Astrometric Noise.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import os\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Ideal, but there's a workaround below if you don't have this package \n",
    "# (https://github.com/lsst-pst/syseng_throughputs) \n",
    "# Does require LSST simulations stack\n",
    "import lsst.syseng.throughputs as st"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "def calcAstrometricError(mag, m5, fwhm_eff, error_sys=10.0):\n",
    "    \"\"\"\n",
    "    Calculate the astrometric error, for object catalog purposes.\n",
    "    fwhm_eff (in same units as returned astrometric error)\n",
    "    error_sys is the systematic error expected as the minimum value for astrometric error.\n",
    "    Returns astrometric error for a given SNR (in same units as fwhm_eff).\n",
    "    \"\"\"\n",
    "    rgamma = 0.039\n",
    "    xval = np.power(10, 0.4*(mag-m5))\n",
    "    # The average FWHMeff is 0.7\" (or 700 mas).\n",
    "    error_rand = fwhm_eff * np.sqrt((0.04-rgamma)*xval + rgamma*xval*xval)\n",
    "    astrom_error = np.sqrt(error_sys * error_sys + error_rand*error_rand)\n",
    "    return astrom_error"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Pull up the throughput curves and calculate m5\n",
    "defaultDirs = st.setDefaultDirs()\n",
    "hardware, system = st.buildHardwareAndSystem(defaultDirs)\n",
    "m5 = st.makeM5(hardware, system, exptime=15, nexp=2, X=1.0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>FWHMeff</th>\n",
       "      <th>m5</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>u</th>\n",
       "      <td>0.92</td>\n",
       "      <td>23.681847</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>g</th>\n",
       "      <td>0.87</td>\n",
       "      <td>24.805485</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>r</th>\n",
       "      <td>0.83</td>\n",
       "      <td>24.366544</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>i</th>\n",
       "      <td>0.80</td>\n",
       "      <td>23.947028</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>z</th>\n",
       "      <td>0.78</td>\n",
       "      <td>23.375466</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>y</th>\n",
       "      <td>0.76</td>\n",
       "      <td>22.467668</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
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      ],
      "text/plain": [
       "   FWHMeff         m5\n",
       "u     0.92  23.681847\n",
       "g     0.87  24.805485\n",
       "r     0.83  24.366544\n",
       "i     0.80  23.947028\n",
       "z     0.78  23.375466\n",
       "y     0.76  22.467668"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "m5[['FWHMeff', 'm5']]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "m5_lim\n",
      "{'u': 23.681847096372046, 'g': 24.805485162309864, 'r': 24.366544272782974, 'i': 23.94702848604054, 'z': 23.37546595033629, 'y': 22.46766827505174}\n",
      "FWHMeff\n",
      "{'u': 0.92, 'g': 0.87, 'r': 0.83, 'i': 0.8, 'z': 0.78, 'y': 0.76}\n"
     ]
    }
   ],
   "source": [
    "# Convenience for someone running this later, without lsst packages: (cut and paste)\n",
    "m5_lim = m5.m5.to_dict()\n",
    "FWHMeff = m5.FWHMeff.to_dict()\n",
    "print('m5_lim')\n",
    "print(m5_lim)\n",
    "print('FWHMeff')\n",
    "print(FWHMeff)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Calculate astrometric error assuming NO systematic noise - just shot noise\n",
    "mags = np.arange(17, 26, 0.5)\n",
    "filterlist = ('u', 'g', 'r', 'i', 'z', 'y')\n",
    "astrom_err = {}\n",
    "for f in filterlist:\n",
    "    astrom_err[f] = np.zeros(len(mags))\n",
    "    for i, mag in enumerate(mags):\n",
    "        astrom_err[f][i] = calcAstrometricError(mag, m5_lim[f], FWHMeff[f]*1000, error_sys=0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>u</th>\n",
       "      <th>g</th>\n",
       "      <th>r</th>\n",
       "      <th>i</th>\n",
       "      <th>z</th>\n",
       "      <th>y</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>17.0</th>\n",
       "      <td>1.395416</td>\n",
       "      <td>0.766870</td>\n",
       "      <td>0.901863</td>\n",
       "      <td>1.064974</td>\n",
       "      <td>1.379232</td>\n",
       "      <td>2.169422</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>17.5</th>\n",
       "      <td>1.795605</td>\n",
       "      <td>0.973472</td>\n",
       "      <td>1.149317</td>\n",
       "      <td>1.364410</td>\n",
       "      <td>1.785911</td>\n",
       "      <td>2.888159</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>18.0</th>\n",
       "      <td>2.336009</td>\n",
       "      <td>1.241401</td>\n",
       "      <td>1.474289</td>\n",
       "      <td>1.763919</td>\n",
       "      <td>2.343815</td>\n",
       "      <td>3.928951</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>18.5</th>\n",
       "      <td>3.085467</td>\n",
       "      <td>1.593987</td>\n",
       "      <td>1.909384</td>\n",
       "      <td>2.309881</td>\n",
       "      <td>3.131772</td>\n",
       "      <td>5.480202</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>19.0</th>\n",
       "      <td>4.156599</td>\n",
       "      <td>2.067351</td>\n",
       "      <td>2.506562</td>\n",
       "      <td>3.077632</td>\n",
       "      <td>4.279170</td>\n",
       "      <td>7.847456</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>19.5</th>\n",
       "      <td>5.734208</td>\n",
       "      <td>2.719248</td>\n",
       "      <td>3.350445</td>\n",
       "      <td>4.190794</td>\n",
       "      <td>5.997584</td>\n",
       "      <td>11.520772</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>20.0</th>\n",
       "      <td>8.119393</td>\n",
       "      <td>3.643898</td>\n",
       "      <td>4.579939</td>\n",
       "      <td>5.851729</td>\n",
       "      <td>8.629411</td>\n",
       "      <td>17.279860</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>20.5</th>\n",
       "      <td>11.797294</td>\n",
       "      <td>4.995973</td>\n",
       "      <td>6.422145</td>\n",
       "      <td>8.388465</td>\n",
       "      <td>12.722838</td>\n",
       "      <td>26.360416</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>21.0</th>\n",
       "      <td>17.542054</td>\n",
       "      <td>7.028081</td>\n",
       "      <td>9.244515</td>\n",
       "      <td>12.326907</td>\n",
       "      <td>19.149173</td>\n",
       "      <td>40.718708</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>21.5</th>\n",
       "      <td>26.582057</td>\n",
       "      <td>10.148372</td>\n",
       "      <td>13.635247</td>\n",
       "      <td>18.503595</td>\n",
       "      <td>29.288785</td>\n",
       "      <td>63.452197</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>22.0</th>\n",
       "      <td>40.862431</td>\n",
       "      <td>15.009477</td>\n",
       "      <td>20.529164</td>\n",
       "      <td>28.244175</td>\n",
       "      <td>45.326925</td>\n",
       "      <td>99.467121</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>22.5</th>\n",
       "      <td>63.462598</td>\n",
       "      <td>22.648005</td>\n",
       "      <td>31.407212</td>\n",
       "      <td>43.647298</td>\n",
       "      <td>70.723847</td>\n",
       "      <td>156.536978</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>23.0</th>\n",
       "      <td>99.259448</td>\n",
       "      <td>34.705858</td>\n",
       "      <td>48.613861</td>\n",
       "      <td>68.035918</td>\n",
       "      <td>110.960790</td>\n",
       "      <td>246.980183</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>23.5</th>\n",
       "      <td>155.979150</td>\n",
       "      <td>53.782314</td>\n",
       "      <td>75.861514</td>\n",
       "      <td>106.673521</td>\n",
       "      <td>174.722620</td>\n",
       "      <td>390.318894</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>24.0</th>\n",
       "      <td>245.864430</td>\n",
       "      <td>83.993457</td>\n",
       "      <td>119.030855</td>\n",
       "      <td>167.899705</td>\n",
       "      <td>275.772236</td>\n",
       "      <td>617.492822</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>24.5</th>\n",
       "      <td>388.316971</td>\n",
       "      <td>131.859680</td>\n",
       "      <td>187.439696</td>\n",
       "      <td>264.930031</td>\n",
       "      <td>435.921201</td>\n",
       "      <td>977.537573</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25.0</th>\n",
       "      <td>614.085186</td>\n",
       "      <td>207.712638</td>\n",
       "      <td>295.853990</td>\n",
       "      <td>418.708486</td>\n",
       "      <td>689.737735</td>\n",
       "      <td>1548.168997</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25.5</th>\n",
       "      <td>971.901249</td>\n",
       "      <td>327.925109</td>\n",
       "      <td>467.674966</td>\n",
       "      <td>662.428208</td>\n",
       "      <td>1092.008265</td>\n",
       "      <td>2452.558190</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "               u           g           r           i            z            y\n",
       "17.0    1.395416    0.766870    0.901863    1.064974     1.379232     2.169422\n",
       "17.5    1.795605    0.973472    1.149317    1.364410     1.785911     2.888159\n",
       "18.0    2.336009    1.241401    1.474289    1.763919     2.343815     3.928951\n",
       "18.5    3.085467    1.593987    1.909384    2.309881     3.131772     5.480202\n",
       "19.0    4.156599    2.067351    2.506562    3.077632     4.279170     7.847456\n",
       "19.5    5.734208    2.719248    3.350445    4.190794     5.997584    11.520772\n",
       "20.0    8.119393    3.643898    4.579939    5.851729     8.629411    17.279860\n",
       "20.5   11.797294    4.995973    6.422145    8.388465    12.722838    26.360416\n",
       "21.0   17.542054    7.028081    9.244515   12.326907    19.149173    40.718708\n",
       "21.5   26.582057   10.148372   13.635247   18.503595    29.288785    63.452197\n",
       "22.0   40.862431   15.009477   20.529164   28.244175    45.326925    99.467121\n",
       "22.5   63.462598   22.648005   31.407212   43.647298    70.723847   156.536978\n",
       "23.0   99.259448   34.705858   48.613861   68.035918   110.960790   246.980183\n",
       "23.5  155.979150   53.782314   75.861514  106.673521   174.722620   390.318894\n",
       "24.0  245.864430   83.993457  119.030855  167.899705   275.772236   617.492822\n",
       "24.5  388.316971  131.859680  187.439696  264.930031   435.921201   977.537573\n",
       "25.0  614.085186  207.712638  295.853990  418.708486   689.737735  1548.168997\n",
       "25.5  971.901249  327.925109  467.674966  662.428208  1092.008265  2452.558190"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pd.DataFrame(astrom_err, index=mags)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 576x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(8,6))\n",
    "colors = {'u': 'cyan', 'g': 'g', 'r':'r', 'i':'orange', 'z': 'b', 'y': 'k'}\n",
    "for f in filterlist:\n",
    "    plt.plot(mags, astrom_err[f], color=colors[f], label=f)\n",
    "plt.legend(loc='upper left', fontsize='large', fancybox=True, numpoints=1)\n",
    "plt.xlabel('Magnitude', fontsize='large')\n",
    "plt.ylabel('Astrometric error (mas)', fontsize='large')\n",
    "plt.grid(True, alpha=0.3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(0, 50)"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(8,6))\n",
    "colors = {'u': 'cyan', 'g': 'g', 'r':'r', 'i':'orange', 'z': 'b', 'y': 'k'}\n",
    "for f in filterlist:\n",
    "    plt.plot(mags, astrom_err[f], color=colors[f], label=f)\n",
    "plt.legend(loc='upper left', fontsize='large', fancybox=True, numpoints=1)\n",
    "plt.xlabel('Magnitude', fontsize='large')\n",
    "plt.ylabel('Astrometric error (mas)', fontsize='large')\n",
    "plt.grid(True, alpha=0.3)\n",
    "plt.xlim(18, 21)\n",
    "plt.ylim(0, 50)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "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": "3.7.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}