wZbU5IxpsPstzYRkR9HTV+8z7r/SWRQ3cm/lj5BpUc4a9jZnfadtU1BrntmCT+avZwjD8vl1ZtP5KovDbXkYIzpUG3VKJdFTd++z7ozEhBLt/Ty2ufJcxxOmNg59w5+uq2Gcx/+J6+v2sHtZ45i1tVTGVKY1SnfbYzpWdpqYpL9TMea75Ea6st5u6WcczIG4M/ISfj3zV22lR/PXkZuhp9ZV0/l2CEFCf9OY0zP1VaC0P1Mx5rvkd5c9BCNHuGs0V9P6PeoKo++/W/ue20Nk4cU8MgVEyjKSU/odxpjTFsJYpyI1BA5Wwi407jzGQmPrBuY99kCisPK+DFXJOw7QmGHO15cwcyFpZw3vh+/vmgs6T4bBsMYk3htPVHOaqE27Ny5jg+1jivzRuHxJmb085aQw40zl/Dayh1cf/JwfnD6SBu91BjTaey5DgfptUUPEhbhrHGJGbm1ORTm+meW8sanO7jrnNF85wTrbWyM6VyWIA7SvO0fcITjYcThHd+hqzkU5tq/LuGt1WXcfd5RfOu4IR3+HcYYcyDWcf4glG5ZyHIJMr1wfIfvO+woN8/8mLdWl/GL88dYcjDGJI0liIMwf8kjAEyf0LH3Pqgqd764gldXbueOs0fzjamDO3T/xhjTHtbE1E6qyryKj5mIn+IBkzt03w+9uZ5nPvqca04axlVfsmsOxpjksjOIdlq9/lU2ehzOKj6+Q/c7c+Hn/PaNtXxtQn9uO2NUh+7bGGMOhiWIdpq3/Al8qnxl8i0dts/XV27np3M+YdrIIu69cKyNxGqM6RIsQbRDOBTklZq1fMmTQ17B4R2yz5JNu7hx5lKO7p/Ho1dMsAH3jDFdhtVG7VCy/I+UeYSzhnRM19bSXQ187+kS+uUHeOrKY8lMs0tCxpiuwxJEO8xf/TcyHeWkY2865H01toS5+i+LcRzlj1ceS+9sG1vJGNO12CFrnJobK1nQvI3T0g8jEOh1SPtSVf7zueWs3l7DU1cea8N1G2O6JDuDiNN7ix6m1uPhrJGXHPK+/vDeRuYu28oPvzKSk0f26YDojDGm41mCiNNLG+dT6CiTx33nkPbz/roK7nnlU84ccxjXTRveQdEZY0zHswQRh8qd63hXazkr9wh8vrSD3s+26kZunLmEw/tkc//F46w7qzGmS0toghCRM0RkjYisF5HbYqy/UkTKReRj95WYoVEP0Ssf/YaQCOeMu+ag9xF2lFtmfUxzyOHxb0wkK90u/xhjuraE1VIi4gUeAU4HNgOLRGSuqq7aZ9NnVfWGRMXREV7a8S9G4WXk4V896H089vZ6Ptq4i/suGsuwouwOjM4YYxIjkWcQk4H1qrpBVVuAWcB5Cfy+hNiwYQErPGHO6Tv1oPex+LNKfvvGOs4Z14+LJg7owOiMMSZxEpkg+gOlUfOb3WX7ulBElovIbBEZmMB4DsrcpY/jVWX65FsP6vM1TUFunrWU4rwMfnnBGLvuYIzpNhKZIGLVhLrP/EvAEFUdC7wB/DnmjkSuFpESESkpLy/v4DD3LxwK8nL1Go73ZFNYOLLdn1dVfjZnBduqm3jwsmPIzfAnIEpjjEmMRCaIzUD0GcEAYGv0Bqq6U1Wb3dkngImxdqSqM1R1kqpOKioqSkiwsXy47A/s8ArnD5l+UJ9/bskW5i7byi2njmDi4EO7uc4YYzpbIhPEImCEiAwVkTTgMmBu9AYiUhw1ey7waQLjabc5a/5GnuMwbfLN7f7sxop67nxxBVOGFnDdyR0zsJ8xxnSmhPViUtWQiNwAvAZ4gadUdaWI3A2UqOpc4CYRORcIAbuAKxPvOEmmAAAPP0lEQVQVT3tV127jrZZyLs4YQFpGXrs+2xJyuGnmUvxeD7+9dDxej113MMZ0PwntjK+q84H5+yy7M2r6duD2RMZwsOYv+i1BEc4f8+12f/Z/X1/DJ1uqefwbE+mXH0hAdMYYk3h2J/V+vFD6FiNDypFHXdauz723rpzfv7uBr08ZxBljDktQdMYYk3iWIGJY89m7rKKZCwongCf+f6Kddc18/2/LGNEnmzvOGp3ACI0xJvFsvIcYXlj8ED5Vpk/9UdyfUVV+NHs51Y1Bnv7uZAJp3gRGaIwxiWdnEPsItjQyr3o1J0sOvfoeHffn/vTBJt5aXcZPzhzFkcW5CYzQGGM6hyWIfby7+GEqPcL5Iy6I+zOrt9dwz/zVnDqqD98+fkjigjPGmE5kCWIfL6ybQ1FYOf7YG+PavjkU5pZZH5Mb8PHri8baUBrGmJRhCSJK2Y5PeM+p4ey8kfj88XVPfeCNdazeXsuvvjbWnittjEkpliCiPPfhvTjAxZO/H9f2iz/bxe/f+TeXThrIaaP7JjY4Y4zpZJYgXMFQM7N3LeN4yWTgwBMOuH1klNaP6d8rwB3nWJdWY0zqsQThervkYco8cNnw8w+4rary06hRWrPt6XDGmBRkCcL17NrZFIcdvjz5lgNuO3vxZl5atpVbTxvBhEE2SqsxJjVZggA2lH7AR1rHJflH403LbHvb8jrumruSqcMKuHaajdJqjEldliCAvy+8H58qFxzf9riBzaEwN81aSprPwwOXHmOjtBpjUlqPTxANjZW8WLOW07359D5sXJvb3v/aGlZsqeHXF47lsLyMTorQGGOSo8cniFf+eQ+1HuGyo9oe1vvtNWU88d5Gvjl1MF85ykZpNcakvh7d/cYJh3j681c5QjwcM/6q/W5XXtvMD/++jJF9c/jpWUd2YoTGGJM8PfoM4u2PfsMGr/LdYecj+xnW23GUH/x9GbVNIR66/Bgy/DZKqzGmZ+ixCUIdhyfXzKR/GL7axsXpp/65kXfXlvOzs0cz8rCcTozQGGOSq8cmiMXL/8xyT4gr+03D5499wfmTzdXc++pqvjK6L9+YMqiTIzTGmOTqsQniyWWPU+Ao5590d8z19c0hbpq1lN5Z6dx7oY3SaozpeXpkgliz9mXep4Erek8gIxD7Tui75q5k0856HrhsPL2y0jo5QmOMSb4emSCeXHgfmY5y6Um/jLn+xY+3MHvxZm44+XCmDuvdydEZY0zX0OMSxOefv89roZ1ckjOCvLyBX1i/dkctP3n+EyYMyufmU0ckIUJjjOkaelyCePDdn5Cu8K0Tf/GFddUNQa5+uoRAmo9Hr5iIz9vj/nmMMWa3HlUDLlsxi9fDlVyZfzRFfY7aa10w7HDDzCVsqWrk8W9MsKE0jDE9Xo+5k1odh/8tuY/ejnLl6Q/uvU6VO19cwXvrKvj1hWOZNKQgSVEaY0zX0WPOIN76169ZKi1cN+B0MrP77LVuxrsbmLmwlOtPHs4lx37xuoQxxvREPeIMIthSzwNrnmGYCF87+Z691s3/ZBv3vLKas8cW84PTRyYpQmOM6Xp6RIL4y4Jb2eSF3428cq+7ppd+Xsmtz37MxMG9uP/icXjs+Q7GGLNbyjcxlW5bzGNlH3AKWUybcuvu5et21HLVn0vom5vBjG9OtEH4jDFmHymdINRx+MWCG/Ci3H7qg+AOl/HZznqu+MNHeD3C09+dTO/s9CRHaowxXU9KJ4iX3/4pH2gdN/U5gcMGTAEiZw6X/P5fBMMOz3xvCkMKs5IcpTHGdE0pmyBKN3/ELz97ifGaxqVffRiAZaVVXDrjQxyFWVcfxxF9bfhuY4zZn5RMEE2NlfxowTV4gF+d/iheXxqvfLKNS2f8i8w0L3+/5jh7toMxxhxAyvViUsfhrjkXskpCPDjySvr1m8wj/1jPfa+tYcKgfGZ8axKFds3BGGMOKLUShCqPzbmE+cFybswfx+QJt/CDvy/j+SVbOHdcP3590VjrrWSMMXFKmQShjsMjL1zK7+vWcF56P44e8wBnPPgumysbufnUEdxy2gh76I8xxrRDQq9BiMgZIrJGRNaLyG0x1qeLyLPu+o9EZMjBfE8o2MRvn7+Q39eu5lx/MY1yD5f/YSEeEf52zXHcevoRlhyMMaadEnYGISJe4BHgdGAzsEhE5qrqqqjNrgIqVfVwEbkMuBe4tD3fs3HjP/jZ299nuSfEtJZCnlt3I47u4JoTh3HzaSPITEuZkyRjjOlUiaw9JwPrVXUDgIjMAs4DohPEecB/udOzgYdFRFRV29pxKNTMsk/nMGvpDBY4ZWSqMmrrZF6rv5gLxg/ghlMOZ2BBZseXyBhjepBEJoj+QGnU/GZgyv62UdWQiFQDvYGK/e10bcVKJv11ImER0h1lfHUB9XoNX548mcemDLIeSsYY00ESmSBiNfrve2YQzzaIyNXA1QC9B2ZyWnAQvQMjGD3yCiaOHMOAXna2YIwxHS2RCWIzEP1whQHA1v1ss1lEfEAesGvfHanqDGAGwKRJk/T+/zc/IQEbY4zZI5G9mBYBI0RkqIikAZcBc/fZZi7wbXf6IuCtA11/MMYY0zkSdgbhXlO4AXgN8AJPqepKEbkbKFHVucCTwF9EZD2RM4fLEhWPMcaY9kloH1BVnQ/M32fZnVHTTcDFiYzBGGPMwUnJwfqMMcYcOksQxhhjYrIEYYwxJiZLEMYYY2KyBGGMMSYm6W63HYhILbAm2XEkUCFtDDWSAqx83Vcqlw1Sv3wjVbVdj9LsjkOdrlHVSckOIlFEpMTK132lcvlSuWzQM8rX3s9YE5MxxpiYLEEYY4yJqTsmiBnJDiDBrHzdWyqXL5XLBla+L+h2F6mNMcZ0ju54BmGMMaYTdKsEISJniMgaEVkvIrclO55DJSJPiUiZiKyIWlYgIgtEZJ373iuZMR4sERkoIv8QkU9FZKWI3OwuT5XyZYjIQhFZ5pbv5+7yoSLykVu+Z92h7rstEfGKyFIRedmdT5nyicgmEflERD5u7eGTQr/PfBGZLSKr3b/B4w6mbN0mQYiIF3gEOBMYDVwuIqOTG9Uh+xNwxj7LbgPeVNURwJvufHcUAn6gqkcCU4Hr3f+vVClfM3CKqo4DxgNniMhU4F7gt275KoGrkhhjR7gZ+DRqPtXKd7Kqjo/q3poqv88HgVdVdRQwjsj/YfvLpqrd4gUcB7wWNX87cHuy4+qAcg0BVkTNrwGK3eliIvd9JD3ODijni8DpqVg+IBNYQuSZ6xWAz12+12+2u72IPAXyTeAU4GUijwhOpfJtAgr3Wdbtf59ALrAR9xrzoZSt25xBAP2B0qj5ze6yVNNXVbcBuO99khzPIRORIcAxwEekUPnc5pePgTJgAfBvoEpVQ+4m3f03+gDwY8Bx53uTWuVT4HURWew+9x5S4/c5DCgH/ug2D/5BRLI4iLJ1pwQhMZZZF6wuTkSygeeAW1S1JtnxdCRVDavqeCJH2pOBI2Nt1rlRdQwRORsoU9XF0YtjbNoty+c6QVUnEGm2vl5ETkx2QB3EB0wAHlPVY4B6DrKprDsliM3AwKj5AcDWJMWSSDtEpBjAfS9LcjwHTUT8RJLDM6r6vLs4ZcrXSlWrgLeJXGvJF5HWIWy682/0BOBcEdkEzCLSzPQAqVM+VHWr+14GzCGS5FPh97kZ2KyqH7nzs4kkjHaXrTsliEXACLcXRRqR51fPTXJMiTAX+LY7/W0ibffdjogIkWeOf6qqv4lalSrlKxKRfHc6AJxG5ELgP4CL3M26bflU9XZVHaCqQ4j8rb2lqleQIuUTkSwRyWmdBr4CrCAFfp+quh0oFZGR7qJTgVUcTNmSfUGlnRdfpgNribT1/jTZ8XRAeWYC24Agkax/FZF23jeBde57QbLjPMiyfYlI88Ny4GP3NT2FyjcWWOqWbwVwp7t8GLAQWA/8HUhPdqwdUNZpwMupVD63HMvc18rW+iSFfp/jgRL39/kC0OtgymZ3UhtjjImpOzUxGWOM6USWIIwxxsRkCcIYY0xMliCMMcbEZAnCGGNMTJYgjDHGxGQJwvQoIjItaujqczti2PioYaO7xAPvRWS4O4R1XbJjMd2b78CbGNO1uXdti6o6B9w4iqrOpePuxj9ZVSvi3VhEfLpn0LsOpar/BsZbgjCHys4gTLckIkPcB6E8SmSo7YEi8piIlEQ/wMfd9gz3wSnvA1+LWn6liDzsTv9JRC6KWlfnvheLyLvuEfkKEflyHLHdKSKL3O1nuAkMEXlbRP5HRN4BbhaRviIyx33o0DIROd4dAmKeO79CRC51PztRRN5xRx59LWpMncNF5A13+yUiMrwj/n2NATuDMN3bSOA7qnodgIj8VFV3uQ+XelNExhIZmuUJIoPNrQeebed3fJ3IMw9+6e43M47PPKyqd7sx/QU4G3jJXZevqie5654F3lHVC9x9ZxN5gNRWVT3L3SbPHfTwd8B5qlruJo1fAt8FngF+papzRCQDO+gzHcgShOnOPlPVD6PmL3HH9fcReSDKaCIV5kZVXQcgIn8Frv7CnvZvEfCUW0m/oKofx/GZk0Xkx0SSSQGRsX5aE0R0gjoF+BZEhg4HqkXkE+B+EbmXyPhH74nIGGAMsMA9GfEC29zB5vqr6hx3H03tKJcxB2RHG6Y7q2+dEJGhwA+BU1V1LDAPyHBXxzPgWAj378FtEkoDUNV3gROBLcBfRORbbe3EPYp/FLhIVY8mcvaSEbVJfcwPtgaquhaYCHwC3CMidxJ5DsNKjTwac7yqHq2qXyH28xmM6TCWIEyqyCVS+VaLSF8iD4EBWA0MjWqbv3w/n99EpGIGOA/wA4jIYCIPznmCyPDlEw4QR2syqHAflnRRG9u+CVzrfo9XRHJFpB/QoKp/Be53v28NUCQix7nb+kXkKI08gGmziJzvLk8XkXiawIyJizUxmZSgqstEZCmR5pwNwD/d5U1us9M8EakA3ifSXLOvJ4AXRWQhkYq79Uh/GvAjEQkCdbhNQm3EUSUiTxA5A9hEpIlqf24GZojIVUCYSLLIBe4TEYfIMPDXqmqLewH9IRHJI/J3+4Bb1m8CvxeRu93tL3bLb8whs+G+jTlEEnnq2qT2dHPtDCJSp6rZyY7DdF/WxGTMoSsn0muqS90oB+xIdiyme7MzCGOMMTHZGYQxxpiYLEEYY4yJyRKEMcaYmCxBGGOMickShDHGmJj+PwEnAnA6+YnhAAAAAElFTkSuQmCC\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": 27,
   "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": 28,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "psf_obs_norm = psfcor / scale_factor"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "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": 30,
   "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 100 $\\mathrm{\\mu m}$ ELAIS-N1 observations, and try to find its normalization factor. \n",
    "\n",
    "Let's load the stacked PSF:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.image.AxesImage at 0x7f5dfd340438>"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "stackhd_im = fits.open('../dmu18_HELP-PACS-maps/data/Bootes_PACS100_v0.9.fits')\n",
    "im=stackhd_im[1].data\n",
    "stackhd = fits.open('./data/output_data/100um/psf_native.fits')\n",
    "psf = stackhd[1].data\n",
    "hd = stackhd[1].header\n",
    "plt.imshow(psf)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "#plt.hist(psf.flatten(),bins=np.arange(-0.1,1.,0.005));\n",
    "#plt.yscale('log')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Convert units MJy/sr to mJy/pixel: http://coolwiki.ipac.caltech.edu/index.php/Units\n",
    "#psf=psf*2.35045e-2*(np.abs(stackhd[1].header['CDELT1'])*3600)**2\n",
    "#print(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": 5,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "resol= np.abs(stackhd[1].header['CDELT1'])/np.abs(stackhd_im[1].header['CDELT1'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.33333333333393333"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "resol"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now let's build the growthcurve for our PSF."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# find the brightest pixel, it will be our center.\n",
    "jmax, imax = np.unravel_index(np.argmax(psf), psf.shape)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "# build the array of coordinates\n",
    "x = np.arange(hd['NAXIS1'])\n",
    "y = np.arange(hd['NAXIS2'])\n",
    "xv, yv = np.meshgrid(x, y, sparse=False, indexing='xy')\n",
    "xp = (xv-imax)*np.abs(hd['CDELT1'])*3600.\n",
    "yp = (yv-jmax)*np.abs(hd['CDELT2'])*3600.\n",
    "r = np.sqrt(xp**2 + yp**2)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# build the growth curve\n",
    "radii = np.unique(r)\n",
    "encircled_flux = np.zeros(radii.shape)\n",
    "nbpix = np.zeros(radii.shape)\n",
    "for i, radius in enumerate(radii):\n",
    "    idj, idi = np.where(r <= radius)\n",
    "    nbpix[i] =len(idi)\n",
    "    encircled_flux[i] = np.sum(psf[idj, idi])*resol**2\n",
    "    #multiply by ((np.abs(hd['CDELT1'])*3600.)**2)/4.25E10 as map is in units of MJy/sr\n",
    "    #encircled_flux[i] = np.sum(psf[idj, idi])*((np.abs(hd['CDELT1'])*3600.)**2)/4.25E10"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-0.6666666828012"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "hd['CDELT1']*3600."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1.63166788e-01 8.03064028e-01 1.43035486e+00 ... 4.87405219e+02\n",
      " 4.87441786e+02 4.87460124e+02]\n"
     ]
    }
   ],
   "source": [
    "print(encircled_flux)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "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(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": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.0452765\n",
      "[[0.04080502 0.02942331 0.03732587 ... 0.02757077 0.04405934 0.04808061]\n",
      " [0.0388182  0.03834286 0.04838108 ... 0.02858602 0.04424912 0.04347631]\n",
      " [0.03575272 0.04104299 0.04964881 ... 0.03767806 0.05119686 0.0464531 ]\n",
      " ...\n",
      " [0.03112435 0.04210944 0.05246858 ... 0.04029489 0.05038077 0.05990204]\n",
      " [0.02227544 0.03510478 0.04908522 ... 0.05478569 0.06336894 0.06043232]\n",
      " [0.02251252 0.03392504 0.04632129 ... 0.06161889 0.05722388 0.0534455 ]]\n"
     ]
    }
   ],
   "source": [
    "# This is clearly. \n",
    "print(np.median(psf[0:5,:]))\n",
    "\n",
    "print(psf)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'Encircled flux')"
      ]
     },
     "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(nbpix, encircled_flux)\n",
    "plt.xlabel('Number of pixels')\n",
    "plt.ylabel('Encircled flux')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Lets do a linear fit to the outer part of the curve to determine the backgound\n",
    "p = np.polyfit(nbpix[5000:], encircled_flux[5000:], 1)\n",
    "bkg = p[0]/resol**2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "9277\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "50101.0"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "print(len(nbpix))\n",
    "nbpix[5000]\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.0452728933046002\n"
     ]
    }
   ],
   "source": [
    "print(bkg)"
   ]
  },
  {
   "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 100 µm PACS, taken with 20\"/s scan speed. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "f = open('./data/EEF_grn_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 0x7f8c8ced56a0>"
      ]
     },
     "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, 50])\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 0x7f8c8cebaef0>"
      ]
     },
     "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, 50])\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 0x7f8c8ce2aa20>"
      ]
     },
     "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, 50])\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 < 6))\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 0x7f8c8c5e2c18>"
      ]
     },
     "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 = 1.119, ff = 1.000, residual = 0.004\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 0x7f8c8c5bdc50>"
      ]
     },
     "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, 200])\n",
    "plt.xlabel('Radius [arcsec]')\n",
    "plt.ylabel('Encircled flux')\n",
    "plt.legend()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1352640500000.0"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# The two curve overlap\n",
    "rad=20\n",
    "psfok = (psf/np.max(encircled_flux)/ffactor[fmin])\n",
    "np.sum(psfok)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "psfok is the PSF that a source of flux 1 Jy has in our data, and is to be used for source extraction"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [],
   "source": [
    "# As units of map in MJy/sr, divide by 1E6\n",
    "psfok=psfok/1.0E6"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Validation\n",
    "To check PSF is reasonable, lets look at a 100 micron source, e.g. `BOO-PACSxID24-Bootes-HerMES-1-29596`. We can see from `Bootes_PACS100_v0.9.fits` that it has a flux of 20.6 mJy. Maximum value in our normalised PSF gives a peak below. Since PSF is three times resolution of map, it could also be off centre. \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from astropy.table import Table"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [],
   "source": [
    "PACScat=Table.read('./data/Bootes-HerMES_PACSxID24_v1.fits')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "&lt;Column name=&apos;HELP_ID&apos; dtype=&apos;bytes35&apos; length=74562&gt;\n",
       "<table>\n",
       "<tr><td>BOO-PACSxID24-Bootes-HerMES-1-00001</td></tr>\n",
       "<tr><td>BOO-PACSxID24-Bootes-HerMES-1-00002</td></tr>\n",
       "<tr><td>BOO-PACSxID24-Bootes-HerMES-1-00003</td></tr>\n",
       "<tr><td>BOO-PACSxID24-Bootes-HerMES-1-00004</td></tr>\n",
       "<tr><td>BOO-PACSxID24-Bootes-HerMES-1-00005</td></tr>\n",
       "<tr><td>BOO-PACSxID24-Bootes-HerMES-1-00006</td></tr>\n",
       "<tr><td>BOO-PACSxID24-Bootes-HerMES-1-00007</td></tr>\n",
       "<tr><td>BOO-PACSxID24-Bootes-HerMES-1-00008</td></tr>\n",
       "<tr><td>BOO-PACSxID24-Bootes-HerMES-1-00009</td></tr>\n",
       "<tr><td>BOO-PACSxID24-Bootes-HerMES-1-00010</td></tr>\n",
       "<tr><td>BOO-PACSxID24-Bootes-HerMES-1-00011</td></tr>\n",
       "<tr><td>BOO-PACSxID24-Bootes-HerMES-1-00012</td></tr>\n",
       "<tr><td>...</td></tr>\n",
       "<tr><td>BOO-PACSxID24-Bootes-HerMES-1-74551</td></tr>\n",
       "<tr><td>BOO-PACSxID24-Bootes-HerMES-1-74552</td></tr>\n",
       "<tr><td>BOO-PACSxID24-Bootes-HerMES-1-74553</td></tr>\n",
       "<tr><td>BOO-PACSxID24-Bootes-HerMES-1-74554</td></tr>\n",
       "<tr><td>BOO-PACSxID24-Bootes-HerMES-1-74555</td></tr>\n",
       "<tr><td>BOO-PACSxID24-Bootes-HerMES-1-74556</td></tr>\n",
       "<tr><td>BOO-PACSxID24-Bootes-HerMES-1-74557</td></tr>\n",
       "<tr><td>BOO-PACSxID24-Bootes-HerMES-1-74558</td></tr>\n",
       "<tr><td>BOO-PACSxID24-Bootes-HerMES-1-74559</td></tr>\n",
       "<tr><td>BOO-PACSxID24-Bootes-HerMES-1-74560</td></tr>\n",
       "<tr><td>BOO-PACSxID24-Bootes-HerMES-1-74561</td></tr>\n",
       "<tr><td>BOO-PACSxID24-Bootes-HerMES-1-74562</td></tr>\n",
       "</table>"
      ],
      "text/plain": [
       "<Column name='HELP_ID' dtype='bytes35' length=74562>\n",
       "BOO-PACSxID24-Bootes-HerMES-1-00001\n",
       "BOO-PACSxID24-Bootes-HerMES-1-00002\n",
       "BOO-PACSxID24-Bootes-HerMES-1-00003\n",
       "BOO-PACSxID24-Bootes-HerMES-1-00004\n",
       "BOO-PACSxID24-Bootes-HerMES-1-00005\n",
       "BOO-PACSxID24-Bootes-HerMES-1-00006\n",
       "BOO-PACSxID24-Bootes-HerMES-1-00007\n",
       "BOO-PACSxID24-Bootes-HerMES-1-00008\n",
       "BOO-PACSxID24-Bootes-HerMES-1-00009\n",
       "BOO-PACSxID24-Bootes-HerMES-1-00010\n",
       "BOO-PACSxID24-Bootes-HerMES-1-00011\n",
       "BOO-PACSxID24-Bootes-HerMES-1-00012\n",
       "                                ...\n",
       "BOO-PACSxID24-Bootes-HerMES-1-74551\n",
       "BOO-PACSxID24-Bootes-HerMES-1-74552\n",
       "BOO-PACSxID24-Bootes-HerMES-1-74553\n",
       "BOO-PACSxID24-Bootes-HerMES-1-74554\n",
       "BOO-PACSxID24-Bootes-HerMES-1-74555\n",
       "BOO-PACSxID24-Bootes-HerMES-1-74556\n",
       "BOO-PACSxID24-Bootes-HerMES-1-74557\n",
       "BOO-PACSxID24-Bootes-HerMES-1-74558\n",
       "BOO-PACSxID24-Bootes-HerMES-1-74559\n",
       "BOO-PACSxID24-Bootes-HerMES-1-74560\n",
       "BOO-PACSxID24-Bootes-HerMES-1-74561\n",
       "BOO-PACSxID24-Bootes-HerMES-1-74562"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "PACScat['HELP_ID']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<i>Table length=1</i>\n",
       "<table id=\"table140417222717960\" class=\"table-striped table-bordered table-condensed\">\n",
       "<thead><tr><th>XID</th><th>RA</th><th>Dec</th><th>F_PACS_100__A4</th><th>F_PACS_100__A5</th><th>F_PACS_100__A6</th><th>F_PACS_100__A7</th><th>F_PACS_100__A8</th><th>F_PACS_100__A10</th><th>F_PACS_100</th><th>Ferr_PACS_100__A4</th><th>Ferr_PACS_100__A5</th><th>Ferr_PACS_100__A6</th><th>Ferr_PACS_100__A7</th><th>Ferr_PACS_100__A8</th><th>Ferr_PACS_100__A10</th><th>Ferr_PACS_100</th><th>F_PACS_100__SKY</th><th>F_PACS_160__A4</th><th>F_PACS_160__A5</th><th>F_PACS_160__A6</th><th>F_PACS_160__A7</th><th>F_PACS_160__A8</th><th>F_PACS_160__A10</th><th>F_PACS_160</th><th>Ferr_PACS_160__A4</th><th>Ferr_PACS_160__A5</th><th>Ferr_PACS_160__A6</th><th>Ferr_PACS_160__A7</th><th>Ferr_PACS_160__A8</th><th>Ferr_PACS_160__A10</th><th>Ferr_PACS_160</th><th>F_PACS_160__SKY</th><th>HELP_ID</th></tr></thead>\n",
       "<thead><tr><th></th><th>deg</th><th>deg</th><th>mJy</th><th>mJy</th><th>mJy</th><th>mJy</th><th>mJy</th><th>mJy</th><th>mJy</th><th>mJy</th><th>mJy</th><th>mJy</th><th>mJy</th><th>mJy</th><th>mJy</th><th>mJy</th><th>mJy / pix</th><th>mJy</th><th>mJy</th><th>mJy</th><th>mJy</th><th>mJy</th><th>mJy</th><th>mJy</th><th>mJy</th><th>mJy</th><th>mJy</th><th>mJy</th><th>mJy</th><th>mJy</th><th>mJy</th><th>mJy / pix</th><th></th></tr></thead>\n",
       "<thead><tr><th>int32</th><th>float32</th><th>float32</th><th>float32</th><th>float32</th><th>float32</th><th>float32</th><th>float32</th><th>float32</th><th>float32</th><th>float32</th><th>float32</th><th>float32</th><th>float32</th><th>float32</th><th>float32</th><th>float32</th><th>float32</th><th>float32</th><th>float32</th><th>float32</th><th>float32</th><th>float32</th><th>float32</th><th>float32</th><th>float32</th><th>float32</th><th>float32</th><th>float32</th><th>float32</th><th>float32</th><th>float32</th><th>float32</th><th>bytes35</th></tr></thead>\n",
       "<tr><td>61476</td><td>217.5566</td><td>35.154453</td><td>10.39559</td><td>9.159832</td><td>7.5879655</td><td>11.147493</td><td>15.02032</td><td>16.322182</td><td>20.638884</td><td>12.979445</td><td>11.790469</td><td>11.588409</td><td>11.695662</td><td>12.26918</td><td>13.787245</td><td>8.447292</td><td>0.0</td><td>22.05226</td><td>24.613283</td><td>29.686157</td><td>30.625038</td><td>29.62856</td><td>23.04083</td><td>11.530272</td><td>18.325686</td><td>15.448104</td><td>14.354498</td><td>13.568823</td><td>13.197677</td><td>13.570398</td><td>10.594307</td><td>0.0</td><td>BOO-PACSxID24-Bootes-HerMES-1-29596</td></tr>\n",
       "</table>"
      ],
      "text/plain": [
       "<Table length=1>\n",
       " XID     RA       Dec    ... F_PACS_160__SKY               HELP_ID              \n",
       "        deg       deg    ...    mJy / pix                                       \n",
       "int32 float32   float32  ...     float32                   bytes35              \n",
       "----- -------- --------- ... --------------- -----------------------------------\n",
       "61476 217.5566 35.154453 ...             0.0 BOO-PACSxID24-Bootes-HerMES-1-29596"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "PACScat[PACScat['HELP_ID']=='BOO-PACSxID24-Bootes-HerMES-1-29596']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Max PSF = 0.0009 Jy/pix, off pixel Max PSF = 0.0008 Jy/pix\n"
     ]
    }
   ],
   "source": [
    "cpix=np.int((hd['NAXIS1']+1)/2.0)\n",
    "\n",
    "print(\"Max PSF = {:.4f} Jy/pix, off pixel Max PSF = {:.4f} Jy/pix\".format(psfok[cpix-1,cpix-1]*0.0206,psfok[cpix-2,cpix-2]*0.0206))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/mc741/anaconda3/lib/python3.6/site-packages/mpl_toolkits/axes_grid/__init__.py:12: MatplotlibDeprecationWarning: \n",
      "The mpl_toolkits.axes_grid module was deprecated in Matplotlib 2.1 and will be removed two minor releases later. Use mpl_toolkits.axes_grid1 and mpl_toolkits.axisartist provies the same functionality instead.\n",
      "  obj_type='module')\n",
      "WARNING: hdu=0 does not contain any data, using hdu=1 instead [aplpy.core]\n",
      "WARNING: Cannot determine equinox. Assuming J2000. [aplpy.wcs_util]\n",
      "WARNING: Cannot determine equinox. Assuming J2000. [aplpy.wcs_util]\n"
     ]
    },
    {
     "data": {
      "image/png": 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CGwAAgCEIbgAAAIYguAEAABiC4AYAAGAIghsAAIAhCG4AAACGILgBAAAYguAGAABgCIIbAACAIQhuAAAAhiC4AQAAGILgBgAAYAiCGwAAgCEIbgAAAIYguAEAABiC4AYAAGAIghsAAIAhCG4AAACGILgBAAAYguAGAABgCIIbAACAIQhuAAAAhiC4AQAAGILgBgAAYAiCGwAAgCEIbgAAAIYguAEAABiC4AYAAGAIghsAAIAhCG4AAACGILgBAAAYguAGAABgCIIbAACAIQhuAAAAhiC4AQAAGILgBgAAYAiCGwAAgCEIbgAAAIYguAEAABiC4AYAAGAIghsAAIAhCG4AAACGILgBAAAYguAGAABgCIIbAACAIQhuAAAAhiC4AQAAGILgBgAAYAiCGwAAgCEIbgAAAIYguAEAABiC4AYAAGAIghsAAIAhCG4AAACGILgBAAAYguAGAABgCIIbAACAIQhuAAAAhiC4AQAAGILgBgAAYAiCGwAAgCEIbgAAAIYguAEAABiC4AYAAGAIghsAAIAhCG4AAACGILgBAAAYguAGAABgCIIbAACAIQhuAAAAhiC4AQAAGILgBgAAYAiCGwAAgCEIbgAAAIYguAEAABiC4AYAAGAIghsAAIAhCG4AAACGILgBAAAYguAGAABgCIIbAACAIfw+uKWlpen666/X8OHDnW07d+7ULbfcooSEBCUnJ6uoqMiHFQIAAFTx++CWnJys1157rUbb888/r/HjxysrK0uTJk3S888/79LvyJEj3ioRAABAEsFNffr0UUhISI02m82m48ePS5LKysoUGhrq0m/jxo1eqQ8AAKBaoK8LaIoeeeQRjRkzRs8995wcDofeeecdl3nsdrsPKgMAAP7M78+4ufP2228rLS1N+fn5SktL06OPPuoyj2VZPqgMAAD4M4KbGytXrtTgwYMlSUOGDHH75YSwsDBvlwUAAPxcvcHt+++/17p167Rs2TJlZGSoqKhIDofDG7X5TGhoqLZu3SpJ2rx5sy6//HKXeW688UYvVwUAAPydx3vcNm/erFdffVVHjhzR1VdfrY4dO6q8vFz//Oc/tXfvXsXFxWn06NFq27atN+u96KZOnaqtW7fq8OHDioqK0v33368nn3xSzzzzjCoqKtSqVSs98cQTkqTt27frnXfe0dNPP6327dv7uHIAAOBvPAa3/Px8Pfnkk7r00ktdplVUVGj9+vX68MMPFRcX16gFNraXXnrJbfuKFStc2iIiIhQREdHYJQEAALjlMbg9/PDDnjsFBmrQoEGNUhAAAADcq/PnQDZs2KB//vOfstvtstlsCg0NVUxMjKKiorxVHwAAAH7gMbg9/fTTKi4uVmJiojp37iyp6rfL/vrXv6qgoEDp6eleKxIAAAB1BLeCggKtWbPGpX3o0KHG39cGAABgIo8/BxIUFOT298u2b9+uVq1aNWpRAAAAcOXxjNuzzz6rmTNn6vjx484fmz1w4IDatm2r2bNne61AAAAAVPEY3Hr27Knly5fru+++k91ul2VZCgsL009/+lNv1gcAAIAf1Pmt0rKyMn300Uc1vlV64403Kjg42Fv1AQAA4Ace73HLzMxUUlKStmzZopMnT+rEiRPavHmzkpOTlZmZ6c0aAQAAoDrOuM2fP18rVqxwObt29OhR3XLLLUpMTGz04gAAAHBWnQ+Zt9lsrh1atJBlWY1WEAAAANzzeMZt3LhxSkpKUv/+/dWlSxdJ0v79+7Vp0ybdd999XisQAAAAVTwGt6SkJEVHR2vjxo3Ob5X27dtXDzzwgEJCQrxZIwAAAFTPt0pDQkLUt2/fGt8qJbQBAAD4hsfgtnPnTj3++OMqKytTWFiYLMtSSUmJgoOD9fjjj6tnz57erBMAAMDveQxu06dP1xNPPKFrrrmmRvu2bduUlpamVatWNXpxAAAAOMvjt0pPnjzpEtokKTIyUidPnmzUogAAAODK4xm3qKgo3XvvvUpMTHQ+q7SkpESZmZm66aabvFYgAAAAqngMbunp6crPz1dubq4OHjwoy7LUuXNn3X777RowYIA3awQAAIDq+VbpgAEDCGkAAABNhMd73CorK/XOO+9o3rx5+uSTT2pMe+WVVxq9MAAAANTkMbjNmDFDH330kdq3b6+nnnpKs2fPdk5bt26dV4oDAADAWR6DW1FRkV588UXdfffdevfdd3XixAlNmDBB5eXlPKsUAADABzwGtzNnzjj/DgwM1JNPPqmrrrpKd955p06cOOGV4gAAAHCWx+DWq1cvFRQU1GibMGGCRo4cqW+//bbRCwMAAEBNHr9V+sILL7htT01NVWpqaqMVBAAAAPc8Bre1a9d67BQUFKTw8HB17dq1UYoCAACAK4/B7YMPPvDYqaKiQl9//bWuvfZapaenN0phAAAAqMljcDv35z/ccTgcio+Pv+gFAQAAwD2PX07IysqSw+Hw2HHfvn2aNWtWoxQFAAAAVx7PuB05ckSJiYnq2bOnevXqpQ4dOqi8vFzffPONPvroI3Xo0EEPPPCAN2sFAADwax6D21133aU77rhDmzdv1ieffKIvv/xSrVq1UteuXTVnzhxdeuml3qwTAADA79X5kPmAgAD1799f/fv391Y9AAAA8MDjPW4AAABoWghuAAAAhiC4AQAAGKLe4PbSSy+ptLTU+fro0aOaO3duoxYFAAAAV/UGt4KCAgUHBztfh4SEuDx8HgAAAI2v3uBWWVmp8vJy5+tTp07VeA0AAADvqPPnQCRpxIgRuuuuu5ScnCybzaa///3vSkxM9EZtAAAAOEe9we2ee+5R9+7dVVhYKMuydN999+mmm27yRm0AAAA4R73BTZK6du2qwMBA3XDDDTp58qSOHTumtm3bNnZtAAAAOEe997i9++67mjhxombMmCFJstvtGj9+fKMXBgAAgJrqDW7Lli3T22+/7TzDdvnll+vQoUONXhgAAABqqje4BQUFKSgoyPm6oqKiUQsCAACAe/Xe49anTx8tWLBAp06d0ocffqi33npL0dHR3qgNAAAA56j3jNuDDz6ojh076he/+IX+9re/acCAAZo8ebI3agMAAMA56j3j1qJFCw0aNEiDBg1Sx44dvVETAAAA3PAY3CzL0p/+9CctXbrU+bpFixa64447NGHCBK8VCAAAgCoeL5UuWbJEn3zyiTIyMrRlyxZt3bpVy5cv16effqrFixd7sUQAAABIdQS3zMxMvfjiiwoPD3e2hYeH6/nnn1dmZqZXigMAAMBZHoNbRUWF23vaOnbsyE+CAAAA+IDH4NayZUuPneqaBgAAgMbh8csJX3zxha699lqXdsuyVF5e3qhFAQAAwJXH4LZz505v1gEAAIB61PsDvAAAAGgaCG4AAACGILgBAAAYguAGAABgCIIbAACAIQhuAAAAhiC4AQAAGILgBgAAYAiCGwAAgCEIbgAAAIYguAEAABiC4AYAAGAIghsAAIAhCG4AAACGILgBAAAYguAGAABgCIIbAACAIQhuAAAAhiC4AQAAGILgBgAAYAiCGwAAgCEIbgAAAIYguAEAABiC4AYAAGAIghsAAIAhCG4AAACGILgBAAAYguAGAABgCIIbAACAIQhuAAAAhgj0dQG+lpaWpvXr16tTp07Kzs6WJD333HP64IMP1LJlS/3Xf/2XZs+ereDgYB9XCgAA/J3fn3FLTk7Wa6+9VqOtf//+ys7O1urVq3X55ZfrL3/5i0u/yspKb5UIAAAgieCmPn36KCQkpEbbjTfeqMDAqpORkZGRKikpcelXVFTklfoAAACq+X1wq8/f//53RUVFubTb7XYfVAMAAPwZwa0O8+fPV0BAgEaMGOEyzbIsH1QEAAD8md9/OcGTlStXav369Vq8eLFsNpvL9LCwMB9UBQAA/BnBzY2CggK9+uqrWrp0qVq3bu12noiICC9XBQAA/J3fXyqdOnWqbr31Vu3evVtRUVFavny5nnzySR0/fly//e1vlZCQoBkzZkiquq/tnnvukSTnlxcAAAC8xe/Tx0svveTSlpqa6nbezp0769VXX23skgAAANzy+zNuAAAApiC4AQAAGILgBgAAYAiCGwAAgCEIbgAAAIYguAEAABiC4AYAAGAIghsAAIAhCG4AAACGILgBAAAYguAGAABgCIIbAACAIQhuAAAAhiC4AQAAGILgBgAAYAiCGwAAgCEIbgAAAIYguAEAABiC4AYAAGAIghsAAIAhCG4AAACGILgBAAAYguAGAABgCIIbAACAIQhuAAAAhiC4AQAAGILgBgAAYAiCGwAAgCEIbgAAAIYguAEAABiC4AYAAGAIghsAAIAhCG4AAACGILgBAAAYguAGAABgCIIbAACAIQhuAAAAhiC4AQAAGILgBgAAYAiCGwAAgCEIbgAAAIYguAEAABiC4AYAAGAIghsAAIAhCG4AAACGILgBAAAYguAGAABgCIIbAACAIQhuAAAAhiC4AQAAGILgBgAAYAiCGwAAgCEIbgAAAIYguAEAABiC4AYAAGAIghsAAIAhCG4AAACGILgBAAAYguAGAABgCIIbAACAIQhuAAAAhiC4AQAAGILgBgAAYAiCGwAAgCEIbgAAAIYguAEAABiC4AYAAGAIghsAAIAhCG4AAACGILgBAAAYguAGAABgCIIbAACAIQhuAAAAhiC4AQAAGILgBgAAYAiCGwAAgCEIbgAAAIYguAEAABiC4AYAAGAIghsAAIAhCG4AAACGILgBAAAYguAGAABgCIIbAACAIQhuAAAAhvBJcJs3b57i4+OVkJCg0aNHy263S5K2bNmiX/7yl0pISFBCQoL+9Kc/Ofvk5OQoKSlJixcvdrbt2LFD8fHxio2N1VNPPSXLsiRJX3zxhX79618rPj5e48aN07Fjx5zLnz59uiTJsiw99dRTio2NVXx8vD777DPncvfv36/Ro0dryJAhGjp0qPbt2+eyDeXl5Rd9vwAAANSl0YPbuWGp2tixY7V69WplZWXp5ptv1p///GfntOuuu05ZWVnKysrShAkTnO05OTnKyMjQv/71Lx0/flySNHPmTD3xxBNau3atiouLVVBQIEl69NFH9cADD2j16tUaNGiQXnvtNZe6CgoKVFxcrLVr1+rJJ5/UzJkzndMefvhhjRkzRv/4xz+0fPlyderUyaX/8uXLL2i/AAAAnC+fnHFr27at8++TJ0/KZrPV26f6bJrNZpNlWTp48KCOHTum3r17y2azKTExUbm5uZKk3bt3q0+fPpKk/v37a+3atZKkli1bOtedm5urxMRE2Ww2RUZGqrS0VAcPHtRXX32liooK9e/fX5LUpk0btW7d2qWevLy8C9gDAAAA589n97jNnTtXAwYM0OrVqzVp0iRn+7Zt2zRixAiNHTtWu3btcrYPHjxYI0eOVK9evdS2bVvZ7XaFhYU5p4eFhTkvuf7iF79whrj3339fBw4ckCRde+21Sk9PlySP/YuLixUcHKwJEyYoMTFRzz33nCorK13qr14XAACAtzRacEtNTVVCQoLS09OVl5fnvG9tw4YNkqQpU6YoPz9f8fHxWrp0qSSpZ8+eysvL06pVqzRq1CiNHz/eubykpCRlZmZq9OjRks6egTtX9Zm7p59+Wm+99ZaSk5N1/PhxBQUFuczrqX9FRYX+53/+Rw8//LAyMjK0b98+rVixokH9AQAAGlNgYy24+h6wLVu2aOXKlXr22Wfdzjd8+HD97ne/08SJE2tcQh0wYIBmzZqlQ4cOqWPHji79wsLCVFJS4nxdUlKi0NBQSVLXrl31xhtvSKq6bLp+/foG96+oqNDVV1+t8PBwSVJMTIz+9a9/ue1/wL63vt0AAABw0fjkUmlxcbHz77y8PF1xxRWSpO+++855JquoqEgOh0MdOnRwu4zQ0FC1adNG27Ztk2VZyszMVExMjCTp+++/lyQ5HA7Nnz9ft956q0v/6OhoZWZmyrIsbdu2Te3atVNoaKgiIiJ09OhRHTp0SFJV8OzWrZvb/gAAAN7UaGfc6vLiiy9q9+7dstlsuuyyyzRr1ixJ0po1a/T2228rICBAl1xyiV566aU6v7gwc+ZMpaWl6dSpU4qKilJUVJQkKTs7W2+99ZYkKTY2ViNHjnTpO2BIvqvcAAAQ00lEQVTAAOXn5ys2NlatW7fWM888I0kKCAjQww8/rLvuuktS1eXb1NRUSdLLL7+sXr16KSYmRikpKVr29pKLt1MAAADqYbO4WetHGzp8sF74Y1qNturd6ZBVq91R1W5ZsuSoMc3xQx+rVp/qdodVc/7q+c5Ot86Z5nBpa9A6fmiv/XZwWJbLtjiXVXveWnV5nu65Ls91y237ufNX7yXnGFju+7jug5rTq1W/dNQ1zWUba9ZQex3u+p1tq1lv9cuz+7P29silvaHzNmRZ1dvhUlc9y/K4PW7mP9v2Q92O+vvUV0P1Murr49LucL/vZDW8LjmXVT3d/fvm3I8AZ1utOjxNd7Y7as9wTnut/erkYd/UeLPXaD7b7mlZLus/+8attbDq+qwar8+d12UdtZflsq1uluXhDWjVbvdwELjW4GZ5tT/jPL3ZPdVQ86Ct3hj36/d4cNaa3219tQa01rpc6/phme62p54+Z9sdNdblUoO72jzUa9U6mOub7mx3VLVf+ctObu9RNx1PTgAAADAEwQ0AAMAQBDcAAABDENwAAAAMQXADAAAwBMENAADAEAQ3AAAAQxDcAAAADEFwAwAAMATBDQAAwBAENwAAAEMQ3AAAAAxBcAMAADAEwQ0AAMAQBDcAAABDENwAAAAMQXADAAAwBMENAADAEAQ3AAAAQxDcAAAADEFwAwAAMATBDQAAwBAENwAAAEMQ3AAAAAxBcAMAADAEwQ0AAMAQBDcAAABDENwAAAAMQXADAAAwBMENAADAEAQ3AAAAQxDcAAAADEFwAwAAMATBDQAAwBAENwAAAEMQ3AAAAAxBcAMAADAEwQ0AAMAQBDcAAABDENwAAAAMQXADAAAwBMENAADAEAQ3AAAAQxDcAAAADEFwAwAAMATBDQAAwBAENwAAAEMQ3AAAAAxBcAMAADAEwQ0AAMAQBDcAAABDENwAAAAMQXADAAAwBMENAADAEAQ3AAAAQxDcAAAADEFwAwAAMATBDQAAwBAENwAAAEMQ3AAAAAxBcAMAADAEwQ0AAMAQBDcAAABDBPq6AJPZrJZKf+CPF7ycjz/++CJU478CAgJUWVnp6zL8GmPQNDAOTQPjcOF++ctfXvAyTp8+fREqaXoIbhegVatWWrFiha/L8HvJycmMg48xBk0D49A0MA5NQ3Jysq9LaBRcKgUAADAEwQ0AAMAQATNnzpzp6yJM1qtXL1+XADEOTQFj0DQwDk0D49A0NMdxsFmWZfm6CAAAANSPS6UAAACGILjBKS0tTddff72GDx/uMu31119X9+7ddejQIbd9e/TooYSEBCUkJGjcuHHO9r179yo1NVWDBw/W5MmTVV5e3mj1NwcXMgYrV67U4MGDNXjwYK1cudLZvmPHDsXHxys2NlZPPfWUOMnumbv9P2/ePMXHxyshIUGjR4+W3W5325dj4OK4kDHwx2PgfD4z/vjHP+r11193me/06dNKSUnRiBEjNGzYMP3hD39wTrvQ9+/cuXM1YMAA9e7du0b7okWLNHToUMXHx+uuu+7St99+67b/qFGjFBcX5zy2vv/+e0lSeXm5Jk+erNjYWKWmpmrfvn3nVZfRLOAHW7dutXbs2GENGzasRvv+/fut0aNHWzfffLP1/fffu+0bGRnptn3ixIlWdna2ZVmW9dhjj1nLli27uEU3Mz92DA4fPmxFR0dbhw8fto4cOWJFR0dbR44csSzLskaOHGl98sknlsPhsMaMGWOtX7/eK9tiInf7v6yszPn3kiVLrMcee8xtX46Bi+PHjoG/HgPn85nxhz/8wXrttddcluFwOKxjx45ZlmVZ5eXlVkpKivXpp59alnXh799PP/3UstvtLsdHYWGhdeLECcuyLGvZsmXWpEmT3Pa/4447rKKiIpf2pUuXOt8H2dnZHvs3R5xxg1OfPn0UEhLi0j579mxNmzZNNpvtvJZnWZY2b96suLg4SVJSUpJyc3MlSf/4xz80fPhwjRgxQrfffvuFF99M/Ngx2Lhxo/r376/27dsrJCRE/fv314YNG3Tw4EEdO3ZMvXv3ls1mU2JionMM3nzzTef/eKdMmdKo22UKd/u/bdu2zr9Pnjx5XscBx8D5+7Fj4K/HwPl+Znz11VcaNWqUYmJi9Oabb0qSbDab2rRpI0mqqKhQRUWFbDZbne/f6dOn6/HHH3cua+vWrUpLS9OQIUM0ffp05/oiIyMVGhrqUl+/fv3UunVr5zwlJSXntd15eXlKSkqSJMXFxamwsFCWZWnXrl1KSUlRQkKC4uPjVVxcfF7LNQE/wIs65ebmKjQ0VFdddVWd850+fVrJyckKDAzUvffeq0GDBunw4cMKDg5WYGDV2ywsLMx5ieOVV17R66+/rs6dO6u0tLTRt8NkDRkDu92usLAw5+vOnTvLbre7tJ87BgsXLlReXp6CgoIYg3rMnTtXmZmZateunfMfu9o4BhpXfWPAMXBWXZ8Zu3fv1ptvvqljx45pyJAh+s1vfqOWLVuqsrJSycnJ2rNnj2677TZdc801OnTokMf3rySVlpbqzTffVG5ursaNG6e3335bV155pVJSUrRz50716NGjQfVmZGQoKirK4/RHHnlELVq00ODBg3XffffJZrPJbrerS5cukqTAwEC1a9dOhw8f1jvvvKM777xTI0aMUHl5uRwOx/nsOiNwxg0enTx5UgsWLNCkSZPqnfeDDz7QihUr9OKLL+qZZ57Rnj173M5X/b+/3r17a/r06Xr33Xd5NEwdGjoGlpt7dqr/x+yuXZK6d++uBx98UFlZWQoICLg4BTdTU6ZMUX5+vuLj47V06VK383AMNK76xoBjoEp9nxkDBgxQUFCQOnbsqI4dOzrvGQsICFBWVpby8/NVVFSkf//73277n3sGb+DAgbLZbOrevbt+8pOfqHv37mrRooW6devm8Z612rKysrRjxw6NHTvW7fQXXnhBq1ev1rJly/Txxx8rKytLkufxjoyM1F/+8hctXLhQ+/fv1yWXXNKgOkxCcINHe/bs0b59+5SQkKDo6GiVlJQoOTlZ3333ncu8nTt3liSFh4frv//7v/X555+rQ4cOKi0tVUVFhSSppKTEecr8iSee0OTJk3XgwAElJibq8OHD3tswgzR0DMLCwmpcarDb7QoNDXVpP3cMFi5cqNtuu02fffaZkpOTneMEz4YPH661a9e6ncYx4B2exoBjoEp9nxlBQUHOeQMCAly2OTg4WH379tWGDRvqfP+euyybzVZjuS1atGjQvty0aZMWLFig+fPn1+h/rurjqm3btho+fLiKiookVY33gQMHJFVd3i0rK1P79u0VHx+v+fPn65JLLtGYMWNUWFhYbx2mIbjBo+7du6uwsFB5eXnKy8tTWFiYVqxYoZ/+9Kc15jt69Kjzm0aHDh3SJ598om7duslms6lv375as2aNpKpvfEVHR0uq+nC55pprNGnSJHXo0OG872/wFw0dgxtvvFEbN27U0aNHdfToUW3cuFE33nijQkND1aZNG23btk2WZSkzM1MxMTFyOBw6cOCA+vXrp2nTpqmsrEwnTpzw0VY2befeI5OXl6crrrjCZR6OgcbVkDHgGKjS0M+Mcx06dMh5qfjUqVPatGmTrrjiijrfvxfq888/14wZMzR//nx16tTJ7TwVFRXOb8SeOXNG69ev15VXXilJio6Odn5zeM2aNerXr59sNpv27t2r8PBw3XnnnYqOjtaXX355UeptSrjHDU5Tp07V1q1bdfjwYUVFRen+++9Xamqq23m3b9+ud955R08//bS+/vprPf74487LEvfcc4+6desmSZo2bZqmTJmiefPmqUePHs7lzZkzR998840sy1K/fv3qvYfOX/zYMWjfvr3uu+8+paSkSJLGjx+v9u3bS5JmzpyptLQ0nTp1SlFRUYqKilJFRYWmTZumY8eOybIs3X333QoODvbadjZV7vZ/QUGBdu/eLZvNpssuu0yzZs2SxDHQWH7sGPjrMXA+nxmeHDx4UNOnT1dlZaUsy9KvfvUrDRw4UJLn929DzZkzR9nZ2Tp58qSioqKUmpqq+++/X3PmzNGJEyecl3S7dOmiBQsWSJISEhKUlZWl8vJyjR07VmfOnJHD4dD111+vW265RZKUkpKiadOmKTY2ViEhIZo7d64k6b333tOqVasUGBion/zkJxo/fvx51WsCnpwAAABgCC6VAgAAGILgBgAAYAiCGwAAgCEIbgAAAIYguAEAABiC4AagyevRo4cSEhI0fPhwjRs3zuXxRIsXL1ZERITKyso8LuPgwYP63e9+J0nasmWL8+9Vq1YpPj5e8fHxuvXWW/XFF184+xQUFCguLk6xsbFauHChs33v3r1KTU3V4MGDNXnyZOdvuJWXl2vy5MmKjY1Vamqq9u3bJ0n68ssvazy/EQB+LIIbgCbvkksuUVZWlrKzsxUSEqJly5bVmJ6dna2IiAitW7fO4zIWLVrk9jeo/vM//1NLly7V6tWr9fvf/16PPfaYJKmyslJPPPGEXnvtNeXk5Cg7O1tfffWVpKrH8Nx9991au3atgoODlZGRIUlavny5goODtW7dOt1999164YUXJFX9KGpJSYn2799/UfYHAP9FcANglMjIyBoPut6zZ49OnDihyZMnKycnx2O/tWvXun2Q9bXXXquQkBDnsqufYFBUVKSf/exnCg8PV1BQkIYNG6bc3FxZlqXNmzcrLi5OkpSUlKTc3FxJVb/qn5SUJEmKi4tTYWGh85mKAwcOrLM+AGgIghsAY1RWVqqwsLDGY3eys7M1bNgwXXfdddq9e7fzodnn2rt3r0JCQjw+D7FaRkaGM9zZ7XaFhYU5p3Xu3Fl2u12HDx9WcHCwAgOrHjwTFhbmDJJ2u11dunSRJAUGBqpdu3bOZ5D26tVLH3/88QVsPQAQ3AAY4NSpU0pISFDfvn119OhR9e/f3zntvffe07Bhw9SiRQvFxsbq/fffd+n/3XffqUOHDnWuY/PmzcrIyNCDDz4oSXL3UBmbzea2b3V7XX06deqkgwcP1lkDANSH4Aagyau+x+2DDz7QmTNnnPe4ffHFFyouLtbo0aMVHR3tvBfNXf/qLxC488UXXyg9PV2vvPKKM+CFhYXVePC73W5XaGioOnTooNLSUlVUVEiSSkpKFBoa6uxz4MABSVUPyC4rK3M+L/P06dNq1arVRdgbAPwZwQ2AMdq1a6f09HS98cYbOnPmjHJycnT//fcrLy9PeXl52rhxo+x2u7799tsa/S6//HKXtmr79+93PvT65z//ubM9IiJCxcXF2rt3r8rLy5WTk6Po6GjZbDb17dtXa9askSStXLnSeek2OjpaK1eulCStWbNG/fr1c55xKy4u1pVXXnnR9wkA/0JwA2CUq6++WldddZVycnKUk5OjQYMG1ZgeGxvr8iWA//iP/1B4eLi++eYbSVX3ylXf7/bnP/9ZR44c0axZs5SQkKDk5GRJVfeozZgxQ2PHjtXQoUM1ZMgQZ/CaNm2aFi1apNjYWB05csT5bdWUlBQdOXJEsbGxWrRokfOyq1T1EyQ333xzo+wTAP7DZrm7KQMAmpl169Zpx44dmjJlipYsWSK73a6HHnrIK+suLy/XHXfcobfeesv5pQYA+DEIbgD8xvLly/Xpp59q165dmjdvni677DKvrLe4uFh2u119+/b1yvoANF8ENwAAAENwjxsAAIAhCG4AAACGILgBAAAYguAGAABgCIIbAACAIQhuAAAAhvh/4Gkr2ZqYsRcAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 720x648 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import aplpy\n",
    "import seaborn as sns\n",
    "sns.set_style(\"white\")\n",
    "cmap=sns.cubehelix_palette(8, start=.5, rot=-.75,as_cmap=True)\n",
    "fig=aplpy.FITSFigure('../dmu18_HELP-PACS-maps/data/Bootes_PACS100_v0.9.fits')\n",
    "fig.recenter(PACScat[PACScat['HELP_ID']=='BOO-PACSxID24-Bootes-HerMES-1-29596']['RA'],PACScat[PACScat['HELP_ID']=='BOO-PACSxID24-Bootes-HerMES-1-29596']['Dec'], radius=0.004)\n",
    "fig.show_colorscale(vmin=0.0,vmax=1.0,cmap=cmap)\n",
    "fig.add_colorbar()\n",
    "fig.colorbar.set_location('top')\n"
   ]
  },
  {
   "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": "markdown",
   "metadata": {},
   "source": [
    "## Create PSF fits file¶\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [],
   "source": [
    "stackhd[1].data=psfok\n",
    "stackhd.writeto('dmu18_PACS_100_PSF_Bootes_20190125.fits',output_verify='fix+warn', overwrite=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "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": 30,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "452.76727"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.max(psfok)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {
    "collapsed": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "90601"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "len(psfok.flatten())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.0"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.mean(~np.isnan(psfok))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python (herschelhelp_internal)",
   "language": "python",
   "name": "helpint"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.6"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}