{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# PSF normalization\n",
    "\n",
    "Let us assume that we have reduced an observation, for which we have determined the PSF by stacking the flux of point-like sources. The PSF we obtain will not be as high S/N as the instrumental PSF that has been determined by the instrument team. Moreover, it is likely to be fattened due to the some small pointing errors. We need to find out what fraction of a point-like flux the PSF we have determined represent. In order to do this, we use the growth curve of the theoretical PSF that has been determine by the instrument team, and compare it to the growth curve we determine from our PSF.\n",
    "\n",
    "We will first look at a theoretical case, then go practical with an example drawn from the PACS observation of the the XMM-LSS.\n",
    "\n",
    "## 1) Theoretical example. \n",
    "\n",
    "Let us suppose we have a perfect telescope, without any central obscuration and spider to support the secondary. Diffraction theory gives us the shape of a PSF in this case, an Airy function. Let's compute it, and assume the resolution is 10\".\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# import what we will need. \n",
    "%matplotlib inline\n",
    "import numpy as np\n",
    "from astropy.io import fits\n",
    "from astropy.table import Table\n",
    "from astropy.io import ascii as asciiread\n",
    "from matplotlib import pyplot as plt\n",
    "from scipy import interpolate \n",
    "from scipy import special\n",
    "from scipy import signal\n",
    "from scipy import fftpack"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# Let us perform our computation with a 0.1\" resolution on a 5' field of view\n",
    "resol = 0.1\n",
    "size = 300.\n",
    "# wavelength\n",
    "wavelength = 250e-6\n",
    "# primary aperture = 3.6 m diameter\n",
    "aperture = 3.6 / 2."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# Ensure we have an odd number of points \n",
    "nbpix = np.ceil(size/resol) // 2 * 2 + 1\n",
    "xcen = int((nbpix - 1) / 2)\n",
    "ycen = int((nbpix - 1) / 2)\n",
    "x = y = (np.arange(nbpix) - xcen)*resol\n",
    "xv, yv = np.meshgrid(x, y, sparse=False, indexing='xy')\n",
    "r = np.sqrt(xv**2+yv**2)\n",
    "# avoid division by 0 problems in the center\n",
    "r[xcen,ycen] = 1e-6\n",
    "# coordinates in fourier\n",
    "q = 2 * np.pi / wavelength * aperture * np.sin(r/3600.*np.pi/180.)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "psf = (2*special.jn(1, q)/q)**2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# put back the correct value at center\n",
    "psf[xcen, ycen] = 1.\n",
    "# and normalize the PSF\n",
    "psf = psf/(np.sum(psf)*resol**2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "$\\int\\int$ psf dx dy = 1.0000000000000018\n"
     ]
    },
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.imshow(np.log10(psf))\n",
    "print(r'$\\int\\int$ psf dx dy = {}'.format(np.sum(psf)*resol**2))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x7fd0841abf98>"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(y[ycen-500:ycen+500], psf[ycen-500:ycen+500, xcen], label='Without obscuration')\n",
    "plt.legend()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let us now suppose that we observe a point source, and our image reconstruction has a ...This will shows a a blurring of the image, with a gaussian of 10\" FWHM. Let's generate this blurring"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "fwhm = 10.\n",
    "sigma = fwhm / 2. / np.sqrt(2. * np.log(fwhm))\n",
    "sigmasq = sigma**2\n",
    "kernel_blur = 1./ 2./ np.pi / sigmasq * np.exp(-(r**2/2./sigmasq))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.9999999999999996"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Check our kernel is properly normalized\n",
    "np.sum(kernel_blur*resol**2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# apply the blur\n",
    "psfblur = signal.convolve(psf, kernel_blur, mode='same')*resol**2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x7fd08292c908>"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\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 0x7f45675aa5c0>"
      ]
     },
     "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/NGP_PACS160_v0.9.fits')\n",
    "stackhd = fits.open('./data/output_data/160um/NGP-160um-psffromstack.fits')\n",
    "psf = stackhd[0].data\n",
    "hd = stackhd[0].header\n",
    "plt.imshow(psf)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Set the resolution of the psf. Because the map is in units of Jy/pixel, this turns out to be:\n",
    "* =1 if psf at same resolution of map\n",
    "* otherwise, should be in factor of map pixel size"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "resol= np.abs(stackhd[0].header['CDELT1'])/np.abs(stackhd_im[1].header['CDELT1'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.0"
      ]
     },
     "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": [
       "-3.0000000726000002"
      ]
     },
     "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": [
      "6.241757035255432\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": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "75\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "193.0"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "print(len(nbpix))\n",
    "nbpix[30]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "#Lets do a linear fit to the outer part of the curve to determine the backgound\n",
    "p = np.polyfit(nbpix[30:], encircled_flux[30:], 1)\n",
    "bkg = p[0]/resol**2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1.321527907940044e-09\n"
     ]
    }
   ],
   "source": [
    "print(bkg)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1.57428117e-09 7.72556243e-09 1.37460764e-08 1.95643516e-08\n",
      " 3.10508905e-08 3.66282873e-08 4.21430626e-08 5.31301728e-08\n",
      " 6.39923118e-08 6.93584950e-08 8.00916460e-08 8.54771011e-08\n",
      " 9.61897012e-08 1.06896503e-07 1.12212657e-07 1.22862097e-07\n",
      " 1.33529044e-07 1.38871270e-07 1.49537865e-07 1.54842915e-07\n",
      " 1.65461886e-07 1.76104390e-07 1.86756133e-07 1.97394750e-07\n",
      " 2.02697567e-07 2.13304718e-07 2.18625095e-07 2.29254503e-07\n",
      " 2.39867233e-07 2.50480635e-07 2.61086651e-07 2.66376879e-07\n",
      " 2.87568004e-07 2.98164430e-07 3.03459044e-07 3.14050779e-07\n",
      " 3.24651089e-07 3.35237900e-07 3.40524547e-07 3.51090408e-07\n",
      " 3.61671958e-07 3.72251223e-07 3.82831007e-07 3.93415255e-07\n",
      " 4.03991728e-07 4.09276986e-07 4.19855433e-07 4.25137783e-07\n",
      " 4.35705037e-07 4.46279492e-07 4.56855512e-07 4.67417019e-07\n",
      " 4.77990181e-07 4.88555297e-07 4.99128371e-07 5.01768167e-07\n",
      " 5.07049291e-07 5.22890472e-07 5.28182939e-07 5.44029486e-07\n",
      " 5.54604029e-07 5.59886917e-07 5.70461547e-07 5.75746962e-07\n",
      " 5.86304606e-07 5.91589936e-07 5.96872313e-07 6.07436430e-07\n",
      " 6.12717115e-07 6.23281900e-07 6.28559595e-07 6.33835973e-07\n",
      " 6.39108738e-07 6.44390006e-07 6.45710443e-07]\n"
     ]
    }
   ],
   "source": [
    "print(encircled_flux)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "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": 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(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": 18,
   "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": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x7f4567402c50>"
      ]
     },
     "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(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": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x7f4567377588>"
      ]
     },
     "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(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": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x7f4567359e10>"
      ]
     },
     "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, 60])\n",
    "plt.xlabel('Radius [arcsec]')\n",
    "plt.ylabel('Encircled flux')\n",
    "plt.legend()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [],
   "source": [
    "rfactor = np.arange(1.,2., 1e-3)\n",
    "ffactor = np.arange(1.,2., 1e-3)\n",
    "# work with the data points between 3 and 10\"\n",
    "idx, = np.where((radii > 2) & (radii < 10))\n",
    "xv = radii[idx]\n",
    "yv = encircled_flux[idx]/np.max(encircled_flux)\n",
    "resid = np.zeros((len(rfactor), len(ffactor)))\n",
    "for i, rf in enumerate(rfactor):\n",
    "    #print(i, rf)\n",
    "    tck = interpolate.splrep(radiuseff*rf, valeff, s=0)\n",
    "    yfit = interpolate.splev(xv, tck, der=0)\n",
    "    for j, ff in enumerate(ffactor):\n",
    "        resid[i, j] = np.sum((yv-yfit*ff)**2)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.image.AxesImage at 0x7f45672c0eb8>"
      ]
     },
     "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.imshow(np.log(resid))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This shows a minimum, with some degeneracy. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "rf = 1.000, ff = 1.102, residual = 0.009\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": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x7f4566a833c8>"
      ]
     },
     "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*rfactor[rmin], valeff, label='Calibration')\n",
    "plt.plot(radii, encircled_flux/np.max(encircled_flux)/ffactor[fmin], label='Our PSF')\n",
    "plt.xlim([0, 100])\n",
    "plt.xlabel('Radius [arcsec]')\n",
    "plt.ylabel('Encircled flux')\n",
    "plt.legend()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "445049083880.2734"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# The two curve overlap\n",
    "psfok = psf/np.max(encircled_flux)/ffactor[fmin]\n",
    "np.sum(psfok)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "psfok is the PSF that a source of flux 1 Jy has in our data, and is to be used for source extraction"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### As units of map in MJy/sr, divide by 1E6"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 910.09738843,  908.95181318,  908.87066246,  908.69687744,\n",
       "         909.45778718,  910.11172552,  911.88482685,  908.91398692,\n",
       "         910.18856119,  909.30394185,  910.57263513,  909.72371932,\n",
       "         909.91493852,  909.55223102,  911.85235961,  910.81838398,\n",
       "         911.71100704,  911.45913359,  908.86474667,  907.27061537,\n",
       "         906.38923232,  907.92744201],\n",
       "       [ 912.06327491,  909.22529665,  909.00989231,  910.61456763,\n",
       "         910.61752553,  911.98772679,  911.97227614,  910.15866905,\n",
       "         908.8472081 ,  910.89556764,  909.82668886,  910.93729136,\n",
       "         910.70657556,  912.68947863,  911.03337074,  910.65698732,\n",
       "         912.55202352,  909.98759833,  909.48667015,  911.09997557,\n",
       "         909.82926397,  909.44365888],\n",
       "       [ 909.98126496,  911.01774609,  910.57482745,  913.29629945,\n",
       "         910.8348438 ,  910.36666125,  910.72609767,  913.82416187,\n",
       "         913.22530997,  912.12994933,  909.81269975,  914.81105477,\n",
       "         911.80263218,  912.01685336,  911.78004778,  911.58503552,\n",
       "         913.92514788,  911.05814746,  910.88349247,  909.85665059,\n",
       "         908.15325118,  907.87120721],\n",
       "       [ 911.04760343,  909.24113008,  911.75836815,  913.06349573,\n",
       "         911.12534387,  911.72008951,  911.85131564,  913.25307939,\n",
       "         914.77949229,  913.03273362,  913.92525228,  912.48955974,\n",
       "         915.94309331,  915.46481912,  912.40739987,  913.46674379,\n",
       "         911.29641458,  911.00967278,  909.0043941 ,  911.34252294,\n",
       "         910.38548738,  908.49024239],\n",
       "       [ 910.38513939,  907.62625872,  908.45666159,  911.773958  ,\n",
       "         913.29817858,  912.36411021,  913.57552472,  913.50651877,\n",
       "         918.33721335,  914.15492411,  913.00019678,  916.93670237,\n",
       "         916.24236266,  916.43041517,  914.05999309,  913.34098106,\n",
       "         914.2002321 ,  911.21815217,  912.30850178,  910.08085902,\n",
       "         909.81388291,  908.02721006],\n",
       "       [ 910.28749407,  910.43601518,  908.94868129,  913.19204236,\n",
       "         913.90402503,  913.96822875,  913.5085023 ,  918.51138116,\n",
       "         918.04507774,  916.87698769,  914.99444425,  916.65838187,\n",
       "         919.42411789,  919.19375009,  919.07188482,  914.54115557,\n",
       "         912.0072837 ,  910.50651748,  911.60066016,  912.17918958,\n",
       "         912.27064073,  911.28684492],\n",
       "       [ 908.53398444,  908.17273849,  911.70592642,  912.41408123,\n",
       "         912.67660309,  913.86811271,  917.1326542 ,  917.72238882,\n",
       "         918.10329607,  918.18524716,  917.55472838,  918.69156915,\n",
       "         921.5212305 ,  921.04145997,  921.83640289,  916.61418744,\n",
       "         914.9845614 ,  912.68512879,  914.56770703,  911.30114721,\n",
       "         912.27951441,  912.10228432],\n",
       "       [ 910.08263375,  909.56228786,  910.8827269 ,  911.70324691,\n",
       "         913.3005797 ,  915.98224191,  915.32788599,  920.07516794,\n",
       "         925.12509472,  922.65361703,  927.10667544,  926.85153091,\n",
       "         927.09828894,  920.63417525,  920.68689538,  919.9327366 ,\n",
       "         917.07238274,  912.41335045,  912.35777683,  910.88571959,\n",
       "         909.29353702,  909.21169033],\n",
       "       [ 910.19204106,  908.18338691,  909.37079027,  911.63545892,\n",
       "         909.71651598,  915.6735073 ,  918.4962089 ,  923.53468689,\n",
       "         932.68133276,  938.24203577,  947.71547682,  949.31465394,\n",
       "         942.96144391,  931.40446177,  924.40086288,  918.12981273,\n",
       "         916.4100927 ,  913.899362  ,  911.40954536,  914.28260077,\n",
       "         912.14338166,  909.35690557],\n",
       "       [ 910.62086621,  911.66493347,  910.78821346,  912.90439579,\n",
       "         914.00939569,  916.27566508,  920.60692782,  927.33335458,\n",
       "         945.52531232,  971.2173081 ,  995.63535599, 1001.04110012,\n",
       "         982.65705321,  951.63319107,  928.7186933 ,  919.80711307,\n",
       "         913.79917636,  914.27062999,  913.42282775,  912.09097472,\n",
       "         908.13800932,  908.50830295],\n",
       "       [ 911.09830523,  911.70944109,  910.00673765,  910.27033828,\n",
       "         914.41445328,  915.07883125,  921.47978518,  928.88214309,\n",
       "         957.71514475, 1003.61909682, 1045.39118306, 1060.51343759,\n",
       "        1031.20546763,  981.97304874,  939.97289141,  918.83848952,\n",
       "         913.32706156,  912.28696135,  911.76929496,  911.14897223,\n",
       "         909.97134731,  909.93943685],\n",
       "       [ 909.72772118,  911.55945843,  907.94271867,  910.77968776,\n",
       "         913.72192311,  914.57560635,  917.34217754,  925.87229374,\n",
       "         954.36016128, 1009.24577829, 1064.94923582, 1085.05662183,\n",
       "        1054.91577829,  998.72990552,  947.97695472,  924.36355861,\n",
       "         914.07203346,  914.29063928,  913.42258416,  911.78175292,\n",
       "         910.28136949,  909.21068117],\n",
       "       [ 908.37248338,  910.62911352,  908.46504809,  910.12230434,\n",
       "         911.96729992,  915.08669577,  916.32466174,  923.94454671,\n",
       "         943.2739716 ,  986.9138814 , 1036.04284357, 1059.32700859,\n",
       "        1036.9359886 ,  989.51341854,  950.05600677,  926.53221747,\n",
       "         919.09391244,  916.51528936,  914.63615619,  912.82387145,\n",
       "         912.56225436,  912.39779541],\n",
       "       [ 905.99457956,  912.92019443,  912.58699628,  912.44484333,\n",
       "         912.20483627,  918.95106352,  920.07179246,  922.11235708,\n",
       "         931.64137175,  955.68557654,  985.1258166 , 1001.16776761,\n",
       "         991.53762774,  965.62556459,  940.30121773,  927.79850963,\n",
       "         921.52895583,  917.94381335,  913.70995234,  913.52478812,\n",
       "         912.01793212,  909.70816427],\n",
       "       [ 907.36439804,  911.37787848,  914.36938888,  912.38077881,\n",
       "         918.11290053,  919.27653634,  921.66835967,  920.53214528,\n",
       "         923.18381097,  931.66047627,  942.50457096,  949.34875673,\n",
       "         948.54981194,  939.12066972,  931.60187515,  925.75759702,\n",
       "         918.7830203 ,  915.57130333,  913.83947333,  913.07170824,\n",
       "         911.77298363,  909.0917738 ],\n",
       "       [ 911.35967873,  911.21230597,  912.54332383,  913.43925276,\n",
       "         914.37746219,  917.18631389,  916.71346831,  920.07280162,\n",
       "         921.18274294,  919.53150687,  921.13743495,  921.49753255,\n",
       "         924.17087786,  923.67551748,  924.60092096,  921.99150098,\n",
       "         920.49678974,  917.03553085,  910.68548751,  909.93171152,\n",
       "         911.03350993,  909.3251343 ],\n",
       "       [ 910.78640392,  910.15261406,  910.59410596,  913.69178738,\n",
       "         913.70299258,  914.46397192,  916.51619412,  918.24837211,\n",
       "         918.13607651,  917.66723278,  913.76089772,  913.99725092,\n",
       "         916.95138744,  919.17948259,  918.40465335,  919.40553535,\n",
       "         918.37970264,  914.34990157,  910.1686215 ,  910.52054138,\n",
       "         908.81919509,  908.53829948],\n",
       "       [ 910.99891996,  910.90353656,  910.08197258,  910.49914014,\n",
       "         910.8376277 ,  911.55994561,  915.40186816,  915.21158853,\n",
       "         917.2365981 ,  915.71871089,  912.37287949,  910.92462461,\n",
       "         913.25408855,  916.0022512 ,  913.78021104,  915.32583286,\n",
       "         913.79924596,  913.22141251,  912.01821051,  911.40676146,\n",
       "         912.26479454,  910.95322919],\n",
       "       [ 910.94818337,  910.80613482,  909.49780576,  912.97642923,\n",
       "         909.23357875,  910.18386335,  914.90807372,  914.38511792,\n",
       "         914.38449154,  914.72482344,  916.58262496,  910.82899761,\n",
       "         912.25432011,  916.05465814,  915.31452326,  914.12339643,\n",
       "         912.35154785,  911.09479055,  907.96739099,  908.60713143,\n",
       "         909.14073566,  910.82868442],\n",
       "       [ 910.58011686,  910.05569951,  910.59066088,  913.49872385,\n",
       "         910.29257469,  908.9342398 ,  909.40221356,  911.40637867,\n",
       "         911.36354139,  910.61637717,  913.39686787,  911.18272703,\n",
       "         912.05060816,  913.39558032,  910.32083128,  912.76123368,\n",
       "         911.52660839,  912.14171132,  913.57907419,  909.87237963,\n",
       "         911.5743523 ,  910.06502558],\n",
       "       [ 908.95560624,  909.26684637,  910.33635153,  911.6952432 ,\n",
       "         911.01624975,  910.79458163,  910.33969221,  910.54671005,\n",
       "         914.03852225,  912.44219863,  910.15762509,  910.73020392,\n",
       "         909.62903189,  911.5264344 ,  908.3804523 ,  910.01310583,\n",
       "         911.0202516 ,  911.59439638,  912.82321028,  909.29499857,\n",
       "         911.75808976,  910.86473594],\n",
       "       [ 911.11556541,  909.36623163,  910.95235922,  912.07058265,\n",
       "         906.96181116,  911.99287701,  909.90630843,  910.12557543,\n",
       "         911.55020195,  910.78807426,  909.35791473,  909.09598445,\n",
       "         908.80082135,  911.15652356,  909.9660579 ,  911.6415835 ,\n",
       "         909.49822334,  910.84396107,  912.39010488,  909.56862124,\n",
       "         912.85459876,  908.65275261]])"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "psfok=psfok/1.0E6\n",
    "psfok"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Validation\n",
    "To check PSF is reasonable, lets look at a 160 micron source, e.g. `-------`. We can see from `NGC_PACS160_v0.9.fits` that it has a flux of -- mJy. Maximum value in our normalised PSF gives a peak ---."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from astropy.table import Table"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "ename": "FileNotFoundError",
     "evalue": "[Errno 2] No such file or directory: './data/NGP_PACSxID24_v1.fits'",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mFileNotFoundError\u001b[0m                         Traceback (most recent call last)",
      "\u001b[0;32m<ipython-input-29-7b9b7488da56>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[0;32m----> 1\u001b[0;31m \u001b[0mPACScat\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mTable\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mread\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m'./data/NGP_PACSxID24_v1.fits'\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m",
      "\u001b[0;32m~/anaconda3/lib/python3.6/site-packages/astropy/table/table.py\u001b[0m in \u001b[0;36mread\u001b[0;34m(cls, *args, **kwargs)\u001b[0m\n\u001b[1;32m   2548\u001b[0m         \u001b[0;31m# RST table and inserts at the end of the docstring.  DO NOT REMOVE.\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   2549\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m-> 2550\u001b[0;31m         \u001b[0mout\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mio_registry\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mread\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mcls\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m*\u001b[0m\u001b[0margs\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m**\u001b[0m\u001b[0mkwargs\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m   2551\u001b[0m         \u001b[0;31m# For some readers (e.g., ascii.ecsv), the returned `out` class is not\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   2552\u001b[0m         \u001b[0;31m# guaranteed to be the same as the desired output `cls`.  If so,\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m~/anaconda3/lib/python3.6/site-packages/astropy/io/registry.py\u001b[0m in \u001b[0;36mread\u001b[0;34m(cls, format, *args, **kwargs)\u001b[0m\n\u001b[1;32m    500\u001b[0m                     \u001b[0;32mtry\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    501\u001b[0m                         \u001b[0mctx\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mget_readable_fileobj\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0margs\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m0\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mencoding\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;34m'binary'\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 502\u001b[0;31m                         \u001b[0mfileobj\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mctx\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m__enter__\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    503\u001b[0m                     \u001b[0;32mexcept\u001b[0m \u001b[0mOSError\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    504\u001b[0m                         \u001b[0;32mraise\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m~/anaconda3/lib/python3.6/contextlib.py\u001b[0m in \u001b[0;36m__enter__\u001b[0;34m(self)\u001b[0m\n\u001b[1;32m     79\u001b[0m     \u001b[0;32mdef\u001b[0m \u001b[0m__enter__\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     80\u001b[0m         \u001b[0;32mtry\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 81\u001b[0;31m             \u001b[0;32mreturn\u001b[0m \u001b[0mnext\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mgen\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m     82\u001b[0m         \u001b[0;32mexcept\u001b[0m \u001b[0mStopIteration\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     83\u001b[0m             \u001b[0;32mraise\u001b[0m \u001b[0mRuntimeError\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m\"generator didn't yield\"\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;32mfrom\u001b[0m \u001b[0;32mNone\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m~/anaconda3/lib/python3.6/site-packages/astropy/utils/data.py\u001b[0m in \u001b[0;36mget_readable_fileobj\u001b[0;34m(name_or_obj, encoding, cache, show_progress, remote_timeout)\u001b[0m\n\u001b[1;32m    191\u001b[0m                 \u001b[0mname_or_obj\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mcache\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mcache\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mshow_progress\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mshow_progress\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    192\u001b[0m                 timeout=remote_timeout)\n\u001b[0;32m--> 193\u001b[0;31m         \u001b[0mfileobj\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mio\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mFileIO\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mname_or_obj\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m'r'\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    194\u001b[0m         \u001b[0;32mif\u001b[0m \u001b[0mis_url\u001b[0m \u001b[0;32mand\u001b[0m \u001b[0;32mnot\u001b[0m \u001b[0mcache\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    195\u001b[0m             \u001b[0mdelete_fds\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mappend\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mfileobj\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;31mFileNotFoundError\u001b[0m: [Errno 2] No such file or directory: './data/NGP_PACSxID24_v1.fits'"
     ]
    }
   ],
   "source": [
    "PACScat=Table.read('./data/NGP_PACSxID24_v1.fits')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "ename": "NameError",
     "evalue": "name 'PACScat' is not defined",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mNameError\u001b[0m                                 Traceback (most recent call last)",
      "\u001b[0;32m<ipython-input-30-c5b280bad8ff>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[0;32m----> 1\u001b[0;31m \u001b[0mPACScat\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m'HELP_ID'\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m",
      "\u001b[0;31mNameError\u001b[0m: name 'PACScat' is not defined"
     ]
    }
   ],
   "source": [
    "PACScat['HELP_ID']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "ename": "NameError",
     "evalue": "name 'PACScat' is not defined",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mNameError\u001b[0m                                 Traceback (most recent call last)",
      "\u001b[0;32m<ipython-input-31-5bb38cfbcf0b>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[0;32m----> 1\u001b[0;31m \u001b[0mPACScat\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mPACScat\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m'HELP_ID'\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m==\u001b[0m\u001b[0;34m'NGP-PACSxID24-1-11000'\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m",
      "\u001b[0;31mNameError\u001b[0m: name 'PACScat' is not defined"
     ]
    }
   ],
   "source": [
    "PACScat[PACScat['HELP_ID']=='NGP-PACSxID24-1-11000']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Max PSF = 4.1816 Jy/sr, off pixel Max PSF = 3.7307 Jy/sr\n"
     ]
    }
   ],
   "source": [
    "cpix=np.int((hd['NAXIS1']+1)/2.0)\n",
    "\n",
    "print(\"Max PSF = {:.4f} Jy/sr, off pixel Max PSF = {:.4f} Jy/sr\".format(psfok[cpix-1,cpix-1]*0.004,psfok[cpix-3,cpix-3]*0.004))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/mc741/anaconda3/lib/python3.6/site-packages/mpl_toolkits/axes_grid/__init__.py:12: MatplotlibDeprecationWarning: \n",
      "The mpl_toolkits.axes_grid module was deprecated in Matplotlib 2.1 and will be removed two minor releases later. Use mpl_toolkits.axes_grid1 and mpl_toolkits.axisartist, which provide the same functionality instead.\n",
      "  obj_type='module')\n",
      "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"
     ]
    },
    {
     "ename": "NameError",
     "evalue": "name 'PACScat' is not defined",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mNameError\u001b[0m                                 Traceback (most recent call last)",
      "\u001b[0;32m<ipython-input-34-185bee66a049>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[1;32m      4\u001b[0m \u001b[0mcmap\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0msns\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mcubehelix_palette\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m8\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mstart\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;36m.5\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mrot\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;34m-\u001b[0m\u001b[0;36m.75\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mas_cmap\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;32mTrue\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      5\u001b[0m \u001b[0mfig\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0maplpy\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mFITSFigure\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m'../dmu18_HELP-PACS-maps/data/EGS_PACS160_v0.9.fits'\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 6\u001b[0;31m \u001b[0mfig\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mrecenter\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mPACScat\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mPACScat\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m'HELP_ID'\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m==\u001b[0m\u001b[0;34m'EGS-PACSxID24-1-69605'\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m'RA'\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mPACScat\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mPACScat\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m'HELP_ID'\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m==\u001b[0m\u001b[0;34m'EGS-PACSxID24-1-69605'\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m'Dec'\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mradius\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;36m0.005\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m      7\u001b[0m \u001b[0mfig\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mshow_colorscale\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mvmin\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;34m-\u001b[0m\u001b[0;36m0.001\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mvmax\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;36m0.002\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mcmap\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mcmap\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      8\u001b[0m \u001b[0mfig\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0madd_colorbar\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;31mNameError\u001b[0m: name 'PACScat' is not defined"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x648 with 1 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[0].data=psfok\n",
    "stackhd.writeto('./data/dmu18_PACS_160_PSF_NGP_20190301sr.fits',output_verify='fix+warn', overwrite=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAXoAAAD8CAYAAAB5Pm/hAAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAADl0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uIDMuMC4wLCBodHRwOi8vbWF0cGxvdGxpYi5vcmcvqOYd8AAADVRJREFUeJzt3V+MXHUZxvHnsQ0QuVgoBcWWsiWLxK03xEnxQhOjCMVmAYVEeqGApA1RvDNxDV6AiUnBCxMChqxK4MLwR4zIpjUEjUhMENnyJ9CQylJrWCC2WrOmqBDk9WJOYVhmt2fmnN0z8/L9JJudOXP+vO+e2aenv3NmjyNCAIC8PtB0AQCA5UXQA0ByBD0AJEfQA0ByBD0AJEfQA0ByBD0AJEfQA0ByBD0AJLe66QIkae3atTE6Otp0GQAwVPbs2fP3iDj1WPMNRNCPjo5qZmam6TIAYKjY/muZ+Ri6AYDkCHoASI6gB4DkCHoASI6gB4DkCHoASI6gB4DkCHoASG4gPjCFttHJXW8/PrBza4OVAMiEoB8AnQEPAHVj6AYAkiPoASA5gh4AkiPoASC5ZQl625fa/rHtX9m+YDm2AQAop3TQ277D9kHbzy2YvsX2PtuzticlKSIeiIjtkq6S9OVaKwYA9KSXI/o7JW3pnGB7laTbJF0kaVzSNtvjHbN8t3gdANCQ0kEfEY9KOrxg8mZJsxGxPyLekHSPpEvcdpOkX0fEk/WVCwDoVdUx+nWSXup4PldM+6ak8yVdbvvabgva3mF7xvbMoUOHKpYBAFhM1U/Gusu0iIhbJN2y1IIRMSVpSpJarVZUrAMAsIiqR/Rzks7oeL5e0isV1wkAqFHVoH9C0tm2N9o+TtIVkh6sXhYAoC69XF55t6THJJ1je872NRHxpqTrJD0k6XlJ90XE3h7WOWF7an5+vte6AQAllR6jj4hti0zfLWl3PxuPiGlJ061Wa3s/ywMAjo0/gQAAyRH0AJAcQQ8AyTUa9JyMBYDl12jQR8R0ROwYGRlpsgwASI2hGwBIjpuDD6jOG4Yf2Lm1wUoADDuO6AEgOU7GAkBynIwFgOQYugGA5Ah6AEiOoAeA5Ah6AEiOoAeA5Li8EgCS4/JKAEiOoRsASI6gB4DkCHoASI6gB4DkCHoASI7LKwEgOS6vBIDkGLoBgOQIegBIjqAHgOQIegBIjqAHgOQIegBIjqAHgOT4wBQAJMcHpgAgOYZuACA5gh4AkiPoASA5gh4AkiPoASA5gh4AkiPoASA5gh4AkiPoASA5gh4Aklvd5MZtT0iaGBsba7KMoTE6uevtxwd2bm2wEgDDpNGgj4hpSdOtVmt7k3UMus6AB4BeMXQDAMkR9ACQHEEPAMkR9ACQHEEPAMkR9ACQHEEPAMkR9ACQHEEPAMkR9ACQHEEPAMkR9ACQHEEPAMkR9ACQXKNBb3vC9tT8/HyTZQBAao0GfURMR8SOkZGRJssAgNQYugGA5Ah6AEiOoAeA5Bq9Z+z7GfeBBbBSOKIHgOQI+iE1OrmL/xUAKIWgB4DkCHoASI6gB4DkCHoASI6gB4DkCHoASI6gB4DkCHoASI6gB4DkCHoASI6gB4DkCHoASI6gB4DkCHoASI6gB4DkCHoASI6gB4Dkag9622fZ/qnt++teNwCgd6WC3vYdtg/afm7B9C2299metT0pSRGxPyKuWY5iAQC9K3tEf6ekLZ0TbK+SdJukiySNS9pme7zW6gAAlZUK+oh4VNLhBZM3S5otjuDfkHSPpEtqrg8AUFGVMfp1kl7qeD4naZ3tU2zfLulc299ZbGHbO2zP2J45dOhQhTIAAEtZXWFZd5kWEfEPSdcea+GImJI0JUmtVisq1AEAWEKVI/o5SWd0PF8v6ZVq5QAA6lYl6J+QdLbtjbaPk3SFpAfrKQsAUJeyl1feLekxSefYnrN9TUS8Kek6SQ9Jel7SfRGxt5eN256wPTU/P99r3QCAkkqN0UfEtkWm75a0u9+NR8S0pOlWq7W933UAAJbGn0AAgOQIegBIjqAHgOSqXEdfme0JSRNjY2NNljHURid3vWfagZ1bG6gEwKBq9Ig+IqYjYsfIyEiTZQBAagzdAEByBD0AJEfQA0ByjQY9n4wFgOXHyVgASI6hGwBIjqAHgOQIegBIjqAHgOQIegBIjssrASA5Lq8EgOQYugGA5Ah6AEiOoAeA5Ah6AEiOoAeA5Li8EgCS4/JKAEiOoRsASI6gB4DkCHoASI6gB4DkCHoASI6gB4DkCHoASI4PTCU3OrlLo5O7mi4DQIP4wBQAJMfQDQAkR9ADQHIEPQAkR9ADQHIEPQAkR9ADQHIEPQAkR9ADQHIEPQAkR9ADQHKrm9y47QlJE2NjY02WkU7Vv21zdPkDO7cuuc7O1wEMLv7WDQAkx9ANACRH0ANAcgQ9ACRH0ANAcgQ9ACRH0ANAcgQ9ACRH0ANAcgQ9ACRH0ANAcgQ9ACRH0ANAcgQ9ACRH0ANAcgQ9ACTHjUfe56repGThOlb6ZiTLse1uN14ZBE3+nDHcuPEIACTH0A0AJEfQA0ByBD0AJEfQA0ByBD0AJEfQA0ByBD0AJEfQA0ByBD0AJEfQA0ByBD0AJEfQA0ByBD0AJEfQA0ByBD0AJEfQA0ByBD0AJEfQA0ByBD0AJEfQA0ByBD0AJEfQA0Byq+teoe0TJf1I0huSHomIn9W9DQBAeaWO6G3fYfug7ecWTN9ie5/tWduTxeQvSbo/IrZLurjmegEAPSo7dHOnpC2dE2yvknSbpIskjUvaZntc0npJLxWz/a+eMgEA/SoV9BHxqKTDCyZvljQbEfsj4g1J90i6RNKc2mFfev0AgOVTZYx+nd45cpfaAX+epFsk3Wp7q6TpxRa2vUPSDknasGFDhTKGy+jkrsa3e2Dn1p6XKft62e10m6+fGo9Vz1I6t1G2l6o1LqWu/uvav91+PnX1vJw/R7xXlaB3l2kREa9JuvpYC0fElKQpSWq1WlGhDgDAEqoMrcxJOqPj+XpJr1QrBwBQtypB/4Sks21vtH2cpCskPVhPWQCAupS9vPJuSY9JOsf2nO1rIuJNSddJekjS85Lui4i9vWzc9oTtqfn5+V7rBgCUVGqMPiK2LTJ9t6Td/W48IqYlTbdare39rgMAsDQufwSA5Ah6AEiOoAeA5BoNek7GAsDyc0Tzn1WyfUjSX/tcfK2kv9dYTpMy9SLl6odeBtP7vZczI+LUY800EEFfhe2ZiGg1XUcdMvUi5eqHXgYTvZTDGD0AJEfQA0ByGYJ+qukCapSpFylXP/QymOilhKEfowcALC3DET0AYAlDEfS219h+2PYLxfeTF5nvymKeF2xf2TH9+7Zfsn1k5ap+T23d7q/b+frxtu8tXn/c9mjHa98ppu+zfeFK1t1Nv73YPsX272wfsX3rStfdTYVePm97j+1ni++fXenaF6rQy2bbTxdfz9j+4krX3k2V35ni9Q3Fe+1bK1XzYirsm1Hb/+nYP7f3VUBEDPyXpJslTRaPJyXd1GWeNZL2F99PLh6fXLz2SUmnSzrSUP2rJL0o6SxJx0l6RtL4gnm+Lun24vEVku4tHo8X8x8vaWOxnlUN7osqvZwo6VOSrpV06wC8r6r0cq6kjxSPPy7p5SHu5YOSVhePT5d08OjzYeyn4/VfSPq5pG8Nay+SRiU9V7WGoTiiV/tetHcVj++SdGmXeS6U9HBEHI6If0p6WMUNzSPijxHx6opU2t1i99ft1Nnj/ZI+Z9vF9Hsi4vWI+Iuk2WJ9Tem7l4h4LSL+IOm/K1fukqr08lREHL3Rzl5JJ9g+fkWq7q5KL/+O9p8dl6QTJA3CibsqvzOyfanaB3s9/en0ZVKplzoMS9B/6GhQF99P6zJPt3vYrluB2sooU9vb8xS/dPOSTim57Eqq0sugqauXyyQ9FRGvL1OdZVTqxfZ5tvdKelbStR3B35S++7F9oqRvS7pxBeoso+r7bKPtp2z/3van+ymgyj1ja2X7N5I+3OWl68uuosu0QTgykcrVttg8g9ZXlV4GTeVebG+SdJOkC2qsqx+VeomIxyVtsv0xSXfZ/nVENPk/ryr93CjphxFxpMaD4iqq9PKqpA0R8Q/bn5D0gO1NEfGvXgoYmKCPiPMXe83232yfHhGv2j46hrjQnKTPdDxfL+mRWovsX5n76x6dZ872akkjkg6XXHYlVell0FTqxfZ6Sb+U9NWIeHH5y11SLfslIp63/Zra5x1mlq/cY6rSz3mSLrd9s6STJL1l+78R0dQFAH33Eu2B+tclKSL22H5R0kfV675p8iRFDyczfqB3n4y9ucs8ayT9Re0TsScXj9csmKepk7Gr1R4v3Kh3TsZsWjDPN/TukzH3FY836d0nY/er2ZOxfffS8fpVGoyTsVX2y0nF/Jc13UcNvWzUOydjz1Q7hNYOaz8L5rlBzZ+MrbJvTj36+672ydyXF+ZaqRqafoOW/EGdIum3kl4ovq8pprck/aRjvq+pfbJyVtLVHdNvVvtfzLeK7zc00MMXJP1Z7bPv1xfTvifp4uLxCWpfITAr6U+SzupY9vpiuX2SLhqA/VGllwNqH3UdKfbF+ErXX0cvkr4r6TVJT3d8nTakvXxF7ZOWT0t6UtKlTb/Hqr7POtZxgxoO+or75rJi3zxT7JuJfrbPJ2MBILlhueoGANAngh4AkiPoASA5gh4AkiPoASA5gh4AkiPoASA5gh4Akvs/m3znGYXS8fQAAAAASUVORK5CYII=\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(-0.01,0.05,0.0005));\n",
    "#plt.yscale('log')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.hist(psfok.flatten(),bins=np.arange(900,1000,1));\n",
    "plt.yscale('log')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1085.0566218338993"
      ]
     },
     "execution_count": 38,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.max(psfok)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.0"
      ]
     },
     "execution_count": 39,
     "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": "3.6.8"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}
