SignalToNoise_DarkClouds.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Signal to Noise Calculations for H clouds\n",
    "\n",
    "In this code, I am calculating the signal-to-noise ratio as a function of exposure time, to find the time required for the Dragonfly telescope to match observations of H$\\alpha$ emission performed by Donahue, Stocke, and Aldering (1995).  They performed narrowband H$\\alpha$ imaging of several intergalactic clouds to low surface brightness of $\\sim 10^{-18}$.  \n",
    "\n",
    "The SNR is calculated following the equation (see, e.g., pg 407 of \"Spectroscopic Instrumentation\" by Eversberg and Vollmann): \n",
    "\n",
    "$SNR = \\frac{I t}{\\sqrt{I t + B t + D t + R^2}}$, \n",
    "\n",
    "where I is the signal over some number of pixels, B is the sky background over some number of pixels, D is the dark current over some number of pixels and R is the readout noise of the detector.  The exposure time, t, is usually given in seconds."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from astropy import constants as const\n",
    "from astropy import units as u"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$6.6260696 \\times 10^{-27} \\; \\mathrm{erg\\,s}$"
      ],
      "text/plain": [
       "<Quantity 6.62606957e-27 erg s>"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Testing out astropy a bit...\n",
    "const.h.cgs"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "4.84813681109536e-06"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "u.arcsec.to(u.rad)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##Add the Dragonfly instrumentation data\n",
    "Listing some values gathered from the Dragonfly Telephoto Instrumentation paper (Abraham and van Dokkum 2014), as well as sky background from the Gemini Sky Observatory (http://www.gemini.edu/sciops/telescopes-and-sites/observing-condition-constraints/optical-sky-background)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def Dragonfly():\n",
    "    area_lens = np.pi*(14.3/2)**2 * 48. * u.cm**2\n",
    "    pix_size = 2.8 # arcsec\n",
    "    ang_size_pixel  = (pix_size * (1./206265.))**2 * u.rad**2   # rad^2, the pixel size of the CCD\n",
    "\n",
    "    tau_l = 0.85  # transmittance of the Dragonfly lens\n",
    "    QE = 0.48     # quantum efficiency of the CCDs\n",
    "    tau_f = 1.    # transmittance of the Halpha filter -- assumed for now\n",
    "\n",
    "    # The following are per pixel\n",
    "    B = 0.52135 *u.photon/u.second/u.nm/u.arcsec**2/u.m**2   # sky background at 565.6 nm \n",
    "    D = 0.04 *u.photon/u.second                             # dark current (electrons / s) -- PER PIXEL??\n",
    "    R_squared = 10.**2 * u.photon                           # read noise (electrons)\n",
    "\n",
    "    # Donahue used 2' x 2' boxes to measure the sky brightness within\n",
    "   # numpixels = [(2*60*2*60)/(pix_size**2)]            # for HI clouds & for back of the envelope calculation\n",
    "    numpixels = np.array([(100.*100.)/(pix_size**2),   # for IGM filaments (from Bertone et al 2010, Fig2)\n",
    "                          (10.*10.)/(pix_size**2),\n",
    "                          1.]) \n",
    "   # numpixels = [7405.]                                  # for azithumally averaged galaxy, at radius 80kpc, distance 50 Mpc\n",
    "   # numpixels = [3700.]                                  # for azithumally averaged galaxy, at radius 80kpc, distance 100 Mpc\n",
    "   # numpixels = [1.]                                      # for H alpha testing fields -Cygnus loop\n",
    "    print('Number of pixels: '+str(numpixels))\n",
    "    print('Area of the lens: '+str(area_lens))\n",
    "    \n",
    "    return [area_lens, ang_size_pixel, tau_l, tau_f, QE, B, D, R_squared, numpixels]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The surface brightness of the clouds stated by Donahue+ (1995) are listed below."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Number of pixels: [  1.27551020e+03   1.27551020e+01   1.00000000e+00]\n",
      "Area of the lens: 7709.09138079 cm2\n",
      "[<Quantity 7709.091380790922 cm2>, <Quantity 1.8427438923353984e-10 rad2>, 0.85, 1.0, 0.48, <Quantity 0.52135 ph / (arcsec2 m2 nm s)>, <Quantity 0.04 ph / s>, <Quantity 100.0 ph>, array([  1.27551020e+03,   1.27551020e+01,   1.00000000e+00])]\n",
      "Surface brightness: 23870.257 ph / (cm2 rad2 s)\n"
     ]
    }
   ],
   "source": [
    "[area_lens, ang_size_pixel, tau_l, tau_f, QE, B, D, R_squared, numpixels] = Dragonfly()\n",
    "print([area_lens, ang_size_pixel, tau_l, tau_f, QE, B, D, R_squared, numpixels])\n",
    "wavelen = 656.3e-9 * u.m\n",
    "\n",
    "### SB of H clouds (from Donahue et al 1995)\n",
    "#SB_cgs = 0.1* 1.4*10**-18 * u.erg / u.second / (u.cm**2) / u.arcsec**2\n",
    "#SB_ph  = SB_cgs * wavelen / (const.h.cgs * const.c) / (u.arcsec.to(u.rad) * u.rad/u.arcsec)**2 * u.photon\n",
    "\n",
    "\n",
    "### SB of extended halos (threshold from Stiedel et al 2011)\n",
    "#SB_cgs = 1.597e-19 erg / (arcsec2 cm2 s)\n",
    "\n",
    "#conversion:\n",
    "SB_cgs = 10**-19.7 *u.erg / u.arcsec**2 / u.cm**2 / u.s\n",
    "SB_ph = SB_cgs * 656.3e-9*u.m/(const.h.to('erg s').value * const.c.to('m/s').value) * (206265.*u.arcsec)**2/u.sr\n",
    "\n",
    "SB_ph = 2245.38 * u.photon / (u.cm**2 * u.rad**2 * u.second) # from Steidel et al 2011 plus long translations\n",
    "SB_ph = 559.60 * u.photon / (u.cm**2 * u.rad**2 * u.second)  # from van de Voort & Schaye 2013\n",
    "\n",
    "### SB of IGM filaments (from Bertone series of papers, see SurfaceBrighnessCalcs.ipynb)\n",
    "SB_ph = 23870.257 * u.photon / (u.cm**2) / u.second / (u.rad**2)\n",
    "## The following are just to check out how long need integrations for:\n",
    "#SB_ph = 20000. * u.photon / (u.cm**2) / u.second / (u.rad**2)\n",
    "#SB_ph = 2000. * u.photon / (u.cm**2) / u.second / (u.rad**2)\n",
    "#SB_ph = 200. * u.photon / (u.cm**2) / u.second / (u.rad**2)\n",
    "SB_ph_1 = 1719. * u.photon / (u.cm**2) / u.second / (u.rad**2)\n",
    "#SB_ph_1 = 543.5 * u.photon / (u.cm**2) / u.second / (u.rad**2)\n",
    "#SB_ph_1 = 861.5 * u.photon / (u.cm**2) / u.second / (u.rad**2)\n",
    "SB_ph_2 = 1.9096 * u.photon / (u.cm**2) / u.second / (u.rad**2)\n",
    "SB_ph_3 = .076 * u.photon / (u.cm**2) / u.second / (u.rad**2)\n",
    "SB_ph_3 = 3.828 * u.photon / (u.cm**2) / u.second / (u.rad**2)\n",
    "SB_ph_3 = 60.4 * u.photon / (u.cm**2) / u.second / (u.rad**2)\n",
    "SB_ph_3 = 100. * u.photon / (u.cm**2) / u.second / (u.rad**2)\n",
    "\n",
    "#1.90962057  861.3697057    95.70774508\n",
    "#7.63848228e-02   1.90962057e+00   1.71865851e+03\n",
    "\n",
    "#SB_ph = 7638. * u.photon / (u.cm**2 * u.rad**2 * u.second)\n",
    "#SB_ph = np.array([])\n",
    "\n",
    "### SB of Cygnus loop (lowest SB of filaments, brightest is 5*10**-5)  Hester+1986\n",
    "#SB_cgs = 10**-6 * u.erg / u.second / (u.cm**2) / u.rad**2  \n",
    "#SB_cgs =  10**-5 * u.erg / u.second / (u.cm**2) / u.rad**2  \n",
    "\n",
    "### SB of IGM filaments (back of the envelope calculation)\n",
    "#SB_cgs =  5./3. * 10**-12 * u.erg / u.second / (u.cm**2) / u.rad**2 \n",
    "#SB_ph  = SB_cgs * wavelen / (const.h.cgs * const.c) * u.photon\n",
    "\n",
    "print('Surface brightness: '+str(SB_ph))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## SNR calculation\n",
    "The signal-to-noise is calculated for the surface brightness listed above for an array of exposure times.  At some time, t, it reaches a SNR ~ 5, which is generally accepted as a reliable detection."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "SB: 1719.0 ph / (cm2 rad2 s)\n",
      "area: 7709.09138079 cm2\n",
      "numpixel:1275.51020408\n",
      "time (hours): 2000000.0 s\n",
      "SNR: 1529.3321236 ph(1/2)\n",
      "SB: 1.9096 ph / (cm2 rad2 s)\n",
      "area: 7709.09138079 cm2\n",
      "numpixel:1275.51020408\n",
      "time (hours): 2000000.0 s\n",
      "SNR: 1.69911898066 ph(1/2)\n",
      "SB: 100.0 ph / (cm2 rad2 s)\n",
      "area: 7709.09138079 cm2\n",
      "numpixel:1275.51020408\n",
      "time (hours): 2000000.0 s\n",
      "SNR: 88.9770939482 ph(1/2)\n",
      "\n",
      "\n",
      "SB: 1719.0 ph / (cm2 rad2 s)\n",
      "Factor more lenses: 1.0\n",
      "numpixel:1275.51020408\n",
      "time (hours): 180.0\n",
      "SNR: 14.5082312545 ph(1/2)\n",
      "21599999\n",
      "\n",
      "\n",
      "SB: 1.9096 ph / (cm2 rad2 s)\n",
      "Factor more lenses: 100.0\n",
      "numpixel:1275.51020408\n",
      "time (hours): 8000000.0\n",
      "SNR: 34.1563736359 ph(1/2)\n",
      "28800000\n",
      "\n",
      "\n",
      "SB: 100.0 ph / (cm2 rad2 s)\n",
      "Factor more lenses: 1.0\n",
      "numpixel:1275.51020408\n",
      "time (hours): 10000.0\n",
      "SNR: 6.29162841891 ph(1/2)\n",
      "36000000\n",
      "\n",
      "\n"
     ]
    }
   ],
   "source": [
    "## For the SNR plot of the different structures marked on the density/temp/SB maps to send to Joop.\n",
    "\n",
    "time = 60.*60*2000000. * u.second\n",
    "\n",
    "for SB_ph in [SB_ph_1,SB_ph_2,SB_ph_3]:\n",
    "    numpixel = numpixels[0]\n",
    "    S = SB_ph * QE * tau_l * tau_f * area_lens * ang_size_pixel\n",
    "    signal = S*time*numpixel\n",
    "    B_tot = B * QE * tau_l * tau_f * 3.*u.nm * area_lens.to(u.m**2) * ang_size_pixel.to(u.arcsec**2)\n",
    "    sigma = np.sqrt(signal + B_tot*time*numpixel + D*time*numpixel + R_squared*numpixel)\n",
    "    SNR = signal/sigma\n",
    "\n",
    "    print('SB: '+str(SB_ph))\n",
    "    print('area: '+str(area_lens))\n",
    "    print('numpixel:'+str(numpixel))\n",
    "    print('time (hours): '+str(time/3600.))\n",
    "    print('SNR: '+str(SNR))\n",
    "    \n",
    "print('\\n')\n",
    "\n",
    "# SB_ph_1 --> best case scenario\n",
    "time = 60.*60*60. *3. * u.second\n",
    "numpixel = numpixels[0]\n",
    "area_lens_1 = area_lens\n",
    "\n",
    "S = SB_ph_1 * QE * tau_l * tau_f * area_lens_1 * ang_size_pixel\n",
    "signal = S*time*numpixel\n",
    "B_tot = B * QE * tau_l * tau_f * 3.*u.nm * area_lens_1.to(u.m**2) * ang_size_pixel.to(u.arcsec**2)\n",
    "sigma = np.sqrt(signal + B_tot*time*numpixel + D*time*numpixel + R_squared*numpixel)\n",
    "SNR = signal/sigma\n",
    "\n",
    "print('SB: '+str(SB_ph_1))\n",
    "print('Factor more lenses: '+str(area_lens_1/area_lens_1))\n",
    "print('numpixel:'+str(numpixel))\n",
    "print('time (hours): '+str(time/(3600.*u.second)))\n",
    "print('SNR: '+str(SNR))\n",
    "\n",
    "time_1_array = np.arange(1,60.*60.*60.*100) * u.second\n",
    "print(str(len(time_1_array)))\n",
    "print('\\n')\n",
    "\n",
    "\n",
    "# SB_ph_2 --> middle case scenario\n",
    "time = 60.*60*8000000. * u.second\n",
    "numpixel = numpixels[0]\n",
    "area_lens_2 = area_lens *100\n",
    "\n",
    "S = SB_ph_2 * QE * tau_l * tau_f * area_lens_2 * ang_size_pixel\n",
    "signal = S*time*numpixel\n",
    "B_tot = B * QE * tau_l * tau_f * 3.*u.nm * area_lens_2.to(u.m**2) * ang_size_pixel.to(u.arcsec**2)\n",
    "sigma = np.sqrt(signal + B_tot*time*numpixel + D*time*numpixel + R_squared*numpixel)\n",
    "SNR = signal/sigma\n",
    "\n",
    "print('SB: '+str(SB_ph_2))\n",
    "print('Factor more lenses: '+str(area_lens_2/area_lens))\n",
    "print('numpixel:'+str(numpixel))\n",
    "print('time (hours): '+str(time/(3600.*u.second)))\n",
    "print('SNR: '+str(SNR))\n",
    "\n",
    "time_2_array = np.arange(1,60.*60.*8000000.*100,100000)\n",
    "print(str(len(time_2_array)))\n",
    "print('\\n')\n",
    "\n",
    "\n",
    "# SB_ph_3 --> middle case scenario\n",
    "time = 60.*60*1000000000. * u.second  #  For the large box\n",
    "time = 60.*60*10000. * u.second    #  For the small box\n",
    "numpixel = numpixels[0]\n",
    "area_lens_3 = area_lens * 1\n",
    "\n",
    "S = SB_ph_3 * QE * tau_l * tau_f * area_lens_3 * ang_size_pixel\n",
    "signal = S*time*numpixel\n",
    "B_tot = B * QE * tau_l * tau_f * 3.*u.nm * area_lens_3.to(u.m**2) * ang_size_pixel.to(u.arcsec**2)\n",
    "sigma = np.sqrt(signal + B_tot*time*numpixel + D*time*numpixel + R_squared*numpixel)\n",
    "SNR = signal/sigma\n",
    "\n",
    "print('SB: '+str(SB_ph_3))\n",
    "print('Factor more lenses: '+str(area_lens_3/area_lens))\n",
    "print('numpixel:'+str(numpixel))\n",
    "print('time (hours): '+str(time/(3600.*u.second)))\n",
    "print('SNR: '+str(SNR))\n",
    "\n",
    "time_3_array = np.arange(1,60.*60.*1000000000.,100000)\n",
    "print(str(len(time_3_array)))\n",
    "print('\\n')\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "first run..\n",
      "second run..\n",
      "third run..\n"
     ]
    },
    {
     "data": {
      "image/png": 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161PbrfIW+Pbtgz594ORJ2LrVmivuK3GlK6d5mcd9lYh8et73E5RSj17uAZ0Q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\nOAhjuA0Gg8FgcBD/D4rpeSWvoJZTAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10b449590>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#  okay, now that we've figured out when we reach SNR that's ok, let's try and plot this (with log10t on the x-axis)\n",
    "plt.figure(figsize=(8,4))\n",
    "numpixel = numpixels[0]\n",
    "\n",
    "for SB_this in [SB_ph_1,SB_ph_2,SB_ph_3]:\n",
    "    if SB_this == SB_ph_1:\n",
    "        time = np.arange(1,60.*60.*60.*100) * u.second\n",
    "        time = np.arange(1,60.*60.*60.*100) * u.second  \n",
    "        print('first run..')\n",
    "    if SB_this == SB_ph_2:\n",
    "        time = np.arange(1,60.*60.*8000000.*100,100000)* u.second\n",
    "        print('second run..')\n",
    "    if SB_this == SB_ph_3:\n",
    "       # time = np.arange(1,60.*60.*1000000000.,100000000)* u.second   # For the large box\n",
    "        time = np.arange(1,60.*60.*1000000.,1000)* u.second   # For the small box\n",
    "       # time = np.concatenate([np.arange(1,60.*60.*1000000.,1000000000),np.arange(60.*60.*1000000.,60.*60.*10000000.,10000000000),\n",
    "       #                       np.arange(60.*60.*10000000.,60.*60.*100000000.,100000000000)])* u.second\n",
    "       # time = 60*60*np.array([10**-3,10**2,10**3,10**4,10**5,10**6,10**7,10**7.5,\n",
    "       #                        10**8.5,10**9])*u.second\n",
    "        print('third run..')\n",
    "        \n",
    "    S = SB_this * QE * tau_l * tau_f * area_lens * ang_size_pixel\n",
    "    signal = S*time*numpixel\n",
    "    B_tot = B * QE * tau_l * tau_f * 3.*u.nm * area_lens.to(u.m**2) * ang_size_pixel.to(u.arcsec**2)\n",
    "    sigma = np.sqrt(signal + B_tot*time*numpixel + D*time*numpixel + R_squared*numpixel)\n",
    "    \n",
    "    if SB_this == SB_ph_1:\n",
    "        plt.semilogx(time/60./60./u.second, (signal/sigma/(u.photon**0.5)),'k-',linewidth=2)\n",
    "        \n",
    "        area_lens_1 = area_lens*10.\n",
    "        S = SB_this * QE * tau_l * tau_f * area_lens_1 * ang_size_pixel\n",
    "        signal = S*time*numpixel\n",
    "        B_tot = B * QE * tau_l * tau_f * 3.*u.nm * area_lens_1.to(u.m**2) * ang_size_pixel.to(u.arcsec**2)\n",
    "        sigma = np.sqrt(signal + B_tot*time*numpixel + D*time*numpixel + R_squared*numpixel)\n",
    "        plt.semilogx((time/60./60./u.second), (signal/sigma/(u.photon**0.5)),'k-',linewidth=2,color='red')\n",
    "\n",
    "    if SB_this == SB_ph_2:\n",
    "        plt.semilogx((time/60./60./u.second), (signal/sigma/(u.photon**0.5)),'k--',linewidth=2)\n",
    "        \n",
    "        area_lens_2 = area_lens*10.\n",
    "        S = SB_this * QE * tau_l * tau_f * area_lens_2 * ang_size_pixel\n",
    "        signal = S*time*numpixel\n",
    "        B_tot = B * QE * tau_l * tau_f * 3.*u.nm * area_lens_2.to(u.m**2) * ang_size_pixel.to(u.arcsec**2)\n",
    "        sigma = np.sqrt(signal + B_tot*time*numpixel + D*time*numpixel + R_squared*numpixel)\n",
    "        plt.semilogx((time/60./60./u.second), (signal/sigma/(u.photon**0.5)),'k--',linewidth=2,color='red')\n",
    "\n",
    "    if SB_this == SB_ph_3:\n",
    "        plt.semilogx((time/60./60./u.second), (signal/sigma/(u.photon**0.5)),'k:',linewidth=2)\n",
    "        \n",
    "        area_lens_3 = area_lens*10.\n",
    "        S = SB_this * QE * tau_l * tau_f * area_lens_3 * ang_size_pixel\n",
    "        signal = S*time*numpixel\n",
    "        B_tot = B * QE * tau_l * tau_f * 3.*u.nm * area_lens_3.to(u.m**2) * ang_size_pixel.to(u.arcsec**2)\n",
    "        sigma = np.sqrt(signal + B_tot*time*numpixel + D*time*numpixel + R_squared*numpixel)\n",
    "        plt.semilogx((time/60./60./u.second), (signal/sigma/(u.photon**0.5)),'k:',linewidth=2,color='red')\n",
    "\n",
    "\n",
    "plt.ylim(0,5)\n",
    "plt.xlim(10**-3,10**7)\n",
    "#plt.xticks([-2,0,2,4,6,8],['10$^{-2}$','10$^{0}$','10$^{2}$','10$^{4}$','10$^{6}$','10$^{8}$'])\n",
    "\n",
    "plt.plot([10**-3,10**7],[5,5],color='gray')\n",
    "plt.xlabel('Integration Time (hours)')\n",
    "plt.ylabel('Signel-to-noise Ratio')\n",
    "plt.savefig('FigSNRLines_100.pdf',bbox_inches='tight')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1275.51020408\n",
      "signal: 0.000996332309138 ph / s\n",
      "7709.09138079 cm2\n",
      "Halpha Signal: 0.000996332309138 ph / s\n",
      "Background Sky: 3.85681880622 ph / s\n",
      "12.7551020408\n",
      "signal: 0.000996332309138 ph / s\n",
      "7709.09138079 cm2\n",
      "Halpha Signal: 0.000996332309138 ph / s\n",
      "Background Sky: 3.85681880622 ph / s\n",
      "1.0\n",
      "signal: 0.000996332309138 ph / s\n",
      "7709.09138079 cm2\n",
      "Halpha Signal: 0.000996332309138 ph / s\n",
      "Background Sky: 3.85681880622 ph / s\n"
     ]
    },
    {
     "data": {
      "image/png": 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vv9rGLFJS4MIL3Zqj1Uj/jGpElcUsVHVJwEOTgLuB+sB1qvpRiMa0BHJVdZeI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\n/YfBf11/VwAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10e50bf50>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "\n",
    "time = np.arange(0,60.*16.) * u.second   # Exposure Times matched to SNR for 100\" pixels (20000 ph)\n",
    "time = np.arange(0,60.*60*20.) * u.second   # Exposure Times matched to SNR for 100\" pixels (2000 ph)\n",
    "time = np.arange(0,60.*60*30.) * u.second   # Exposure Times matched to SNR for 100\" pixels (800 ph)\n",
    "\n",
    "#time = np.arange(60.*60*1800000,60.*60*2000000.) * u.second   # Exposure Times matched to SNR for 100\" pixels (0.07 ph)\n",
    "\n",
    "\n",
    "plt.figure(figsize=(4,4))\n",
    "size = np.array(['2.8\"','10\"','100\"'])\n",
    "size = np.array(['100\"','10\"','2.8\"'])\n",
    "binning = np.array(['Binned 100\"x100\"','Binned 10\"x10\"','No binning'])\n",
    "\n",
    "\n",
    "i = 0\n",
    "for numpixel in numpixels:\n",
    "    print(numpixel)\n",
    "    ## Signal = signal flux * QE * transmission * angular pixel size * area of the lens\n",
    "    S = SB_ph_1 * QE * tau_l * tau_f * area_lens * ang_size_pixel\n",
    "    print('signal: '+str(S))\n",
    "    signal = S*time*numpixel\n",
    "    print(area_lens)\n",
    "    ## Noise\n",
    "    B_tot = B * QE * tau_l * tau_f * 3.*u.nm * area_lens.to(u.m**2) * ang_size_pixel.to(u.arcsec**2)\n",
    "    sigma = np.sqrt(signal + B_tot*time*numpixel + D*time*numpixel + R_squared*numpixel)\n",
    "\n",
    "    # Note that the signal is about an eighth the strength of the background sky signal:\n",
    "    print('Halpha Signal: '+str(S))\n",
    "    print('Background Sky: ' +str(B_tot))\n",
    "\n",
    "    #plt.plot(time, signal/np.sqrt(signal),label='Signal')\n",
    "    #plt.plot(time, signal/np.sqrt(signal + B_tot*time),label='Signal + bkgd')\n",
    "    #plt.plot(time, signal/np.sqrt(signal + B_tot*time + D*time),label='Signal + bkgd + dark curr')\n",
    "  #  plt.plot(time/60./60., signal/sigma,label= 'Binned '+size[i])\n",
    "    plt.plot(time/60./60., signal/sigma,label= binning[i])\n",
    "\n",
    "    i = i+1\n",
    "    \n",
    "   # print('background is:'+str(B_tot*time*numpixel))\n",
    "   # print('detector noise is:'+str(D*time*numpixel + R_squared*numpixel))\n",
    "\n",
    "#plt.plot([0,16.],[5,5],'k--') \n",
    "plt.plot([0,30.],[5,5],'k--') \n",
    "#plt.plot([22.,22],[0,6])\n",
    "plt.title(str(SB_ph_1))\n",
    "plt.legend(fancybox=True,loc=2,fontsize = 'small')\n",
    "    \n",
    "#plt.xlabel('time (minutes)')\n",
    "plt.xlabel('time (hours)')\n",
    "\n",
    "plt.ylabel('SNR')\n",
    "plt.savefig('FigSNR100.pdf')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1275.51020408\n",
      "0.000996332309138 ph / s\n",
      "Halpha Signal: 0.000996332309138 ph / s\n",
      "Background Sky: 3.85681880622 ph / s\n",
      "12.7551020408\n",
      "0.000996332309138 ph / s\n",
      "Halpha Signal: 0.000996332309138 ph / s\n",
      "Background Sky: 3.85681880622 ph / s\n",
      "1.0\n",
      "0.000996332309138 ph / s\n",
      "Halpha Signal: 0.000996332309138 ph / s\n",
      "Background Sky: 3.85681880622 ph / s\n"
     ]
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x12b193ad0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "time = np.arange(0,2200.*3600.) * u.second   # Exposure Time matched for SNR of 10\n",
    "\n",
    "plt.figure(figsize=(4,4))\n",
    "\n",
    "for numpixel in numpixels:\n",
    "    print(numpixel)\n",
    "    ## Signal = signal flux * QE * transmission * angular pixel size * area of the lens\n",
    "    S = SB_ph_1 * QE * tau_l * tau_f * area_lens * ang_size_pixel\n",
    "    print(S)\n",
    "    signal = S*time*numpixel\n",
    "\n",
    "    ## Noise\n",
    "    B_tot = B * QE * tau_l * tau_f * 3.*u.nm * area_lens.to(u.m**2) * ang_size_pixel.to(u.arcsec**2)\n",
    "    sigma = np.sqrt(signal + B_tot*time*numpixel + D*time*numpixel + R_squared*numpixel)\n",
    "\n",
    "    # Note that the signal is about an eighth the strength of the background sky signal:\n",
    "    print('Halpha Signal: '+str(S))\n",
    "    print('Background Sky: ' +str(B_tot))\n",
    "\n",
    "    plt.plot(time/3600., signal/sigma,label= 'num pixels '+str(round(numpixel)))\n",
    "\n",
    "plt.plot([0,2200.],[5,5],'k--')   \n",
    "plt.title(str(SB_ph_1))\n",
    "#plt.legend()\n",
    "plt.xlim(0,2200)\n",
    "plt.ylim(0,10)\n",
    "plt.xlabel('time (hours)')\n",
    "plt.ylabel('SNR')\n",
    "plt.savefig('FigSNR10.pdf')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1275.51020408\n",
      "0.000996332309138 ph / s\n",
      "Halpha Signal: 0.000996332309138 ph / s\n",
      "Background Sky: 3.85681880622 ph / s\n",
      "12.7551020408\n",
      "0.000996332309138 ph / s\n",
      "Halpha Signal: 0.000996332309138 ph / s\n",
      "Background Sky: 3.85681880622 ph / s\n",
      "1.0\n",
      "0.000996332309138 ph / s\n",
      "Halpha Signal: 0.000996332309138 ph / s\n",
      "Background Sky: 3.85681880622 ph / s\n"
     ]
    },
    {
     "data": {
      "image/png": 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5innVSUTqA+8DPwMUeFNV/xFu2w17N9C4SuNYhhfeli3w61+7/kkffwwXX+x3\nRMbEFT9+jk8Aj6rqOUBH4Nci0iLchhv3baRxVR8TTWYm/OMf0K6duxdm8WJLMsYUQsxLNKq6A9jh\nPT8kIquAOsCq7Ntu2b+FSxteGuMIPRs3ugGoTp5005k0T/DxcIyJIl8bGESkEdAWmB9uffqBdOpV\nqhfLkFxbzFtvQYcO0LOnG6PXkowxReLb5W0RqQCMBn6jqoeyrx88eDCr56zmw40fcvSqo6SkpEQ/\nqIwMuO8+19M6NRXOOSf6xzTGR6mpqaSmpkb9OKKqUT/IaQcVKQlMACaq6t/DrNfjJ49T7s/lOPrk\nUUoUi0E+/PRTuP9++NWv4A9/sJvuTKBJaioahR9fEUFVI34/iR9XnQT4D7AyXJLJsv3QdmqWrxn9\nJPP9924StnHjYOxYN62sMSai/GijuRj4BXCZiCz2Ht2zbxST9plvvnGJJT3dXVGyJGNMVPhx1WkW\n+UhwGQcyqFupbvQC+egjd2/Ms8+6+ZOCdPexMQkmsH2d0g+kU69iFEo0p07BE0+4G+8mT3YzDxhj\noirYiSbSVafvvnNTm2RmwsKFUKNGZPdvjAkrsB11th/aTu2KtSO3w2XL3MwDrVu7EfAsyRgTM4Et\n0ew6vIuflf9ZZHY2dSrcfju88grccUdk9mmMybfAJprdR3ZHJtG8+y4MHAijR8MllxR9f8aYAgts\notl1eBdnlDuj8DtQhT/+0c1EMH26GwXPGOOLwCaab498yxnlC5loMjPdGL5z5sDcuVAzziefMybO\nBTbRVChVgVLFSxX8jadOua4Eq1fDV1/ZTJDGBEBgE02hqk0nTkDfvrBzJ0yaZPNZGxMQgU00BW4I\nPnUK7roL9u6FCROgbNmoxGWMKbjAJpoCtc+oul7X27bB559bkjEmYIKbaPJbdVJ1088uWeLul7Ek\nY0zgBDbRVC1TNX8bvvoqTJwIM2ZAxYrRDcoYUyiBTTSVy+TjatGECfDSS+4SdrVq0Q/KGFMowU00\npfNINGlpbvDw8eOhYcPYBGWMKZTAdqqsUqZKziv37YPrr3dToXTsGLugjDGFEthEk2PVSRXuvReu\nvhpuuy22QRljCiX+qk5Dh8KmTfDBBzGNxxhTeIFNNGGrTqtWuaE358+H0qVjH5QxplDip+p06pSr\nMj37LDRt6k9QxphCCW6iyV51eu01N9dSv37+BGSMKbTAVp0qlArpELlrFzz3nBv2oVhgc6MxJgeB\n/dYWL1a2ckVRAAAH5ElEQVT8xxfPPAN9+kCzZv4FZIwptMCWaH6wYgV88okbX8YYE5cCW6L5wZ//\nDI8+ClXz2ffJGBM4wS7RrF/vBrB6/XW/IzHGFEGwSzSvvAIPPgiVKvkdiTGmCIJbojl6FEaOdOPM\nGGPiWnBLNGPGQIcOUL++35EYY4oouInmgw/cQOPGmLgX3EQzaxb06OF3FMaYCAhuounQweZkMiZB\nBDfRXH653xEYYyIkuInGRs4zJmEEN9Gcf77fERhjIsSXRCMi3UVktYh8IyIDw25kN+kZkzBinmhE\npDgwFOgOtARuE5EWsY6joFJTU/0O4TRBjAmCGZfF5C8/SjQdgHWquklVTwCjgGt9iKNAgvihCGJM\nEMy4LCZ/+ZFo6gJbQ16ne8uMMQnKj0SjPhzTGOMjUY3t915EOgKDVbW79/oJIFNVXwzZxpKRMT5R\nVYn0Pv1INCWANcAVwDZgAXCbqq6KaSDGmJiJ+TARqnpSRB4CJgHFgf9YkjEmscW8RGOMST6BuzM4\nXzfzRe5Ym0RkqYgsFpEF3rJqIjJFRNaKyGQRqRKy/RNeXKtFpFvI8vYissxb92oBYxgmIjtFZFnI\nsojFICKlReRDb/k8EWlYhLgGi0i6d74Wi0iPkHVRj0tE6ovINBFZISLLReQRv89XLjH5dq5EpIyI\nzBeRJSKyUkRe8Ps8oaqBeeCqUuuARkBJYAnQIorH2whUy7bsJWCA93wgMMR73tKLp6QX3zp+LBEu\nADp4zz8Huhcghi5AW2BZNGIAfgX8y3t+CzCqCHENAn4XZtuYxAXUAtp4zyvg2vpa+Hm+conJ73NV\nzvu3BDAP6OzreYrWl7gwD+Ai4IuQ148Dj0fxeBuB6tmWrQZqhnyIVnvPnwAGhmz3BdARqA2sCll+\nK/BGAeNoxE+/0BGLwdvmwpAP3e4ixDUI6B9mu5jGFbK/sUDXoJyvbDEF4lwB5YCFwDl+nqegVZ1i\nfTOfAlNFZJGI/NJbVlNVd3rPdwI1ved1vHiyx5Z9eQZFjzmSMfxwTlX1JLBfRKoVIbaHRSRNRP4T\nUvSOeVwi0ghX4ppPQM5XSEzzvEW+nSsRKSYiS3DnY5qqrsDH8xS0RBPrlumLVbUt0AP4tYh0+Ukw\nLl372loehBhCvA40BtoA24G/+RGEiFQAxgC/UdWDoev8Ol9eTKO9mA7h87lS1UxVbQPUAy4Rkcuy\nrY/peQpaoskAQkcjr89PM2pEqep279/dwCe4flg7RaQWgIjUBnblEFs9L7YM73no8owihhaJGNJD\n3tPA21cJoLKqfleYoFR1l3qAt3HnK6ZxiUhJXJIZrqpjvcW+nq+QmEZkxRSEc+XFsR/4DGiPj+cp\naIlmEXCWiDQSkVK4RqZx0TiQiJQTkYre8/JAN2CZd7ysUdH74urceMtvFZFSItIYOAtYoKo7gAMi\ncqGICHBnyHsKKxIxfBpmX72BLwsblPfhzHI97nzFLC5vH/8BVqrq30NW+Xa+corJz3MlIjWyqmoi\nUha4Eljs53mKSiNrUR64aswaXMv3E1E8TmNcS/sSYHnWsYBqwFRgLTAZqBLynj94ca0GrgpZ3h73\nQVoH/KOAcYzE3SF9HFfnvTuSMQClgY+Ab3BtB40KGdc9wPvAUiDN+5DWjGVcuCsnmd7/2WLv0d3P\n85VDTD38PFdAK+BrL6alwGOR/mwXNCa7Yc8YE3VBqzoZYxKQJRpjTNRZojHGRJ0lGmNM1FmiMcZE\nnSUaY0zUWaJJUCJSWUT6hbyuIyIfR+lYPUVksPf8XRG5MRrHyeHYvUTk6VgdzxSOJZrEVRXXlR8A\nVd2mqjdF6Vj9cX17IEr9Z0Qkp8/qeOBGrxuACShLNIlrCNBU3KBLL4pIQ/EGsRKRu0RkrDf40UYR\neUhEfi8iX4vIXBGp6m3XVEQmer3bZ4hI8+wHEZH6QCn9sVcwuE58s0VkfVbpRpy/eIMoLRWRm73l\nKSIyPmR/Q0Wkr/d8k4gMEZH/ATeJyCPiBphKE5GR8EPnwLm4LiQmoGI+ZrCJmYHAOep6p2cNYRDq\nHFzP4rLAetxt6u1E5GWgD/Aq8CbwgKquE5ELgX/hBpUPdTHudvcsAtRS1YvFzUA6Dtfh8AbgPKA1\ncAawUERmhIk7tFexAt+qanvvb8jA3ep+QkRC50xeAFyC6zxoAsgSTeLKa8qMaap6GDgsIvtwVRBw\n/Vpaex1NOwEfu/50AJQKs58GuGEQsiheZz1VXSUiWWOedAY+8Eogu0RkOnABcCCPOD8Meb4U+EBE\nxvLTjqvbcH2eTEBZokle34c8zwx5nYn7XBQD9maViPKQPakdD7NOw2ynwEl+WoUvm22bwyHPr8aV\nXK4BnhSRc1U103u/ddoLMGujSVwHgYqFeJ8AqBtQaqOI9IYf2lhah9l+M25YyLzMBG4RN/LbGbiE\nsQDYArT0hiioAlweNihXrGqgqqm4IV4r48boBTfk5OZ8/n3GB5ZoEpSq7gFme42vL3J620doCSD7\n86zXdwD3ihsScjnQK8yhZgPtsh8++3NV/YQfh034EtcmtEtVt+KGG1iOqyZ9TXjFgeEistTb5lVV\nzap2dQDCtfeYgLBhIkyRichXwB3qjVgY42MXwyWe89WNXWsCyEo0JhL+Cjzo07F7AqMtyQSblWiM\nMVFnJRpjTNRZojHGRJ0lGmNM1FmiMcZEnSUaY0zUWaIxxkTd/wPtyZBKCiWXXgAAAABJRU5ErkJg\ngg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10fa4e310>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "time = np.arange(0,200.*3600.) * u.second   # Exposure Time matched to 2.8\" pixels\n",
    "time = np.arange(0,30000.*3600.,100) * u.second   # Exposure Time matched to 2.8\" pixels\n",
    "\n",
    "\n",
    "plt.figure(figsize=(4,4))\n",
    "\n",
    "for numpixel in numpixels:\n",
    "    print(numpixel)\n",
    "    ## Signal = signal flux * QE * transmission * angular pixel size * area of the lens\n",
    "    S = SB_ph_1 * QE * tau_l * tau_f * area_lens * ang_size_pixel\n",
    "    print(S)\n",
    "    signal = S*time*numpixel\n",
    "\n",
    "    ## Noise\n",
    "    B_tot = B * QE * tau_l * tau_f * 3.*u.nm * area_lens.to(u.m**2) * ang_size_pixel.to(u.arcsec**2)\n",
    "    sigma = np.sqrt(signal + B_tot*time*numpixel + D*time*numpixel + R_squared*numpixel)\n",
    "\n",
    "    # Note that the signal is about an eighth the strength of the background sky signal:\n",
    "    print('Halpha Signal: '+str(S))\n",
    "    print('Background Sky: ' +str(B_tot))\n",
    "\n",
    "    plt.plot(time/3600., signal/sigma,label= 'num pixels '+str(round(numpixel)))\n",
    "\n",
    "plt.plot([0,30000.],[5,5],'k--')   \n",
    "plt.title(str(SB_ph_1))\n",
    "#plt.legend()\n",
    "plt.plot([27000.,27000.],[0,6])\n",
    "plt.xlim(0,30000)\n",
    "plt.ylim(0,10)\n",
    "plt.xlabel('time (hours)')\n",
    "plt.ylabel('SNR')\n",
    "plt.savefig('FigSNR1.pdf')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Number of pixels: [  1.27551020e+03   1.27551020e+01   1.00000000e+00]\n",
      "Area of the lens: 7709.09138079 cm2\n",
      "1275.51020408\n",
      "0.138351996955 ph / s\n",
      "Halpha Signal: 0.138351996955 ph / s\n",
      "Background Sky: 38.5681880622 ph / s\n",
      "12.7551020408\n",
      "0.138351996955 ph / s\n",
      "Halpha Signal: 0.138351996955 ph / s\n",
      "Background Sky: 38.5681880622 ph / s\n",
      "1.0\n",
      "0.138351996955 ph / s\n",
      "Halpha Signal: 0.138351996955 ph / s\n",
      "Background Sky: 38.5681880622 ph / s\n"
     ]
    },
    {
     "data": {
      "image/png": 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FvhmiqgxdPJQHmj1Ai2ta5E2lhhGEFPjIYt6WeWz7Yxuze8zOmwoNI0gp0GJx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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10e8c4250>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "[area_lens, ang_size_pixel, tau_l, tau_f, QE, B, D, R_squared, numpixels] = Dragonfly()\n",
    "wavelen = 656.3e-9 * u.m\n",
    "SB_ph = 23870.257 * u.photon / (u.cm**2) / u.second / (u.rad**2)\n",
    "\n",
    "time = np.arange(0,15.*3600.) * u.second   # Exposure Times \n",
    "area_lens = area_lens*10.                   # Increase size of Dragonfly to 500 lenses\n",
    "plt.figure(figsize=(4,4))\n",
    "\n",
    "for numpixel in numpixels:\n",
    "    print(numpixel)\n",
    "    ## Signal = signal flux * QE * transmission * angular pixel size * area of the lens\n",
    "    S = SB_ph * QE * tau_l * tau_f * area_lens * ang_size_pixel\n",
    "    print(S)\n",
    "    signal = S*time*numpixel\n",
    "\n",
    "    ## Noise\n",
    "    B_tot = B * QE * tau_l * tau_f * 3.*u.nm * area_lens.to(u.m**2) * ang_size_pixel.to(u.arcsec**2)\n",
    "    sigma = np.sqrt(signal + B_tot*time*numpixel + D*time*numpixel + R_squared*numpixel)\n",
    "\n",
    "    # Note that the signal is about an eighth the strength of the background sky signal:\n",
    "    print('Halpha Signal: '+str(S))\n",
    "    print('Background Sky: ' +str(B_tot))\n",
    "\n",
    "    #plt.plot(time, signal/np.sqrt(signal),label='Signal')\n",
    "    #plt.plot(time, signal/np.sqrt(signal + B_tot*time),label='Signal + bkgd')\n",
    "    #plt.plot(time, signal/np.sqrt(signal + B_tot*time + D*time),label='Signal + bkgd + dark curr')\n",
    "    plt.plot(time/3600., signal/sigma,label= 'num pixels '+str(round(numpixel)))\n",
    "\n",
    "plt.plot([0,15],[5,5],'k--')    \n",
    "plt.legend()\n",
    "plt.ylim(0,20)\n",
    "plt.xlim(0,15)\n",
    "plt.xlabel('time (hours)')\n",
    "plt.ylabel('SNR')\n",
    "plt.savefig('FigSNR.pdf')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##Double Check Donahue's values\n",
    "Okay, this seems good.  Let's double check this calculation using values from the Donahue paper.  I can't find values for the quantum efficiency of the CCD or the transmission of the Kitt Peak telescope or the dark current, so I'm just going to use the same value as that of the Dragonfly CCD."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Number of pixels: 3494.38229513\n",
      "Area of the lens: 2922.466566 cm2\n",
      "19679.0446881 ph / (cm2 rad2 s)\n",
      "Halpha Signal: 0.00227276597993 ph / s\n",
      "Background Sky: 0.768513687779 ph / s\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0x10b449c10>"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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nnQdz5nhyoqRVZXTFOsa4CDgkxrgX0Bw4JITQai1PHRlj3HvFL0u1JCnrLFkC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\nSZJUBQZrSZIkqQr+P/o0HUGOPUYRAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10b1769d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def Donahue():\n",
    "    ## Donahue instrumention\n",
    "    area_lens = np.pi*(61./2)**2 * u.cm**2\n",
    "    pix_size = 2.03\n",
    "    ang_size_pixel  = (pix_size * (1./206265.))**2 * u.rad**2   # rad^2, the pixel size of the telescope\n",
    "\n",
    "    tau_l = 0.85  # transmittance of the Dragonfly lens\n",
    "    QE = 0.48     # quantum efficiency of the Dragonfly CCDs\n",
    "    tau_f = 1.    # transmittance of the Halpha filter -- UNKNOWN\n",
    "\n",
    "    B = 0.52135 *u.photon/u.second/u.nm/u.arcsec**2/u.m**2   # avg sky background at 565.6 nm \n",
    "    D = 0.04 *u.photon/u.second     # dark current (electrons / s) \n",
    "    R_squared = 3.**2 * u.photon       # read noise (electrons)\n",
    "\n",
    "    # Donahue used 2' x 2' boxes to measure the sky brightness within\n",
    "    numpixels = (2*60*2*60)/(pix_size**2)\n",
    "    print('Number of pixels: ' + str(numpixels))\n",
    "    print('Area of the lens: '+str(area_lens))\n",
    "    \n",
    "    return [area_lens, ang_size_pixel, tau_l, tau_f, QE, B, D, R_squared, numpixels]\n",
    "\n",
    "[area_lens, ang_size_pixel, tau_l, tau_f, QE, B, D, R_squared, numpixels] = Donahue()\n",
    "\n",
    "wavelen = 656.3e-9 * u.m\n",
    "SB_cgs = 1.4*10**-18 * u.erg / u.second / (u.cm**2) / u.arcsec**2\n",
    "SB_ph  = SB_cgs * wavelen / (const.h.cgs * const.c) / (u.arcsec.to(u.rad) * u.rad/u.arcsec)**2 * u.photon\n",
    "print(SB_ph)\n",
    "\n",
    "time = np.arange(0,900.) * u.second   # Exposure Times \n",
    "S = SB_ph * QE * tau_l * tau_f * area_lens * ang_size_pixel\n",
    "signal = S*time*numpixels\n",
    "\n",
    "B_tot = B * QE * tau_l * tau_f * 3.*u.nm * area_lens.to(u.m**2) * ang_size_pixel.to(u.arcsec**2)\n",
    "sigma = np.sqrt(signal + B_tot*time*numpixels + D*time*numpixels + R_squared*numpixels)\n",
    "\n",
    "# Note that the signal is about an eighth the strength of the background sky signal:\n",
    "print('Halpha Signal: '+str(S))\n",
    "print('Background Sky: ' +str(B_tot))\n",
    "\n",
    "plt.figure(figsize=(12,12))\n",
    "#plt.plot(time, signal/np.sqrt(signal),label='Signal')\n",
    "#plt.plot(time, signal/np.sqrt(signal + B_tot*time),label='Signal + bkgd')\n",
    "#plt.plot(time, signal/np.sqrt(signal + B_tot*time + D*time),label='Signal + bkgd + dark curr')\n",
    "plt.plot(time, signal/sigma,label='Signal + bkgd + dark curr + read noise')\n",
    "plt.legend()\n",
    "plt.xlabel('time (seconds)')\n",
    "plt.ylabel('SNR')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "So this seems about right.  "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## SB of Donahue's non-detections\n",
    "\n",
    "Donahue+ (2014) speculate that the above Halpha emission corresponding to the above SB of ~$1.9 * 10^4$ph/s/cm^2/sr is due to excitation of the gas from local effects from being near the two galaxies (since the spatial distribution looks like outflows and the Leo field of similar depth did not have a Halpha detection). \n",
    "\n",
    "I want to estimate the surface brightness of Halpha emission from the ionizing background radiation (more of an IGM effect).  I thought I'd do that by reversing the equation for the ionizing background and using some previous estimates of the ionizing background to predict how bright the Halpha emission should be (using the physics that Donahue+ 2014 assumed, as a first guess).  We can then repeat the above calculation, and figure out how much longer we'd have to observe to see Halpha emission in the regions where Donahue+ got non-detections.\n",
    "\n",
    "The equation used by Donahue+(2014) has several factors that depend on the geometry of the cloud and the spectral shape of the ionizing background.  Since we don't really know what either of those are, I figured I could take the best case scenario, a good case scenario, a bad case scenario, and the worst case scenario.\n",
    "\n",
    "1. Best case: Spherical cloud, high ionization background (assumed by Donahue et al 2014):  J$_0=2*10^{-22}$, f$_g$ = 1. , f$_s$ = 1. \n",
    "2. Medium case: Weird shaped clouds, high ionization background with sharp profile: J$_0=2*10^{-22}$, f$_g$ = 2., f$_s$ = 1.63\n",
    "3. Medium case: Spherical clouds, low ionization background: J$_0=10^{-23}$, f$_g$ = 1., f$_s$ = 1.\n",
    "4. Worst case: Weird shaped clouds, low ionization background: J$_0=10^{-23}$, f$_g$ = 2., f$_s$ = 1.63"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "6791.35640286 ph / (cm2 s sr)\n",
      "0.306748466258\n"
     ]
    }
   ],
   "source": [
    "# 1. Best case\n",
    "J_0 = 2.*10**-22 *u.erg/u.second/u.cm**2/u.sr/u.Hz # to 10**-23\n",
    "J_0 = 1.*10**-22 *u.erg/u.second/u.cm**2/u.sr/u.Hz # to 10**-23\n",
    "f_Halpha = 0.45\n",
    "f_g = 1.  # max of 2\n",
    "f_s = 1.  # max of 1.63\n",
    "SB_Halpha_max = J_0 * f_Halpha / (const.h.cgs * f_g * f_s) * u.Hz * u.second * u.photon\n",
    "\n",
    "print(SB_Halpha_max)\n",
    "#print(SB_Halpha_max/SB_ph)\n",
    "print(1./(2.*1.63))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This surface brightness is about 2/3 of the SB calculated above.  If we use the lower bound for the ionizing background, the surface brightness is decreased by another order of magnitude.  If we use the non-ideal conditions for f_g and f_s and max them out, the surface brightness is a third of its value again.  Below, we do this calculation for two medium cases and for the most extreme case:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "4166.47632077 ph / (cm2 s sr)\n",
      "0.211721472602 rad2 / sr\n",
      "679.135640286 ph / (cm2 s sr)\n",
      "0.0345106000342 rad2 / sr\n",
      "208.323816039 ph / (cm2 s sr)\n",
      "0.0105860736301 rad2 / sr\n"
     ]
    }
   ],
   "source": [
    "# 2. Medium case 1:  Weird shaped clouds, high ionization background with sharp spectral profile\n",
    "J_0 = 2*10**-22 *u.erg/u.second/u.cm**2/u.sr/u.Hz # to 10**-23\n",
    "f_Halpha = 0.45\n",
    "f_g = 2. #2.  # max of 2\n",
    "f_s = 1.63 #1.63  # max of 1.63\n",
    "SB_Halpha_med1 = J_0 * f_Halpha / (const.h.cgs * f_g * f_s) * u.Hz * u.second * u.photon\n",
    "\n",
    "print(SB_Halpha_med1)\n",
    "print(SB_Halpha_med1/SB_ph)\n",
    "\n",
    "# 3. Medium case 2: Spherical clouds, low ionization background\n",
    "J_0 = 10**-23 *u.erg/u.second/u.cm**2/u.sr/u.Hz # to 10**-23\n",
    "f_Halpha = 0.45\n",
    "f_g = 1. #2.  # max of 2\n",
    "f_s = 1. #1.63  # max of 1.63\n",
    "SB_Halpha_med2 = J_0 * f_Halpha / (const.h.cgs * f_g * f_s) * u.Hz * u.second * u.photon\n",
    "\n",
    "print(SB_Halpha_med2)\n",
    "print(SB_Halpha_med2/SB_ph)\n",
    "\n",
    "# 4. Worst case:  Weird shaped clouds, low ionization background with sharp spectral profile\n",
    "J_0 = 10**-23 *u.erg/u.second/u.cm**2/u.sr/u.Hz # to 10**-23\n",
    "f_Halpha = 0.45\n",
    "f_g = 2. #2.  # max of 2\n",
    "f_s = 1.63 #1.63  # max of 1.63\n",
    "SB_Halpha_min = J_0 * f_Halpha / (const.h.cgs * f_g * f_s) * u.Hz * u.second * u.photon\n",
    "\n",
    "print(SB_Halpha_min)\n",
    "print(SB_Halpha_min/SB_ph)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In the worst case, the surface brightness is about a hundredth of the SB that Donahue+ reached.\n",
    "\n",
    "I'll plot the SNR ratios as a function of exposure time for the four cases below."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Number of pixels: [1836.7346938775513]\n",
      "Area of the lens: 7709.09138079 cm2\n",
      "Background Sky: 3.85681880622 ph / s\n",
      "7709.09138079 cm2\n",
      "7709.09138079 cm2\n"
     ]
    },
    {
     "data": {
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DhjBy5EgaNmxISkoKM2bMKDBOiW9B5hjfvqNz584MGjQoz+EoBeWalStXUr9+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\nRSpEjlrU9DOYHnwwFbjx43MnkdRILrgAdt/d5pKkcrj8cvjqV20uSco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rbDBJUsWzz6ap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\neWPHAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x113d75dd0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Load values from Dragonfly instrumentation\n",
    "[area_lens, ang_size_pixel, tau_l, tau_f, QE, B, D, R_squared, numpixels] = Dragonfly()\n",
    "\n",
    "B_tot = B * QE * tau_l * tau_f * 3.*u.nm * area_lens.to(u.m**2) * ang_size_pixel.to(u.arcsec**2)\n",
    "print('Background Sky: ' +str(B_tot))\n",
    "\n",
    "#fig, ((ax1,ax2),(ax3,ax4)) = plt.subplots(2,2, figsize=(12,12))\n",
    "fig, ((ax1,ax2,ax3,ax4)) = plt.subplots(1,4, figsize=(20,6))\n",
    "\n",
    "\n",
    "time = np.arange(0,900.) * u.second   # Exposure Times \n",
    "\n",
    "signal_max  = SB_Halpha_max  * QE * tau_l * tau_f * area_lens * ang_size_pixel *time*numpixels\n",
    "sigma_max  = np.sqrt(signal_max  + B_tot*time*numpixels + D*time*numpixels + R_squared*numpixels)\n",
    "one = ax1.plot(time, signal_max/sigma_max,label='Best case, 48 lenses')\n",
    "ax1.set_xlabel('time (seconds)')\n",
    "ax1.set_ylabel('SNR')\n",
    "ax8 = ax1.twiny()\n",
    "ax8.set_xlim(0,900./3600.)\n",
    "ax8.set_xlabel('time (hours)')\n",
    "ax1.legend()\n",
    "\n",
    "time = np.arange(0,9000.) * u.second   # Exposure Times \n",
    "\n",
    "signal_med1 = SB_Halpha_med1 * QE * tau_l * tau_f * area_lens * ang_size_pixel *time*numpixels\n",
    "sigma_med1 = np.sqrt(signal_med1 + B_tot*time*numpixels + D*time*numpixels + R_squared*numpixels)\n",
    "two= ax2.plot(time, signal_med1/sigma_med1,label='Med case 1, 48 lenses')\n",
    "ax2.set_xlabel('time (seconds)')\n",
    "ax2.set_ylabel('SNR')\n",
    "ax7 = ax2.twiny()\n",
    "ax7.set_xlim(0,9000./3600.)\n",
    "ax7.set_xlabel('time (hours)')\n",
    "ax2.legend()\n",
    "\n",
    "time = np.arange(0,300000.) * u.second   # Exposure Times \n",
    "print(area_lens)\n",
    "signal_med2 = SB_Halpha_med2 * QE * tau_l * tau_f * area_lens * ang_size_pixel *time*numpixels\n",
    "sigma_med2 = np.sqrt(signal_med2 + B_tot*time*numpixels + D*time*numpixels + R_squared*numpixels)\n",
    "three=ax3.plot(time, signal_med2/sigma_med2,label='Med case 2, 48 lenses')\n",
    "ax3.set_xlabel('time (seconds)')\n",
    "ax3.set_ylabel('SNR')\n",
    "ax6 = ax3.twiny()\n",
    "ax6.set_xlim(0,300000./3600.)\n",
    "ax6.set_xlabel('time (hours)')\n",
    "ax3.legend()\n",
    "\n",
    "#area_lens = area_lens*10.\n",
    "B_tot = B * QE * tau_l * tau_f * 3.*u.nm * area_lens.to(u.m**2) * ang_size_pixel.to(u.arcsec**2)\n",
    "time = np.arange(0,3000000.) * u.second   # Exposure Times \n",
    "print(area_lens)\n",
    "signal_min  = SB_Halpha_min  * QE * tau_l * tau_f * area_lens * ang_size_pixel *time*numpixels\n",
    "sigma_min  = np.sqrt(signal_min  + B_tot*time*numpixels + D*time*numpixels + R_squared*numpixels)\n",
    "four = ax4.plot(time, signal_min/sigma_min,label='Worst case, 500 lenses')\n",
    "ax4.set_xlabel('time (seconds)')\n",
    "ax4.set_ylabel('SNR')\n",
    "ax5 = ax4.twiny()\n",
    "ax5.set_xlim(0,3000000/3600.)\n",
    "ax5.set_xlabel('time (hours)')\n",
    "ax4.legend()\n",
    "\n",
    "plt.savefig('FigSNRclouds.pdf')\n",
    "#print(signal_med2[9000])\n",
    "#print(signal_min[9000])\n",
    "#print(sigma_med2[9000])\n",
    "#print(sigma_min[9000])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The best case scenario is definitely doable.  The medium cases are pushing it, need to increase time by a factor of ten (at least) additionally for each case.\n",
    "\n",
    "For the worst case, it appears that we would need 500 Dragonfly lenses and then integrate for an exposure time of ~80 hours."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Need to answer:\n",
    "1.  Which case is the most likely?\n",
    "2.  Would Donahue et al (2014) have seen the best case?  (if so, should scratch that one)\n",
    "3.  What is the physics for that the Halpha emission rate is 0.45 times the ionization background?\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "1. \n",
    "2. In their Table 2, they give limits for the Halpha in the two non-detection fields of $1.62 * 10^{-19}$ erg/s/cm^2/arcsec^2 and $3.68 * 10^{-19}$ erg/s/cm^2/arcsec^2 (I believe these correspond to the limits of the confidence intervals that they calculated for each set of boxes for each field http://evolution.gs.washington.edu/gs560/2011/lecture3.pdf).  These correspond to $\\sim$ 2277 ph/cm^2/sr/s and 5172 ph/cm^2/sr/s.  So they would have observed the best case of Halpha emission, probably, but not the medium cases.  Do we have any other advantage over this group, other than the times two detection rate?\n",
    "3. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "5172.77746087 ph / (cm2 rad2 s)\n"
     ]
    }
   ],
   "source": [
    "wavelen = 656.3e-9 * u.m\n",
    "SB_cgs = 3.68*10**-19 * u.erg / u.second / (u.cm**2) / u.arcsec**2\n",
    "SB_ph  = SB_cgs * wavelen / (const.h.cgs * const.c) / (u.arcsec.to(u.rad) * u.rad/u.arcsec)**2 * u.photon\n",
    "print(SB_ph)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3.4917000000000005e-19"
      ]
     },
     "execution_count": 62,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sigma_rms = 0.113 # adu\n",
    "sigma_rms * 3.09e-18"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.12324969082746885"
      ]
     },
     "execution_count": 63,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "2.086*0.108/np.sqrt(20)\n",
    "2.131*0.224/np.sqrt(15)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.9377179122251858e+20"
      ]
     },
     "execution_count": 64,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "5*10**-4.6 * 0.5 * u.Mpc.to(u.cm)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Investigating the sky background flux:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "wavelen = [ 654.78,  655.04,  655.31,  655.57,  655.84,  656.1 ,  656.37,\n",
    "        656.63,  656.9 ,  657.16,  657.43,  657.69,  657.96]\n",
    "flux = [0.4887,  0.5453,  0.5547,  0.5547,  0.4976,  0.4889,  0.4716,\n",
    "        0.5385,  0.5485,  0.5556,  0.5179,  0.5079,  0.5077]\n",
    "wavelen = np.array(wavelen,'d')\n",
    "flux = np.array(flux,'d')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.521353846154\n",
      "(654.8, 657.8)\n",
      "13\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x10ea477d0>]"
      ]
     },
     "execution_count": 66,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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Syo4uUstAkkLJQFLj0kth6VL4wx8q956aYyBJoWQgqdG+Pdx1F3z967BhQ2Xe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\njBlqAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x107689c10>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "print(np.mean(flux))\n",
    "print(656.3-1.5,656.3+1.5)\n",
    "print(len(flux))\n",
    "plt.plot(wavelen,flux)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1.56406153846\n",
      "1.56406153846\n"
     ]
    }
   ],
   "source": [
    "delta_nm = 3. / len(flux)\n",
    "sum_flux = np.sum(flux*delta_nm)\n",
    "print(sum_flux)\n",
    "print(np.mean(flux)*3.)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Those are weirdly the exact same value... So we can just use the mean sky background flux in this 3nm range, which is 0.52135."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {},
   "outputs": [
    {
     "ename": "TypeError",
     "evalue": "only length-1 arrays can be converted to Python scalars",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mTypeError\u001b[0m                                 Traceback (most recent call last)",
      "\u001b[0;32m<ipython-input-49-c49b6f3a2861>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m()\u001b[0m\n\u001b[1;32m      1\u001b[0m \u001b[0ma\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0marray\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;36m2\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;36m3\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      2\u001b[0m \u001b[0mb\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0marray\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m4\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;36m5\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;36m6\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 3\u001b[0;31m \u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mconcatenate\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0ma\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mb\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m",
      "\u001b[0;31mTypeError\u001b[0m: only length-1 arrays can be converted to Python scalars"
     ]
    }
   ],
   "source": [
    "a = np.array([1,2,3])\n",
    "b = np.array([4,5,6])\n",
    "np.concatenate(a,b)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "Adding some stuff for the "
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 2",
   "language": "python",
   "name": "python2"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 2
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython2",
   "version": "2.7.12"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 1
}