Strehl_Ratio.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Trap Shape Vs. Aperture for Gaussian Input"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "from scipy.integrate import quad, dblquad\n",
    "import scipy.special as sp\n",
    "from matplotlib.pyplot import *\n",
    "from matplotlib import style\n",
    "%matplotlib inline\n",
    "\n",
    "# ## set matplotlib plot defaults :D\n",
    "# Style controls many default colors in matplotlib plots.\n",
    "# Change the following if you don't like dark backgrounds. Many other options.\n",
    "#style.use(['dark_background'])\n",
    "#style.use(['seaborn-dark-palette'])\n",
    "style.use(['dark_background'])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### sq conv test"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 212,
   "metadata": {},
   "outputs": [],
   "source": [
    "def square(x):\n",
    "    if abs(x)<0.5:\n",
    "        return 1.0\n",
    "    return 0.0"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### actual integration"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 257,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\ProgramData\\Anaconda3\\lib\\site-packages\\ipykernel_launcher.py:1: DeprecationWarning: object of type <class 'float'> cannot be safely interpreted as an integer.\n",
      "  \"\"\"Entry point for launching an IPython kernel.\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x16ad6f7d908>,\n",
       " <matplotlib.lines.Line2D at 0x16ad6f7da90>]"
      ]
     },
     "execution_count": 257,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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oAACvv/46FixYgB/96EfweDxob2/HwoULI140KYMuzYDmFnmHuyAIaG6xc+ROYRc03B96\n6KF+31+3bh3WrVsXtoKIAGDUqFRoNFq0yDzcAaClmeFO4ccVqhSTdGkGAECzzNsyQNcqVS5kojBj\nuFNM0um6wl3mF1QB3zFy5E7hxnCnmBQYuSugLeNobsKoUSnQahPELoVkhOFOMSmtK9yV0HMPTIfs\nOmaicGC4U0zS6dJx4cJ5OJ3tYpcScZfmumcE2ZModAx3iklKmAbp53BwlSqFH8OdYlJamgEtCriY\nCnCVKkUGw51ikpJG7mfPnYHL1QG9nm0ZCh+GO8UkJdx64HItLXZeUKWwYrhTzBk2bDiSkoYpZuQO\noOsWBAx3Ch+GO8Uc/0M6/L1oJWhubgpM/yQKB4Y7xZw0BS1g8mtmW4bCjOFOMUdJtx7wa26xY+TI\nZK5SpbBhuFPMUdJNw/z8F4/ZmqFwYbhTzNHp0tHR4cSFC+fELiVq/C0oLmSicGG4U8zRpaUrqt8O\nAM3NNgAcuVP4MNwp5vhWpyos3LuOlxdVKVwY7hRzdDqDoqZBApeepcq57hQuDHeKOUq69YCfIAho\nbW1mW4bChuFOMUWrTcCIEaMU15YB/HPdeUGVwoPhTjFFSU9gulJzcxN77hQ2DHeKKf7b3ippjruf\n7/4yHLlTeDDcKaZceryesi6oAr6Re0pKGuLjNWKXQjLAcKeYouS2jP86Q2qqTuRKSA4Y7hRTdLp0\nuN0utLW1il1K1HGuO4UTw51iil7nW50qCILYpURd4HF7nDFDYcBwp5ii12cobgGTn3/knsaFTBQG\nDHeKKTpdOhwOm9hliKK1tRler5dtGQoLhjvFFL0uXbEjd6+3E2fONHM6JIUFw51iRmJiEkaMGAWH\nQsMd4BOZKHyChvuGDRtgs9lQXl7e5z4vv/wyqqurUVZWhtzc3LAWSMrhH7EqOty5SpXCJGi4v/nm\nm7jnnnv6fL+goADZ2dnIzs7GsmXLsH79+rAWSMqhD6xOVWbPHfCN3NPYlqEwCBru+/btQ0tLS5/v\nz58/Hxs3bgQAFBcXIyUlBUajMXwVkmLodRkAlD5ytyM1RQeVih1TGpr4of4Ak8mE+vr6wNcWiwUm\nkwlWq3WoP5oUJtCW6ZotkzraiPufehzxWq2YZUWHIGDvm5vQ0mKHWq1GcnIaWlsdYldFEjbkcI+L\ni+vxWl8LUJYuXYply5YBAPR6/VA/mmRGr0tHe/sFXLx4AQBw9YxpmHrX7ThdfRwet1vk6iJrzKSr\n0XraCvs/DwPwrVJluNNQDDncLRYLxo4dG/g6MzMTjY2Nve5bWFiIwsJCAIDZbB7qR5PM6HTp3Voy\nmsREAMBrjzyO8y3yvh3BM7vfhyYh4dIqVZ0BNcerRK6KpGzIjb2ioiIsWrQIADBz5ky0tbWxJUOD\notdnwOG4FO7arnB3tTvFKilq3O1OaJISA7c65lx3GqqgI/fNmzfjtttug16vR319PZ599lloNL5b\nkr7++uvYtWsX7r33XtTU1ODixYt4+OGHI140yZNOl46qqrLA15okX7i7OzrEKilqXE4ntIkJaOlq\nxfD+MjRUQcP9oYceCvpDli9fHpZiSNn0V7RltIkJcHd0QPB6RawqOtzODmgSE+HxuNHW1sq57jRk\nnG9FMWHkyGQkJCR2u6+MJjERbqf8R+2Af+Tu+5eKw2GDXp8hckUkdQx3igmXHq/Xvefucsq/3w50\n9dy7wr3JfhoGA9eK0NAw3Ckm6Hu59YAmKRFuBVxMBbpG7l3XGOwOGwx6hjsNDcOdYoK/DeG47NYD\n2sQE5YzcnR3QJCYA8I3cU1N10GgUsHiLIobhTjGht7aMYnvudt9UYgP77jQEDHeKCXpdOtrOtsLt\ndgVeU27PvSvcDaPFLIkkjuFOMUGv676ACegauSus5x4XFwd7V7inpzPcafAY7hQTdL08gUmbpKCR\ne9dxxidoYXewLUNDx3CnmNDb4/U0iQkK6rn7jlObmIiODifazrYinW0ZGgKGO4lOpVIhLU0P+xUP\nxlZazx24dLM0u90KPee60xAw3El0KSk6qNXxvYzcldVzBxCY697UdBrpDHcaAoY7iU7fyzTIuLg4\nRfbc/XPd7Q4b2zI0JAx3Ep1/jrv9sgVM8Qm+BTxuhYT75T13ALDbTyM5ORVabYKYZZGEMdxJdP7V\nqVfeVwa4FHpy11vPHQDvMUODxnAn0el1Gejs7ERra3PgNX/IKbbnHlilynCnwWG4k+iMRhPs9tPw\nejsDr/lDTik9d5fzipF711x3XlSlwWK4k+iMGSZYbQ3dXvNfWFRKz91/nFr/BVX/yJ2rVGmQGO4k\nutHGTJy2Wrq9prSeu6vdd5z+kbvL1YEzZ1rYlqFBY7iTqDQaDXS6dFitV47cldVzd1/Rcwd8rRm2\nZWiwGO4kKoNhNFQqFWxXtGWU1nP3uFzwer2Bv9QA30VVznWnwWK4k6hGGzMBoEdbJtCeUEi4A77R\nu/aycHfYrdAbePMwGhyGO4nKmGECgB5tGa3CLqgCgKvdGbiQDPieyJQ8KhUJCYn9fBdR7xjuJCqj\n0QSPx93t8XrAZSP3dmVcUAV8j9rr3nP3/Z7woioNBsOdRDXamAlb02l4vd5ur/tDTlEjd6eze8+9\n6TQAID2d4U4Dx3AnUWVkmHpcTAV8I3ev1wuPy9XLd8nTlT13u90X7nzcHg0Gw51EZexljjvgm+eu\npFE74B+5X+q5sy1DQ8FwJ9FotQnQ9zLHHfCtUHUpZI67n7u9o9vI3e12obW1mXPdaVAY7iSajPQx\nANDj1gOAr+fu7lDOxVSga+Se1H1mjN1+GhldM4qIBoLhTqIxds1xt/bSltEkJirm+al+V/bcAcDS\nUAfTmKtEqoikjOFOojEa/XPce++5K2kBE9Cz5w4AloaTMBozER+vEakqkiqGO4nGmGGCy+VCc4u9\nx3uaxATF3FfG78qeOwDUW05CrVZj9OixIlVFUhVSuN999904cuQIqqursWrVqh7vL168GE1NTSgt\nLUVpaSmWLFkS9kJJfnxz3BsgCEKP9xQ7W+aKnrvFUgsAGJs5ToSKSMrig+2gUqmwbt063HnnnbBY\nLDCbzSgqKkJVVVW3/d555x08/vjjESuU5Ke3+7j7aZIScdbR3Ot7cuV2OhGv0UAVr4bX43twiaWh\nDgCQaRonYmUkRUFH7jNmzEBNTQ1qa2vhdruxZcsWzJ8/Pxq1kcxlGE2wnu7ZbweUO3IHAE3Cpb77\n+fNn0drazJE7DVjQcDeZTKivrw98bbFYYDL1nJr1wAMPoKysDO+99x4yMzN7/VlLly6F2WyG2WyG\nXq8fQtkkdYmJSUhL1fc9clfoPHcAvcyYOYlMhjsNUNBwj4uL6/HalT3SnTt3Yty4cZg6dSp2796N\nt956q9efVVhYiLy8POTl5cHhcAyyZJKD/ua4A8qdLQOgl777SYzNHC9GSSRhQcPdYrFg7NhLV+oz\nMzPR2NjYbZ+Wlha4uu4BUlhYiOnTp4e5TJIb/zTI3m49APgCTonz3IGeI/dTllrodOkYNmy4GGWR\nRAUNd7PZjOzsbIwbNw4ajQYLFy5EUVFRt32MxkvLo+fNm9fjYivRlUYHFjD1HLmr1GrEazTKHbkn\nXDHXvWvGDC+q0kAEnS3T2dmJ5cuX46OPPoJarcYbb7yByspKPP/88/jyyy+xc+dOrFixAvPmzYPH\n40FLSwt+8IMfRKF0kjKjMRMdHU60tvZsz/nDTXnz3PtuywBAZuY4HKv+KtplkUQFDXcA+OCDD/DB\nBx90e+3ZZ58N/HrNmjVYs2ZNeCsjWRuXlY1T9Sd6fU+T5At35Y3c/RdUu4/cGxpPwev1cuROA8IV\nqiSKiRMn48SJo72+5+85K7Xnrrmi5+52u2CzNfKiKg0Iw52iLjk5FXpdOo6fONLr+0p8ODZw6Xiv\nvKAKAJaGWk6HpAFhuFPUTZxwDQD0Ge6BkTt77gH1Fs51p4FhuFPUTZwwGQBwvI+2jD/cOHK/xGI5\niRHDRyI1RRftskiiGO4UdRMmXANHcxPa2lp7fd9/QVFptx/wP5zkytv+Ar5VqgA4eqeQMdwp6iZO\nmIzjx3tvyQCX99yVdUHV6+mEx+3udeRe3zUdkhdVKVQMd4oqtToeWVdd3We/HVBuzx3wHXNvPfem\npka4XB0cuVPIGO4UVVeNnQCtVtvnNEhAuT13wHfMvY3cvV4vGhrqONedQsZwp6gKNlMGuHyeu/LC\n3e3s6LXnDgAn62qQfXVOlCsiqWK4U1RNnDAZLpcLp+pr+9zHH25KHLm7O3o+as/vq8pSGI2Z0Osz\nolwVSRHDnaJq4sRrcLKuGl5vZ5/7aBMT0en2BJ5GpCSuPnruAFBecRAAcP2106JZEkkUw52iauKE\nyf22ZABfz12Jo3bA14rqa+Rec/wI2tsv4LrreEttCo7hTlGTmqJDWpoBx4/3fTEVUOYj9vxcTmef\nPXevtxOVVWW4jiN3CgHDnaJmQggXU4GuR+wpNNzdzr577gBQ8VUJJk6YjKQkPriD+sdwp6jx33ag\nv2mQgH/krqwFTH6udmePu0JerrziINRqNabkTI1iVSRFDHeKmknZU2C3W3H23Jl+99MkJSru4dh+\nbqcT2j4uqAJAZVUZOjs7cT377hQEw52iQqVSI++mW1FS+nnQfdlz773nDgDt7Rdw/MQR9t0pKMmF\nu0YTj4ULvyZ2GTRAN1x/E0aNSsH+zz8Nui977n2P3AFf331KzlSoVOooVUVSJLlwX7z4dmz+y8/w\n7nurMWrUMLHLoRDl3zwXLlcHzF/uD7qv0nvuKrUaao2mz30qKg4iKWk4rp44OYqVkdRILtw3bPgE\nP3vqDXzzm7NwsOQlTJ9+tdglUQjyZ8/FwZLP4HReDLqvRsHh7m9H9dd3L/+qBADYd6d+SS7cBUHA\n73+/HXO+thoaTTz2f/Zb3HlnrthlUT8mjL8Go0dnYv9nwVsygC/YlNqWcfXxHNXLORw2WK0W9t2p\nX5ILd7/PPz+Cabn/B1VVFrz73ipMmXKV2CVRH/Jvnguv14vPDuwNaX9NYoJiL6gGRu79XFQFgLLD\nZkyfdjMSEvrvz5NySTbcAaCl5Rzm3f8rtLe7sPNv/wm9fpTYJVEv8m+ei6ojZWhtdYS0vzZRwSP3\ndv/TmPoP7V0fbsXIkcmYe/s3olEWSZCkwx0A6uvtmD/vVzAaU7B9x38gIaHvC1EUfQaDEddMui7k\nloxao4FKrYa7nT33/hwu/xLHjx/Bv83/fjTKIgmSfLgDgNlcjcWL1iI/fwoK//S42OXQZfJn3w4A\n+NcA+u2AMm/3C/T/kOwr/fX9tzFx4mTccP1NkS6LJEgW4Q4AW7fuxzO/eBvf+97XsWbNt8UuhwDE\nxcXhrju/hVP1taivPxHS92gU/KAO4NJxB2vLAMCne/6Gs2fP4Fvf5OidepJNuAPAr3/9Lv7nf/bi\n//76+3jggZvFLkfxCu55ADmTb8Dmv7wW8vdoFfygDgCB2y4Eu6AKAB0dTuz6YCtuzb8DBoMx0qWR\nxMgq3AFg6SP/jf37K/HWxp/i5pv5SDKxjBqVimWPPIWyw1/go092hPx9GgU/HBtAYH5/Xw/suNKO\nnZsBxGHeNxZGsCqSItmFe0eHG//2rd/AYnHg409+hfvuyxO7JEV6bOnPMHzYCLz0h+cH9H2Xeu7K\nvKA6kJ47ANhsDfjs8z345rzvYlwWF/TRJbILdwCw29twS/7T+OqrU9i+4z+wePFcsUtSlOuunY6C\nex7Au1v/jJN1NQP6XiU/HBsYWM/db91r/wVnhxO//a8NyEgfE6nSSGJCCve7774bR44cQXV1NVat\nWtXjfa1Wiy1btqC6uhoHDhxAVlZW2AsdKIfjLObe/h/Yu/cw/vzmSrz66o9gMCSLXZbsTcudhf/8\nxVpYrRa8venVAX+/P9SUe8tf379YQum5+9lsDXh69RIkJibhty+8geTk1EiVRxISNNxVKhXWrVuH\ngoICTJkyBd/5zneQk9O9l71kyRK0trYiOzsba9euxYsvvhixggfi/Pl2fOO+X+IPLxfhkaV3o7rm\nj/j5z/+dNxyLAK02AT9+7Of4/W/fwsWL5/GLZ38Mp7N94D+nK9SUOnIXBAFuZ0fIPXe/2pPHsOaZ\nHyEjfTTW/r+NuCX/DqhUsvyHOYUoPtgOM2bMQE1NDWprawEAW7Zswfz581FVVRXYZ/78+XjuuecA\nAFu3bsUrr7wSmWoHwe32YOWjWuCXAAAHsElEQVTKQrz66i688OIP8OvfLMLzv/wuDhw4io8/KsHB\ngzWor3fg1Ck7zp4NflMr8hkxYhRSU/WYMvkG3HjjTNw0/Rboden464638cc//Q4dHYMLZ43C57kD\nvmMPted+uYqvDuKZ536Cn678JX713DqcPm3B3z98D8drqlDfcBJWawM6Oz0RqJhiUdBwN5lMqK+v\nD3xtsVgwc+bMPvfp7OxEW1sbdDodmpubw1wusOOJxzFr7NjBfXMtYH+pCqq4OEyJU+Ha9JuAgisW\ngAi9f2sfLytH4DcgDoLg+2/glTgBKvtniG/zYEauFi+sWzP4z4mLQ5z5Uyz5xSOK/U3XHDMDV6cC\nf/rl4H6A81/wHI+HxxWPO/Oygbzsy94UEBfn++9lp5CizKYWcO3ypyP6GUHDPS6u558AQRAGvA8A\nLF26FMuWLQMA6PX6kIu8XEeHE+4wjT7i4gBVnK9+338BIA69HE7wnxWWimKYCvCnbRwEIM63xcV1\nAnFeCADcnb5tqASvFx0K7bkDgKZTgDo+6P+aQXQC8R1QxccBggqCVwVA1XUKu/60CrL/Uxuz2qMw\nGyzonyCLxYKxl42UMzMz0djY2Os+DQ0NUKvVSE5ORktLS4+fVVhYiMLCQgCA2WweVMEPvlo4qO8j\nIlKSoFdczGYzsrOzMW7cOGg0GixcuBBFRUXd9ikqKsLixYsBAAsWLMCePXsiUy0REYUk6Mi9s7MT\ny5cvx0cffQS1Wo033ngDlZWVeP755/Hll19i586d2LBhA95++21UV1ejpaUFCxdytRwRkZjiINJl\nK7PZjLw8rh4lIhqIULOTE2GJiGSI4U5EJEMMdyIiGWK4ExHJEMOdiEiGRJst09TUhLq6ukF9r16v\nh8PhCHNFsU+Jx63EYwaUedxKPGZg4MedlZWF9PT0kPYVpLaZzWbRa+Bx85h53DzmWD5utmWIiGSI\n4U5EJENqAM+JXcRglJSUiF2CKJR43Eo8ZkCZx63EYwYic9yiXVAlIqLIYVuGiEiGJBfuwR7WLQeZ\nmZnYs2cPKisrUVFRgRUrVgAAUlNT8fHHH+PYsWP4+OOPkZKSInKlkaFSqVBSUoKdO3cCAMaNG4cD\nBw7g2LFj2LJlCzQajcgVhldycjLee+89VFVVobKyErNmzVLEuV65ciUqKipQXl6OzZs3IyEhQZbn\nesOGDbDZbCgvLw+81t/5ffnll1FdXY2ysjLk5uYO6bNFnwoU6qZSqYSamhph/PjxgkajEQ4dOiTk\n5OSIXle4N6PRKOTm5goAhBEjRghHjx4VcnJyhBdffFFYtWqVAEBYtWqV8MILL4heayS2J554Qti0\naZOwc+dOAYDwzjvvCA8++KAAQFi/fr3w2GOPiV5jOLc333xTWLJkiQBA0Gg0QnJysuzP9ZgxY4QT\nJ04IiYmJgXO8ePFiWZ7rW2+9VcjNzRXKy8sDr/V1fgsKCoRdu3YJAISZM2cKBw4cGMpni3/woW6z\nZs0SPvzww8DXq1evFlavXi16XZHeduzYIdxxxx3CkSNHBKPRKAC+vwCOHDkiem3h3kwmk7B7927h\n61//eiDc7Xa7oFare/0zIPVt5MiRwokTJ3q8LvdzPWbMGOHUqVNCamqqoFarhZ07dwp33XWXbM91\nVlZWt3Dv6/y+9tprwsKFC3vdb6CbpNoyvT2s22QyiVhR5GVlZSE3NxfFxcXIyMiA1WoFAFit1pBX\nqUnJSy+9hKeffhperxcAoNPpcObMGXR2+h7OKrdzPmHCBNjtdvz5z39GSUkJCgsLMWzYMNmf68bG\nRvzud7/DqVOncPr0abS1teHgwYOyPteX6+v8hjPjJBXuoT6IWy6GDx+Obdu2YeXKlTh37pzY5UTc\nfffdh6ampm7TwuR+zuPj4zFt2jSsX78e06ZNw4ULF7B69Wqxy4q4lJQUzJ8/H+PHj8eYMWMwfPhw\nFBQU9NhPTuc6FOH88y6pcA/lYd1yER8fj23btmHTpk3Yvn07AMBms8FoNAIAjEYjmpqaxCwx7PLz\n8zFv3jzU1tZiy5YtuP322/HSSy8hJSUFarUagPzOucVigcViwRdffAEA2Lp1K6ZNmyb7c33HHXeg\ntrYWDocDHo8Hf/3rX3HzzTfL+lxfrq/zG86Mk1S4h/KwbrnYsGEDqqqqsHbt2sBrlz+IfPHixXj/\n/ffFKi8i1qxZg7Fjx2L8+PFYuHAh9uzZg+9973vYu3cvFixYAEB+x22z2VBfX49JkyYBAObOnYvK\nykrZn+tTp05h1qxZSEpKAnDpuOV8ri/X1/ktKirCokWLAAAzZ85EW1tboH0zGKJfbBjIVlBQIBw9\nelSoqakR1qxZI3o9kdjy8/MFQRCEsrIyobS0VCgtLRUKCgqEtLQ0Yffu3cKxY8eE3bt3C6mpqaLX\nGqltzpw5gQuq48ePF4qLi4Xq6mrh3XffFbRarej1hXObOnWqYDabhbKyMmH79u1CSkqKIs71c889\nJ1RVVQnl5eXCxo0bBa1WK8tzvXnzZqGxsVFwuVxCfX298MMf/rDf8/vKK68INTU1wuHDh4Xp06cP\n+nO5QpWISIYk1ZYhIqLQMNyJiGSI4U5EJEMMdyIiGWK4ExHJEMOdiEiGGO5ERDLEcCcikqH/BRQI\nAK9OryctAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "xpts = np.linspace(1,2e2,1e2)\n",
    "Z = [square((x-100)/40) for x in xpts]\n",
    "plot(Z);\n",
    "w = 5\n",
    "gpt = [1/w*np.exp(-x**2/(2*w**2)) for x in xpts]\n",
    "ypts = [quad(lambda x: 1/w*np.exp(-(x_-x)**2/(2*w**2))*square((x-100)/40),0.0,1.0e3) for x_ in xpts]\n",
    "plot(gpt)\n",
    "plot(ypts)\n",
    "\n",
    "#ypts = [w_0**2*dblquad(lambda x, y: sp.jv(1,2*np.pi*D*np.sqrt(x**2+y**2))/np.sqrt(x**2+y**2)*np.exp(-np.pi**2*w_0**2*((x_-x)**2 + y**2)), -np.inf, np.inf, lambda x: -np.inf, lambda x: np.inf)[0] for x_ in xpts]\n",
    "#plot(xpts,[square((x-6)/3,0) for x in xpts])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### numerical convolution"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 259,
   "metadata": {},
   "outputs": [],
   "source": [
    "from scipy.signal import convolve"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 289,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\ProgramData\\Anaconda3\\lib\\site-packages\\ipykernel_launcher.py:1: DeprecationWarning: object of type <class 'float'> cannot be safely interpreted as an integer.\n",
      "  \"\"\"Entry point for launching an IPython kernel.\n",
      "C:\\ProgramData\\Anaconda3\\lib\\site-packages\\scipy\\signal\\signaltools.py:375: FutureWarning: Conversion of the second argument of issubdtype from `complex` to `np.complexfloating` is deprecated. In future, it will be treated as `np.complex128 == np.dtype(complex).type`.\n",
      "  complex_result = (np.issubdtype(in1.dtype, complex) or\n",
      "C:\\ProgramData\\Anaconda3\\lib\\site-packages\\scipy\\signal\\signaltools.py:376: FutureWarning: Conversion of the second argument of issubdtype from `complex` to `np.complexfloating` is deprecated. In future, it will be treated as `np.complex128 == np.dtype(complex).type`.\n",
      "  np.issubdtype(in2.dtype, complex))\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x16ae420c320>]"
      ]
     },
     "execution_count": 289,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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7EAdQuIvEmFFADWbA26/zLxRNqoaPwl0kxoym80qZuNOnqNpQDadPkQWqQDfuCBOFu0gM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\nFxFxIIW7iIgDKdxFRBzo/wOAZFbejoTQMAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "xpts = np.linspace(-2e2,2e2,1e3)\n",
    "Z = [square((x-100)/40) for x in xpts]\n",
    "plot(xpts,Z);\n",
    "w = 20\n",
    "gpt = [1/w*np.exp(-x**2/(2*w**2)) for x in xpts]\n",
    "ypts = convolve(gpt, Z,'same') / 5\n",
    "plot(xpts,gpt)\n",
    "plot(xpts,ypts,color='r')\n",
    "\n",
    "#ypts = [w_0**2*dblquad(lambda x, y: sp.jv(1,2*np.pi*D*np.sqrt(x**2+y**2))/np.sqrt(x**2+y**2)*np.exp(-np.pi**2*w_0**2*((x_-x)**2 + y**2)), -np.inf, np.inf, lambda x: -np.inf, lambda x: np.inf)[0] for x_ in xpts]\n",
    "#plot(xpts,[square((x-6)/3,0) for x in xpts])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "sq conv test"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 198,
   "metadata": {},
   "outputs": [],
   "source": [
    "def square2D(x,y):\n",
    "    if abs(x)<0.5:\n",
    "        if abs(y)<0.5:\n",
    "            return 1.0\n",
    "    return 0.0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 196,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\ProgramData\\Anaconda3\\lib\\site-packages\\ipykernel_launcher.py:1: DeprecationWarning: object of type <class 'float'> cannot be safely interpreted as an integer.\n",
      "  \"\"\"Entry point for launching an IPython kernel.\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<matplotlib.image.AxesImage at 0x16aa92c3a58>"
      ]
     },
     "execution_count": 196,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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AiEAAMCIQAIwIBAAjAgHAiEAAMCIQAIwIBAAjAgHAiEAAMCIQAIwIBACjuPxFqd7eXv38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\nQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "xpts = np.linspace(1,1e3,2e1)\n",
    "ypts = xpts[:]\n",
    "X, Y = np.meshgrid(xpts,ypts)\n",
    "Z = np.zeros(X.shape)\n",
    "Zp = Z[:]\n",
    "for i in range(len(X)):\n",
    "    for j in range(len(X[0])):\n",
    "        Z[i,j] = square((X[i,j]-100)/40,(Y[i,j]-100)/40)\n",
    "imshow(Z)\n",
    "#ypts = [w_0**2*dblquad(lambda x, y: sp.jv(1,2*np.pi*D*np.sqrt(x**2+y**2))/np.sqrt(x**2+y**2)*np.exp(-np.pi**2*w_0**2*((x_-x)**2 + y**2)), -np.inf, np.inf, lambda x: -np.inf, lambda x: np.inf)[0] for x_ in xpts]\n",
    "#plot(xpts,[square((x-6)/3,0) for x in xpts])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 197,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "................................................................................................................................................................................................................................................................................................................................................................................................................"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<matplotlib.image.AxesImage at 0x16aa948ee80>"
      ]
     },
     "execution_count": 197,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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AiEAAMCIQAIwIBAAjAgHAiEAAMCIQAIwIBAAjAgHAiEAAMCIQAIwIBACjuPxFqd7eXv38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\nQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "for i in range(len(X)):\n",
    "    for j in range(len(X[0])):\n",
    "        print('.',end='')\n",
    "        Zp[i,j] = dblquad(lambda x, y: np.exp(-(x**2+y**2)/0.1)*square((X[i,j]-x-100)/40,(Y[i,j]-y-100)/40),0,1e3,lambda x: 0, lambda x: 1e3)[0]\n",
    "imshow(Zp)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 2d convolve numeric"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 290,
   "metadata": {},
   "outputs": [],
   "source": [
    "from scipy.signal import convolve2d"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 291,
   "metadata": {},
   "outputs": [],
   "source": [
    "def square2D(x,y):\n",
    "    if abs(x)<0.5:\n",
    "        if abs(y)<0.5:\n",
    "            return 1.0\n",
    "    return 0.0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 362,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\ProgramData\\Anaconda3\\lib\\site-packages\\ipykernel_launcher.py:1: DeprecationWarning: object of type <class 'float'> cannot be safely interpreted as an integer.\n",
      "  \"\"\"Entry point for launching an IPython kernel.\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<matplotlib.image.AxesImage at 0x16b13ca6d30>"
      ]
     },
     "execution_count": 362,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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TUCr1CRgL130dtQ0bNuRb3/pWDhw4kAULFmTz5s1jOS6A66I2AaVSn4BrMerrqCXJT3/6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\nYII=\n",
      "text/plain": [
       "<Figure size 1080x360 with 3 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "xpts = np.linspace(1,1e3,1e2)\n",
    "ypts = xpts[:]\n",
    "X, Y = np.meshgrid(xpts,ypts)\n",
    "Z = np.zeros(X.shape)\n",
    "Zp = np.zeros(X.shape)\n",
    "for i in range(len(X)):\n",
    "    for j in range(len(X[0])):\n",
    "        Z[i,j] = square2D((X[i,j]-400)/100,(Y[i,j]-400)/50)\n",
    "f, ax = subplots(1,3,figsize=(15,5))\n",
    "w = 30\n",
    "for i in range(len(X)):\n",
    "    for j in range(len(X[0])):\n",
    "        Zp[i,j] = np.exp(-((X[i,j]-4e2)**2+(Y[i,j]-4e2)**2)/w**2)\n",
    "\n",
    "Zc = convolve2d(Zp,Z,'same')\n",
    "ax[0].imshow(Z)\n",
    "ax[1].imshow(Zp)\n",
    "ax[2].imshow(Zc)\n",
    "#ypts = [w_0**2*dblquad(lambda x, y: sp.jv(1,2*np.pi*D*np.sqrt(x**2+y**2))/np.sqrt(x**2+y**2)*np.exp(-np.pi**2*w_0**2*((x_-x)**2 + y**2)), -np.inf, np.inf, lambda x: -np.inf, lambda x: np.inf)[0] for x_ in xpts]\n",
    "#plot(xpts,[square((x-6)/3,0) for x in xpts])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Real problem"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 446,
   "metadata": {},
   "outputs": [],
   "source": [
    "from fitters.Gaussian import gaussian_2d"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 609,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "9749.22760398087\n",
      "9749.234982772941\n",
      "9749.234982772927\n",
      "9749.234982772912\n",
      "9749.234982772923\n",
      "9749.234982772921\n",
      "9749.234982772914\n",
      "9749.234982768932\n",
      "9749.234980647565\n",
      "9749.234793314246\n"
     ]
    }
   ],
   "source": [
    "npts = 100\n",
    "l = 2e-1\n",
    "xpts = np.linspace(-l,l,npts)\n",
    "ypts = np.linspace(-l,l,npts)\n",
    "X, Y = np.meshgrid(xpts,ypts)\n",
    "maxes = []\n",
    "nplts = 10\n",
    "diameters = np.linspace(1e-3,100,nplts);\n",
    "waists = np.linspace(4,40,nplts)\n",
    "convIms = []\n",
    "D = 30\n",
    "#w = 15\n",
    "#for D in diameters:\n",
    "for w in waists:\n",
    "    #print('.',end='')\n",
    "    jincIm = np.zeros(X.shape)\n",
    "    for i in range(len(X)):\n",
    "        for j in range(len(X[0])):\n",
    "            x = X[i,j]\n",
    "            y = Y[i,j]\n",
    "            jincIm[i,j] = D*sp.jv(1,2*np.pi*D*np.sqrt(x**2+y**2))/np.sqrt(x**2+y**2)\n",
    "    gaussIm = np.zeros(X.shape)\n",
    "    for i in range(len(X)):\n",
    "        for j in range(len(X[0])):\n",
    "            x = X[i,j]\n",
    "            y = Y[i,j]\n",
    "            gaussIm[i,j] = w*np.exp(-np.pi**2*w**2*(x**2+y**2))\n",
    "    print(sum(gaussIm.flatten()**2))\n",
    "    convIm = convolve2d(jincIm,gaussIm,'same')\n",
    "    convIms.append(convIm)\n",
    "    maxes.append(max(convIm.flatten())**2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 670,
   "metadata": {},
   "outputs": [],
   "source": [
    "import Miscellaneous as misc"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 675,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "37600.0 143000000.0 4.97e+16\n",
      "497000.0 143000000.0 6.74e+17\n",
      "1860000.0 143000000.0 2.62e+18\n",
      "4030000.0 143000000.0 5.88e+18\n",
      "6640000.0 143000000.0 9.77e+18\n",
      "9670000.0 143000000.0 1.38e+19\n",
      "13400000.0 143000000.0 1.8e+19\n",
      "18000000.0 143000000.0 2.27e+19\n",
      "23300000.0 143000000.0 2.76e+19\n",
      "29000000.0 143000000.0 3.23e+19\n",
      "35300000.0 143000000.0 3.66e+19\n",
      "42300000.0 143000000.0 4.03e+19\n",
      "50000000.0 143000000.0 4.37e+19\n",
      "58400000.0 143000000.0 4.67e+19\n",
      "67300000.0 143000000.0 4.93e+19\n",
      "76800000.0 143000000.0 5.15e+19\n",
      "87000000.0 143000000.0 5.31e+19\n",
      "97900000.0 143000000.0 5.44e+19\n",
      "109000000.0 143000000.0 5.54e+19\n",
      "122000000.0 143000000.0 5.62e+19\n",
      "134000000.0 143000000.0 5.68e+19\n",
      "148000000.0 143000000.0 5.72e+19\n",
      "162000000.0 143000000.0 5.74e+19\n",
      "176000000.0 143000000.0 5.76e+19\n",
      "192000000.0 143000000.0 5.78e+19\n",
      "207000000.0 143000000.0 5.79e+19\n",
      "224000000.0 143000000.0 5.79e+19\n",
      "241000000.0 143000000.0 5.79e+19\n",
      "259000000.0 143000000.0 5.8e+19\n",
      "278000000.0 143000000.0 5.8e+19\n",
      "297000000.0 143000000.0 5.8e+19\n",
      "316000000.0 143000000.0 5.8e+19\n",
      "337000000.0 143000000.0 5.8e+19\n",
      "358000000.0 143000000.0 5.8e+19\n",
      "379000000.0 143000000.0 5.8e+19\n",
      "402000000.0 143000000.0 5.8e+19\n",
      "425000000.0 143000000.0 5.79e+19\n",
      "448000000.0 143000000.0 5.79e+19\n",
      "472000000.0 143000000.0 5.79e+19\n",
      "497000000.0 143000000.0 5.79e+19\n"
     ]
    }
   ],
   "source": [
    "npts = 401\n",
    "l = 1e-1\n",
    "xpts = np.linspace(-l,l,npts)\n",
    "ypts = np.linspace(-l,l,npts)\n",
    "X, Y = np.meshgrid(xpts,ypts)\n",
    "maxes_d = []\n",
    "nplts = 40\n",
    "diameters = np.linspace(1,40,nplts);\n",
    "waists = np.linspace(4,40,nplts)\n",
    "convIms_d = []\n",
    "#D = 30\n",
    "w = 15\n",
    "for D in diameters:\n",
    "#for w in waists:\n",
    "    #print('.',end='')\n",
    "    jincIm = np.zeros(X.shape)\n",
    "    for i in range(len(X)):\n",
    "        for j in range(len(X[0])):\n",
    "            x = X[i,j]\n",
    "            y = Y[i,j]\n",
    "            if abs(x) < 1e-5 and abs(y) < 1e-5:\n",
    "                jincIm[i,j] = 1/2\n",
    "            else:\n",
    "                jincIm[i,j] = D*sp.jv(1,2*np.pi*D*np.sqrt(x**2+y**2))/(2*np.pi*np.sqrt(x**2+y**2))\n",
    "    gaussIm = np.zeros(X.shape)\n",
    "    for i in range(len(X)):\n",
    "        for j in range(len(X[0])):\n",
    "            x = X[i,j]\n",
    "            y = Y[i,j]\n",
    "            gaussIm[i,j] = w**2*np.exp(-np.pi**2*w**2*(x**2+y**2))\n",
    "    #figure()\n",
    "    #imshow(jincIm)\n",
    "    #colorbar()\n",
    "    convIm = convolve2d(jincIm,gaussIm,'same')\n",
    "    print(misc.round_sig(sum(jincIm.flatten()**2)),misc.round_sig(sum(gaussIm.flatten()**2)), misc.round_sig(sum(convIm.flatten()**2)))\n",
    "    #f, ax = subplots(1,3)\n",
    "    #ax[0].imshow(jincIm)\n",
    "    #ax[0].set_title('jinc')\n",
    "    #ax[1].imshow(gaussIm)\n",
    "    #ax[2].imshow(convIm)\n",
    "    \n",
    "    convIms_d.append(convIm)\n",
    "    maxes_d.append(max(convIm.flatten())**2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### fitting..."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 517,
   "metadata": {},
   "outputs": [],
   "source": [
    "import scipy.optimize as opt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "guess = [1e6,0,0,3e-2,3e-2,0,0]\n",
    "im = convIms[0]\n",
    "Z_guess = np.reshape(gaussian_2d.f((X,Y),*guess),X.shape)\n",
    "try:\n",
    "    vals, cov = opt.curve_fit(gaussian_2d.f,(X,Y),im.flatten(), p0=guess);\n",
    "except RuntimeError:\n",
    "    print('fail')\n",
    "    vals = guess\n",
    "    pass\n",
    "Z = np.reshape(gaussian_2d.f((X,Y),*vals),X.shape)\n",
    "imshow(Z_guess)\n",
    "colorbar()\n",
    "figure()\n",
    "imshow(Z)\n",
    "title('fit')\n",
    "colorbar()\n",
    "figure()\n",
    "imshow(im)\n",
    "colorbar()\n",
    "print(vals)\n",
    "figure()\n",
    "imshow(im-Z)\n",
    "colorbar()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 565,
   "metadata": {},
   "outputs": [],
   "source": [
    "centered_gaussian = lambda C, A, sx, sy, o, t: gaussian_2d.f(C,A,1,1,sx,sy,o,t)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 566,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0,1,2,3,4,5,6,7,"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\ProgramData\\Anaconda3\\lib\\site-packages\\scipy\\optimize\\minpack.py:779: OptimizeWarning: Covariance of the parameters could not be estimated\n",
      "  category=OptimizeWarning)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "8,9,10,11,12,13,14,15,16,17,18,19,"
     ]
    },
    {
     "data": {
      "image/png": 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E86+Cm1/3iaYagu1ChK9vUplqBTNddbLhNCPn88q3/Couf+1/wGff/1e49Z+2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\nCfkhKBBFC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jHau55R7NzGH9hxNFonjlExrCkLjPoFPO45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soQ+vxhgdFxJBiGJOJdxaPUP3WIXPVXqcvnaehVrM7XNn+eGpb3Eq2KKaVaQ6KL5iH15NfOP6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\n",
      "text/plain": [
       "<Figure size 1440x720 with 80 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "f, ax = subplots(4,len(convIms), figsize=(20,10))\n",
    "fitList = []\n",
    "for i, im in enumerate(convIms):\n",
    "    print(i,end=',')\n",
    "    guess = [1e6,3e-2/np.sqrt(i+1),3e-2/np.sqrt(i+1),0,0]\n",
    "    Z_guess = np.reshape(centered_gaussian((X,Y),*guess),X.shape)\n",
    "    try:\n",
    "        vals, cov = opt.curve_fit(centered_gaussian,(X,Y),im.flatten(), p0=guess);\n",
    "    except RuntimeError:\n",
    "        print('fail!')\n",
    "        vals = guess\n",
    "    fitList.append(vals)\n",
    "    Z = np.reshape(centered_gaussian((X,Y),*vals),X.shape)\n",
    "    ax[0,i].imshow(Z)\n",
    "    ax[1,i].imshow(im)\n",
    "    ax[2,i].imshow(Z_guess)\n",
    "    ax[3,i].imshow(Z-im)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 564,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x16b1ddcd898>]"
      ]
     },
     "execution_count": 564,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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tb0dne9f0jvb2a+btwDh3Bbz8/bp9+Hv6+8LNxxvOzj8d6TxX34C6cgO0mcdR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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot([fit[4] for fit in fitList])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Increasing Waist"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 664,
   "metadata": {},
   "outputs": [
    {
     "ename": "ValueError",
     "evalue": "x and y must have same first dimension, but have shapes (25,) and (10,)",
     "output_type": "error",
     "traceback": [
      "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[1;31mValueError\u001b[0m                                Traceback (most recent call last)",
      "\u001b[1;32m<ipython-input-664-7c1b1084926d>\u001b[0m in \u001b[0;36m<module>\u001b[1;34m()\u001b[0m\n\u001b[0;32m     10\u001b[0m     \u001b[0mtotals\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mappend\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0msum\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mim\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mflatten\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m**\u001b[0m\u001b[1;36m2\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m     11\u001b[0m \u001b[0mfigure\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mfigsize\u001b[0m\u001b[1;33m=\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;36m20\u001b[0m\u001b[1;33m,\u001b[0m\u001b[1;36m10\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m---> 12\u001b[1;33m \u001b[0mplot\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mwaists\u001b[0m\u001b[1;33m/\u001b[0m\u001b[0mD\u001b[0m\u001b[1;33m,\u001b[0m\u001b[0mmaxes\u001b[0m\u001b[1;33m/\u001b[0m\u001b[0mmax\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mmaxes\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mlabel\u001b[0m\u001b[1;33m=\u001b[0m\u001b[1;34m'Maximum Light'\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m     13\u001b[0m \u001b[0mplot\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mwaists\u001b[0m\u001b[1;33m/\u001b[0m\u001b[0mD\u001b[0m\u001b[1;33m,\u001b[0m\u001b[0mtotals\u001b[0m\u001b[1;33m/\u001b[0m\u001b[0mmax\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mtotals\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mlabel\u001b[0m\u001b[1;33m=\u001b[0m\u001b[1;34m'Total Light'\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m     14\u001b[0m \u001b[0mlegend\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;32mC:\\ProgramData\\Anaconda3\\lib\\site-packages\\matplotlib\\pyplot.py\u001b[0m in \u001b[0;36mplot\u001b[1;34m(*args, **kwargs)\u001b[0m\n\u001b[0;32m   3356\u001b[0m                       mplDeprecation)\n\u001b[0;32m   3357\u001b[0m     \u001b[1;32mtry\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m-> 3358\u001b[1;33m         \u001b[0mret\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0max\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mplot\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m*\u001b[0m\u001b[0margs\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;33m**\u001b[0m\u001b[0mkwargs\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m   3359\u001b[0m     \u001b[1;32mfinally\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m   3360\u001b[0m         \u001b[0max\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0m_hold\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mwashold\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;32mC:\\ProgramData\\Anaconda3\\lib\\site-packages\\matplotlib\\__init__.py\u001b[0m in \u001b[0;36minner\u001b[1;34m(ax, *args, **kwargs)\u001b[0m\n\u001b[0;32m   1853\u001b[0m                         \u001b[1;34m\"the Matplotlib list!)\"\u001b[0m \u001b[1;33m%\u001b[0m \u001b[1;33m(\u001b[0m\u001b[0mlabel_namer\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mfunc\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0m__name__\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m,\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m   1854\u001b[0m                         RuntimeWarning, stacklevel=2)\n\u001b[1;32m-> 1855\u001b[1;33m             \u001b[1;32mreturn\u001b[0m \u001b[0mfunc\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0max\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;33m*\u001b[0m\u001b[0margs\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;33m**\u001b[0m\u001b[0mkwargs\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m   1856\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m   1857\u001b[0m         inner.__doc__ = _add_data_doc(inner.__doc__,\n",
      "\u001b[1;32mC:\\ProgramData\\Anaconda3\\lib\\site-packages\\matplotlib\\axes\\_axes.py\u001b[0m in \u001b[0;36mplot\u001b[1;34m(self, *args, **kwargs)\u001b[0m\n\u001b[0;32m   1525\u001b[0m         \u001b[0mkwargs\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mcbook\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mnormalize_kwargs\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mkwargs\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0m_alias_map\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m   1526\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m-> 1527\u001b[1;33m         \u001b[1;32mfor\u001b[0m \u001b[0mline\u001b[0m \u001b[1;32min\u001b[0m \u001b[0mself\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0m_get_lines\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m*\u001b[0m\u001b[0margs\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;33m**\u001b[0m\u001b[0mkwargs\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m   1528\u001b[0m             \u001b[0mself\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0madd_line\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mline\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m   1529\u001b[0m             \u001b[0mlines\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mappend\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mline\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;32mC:\\ProgramData\\Anaconda3\\lib\\site-packages\\matplotlib\\axes\\_base.py\u001b[0m in \u001b[0;36m_grab_next_args\u001b[1;34m(self, *args, **kwargs)\u001b[0m\n\u001b[0;32m    404\u001b[0m                 \u001b[0mthis\u001b[0m \u001b[1;33m+=\u001b[0m \u001b[0margs\u001b[0m\u001b[1;33m[\u001b[0m\u001b[1;36m0\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m,\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    405\u001b[0m                 \u001b[0margs\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0margs\u001b[0m\u001b[1;33m[\u001b[0m\u001b[1;36m1\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m--> 406\u001b[1;33m             \u001b[1;32mfor\u001b[0m \u001b[0mseg\u001b[0m \u001b[1;32min\u001b[0m \u001b[0mself\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0m_plot_args\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mthis\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mkwargs\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m    407\u001b[0m                 \u001b[1;32myield\u001b[0m \u001b[0mseg\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    408\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;32mC:\\ProgramData\\Anaconda3\\lib\\site-packages\\matplotlib\\axes\\_base.py\u001b[0m in \u001b[0;36m_plot_args\u001b[1;34m(self, tup, kwargs)\u001b[0m\n\u001b[0;32m    381\u001b[0m             \u001b[0mx\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0my\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mindex_of\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mtup\u001b[0m\u001b[1;33m[\u001b[0m\u001b[1;33m-\u001b[0m\u001b[1;36m1\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    382\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m--> 383\u001b[1;33m         \u001b[0mx\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0my\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mself\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0m_xy_from_xy\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mx\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0my\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m    384\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    385\u001b[0m         \u001b[1;32mif\u001b[0m \u001b[0mself\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mcommand\u001b[0m \u001b[1;33m==\u001b[0m \u001b[1;34m'plot'\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;32mC:\\ProgramData\\Anaconda3\\lib\\site-packages\\matplotlib\\axes\\_base.py\u001b[0m in \u001b[0;36m_xy_from_xy\u001b[1;34m(self, x, y)\u001b[0m\n\u001b[0;32m    240\u001b[0m         \u001b[1;32mif\u001b[0m \u001b[0mx\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mshape\u001b[0m\u001b[1;33m[\u001b[0m\u001b[1;36m0\u001b[0m\u001b[1;33m]\u001b[0m \u001b[1;33m!=\u001b[0m \u001b[0my\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mshape\u001b[0m\u001b[1;33m[\u001b[0m\u001b[1;36m0\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    241\u001b[0m             raise ValueError(\"x and y must have same first dimension, but \"\n\u001b[1;32m--> 242\u001b[1;33m                              \"have shapes {} and {}\".format(x.shape, y.shape))\n\u001b[0m\u001b[0;32m    243\u001b[0m         \u001b[1;32mif\u001b[0m \u001b[0mx\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mndim\u001b[0m \u001b[1;33m>\u001b[0m \u001b[1;36m2\u001b[0m \u001b[1;32mor\u001b[0m \u001b[0my\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mndim\u001b[0m \u001b[1;33m>\u001b[0m \u001b[1;36m2\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    244\u001b[0m             raise ValueError(\"x and y can be no greater than 2-D, but have \"\n",
      "\u001b[1;31mValueError\u001b[0m: x and y must have same first dimension, but have shapes (25,) and (10,)"
     ]
    },
    {
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orV7Do48+Wv75n/+54+d6rbn//vvL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\nAACguv8FRQs8ySSj2/oAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 1800x576 with 24 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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vWL58+Zz/i7as+bBqnb0//vGPxVtvvVXs37+/2L9/f7Fjx445n9my5sOqdfb+\ne4lEljV7azpn76c//Wlx8ODB4pVXXiluueWWOZ/ZsubLqnX+2traihdeeKF4+eWXi/379xc33HDD\nnM9sWR/19dRTTxVjY2PF+++/X4yOjhbf+ta3ijvuuKO44447Jvb8/Oc/L4aHh4tXXnll2n/mbPjP\nLwAAAAD4GKvrM4kAAAAA+GgQiQAAAAAQiQAAAAAQiQAAAACISAQAAABARCIAAAAAIhIBAAAAEJEI\nAAAAgCT/A2q7GpRr3gBbAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 1440x720 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "f, ax = subplots(2,int(nplts/2), figsize=(25, 8))\n",
    "minv = min(arr(convIms).flatten())**2\n",
    "maxv = max(arr(convIms).flatten())**2\n",
    "maxes = []\n",
    "totals = []\n",
    "for im, a in zip(convIms, ax.flatten()):\n",
    "    a.imshow( im**2 )\n",
    "    a.axis( 'off')\n",
    "    maxes.append(max(im.flatten())**2)\n",
    "    totals.append(sum(im.flatten())**2)\n",
    "figure(figsize=(20,10))\n",
    "plot(waists/D,maxes/max(maxes), label='Maximum Light')\n",
    "plot(waists/D,totals/max(totals), label='Total Light')\n",
    "legend()\n",
    "xlabel('w/D')\n",
    "grid(alpha=0.1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### increasing Aperture"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 667,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "25"
      ]
     },
     "execution_count": 667,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "len(diameters)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 681,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.0667 : 403000000000.0\n",
      "0.133 : 6370000000000.0\n",
      "0.2 : 31500000000000.0\n",
      "0.267 : 96600000000000.0\n",
      "0.333 : 227000000000000.0\n",
      "0.4 : 448000000000000.0\n",
      "0.467 : 785000000000000.0\n",
      "0.533 : 1260000000000000.0\n",
      "0.6 : 1870000000000000.0\n",
      "0.667 : 2640000000000000.0\n",
      "0.733 : 3550000000000000.0\n",
      "0.8 : 4580000000000000.0\n",
      "0.867 : 5720000000000000.0\n",
      "0.933 : 6930000000000000.0\n",
      "1.0 : 8190000000000000.0\n",
      "1.07 : 9470000000000000.0\n",
      "1.13 : 1.07e+16\n",
      "1.2 : 1.19e+16\n",
      "1.27 : 1.31e+16\n",
      "1.33 : 1.42e+16\n",
      "1.4 : 1.51e+16\n",
      "1.47 : 1.6e+16\n",
      "1.53 : 1.68e+16\n",
      "1.6 : 1.75e+16\n",
      "1.67 : 1.8e+16\n",
      "1.73 : 1.85e+16\n",
      "1.8 : 1.89e+16\n",
      "1.87 : 1.93e+16\n",
      "1.93 : 1.95e+16\n",
      "2.0 : 1.97e+16\n",
      "2.07 : 1.99e+16\n",
      "2.13 : 2.01e+16\n",
      "2.2 : 2.02e+16\n",
      "2.27 : 2.02e+16\n",
      "2.33 : 2.03e+16\n",
      "2.4 : 2.03e+16\n",
      "2.47 : 2.04e+16\n",
      "2.53 : 2.04e+16\n",
      "2.6 : 2.04e+16\n",
      "2.67 : 2.04e+16\n"
     ]
    }
   ],
   "source": [
    "for d, m in zip(diameters, maxes):\n",
    "    print(misc.round_sig(d/w),':',misc.round_sig(m))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 683,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.9656862745098039"
      ]
     },
     "execution_count": 683,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "1.97/2.04"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 676,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 1800x576 with 40 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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uXqeDmyJkTUkxOiYA4D6iEAIAAKpRo6y6dG2iFi2qy8XFWStXblPPHpM0f/5f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\nVsmSBVX3w+G6deu+6RzAOCdnZ3WZPlG5ixRWZK9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JierbJ9J0CvDK0mXKKJ+IcDm7uCjK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      "text/plain": [
       "<Figure size 1440x720 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "f, ax = subplots(5,int(nplts/5), figsize=(25, 8))\n",
    "minv = min(arr(convIms_d).flatten())**2\n",
    "maxv = max(arr(convIms_d).flatten())**2\n",
    "maxes = []\n",
    "totals = []\n",
    "for im, a in zip(convIms_d, ax.flatten()):\n",
    "    a.imshow( im**2, vmin=minv, vmax=maxv )\n",
    "    a.axis( 'off' )\n",
    "    maxes.append(max(im.flatten()**2))\n",
    "    totals.append(sum(im.flatten()**2))\n",
    "figure(figsize=(20,10))\n",
    "plot(diameters/w,maxes/max(maxes), label='Maximum Light')\n",
    "plot(diameters/w,totals/max(totals), label='Total Light')\n",
    "legend()\n",
    "xlabel('D/w')\n",
    "grid(alpha=0.1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 341,
   "metadata": {},
   "outputs": [],
   "source": [
    "from numpy import array as arr"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 119,
   "metadata": {},
   "outputs": [],
   "source": [
    "xpts = np.linspace(1e-5,1.5e1,40)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 114,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\ProgramData\\Anaconda3\\lib\\site-packages\\scipy\\integrate\\quadpack.py:364: IntegrationWarning: The integral is probably divergent, or slowly convergent.\n",
      "  warnings.warn(msg, IntegrationWarning)\n"
     ]
    }
   ],
   "source": [
    "ypts = [w_0**2*dblquad(lambda x, y: sp.jv(1,2*np.pi*D*np.sqrt(x**2+y**2))/np.sqrt(x**2+y**2)*np.exp(-np.pi**2*w_0**2*((x_-x)**2 + y**2)), -np.inf, np.inf, lambda x: -np.inf, lambda x: np.inf)[0] for x_ in xpts]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " real thing"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "val = dblquad(lambda x, y: x*y, 0, 0.5, lambda x: 0, lambda x: 1-2*x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 112,
   "metadata": {},
   "outputs": [],
   "source": [
    "w_0 = 0.5\n",
    "D = 10"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 113,
   "metadata": {},
   "outputs": [],
   "source": [
    "xpts = np.linspace(1e-5,1.5e1,40)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 114,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\ProgramData\\Anaconda3\\lib\\site-packages\\scipy\\integrate\\quadpack.py:364: IntegrationWarning: The integral is probably divergent, or slowly convergent.\n",
      "  warnings.warn(msg, IntegrationWarning)\n"
     ]
    }
   ],
   "source": [
    "ypts = [w_0**2*dblquad(lambda x, y: sp.jv(1,2*np.pi*D*np.sqrt(x**2+y**2))/np.sqrt(x**2+y**2)*np.exp(-np.pi**2*w_0**2*((x_-x)**2 + y**2)), -np.inf, np.inf, lambda x: -np.inf, lambda x: np.inf)[0] for x_ in xpts]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 118,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x16aa0be92e8>]"
      ]
     },
     "execution_count": 118,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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ToONIkiRJkhQ4S6Qazvsile71h0dTWFjAJcP/EHQUSZIkSZICZ4lUwy0FtuKS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\n",
      "text/plain": [
       "<Figure size 1440x360 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "figure(figsize=(20,5))\n",
    "#xpts = np.linspace(1e-5,2e1,1e6)\n",
    "grid(alpha=0.1)\n",
    "plot(xpts,ypts,'r')\n",
    "plot(xpts,0.1*(sp.jv(1,xpts)/xpts)**2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Calculating expected strehl ratio"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Assuming that we are clipping at the 1/e^2 gaussian waist, the relevant ratio is D/w=2 in the above charts. Therefore, the expected depth is $0.965\\times$ the depth we'd get for an unclipped gaussian with the focal length we observe. What is expected from the perfect gaussian can be calculated by using the measured waist, figuring out how much loss we expect from the sill and other optics, and properly normalizing the shrunk gaussian. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 686,
   "metadata": {},
   "outputs": [],
   "source": [
    "power = 3e-3*0.9"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$\n",
    "I=I_0 \\exp\\{-2r^2/w^2\\}=P\\big( \\frac{1}{w}\\sqrt{\\frac{2}{\\pi}}\\big)^2\\exp\\{-2r^2/w^2\\}=\\frac{2P}{w^2\\pi}\\exp\\{-2r^2/w^2\\}\\\\\n",
    "I_0 = \\frac{2P}{\\pi w^2} \n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 694,
   "metadata": {},
   "outputs": [],
   "source": [
    "def trapDepthFromIntensity_Feb_1st_2019(intensity):\n",
    "    # assumes 852nm\n",
    "    # 1e3 * ManifoldShift(2, 2, intensity, '5S12', wavelength)/mc.k_B = -4.652899246307172e-10\n",
    "    return intensity*(-4.652899246307172e-10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 693,
   "metadata": {},
   "outputs": [],
   "source": [
    "waist=650e-9\n",
    "power = 3e-3*0.85\n",
    "expectedIntensity = 2*power/(np.pi*waist**2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "this is the expected depth for 3mW input: -1.79mK"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 695,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-1.787793024978716"
      ]
     },
     "execution_count": 695,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "trapDepthFromIntensity_Feb_1st_2019(expectedIntensity)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$\n",
    "2/w^2=m\\omega/2\\hbar\\\\\n",
    "w=\\sqrt{\\frac{4\\hbar}{m\\omega}}\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 698,
   "metadata": {},
   "outputs": [],
   "source": [
    "import MarksConstants as mc"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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