{
 "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": 31,
   "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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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(y[ycen-500:ycen+500], psf[ycen-500:ycen+500, xcen], label='Original')\n",
    "plt.plot(y[ycen-500:ycen+500], psfblur[ycen-500:ycen+500, xcen], label='With blurring')\n",
    "plt.legend()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We see the effect of blurring, the, observed PSF is wider, and we have lost some flux in the central core. Suppose now that we observed this psf with sources of unknown fluxes, so that we re unsure of its scaling, and that a background remain in our observation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "psfobs = psfblur * 2. + 1e-4"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The question is now how to recover the PSF that serve for our observation. For this, we will use the PSFs curve of growth. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.0 212.10000000000002\n",
      "10.0 212.10000000000002\n",
      "20.0 212.10000000000002\n",
      "30.0 212.10000000000002\n",
      "40.0 212.10000000000002\n",
      "50.0 212.10000000000002\n",
      "60.0 212.10000000000002\n",
      "70.0 212.10000000000002\n",
      "80.0 212.10000000000002\n",
      "90.0 212.10000000000002\n",
      "100.0 212.10000000000002\n",
      "110.0 212.10000000000002\n",
      "120.0 212.10000000000002\n",
      "130.0 212.10000000000002\n",
      "140.0 212.10000000000002\n",
      "150.0 212.10000000000002\n",
      "160.0 212.10000000000002\n",
      "170.0 212.10000000000002\n",
      "180.0 212.10000000000002\n",
      "190.0 212.10000000000002\n",
      "200.0 212.10000000000002\n",
      "210.0 212.10000000000002\n"
     ]
    }
   ],
   "source": [
    "radii = np.arange(0, np.max(r), resol)\n",
    "growth_psf = np.zeros(radii.shape)\n",
    "growth_psfobs = np.zeros(radii.shape)\n",
    "nbpix_psfobs = np.zeros(radii.shape)\n",
    "for i, radius in enumerate(radii):\n",
    "    if ((i % 100) == 0):\n",
    "        print(radius, np.max(radii))\n",
    "    if i == 0:\n",
    "        idj, idi = np.where(r <= radius)\n",
    "        growth_psf[i] = np.sum(psf[idj, idi])*resol**2\n",
    "        growth_psfobs[i] = np.sum(psfobs[idj, idi])*resol**2\n",
    "        nbpix_psfobs[i] =len(idi)\n",
    "    else:\n",
    "        idj, idi = np.where((r > radii[i-1]) & (r <= radius))\n",
    "        growth_psf[i] = growth_psf[i-1]+np.sum(psf[idj, idi])*resol**2\n",
    "        growth_psfobs[i] = growth_psfobs[i-1]+np.sum(psfobs[idj, idi])*resol**2\n",
    "        nbpix_psfobs[i] = nbpix_psfobs[i-1]+len(idi)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x7fd0828a2e10>"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(radii, growth_psf, label='PSF')\n",
    "plt.plot(radii, growth_psfobs, label='Observed PSF')\n",
    "plt.xlabel('Radius [arcsec]')\n",
    "plt.ylabel('Encircled flux')\n",
    "plt.legend()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This strongly rising shape of the observed PSF is a sure sign of an non zero background. Let's determine it. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'Encircled flux')"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(nbpix_psfobs, growth_psfobs)\n",
    "plt.xlabel('Number of pixels')\n",
    "plt.ylabel('Encircled flux')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "When plotted as a function of the intergated area, there is a clear linear relation, that we will fit:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "idx, = np.where(radii > 50)\n",
    "p = np.polyfit(nbpix_psfobs[idx], growth_psfobs[idx], 1)\n",
    "bkg = p[0]/resol**2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# Correct PSF and curve of growth\n",
    "psfcor = psfobs-bkg\n",
    "growth_psfcor = growth_psfobs - bkg*nbpix_psfobs*resol**2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x7fd0827ea278>"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(radii, growth_psf, label='PSF')\n",
    "plt.plot(radii, growth_psfcor, label='Observed PSF')\n",
    "plt.xlabel('Radius [arcsec]')\n",
    "plt.ylabel('Encircled flux')\n",
    "plt.legend()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<a id='direct_ratio'></a> Let's have a look at the ratio of the two:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'Ratio of encircled flux')"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(radii[1:], growth_psfcor[1:]/growth_psf[1:])\n",
    "plt.xlabel('Radius [arcsec]')\n",
    "plt.ylabel('Ratio of encircled flux')\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Due to the different resolution, the ratio is not constant. Let's note the calibration $C(r)$. Let us assume that our observed PSF encirled energy is of the form:\n",
    "\n",
    "$E(r) = \\alpha C(r \\times \\beta)$\n",
    "\n",
    "Where $\\beta$ is the fattening of the PSF. If we differentiate as a function of $r$:\n",
    "\n",
    "$E'(r) = \\alpha \\beta C'(r \\times \\beta)$\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# compute the derivatives\n",
    "deriv_growth_psf = (growth_psf[2:]-growth_psf[0:-2])/(radii[2:]-radii[0:-2])\n",
    "deriv_growth_psfcor  = (growth_psfcor[2:]-growth_psfcor[0:-2])/(radii[2:]-radii[0:-2])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(0, 60)"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(radii[1:-1], deriv_growth_psf)\n",
    "plt.plot(radii[1:-1], deriv_growth_psfcor)\n",
    "plt.xlim([0,60])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Compared with the growth curve plot, the derivative show clear maxima and minima that are out of phase. Findind the positions of the these will tell us if our assumption of homothetical variation is correct."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[ 0.          6.18050404 17.4854638  23.79928199 32.07353691 38.40607579\n",
      " 46.76238796] [ 0.          6.5206172  18.75895207 24.07489413 32.78746844 38.5386345\n",
      " 47.21468159]\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Find the local minima and maxima of the two curves.\n",
    "# To find a local extremum, we will fit the portion of curve with a degree 3 polynomial, \n",
    "# extract the roots of its derivative and only retain the one that are between the bounds.\n",
    "# This is what the following function does.\n",
    "def local_max(xvalues, yvalues, lower_bound, upper_bound, check_plot=False):\n",
    "    idx,=np.where((xvalues > lower_bound) & (xvalues < upper_bound))\n",
    "    p = np.polyfit(xvalues[idx], yvalues[idx], 3)\n",
    "    delta = (2.*p[1])**2 - 4.*3.*p[0]*p[2]\n",
    "    r1 = (-2*p[1]+np.sqrt(delta))/(2*3*p[0])\n",
    "    r2 = (-2*p[1]-np.sqrt(delta))/(2*3*p[0])\n",
    "    result = r1 if ((r1 > lower_bound) and (r1 < upper_bound)) else r2\n",
    "    if check_plot:\n",
    "        plt.plot(xvalues[idx], yvalues[idx])\n",
    "        plt.plot(xvalues[idx], p[0]*xvalues[idx]**3+p[1]*xvalues[idx]**2+\n",
    "                 p[2]*xvalues[idx]+p[3], '--')\n",
    "        plt.plot(np.array([result, result]), np.array([np.min(yvalues), np.max(yvalues)]), '-')\n",
    "    return result\n",
    "    \n",
    "    \n",
    "max_dpsf_1 = local_max(radii[1:-1], deriv_growth_psf, 3, 10, check_plot=True)\n",
    "max_dpsfcor_1 = local_max(radii[1:-1], deriv_growth_psfcor, 3, 10, check_plot=True)\n",
    "\n",
    "max_dpsf_2 = local_max(radii[1:-1], deriv_growth_psf, 14, 21, check_plot=True)\n",
    "max_dpsfcor_2 = local_max(radii[1:-1], deriv_growth_psfcor, 14, 21, check_plot=True)\n",
    "\n",
    "max_dpsf_3 = local_max(radii[1:-1], deriv_growth_psf, 21, 28, check_plot=True)\n",
    "max_dpsfcor_3 = local_max(radii[1:-1], deriv_growth_psfcor, 21, 28, check_plot=True)\n",
    "\n",
    "max_dpsf_4 = local_max(radii[1:-1], deriv_growth_psf, 28, 35, check_plot=True)\n",
    "max_dpsfcor_4 = local_max(radii[1:-1], deriv_growth_psfcor, 28, 35, check_plot=True)\n",
    "\n",
    "max_dpsf_5 = local_max(radii[1:-1], deriv_growth_psf, 35, 45, check_plot=True)\n",
    "max_dpsfcor_5 = local_max(radii[1:-1], deriv_growth_psfcor, 35, 45, check_plot=True)\n",
    "\n",
    "max_dpsf_6 = local_max(radii[1:-1], deriv_growth_psf, 40, 50, check_plot=True)\n",
    "max_dpsfcor_6 = local_max(radii[1:-1], deriv_growth_psfcor, 40, 50, check_plot=True)\n",
    "\n",
    "plt.xlabel('Radius [arcsec]')\n",
    "\n",
    "# Lets pack all of them, adding the r=0 point. \n",
    "max_dpsf = np.array([0, max_dpsf_1, max_dpsf_2, max_dpsf_3, max_dpsf_4, max_dpsf_5, max_dpsf_6])\n",
    "max_dpsfcor = np.array([0, max_dpsfcor_1, max_dpsfcor_2, max_dpsfcor_3, max_dpsfcor_4, \n",
    "                        max_dpsfcor_5, max_dpsfcor_6])\n",
    "\n",
    "print(max_dpsf,max_dpsfcor)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "From the plot, we can deduce that our homothetical assumption is not perfect: the spacing increases for the first three (don't forget the point at 0, 0, not shown), is very small for the 4th and 6th, and gets narrower for the 5th and 7th...\n",
    "Let's plot the situation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[ 1.07402639 -0.04610159]\n",
      "1.0550300032613567\n",
      "1.072831254463463\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(max_dpsf, max_dpsfcor, 'o-')\n",
    "p = np.polyfit(max_dpsf[0:3], max_dpsfcor[0:3], 1)\n",
    "plt.plot(max_dpsf, p[0]*max_dpsf+p[1])\n",
    "plt.xlabel('extremum position of theoretical psf [arcsec]')\n",
    "plt.ylabel('extremum position of observed blurred psf [arcsec]')\n",
    "\n",
    "\n",
    "print(p)\n",
    "print((max_dpsfcor[1]-max_dpsfcor[0])/(max_dpsf[1]-max_dpsf[0]))\n",
    "print((max_dpsfcor[2]-max_dpsfcor[0])/(max_dpsf[2]-max_dpsf[0]))\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'Encircled flux')"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Lets use the data before 20\", corresponding to the central core\n",
    "beta = (max_dpsfcor[2]-max_dpsfcor[0])/(max_dpsf[2]-max_dpsf[0])\n",
    "\n",
    "# lets interpolate at the scaled radius\n",
    "tckpsfcor = interpolate.splrep(radii, growth_psfcor, s=0)\n",
    "interp_growth_psfcor = interpolate.splev(radii*beta, tckpsfcor, der=0)\n",
    "\n",
    "# check interpolation\n",
    "plt.plot(radii*beta, growth_psf)\n",
    "plt.plot(radii, growth_psfcor)\n",
    "plt.plot(radii*beta, interp_growth_psfcor)\n",
    "plt.xlim([0,60])\n",
    "plt.xlabel('radius [arcsec]')\n",
    "plt.ylabel('Encircled flux')\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let us check the ratio, using the psf with a corrected radius"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "alpha = 2.005\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(radii[1:]*beta, interp_growth_psfcor[1:]/growth_psf[1:])\n",
    "plt.xlabel('radius [arcsec]')\n",
    "plt.ylabel('Ratio of encircled flux')\n",
    "plt.xlim([0,60])\n",
    "idx, = np.where(((radii*p[0]) > 0) & ((radii*p[0]) < 60))\n",
    "scale_factor = np.median(interp_growth_psfcor[idx]/growth_psf[idx])\n",
    "print(\"alpha = {:.3f}\".format(scale_factor))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We now have a much better looking ratio [compared with the cell where we computed the direct ratio](#the_ratio), and we have a decent determination of the psf scaling. The normalized PSF to use for our observations is then:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "psf_obs_norm = psfcor / scale_factor"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\\int \\int psf_obs_norm dx dy = 0.966450534666256\n"
     ]
    }
   ],
   "source": [
    "print('\\int \\int psf_obs_norm dx dy = {}'.format(np.sum(psf_obs_norm)*resol**2))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Indeed, let's look at the encircled energy in the core of our psf:\n",
    "In this example, we have used the derivative of the scale factor"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "central core for observation: 0.8526531289184243\n",
      "central core for theoretical: 0.8526789463354869\n"
     ]
    }
   ],
   "source": [
    "idj, idi = np.where(r<max_dpsfcor_2)\n",
    "print('central core for observation: {}'.format(np.sum(psf_obs_norm[idj, idi])*resol**2))\n",
    "idj, idi = np.where(r<max_dpsf_2)\n",
    "print('central core for theoretical: {}'.format(np.sum(psf[idj, idi])*resol**2))\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The two agree extremely well. \n",
    "\n",
    "Unfortunately, with real data, it is not always possible as we will see to use the derivative of the curve of growth to derive the factor beta of PSF fattening. For real observation, one can use a brute force approach to try all the reasonable couples alpha, beta and try to match the theoretical psf to the observed one. This is how we will proceed next on real data."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 2) Real data: PACS observations\n",
    "\n",
    "We will look at a real stack of point sources in the PACS ELAIS-N1 observations, and try to find its normalization factor. \n",
    "\n",
    "Let's load the stacked PSF:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.image.AxesImage at 0x7ff64b41a9e8>"
      ]
     },
     "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/EGS_PACS160_v0.9.fits')\n",
    "stackhd = fits.open('./data/output_data/160um/psf_native.fits')\n",
    "psf = stackhd[1].data\n",
    "hd = stackhd[1].header\n",
    "plt.imshow(psf)"
   ]
  },
  {
   "cell_type": "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": 3,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "resol= np.abs(stackhd[1].header['CDELT1'])/np.abs(stackhd_im[1].header['CDELT1'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.3333333333333333"
      ]
     },
     "execution_count": 4,
     "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": 5,
   "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": 6,
   "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": 7,
   "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": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-1.0000000242"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "hd['CDELT1']*3600."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'Encircled flux')"
      ]
     },
     "execution_count": 9,
     "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": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "-0.01171507\n"
     ]
    }
   ],
   "source": [
    "# This is clearly. \n",
    "print(np.median(psf[0:5,:]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'Encircled flux')"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(nbpix, encircled_flux)\n",
    "plt.xlabel('Number of pixels')\n",
    "plt.ylabel('Encircled flux')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "4252"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "len(nbpix)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [],
   "source": [
    "#Lets do a linear fit to the outer part of the curve to determine the backgound\n",
    "p = np.polyfit(nbpix[600:], encircled_flux[600:], 1)\n",
    "bkg = p[0]/resol**2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "5265.0"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "nbpix[600]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "-0.007190026380257392\n"
     ]
    }
   ],
   "source": [
    "print(bkg)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[  0.09100489   0.44462241   0.79005199 ... -14.67841254 -14.694163\n",
      " -14.70250787]\n"
     ]
    }
   ],
   "source": [
    "print(encircled_flux)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "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": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'Encircled flux')"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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emA/A98flckDvziFHI7srjPT+EzOba2aPmllj9fG+QP130LpgW6PMbKKZzTCzGfn5bfPbWlFFNdNXFDCoRybXnfq1sMORFnDm8D47Hwz81XNzeWfh5pAjir0z7/uQl+ds4Nj9czTsRysV74TxADAEGAFsBO5opExjw1I22dDi7g+5+xh3H5OTk9MyUSaQ7WVVnP/QdBz447kHhx2OtKAR/bOZ9b8nAXDp4zP42VOfhxxR7Hy4dAtz1xUC8Ofvjgo5GtlTcU0Y7r7Z3WvdvQ54mMjtp4bWAfXvufQDNsQjvkR077vLWLChiOtO+ZoGFWyDumV24O1fHAPAS3M28OrcjSFH1LJqaut48P3lXPDIJwB8/r8naQTgViyuCcPM6k/Q8E1gfiPFPgOGmtkgM+sATABeikd8iWZzUQV//WglZw7vw8SjB4cdjsTIvj2zmHvzePpmp3PlP2axLK847JD22hcbivj+Xz9l30lTuG3KIgAe+8EhdM3U9KqtWcxSvZk9BRwL9DCzdcBNwLFmNoLILaZVwGVB2T5Eus+e5u41ZvYT4A0i3WofdfcFsYozUbk7t7wc6bv/3cMGaAKZNq5zx/Y8eOFozrj3Q07801Rm3HAiPbLSwg5rt20sLOfw29790rZfnrw/lx09WKP9tgF60jtBTX5/ObdPWcQZB/fm3vNHKmEkicc+WsnNL39Bny4d+ei641vV//vqglLOmTyN/OJKAF688gj269WJ9A4pIUcmzUmU5zBkDxWUVPLHNxYzon82d503olV9aMje+f4Rg7hg7AA2FFa0qkEOF24s4pg//If84kquOWk/Vt1+OsP7ZytZtDFKGAnotXkbqalzrhm/n6rxSeiWMw+iR1YHnvp0Lfe9uyzscHZp1pptfOv+jwF48tLD+OkJQ0OOSGJFn0YJZtGmIm59ZSFZaamMGpB8w0YIpLQz/vPL4+jcMZU73lpC7nWvUluXmDWNJZuL+db9H5OaYnzwq+M4cmiPsEOSGFLCSCB1dc4VT84ivUMKL//0SHU/TGJZaalM//UJdEiNvEWP/P27/L/XFyXUBE7vLNzM+DunAnDbt75O/24ZIUcksaaEkUCmryxgxZZSJp12AIN6ZIYdjoQso0Mqc24cz8WHD6S8upb7/7OccydPY/D1rzI15DGolueXcOnjkQ4m/3f2QZxxcJ9Q45H4UC+pBOHunHTnVFYXlDL3ppPVWChfUlxRzT3vLOXhD1bu3PatkX3547nDadcufp0i6uqcwb/+75ihL1wxjpG6ddqqqZdUK3Tn20tZllfCt0f1U7KQr+jUsT2TTj+QVbefzpSrjqJbZgee/3w9g3/9GnPWbm/Rc+34Ernj9/ayKlYXlJJ73atfShZ3nTdCySLJqIaRABZvKubku6byjeF9uGeCutHKrrk7lz0xkze/iAxa+PJPjuTr/brs8fGmryhgwkPToyp74gG9ePii0fo7bSM0414r88/P1pCW2o7fnDlMb0KJipnx0EVjeOrTNVz//Dy++/B03vrFMbs9/et7i/L4wWOfRVX2gN6defHKI3Y2xEvyUcII2eJNxTw3cx2HDe6ucXZkt51/6ACG9enMmfd9xNjb3mH0wK48e/nhu/zikVdcwa+fn8fbC/N2bvvDOQcztFcnhvfrQm2d086MWndNciQ76S8hRAUllXz34em4w69O3j/scKSVOrhfNt8flwvAzNXbGHT9a6wpKGuy/IdLt3Dob9/ZmSx+dNQgFt16CueO6c+I/tmYGakp7WjXzpQs5EvUhhGiO95czL3vLuP5K8bpIT3Za1U1dex3w5Qvbdu3ZxaTTjuAgd0zWLChiGufmUNlTd3O/VOuOkoz3yU5tWG0AgUllTwxfTWHD+6uZCEtokNqO1bdfjpvLNjEZU/MBGBZXkmjbRRP/Wgshw/pHu8QpZVTwghBUUU150yexvayas4/bEDY4Ugbc/KwfVj8f6dw99tLeeD95bjD6IFdKSqv5tHvH6InsmWPKWGE4HevLmTt1jIe+8EhHLt/z7DDkTYoLTWFX53yNX51iuaAl5ajFq04c3denbeRbwzvo2QhIq2KahhxVF1bxy0vL6C4oobhe/GQlYhIGFTDiKN73lnKk9PX8KOjBnHR4blhhyMisltiljDM7FEzyzOz+fW2/cHMFpnZXDN7wcyym3jtKjObZ2azzaz19JPdhednreeEr/Vk0ukHxnXAOBGRlhDLGsZjwCkNtr0FHOTuBwNLgOubef1x7j4i2v7BiW7hxiLWby/n4H6N5kgRkYQXs4Th7lOBrQ22venuNcHqdKBfrM6fSDYWlnP+w9PpkNqO8cN6hR2OiMgeCbMN4xJgShP7HHjTzGaa2cTmDmJmE81shpnNyM8Pd1KZptz/3nK2l1Xz2A8O0VO1ItJqhZIwzGwSUAP8vYkiR7j7KOBU4EozO7qpY7n7Q+4+xt3H5OTkxCDavVNdW8dzs9Yxbkh3xg3RfMci0nrtMmGY2YGNbDt2T09oZhcDZwDf8yYGsnL3DcHvPOAF4NA9PV/YFm4soqyqlgmH6oluEWndoqlh/MvM/sci0s3sXuC2PTmZmZ0C/A9wprs3OpymmWWaWacdy8B4YH5jZVuDJ6atpp3BCDV2i0grF03COAzoD3wMfAZsAI7Y1YvM7ClgGrC/ma0zs0uB+4BOwFtBl9nJQdk+ZrZj7sdewIdmNgf4FHjV3V/fzX9XQli7tYxX523kmyP7MaC7xu8RkdYtmie9q4FyIB3oCKx097rmXwLufn4jmx9pouwG4LRgeQUwPIq4Et79/1lOnTtXnzg07FBERPZaNDWMz4gkjEOAI4HzzezZmEbVBtTWOVPmb2T8gftodFARaROiqWFc6u47nrbeBJxlZhfGMKY2YeWWEraXVXPUUPWMEpG2IZqEkWdmDbv4vB+LYNqSeesLAfi6BhkUkTYimoTxKpEH6YxIG8YgYDEwLIZxtXrz1hXRsX079s3JCjsUEZEWscuE4e5fr79uZqOAy2IWURuwblsZ/569npH9u5KaogGBRaRt2O1PM3efRaQBXJrwt2mrKamo4dazVQkTkbZjlzUMM/tFvdV2wCggMQdtShDz1xcyoHsG+/bsFHYoIiItJpoaRqd6P2lE2jTOimVQrdmmwgo+Xl7AWcP7hB2KiEiLiqYN45Z4BNJWLMsrAWB0bteQIxERaVlNJgwze5lI76hGufuZMYmolVtZUArAoB6ZIUciItKymqth/DFuUbQhmwrLSWln9OrUMexQRERaVHMJ40Z3P8HMfu/u/xO3iFq5jdsr6JHVQXN2i0ib01zC6G1mxwBnmtk/iTy4t1PQvVbq2VxUwZT5mzjpQE3DKiJtT7M1DOA6IvNu38GXE4YDx8cwrlbp5TkbKK+u5Rcn7Rd2KCIiLa7JhOHuzwLPmtn/uvutcYyp1covriQttR0DNfeFiLRBu3wOQ8kiegWlVXTP7ICZ2i9EpO3RQEctpLKmlpmrt7FPF/WOEpG2SQmjhXy8vICVW0qZePSQsEMREYmJJhOGmXVr7ieag5vZo2aWZ2bzGxz3LTNbGvxu9JFoM7s4KLPUzC7e/X9afH2+ehvtDE2YJCJtVnM1jJnAjOB3PrAEWBosz4zy+I8BpzTYdh3wjrsPBd4J1r8kSEg3AYcBhwI3NZVYEsX67RXs07kjmWnRTDEiItL6NJkw3H2Quw8G3gC+4e493L07cAbwfDQHd/epwNYGm88CHg+WHwfObuSlJwNvuftWd98GvMVXE09CqaippWOHlLDDEBGJmWjaMA5x99d2rLj7FOCYvThnL3ffGBxrI9CzkTJ9gbX11tcF277CzCaa2Qwzm5GfH96o65XVtXRMVcIQkbYrmoSxxcxuMLNcMxtoZpOAghjH1Vi/1EYHQnT3h9x9jLuPycnJiXFYTSuuqKFje/UhEJG2K5pPuPOBHOCF4Ccn2LanNptZb4Dgd14jZdYB/eut9wM27MU5Y2pbaRWz1mxj1ICEbmYREdkr0cyHsRW4ysyy3L2kBc75EnAxcHvw+8VGyrwB/K5eQ/d44PoWOHdMzFqzjepaZ/ywfcIORUQkZnZZwzCzcWb2BfBFsD7czO6P5uBm9hQwDdjfzNaZ2aVEEsVJZrYUOClYx8zGmNlfYGeSuhX4LPj5TbAtIc1Zu512BsP6dA47FBGRmImmD+idRHotvQTg7nPM7OhoDu7uTd26OqGRsjOAH9ZbfxR4NJrzhO3thXkM75+tLrUi0qZF1Urr7msbbKqNQSyt0sotpXyxsYjTv9477FBERGIqmq/Ea81sHOBm1gH4GbAwtmG1Hos3FQEwdnD3kCMREYmtaGoYlwNXEnkOYh0wIlgXoKi8BoDsjPYhRyIiElvR9JLaAnwvDrG0SoXl1QB0TlfCEJG2rcmEYWb30sTDcgDu/rOYRNTKrN9eTlZaKp3U4C0ibVxzn3Iz4hZFK7Z+ezl9s9M1aZKItHnNTdH6eFP75L+2l1XRLbND2GGIiMRcNA/uvWVm2fXWu5rZG7ENq/Uor64lXaPUikgSiKaXVI67b9+xEgw33tgIs0mpvKqW9PZKGCLS9kWTMGrNbMCOFTMbSDON4cnE3SmprCFNo9SKSBKIpmvPJOBDM3s/WD8amBi7kFqPz1ZtY3NRJSP6Z++6sIhIK9dswrBI158FwChgLJF5Kn4ePJuR9F6as56stFTOHd1/14VFRFq5ZhOGu7uZ/dvdRwOvxCmmVmPm6u2MHJCtRm8RSQrR3HyfbmaHxDySVqaksobFm4oYqUmTRCRJRNOGcRxwmZmtBkqJ3JZydz84ppEluFVbSqlzOLB3p7BDERGJi2gSxqkxj6IVKq6IDDrYuaPGkBKR5NDcWFKd3b0IKI5jPK1GaWUkYWR11BhSIpIcmmvD+EfweyaRcaVm1vvZ43GmzGx/M5td76fIzK5uUOZYMyusV+bGPT1frGwrqwJUwxCR5NHcWFJnBL8HteQJ3X0xkTk1MLMUYD3wQiNFP9gRQyJauaWU1HZG367pYYciIhIX0Ywl9U0z61JvPdvMzm6h858ALHf31S10vLhZlldCbo9M2qfoKW8RSQ7RfNrd5O6FO1aCcaVuaqHzTwCeamLf4WY2x8ymmNmwFjpfi1mxpZTBPTLDDkNEJG6iSRiNldnrlt5gfvAzgWca2T0LGOjuw4F7gX83c5yJZjbDzGbk5+fvbVhR215WRfestLidT0QkbNEkjBlm9iczG2Jmg83sTiIN33vrVGCWu29uuMPdi9y9JFh+DWhvZj0aO4i7P+TuY9x9TE5OTguEFZ2Syhqy0vSEt4gkj2gSxk+BKuBpIrWBCuDKFjj3+TRxO8rM9gnGscLMDg3iLGiBc7aImto6KqrryNS0rCKSRHb5iefupcB1LXlSM8sATgIuq7ft8uB8k4FzgB+bWQ1QDkxw94QZUn1zcSWAbkmJSFLZZcIws/2Aa4Hc+uXd/fg9Pam7lwHdG2ybXG/5PuC+PT1+rM1bF5lP6ut9u+yipIhI2xHNPZVngMnAX4Da2IbTOqwqKANg355ZIUciIhI/0SSMGnd/IOaRtCKbiyrI7JBCltowRCSJRNPo/bKZXWFmvc2s246fmEeWwPKKK+nZuWPYYYiIxFU0X5EvDn7/st42Bwa3fDitw6bCCnI6qcFbRJJLNL2kWnQsqdaupLKGeesKuejwgWGHIiISV03ekjKzX9VbPrfBvt/FMqhENm15AVW1dRx/QM+wQxERiavm2jAm1Fu+vsG+U2IQS6uweFMRACP6Z4cciYhIfDWXMKyJ5cbWk8bKLWX06pxGRgf1kBKR5NJcwvAmlhtbTxort5SQ212j1IpI8mnua/JwMysiUptID5YJ1pO2T+mqgjLGH9gr7DBEROKuuRn3NBRrA7V1ztbSKnrpGQwRSUKaLm43lFXVAOgJbxFJSkoYu6GsKjKUVobmwRCRJKSEsRtKKyM1jEz1kBKRJKSEsRuKKnRLSkSSlxLGbliRXwJAbg91qxWR5KOEsRuW5pXQPsUY2D0j7FBEROJOCWM3LN0ceWivfYoum4gkn9A++cxslZnNM7PZZjajkf1mZveY2TIzm2tmo8KIs75lecUM7aVZ9kQkOYX9Vfk4dx/h7mMa2Xfqrxe+AAAO10lEQVQqMDT4mQiEOutfRXUta7aWsW/PTmGGISISmrATRnPOAv7mEdOBbDPrHVYwK7eUUueax1tEkleYCcOBN81spplNbGR/X2BtvfV1wbZQrMgvBWBIjnpIiUhyCvOBgiPcfYOZ9QTeMrNF7j613v7GhlD/yii5QbKZCDBgwIDYRApsLqoAoHeX9JidQ0QkkYVWw3D3DcHvPOAF4NAGRdYB/eut9wM2NHKch9x9jLuPycnJiVW45JdU0j7FyE5vH7NziIgkslAShpllmlmnHcvAeGB+g2IvARcFvaXGAoXuvjHOoe6UV1RJj6w02rVL2rmjRCTJhXVLqhfwgpntiOEf7v66mV0O4O6TgdeA04BlQBnwg5BiBSI1jJ6d0sIMQUQkVKEkDHdfAQxvZPvkessOXBnPuJqTX1xJ32zNgyEiySuRu9UmlPziCnJUwxCRJKaEEYWa2joKSqvI6aQahogkLyWMKGwrq8YdemR1CDsUEZHQKGFEYcfESZoHQ0SSmRJGFEqDubwzNNOeiCQxJYwolFZG5vJWDUNEkpkSRhR21jDSUkKOREQkPEoYUSgO5vLO1C0pEUliShhRmLlqKx3bt2NAN03NKiLJSwljF9ydtxfmceS+OaR30C0pEUleShi7sCyvhPXbyznxgJ5hhyIiEioljF1YtKkYgOH9s0OOREQkXEoYu7A8vwQzGNRDM+2JSHJTwtiFZXkl9O+aQcf2ar8QkeSmhLELy/NLNY+3iAhKGM2qq3NW5JcwJCcr7FBEREKnhNGMDYXlVNbUMaSnEoaIiBJGM7aXVQPQPVPDmouIxD1hmFl/M3vPzBaa2QIzu6qRMseaWaGZzQ5+box3nPDfIUE6dWwfxulFRBJKGIMj1QDXuPssM+sEzDSzt9z9iwblPnD3M0KIb6eSyh0JQ2NIiYjEvYbh7hvdfVawXAwsBPrGO45olFRGbklpWHMRkZDbMMwsFxgJfNLI7sPNbI6ZTTGzYXENLFAS3JLKUg1DRCSUW1IAmFkW8BxwtbsXNdg9Cxjo7iVmdhrwb2BoE8eZCEwEGDBgQIvGWKypWUVEdgqlhmFm7Ykki7+7+/MN97t7kbuXBMuvAe3NrEdjx3L3h9x9jLuPycnJadE4t5ZUkd4+hbRUdSYTEQmjl5QBjwAL3f1PTZTZJyiHmR1KJM6C+EUZsaGwnN7ZHQlCERFJamHcazkCuBCYZ2azg22/BgYAuPtk4Bzgx2ZWA5QDE9zd4x3ohu0V9OmSHu/TiogkpLgnDHf/EGj2K7u73wfcF5+IGldWVcPSzcWcPTIhO3CJiMSdbs43Ycq8TZRW1XLm8D5hhyIikhCUMJrwzMy15HbP4NBB3cIORUQkIShhNCKvqILpK7Zyzuh+avAWEQkoYTRiY2EFAAf07hxyJCIiiUMJoxHbyqoAyM7QKLUiIjsoYTSisDwyhlR2hkapFRHZQQmjEdtKIzWMrqphiIjspITRiO1BDaOzBh0UEdlJCaMR28uq6dwxldQUXR4RkR30idiIvOIKNXiLiDSghNFARXUtU5ds0QN7IiINKGE08N6iPEoqazhrhIYEERGpTwmjgZfmbKBHVhqHD+4edigiIglFCaOeqpo63lucx6kH7aMGbxGRBvSpWM/8DYVUVNdx+BDVLkREGlLCqOezlVsBOCRXDd4iIg0pYdTz6cqtDOqRSU6ntLBDERFJOEoYgcWbinlvcR4nHtAz7FBERBJSKAnDzE4xs8VmtszMrmtkf5qZPR3s/8TMcmMd029fW0hWWipXHLtvrE8lItIqxT1hmFkK8GfgVOBA4HwzO7BBsUuBbe6+L3An8PtYxvT+knymLsnnZycMpWumnvAWEWlMGDWMQ4Fl7r7C3auAfwJnNShzFvB4sPwscILFaOq72jrnd68uZEC3DC48fGAsTiEi0iaEMRxrX2BtvfV1wGFNlXH3GjMrBLoDW1o6mPLqWkb0z+bY/XNIS01p6cOLiLQZYSSMxmoKvgdlIgXNJgITAQYMGLDbwWSlpfL7cw7e7deJiCSbMG5JrQP611vvB2xoqoyZpQJdgK2NHczdH3L3Me4+JicnJwbhiogIhJMwPgOGmtkgM+sATABealDmJeDiYPkc4F13b7SGISIi8RH3W1JBm8RPgDeAFOBRd19gZr8BZrj7S8AjwBNmtoxIzWJCvOMUEZEvC2UOUnd/DXitwbYb6y1XAOfGOy4REWmanvQWEZGoKGGIiEhUlDBERCQqShgiIhIVa0u9Vc0sH1i9hy/vQQyeJI8RxRobijU2FGtstFSsA909qofY2lTC2BtmNsPdx4QdRzQUa2wo1thQrLERRqy6JSUiIlFRwhARkagoYfzXQ2EHsBsUa2wo1thQrLER91jVhiEiIlFRDUNERKKS9AljV/OLh8nM+pvZe2a20MwWmNlVwfZuZvaWmS0NfncNO9YdzCzFzD43s1eC9UHBvOxLg3naE2IOXDPLNrNnzWxRcH0PT9TramY/D/7/55vZU2bWMZGuq5k9amZ5Zja/3rZGr6VF3BO83+aa2agEiPUPwd/BXDN7wcyy6+27Poh1sZmdHHas9fZda2ZuZj2C9bhc16ROGFHOLx6mGuAadz8AGAtcGcR3HfCOuw8F3gnWE8VVwMJ6678H7gxi3UZkvvZEcDfwurt/DRhOJOaEu65m1hf4GTDG3Q8iMsLzBBLruj4GnNJgW1PX8lRgaPAzEXggTjHu8BhfjfUt4CB3PxhYAlwPELzXJgDDgtfcH3xmxMtjfDVWzKw/cBKwpt7muFzXpE4YRDe/eGjcfaO7zwqWi4l8qPXly3OePw6cHU6EX2Zm/YDTgb8E6wYcT2RedkiQWM2sM3A0kWH0cfcqd99Ogl5XIqNKpweTiWUAG0mg6+ruU/nqBGdNXcuzgL95xHQg28x6xyfSxmN19zfdvSZYnU5kUrcdsf7T3SvdfSWwjMhnRmixBu4EfsWXZyGNy3VN9oTR2PzifUOKpVlmlguMBD4Bern7RogkFaBneJF9yV1E/pDrgvXuwPZ6b8ZEub6DgXzgr8Hts7+YWSYJeF3dfT3wRyLfJjcChcBMEvO61tfUtUz099wlwJRgOeFiNbMzgfXuPqfBrrjEmuwJI+q5w8NkZlnAc8DV7l4UdjyNMbMzgDx3n1l/cyNFE+H6pgKjgAfcfSRQSgLcfmpMcO//LGAQ0AfIJHL7oaFEuK7RSNS/CcxsEpHbwH/fsamRYqHFamYZwCTgxsZ2N7KtxWNN9oQRzfzioTKz9kSSxd/d/flg8+Yd1c3gd15Y8dVzBHCmma0icmvveCI1juzgVgokzvVdB6xz90+C9WeJJJBEvK4nAivdPd/dq4HngXEk5nWtr6lrmZDvOTO7GDgD+F696aATLdYhRL44zAneZ/2AWWa2D3GKNdkTRjTzi4cmaAN4BFjo7n+qt6v+nOcXAy/GO7aG3P16d+/n7rlEruO77v494D0i87JD4sS6CVhrZvsHm04AviABryuRW1FjzSwj+HvYEWvCXdcGmrqWLwEXBb16xgKFO25dhcXMTgH+BzjT3cvq7XoJmGBmaWY2iEiD8qdhxAjg7vPcvae75wbvs3XAqODvOT7X1d2T+gc4jUjPiOXApLDjaRDbkUSqlXOB2cHPaUTaBt4Blga/u4Uda4O4jwVeCZYHE3mTLQOeAdLCji+IawQwI7i2/wa6Jup1BW4BFgHzgSeAtES6rsBTRNpXqol8iF3a1LUkcuvkz8H7bR6R3l9hx7qMyP3/He+xyfXKTwpiXQycGnasDfavAnrE87rqSW8REYlKst+SEhGRKClhiIhIVJQwREQkKkoYIiISFSUMERGJihKGiIhERQlD2hQzqzWz2cFQ4C/XH6o6ytffbGbXBsu/MbMT9zKeXDMrN7PZe3OclmRm5wXDYL8SdizSuihhSFtT7u4jPDIU+Fbgyj09kLvf6O5vt0BMy919xO68IJbDaLv708APY3V8abuUMKQtm0YwYqeZZZnZO2Y2y8zmmdnOYezNbFIwQc7bwP71tj9mZucEy6vqTVYzxsz+EywfE9RoZgcj33baVVBm9m8zm2mRSZEm1tteEtRqPgEON7NDzOxjM5tjZp+aWSczGxYszw4myhkavPaCetsf3JFwLDJB2KzgGO/s/SWVZJa66yIirU/wgXkCwZwXQAXwTXcvCj74p5vZS0QGHZxAZOj4VGAWkeHDo3UtcKW7fxSMKlwRxWsucfetZpYOfGZmz7l7AZGRaOe7+43B2GaLgPPc/bNgDo9y4HLgbnf/e1AmxcwOAM4DjnD3ajO7H/iemU0BHgaOdveVZtZtN/5dIl+hhCFtTXrQXpBL5IP/rWC7Ab8zs6OJzNfRF+gFHAW84MGgc0ES2R0fAX8ys78Dz7v7uihe8zMz+2aw3J/IoHYFQC2RkYkhUtPZ6O6fAXgwrL2ZTQMmWWSyqufdfamZnQCMJpJ8ANKJjA47Fpjqkcl/cPfGJuMRiZpuSUlbUx60FwwEOvDfNozvATnA6GD/ZqBjsC+aAdVq+O/7ZcfrcPfbibQHpBOptXytuYOY2bFEhiw/3N2HA5/XO16Fu9fuKNpYXO7+D+BMIrWNN8zs+KDs40HbzQh339/db27qGCJ7SglD2iR3LyQyF/a1wZwiXYhM8FRtZscRSSgAU4Fvmll60P7wjSYOuYrIt3iAb+/YaGZDPDLs9O+JjH7bbMII4tjm7mVBchnbRLlFQB8zOyQ4TyczSzWzwcAKd7+HyJDWBxMZDfYcM+sZlO1mZgOJtOEcEwzNjW5Jyd7SLSlps9z9czObQ6SN4u/Ay2Y2g8gQ1ouCMrPM7Olg22rggyYOdwvwiJn9msg0uTtcHSSgWiLzVExp7MX1vA5cbmZziQyZPb2J2KvM7Dzg3qCto5xIzeQ84AIzqwY2Ab8J2kNuAN40s3ZEhsO+0t2nB43qzwfb84CTdhGfSJM0vLlIDFlkLvZXgm6+CSO4NXatu58RdizSeuiWlEhs1QJdEu3BPeB+YFvYsUjrohqGiIhERTUMERGJihKGiIhERQlDRESiooQhIiJRUcIQEZGo/H/MA0OypeouyAAAAABJRU5ErkJggg==\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": 24,
   "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": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x7ff648e1b3c8>"
      ]
     },
     "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.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": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x7ff648d87c88>"
      ]
     },
     "execution_count": 26,
     "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": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x7ff648d747b8>"
      ]
     },
     "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, 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": 28,
   "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 < 9))\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": 29,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.image.AxesImage at 0x7ff648cdc550>"
      ]
     },
     "execution_count": 29,
     "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": 30,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "rf = 1.000, ff = 1.036, residual = 0.002\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": 31,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x7ff648513ac8>"
      ]
     },
     "execution_count": 31,
     "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": 32,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "8.277132"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# The two curve overlap\n",
    "psfok = psf/np.max(encircled_flux)/ffactor[fmin]\n",
    "np.sum(psfok)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "psfok is the PSF that a source of flux 1 Jy has in our data, and is to be used for source extraction"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [],
   "source": [
    "### As units of map in MJy/sr, divide by 1E6"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [],
   "source": [
    "#psfok=psfok/1.0E6\n",
    "#np.sum(psfok)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Validation\n",
    "To check PSF is reasonable, lets look at a 100 micron source, e.g. `XMM-PACSxID24-1-69605`. We can see from `HerMES_PACS_level6_XMM_LSS_SWIRE_100um_EdoIbar_Unimap.fits` that it has a flux of 17 Jy. Maximum value in our normalised PSF gives a peak below. Since PSF is double resolution of map, it could also be off centre."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from astropy.table import Table"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [],
   "source": [
    "PACScat=Table.read('./data/EGS_PACSxID24_v1.fits')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "&lt;Column name=&apos;HELP_ID&apos; dtype=&apos;bytes21&apos; length=17582&gt;\n",
       "<table>\n",
       "<tr><td>EGS-PACSxID24-1-00001</td></tr>\n",
       "<tr><td>EGS-PACSxID24-1-00002</td></tr>\n",
       "<tr><td>EGS-PACSxID24-1-00003</td></tr>\n",
       "<tr><td>EGS-PACSxID24-1-00004</td></tr>\n",
       "<tr><td>EGS-PACSxID24-1-00005</td></tr>\n",
       "<tr><td>EGS-PACSxID24-1-00006</td></tr>\n",
       "<tr><td>EGS-PACSxID24-1-00007</td></tr>\n",
       "<tr><td>EGS-PACSxID24-1-00008</td></tr>\n",
       "<tr><td>EGS-PACSxID24-1-00009</td></tr>\n",
       "<tr><td>EGS-PACSxID24-1-00010</td></tr>\n",
       "<tr><td>EGS-PACSxID24-1-00011</td></tr>\n",
       "<tr><td>EGS-PACSxID24-1-00012</td></tr>\n",
       "<tr><td>...</td></tr>\n",
       "<tr><td>EGS-PACSxID24-1-17571</td></tr>\n",
       "<tr><td>EGS-PACSxID24-1-17572</td></tr>\n",
       "<tr><td>EGS-PACSxID24-1-17573</td></tr>\n",
       "<tr><td>EGS-PACSxID24-1-17574</td></tr>\n",
       "<tr><td>EGS-PACSxID24-1-17575</td></tr>\n",
       "<tr><td>EGS-PACSxID24-1-17576</td></tr>\n",
       "<tr><td>EGS-PACSxID24-1-17577</td></tr>\n",
       "<tr><td>EGS-PACSxID24-1-17578</td></tr>\n",
       "<tr><td>EGS-PACSxID24-1-17579</td></tr>\n",
       "<tr><td>EGS-PACSxID24-1-17580</td></tr>\n",
       "<tr><td>EGS-PACSxID24-1-17581</td></tr>\n",
       "<tr><td>EGS-PACSxID24-1-17582</td></tr>\n",
       "</table>"
      ],
      "text/plain": [
       "<Column name='HELP_ID' dtype='bytes21' length=17582>\n",
       "EGS-PACSxID24-1-00001\n",
       "EGS-PACSxID24-1-00002\n",
       "EGS-PACSxID24-1-00003\n",
       "EGS-PACSxID24-1-00004\n",
       "EGS-PACSxID24-1-00005\n",
       "EGS-PACSxID24-1-00006\n",
       "EGS-PACSxID24-1-00007\n",
       "EGS-PACSxID24-1-00008\n",
       "EGS-PACSxID24-1-00009\n",
       "EGS-PACSxID24-1-00010\n",
       "EGS-PACSxID24-1-00011\n",
       "EGS-PACSxID24-1-00012\n",
       "                  ...\n",
       "EGS-PACSxID24-1-17571\n",
       "EGS-PACSxID24-1-17572\n",
       "EGS-PACSxID24-1-17573\n",
       "EGS-PACSxID24-1-17574\n",
       "EGS-PACSxID24-1-17575\n",
       "EGS-PACSxID24-1-17576\n",
       "EGS-PACSxID24-1-17577\n",
       "EGS-PACSxID24-1-17578\n",
       "EGS-PACSxID24-1-17579\n",
       "EGS-PACSxID24-1-17580\n",
       "EGS-PACSxID24-1-17581\n",
       "EGS-PACSxID24-1-17582"
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "PACScat['HELP_ID']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<i>Table length=1</i>\n",
       "<table id=\"table140695760435464\" 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>bytes21</th></tr></thead>\n",
       "<tr><td>11505</td><td>214.99983</td><td>52.988686</td><td>0.9594532</td><td>0.53793895</td><td>3.5568151</td><td>6.680657</td><td>7.2129292</td><td>9.633122</td><td>-4.9660807</td><td>8.12622</td><td>7.450976</td><td>7.393615</td><td>7.5411887</td><td>7.981477</td><td>9.052729</td><td>5.4869013</td><td>0.0</td><td>4.3846765</td><td>-0.82424206</td><td>-3.958346</td><td>-3.195391</td><td>-2.1416974</td><td>-5.2478395</td><td>4.3550415</td><td>13.143023</td><td>11.100815</td><td>10.392856</td><td>9.921859</td><td>9.662194</td><td>9.975699</td><td>6.8872256</td><td>0.0</td><td>EGS-PACSxID24-1-11000</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            bytes21       \n",
       "----- --------- --------- ... --------------- ---------------------\n",
       "11505 214.99983 52.988686 ...             0.0 EGS-PACSxID24-1-11000"
      ]
     },
     "execution_count": 37,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "PACScat[PACScat['HELP_ID']=='EGS-PACSxID24-1-11000']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Max PSF = 0.0002 Jy/pix, off pixel Max PSF = 0.0001 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]*0.004,psfok[cpix-3,cpix-3]*0.004))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "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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\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/EGS_PACS160_v0.9.fits')\n",
    "fig.recenter(PACScat[PACScat['HELP_ID']=='EGS-PACSxID24-1-69605']['RA'],PACScat[PACScat['HELP_ID']=='EGS-PACSxID24-1-69605']['Dec'], radius=0.005)\n",
    "fig.show_colorscale(vmin=-0.001,vmax=0.002,cmap=cmap)\n",
    "fig.add_colorbar()\n",
    "fig.colorbar.set_location('top')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In summary, the PSF is within 10% of this source, and given noise and shape of source will add additional uncertianty, as well as non-zero background, this seems reasonable.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [],
   "source": [
    "stackhd[1].data=psfok\n",
    "stackhd.writeto('dmu18_PACS_160_PSF_EGS_20190123.fits',output_verify='fix+warn', overwrite=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "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.hist(psfok.flatten(),bins=np.arange(-10,200,1));\n",
    "plt.yscale('log')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "202.59793"
      ]
     },
     "execution_count": 37,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.max(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
}
