{
 "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"
   ]
  },
  {
   "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": "markdown",
   "metadata": {},
   "source": [
    "## 2) Real data: MIPS observations\n",
    "\n",
    "We will look at a real stack of point sources in the MIPS Bootes 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.colorbar.Colorbar at 0x10e699ac8>"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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izviwncD9RRt1HKflWMGlZRTR0LYBd8cBclPAvWb2E0n/DNwr6WbgBeD6Bvs5GnWammmX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\n/w/1l7LUEo93vgAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10b1b79e8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "stackhd = fits.open('./data/MIPS_PSF_STACK/output_data/psf_hires.fits')\n",
    "psf = stackhd[1].data\n",
    "hd = stackhd[1].header\n",
    "cpix=np.int((hd['NAXIS1']+1)/2.0)\n",
    "rad=40\n",
    "plt.imshow(psf[cpix-rad-1:cpix+rad,cpix-rad-1:cpix+rad])\n",
    "plt.colorbar()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "resol= 0.5"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Change the header information from CD_1_1 to CDELT1 and CDELT2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "hd['CDELT1']=hd['CD1_1']\n",
    "hd['CDELT2']=hd['CD2_2']"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Read in MIPS 24 $\\mathrm{\\mu m}$ Instrumental PSF\n",
    "We take the instrumental PSF from [Gonzalo J.Aniano's webpage](http://www.astro.princeton.edu/~ganiano/Kernels/Ker_2017/PSF_FITS_Files/)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "insthd = fits.open('../../dmu26/data/ELAIS_N1/MIPS/PSF_Original_MIPS_24.fits.gz')\n",
    "psf_inst_full = insthd[0].data\n",
    "hdinst = insthd[0].header"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "SIMPLE  =                    T /image conforms to FITS standard                 \n",
       "BITPIX  =                  -32 /bits per data value                             \n",
       "NAXIS   =                    2 /number of axes                                  \n",
       "NAXIS1  =                 4001 /                                                \n",
       "NAXIS2  =                 4001 /                                                \n",
       "EXTEND  =                    T /file may contain extensions                     \n",
       "INSTRUME= '    MIPS_24_micron' / Simulated instrument                           \n",
       "FOCUS   =              -0.1939 / RMS focus in microns                           \n",
       "X_COMA  =               0.0946 / RMS X-coma in microns                          \n",
       "Y_COMA  =              -0.0066 / RMS Y-coma in microns                          \n",
       "X_ASTIG =               0.5911 / RMS 0 degree astigmatism in microns            \n",
       "Y_ASTIG =              -0.1078 / RMS 45 degree astigmatism in microns           \n",
       "SPHERICL=              -0.2730 / RMS 3rd order spherical in microns             \n",
       "PIXSCALX=             0.500000 / Arcseconds per array X pixel                   \n",
       "X_POS   =                   64 / X position of PSF center in detector pixels    \n",
       "Y_POS   =                   64 / Y position of PSF center in detector pixels    \n",
       "SPECTRUM= '    Blackbody(25K)' / Spectrum type or file                          \n",
       "XFIELD  =             -6.71600 / OTA X field position (arcmin)                  \n",
       "YFIELD  =              4.24600 / OTA Y field position (arcmin)                  \n",
       "SCANPOS =             0.000000 / Scan field offset (arcsec)                     \n",
       "CD1_1   =    0.000138888888889 /                                                \n",
       "CD1_2   =                    0 /                                                \n",
       "CD2_1   =                    0 /                                                \n",
       "CD2_2   =    0.000138888888889 /                                                \n",
       "UNITS   = 'counts  '           /Flux normalized to max = 1                      \n",
       "CTYPE1  = 'RA---TAN'           /                                                \n",
       "CTYPE2  = 'DEC--TAN'           /                                                \n",
       "EQUINOX =              2000.00 /                                                \n",
       "CRVAL1  =              0.00000 /                                                \n",
       "CRVAL2  =              0.00000 /                                                \n",
       "CRPIX1  =              2001.00 /                                                \n",
       "CRPIX2  =              2001.00 /                                                \n",
       "COMMENT ===============================================================         \n",
       "COMMENT                                                                         \n",
       "COMMENT This File was written by make_kernel.                                   \n",
       "COMMENT                                                                         \n",
       "COMMENT This run started on 22 March 2017, 12:57                                \n",
       "COMMENT                                                                         \n",
       "COMMENT The file correspond to the MIPS 24um.                                   \n",
       "COMMENT                                                                         \n",
       "COMMENT ===============================================================         "
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "hdinst"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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s19FM0not6qk14xoqZwM/Hrh/1K/0j7EC7k7yYH/aARz71IZJW9/5rsvZzPE0jTFwXZLt\n/ebR7CbCRK7XPE6tabZu4xoqS8E7q2ot8H66M7svHnywT/4lcTx/Ka0L3Zn0q4G1wF7gxsWdzvAO\nP7Vm8LHj+Tcb11A52lf9J0ZV7el/7gfupNucme+pDeNsSZ6mUVX7qupQVc0AN/PSZuhErddinloz\nrqFyP7AmyaokJ9Fdn2XzIs9pzpK8Osmps8vAe4FHmOepDQs763lbkqdpzP7T9S6n+7vBBK3Xop9a\ns5h7qV9hD/ZldHutdwGfXuz5zHPuq+n2pn8f2DE7f+D1dBe0egK4G1g58JpP9+v6OIt89OAI63Mb\n3abA7OUrrh5mXYB1dP+ku4Av0n+je8zW65+Ah4Ht/T/bWRO4Xu+k27TZDmzrb5ct1N/Mr+lLampc\nN38kTShDRVJThoqkpgwVSU0ZKpKaMlQkNWWoSGrq/wAo5o8doQ8BiAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10e6a9be0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "rad=1000\n",
    "cpix=np.int((hdinst['NAXIS1']+1)/2.0)\n",
    "\n",
    "plt.imshow(psf_inst_full[cpix-rad-1:cpix+rad,cpix-rad-1:cpix+rad])\n",
    "#psf_inst=psf_inst_full[hdinst['CRPIX1']-rad-1:hdinst['CRPIX1']+rad,hdinst['CRPIX2']-rad-1:hdinst['CRPIX2']+rad]\n",
    "psf_inst=psf_inst_full[cpix-rad-1:cpix+rad,cpix-rad-1:cpix+rad]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Normalise instrumental PSF such that integral=1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "psf_inst=psf_inst/(np.sum(psf_inst))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now let's build the growthcurve for our PSFs."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "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)\n",
    "jmax_inst, imax_inst = np.unravel_index(np.argmax(psf_inst), psf_inst.shape)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "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",
    "\n",
    "x_inst = np.arange(1+rad*2)\n",
    "y_inst = np.arange(1+rad*2)\n",
    "xv_inst, yv_inst = np.meshgrid(x_inst, y_inst, sparse=False, indexing='xy')\n",
    "xp_inst = (xv_inst-imax_inst)*np.abs(hdinst['CD1_1']*3600.0)\n",
    "yp_inst = (yv_inst-jmax_inst)*np.abs(hdinst['CD1_1']*3600.0)\n",
    "r_inst = np.sqrt(xp_inst**2 + yp_inst**2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "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",
    "    #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": "markdown",
   "metadata": {},
   "source": [
    "Normally we run the code below for the instrumental PSF. This is slow and remains the same for each field so I just load up the result instead."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "```python\n",
    "radii_inst = np.unique(r_inst)\n",
    "encircled_flux_inst = np.zeros(radii_inst.shape)\n",
    "nbpix_inst = np.zeros(radii_inst.shape)\n",
    "for i, radius in enumerate(radii_inst):\n",
    "    if i % 1000 == 0:\n",
    "        print(i,len(radii_inst))\n",
    "    idj, idi = np.where(r_inst <= radius)\n",
    "    nbpix_inst[i] =len(idi)\n",
    "    encircled_flux_inst[i] = np.sum(psf_inst[idj, idi])\n",
    "```"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "inst_data=np.load('../data/MIPS_encircled_flux_inst.npz')\n",
    "encircled_flux_inst=inst_data['encircled_flux_inst']\n",
    "radii_inst=inst_data['radii_inst']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0x11624d1d0>"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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PgogkvPYmxPvzIR57AzC4xfNBwbaWSoHtwU1xlWb2GjAJWE4Xq6lv0j0KIpLw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\nRK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x102152668>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(radii, encircled_flux)\n",
    "\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": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "3.25058e-05\n"
     ]
    }
   ],
   "source": [
    "# This is clearly. \n",
    "print(np.median(psf[0:5,:]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0x10e7c6e80>"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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A89nAIqAV0Ad4RkSSK++kqi+qan9V7Z+WlhboGI3xy4D2TXnhypNYl3OQi57/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\nppwlBWOMMeUsKRhjjClnScEYY0y5/w9E1UjMs+8degAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x108db32e8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(nbpix[50:], encircled_flux[50:])\n",
    "plt.xlabel('Number of pixels')\n",
    "plt.ylabel('Encircled flux')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# Lets do a linear fit to the outer part of the curve to determine the backgound\n",
    "p = np.polyfit(nbpix[5000:], encircled_flux[5000:], 1)\n",
    "bkg=p[0]/(((np.abs(hd['CDELT1'])*3600.)**2)/4.25E10)\n",
    "#bkg = p[0]/resol**2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "-2.81920764491e-05\n"
     ]
    }
   ],
   "source": [
    "print(bkg)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[  49381.   49389.   49397. ...,  112213.  112221.  112225.]\n"
     ]
    }
   ],
   "source": [
    "print(nbpix[5000:])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# Lets correct the psf and encircled flux\n",
    "psf = psf - bkg\n",
    "encircled_flux = encircled_flux - p[0]* nbpix"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0x10ec96198>"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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+jy4Iv0/ovTipUdPQihkMVmd4IpLhEun76GIzK42bHmRmH0turN61u6GVQYW5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\nRK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10ec927b8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(radii, encircled_flux)\n",
    "plt.xlabel('Radius [arcsec]')\n",
    "plt.ylabel('Encircled flux')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    ""
   ]
  },
  {
   "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 from the instrumental PSF.  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x110953dd8>"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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41XkTER9PSymlVH/TYbIwxjwPPC8ivzDG/LorOzfGLAOWHbHskSPm7wXu7cr+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\nKeXT/w+et4pPsfXoCAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x108e29588>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(radii_inst, encircled_flux_inst, label='Calibration')\n",
    "plt.plot(radii, encircled_flux/np.max(encircled_flux), label='Our PSF')\n",
    "plt.xlim([0, 100])\n",
    "plt.xlabel('Radius [arcsec]')\n",
    "plt.ylabel('Encircled flux')\n",
    "plt.legend()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We will work below 30\" where our PSF is well behaved"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x10e8d4fd0>"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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7zd7SnmTBeTX28sHtuGpYR7rFx1iSMCbAiWrlT3tE5M+q+nAtxVOlpKQkXb58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\nMcZrljSMMcZ4zZKGMcYYr/0/jH5oHIUqj78AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10f94b3c8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(radii_inst, encircled_flux_inst, label='Calibration')\n",
    "plt.plot(radii, encircled_flux/np.max(encircled_flux), label='Our PSF')\n",
    "plt.xlim([0, 20])\n",
    "plt.xlabel('Radius [arcsec]')\n",
    "plt.ylabel('Encircled flux')\n",
    "plt.legend()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    ""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We see that while the calibration curve still rises beyond 30\", our PSF has reached a plateau. Let's note the calibration $C(r)$. Our PSF encirled energy is of the form:\n",
    "\n",
    "$E(r) = \\alpha C(r \\times \\beta)$\n",
    "\n",
    "Where $\\beta$ is the fattening of the PSF.\n",
    "\n",
    "We could take the derivative, but this too noisy. Instead we do a brute force approach"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x10ee99e48>"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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7zd7SnmTBeTX28sHtuGpYR7rFx1iSMCbAiWrlT3tE5M+q+nAtxVOlpKQkXb58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\nMcZrljSMMcZ4zZKGMcYYr/0/jH5oHIUqj78AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10e913518>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(radii_inst, encircled_flux_inst, label='Calibration')\n",
    "plt.plot(radii, encircled_flux/np.max(encircled_flux), label='Our PSF')\n",
    "plt.xlim([0, 20])\n",
    "plt.xlabel('Radius [arcsec]')\n",
    "plt.ylabel('Encircled flux')\n",
    "plt.legend()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "rf = 1.210, ff = 1.000, residual = 0.006\n",
      "7.52045e+08\n",
      "rf = 1.000, ff = 1.080, residual = 0.038\n",
      "6.96338e+08\n",
      "rf = 1.000, ff = 1.190, residual = 0.086\n",
      "6.31971e+08\n",
      "rf = 1.000, ff = 1.240, residual = 0.108\n",
      "6.06488e+08\n",
      "rf = 1.000, ff = 1.250, residual = 0.110\n",
      "6.01636e+08\n",
      "rf = 1.000, ff = 1.240, residual = 0.115\n",
      "6.06488e+08\n",
      "rf = 1.000, ff = 1.220, residual = 0.126\n",
      "6.1643e+08\n",
      "rf = 1.000, ff = 1.210, residual = 0.135\n",
      "6.21525e+08\n",
      "rf = 1.000, ff = 1.210, residual = 0.139\n",
      "6.21525e+08\n",
      "rf = 1.000, ff = 1.200, residual = 0.143\n",
      "6.26704e+08\n",
      "rf = 1.000, ff = 1.200, residual = 0.155\n",
      "6.26704e+08\n",
      "rf = 1.000, ff = 1.190, residual = 0.187\n",
      "6.31971e+08\n"
     ]
    }
   ],
   "source": [
    "rfactor = np.arange(1.,3., 1e-2)\n",
    "ffactor = np.arange(1.,3., 1e-2)\n",
    "# work with the data points between 3 and 25\"\n",
    "for r in np.arange(3,15):\n",
    "    idx, = np.where((radii > 2) & (radii < r))\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",
    "        tck = interpolate.splrep(radii_inst*rf,encircled_flux_inst , s=1)#changed s=0 to 1 as I was getting NaNs\n",
    "        yfit = interpolate.splev(xv, tck, der=0)\n",
    "\n",
    "        for j, ff in enumerate(ffactor):\n",
    "            resid[i, j] = np.sum((yv-yfit*ff)**2)\n",
    "    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]))\n",
    "    print(np.max((psf/np.max(encircled_flux)/ffactor[fmin])))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This shows a minimum, with some degeneracy. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "rf = 1.000, ff = 1.190, residual = 0.187\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": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.image.AxesImage at 0x10f0d1c50>"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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jGdpvhtwIGakT8uu8KW0KTT0W+q1VCO7HrLaRbQGooPGwgc8M3k/gnUGPO/hc2cJ5B3FP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\nAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x108e0a7f0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.imshow(np.log(resid))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x10f230ef0>"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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28T/DO/OzC9KCHaExppnx50G5/cBtIhLvdqpnGlthLsy5FHIyoOdYMk67lmtm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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x110f1a5c0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(radii_inst*rfactor[rmin],encircled_flux_inst, label='Calibration')\n",
    "plt.plot(radii, encircled_flux/np.max(encircled_flux)/ffactor[fmin], label='Our PSF')\n",
    "plt.xlim([0, 30])\n",
    "plt.xlabel('Radius [arcsec]')\n",
    "plt.ylabel('Encircled flux')\n",
    "plt.legend()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.75911591736871142"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# The two curve overlap\n",
    "rad=20\n",
    "psfok = (psf/np.max(encircled_flux)/ffactor[fmin])\n",
    "cpix=np.int((hd['NAXIS1']+1)/2.0)\n",
    "np.sum(psfok[cpix-rad-1:cpix+rad,cpix-rad-1:cpix+rad])*((np.abs(hd['CDELT1'])*3600.)**2)/4.25E10"
   ]
  },
  {
   "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.\n",
    "## As units of map in MJy/sr, divide by 1E6"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "psfok=psfok/1.0E6"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Validation\n",
    "To check PSF is reasonable, lets look at a 24 micron source (ID 129698 from [bootes-mips24-sextractor-faint.fits.gz](http://mattiavaccari.net/df/m24/) ) a flux of 274.48 microJy. Maximum value in our normalised PSF gives a peak below. Since PSF is double resolution of map, it could also be off centre. Map has value of 0.2425 MJy/sr but does appear to be off centre. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Max PSF = 0.228 MJy/sr, off pixel Max PSF = 0.165 MJy/sr\n"
     ]
    }
   ],
   "source": [
    "print(\"Max PSF = {:.3f} MJy/sr, off pixel Max PSF = {:.3f} MJy/sr\".format(psfok[cpix-1,cpix-1]*3.E-04,psfok[cpix-2,cpix-2]*2.74E-04))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "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",
      "/Users/pdh21/anaconda3/envs/new/lib/python3.6/site-packages/aplpy/normalize.py:115: RuntimeWarning: invalid value encountered in less\n",
      "  negative = result < 0.\n"
     ]
    },
    {
     "data": {
      "image/png": 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TEcLyFUbu2Pki/O9qjHE6QliBmMjN5nFF9r/Xq8cmOB2hUtpftN/pCGXyuDxOR/jLRfYr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\nALCI8gUAAGDR/wHuQlagXCTk2AAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x12693def0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import aplpy\n",
    "import seaborn as sns\n",
    "sns.set_style(\"white\")\n",
    "cmap=sns.cubehelix_palette(8, start=.5, rot=-.75,as_cmap=True)\n",
    "fig=aplpy.FITSFigure('./data/wp4_bootes_mips24_map_v1.0.fits.gz')\n",
    "fig.recenter(218.1546,35.7837, radius=0.002)\n",
    "fig.show_colorscale(vmin=0.0,vmax=1.0,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 this seems reasonable."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Create PSF fits file"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "stackhd[1].data=psfok\n",
    "stackhd.writeto('dmu17_MIPS_Bootes_20180129.fits',overwrite=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    ""
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python [default]",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3.0
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.0"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}