A499_Winter22_Assignment2_A.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# DCR Research - Assingment 2\n",
    "Astronomy 499: (Winter 2022)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import scipy.constants as const\n",
    "import matplotlib\n",
    "import matplotlib.pyplot as plt\n",
    "from astropy import units as u\n",
    "from astropy.units import cds\n",
    "cds.enable()\n",
    "import pandas as pd"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## From Assignment 1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "latitude = -30.24463 * u.deg\n",
    "longitude = -70.74942 * u.deg\n",
    "altitude = 2647 * u.m\n",
    "p0 = 101325 * u.Pa # sea level air presssure\n",
    "g = const.g * (u.m/u.s**2)\n",
    "R0 = 8.31447 * u.J/(u.mol*u.K) # gas constant\n",
    "T0 = 19. * u.deg_C # typical sea level temperature\n",
    "lapseRate = -6.5 * (u.deg_C/u.km) # typical rate of change of temperature with altitude\n",
    "M = 0.0289644 * (u.kg/u.mol) # molar mass of dry air\n",
    "humidity = 40. # typical humidity at many ovservatory sites"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "temperature = T0 + (lapseRate * altitude)\n",
    "temperatureK = temperature.to(u.K, equivalencies = u.temperature())\n",
    "\n",
    "pressure = (p0 * np.exp((-g * M * altitude) / (R0 * temperatureK))).to(u.Pa)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "# calculating the water-vapor pressure (mm)\n",
    "def power_vapor_pressure(temp, RH):\n",
    "    t = temp.value\n",
    "    x = np.log(RH/100)\n",
    "    tdC_numerator = (((t + 238.3)*x) + (17.2694 * t))\n",
    "    tdC_demoninator = ((t + 238.3) * (17.2694 - x)) - (17.2694 * t)\n",
    "    tdC = (238.3 * (tdC_numerator/tdC_demoninator)) * u.deg_C\n",
    "    t_dewpoint_C = tdC.value\n",
    "    pressure = (4.50874 + (0.341724 * t_dewpoint_C) + (0.0106778 * t_dewpoint_C**2) + (0.184889e-3 * t_dewpoint_C**3) + (0.238294e-5 * t_dewpoint_C**4) + (0.203447e-7 * t_dewpoint_C**5)) * u.cds.mmHg\n",
    "    return pressure\n",
    "\n",
    "p_w = (power_vapor_pressure(temperature, humidity)).to(u.cds.mbar)\n",
    "p_s = pressure.to(u.cds.mbar)\n",
    "zin = 30 * u.deg"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Using Equations: 4, 5, 9, 10, 14, 15, 16, 18, 20, 21 + 2\n",
    "\n",
    "def gammafunction(wavelength, Ps_in, Tinitial, Pw_in):\n",
    "    T = Tinitial.to(u.K, equivalencies = u.temperature()).value\n",
    "    sigma = 1/wavelength.to(u.um).value\n",
    "    \n",
    "    Ps = Ps_in.to(u.cds.mbar).value\n",
    "    Pw = Pw_in.to(u.cds.mbar).value\n",
    "    \n",
    "    Ds = (1 + (Ps * (57.90e-8 - (9.3250e-4/T) + (0.25844/T**2)))) * (Ps/T)\n",
    "    Dw = (1 + (Pw * (1 + 3.7e-4 * Pw) * (-2.37321e-3 + ((2.23366/T)-(710.792/T**2) + (7.75141e4/T**3))))) * (Pw/T)\n",
    "    term_one = (2371.34 + (683939.7/(130 - sigma**2)) + (4547.3/(38.9 - sigma**2))) * Ds\n",
    "    term_two = ((6487.31 + (58.058 * sigma**2) - (0.71150 * sigma**4) + (0.08851 * sigma**6))) * Dw\n",
    "    n = ((term_one + term_two) / (1e8))\n",
    "    return n\n",
    "\n",
    "def calc_beta(tin):\n",
    "    t = tin.value\n",
    "    beta = 0.001254 * ((273.15 + t)/273.15)\n",
    "    return beta\n",
    "\n",
    "def calc_kappa(phi_degrees, height): # 10\n",
    "    phi = phi_degrees.to(u.rad).value\n",
    "    h = height.value\n",
    "    kappa = 1 + (0.005302 * (np.sin(phi)**2)) - (0.00000583 * (np.sin(2 * phi)**2)) - (0.000000315 * h)\n",
    "    return kappa\n",
    "    \n",
    "# Atmospheric refraction\n",
    "def atm_refraction(wavelength, Ps, Tinitial, Pw, phi, h, z0):\n",
    "    gamma = gammafunction(wavelength, Ps, Tinitial, Pw)\n",
    "    beta = calc_beta(Tinitial)\n",
    "    kappa = calc_kappa(phi , h)\n",
    "    \n",
    "    refraction = (kappa * gamma * (1 - beta) * np.tan(z0.to(u.rad))) - (kappa * gamma * (beta - (gamma / 2)) * (np.tan(z0.to(u.rad))**3))\n",
    "    \n",
    "    return refraction\n",
    "    \n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "rad2arcsec = (206265 * u.arcsec) # conversion between radians and arcseconds"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Import Data\n",
    "\n",
    "# g-band\n",
    "gband = pd.read_csv('total_g.dat', delimiter = \" \", comment = \"#\", header=None, skipinitialspace = True)\n",
    "gband_wavelength = np.array(gband[0]) * u.nm\n",
    "gband_throughput = np.array(gband[1])\n",
    "\n",
    "# i-band\n",
    "iband = pd.read_csv('total_i.dat', delimiter = \" \", comment = \"#\", header=None, skipinitialspace = True)\n",
    "iband_wavelength = np.array(iband[0]) * u.nm\n",
    "iband_throughput = np.array(iband[1])\n",
    "\n",
    "# General\n",
    "column_names = ['Wave', 'FluxD', 'e_FluxD'] #, 'None1', 'None2', 'None3', 'None4', 'None5', 'None6', 'None7', 'None8']\n",
    "simulatedquasarspectrum = pd.read_csv('Vanden_Berk_quasars.txt', delimiter = \" \", header=None, skipinitialspace = True, names = column_names, skiprows=23)\n",
    "subsection = simulatedquasarspectrum\n",
    "subsection = simulatedquasarspectrum.apply(pd.to_numeric, errors='coerce')\n",
    "\n",
    "data = subsection[['Wave', 'FluxD', 'e_FluxD']]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Wavelength\n",
    "wavelength_or = np.array(subsection['Wave']) * u.Angstrom\n",
    "wavelength_nm = (wavelength_or[23:]).to(u.nm)\n",
    "\n",
    "# Relative Flux Density\n",
    "relative_fluxdensity = subsection['FluxD'][23:]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Defining Redshift Function\n",
    "def redshift(z, spectrum_wavelength):\n",
    "    redshiftspectrum = (1 + z) * spectrum_wavelength\n",
    "    return redshiftspectrum\n",
    "\n",
    "# Redshifts\n",
    "spectra_obs = [wavelength_nm, redshift(1.0, wavelength_nm), redshift(1.5, wavelength_nm), redshift(2.0, wavelength_nm), redshift(2.5, wavelength_nm)]\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Calculate the effective wavelength\n",
    "\n",
    "gWeightedWavelength = np.average(gband_wavelength[0:7755], weights = gband_throughput[0:7755])\n",
    "iWeightedWavelength = np.average(iband_wavelength[0:7755], weights = iband_throughput[0:7755])\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$480.00049 \\; \\mathrm{nm}$"
      ],
      "text/plain": [
       "<Quantity 480.00048773 nm>"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "gWeightedWavelength"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$754.222 \\; \\mathrm{nm}$"
      ],
      "text/plain": [
       "<Quantity 754.22199777 nm>"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "iWeightedWavelength"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Part 1: Basic Point Spread Function (PSF) Modeling"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Part 1a \n",
    "\n",
    "Recall the 2D gaussian modeling from last quarter. In a 32X32 pixel numpy array, plot a 2D gaussian with a Full Width Half Maximum (FWHM) of 0.8 arcseconds, using 0.26 arcseconds per pixel. The gaussian should be centered on pixel (16, 16). Verify the result with a 1D plot of the values along the y-axis through the center of the gaussian."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x1728 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Convert from fwhm to sigma\n",
    "fwhm_conversion = 2 * np.sqrt(2 * np.log(2))\n",
    "\n",
    "# Creating 2D Gaussian Functions\n",
    "def gaussian2d(x_dimension = 32, y_dimension = 32, xcenter = 16, ycenter = 16, sigmax = (0.8/0.26)/fwhm_conversion, sigmay = (0.8/0.26)/fwhm_conversion):\n",
    "    x = np.linspace(0, x_dimension-1, x_dimension)\n",
    "    y = np.linspace(0, y_dimension-1, y_dimension)\n",
    "    x, y = np.meshgrid(x, y)\n",
    "    \n",
    "    diffx = x - xcenter\n",
    "    diffy = y - ycenter\n",
    "    gaussian = np.exp(-((diffx**2/(2*sigmax**2))+(diffy**2/(2*sigmay**2))))\n",
    "    \n",
    "    return gaussian\n",
    "\n",
    "# Defining X, Y & Gaussian Values\n",
    "gaussian_2d = gaussian2d()\n",
    "\n",
    "# Plot of Gaussian Distribution\n",
    "plt.style.use('ggplot')\n",
    "fig, ax = plt.subplots(1, 1, figsize = (8, 24))\n",
    "ax.imshow(gaussian_2d)\n",
    "ax.set_title('2D Gaussian Distribution');"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x432 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Verify with 1D Plot (slice of numpy array at x = 16)\n",
    "sliced_gaussian = gaussian_2d[:,16] #y, x\n",
    "\n",
    "# Plot\n",
    "fig, ax = plt.subplots(1, 1, figsize = (6, 6))\n",
    "ax.plot(sliced_gaussian, color = 'b')\n",
    "ax.set_title('2D Sliced Gaussian Distribution');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Part 1b \n",
    "\n",
    "Write a function to plot a 2D gaussian at an arbitrary offset from the center. The function should add the new gaussian to an existing image, and should take the FWHM of the gaussian and the flux as keyword parameters."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "def offset_2dgaussian(fwhm, flux, xoffset, yoffset, xcenter, ycenter):\n",
    "    \n",
    "    sigma = fwhm / 0.26\n",
    "    gaussian = gaussian2d(x_dimension=32, y_dimension=32, xcenter=xcenter, ycenter=ycenter+yoffset, sigmax=sigma, sigmay=sigma)\n",
    "    gaussian /= np.sum(gaussian)\n",
    "    \n",
    "    return gaussian*flux "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x1728 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Plot of Gaussian Distribution\n",
    "plt.style.use('ggplot')\n",
    "fig, ax = plt.subplots(1, 1, figsize = (8, 24))\n",
    "temp = offset_2dgaussian(.8, 2.3456, 0,1,16,16)\n",
    "ax.imshow(temp)\n",
    "ax.set_title('2D Gaussian Distribution');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Part 2: Model An Observed Quasar"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Part 2a \n",
    "\n",
    "Take the quasar spectrum from 2a and the DCR calculation from 3b of assignment 1. For each wavelength (at 1nm resolution) use your function from 1b above to model the total observed quasar image. Recall that the *differential* shift is relative to the refraction at the effective wavelength of the band. Use 0.26 arcseconds/pixel as the platescale of the image, and assume the shift is purely along the y-axis. Use a quasar at redshift 2.5, the same observing conditions as in assignment 1, and make images for both g- and i-bands."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [],
   "source": [
    "def totalImage(band_wavelength, band_throughput, observed_spectra, relative_fluxdensity, WeightedWavelength, p_s, temperature, p_w, latitude, altitude, zin, fwhm, xcenter, ycenter):\n",
    "    image_comp = np.zeros((32, 32), ) # float by default\n",
    "    refractionindex_eff = atm_refraction(WeightedWavelength, p_s, temperature, p_w, latitude, altitude, zin)\n",
    "    yoffset_value = []\n",
    "    \n",
    "    fmin = max(band_throughput)*.01\n",
    "    w_use = []\n",
    "    for w,f in zip(band_wavelength, band_throughput):\n",
    "        if f < fmin:\n",
    "            continue\n",
    "        w_use.append(w.value)\n",
    "        \n",
    "        # calculate flux - 2a\n",
    "        interpolate = np.interp(w, observed_spectra, relative_fluxdensity)\n",
    "        flux = f * interpolate\n",
    "        \n",
    "        # dcr shift - 3b\n",
    "        refraction = atm_refraction(w, p_s, temperature, p_w, latitude, altitude, zin)\n",
    "        yoffset = (refraction - refractionindex_eff)* rad2arcsec.value / 0.26\n",
    "        yoffset_value.append(yoffset)\n",
    "        xoffset = 0 / 0.26 # shift purely in the y-direction\n",
    "        \n",
    "        # creating gaussian\n",
    "        newgaussian = offset_2dgaussian(fwhm, flux, xoffset, yoffset, xcenter, ycenter)\n",
    "        image_comp += newgaussian.value\n",
    "\n",
    "    fig, ax = plt.subplots(1, 1, figsize = (6, 6))\n",
    "    im = ax.imshow(image_comp)\n",
    "    fig.colorbar(im, orientation = 'vertical')\n",
    "    ax.set_title('2D Offset Gaussian Distribution');  \n",
    "    \n",
    "    return w_use, yoffset_value, image_comp"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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jDvj5+V11dzFJkjB//nzrRcCnn34aQUFBmDZtGgBg5MiR6N69OzIzM7Fo0SJ8++23eO6552zK6NevHwwGAz7++GP86le/Qrdu3Rx2n1y4cCF+/vOfIycnB3fffTf27t2LJUuW4IknnrCrBXubrmxicFmX9c/oJGjTPefy44EHHrBu07pbmSRJIiQkRNx4443iqaeeEj/88INTxzl06JCYMWOG6NWrl/Dx8RG9evUS999/vzhy5IjNdtu2bRMAbMq93I1o586d1mXPPfecSEhIEEFBQSIkJETceuutNuuFEOKvf/2ruOGGG0S3bt1EWFiYGDlypFizZo11fWlpqRg+fLjw9/dX7L4mhBD19fVi6dKl4oYbbhABAQHCz89P9O/fX/zmN78R+/bts263b98+MXr0aOHv7y/69esnCgoKxPjx423OZ21trZg+fboICwsTkZGRIjs726b72qlTp8QvfvELER0dLfz8/MQ111wjZs2aJaqrq4UQQrz77rti9OjRIiwsTAQEBIiEhATx17/+1Vp+225Z1dXV4pe//KXo3r27CA8PF7NnzxaLFy8W/fr1s27TtmuZEEK88cYbQu0j3roboI+Pj4iIiBC33nqryM3NtXanc3SMxsZGMXXqVHHttdeKbt26icjISDFlyhRx/Phx6/affPKJGDRokPDz87PrvtZWe93XtmzZYi0jKSlJlJaW2uz34YcfikGDBgl/f38xZswYsXnzZmv3tcteeukl0bt3b2EwGFS7rw0aNEj4+vqK3r17i0WLFjnsvtba0qVLbd4HT7TveLTLj67CuzgTka7957h9t05n3RDj3MjbjvL6pgkiIiXe0DShi4t1RETejDViItI1ixfUN5mIiUjXZOH5TRNMxESka97QRtyhRLx3716sW7cOsixj/PjxSE9Pd1dcRERuYfGCuc1cTsSyLOO1117D4sWLERERgYULFyIpKUl1jofbDL+0/r9gdw4eHZnpaghdhnG6F+N0H2+IEXAtzq2y85PwezuXfyqOHDmCXr16ISoqCj4+PhgzZgxKS0vdGRsRUYfJMLj86CouH6mystJmMpSIiAhUVla6JSgiInfxhtnXXG6acDQgz9F8C0VFRSgqKgJwac7Tgt051nUxg6NtnnsqxulejNN9vCFGQNs4dd1GHBERgfPnz1ufnz9/3uEkLGlpaTYzorVuJ9Jz+5YWGKd7eUOc3hAjwDZiNS7/VPTv3x+nT59GRUUFzGYzPvvsM4d3uCAi0pIMyeVHV3G5Rmw0GjFz5ky88MILkGUZP/vZzxzeM42ISEu6H1k3fPhw6xyzRESeSNdtxERE3qAru6G5iomYiKgD6uvr8corr+CHH36AJEn43e9+h969eyMvLw9nz55FZGQk5s6di+Dg4HbLYCImIl2zdPKkP+vWrcOwYcPwxBNPwGw24+LFi/jHP/6BxMREpKeno7CwEIWFhZg+fXq7ZXh+nZ2IqAMsMLj8UNPQ0ICvv/4a48aNAwD4+PggKCgIpaWlSE1NBQCkpqaqjjpmjZiIdE3uxIt1FRUVCAkJwZo1a/D9998jLi4OGRkZqKmpsY6rMJlMqK2tVSyHiZiIdK2j3dcyM68MRGk7QM1iseDo0aOYOXMmrrvuOqxbtw6FhYVXfQwmYiIiBTk57Q/NjoiIQEREBK677joAQEpKCgoLCxEaGoqqqiqYTCZUVVUhJCRE8RhsIyYiXbMIyeWHmrCwMERERODUqVMAgP3796NPnz5ISkpCSUkJAKCkpATJycmK5bBGTES61tn9iGfOnInVq1fDbDajZ8+emD17NoQQyMvLQ3FxMXr06IF58+YplsFETES61tkj66699lqHzRdZWVlOl8GmCSIijbFGTES61pWzqLmKiZiIdI2T/hARaUz302ASEXk6uZPnmnAHz/+pICLSOdaIiUjX2DRBRKSxzpz0x12YiIlI1yzsvkZEpC1vqBF7foRERDrHGjER6RqbJoiINOYNTRNMxESka94wxNnzIyQi0jnWiIlI1zj7GhGRxryhaYKJmIh0zRsm/WEiJiJd84a5Jjw/QiIinWONmIh0jU0TREQak73gD38mYiLSNYvea8SPPvoo/P39YTAYYDQakZOT4664iIjc4ifRNJGdnY2QkBB3xEJE9JPEpgki0rWfxKQ/L7zwAgDgtttuQ1paWocDIiJyJ2+YBlMSQghXd66srER4eDhqamrw/PPP48EHH0R8fLzNNkVFRSgqKgIA5OTk4NC/v7WuixkcjeNfn3T18F2GcboX43Qfb4gRcC3O65P6u+XYj3w5w+V9XxnxhltiUNOhRNzaxo0b4e/vj8mTJytud5vhl9b/F+zOwaMjM91x+E7FON2LcbqPN8QIuBbnVnmTW47tDYnY5caTpqYmNDY2Wv+/b98+xMTEuC0wIiJ3kIXB5UdXcbmNuKamBitXrgQAWCwW3HzzzRg2bJjbAiMicgddT4MZFRWFFStWuDMW8kaSix9yV/dzlXta4MgL6X5ABxGRp/OG7mueHyERkc6xRkxEuvaTGOJMROTJdH2xjojIG3hDjZhtxEREGmONmIh0rbN7TTiaDriurg55eXk4e/YsIiMjMXfuXAQHB7dbBhMxEelaVzRNtJ0OuLCwEImJiUhPT0dhYSEKCwsxffr0dvdn08RPmSSpPwxG5YdkUH1IRqPNA5Jkt6yjD9U4VF+Hg9fe9hyRV5IhufxwVWlpKVJTUwEAqampKC0tVdyeNWIi0rWuqBG3nQ64pqYGJpMJAGAymVBbW6u4PxMxEZGCzMwrs8alpaXZzbu+dOlSm+mAe/fufdXHYCImIl3raI1Y7V6c4eHhAIDQ0FAkJyfjyJEjCA0NRVVVFUwmE6qqqlRvJ8c2YiLSNVlILj/UtDcdcFJSEkpKSgAAJSUlSE5OViyHNWIi0rXObCNubzrg/v37Iy8vD8XFxejRowfmzZunWA4TMRHpWmcOcW5vOuDu3bsjKyvL6XLYNEFEpDHWiL2Zo76trZdJyr+zksGJmoLRqBKCC2VIEqRu3dT3uwqSxaK4XvXWjI72/29/Z2sZskoZQlZefykQ9W3IrbxhrgkmYiLSNSZiIiKNeUMiZhsxEZHGWCMmIl3zhhoxEzER6ZpgIiYi0hZvlUREpDE2TZDrnOmf66ifcKtlklofYD9f9UP4qnxEfP3UyzC2idNohKF7q7sVqL1WJ/reCotyH16ppVl5/xazg53a9HdublGJQXH1f6n0NWY/458kJmIi0jW2ERMRaYxNE0REGmONmIhIY95QI+bIOiIijbFGTES65g0dUZiIiUjXOKCDiEhjurhYt2bNGpSVlSE0NBS5ubkAgLq6OuTl5eHs2bOIjIzE3LlzERwcrFIS2VAbxKAyqTvgYLCFJNksk/yUB1tI/v7qxwhU3kb4q0/wLvu3GTjia4QcFd7qIB0f0CE1KQ+2kJouKhfQ0GS/zGCAFBjY6rmDbVprVh40ArQzcMQGB3z8FKl+28eOHYtFixbZLCssLERiYiJWr16NxMREFBYWdlqAREQd0Zl3cXYX1UQcHx9vV9stLS1FamoqACA1NRWlpaWdEx0RUQcJ4fqjq7jURlxTUwOTyQQAMJlMqK2tdWtQRETuoos24o4qKipCUVERACAnJwcFu3Os62IGR9s891QeG2ebttWYQdH407+eu7LAoPIHjzMTC6mV4cwNSNtsExMbiT+++Vv1/a6G2o09Vdfbt83GXN8Lq7csuLJArYrkoAw7bq5meexnsw0t49RtIg4NDUVVVRVMJhOqqqoQEhLS7rZpaWlIS0uzPn90ZKb1/wW7c2yee6pOibMTLtb96V/P4fc3Z11Z7yEX60Sbi3V/fPO3mHPf2lYH0f5inXBwsW71lgV4bMJLV7ZpUr5YJ9xxsU7tTtBtzoWev0Nb5U2dFI3ncWlkXVJSEkpKSgAAJSUlSE5OdmtQRETu4g0X61RrxPn5+Thw4AAuXLiARx55BFOmTEF6ejry8vJQXFyMHj16YN68eV0RKxHRVfOGHn+qifjxxx93uDwrK8vhcnKSStOD2qTugIOmB4PBZpkhKBBKRIh6329zmHIZLSHqE8Obg2xfi+xnRP213a8891GueRjM6t8kn3rlWdl9a5WbDYzVDQ4KNQKmK81uhlrl98yJFmLVtmrVyeWdm32eWtFtGzERkbfwhkTM2deIiDTGGjER6ZoXNBEzERORvnlD0wQTMRHpmxdUidlGTESkMdaIiUjX2DTxU6YybFdSmaNB8vNVXA84GKIsSTbL1PoJmyO7K64HgIZeykOYG3uo/1HVHGL7Ws3+Eqquv/LRk1VeqkF59DIAwK9Wud91wDnlj3qgr/3+wsdoc47UviySxYmexGrzUVxUXu8wqbT9rHnDCIYu5A2ng4mYiHSNNWIiIq15QSLmxToiIo2xRkxEutbZbcSyLCMzMxPh4eHIzMxERUUF8vPzUVdXh9jYWMyZMwc+PsqpljViItI30YGHEz7++GNER0dbn//tb3/DpEmTsHr1agQFBaG4uFi1DCZiItI1ISSXH2rOnz+PsrIyjB8//r/HEigvL0dKSgqASzdfduaenkzERKRvnVgjXr9+PaZPnw7pv10IL1y4gMDAQBj/O41teHg4KisrVcthGzERkYLMzCu3eGp967cvv/wSoaGhiIuLQ3l5eYeOwUTcWdTuOacy8Xvb+9E53CYooE2ZBptlapO6qw3WAIALMcpx1kerD2KQe9hOyi77y6hPuHIPOZ9uyvdxM19UPxeN55RHhZgD1Sbatz8Xsq9kc46CWpQnZfdpdmLkSYvyBPXCrHJPO0cTy7f9rHHyeBsd7Ueck+P4pqfffPMN/v3vf2PPnj1obm5GY2Mj1q9fj4aGBlgsFhiNRlRWViI8PFz1GEzERKRvndRrYtq0aZg2bRoAoLy8HB988AEee+wxrFq1Cp9//jluuukmbN++HUlJSaplsY2YiHRO6sDj6t1333348MMPMWfOHNTV1WHcuHGq+7BGTETUQQkJCUhISAAAREVFYdmyZVe1PxMxEekbJ/0hItIYEzERkca8YNIfJmIi0jXOR6xXKpO+O1eEShm+fqpliIA2fV8lyWZZS5hyP+GGSPVOM/V9lPsJB/WvUS1jeK8TNs+7B1xE6qBD1uc9u11Q3L/iovoE9mVn+iiur5dCFdcbG+3Phexje478LiifT6PK+kuBKL+vUtNFxfVO5RS1z5Y3ZKafGCZiItI3L/jdYSImIn1jGzERkbYk1oiJiDTmBYmYQ5yJiDTGGjER6RvbiImINOYFTRNMxESkb3pIxGvWrEFZWRlCQ0ORm5sLANi4cSM+/fRThISEAACmTp2K4cOHd26kXkYyqPw5pDYxvI/aROaA7Nfm7TNIEK2WtQQpl9Ecpv4nm+jZpLh+5DXHVcu4J+LfNs/Dferxqx67rc/7+VQp7v+92aR6DB9JeeBJ8YXrFdc3nw2wWyaMks05Ujuf3dq+Hw4YVN5Xofa5MLSZOF6S7D5rnBfe+6h+csaOHYuJEyeioKDAZvmkSZMwefLkTguMiMgtvKBGrNprIj4+HsHBwV0RCxGR+wnJ9UcXcbmNeMuWLdixYwfi4uJw//33M1kTkUfyhgEdkhDqM4BUVFTgpZdesrYRV1dXW9uH3377bVRVVWH27NkO9y0qKkJRURGASzfhO/Tvb63rYgZH4/jXJzv8IjqbS3GqTbyitl6lrRAA4Gu7TUxsJI4fPWt9Lvspl2H2V//FlwOU215D/JXbkAHA5NNg8zzINw71Ld9Zn/tB+YaZzU7UF6rMyjdKrW3yV1xvcDDpT/+e4fi24sqt0H2alL8qhmYnGmdVbkAKi8r6Nl/XmEHROH7wpOI2nsCV79D1Sf3dcuzYP+a6vO/ROU+4JQY1LtWIw8LCrP8fP348XnrppXa3bX37aQB4dOSVW1MX7M6xee6p7OJ0YvY1Se2iSzflmboMIeozjsk9bS9i/fHN32LOfWutz+viQhT3rxqonuwbExoV14+7/pDiesD+Yt1N0W9j18lfWZ+742Ldu+eVb9BYfEj5Yl1Auf3Fuo2zp2HKmg3W56ZvlJNk8He1iusBwFCh/FrlWuWZ6MRF29nZ/vT/XsDvRz9tu82MSoHnAAAVw0lEQVRVJvOu4Mp3fau8qZOi8TwujayrqrryYdq9ezf69u3rtoCIiH5qVGvE+fn5OHDgAC5cuIBHHnkEU6ZMQXl5OY4dOwZJkhAZGYmHH364K2IlIrpq3tBGrJqIH3/8cbtlztwemjrIoP7HivBpu41ks0xWeXdlX/UwugW0KK7vF3BetYyBvrbbdJPMNstifZUv9PpL6sdQi0Ptdci+9k0TkGzPkdr5tH8/HHDifSU34xBnIiKNeUGNmD/PREQaY42YiPTNC2rETMREpGu6uFhHROTVvCARs42YiEhjrBETkb55QY2YidhTycpzPACAZGn7CRM2ywwqI10l5SkeAADNzcofkXMt6pM9/Wix7aMbJQw2y4IM9Ve1vytxtKi8Dr92zkXrc6R6Pu3eDweceF/JvdhGTESkNQ7oICLSmBfUiHmxjohIY6wRE5GusY2YiEhrTMRERNryhhox24iJiDTGGjER6ZsX1IiZiDuJkJXffUnlvmHCmQEdzW1GIQjbZcZG5TL8Ljhxz7rzyvfW+/fZGNUyuhls4+zbMxD/qBlhfd7HT/k+biea1e9ZpxaHReV1+Dm4VZxksV2udj7t3g8HVN9X1c9Fm/VCqH7WfvI68fQ0NzcjOzsbZrMZFosFKSkpmDJlCioqKpCfn4+6ujrExsZizpw58PFpP90yERORrnVmG7Gvry+ys7Ph7+8Ps9mMrKwsDBs2DB9++CEmTZqEm266Ca+++iqKi4tx++23t1sO24iJiFwkSRL8/f0BABaLBRaLBZIkoby8HCkpKQCAsWPHorS0VLEc1oiJiDpAlmUsWLAAZ86cwYQJExAVFYXAwEAYjZea/sLDw1FZWalYBhMxEelbB5smMjMzrf9PS0tDWlqazXqDwYAVK1agvr4eK1euxMmTJ6/6GEzERKRrHW0jzsnJcWq7oKAgxMfH4/Dhw2hoaIDFYoHRaERlZSXCw8MV92UbMRHpm+jAQ0VtbS3q6y9N49rc3Iz9+/cjOjoaCQkJ+PzzzwEA27dvR1JSkmI5rBETkb51Yq+JqqoqFBQUQJZlCCEwevRojBgxAn369EF+fj7eeustxMbGYty4cYrlMBG7QqWvJwBAZQpUYVGeZVxqblE/RFOz7QJZtlnmV9NmfRsB59T7ETd3V97mpLGHahn/vBBk8/yBmAD880ii9Xmg/0XF/RualPsAA0DTWeXJ4wNPKb+OgHP2/XsNZmGzXO182r0fDgiV91Xtc+EUZz6f5Bb9+vXD8uXL7ZZHRUVh2bJlTpfDRExEuuYNc00wERORvjERExFpyxtqxOw1QUSkMdaIiUjfvKBGzERMRPrGRExEpC1vaCNWTcTnzp1DQUEBqqurIUkS0tLScOedd6Kurg55eXk4e/YsIiMjMXfuXAQHB3dFzN5BqMw7qzKHrGhW75MqNTTal9lqmU+1n+L+gd3U+xELg3IZPo3qv+XNFd1tF4w2AuVXll3wU/7cGJtVOmUDCKlWXh9Yofx+BP5of74NLcJmuU91o902Ntq+Hw6ovq9qcws7+lypfdZ+6vSQiI1GI2bMmIG4uDg0NjYiMzMTQ4cOxfbt25GYmIj09HQUFhaisLAQ06dP74qYiYh0RbXXhMlkQlxcHAAgICAA0dHRqKysRGlpKVJTUwEAqampqvNtEhFpohPnmnCXq2ojrqiowNGjRzFgwADU1NTAZLp0CxuTyYTa2tpOCZCIqCN00UZ8WVNTE3Jzc5GRkYHAwECnD1BUVISioiIAl6aTK9h9ZUq5mMHRNs89VafEKam0e6qtBwCjbRtvzHVRePmT+VcW+Ci3AQsf9W7ksq9yHGrrAUC0CaN/j3C8O2valfUq3xRJqB9DUpmiwdCifAxH6/v1i8Cf12RcOYZZpS3W7MQ8EWpzSajNE9FmfczgaBR84fycBlrR9Luul0RsNpuRm5uLW265BaNGjQIAhIaGoqqqCiaTCVVVVQgJCXG4b9uJlB8deWWS5YLdOTbPPZVLcaokUsnHV3m9n/J6ADB0t73I9fIn8/GHO65MQCLCQxX3b45Sv7haf43yxbqGnurJvDnM9vm7s6bhnr9usD63+Cl/U5y5WOfXwYt1QaftL6L9eU0Gfjd7/ZVj/FinWIZUWaMcBAD5gnIZqpMCmW3XF3yxDI+OWthmI8/LPK58h7bKm9xybG+oEat+i4QQeOWVVxAdHY277rrLujwpKQklJSUAgJKSEiQnJ3delEREOqZaI/7mm2+wY8cOxMTE4KmnngIATJ06Fenp6cjLy0NxcTF69OiBefPmdXqwRERXzQtqxKqJeNCgQdi4caPDdVlZWW4PiIjIrfSQiKlzqE4AbnbiIlhTk+0CWbZZJtUqv71+TlwQlFqU21b9Lii3IQNAS5BtC5ixScB08Eq5ssqn0GBW/yb51qvEWaU8kMK3yn4whmSW4VdRf+V5bb3dNq3ZvR+OtjGblde7Y2J4suHEZW/NcfY1IiKNsUZMRPrGpgkiIm15Q/c1JmIi0jcmYiIijXlBIubFOiIijbFGTES6xjbinzLV8f4qE8g40Z9UNF1ss0C2X6ZAcuIYvheV+9/6XPBXLUPuZvsxM16U0f27K31yhVH5DzPJoj7xueGicv9cqV65j69U72BSd7PFZv4I0ag88btT51510h+V1+roc+WBc0t4FC84PUzERKRrrBETEWnNCxIxL9YREWmMNWIi0jU2TRARaY2JmIhIY16QiNlGTESkMdaIiUjX2EZM7VPphO/SBOGizcTjKvOUCycGSkjNygM6DI4GQrTdxqfNx6zFAp/TVa02UJm6W3bim6Q24brK65Ad3bRTliHXtZoMvkXtxp7KMQBOvK8cnOF+XnBKmYiJSNckL/hxYyImIn3z/DzMi3VERFpjjZiIdI0X64iItNaJifjcuXMoKChAdXU1JElCWloa7rzzTtTV1SEvLw9nz55FZGQk5s6di+Dg4HbLYSImIl3rzBqx0WjEjBkzEBcXh8bGRmRmZmLo0KHYvn07EhMTkZ6ejsLCQhQWFmL69OntlsM2YiLSN9GBhwqTyYS4uDgAQEBAAKKjo1FZWYnS0lKkpqYCAFJTU1FaWqpYDmvEnsqJLjd2fVKFsFkmVPrfOjPhumrfWWcmQze0+b23WCBXX5lwXZKU+xELZ7ofyR2baN9hn2rZdqJ99T7ATpxPL+hKRa6pqKjA0aNHMWDAANTU1MBkMgG4lKxra2sV92UiJiJd62jTRGZmpvX/aWlpSEtLs9umqakJubm5yMjIQGBg4FUfg4mYiPStg4k4JydHcb3ZbEZubi5uueUWjBo1CgAQGhqKqqoqmEwmVFVVISQkRLEMthETka5JwvWHGiEEXnnlFURHR+Ouu+6yLk9KSkJJSQkAoKSkBMnJyYrlsEZMROSib775Bjt27EBMTAyeeuopAMDUqVORnp6OvLw8FBcXo0ePHpg3b55iOUzERKRvnXiBdNCgQdi4caPDdVlZWU6Xw0RMRLrGkXVERFrTQyJubwjfxo0b8emnn1qvBk6dOhXDhw/v9ICpFUd/ctksU+7XKszq/V6FRfl6rmRQn4MXUpsy2vbPVS9BnUofXrU+1Q73FwLCrNyPuu325HkkJ7p3a001Ebc3hA8AJk2ahMmTJ3d6kEREeqaaiE0mk3WESOshfEREXsEL/lC5qjbi1kP4Dh48iC1btmDHjh2Ii4vD/fffrzi7EBGRFrzhYp0knBrIf2kIX3Z2Nu6++26MGjUK1dXV1vbht99+G1VVVZg9e7bdfkVFRSgqKgJwaYTKoX9/a10XMzgax78+6Y7X0akYpwKVeSIciRkUjeMHuzhOF9pvveF994YYAdfivD6pv1uOfdO9K13ed9c7T7olBjVO1YgdDeELCwuzrh8/fjxeeuklh/u2HZv96Mgr47YLdufYPPdUXhunC0nSTtsLbXarnThGmzL+9NlS/H7MMx2Jyl4nXKwr+GIZHh218Cpi6Pqql9d+Np2wVd7klmN7Q41YdYhze0P4qqqu3IV39+7d6Nu3b+dESESkc6o14vaG8O3atQvHjh2DJEmIjIzEww8/3OnBEhFdNS+oEasm4vaG8LHPMBF5A29omuDIOj1zS5ulSturylzplziYwP5qBkp0hfbOFQdpeD8veA85DSYRkcZYIyYiXWPTBBGR1piIiYi0xRoxEZHW1AbzeABerCMi0hhrxESkb55fIWYiJhWd1QfTC/p2kj6wjZiISGte8KPPRExEuuYNNWJerCMi0hhrxESkb15QI2YiJiJdk9hGTESkMeUJBD0C24iJiDTGGjER6RqbJoiItOb5eZiJmIh0jjViIiJtcUAHERGpYo2YiPSNTRNERNqSvKAfMRMxEembF9SI2UZMRKQx1oiJSN88v0LMRExE+saRdUREWmMiJiLSWCf2mlizZg3KysoQGhqK3NxcAEBdXR3y8vJw9uxZREZGYu7cuQgODlYshxfriIhcNHbsWCxatMhmWWFhIRITE7F69WokJiaisLBQtRwmYiLSNUkIlx9q4uPj7Wq7paWlSE1NBQCkpqaitLRUtRw2TRCRvnVxG3FNTQ1MJhMAwGQyoba2VnUfJmIi0rcOJuLMzEzr/9PS0pCWltbRiOyoJuLm5mZkZ2fDbDbDYrEgJSUFU6ZMQUVFBfLz81FXV4fY2FjMmTMHPj7M60TkYTp4sS4nJ+eqtg8NDUVVVRVMJhOqqqoQEhKiuo9qG7Gvry+ys7OxYsUKLF++HHv37sWhQ4fwt7/9DZMmTcLq1asRFBSE4uLiqwqWiEiPkpKSUFJSAgAoKSlBcnKy6j6qiViSJPj7+wMALBYLLBYLJElCeXk5UlJSAFy6cuhMgzQRUVfrzIt1+fn5WLx4MU6dOoVHHnkExcXFSE9Px759+/DYY49h3759SE9PVy3HqbYEWZaxYMECnDlzBhMmTEBUVBQCAwNhNBoBAOHh4aisrHSmKCKirtWJF+sef/xxh8uzsrKuqhynErHBYMCKFStQX1+PlStX4uTJk04foKioCEVFRQAutbUU7L7S3hIzONrmuadinO7FON3HG2IENI5TbyPrgoKCEB8fj8OHD6OhoQEWiwVGoxGVlZUIDw93uE/bq4yPjrxyBbJgd47Nc0/FON2LcbqPN8QIuBbnVnlTJ0XjeVTbiGtra1FfXw/gUg+K/fv3Izo6GgkJCfj8888BANu3b0dSUlLnRkpE5AohXH90EdUacVVVFQoKCiDLMoQQGD16NEaMGIE+ffogPz8fb731FmJjYzFu3LiuiJeI6Oro4Q4d/fr1w/Lly+2WR0VFYdmyZZ0SFBGRu3AaTCIirXlBIuakP0REGmONmIj0Tfb8GjETMRHpmxc0TTARE5G+MRETEWnMCxIxL9YREWmMNWIi0jcvuFgnCeEF9XYiIhfdETvP5X0/ObrKjZG0T9Omida3IPFkjNO9GKf7eEOMgMZxesFcE2wjJiLSGNuIiUjfvKCNWNNE3Bl3Q+0MjNO9GKf7eEOMgMZxesFlMF6sIyJdu6PPYy7v+8mJ1W6MpH1smiAiffOCuqZmiXjv3r1Yt24dZFnG+PHjnbrTqRYeffRR+Pv7w2AwwGg0IifHM+4PtmbNGpSVlSE0NBS5ubkAgLq6OuTl5eHs2bOIjIzE3LlzERwc7FExbty4EZ9++ilCQkIAAFOnTsXw4cM1ixEAzp07h4KCAlRXV0OSJKSlpeHOO+/0uPPZXpyedk6bm5uRnZ0Ns9kMi8WClJQUTJkyBRUVFcjPz0ddXR1iY2MxZ84c+PiwLgholIhlWcZrr72GxYsXIyIiAgsXLkRSUhL69OmjRTiqsrOzrR9yTzF27FhMnDgRBQUF1mWFhYVITExEeno6CgsLUVhYiOnTp3tUjAAwadIkTJ48WaOo7BmNRsyYMQNxcXFobGxEZmYmhg4diu3bt3vU+WwvTsCzzqmvry+ys7Ph7+8Ps9mMrKwsDBs2DB9++CEmTZqEm266Ca+++iqKi4tx++23d35AsuffokOT7mtHjhxBr169EBUVBR8fH4wZMwalpaVahOK14uPj7WpnpaWlSE1NBQCkpqZqfk4dxeiJTCYT4uLiAAABAQGIjo5GZWWlx53P9uL0NJIkwd/fHwBgsVhgsVggSRLKy8uRkpIC4NKPdJedTy/oR6xJjbiyshIRERHW5xERETh8+LAWoTjlhRdeAADcdtttHn2VuqamBiaTCcClL21tba3GETm2ZcsW7NixA3Fxcbj//vs9KllXVFTg6NGjGDBggEefz9ZxHjx40OPOqSzLWLBgAc6cOYMJEyYgKioKgYGBMBqNAIDw8PCu+xFhG7FjjjpqSJKkQSTqli5divDwcNTU1OD5559H7969ER8fr3VYXuv222/HvffeCwB4++238frrr2P27NkaR3VJU1MTcnNzkZGRgcDAQK3DaVfbOD3xnBoMBqxYsQL19fVYuXIlTp48qV0wXtCPWJOmiYiICJw/f976/Pz589aah6cJDw8HAISGhiI5ORlHjhzROKL2hYaGoqqqCsClu297Wrs2AISFhcFgMMBgMGD8+PH49ttvtQ4JAGA2m5Gbm4tbbrkFo0aNAuCZ59NRnJ56TgEgKCgI8fHxOHz4MBoaGmCxWABc+qv48neLNErE/fv3x+nTp1FRUQGz2YzPPvsMSUlJWoSiqKmpCY2Njdb/79u3DzExMRpH1b6kpCSUlJQAAEpKSpCcnKxxRPYuJzYA2L17N/r27athNJcIIfDKK68gOjoad911l3W5p53P9uL0tHNaW1uL+vp6AJd6UOzfvx/R0dFISEjA559/DgDYvn17l33nhZBdfnQVzQZ0lJWV4X//938hyzJ+9rOf4e6779YiDEU//vgjVq5cCeDSRYebb77ZY+LMz8/HgQMHcOHCBYSGhmLKlClITk5GXl4ezp07hx49emDevHmathU6irG8vBzHjh2DJEmIjIzEww8/rPlfQwcPHkRWVhZiYmKsTWRTp07Fdddd51Hns704d+3a5VHn9Pvvv0dBQQFkWYYQAqNHj8a9996LH3/80a77mq+vb6fHMzH8Ny7vu7nyL26MpH0cWUdEujbRNMvlfTdX/dWNkbSPs68REWmMw1qISN+8YEAHEzER6ZsXtL4yERORrgnWiImINOYFNWJerCMi0hhrxESkb14wxJmJmIj0rQtHyLmKiZiIdE2wRkxEpLFOrBG7605DvFhHROSCy3caWrRoEfLy8rBr1y6cOHHCpbKYiIlI14QsXH4oceedhpiIiUjfhOz6Q4GjOw25etcRthETka5tlTe5vG9jYyOeffZZ6/O0tDTr7dLceachJmIionYEBAQgJyfH4Tp33mmITRNERC5w552GODE8EZGL3HWnISZiIiKNsWmCiEhjTMRERBpjIiYi0hgTMRGRxpiIiYg0xkRMRKQxJmIiIo0xERMRaez/A2n1/7BzjBgIAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x432 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# G-Band Image\n",
    "g_wls, gimage, gdistribution = totalImage(gband_wavelength, gband_throughput, spectra_obs[4], relative_fluxdensity, gWeightedWavelength, p_s, temperature, p_w, latitude, altitude, zin, 0.8, 16, 16)\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$-0.69517074 \\; \\mathrm{}$"
      ],
      "text/plain": [
       "<Quantity -0.69517074>"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "min(gimage)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x432 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# I-Band Image\n",
    "w_use, iimage, idistribution = totalImage(iband_wavelength, iband_throughput, spectra_obs[4], relative_fluxdensity, iWeightedWavelength, p_s, temperature, p_w, latitude, altitude, zin, 0.8, 16, 16)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Part 2b \n",
    "\n",
    "As in 1a, verify the results of 2a with 1D plots of the values of the images along the y-axis through the center of the image (this should be aligned with the direction of the DCR shifts from 2a)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x432 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# G-Band 1D plot check\n",
    "sliced_gtotal = gdistribution[:,16] #y, x\n",
    "\n",
    "type(gimage[0])\n",
    "\n",
    "\n",
    "# Plot\n",
    "fig, ax = plt.subplots(1, 1, figsize = (6, 6))\n",
    "ax.plot(sliced_gtotal, color = 'b')\n",
    "ax.set_title('2D Sliced Gaussian Distribution [G-Band]');"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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xMQCA3r17Q5IkpKWl4a677sKhQ4fwl7/8pdHjxcXFISYmBsuWLcPq1atRVFSEZ555plHPZuPGjTCbzRgxYgRCQkKwc+dOVFZWom/fvgCAP/3pT5g8eTLi4+NRV1eHTz/91DbEc6XQ0FBERETgrbfeQq9evVBcXIwnn3yy0S+L9iopKcHFixdRX1+PU6dOYevWrdiwYQOefPLJRlNfG/r888/xyy+/YNy4cYiIiMCBAwdw9uxZWxtjY2MBAF988QXGjBkDX1/fNk91Ky4uxsMPP4zHHnsMv/zyC5577jk88MADth5+amoqHnroIWzbtg1DhgzBxx9/jL179yIkJMT2GLGxsfjXv/6Fo0ePIjIyEoGBgY2GHQDLr9M//OEPmD9/PjZs2ICYmBj84x//wJEjR2xfUHKyrh+z2YzTp0/jySefRKdOnWzDI/Hx8di8eTMyMjIQHR2NTZs2ITMzE6GhoW16nieeeAJ/+MMfMGLECEyePBn/+c9/sHnzZmc0yfFkGrt3OFwxLcv6Z50mJkTj6VuSJImgoCAxePBgsXjx4qs2dlyprq5OPP3002L48OEiNDTUNs3uwQcfFGfOnLEt15ppi1999ZVITk4WPj4+IigoSIwfP16cOHHCdvtnn30mkpOTha+vrwgMDBQDBw4UL7zwgu32mpoaMXfuXBEUFCSCgoLEAw880OK0RasjR46Ie+65R3Tt2lWo1WoRGBgoRo4cKV555RVRUVFhW+7vf/+76Nq1q/Dx8RGjR48WX375pQAgMjIybMvs27dPDBkyRPj4+IikpCSxZ8+eRhtFP/nkEzFq1CgREhIifH19Rb9+/cTbb79tu//8+fNF7969hY+PjwgLCxOTJ08WR44csd1+5ca+Xbt2iaSkJKHVakWfPn3Exx9/LHr16tVowyqumFIohBATJ05s9D64knWjm/XPx8dH9OjRQ8yYMUN8/fXXVy3f8Dl2794tJkyYYJvmFxcXJ15++eVGU+Uee+wx0alTJyFJUqNpi01t8G1u2uKiRYtEWFiYCAgIELNmzRLV1dW2ZfR6vXjsscdERESECA4OFvPnzxfPPfdco42ixcXF4qabbhJBQUHXnLZYXl5um7ao0WianbZ45QbkK9fDlRyxUbThZzcyMlJMnz5dHD582LZcWVmZ+MMf/iACAwNFWFiYmD9/vnj22WcbvQ5Xfj6FaHrD9Zo1a0RUVJTw8fEREydOFO+9955bbBSVhOAZi4jIud577z3MmTMHRqNR7lIcatmyZdiyZQuOHz8udykAPGwMnYhcl8lkQkBAAO655x65S2m3Y8eOISAgAH/961/lLqUR9tCJyOkqKyttG9YDAgKccviEjqTX63HmzBkAlg3O3bt3l7kiCwY6EZGH4JALEZGHYKATEXkIBjoRkYfo8B2LrtyjrbV0Ol2rj5HhqtgG1+AJbQA8ox1sQ+tERUW1ajn20ImIPAQDnYjIQzDQiYg8BAOdiMhDMNCJiDwEA52IyEMw0ImIPAQDnYjIQzDQiYg8BAOdiMhDMNCJiDwEA52oCQYDcPq0Uu4yiNqEgU7UhMcfD8HYsZ2Qk6OWuxSiVmOgE10hI0OL7dv9IASwcGEI9Hq5KyJqHQY6UQO1tRKeeSYYvXoZsGFDKY4dU+ONNwLlLouoVRjoRA2sXh2AM2dUeOWVckyeXIfbbqvB3/4WgCNHOvzUAURtxkAn+q/cXBXWrw/AHXdUY9QoyzjLsmXlCAszY8GCUA69kMtjoBMBMJuBJ58MQUiIGc8+W2G7PjRU4JVXypCbq8batQEyVkjUMgY6EYBNm/zw008aLF1agdBQ0ei2SZPqcfPNNVizJhBHj3LohVwXA5283sWLCqxYEYSxY+txyy21TS7zl7+UIyTEjIULQ2AwdHCBRK3EQCev9/zzwTAYJLz8chkkqellwsIEVqwox5EjGqxbx6EXck0t/n7U6/VYunQpjEYjTCYTkpOTMWPGDBQWFmLNmjWoqqpCbGwsHnnkEahU/DlK7uWbb7T497998dRTFYiNNV1z2ZtuqsO0abVYvToQN9xQh4QEYwdVSdQ6LfbQ1Wo1li5dipUrV+LVV19FdnY2fv75Z2zZsgVTpkzBG2+8AX9/f3z77bcdUS+Rw1RXS/jzn4MRH2/AvHlVrbrPiy+WIyjIjAULQmBknpOLaTHQJUmCj48PAMBkMsFkMkGSJBw9ehTJyckAgPHjxyMrK8u5lRI5WFpaIM6ds8w512had5/wcDNeeqkcOTkarF/PoRdyLa0aQzebzVi8eDHmzJmDAQMGIDIyEn5+flAqLQcvCgsLQ0lJiVMLJXKkI0dUePttf9x1VzWGD2/bBPP/+Z86TJlSi7S0QPz8M4cZyXW06t2oUCiwcuVKVFdXY9WqVTh37lyrnyA9PR3p6ekAgBUrVkCn09lXqEpl931dBdvgGiRJhWee0UGnA9LS1AgNbXt71q8HBg0CnnxSh127jJBj85EnrAu2wbHa9Db09/dH3759UVBQgJqaGphMJiiVSpSUlCAsLKzJ+6SmpiI1NdV2uaioyK5CdTqd3fd1FWyDa/jnPzvhwAEV1q0rgclUB3uao1AAy5f7YP78MLz8ci0eeqja8YW2wBPWBdvQOlFRUa1arsUhl4qKClRXW96ser0ehw8fRnR0NPr164d9+/YBAHbt2oVhw4a1o1yijnHxogJLlyoxYUIdpk2ra9djTZtWhwkT6vDWWwEQouXliZytxR56aWkp1q5dC7PZDCEERo0ahaFDh6Jr165Ys2YN/vnPfyI2NhbXX399R9RL1C5ffumDqioJy5ZVNDvnvLUkCZg0qQ4ZGT44dUrZ4rRHImdrMdBjYmLw6quvXnV9ZGQkXn75ZacUReQsmZladOsmEBfnmDmHycmWDar792sQG9v0XqZEHYV7ipLXEALIytLguuvMDnvM3r2NCA01ITNT67DHJLIXA528xpkzSly8qMTo0Y4b8JYkYORIPTIzWzmRnciJGOjkNayhO2aMY7dgjhihx6lTKly8yI8TyYvvQPIaWVkahISYkZjo2EC3jqOzl05yY6CT18jM1GDYMD0UDn7X9+tngL+/Gfv3cxyd5MVAJ69QXKzAiRNqjBjh+PPIqVTAsGEcRyf5MdDJK+zfbwnbESPqnfL4I0bokZenQmlpOye3E7UDA528QmamBlqtQFKSc043lJyshxASsrLYSyf5MNDJK2RlaTB4sB5aJw1zDxqkh0YjOI5OsmKgk8errpZw+LBzxs+tfHwsob5vH3voJB8GOnm8gwfVMJkkpwY6YBlHP3xYjZoajqOTPBjo5PH279dCoRAYNsy5gZ6crIfRKOHAAbVTn4eoOQx08niZmRokJhoRGOjcY9xa5rhzHJ3kw0Anj2YwWIZcRo50znTFhgIDBfr1M3AcnWTDQCePduSIGrW1CqePn1uNGKHHwYNq6Dvm6YgaYaCTR7PuvdlRgZ6crEddnQI5ORxHp47HQCePlpWlQY8eRkRGOu4Y6Ndi/eLgODrJgYFOHksIyy7/w4d33PiHTmdGXBzH0UkeDHTyWCdOqFBSosTIkR07oD1ypB5ZWRqYeIpR6mAMdPJYv42fO3+GS0MjR+pRUaFAXl6Lp+wlcigGOnmszEwNdDoTevbs2K6y9ReB9QiPRB2FgU4eKytLgxEj9JA6eE/8rl1NiI42Yt8+bhiljsVAJ4904YICZ86oOnSDaEMjR+qxf78Gwrk7pxI1wkAnj2Qd7ujoDaJWI0fqUVioxMmTSlmen7wTA5080v79Wvj5mdGvn3NOaNESjqOTHBjo5JEyMzUYOtQAlUwTTeLijAgLM3EcnToUA508Tnm5hLw8VYcckKs5kvTbODpRR2Ggk8f58UcNhJBk2yBqNWKEHqdPq3DhAj9m1DH4TiOPs3+/BiqVwJAh8oyfWyUncxydOhYDnTzO/v0aDBhggJ+fvHMG+/Y1wN/fzHF06jAMdPIodXVAdramww6Xey0qFTB8OMfRqeMw0Mmj5ORooNdLss0/v9KIEXrk5alRUsITR5PzMdDJo1gPyCX3BlEr6zj6jz+yl07Ox0Anj7J/vwa9exsQFtYxJ7RoycCBemg0guPo1CEY6OQxTCZLT9gVxs+tfHyAwYM5jk4dg4FOHiMvT4WKio47IXRrjRihR06OGtXVHEcn52Kgk8fIypL3gFzNSU7Ww2SScOAATxxNzsVAJ4+RmalF584mdO3qWud+GzpUD4VCIDOT4+jkXAx08gjWE0KPHFnf4Se0aElgoEBCghHZ2eyhk3O1eCy6oqIirF27FmVlZZAkCampqZg8eTK2bduGnTt3IigoCAAwc+ZMDBkyxOkFEzXl3DklLl5Uusx0xSslJhrw3XfsoZNztRjoSqUS99xzD3r27Ina2losWbIESUlJAIApU6Zg2rRpTi+SqCW5uZa3cv/+8h6/pTmJiQZ88okfSkslhIbyNEbkHC0OuYSGhqJnz54AAF9fX0RHR6OkpMTphRG1xbFjluGMhASjzJU0zVpXXh6HXch52nT4/8LCQpw8eRJxcXHIy8vDjh07sGfPHvTs2RP33nsvAgICrrpPeno60tPTAQArVqyATqezr1CVyu77ugq2wXlOnlQiJkYgNja8xWXlaMPo0ZZ/z54Nwf/8j2N2enLVddEWbINjSUK07jS2dXV1WLp0KW655RaMHDkSZWVltvHzrVu3orS0FPPnz2/xcc6fP29XoTqdDkVFRXbd11WwDc4zYUIEunc34f33W/71KEcbhAD69++MKVNq8eqr5Q55TFddF23BNrROVFRUq5Zr1SwXo9GItLQ0jB07FiNHjgQAhISEQKFQQKFQYOLEiThx4oT91RK1Q309cOKECgkJrjl+DljOYJSYaLANDRE5Q4uBLoTA+vXrER0djalTp9quLy0ttf1///796Natm3MqJGrB8eMqmEwSEhNdc/zcKiHBgPx8FcyucZgZ8kAtjqHn5+djz5496N69OxYvXgzAMkXxu+++w6lTpyBJEiIiIjB37lynF0vUFOuGRlfuoQNAYqIR1dUK/PqrEt27u9bOT+QZWgz0hIQEbNu27arrOeecXEVengpqtUCvXq7fQwcsM3IY6OQM3FOU3F5enhpxcUaoXXx4Oj7e8oVz7FibJpcRtRoDndzesWNqJCa69nALAAQECHTvbuRcdHIaBjq5tbIyCRcuKF12h6IrJSYakJfHHjo5BwOd3Fp+vntsELVKSDDil19UqKuTuxLyRAx0cmvW8Wj3CXQDTCYJx4+zl06Ox0Ant5aXp0ZQkBlRUe4xuds6V547GJEzMNDJreXlWfYQdbVjoDcnNtYIrVZwwyg5BQOd3JYQljF0d9kgCgAqFdC7NzeMknMw0MltnT+vREWFwm3Gz60SEowcciGnYKCT27JuEHX1Y7hcKTHRgEuXlCgpcZNxInIbDHRyW9Zx6Ph49+qhW7+AOI5OjsZAJ7eVl6dCVJQRwcHudUo36xARA50cjYFObuvYMffaIGrVqZMZoaEmHtOFHI6BTm5Jr7ccB90djuFyJUnihlFyDgY6uaUTJ1QwGl3/pBbN6duXJ7sgx2Ogk1tyl5NaNCchwYiaGgXOnlXKXQp5EAY6uaW8PBVUKtc/qUVzGp7sgshRGOjklo4ds5zUQqORuxL78GQX5AwMdHJL1mO4uCt/f4EePXiyC3IsBjq5nYoKCefOqdxyymJDCQk8pgs5FgOd3I67ndSiOdaTXdTWyl0JeQoGOrkddz2Gy5USEgwwmyUcP85hF3IMBjq5nbw8NQIDzYiONsldSrtYd4rihlFyFAY6uZ28PBXi441uc1KL5sTGmuDjw5NdkOMw0MmtCGHpobv7+DkAKJWWk12wh06OwkAnt3LhggLl5Qq3PIZLUxISOHWRHIeBTm7lt13+3XuDqFViogGFhUqUlPCjSO3HdxG5FXc/hsuVrDN1OOxCjsBAJ7dy7JgKXbqYEBLiXie1aA6P6UKOxEAnt5KXp/aY8XMAiIgwIyzMxD1GySEY6OQ2DAagoMC9j+FyJUmyDLtwwyg5AgOd3MYvv6hgMEges0HUynpMF57sgtqLgU5uwzos4Uk9dMDSQ6+tVeD0aZ7sgtqHgU5u49gxNZRKgbg4z+s/7gn4AAAgAElEQVShA+CwC7UbA53cRl6eGr16GaHVyl2JY1kOYyC4YZTajYFObsNyUgvP6p0DgJ+fQEyMiVMXqd0Y6OQWqqoknD3rWTNcGkpMNDDQqd0Y6OQWrMMRnjQHvaGEBCNOnVLyZBfULi0O2hUVFWHt2rUoKyuDJElITU3F5MmTUVVVhdWrV+Py5cuIiIjAggULEBAQ0BE1kxfytGO4XCkx0XKyi4ICNZKSPPNLi5yvxUBXKpW455570LNnT9TW1mLJkiVISkrCrl27MGDAAEyfPh3bt2/H9u3bcffdd3dEzeSF8vJU8Pc3o2tX9z6pRXN+OwSAioFOdmtxyCU0NBQ9e/YEAPj6+iI6OholJSXIyspCSkoKACAlJQVZWVnOrZS8Wl6eGvHxRig8dJCwRw8TfHzMHEendmnTx6OwsBAnT55EXFwcysvLERoaCsAS+hUVFU4pkEgIyxx0Tx0/Bywnu+jTh4cAoPZp9cTXuro6pKWl4b777oOfn1+rnyA9PR3p6ekAgBUrVkCn07W9SgAqlcru+7oKtsE+588DZWUKDBumdchzu+p6GDxYia++UrS6NldtR1uwDY7VqkA3Go1IS0vD2LFjMXLkSABAcHAwSktLERoaitLSUgQFBTV539TUVKSmptouFxUV2VWoTqez+76ugm2wz/ffawGEo1u3MhQV6dv9eK66Hnr08MelS8HIyyuBTtfygV1ctR1twTa0TlRUVKuWa3HIRQiB9evXIzo6GlOnTrVdP2zYMOzevRsAsHv3bgwfPtzOUomuzVOP4XKlhhtGiezR4jsnPz8fe/bsQffu3bF48WIAwMyZMzF9+nSsXr0a3377LXQ6HRYuXOj0Ysk7HTumRufOJoSGesZJLZpjPXtRXp4aY8e2/5cIeZ8WAz0hIQHbtm1r8rbnn3/e4QURXcmyy79n984By8kuwsNNyM9nD53s46GTwMhTGI1AQYFlyqI3iI/nTBeyHwOdXNqpU0rU10te0UMHLOPoP//Mk12QfRjo5NLy8y29Vev4sqeLjzeiulqBc+d4sgtqOwY6ubT8fBUkSSAuzjt66PHx1pNdcByd2o6BTi7t2DE1evQwwddX7ko6hvXgY9ZfJkRtwUAnl5af7x0zXKwCAwWio42c6UJ2YaCTy6qrA06eVHnNDBcrznQhezHQyWUdP66C2ew9M1ysEhIMOH5cBaN3fY+RAzDQyWVZx5E99aQWzYmPN0Kvl3DqFIddqG0Y6OSy8vJU0GgEevTwrkDnMV3IXgx0cll5eWr06mWE2suGk3v1MkKhEJzpQm3GQCeX5W0zXKx8fS1nMOJMF2orBjq5pMpKCefOed8MF6uEBANnulCbMdDJJVl7p97YQwcsG0ZPnVKitlbuSsidMNDJJXnrDBer+HgDzGYJJ05w2IVaj4FOLikvTwV/fzOio01ylyIL6xcZh12oLRjo5JLy8tTo08cIhZe+Q3v0MEKjEdwwSm3ipR8XcnXeOsPFSq22TF9kD53agoFOLqeoSIHiYqXXjp9bJSYa2EOnNmGgk8uxHgvcemxwbxUfb8S5cypUVkpyl0JugoFOLsc6zODtPXTrFxp76dRaDHRyOfn5KoSFmaDTefeJNTnThdqKgU4uJy9Pjfh4IyQvH2mIjjbB39/MHjq1GgOdXIoQlh56YqJ3j58DgEIB9OnDmS7Uegx0cinnzilRXa3w2mO4XCkhgTNdqPUY6ORSrMcA9/YZLlbx8UYUFytRVMSPKrWM7xJyKdZjuLCHbmH9YrNO5SS6FgY6uZT8fBWioowIChJyl+ISrDNdeLILag0GOrmUvDy1188/bygiwozQUJ7sglqHgU4uw2gEjh/37mO4XEmSLL10znSh1mCgk8s4dUoFvV7i+PkV4uONyM9XQXAUilrAQCeXYZ3hwh56Y/HxBlRVKXD+vFLuUsjFMdDJZeTnq6FQCPTqxR56Q4mJ1kMAcBydro2BTi4jP1+FHj1M8PWVuxLX0qePdeoix9Hp2hjo5DIsM1w43HKl4GCBLl1M7KFTixjo5BJqa4FTp3hSi+ZYDgHAHjpdGwOdXMLx42qYzRJ3+W9GfLwRx4+rYOT3HV0DA51cgnU4gT30psXHG1BfL+HUKc50oea1OCi3bt06HDx4EMHBwUhLSwMAbNu2DTt37kRQUBAAYObMmRgyZIhzKyWPlp+vhlYr0KMHA70pDQ8BEBdnkrkaclUtBvr48eNx4403Yu3atY2unzJlCqZNm+a0wsi75OerEBdnhIrb/ZrUu7cRkiSQn6/ClClyV0OuqsUhl759+yIgIKAjaiEvlpen4vj5Nfj6CsTEmDh1ka7J7v7Qjh07sGfPHvTs2RP33nsvQ5/sVl4u4fx5FRISauQuxaXxZBfUErveHZMmTcJtt90GANi6dSs2bdqE+fPnN7lseno60tPTAQArVqyATqezr1CVyu77ugq2oWk//2w5eejw4b7Q6Xwc+thNcdf1MHiwEt98o0BAgA4+Pu7bjobYBseyK9BDQkJs/584cSJeeeWVZpdNTU1Famqq7XJRUZE9TwmdTmf3fV0F29C0zEw/ACGIiipBUZHzN/i563ro1s0HJlMYMjPL0K+f0W3b0RDb0DpRUVGtWs6uaYulpaW2/+/fvx/dunWz52GIAFg2iAYEmBEdzdkb18KTXVBLWuyhr1mzBrm5uaisrMS8efMwY8YMHD16FKdOnYIkSYiIiMDcuXM7olbyUHl5asTHGyFJclfi2mJjjVCrBQ8BQM1q8Z3x+OOPX3Xd9ddf75RiyPsIYZnhMnlyndyluDyNBujViye7oOZxT1GS1eXLCpSWKnlSi1biTBe6FgY6yco6fMA56K0TH2/Er7+qUFnJ8Sm6GgOdZGXdwMdjuLSO9fDCP//MXjpdjYFOssrPV0GnM0GnM8tdiluwDk1xpgs1hYFOsrLOcKHW6dbNBF9fM2e6UJMY6CQbs9nSQ+dZilpPobD00tlDp6Yw0Ek2v/6qRE2Ngj30NrIEOnvodDUGOsmGM1zsEx9vwOXLSly+LHcl5GoY6CQb67ABe+htY50RdOQIpy5SYwx0kk1+vgpduxoRGCjkLsWt9Otn+UXz008MdGqMgU6yOXpUzfnndtDpzIiONuLgQQY6NcZAJ1lUV0soKFBh4EC93KW4pYEDDThwgB9faozvCJLFkSNqCCEhKYkbRO2RlGTAL79IKCtjL51+w0AnWWRnWzaIDhzIQLeH9XU7fJjz0ek3DHSSRU6OGlFRRkREcJd/ewwYYBmqysnRyFwJuRIGOsni0CENe+ftEBoqEBsrcOgQe+j0GwY6dbjycgknT6oY6O00dKgZOTkMdPoNA506nDWEGOjtM2SIwNmzKpSU8GNMFnwnUIc7dMgy7msdByb7DB1q2SGLvXSyYqBThzt0SI0ePYwIDeUeou0xeLDl9eM4Olkx0KnD5eSoOf/cAYKDgZ49jeyhkw0DnTpUcbECv/7KPUQdZeBAvW0Ii4iBTh3KOjzADaKOkZRkwIULShQW8qNMDHTqYIcOqSFJAv37M9AdwfrFyGEXAhjo1MEOHdKgVy8eMtdR+vc3QJIEA50AMNCpg+XkqDnc4kD+/gK9exs5jk4AGOjUgS5eVODSJSUD3cGSkgzIyVFD8EeP12OgU4ex9iKTkjjDxZEGDjSgsFCJixf5cfZ2fAdQhzl0SA2lUqB/f56lyJGsX5A88iIx0KnD5OSo0aePEb6+HBtwpH79jFAqeeRFYqBTBxHCclIL7lDkeL6+An36cI9RYqBTB/n1VyVKS7lB1Fkse4xyw6i3Y6BTh+Ap55wrKcmAkhIlzp1Tyl0KyYiBTh0iJ0cNtVogIYGB7gzWL0qOo3s3Bjp1iEOHNOjb1wCtVu5KPFNiogFqNfcY9XYMdHI6s5mHzHU2rRZISDBwj1Evx0Anpzt5UonKSgXHz52Me4wSA52czrrDC6csOtfAgQaUlytw+jQ3jHorBjo5XXa2Gj4+lrnS5DzWL0xuGPVeqpYWWLduHQ4ePIjg4GCkpaUBAKqqqrB69WpcvnwZERERWLBgAQICApxeLLmnnBw1+vUzQNXiu43ao08fI7RagZwcDX7/+zq5yyEZtNhDHz9+PJ555plG123fvh0DBgzAG2+8gQEDBmD79u1OK5Dcm8kEHD6sxqBBHG5xNo0G6NvXwB66F2sx0Pv27XtV7zsrKwspKSkAgJSUFGRlZTmnOnJ7BQUq1NYqOMOlgyQlGXD4sBpms9yVkBzs+hFcXl6O0NBQAEBoaCgqKiqaXTY9PR3p6ekAgBUrVkCn09nzlFCpVHbf11V4Yxt++cXSZ0hJ8YdO5++sstrEE9YD0HQ7Ro9W4P33FSgr06FPH5kKawNPWBeu1Aanj2qmpqYiNTXVdrmoqMiux9HpdHbf11V4Yxu++y4Y/v4KhIcXwVWa7gnrAWi6HT17qgB0wu7d1QgLq5WnsDbwhHXREW2Iiopq1XJ2zXIJDg5GaWkpAKC0tBRBQUH2PAx5gUOHLDsUKTifqkP07m2Ej4+Z4+heyq6P2bBhw7B7924AwO7duzF8+HCHFkWeQa8HcnO5h2hHUqmA/v15KF1v1eKQy5o1a5Cbm4vKykrMmzcPM2bMwPTp07F69Wp8++230Ol0WLhwYUfUSm7m559VqK+XuENRBxs4UI+PPvKDyQQouY+RV2kx0B9//PEmr3/++ecdXgx5luxs6x6i7KF3pKQkAzZuVODECRV35vIyHNkkp8nJUSMkxIyYGJPcpXgVHkrXezHQyWmyszVIStJDkuSuxLv07GmEv7+Z4+heiIFOTlFbC+Tnq7hBVAZKJTBgAA+l640Y6OQUx46pYTRKHD+XSVKSAUePqmHkELpXYaCTU1jHbznDRR4DBxpQVyfh5595RDRvwkAnpzh0SAOdzoSoKB5URA5JSZYvUo6jexcGOjmF9ZRz3CAqjx49TAgKMnMc3csw0MnhqqslFBSoMGgQx8/lolBYNoyyh+5dGOjkcEeOqGE2S7af/SSPgQP1yM1VQ8/V4DUY6ORwv20QZQ9dTkOHGqDXSzh4kMMu3oKBTg63f78G0dFGdOrEDaJyuu66eqhUArt2aeUuhToIA50cymAA9u7VYvz4erlL8XpBQQJDh+oZ6F6EgU4O9eOPGlRVKTBhAgPdFYwfX4/DhzUoKuJH3RtwLZND7dqlhUolMHo0A90VWH8p7d7NXro3YKCTQ2Vk+GDYMD2CgoTcpRCA/v0NCA83cdjFSzDQyWEuXVLg6FE1h1tciEIBpKTUY/duLczcRu3xGOjkMNZe4PjxdTJXQg2NH1+P4mIljhzhTkaejoFODrNrlw86dTKhXz8e4s+VpKRYfjFx2MXzMdDJIYxGYM8ey3RFHr/Fteh0ZgwYwOmL3oCBTg6Rna1GWZmCwy0uavz4evz4owYVFfy29WQMdHKIjAwfKBQC48Zxg6grmjChHiaThO++Yy/dkzHQySF27dJi8GADQkM5XdEVDRmiR0CAGRkZDHRPxkCndisuVuDQITUmTOBwi6tSq4GxYy3TFwW/cz0WA53azRISEuefu7iUlHr8+qsKJ07wtHSeioFO7ZaRoUVYmAlJSTxcriuzHgaAwy6ei4FO7WI2W3ro48fXQ8F3k0vr1s2EXr0MPK6LB+NHkNrl8GE1iouVPFyumxg/vh4//KBFba3clZAzMNCpXTIytJAkwUB3ExMm1KOuTsL+/eyleyIGOrVLRoYPkpIMCA/nkZ/cQXKyHlqt4Di6h2Kgk93KyiQcPMijK7oTX1+B5OR6HgbAQzHQyW5792phNkvc3d/NpKTUo6BAjXPnlHKXQg7GQCe7ZWT4IDjYjMGDOV3RnVh/UbGX7nkY6GQXISyBMG5cPVTcT8Wt9O5tRFSUkYHugRjoZJfcXBUuXVJyd383JEmW6Yt792ph4I8rj8JAJ7vs2uUDAJyu6KbGj69HZaUCP/2kkbsUciAGOtklI0OLvn0NiIzkdEV3NGZMPZRKwWEXD8NApzarrJSQlaXB9ddzuMVdBQcLDBnCsxh5GgY6tdl332lhNEocbnFzKSn1yMlRo7iYMeAp2jU/4eGHH4aPjw8UCgWUSiVWrFjhqLrIhWVkaBEQYMawYXq5S6F2mDChHqtWBWHPHi1uvpkHd/EE7Z5wtnTpUgQFBTmiFnIDQlgCfezYeqjVcldD7ZGUZEBYmAkZGQx0T8HfWtQmeXnAuXMqDrd4AIUCGDeuHnv2aGHmtm2P0O5Af+mll/DUU08hPT3dEfWQi9uxw/KW4fFbPMP48fW4fFmJ3FzuHeYJJCHsP8NgSUkJwsLCUF5ejhdffBGzZs1C3759Gy2Tnp5uC/sVK1ZAr7dv3FWlUsFoNNpbqkvwhDZMmaLGuXMC2dnu2w5PWA+AY9px8SIQE6PBiy8asXhxx3fTPWFddEQbNJrW7S/QrkBvaNu2bfDx8cG0adOuudz58+ftenydToeioiK77usq3L0NNTUS+vXrjFmzqvH88xVyl2M3d18PVo5qx6RJEQgMNOOTT4odUFXbeMK66Ig2REVFtWo5u4dc6urqUPvf057U1dUhJycH3bt3t/fhyA18950Gej2PruhpJk2qQ2amBqdP8+iL7s7ugbPy8nKsWrUKAGAymTBmzBgMGjTIYYWR69m82R8REQIjR3K6oie5665q/O1vAdi40R9/+Yv7/vKidgR6ZGQkVq5c6chayIUVFKiwc6cPnnvOCC13LvQoXbqYMW1aLf75Tz8sWlSJoCCHjMKSDDhtkVrlrbf84eMj8OCDnN/miebOrUZ1tQIffugndynUDgx0alFRkQIff+yHW2+tQUSE3NWQMwwYYEBycj3eeccfbj7pxKsx0KlF77/vj/p6CXPnVstdCjnR3LnVOHdOhS+/9JG7FLITA52uqbYWeO89P6Sm1iEujl03T5aaWocePYx4880AuUshOzHQ6Zo++cQPJSVKPPhgldylkJMplcDs2dU4eFCDAwd4oB53xECnZpnNwJtv+mPAAD1GjeJURW9w++01CAoy46232Et3Rwx0atbOnVqcOKHGgw9WQ5LkroY6gr+/wF131eDf//bBr79yRyN3w0CnZm3YEIAuXUyYOpWHVvUms2ZVQZKAd97xl7sUaiMGOjXp8GE1fvhBizlzqnjccy8THW3GlCl1+PBDP1RV8aeZO2GgU5M2bPBHQIAZd95ZI3cpJIO5c6tQWanA1q3c0cidMNDpKufOKfDFF76YObOGu4F7qcGDDRg2TI+33/aHySR3NdRaDHS6yjvvWGY4zJnDHYm82QMPVOHMGRW+/po7GrkLBjo1Ulkp4YMP/DBlSh26dmXXzJvdeGMdunY14q23uHHUXTDQqZGPPvJDZaWCOxIRVCrLjkaZmVocOsQt4+6AgU42RiOwcaM/Ro6sx6BBBrnLIRcwc2YNAgLM7KW7CQY62Vh2JlHhwQc5dk4WgYECd9xRg//9X19cuMC4cHVcQwQAEAJ4880AxMYa8bvf8RRz9JvZs6thNgPvvcdeuqtjoBMAYP9+DbKzNXjggSoo+K6gBrp3N+HGG+uwZYs/amq4o5Er40eXAFh2JAoNNWHGDO7mT1ebO7caZWUKbNvmK3cpdA0MdMLhw2p8/bUP7r23Br6+3JGIrjZsmB5DhuiRlhaIc+d40C5XxUD3csXFCsyeHYrOnc3ckYiaJUnA6tWlMBgkzJkTilr+kHNJDHQvZjAAc+eGorhYiXfeKUFYGE8ATc2LizPhjTdKkZOjwZIlIRD8MedyGOhebNmyYOzbp8XKlWVISuK8c2rZpEn1WLiwEh9/7If33uOBu1wNA91LffCBH957zx8PPVSFW27h72dqvQULKpGaWodly4KRmamRuxxqgIHuhbKyNPjzn4Mxfnwdnn66Qu5yyM0oFMDf/laK7t1NmDs3FOfPM0ZcBdeElzl/XoEHHghFdLQJa9eWQskJC2SHoCCBjRtLUFsrYe7cMNTXy10RAQx0r1JbC8yZE4aaGgnvvluCkBBu1SL79eljxJo1ZfjpJw2efTZY7nIIDHSvIQTw5JMhOHRIg7//vRR9+hjlLok8wOTJdXjkkUp8+KE/tmzhRlK5MdC9xJtv+uPTT/2waFEFJk3i72NynMWLKzFhQh2efTYYP/7Iw+zKiYHuBfbs0eLFF4MweXItHnuMxzknx1Iqgb//vRRRUSbMnRuGS5cYK3LhK+/hTp1S4qGHQhEfbxnv5IG3yBlCQiwbSSsqLBtJ9Xq5K/JO/Hh7sMOH1bj33jAAwMaNJfD350ZQcp7ERCNee60MP/6owd13h+OXXziFqqMx0D1QebmEP/85GJMn61BersDbb5cgJobnByXnmzatDitXliEnR43U1E547bUATmnsQAx0DyIE8K9/+WLcuE7YtMkP991XjT17CjFqFH//Use5884a7N5diBtvrEVaWhBSUzth717uUdoRGOge4tgxFW65JRyPPx6K7t1N+PLLy1i+vALBwRxmoY4XGWnGunVl+PDDYpjNwB136PDIIyG4fJmR40x8dd1cZaWEpUuDcMMNESgoUGHVqjJ8/nkR+vfnPHOSX0pKPXbuLMSCBZX4f//PFykpnbB5sx/MPLCnUzDQ3ZQQwPbtlg/Ixo3+mDmzBnv3FmLmzBrOZCGX4uMDLFpUiW++KUT//gYsWRKC3/9eh6NHVXKX5nH4irqR+nrgwAEN9u7VIiNDi8OHNUhK0uOdd0owaBAPf0uuLS7OhK1bi/HZZ7544YUg3HhjBEaPFkhODsC4cfUYONDAYwu1EwPdhZlMwNGjavznP1rs3avB/v0a1NUpoFAIDBpkwIoVZbjzzhp+CMhtSBJwyy21uP76Orz5ZgD27PHHypVBWLkSCA42Y/ToeowdW49x4+rRowdnZrVVuwI9Ozsb7777LsxmMyZOnIjp06c7qi6vYzAAhYUKXLqkxJEjauzdq8X332tRVmYZP4mPN+Cuu2owZkw9kpP1CArixk5yXyEhAk8+WYlXX9Xi559LsHev5Zfnnj1a/N//WU5E3b27EWPH1mP06Hp0725C584mRESYoWI3tFl2vzRmsxkbN27Es88+i/DwcDz99NMYNmwYunbt6sj63IoQQF0dUFcnNfknSRKOH/fDpUtKXLqkwIULStv/i4sVEEKyPVZUlBE33FCHMWMsb+jISG5FIs8UFmbG739fh9//vg5CACdOKG3h/vnnvvjgA3/bsgqFQKdOZnTubEJkpAmdO1v+bw17X18BX18BH5/f/qyX1WrLLwRPZnegHz9+HJ07d0ZkZCQA4LrrrkNWVpZTAn39en98/bUKBoPumsu19hyH1uWEuPr/1lD97bJl6MNkkmA2W/8PmM0NL/8W2i0LgSQJRESYERlpQpcuJgwapP/vG9RyXc+eRsTGmjz+zUd0JUmyjLXHxdVg1qwaGAxAfr4K588rcfFiwz8FTp9WITNTafsV2xKFwhLuajWgVAoolZaTdTT8f8PL1s+fJFn/RBPXAWq1CkbjtbMJAJYtK8ewYc7d1mV3oJeUlCA8PNx2OTw8HAUFBVctl56ejvT0dADAihUroNO13PArhYUpEBQkQYiWy20qBK91nXWlNPx/w8tXrvSGf9bbVSprTwDw8xPw8QF8fa1/v10OCVGiUycjIiPR4Gej4r9/7nGUOpVKZdc6dCWe0AbAM9rRmjZ06dLcLQKAETU1wPnzwOXLEmpr8d+/3/5fU2P55VxbK6GmBtDrG3bMru6smUwKmEyNO3VNd/4sf5LUOJua61hGRIRAp3PuUKndgS6aqFpqIjlTU1ORmppqu1xUVNTm55oxA5g/X2fXfV2JTmdpQ1mZ3JXYz9oGd+YJbQA8ox2OakNIiOVPDm1pg71NjYqKatVyds9YDg8PR3Fxse1ycXExQkND7X04IiJqJ7sDvVevXrhw4QIKCwthNBrx/fffY9iwYY6sjYiI2sDuIRelUon7778fL730EsxmMyZMmIBu3bo5sjYiImqDds3oHDJkCIYMGeKoWoiIqB141A8iIg/BQCci8hAMdCIiD8FAJyLyEAx0IiIPwUAnIvIQDHQiIg/BQCci8hAMdCIiDyGJpg6bSEREbsdteuhLliyRu4R2Yxtcgye0AfCMdrANjuU2gU5ERNfGQCci8hDKZcuWLZO7iNbq2bOn3CW0G9vgGjyhDYBntINtcBxuFCUi8hAcciEi8hDtOsFFR8nOzsa7774Ls9mMiRMnYvr06XKX1GYPP/wwfHx8oFAooFQqsWLFCrlLatG6detw8OBBBAcHIy0tDQBQVVWF1atX4/Lly4iIiMCCBQsQEBAgc6XNa6oN27Ztw86dOxEUFAQAmDlzpkufqKWoqAhr165FWVkZJElCamoqJk+e7Fbrork2uNO60Ov1WLp0KYxGI0wmE5KTkzFjxgwUFhZizZo1qKqqQmxsLB555BGoVDJFq3BxJpNJ/OlPfxIXL14UBoNBLFq0SJw9e1bustps/vz5ory8XO4y2uTo0aPixIkTYuHChbbrNm/eLD777DMhhBCfffaZ2Lx5s1zltUpTbdi6dav4/PPPZayqbUpKSsSJEyeEEELU1NSIRx99VJw9e9at1kVzbXCndWE2m0Vtba0QQgiDwSCefvppkZ+fL9LS0sR//vMfIYQQGzZsEDt27JCtRpcfcjl+/Dg6d+6MyMhIqFQqXHfddcjKypK7LK/Qt2/fq3p8WVlZSElJAQCkpKS4/Lpoqg3uJjQ01LbRzdfXF9HR0SgpKXGrddFcG9yJJEnw8fEBAJhMJphMJkiShKNHjyI5ORkAMH78eFnXg8sPuZSUlCA8PNx2OTw8HAUFBTJWZL+XXnoJAPC73/0OqampMldjn/LycoSGhgKwfEgrKipkrsg+O3bswJ49e9CzZ0/ce++9bhP6hYWFOHnyJOLi4tx2XTRsQ15enlutC7PZjKeeegoXL17EDZPRu0sAAAJtSURBVDfcgMjISPj5+UGpVAIAwsLCZP2icvlAF01MwpEkSYZK2mf58uUICwtDeXk5XnzxRURFRaFv375yl+WVJk2ahNtuuw0AsHXrVmzatAnz58+XuaqW1dXVIS0tDffddx/8/PzkLscuV7bB3daFQqHAypUrUV1djVWrVuHcuXNyl9SIyw+5hIeHo7i42Ha5uLjY1itxJ2FhYQCA4OBgDB8+HMePH5e5IvsEBwejtLQUAFBaWmrbmOVOQkJCoFAooFAoMHHiRJw4cULuklpkNBqRlpaGsWPHYuTIkQDcb1001QZ3XBcA4O/vj759+6KgoAA1NTUwmUwALCMK1s+6HFw+0Hv16oULFy6gsLAQRqMR33//PYYNGyZ3WW1SV1eH2tpa2/9zcnLQvXt3mauyz7Bhw7B7924AwO7duzF8+HCZK2o7awgCwP79+9GtWzcZq2mZEALr169HdHQ0pk6darvendZFc21wp3VRUVGB6upqAJYZL4cPH0Z0dDT69euHffv2AQB27dolaz65xY5FBw8exPvvvw+z2YwJEybglltukbukNrl06RJWrVoFwLIxZcyYMW7RhjVr1iA3NxeVlZUIDg7GjBkzMHz4cKxevRpFRUXQ6XRYuHChS495NtWGo0eP4tSpU5AkCREREZg7d65L/+rLy8vD888/j+7du9uGG2fOnInevXu7zbporg3fffed26yL06dPY+3atTCbzRBCYNSoUbjttttw6dKlq6YtqtVqWWp0i0AnIqKWufyQCxERtQ4DnYjIQzDQiYg8BAOdiMhDMNCJiDwEA52IyEMw0ImIPAQDnYjIQ/x/oGNjaaKTacMAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x432 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# I-Band 1D plot check\n",
    "sliced_itotal = idistribution[:,16] #y, x\n",
    "\n",
    "type(iimage[0])\n",
    "\n",
    "# Plot\n",
    "fig, ax = plt.subplots(1, 1, figsize = (6, 6))\n",
    "ax.plot(sliced_itotal, color = 'b')\n",
    "ax.set_title('2D Sliced Gaussian Distribution [I-Band]');"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.4"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}