{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<font size = \"5\"> **Chapter 4: [Spectroscopy](CH4_00-Spectroscopy.ipynb)** </font>\n",
    "\n",
    "\n",
    "<hr style=\"height:1px;border-top:4px solid #FF8200\" />\n",
    "\n",
    "# Bremsstrahlung\n",
    "\n",
    "[Download](https://raw.githubusercontent.com/gduscher/MSE672-Introduction-to-TEM/main/Spectroscopy/CH4_13-Bremsstrahlung.ipynb)\n",
    " \n",
    "\n",
    "[![OpenInColab](https://colab.research.google.com/assets/colab-badge.svg)](\n",
    "    https://colab.research.google.com/github/gduscher/MSE672-Introduction-to-TEM/blob/main//Spectroscopy/CH4_13-Bremsstrahlung.ipynb)\n",
    "\n",
    "part of \n",
    "\n",
    "<font size = \"5\"> **[MSE672:  Introduction to Transmission Electron Microscopy](../_MSE672_Intro_TEM.ipynb)**</font>\n",
    "\n",
    "**Spring 2026**<br>\n",
    "by Gerd Duscher\n",
    "\n",
    "Microscopy Facilities<br>\n",
    "Institute of Advanced Materials & Manufacturing<br>\n",
    "Materials Science & Engineering<br>\n",
    "The University of Tennessee, Knoxville\n",
    "\n",
    "Background and methods to analysis and quantification of data acquired with transmission electron microscopes.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Load relevant python packages\n",
    "### Check Installed Packages"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "done\n"
     ]
    }
   ],
   "source": [
    "import sys\n",
    "import importlib.metadata\n",
    "def test_package(package_name):\n",
    "    \"\"\"Test if package exists and returns version or -1\"\"\"\n",
    "    try:\n",
    "        version = importlib.metadata.version(package_name)\n",
    "    except importlib.metadata.PackageNotFoundError:\n",
    "        version = '-1'\n",
    "    return version\n",
    "\n",
    "if test_package('pyTEMlib') < '0.2024.2.3':\n",
    "    print('installing pyTEMlib')\n",
    "    !{sys.executable} -m pip install  --upgrade pyTEMlib -q\n",
    "\n",
    "print('done')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## First we import the essential libraries\n",
    "All we need here should come with the annaconda or any other package"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "notebook version:  2026.01.22\n"
     ]
    }
   ],
   "source": [
    "%matplotlib widget\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "import sys\n",
    "import os\n",
    "if 'google.colab' in sys.modules:\n",
    "    from google.colab import output\n",
    "    from google.colab import drive\n",
    "    output.enable_custom_widget_manager()\n",
    "\n",
    "__notebook_version__ = '2026.01.22'\n",
    "print('notebook version: ', __notebook_version__)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Bremsstrahlung\n",
    "The Bremsstrahlung causes the background the characteristic X-ray peaks are sitting on.\n",
    "\n",
    "\n",
    "Because of the repulsion a fast electron by the negative electron cloud in a solid. such an electron will be de-accelerated or deflected. Any acceleration (negative or positive) is related with a photon (possibly only as an exchagne particle which is the basis of Quantum Eletrodynamics).\n",
    "\n",
    "![X-Ray_Auger](./images/Bremsstrahlung1.jpg)\n",
    "\n",
    "The energy loss in the braking of an electron will cause the emission of Bremsstrahlung (braking radiation). The energy of the photon of this electromagnetic radiation is directly the photon energy.\n",
    "\n",
    "Thus the Bremsstrahlung spans the energies from the incident electron's energy down to a practical limit of about 100eV. The Bremsstrahlung is therefore sometimes refered to as X-ray continuum.\n",
    "\n",
    "\n",
    "\n",
    "The Bremsstrahlung is anoistropic, peaked in the forwad direction of the incident electron.\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Kramer's formulation of Bremsstrahlung\n",
    "\n",
    "Kramers' formula for Bremsstrahlung is the most basic (and not very accurate) description of Bremsstrahlung vs energy:\n",
    "\n",
    "$$ N_E = IKZ \\frac{(E-E_0)}{E}$$\n",
    "\n",
    "- K -- A constant,\n",
    "- Z -- The average atomic number of the specimen,\n",
    "- E0 -- The incident beam energy, \n",
    "- I -- The electron beam current,\n",
    "- E -- The continuum photon energy.\n",
    "\n",
    "The factor K in Kramers’ law actually takes\n",
    "account of numerous parameters. These include\n",
    "- Kramers’ original constant.\n",
    "- The collection efficiency of the detector.\n",
    "- The processing efficiency of the detector.\n",
    "- The absorption of X-rays within the specimen."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "83f42638b1fa4608b97a797090b8a966",
       "version_major": 2,
       "version_minor": 0
      },
      "image/png": "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",
      "text/html": [
       "\n",
       "            <div style=\"display: inline-block;\">\n",
       "                <div class=\"jupyter-widgets widget-label\" style=\"text-align: center;\">\n",
       "                    Figure\n",
       "                </div>\n",
       "                <img src='data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAoAAAAHgCAYAAAA10dzkAAAAOnRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjEwLjcsIGh0dHBzOi8vbWF0cGxvdGxpYi5vcmcvTLEjVAAAAAlwSFlzAAAPYQAAD2EBqD+naQAAVXpJREFUeJzt3Xl8FdXh///3XZKbPYHsgQARRFAQWVxAEUSNRUWpfCpqK6JYpW5FtIvVn9vXlmqV+mkp1lYR/dQFF3CpVEmLgApaQVAEFIRAWBJCWLLvd35/TG4gJmDI3ZKZ1/PxuI+ZO3funHMvA/fNOXPOOAzDMAQAAADbcIa7AgAAAAgtAiAAAIDNEAABAABshgAIAABgMwRAAAAAmyEAAgAA2AwBEAAAwGYIgAAAADZDAAQAALAZAiAAAIDNEAABAABshgAIAABgMwRAAAAAmyEAAgAA2AwBEAAAwGYIgAAAADZDAAQAALAZAiAAAIDNEAABAABshgAIAABgMwRAAAAAmyEAAgAA2AwBEAAAwGYIgAAAADZDAAQAALAZAiAAAIDNEAABAABshgAIAABgMwRAAAAAmyEAAgAA2AwBEAAAwGYIgAAAADZDAAQAALAZAiAAAIDNEAABAABshgAIAABgMwRAAAAAmyEAAgAA2AwBEAAAwGYIgAAAADZDAAQAALAZAiAAAIDNEAADZMWKFZowYYKysrLkcDj05ptvHvcxDMPQ448/rv79+8vj8Sg7O1u/+93vAl9ZAABga+5wV8AqKisrNWTIEF1//fWaNGlSh47x85//XEuWLNHjjz+uwYMHq7S0VCUlJQGuKQAAsDuHYRhGuCthNQ6HQ4sWLdLEiRObt9XV1em+++7Tiy++qEOHDmnQoEF69NFHNXbsWEnSpk2bdOqpp+qrr77SSSedFJ6KAwAAW6ALOESuv/56ffzxx3rllVf05Zdf6kc/+pF+8IMfaMuWLZKkd955RyeccIL++c9/KicnR3369NGNN96oAwcOhLnmAADAagiAIbB161a9/PLLeu211zR69Gj17dtXd999t8455xw999xzkqRt27Zpx44deu211/TCCy9o/vz5WrNmjf7nf/4nzLUHAABWwzWAIfD555/LMAz179+/xfba2lolJydLkrxer2pra/XCCy807/fss89q+PDh+uabb+gWBgAAAUMADAGv1yuXy6U1a9bI5XK1eC0uLk6SlJmZKbfb3SIkDhw4UJJUUFBAAAQAAAFDAAyBoUOHqrGxUcXFxRo9enSb+5x99tlqaGjQ1q1b1bdvX0nS5s2bJUm9e/cOWV0BAID1MQo4QCoqKvTtt99KMgPf7Nmzdd5556l79+7q1auXfvKTn+jjjz/WE088oaFDh6qkpERLly7V4MGDdfHFF8vr9er0009XXFycnnzySXm9Xt16661KSEjQkiVLwvzpAACAlRAAA2TZsmU677zzWm2/7rrrNH/+fNXX1+uRRx7RCy+8oN27dys5OVkjR47UQw89pMGDB0uS9uzZo9tvv11LlixRbGysxo8fryeeeELdu3cP9ccBAAAWZpkAuGLFCv3hD3/QmjVrVFhY2GoevrYsX75cM2fO1IYNG5SVlaVf/vKXmj59emgqDAAAECaWmQbGdyeOOXPmtGv//Px8XXzxxRo9erTWrl2r3/zmN7rjjjv0xhtvBLmmAAAA4WWZFsAjtXUnju/61a9+pbffflubNm1q3jZ9+nR98cUXWrVqVQhqCQAAEB6WaQE8XqtWrVJubm6LbRdddJFWr16t+vr6MNUKAAAg+Gw7DUxRUZHS09NbbEtPT1dDQ4NKSkqUmZnZ6j21tbWqra1tfu71enXgwAElJyfL4XAEvc4AAMB/hmGovLxcWVlZcjrt2RZm2wAoqVVo8/WGHy3MzZo1Sw899FDQ6wUAAIJv586d6tmzZ7irERa2DYAZGRkqKipqsa24uFhut7v59mzfdc8992jmzJnNz0tLS9WrVy/t3LlTCQkJQa3v97n1xTVavrlED112siYNz27/G1f+WVr+qDT4SunS2cGrIAAAnURZWZmys7MVHx8f7qqEjW0D4MiRI/XOO++02LZkyRKNGDFCERERbb7H4/HI4/G02p6QkBD2AJiQkCinp0qOyJjjq0tKluRxSI5KKcyfAQCAULLz5VuW6fiuqKjQunXrtG7dOknmNC/r1q1TQUGBJLP1bsqUKc37T58+XTt27NDMmTO1adMmzZs3T88++6zuvvvucFTfb1ER5j2Gaxq8x/fG6G7msupAgGsEAAA6K8u0AK5evbrFnTh8XbW+O3EUFhY2h0FJysnJ0eLFi3XnnXfqL3/5i7KysvSnP/1JkyZNCnndAyE60szy1XWNx/fGmKa7jFQTAAEAsAvLBMCxY8fqWFMazp8/v9W2MWPG6PPPPw9irUInyu1rATzOABjtC4AHA1wjAADQWVkmANpddGRTADzeFkBfF3D1QckwJBtfDwEAgWQYhhoaGtTYeJz/LsNvLpdLbrfb1tf4fR8CoEX4rgGsru9gF7C3Qaotl6IYCAIA/qqrq1NhYaGqqqrCXRXbiomJUWZmpiIjI8NdlU6JAGgRzYNA6o9zEEhEtOSOlhqqzesACYAA4Bev16v8/Hy5XC5lZWUpMjKSlqgQMgxDdXV12rdvn/Lz83XiiSfadrLnYyEAWkR0R1sAJbMbuLzaHAncrU9gKwYANlNXVyev16vs7GzFxMSEuzq2FB0drYiICO3YsUN1dXWKiooKd5U6HSKxRURFmH+UNR0JgDEMBAGAQKPVKbz4/o+Nb8ciopu7gDvYAigRAAEAsAkCoEV0eBCIRAAEAATV1KlTNXHixHBXA0cgAFqEbxqYquOdBkY63AXM3UAAwNZWrFihCRMmKCsrSw6HQ2+++WarfQzD0IMPPqisrCxFR0dr7Nix2rBhQ9Dq9MQTTygxMbHNEdU1NTVKSkrS7Nncy/54EQAtIjbSHM9z3HcCkY6YDJoACAB2VllZqSFDhmjOnDlH3eexxx7T7NmzNWfOHH322WfKyMjQhRdeqPLy8qDUacqUKaqurtYbb7zR6rU33nhDVVVVuvbaa4NStpURAC3C1wJYWdvQgTfTBQwAkMaPH69HHnlEV1xxRZuvG4ahJ598Uvfee6+uuOIKDRo0SM8//7yqqqr00ksvtbucNWvWKC0tTb/97W8lSaWlpbrpppuUlpamhIQEjRs3Tl988YUkKTU1VRMmTNC8efNaHWfevHm67LLLlJqa2oFPa29MA2MRsR4/rgGkCxgAgsowjI79+xwA0RGugM1DmJ+fr6KiIuXm5jZv83g8GjNmjFauXKmbb775e4+xbNkyTZw4UbNmzdLPfvYzGYahSy65RN27d9fixYuVmJiop59+Wueff742b96s7t27a9q0abr00kuVn5+vnJwcSdL27dv1wQcf6N133w3IZ7MbAqBFxESYf5T1jYbqGryKdB9H4y4tgAAQVNX1jTr5/vfDUvbGhy9STGRgfu6LiookSenp6S22p6ena8eOHd/7/rfeekvXXnutnn76aV199dWSpA8++EDr169XcXGxPB6PJOnxxx/Xm2++qddff1033XSTLrroImVlZWn+/Pl66KGHJEnPPfecsrKyWoRRtB9dwBbh6wKWOnAdINcAAgCOw3dbFA3D+N5Wxk8//VSTJk3S888/3xz+JLM7uKKiQsnJyYqLi2t+5Ofna+vWrZLMe/ted911mj9/vrxerwzD0PPPP6+pU6fK5XIdrUgcAy2AFhHpdirC5VB9o6HKugYlxkS0/810AQNAUEVHuLTx4YvCVnagZGRkSDJbAjMzM5u3FxcXt2oV/K6+ffsqOTlZ8+bN0yWXXNJ8j16v16vMzEwtW7as1XuSkpKa12+44QbNmjVLS5culSQVFBTo+uuv9/MT2RcB0EJiIt0qra4//qlgfF3ANaWSt1Fy8r8pAAgkh8MRsG7YcMrJyVFGRoby8vI0dOhQSeat75YvX65HH330mO9NSUnRwoULNXbsWE2ePFmvvvqqIiIiNGzYMBUVFcntdqtPnz5HfX/fvn01ZswYPffcczIMQ2PHjlXfvn0D+fFshS5gC4lpngvwOEcC+wKgDDMEAgBsqaKiQuvWrdO6deskmYM+1q1bp4KCAklmkJ0xY4Z+97vfadGiRfrqq680depUxcTE6Jprrvne46elpWnp0qX6+uuvdfXVV6uhoUEXXHCBRo4cqYkTJ+r999/X9u3btXLlSt13331avXp1i/dPmzZNCxcu1KJFizRt2rSAf347IQBaSExHJ4N2RUieBHOdgSAAYFurV6/W0KFDm1v3Zs6cqaFDh+r+++9v3ueXv/ylZsyYoVtuuUUjRozQ7t27tWTJEsXHx7erjIyMDC1dulTr16/Xj3/8Y3m9Xi1evFjnnnuubrjhBvXv319XXXWVtm/f3qpbedKkSfJ4PPJ4PEedqgbt4zAMwwh3JbqqsrIyJSYmqrS0VAkJCeGujib8+SOt312qeVNHaNyAY1+L0cqTg6VDBdK0PCn7jOBUEABsoKampnm6kqioqHBXx7aO9efQ2X6/w4EWQAvx73ZwKeayan8AawQAADojAqCFxPoCYG0HAmBsUwCsLAlgjQAAQGdEALQQ3wiz4x4EIh3RAkgABADA6giAFtI8CKQjtxuKTTaXtAACAGB5BEALifGnCziGLmAAAOyCAGghMR5fF7Af1wDSBQwAgOURAC0kJqKDE0FLtAACAGAjBEALCUwLINPAAABgdQRAC+nwreAkKYZBIAAA2AUB0EI6fCs46XALYEO1VFcZwFoBAOxu6tSpmjhxYrirgSMQAC3ENw9gZUcCYGSc5PKY67QCAoAtrVixQhMmTFBWVpYcDofefPPNVvsYhqEHH3xQWVlZio6O1tixY7Vhw4ag1emJJ55QYmKiqqqqWr1WU1OjpKQkzZ49O2jlWxUB0EJ8dwKp7kgXsMPB3UAAwOYqKys1ZMgQzZkz56j7PPbYY5o9e7bmzJmjzz77TBkZGbrwwgtVXl4elDpNmTJF1dXVeuONN1q99sYbb6iqqkrXXnttUMq2MgKghfjuBVzZkXkAJaaCAQCbGz9+vB555BFdccUVbb5uGIaefPJJ3Xvvvbriiis0aNAgPf/886qqqtJLL73U7nLWrFmjtLQ0/fa3v5UklZaW6qabblJaWpoSEhI0btw4ffHFF5Kk1NRUTZgwQfPmzWt1nHnz5umyyy5TampqBz6tvREALcTXBVzdkTuBSEwFAwDBYhjm9dXheBhGwD5Gfn6+ioqKlJub27zN4/FozJgxWrlyZbuOsWzZMp1//vl66KGHdO+998owDF1yySUqKirS4sWLtWbNGg0bNkznn3++Dhw4IEmaNm2ali9frvz8/ObjbN++XR988IGmTZsWsM9nJ+5wVwCBE9PcAtiBLmCJFkAACJb6Kul3WeEp+zd7pMjYgByqqKhIkpSent5ie3p6unbs2PG973/rrbd07bXX6umnn9bVV18tSfrggw+0fv16FRcXy+Mxr0V//PHH9eabb+r111/XTTfdpIsuukhZWVmaP3++HnroIUnSc889p6ysrBZhFO1HC6CF+AJgbYNXjd4O/I+PFkAAQDs4HI4Wzw3DaLXtuz799FNNmjRJzz//fHP4k8zu4IqKCiUnJysuLq75kZ+fr61bt0qSXC6XrrvuOs2fP19er1eGYej555/X1KlT5XK5Av8BbYAWQAuJ9Rz+46yqa1B8VMRxHqBpLkAmgwaAwIqIMVviwlV2gGRkZEgyWwIzMzObtxcXF7dqFfyuvn37Kjk5WfPmzdMll1yiyMhISZLX61VmZqaWLVvW6j1JSUnN6zfccINmzZqlpUuXSpIKCgp0/fXX+/mJ7IsAaCEet1MOh3m5R3Vd4/EHQFoAASA4HI6AdcOGU05OjjIyMpSXl6ehQ4dKkurq6rR8+XI9+uijx3xvSkqKFi5cqLFjx2ry5Ml69dVXFRERoWHDhqmoqEhut1t9+vQ56vv79u2rMWPG6LnnnpNhGBo7dqz69u0byI9nK3QBW4jD4VBc00CQio5cB8g1gABgaxUVFVq3bp3WrVsnyRz0sW7dOhUUFEgyf2dmzJih3/3ud1q0aJG++uorTZ06VTExMbrmmmu+9/hpaWlaunSpvv76a1199dVqaGjQBRdcoJEjR2rixIl6//33tX37dq1cuVL33XefVq9e3eL906ZN08KFC7Vo0SIGf/iJAGgxvm7gDk0FQwsgANja6tWrNXTo0ObWvZkzZ2ro0KG6//77m/f55S9/qRkzZuiWW27RiBEjtHv3bi1ZskTx8fHtKiMjI0NLly7V+vXr9eMf/1her1eLFy/WueeeqxtuuEH9+/fXVVddpe3bt7fqVp40aZI8Ho88Hs9Rp6pB+zgMI4Djw22mrKxMiYmJKi0tVUJCQrirI0m6YPZyfVtcoZd/epZG9k0+vjfv3yr9eZgUESvdG6ZrVQCgi6upqVF+fr5ycnIUFRUV7urY1rH+HDrj73eo0QJoMb4WwA51Acc0Bcb6Sqm+OoC1AgAAnQkB0GLim7uAOxAAoxIlZ9PAEbqBAQCwLAKgxcR6zPmQyjsSAB2Ow62ADAQBAMCyCIAWE+cxW/Aqajp4N5C4NHNZsS9ANQIAAJ0NAdBi4jx+3g4urmnEVcXeANUIAAB0NgRAi4mL8mMQiEQABIAAYZKN8OL7PzYCoMU0dwF3OACmmsuK4gDVCADsJSLC/He4qqoqzDWxN9/37/vzQEvcCs5ifF3AHb8GkBZAAPCHy+VSUlKSiovN/0jHxMTI4XCEuVb2YRiGqqqqVFxcrKSkJLlcrnBXqVMiAFqMrwu4ss7fQSC0AAJAR2VkZEhScwhE6CUlJTX/OaA1AqDFxDbdC7jc3xbASv7RAoCOcjgcyszMVFpamurr68NdHduJiIig5e97EAAtprkF0O9BIARAAPCXy+UiiKBTYhCIxcT5cys46XAXcG2ZVMcFzAAAWBEB0GL8DoCeBMnddNNsuoEBALAkAqDFxB1xL+AOzYHkcDAQBAAAiyMAWozvGkCvIVXXN3bsILG+AMhUMAAAWBEB0GKiI1xyNk03xVyAAACgLQRAi3E4HIoN1ECQin0BqhUAAOhMLBUA586dq5ycHEVFRWn48OH68MMPj7n/iy++qCFDhigmJkaZmZm6/vrrtX///hDVNnji/Q6AtAACAGBllgmACxYs0IwZM3Tvvfdq7dq1Gj16tMaPH6+CgoI29//oo480ZcoUTZs2TRs2bNBrr72mzz77TDfeeGOIax54gWsBZBAIAABWZJkAOHv2bE2bNk033nijBg4cqCeffFLZ2dl66qmn2tz/k08+UZ8+fXTHHXcoJydH55xzjm6++WatXr06xDUPPN9AEK4BBAAAbbFEAKyrq9OaNWuUm5vbYntubq5WrlzZ5ntGjRqlXbt2afHixTIMQ3v37tXrr7+uSy65JBRVDir/J4PmbiAAAFiZJQJgSUmJGhsblZ6e3mJ7enq6ioqK2nzPqFGj9OKLL2ry5MmKjIxURkaGkpKS9Oc///mo5dTW1qqsrKzFozM6ci7Ajh3giGlgOjKXIAAA6NQsEQB9HA5Hi+eGYbTa5rNx40bdcccduv/++7VmzRq99957ys/P1/Tp0496/FmzZikxMbH5kZ2dHdD6B4ovAJZ1uAu4KQA21pq3hAMAAJZiiQCYkpIil8vVqrWvuLi4Vaugz6xZs3T22WfrF7/4hU499VRddNFFmjt3rubNm6fCwsI233PPPfeotLS0+bFz586Af5ZASIiOkCSVdzQARkSbt4STpHKuAwQAwGosEQAjIyM1fPhw5eXltdiel5enUaNGtfmeqqoqOZ0tP77L5ZKko95CzePxKCEhocWjM0qIMgNgWU19xw/iuw6wvO0wDAAAui5LBEBJmjlzpp555hnNmzdPmzZt0p133qmCgoLmLt177rlHU6ZMad5/woQJWrhwoZ566ilt27ZNH3/8se644w6dccYZysrKCtfHCIiE6KYu4Go/AmBCprksb/saSgAA0HW5w12BQJk8ebL279+vhx9+WIWFhRo0aJAWL16s3r17S5IKCwtbzAk4depUlZeXa86cObrrrruUlJSkcePG6dFHHw3XRwiYwy2AHewClqT4phBcvicANQIAAJ2JZQKgJN1yyy265ZZb2nxt/vz5rbbdfvvtuv3224Ncq9DzXQMYkBbAMrqAAQCwGst0AeOwhCjfKGA/AiAtgAAAWBYB0IIOtwD60wWcYS5pAQQAwHIIgBbUHAD9aQFM8LUAMggEAACrIQBakK8LuK7Bq5r6xo4dJL7pGsCKIsnrDVDNAABAZ0AAtKDYSLecTTdA6XArYFy65HBK3gapcl/gKgcAAMKOAGhBTqdD8VF+XgfockuxTbeEYyAIAACWQgC0qPiAjARmIAgAAFZEALSo5smg/ZoL0DcQhAAIAICVEAAtqvl2cH7dDcR3OzgCIAAAVkIAtKjAtAByNxAAAKyIAGhRAZkLkLuBAABgSQRAi0rwdxSwRAsgAAAWRQC0qMPXAPrTAsg1gAAAWBEB0KICcg2gLwDWHJLqq/2vFAAA6BQIgBZ1+BpAP7qAoxKliBhzvYzrAAEAsAoCoEX57gfsVwugwyEl9DDXy3YHoFYAAKAzIABaVEBGAUtSYk9zWbrLzxoBAIDOggBoUQEZBSwRAAEAsCACoEU1jwL2pwtYkhKzzWXpTj9rBAAAOgsCoEUlNnUB1zV6VV3X6MeBfC2AXAMIAIBVEAAtKs7jltvpkCQdrKrr+IESmwaB0AUMAIBlEAAtyuFwKCnGbAX0LwD6uoB3SYYRgJoBAIBwIwBaWFJMpCSptMqP6wATmu4HXF8pVR8MQK0AAEC4EQAtrFtzC6AfATAiWopNNdfpBgYAwBIIgBbmawH0qwtYYioYAAAshgBoYUlNI4EPEQABAMARCIAW1i3WbAE85E8XsMRcgAAAWAwB0MKSAnENoEQLIAAAFkMAtLBuMb4WQLqAAQDAYQRAC+sWiHkAJQIgAAAWQwC0sMTophbAQN0PuLxQavTzWAAAIOwIgBbWLdY3CtjP0BaTIrk8kgypjHsCAwDQ1REALezIawC9Xj9u4+Z0Hu4GPlQQgJoBAIBwIgBamG8UsNeQymsa/DtYtz7m8uAO/44DAADCjgBoYR63SzGRLkkBGAjSrbe5PEQABACgqyMAWlzz3UD8HQiS1BQAD2737zgAACDsCIAWF7D7AdMFDACAZRAALe7wSOAAdQHTAggAQJdHALS45hbASj+7gH0tgJXFUl2Vf8cCAABhRQC0uOZrAP1tAYzuJnkSzXUGggAA0KURAC0uOdZsATzgbwCUpG69zCXXAQIA0KURAC0uOc4jSdpfEYgA2Mdc0gIIAECXRgC0uOQ4swUwIAGQqWAAALAEAqDFJceaLYAllbX+H4ypYAAAsAQCoMWlNLUAHqgMYBcwLYAAAHRpBECL6940CORQVb3qG73+HSzpiNvBGYafNQMAAOFCALS4pJhIOR3m+kF/WwGTmkYB11VIVfv9OxYAAAgbAqDFuZyO5lbAEn8HgkRESfGZ5jrXAQIA0GURAG3ANxBkfyAGgjSPBM73/1gAACAsCIA2ENCpYLqfYC4PbPP/WAAAICwIgDbgmwy6pCIALYDJfc3l/q3+HwsAAIQFAdAGfLeD2x+IqWB8AfAAARAAgK6KAGgDzQEwEC2A3WkBBACgqyMA2oCvCzggk0H7rgGsPiBVHfD/eAAAIOQIgDbgGwTi9zQwkuSJOzwVDANBAADokgiANuC7HVxApoGR6AYGAKCLIwDaQPM8gIFoAZSkZN9UMARAAAC6IksFwLlz5yonJ0dRUVEaPny4Pvzww2PuX1tbq3vvvVe9e/eWx+NR3759NW/evBDVNnR8XcBVdY2qqmsIwAH7mcv93/p/LAAAEHLucFcgUBYsWKAZM2Zo7ty5Ovvss/X0009r/Pjx2rhxo3r16tXme6688krt3btXzz77rPr166fi4mI1NAQgIHUycR63PG6nahu8KimvU69kP//Y6QIGAKBLs0wAnD17tqZNm6Ybb7xRkvTkk0/q/fff11NPPaVZs2a12v+9997T8uXLtW3bNnXv3l2S1KdPn1BWOWQcDofSEjzaeaBaxeU16pUc498Bm+cC3CYZhuRw+F9JAAAQMpboAq6rq9OaNWuUm5vbYntubq5WrlzZ5nvefvttjRgxQo899ph69Oih/v376+6771Z1dfVRy6mtrVVZWVmLR1eRFh8lSdpbFoCBIN1yJDmk2jKpssT/4wEAgJCyRAtgSUmJGhsblZ6e3mJ7enq6ioqK2nzPtm3b9NFHHykqKkqLFi1SSUmJbrnlFh04cOCo1wHOmjVLDz30UMDrHwpp8eZAkOLyGv8PFhElJWZLpQXmQJC4VP+PCQAAQsYSLYA+ju90RRqG0Wqbj9frlcPh0IsvvqgzzjhDF198sWbPnq358+cftRXwnnvuUWlpafNj586dAf8MwZKeYLYAFpcHaCoY30hgBoIAANDlWCIApqSkyOVytWrtKy4ubtUq6JOZmakePXooMTGxedvAgQNlGIZ27drV5ns8Ho8SEhJaPLqKVF8LYCC6gKUjBoIQAAEA6GosEQAjIyM1fPhw5eXltdiel5enUaNGtfmes88+W3v27FFFRUXzts2bN8vpdKpnz55BrW84BLQLWJJS+pvLki2BOR4AAAgZSwRASZo5c6aeeeYZzZs3T5s2bdKdd96pgoICTZ8+XZLZfTtlypTm/a+55holJyfr+uuv18aNG7VixQr94he/0A033KDo6OhwfYygSWvqAt4XqC7g1KYAuO+bwBwPAACEjCUGgUjS5MmTtX//fj388MMqLCzUoEGDtHjxYvXu3VuSVFhYqIKCgub94+LilJeXp9tvv10jRoxQcnKyrrzySj3yyCPh+ghBdbgFMEABMOUkc3lgm9RQJ7kjA3NcAAAQdA7DMIxwV6KrKisrU2JiokpLSzv99YAHKus07P+ZXeSbHxmvSLefjb+GIc3KlurKpVs+kdIGBqCWAAAEX1f6/Q4Wy3QB49i6xUQowmWOiN5XEYBWQIeDbmAAALooAqBNOBwOpcb5RgIHaiBIUzdwyebAHA8AAIQEAdBGUgM9F2BqUwCkBRAAgC6FAGgjAR8IQgAEAKBLIgDaSHqCGQD3BawLuOkawP1bJG9jYI4JAACCjgBoI2nxZhfw3kDdDaRbH8nlkRpqpEMF37s7AADoHAiANpKRaAbAwkC1ADpdUsqJ5jrdwAAAdBkEQBvJSjTvcFJ4qDpwB22+JRwBEACAroIAaCPNLYClAWoBlI4YCMJUMAAAdBUEQBvJSjIDYEVtg8pq6gNz0OYAuCkwxwMAAEFHALSRmEi3EqMjJEmFhwLUCph2irks3iR5vYE5JgAACCoCoM1kNnUD7ykN0HWA3U+Q3FFSfZV0MD8wxwQAAEFFALSZrCTfQJAAtQC63Ie7gYs3BuaYAAAgqAiANpPZPBAkgCOB0weZy70bAndMAAAQNARAm/G1AO4JVAugJKWdbC73fhW4YwIAgKAhANpMcFoAmwaC7KULGACAroAAaDOZTZNBFwVyLkBfF/CBbVJdZeCOCwAAgoIAaDNHjgI2DCMwB41LlWJTJRnSvq8Dc0wAABA0BECb8d0NpKbeq0NVAZoMWjqiG5iBIAAAdHYEQJuJinApOTZSUgDnApQYCQwAQBdCALShzKZbwgVsLkDpiJHABEAAADo7AqANZTUNBNl9KBgjgb+SAnVtIQAACAoCoA1ld4+RJO08UBW4g6YOkJxuqfqgVLorcMcFAAABRwC0oexuZgvgzoMBDIARUVLqQHO98IvAHRcAAAQcAdCGeiX7WgAD2AUsSVlDzCUBEACATo0AaEPZ3Q53AQdsLkBJyjzNXBauC9wxAQBAwBEAbahnUwAsr21QaXUA5wLMpAUQAICugABoQ9GRLqXEeSQFuBs4fZDkcEoVe6WywsAdFwAABBQB0KZ6dQ/CQJDIGCnlJHOdVkAAADotAqBNBWUqGIluYAAAugACoE35BoIUBDoAZp1mLhkIAgBAp0UAtKns5i7gAE8FQwsgAACdHgHQpnxdwLsC3QKYMdhclu2WKvYF9tgAACAgCIA25esC3nWwWl5vAOcC9MRLyf3MdbqBAQDolAiANpWZGCW306G6Rq/2ltcE9uBZQ83lnrWBPS4AAAgIAqBNuV1O9Wy6J/D2kgB3A/cYYS53fRbY4wIAgIAgANpYTkqsJCm/pDKwB+55urnctVoK5K3mAABAQBAAbSwnJU6SlF9SEdgDZwySXJFS9QHpwLbAHhsAAPiNAGhjOalBagF0ew5PB7N7TWCPDQAA/EYAtLETmrqAtwU6AEpHdANzHSAAAJ0NAdDGfNcAFuyvUkOjN7AH7zHcXBIAAQDodAiANpaREKWoCKcavIZ2BfqOIL4WwKL1Un2Ajw0AAPxCALQxp9OhPslBug4wqZcUmyp5G6TCLwN7bAAA4BcCoM2dkBqk6wAdjsOtgLtXB/bYAADALwRAmzs8F2CAp4KRpJ5MCA0AQGdEALS5oHUBS4dbAHf+lwmhAQDoRAiANtfcBbwvCAGwxwjJ6ZbKdkuHCgJ/fAAA0CEEQJvrlxovSSosrVF5TX1gDx4ZI2WeZq4XrArssQEAQIcRAG0uMSZCafEeSdK3xUG4DrDXWeZyx8rAHxsAAHQIARDqn262Am7ZG4QA2HuUuaQFEACAToMACPVLi5Mkbd5bHviD9xppLks2S5UlgT8+AAA4bgRANLcAbg5GF3BMdyl1gLlOKyAAAJ0CARDqn262AG4JRgugdLgVcAcBEACAzoAACJ2YHsSRwNIR1wEyEAQAgM6AAAglRkcoPcEcCbwlKCOBm1oAC7+UaoNwfAAAcFwIgJB05EjgIHQDJ2VLidmS0Sjt/CTwxwcAAMfFUgFw7ty5ysnJUVRUlIYPH64PP/ywXe/7+OOP5Xa7ddpppwW3gp3Y4ZHAQWqhyznXXOavCM7xAQBAu1kmAC5YsEAzZszQvffeq7Vr12r06NEaP368CgqOfQuy0tJSTZkyReeff36Iato5ndTUAvhNUZAGguSMMZfblgfn+AAAoN0sEwBnz56tadOm6cYbb9TAgQP15JNPKjs7W0899dQx33fzzTfrmmuu0ciRI0NU087p5KwESdLGwjIZhhH4AnwtgIVfSFUHAn98AADQbpYIgHV1dVqzZo1yc3NbbM/NzdXKlUcfefrcc89p69ateuCBB9pVTm1trcrKylo8rKJ/erxcTocOVNapqKwm8AUkZEopJ0kypO0fBf74AACg3SwRAEtKStTY2Kj09PQW29PT01VUVNTme7Zs2aJf//rXevHFF+V2u9tVzqxZs5SYmNj8yM7O9rvunUVUhEv9Us3rADfuCVKwPaGpGzifbmAAAMLJEgHQx+FwtHhuGEarbZLU2Nioa665Rg899JD69+/f7uPfc889Ki0tbX7s3LnT7zp3Js3dwMEKgFwHCABAp9C+pq9OLiUlRS6Xq1VrX3FxcatWQUkqLy/X6tWrtXbtWt12222SJK/XK8Mw5Ha7tWTJEo0bN67V+zwejzweT3A+RCdwSlaCFq3drQ3BCoB9zpEcTmn/Fqlsj5SQFZxyAADAMVmiBTAyMlLDhw9XXl5ei+15eXkaNWpUq/0TEhK0fv16rVu3rvkxffp0nXTSSVq3bp3OPPPMUFW9Uzk58/BAkKCITpIyTzPXaQUEACBsLNECKEkzZ87UtddeqxEjRmjkyJH629/+poKCAk2fPl2S2X27e/duvfDCC3I6nRo0aFCL96elpSkqKqrVdjvxdQEXHKhSWU29EqIiAl/ICWOkPZ+b1wGednXgjw8AAL6XZQLg5MmTtX//fj388MMqLCzUoEGDtHjxYvXu3VuSVFhY+L1zAtpdUkykeiRFa/eham3aU6YzT0gOfCE5Y6SP/ihtWyYZhtTGNZoAACC4HEZQJn2zh7KyMiUmJqq0tFQJCQnhrk5A3Pj8av170149MOFkXX92TuALqK+RHsuR6quk6R9JGYMDXwYAAMdgxd/v42WJawAROL5u4K92B+k6wIiow5NCb8k79r4AACAoCIBo4dQeiZKkL3cdCl4hJ15oLgmAAACEBQEQLQzJTpIkfbuvQuU19cEppF9TANz5qVR9KDhlAACAoyIAooXUeI96JEXLMKT1u0qDU0i33uZt4YxGadsHwSkDAAAcFQEQrZzWK0mStHbnoeAV0twN/O/glQEAANpEAEQrQ5u6gb8IRQD8Nk/yeoNXDgAAaIUAiFZ81wGu23lIQZslqNdIKSJWqtgr7V0fnDIAAECbCIBoZVBWolxOh4rLa1VYWhOcQtwe864gkrR5SXDKAAAAbSIAopXoSJcGZMRLCnI3cP8fmMtv3g1eGQAAoBUCINp0ZDdw0Jw0XpJD2rNWKt0VvHIAAEALBEC0aVivbpKk1TsOBq+QuDSp11nm+teLg1cOAABogQCINp3Rp7sk844gNfWNwStowCXm8ut3glcGAABogQCINmV3j1Z6gkf1jYbWFhwKXkG+ALj9Y6nqQPDKAQAAzQiAaJPD4dAZOcmSpM+2BzGYdT9BSjvFvCvIFkYDAwAQCgRAHNUZfczrAP+bH+SWOV8r4Ca6gQEACAUCII7q9BzzOsDPCw6qoTGId+sYeKm5/PY/Ul1V8MoBAACSCIA4hv5p8UqMjlBVXaM27CkLXkEZp0qJvaSGavPWcAAAIKgIgDgqp9Oh00PRDexwSIN+aK5/9UbwygEAAJIIgPgeZzR1A6/atj+4BQ2aZC43vy/Vlge3LAAAbI4AiGMa1TdFkvTJtv2qD+Z1gBmnSt37Sg010jfvBa8cAABAAMSxnZyZoOTYSFXVNQZ3PkCH43ArIN3AAAAEFQEQx+R0OjSqn9kK+NGWfcEtzBcAv/23VB3EW9ABAGBzBEB8r9FNAfDDb0uCW1DaAHNSaG+9tOmfwS0LAAAbIwDie519ohkAv9h5SGU19cEtzDcaeMPC4JYDAICNEQDxvXokReuElFh5DWnV1iCPBj7lCnO5bblUvje4ZQEAYFMEQLTLOSf6rgMMcjdwcl+p5xnmvYHXvxrcsgAAsCkCINrlnKbrAJdv3ifDMIJb2GnXmMt1L0nBLgsAABsiAKJdzu6XokiXUwUHqrR1X0VwCzvlh5I7SireKBWuC25ZAADYEAEQ7RLrceusvsmSpH9vKg5uYdFJ0oBLzfV1LwW3LAAAbIgAiHa7YGCaJOk/m0IwOMPXDbz+NamhNvjlAQBgIwRAtNu4AWYAXLPjoA5U1gW3sBPGSvFZ5oTQm7k1HAAAgUQARLv17BajARnx8hrSB18HuRvY6ZKGTDbX174Y3LIAALAZAiCOywUD0yVJ//k6FN3APzaX3+ZJpbuCXx4AADZBAMRxOb/pOsAVm0tU29AY3MJSTpT6jJYMr/T5C8EtCwAAGyEA4rgM6Zmk9ASPKmob9OHmIE8KLUkjrjeXa56XGoN8GzoAAGyCAIjj4nQ6dPHgTEnSu+sLg1/ggAlSbKpUUSR986/glwcAgA0QAHHcLj3VDIB5G/eqpj7I3cDuSGnoteb66nnBLQsAAJsgAOK4Dc3upoyEKLMbONj3Bpak4VMlOaRtH0j7twa/PAAALI4AiOPWohv4yz3BL7Bbb+nEC811WgEBAPAbARAdckkou4ElacQ0c7n2/6TaIN+LGAAAiyMAokOGZicpKzFKlXWN+k+w7w0sSSfmSt1PkGpKpS9eDn55AABYGAEQHeJ0OjRxaA9J0hufh2CSZqdTOusWc/2TuZLXG/wyAQCwKAIgOmzS8J6SpOWb96m4vCb4BQ65WopKlA5s4/7AAAD4gQCIDuubGqehvZLU6DX01toQDAbxxEnDmyaGXvWX4JcHAIBFEQDhl/9pagV8fc0uGYYR/ALPuElyuqUdH0l71gW/PAAALIgACL9cemqWIt1OfbO3XBv2lAW/wMQe0ik/NNdpBQQAoEMIgPBLYnSEck9OlyS9tnpnaAodeau5/OoN6eD20JQJAICFEADhtytHZEuSFn6+W5W1DcEvMGuo1HecZDRKH/9v8MsDAMBiCIDw2zn9UtQnOUbltQ16a10IBoNI0ui7zeXaf0hlISoTAACLIADCb06nQz85q7ck6YVV20MzGKTP2VKvkVJjnbRyTvDLAwDAQgiACIgfDc9WVIRTXxeV6/OCg6Ep9NymVsDV86TKktCUCQCABRAAERCJMRG6bEiWJOmFVTtCU2jf86XM06SGavPuIAAAoF0IgAiYa8/qI0lavL5QxWUhuDOIwyGd+wtz/dO/SZX7g18mAAAWQABEwAzumajhvbupvtHQcyu3h6bQky6WMgZLdeXSx38MTZkAAHRxBEAE1E3nniBJ+scnO1QRiilhnE5p3P3m+n//LpUVBr9MAAC6OAIgAurCgek6ISVW5TUNeuW/BaEp9MQLpeyzpIYaacUfQlMmAABdmKUC4Ny5c5WTk6OoqCgNHz5cH3744VH3XbhwoS688EKlpqYqISFBI0eO1Pvvvx/C2lqT0+nQT5taAZ/9KF/1jd7gF+pwSOc3tQJ+/rx0ID/4ZQIA0IVZJgAuWLBAM2bM0L333qu1a9dq9OjRGj9+vAoK2m6FWrFihS688EItXrxYa9as0XnnnacJEyZo7dq1Ia659fxwaA+lxHlUWFoTuomh+5xtjgr2NkjLfh+aMgEA6KIcRkhm7Q2+M888U8OGDdNTTz3VvG3gwIGaOHGiZs2a1a5jnHLKKZo8ebLuv//+du1fVlamxMRElZaWKiEhoUP1tqq5y77VY+99oz7JMfr3zDFyu0Lwf409a6W/jZXkkG5eIWWeGvwyAQBdDr/fFmkBrKur05o1a5Sbm9tie25urlauXNmuY3i9XpWXl6t79+5H3ae2tlZlZWUtHmjblJF91D02Utv3V2nR2t2hKTRrqDRokiRDev83kjX+bwMAQMBZIgCWlJSosbFR6enpLbanp6erqKioXcd44oknVFlZqSuvvPKo+8yaNUuJiYnNj+zsbL/qbWVxHrdubroW8M9Lvw3NtYCSdMGDkjtK2v6h9M3i0JQJAEAXY4kA6ONwOFo8Nwyj1ba2vPzyy3rwwQe1YMECpaWlHXW/e+65R6Wlpc2PnTt3+l1nK7t2ZG+lxEWq4ECVFn6+KzSFJvWSRt5qri+5T2qoC025AAB0IZYIgCkpKXK5XK1a+4qLi1u1Cn7XggULNG3aNL366qu64IILjrmvx+NRQkJCiweOLibSrelj+kqS/vSfb1XXEKJWwHPulGLTpAPbpM/+HpoyAQDoQiwRACMjIzV8+HDl5eW12J6Xl6dRo0Yd9X0vv/yypk6dqpdeekmXXHJJsKtpSz85q7fS4j3afahaL6zaHppCPfHSuPvM9eWPcos4AAC+wxIBUJJmzpypZ555RvPmzdOmTZt05513qqCgQNOnT5dkdt9OmTKlef+XX35ZU6ZM0RNPPKGzzjpLRUVFKioqUmlpabg+giVFRbh0d+5JkqQ//WeLDlaGqEt26E+k9MFSTan07wdCUyYAAF2EZQLg5MmT9eSTT+rhhx/WaaedphUrVmjx4sXq3bu3JKmwsLDFnIBPP/20GhoadOuttyozM7P58fOf/zxcH8GyJg3vqQEZ8SqradD//mdLaAp1uqSLm+4Ksvb/pIJPQ1MuAABdgGXmAQwH5hFqv4+2lOgnz34qt9OhJXeeqxNS40JT8Ju3Suv+IaUPkm5aLrncoSkXANBp8fttoRZAdG7nnJiicQPS1OA19Nt3N4Wu4AsflqK7SXu/kj79a+jKBQCgEyMAImR+c/FAuZ0O/efrYi3Z0L75Gf0Wmyxd8JC5vmyWVBqiSakBAOjECIAImX5pcbqpaXLoB9/eoMrahtAUPPRaqecZUl2FtPhu7hACALA9AiBC6vZxJ6pnt2jtKa0J4YAQpzThSckZYd4dZP3roSkXAIBOigCIkIqOdOn/XT5IkvTsR/nauCdE91NOP0Ua80tz/V+/kCqKQ1MuAACdEAEQIXfegDSNH5ShRq+hu1/7IrR3CMkYLFUflN6dSVcwAMC2CIAIi4cuP0XdYiK0sbBMc5aGqCvYFSFdPldyuqVN70gbFoWmXAAAOhkCIMIiLT5K/2+i2RX8l2Vb9eWuQ6EpOPNUafRd5vriu6XyvaEpFwCAToQAiLC59NQsXXJqphq9hu569QvV1DeGpuDRd5u3iavaL711i+QNURc0AACdBAEQYfX/Lh+klLhIbSmuCN0E0e5IadIzkjtK+vbfTBANALAdAiDCqntspB7/0RBJ0v99skOL1xeGpuC0AdJFvzXX//2AVPhlaMoFAKATIAAi7MaelKbpY/pKkn71+pcq2F8VmoJHTJNOulhqrJPeuFGqC1G5AACEGQEQncJduf01vHc3ldc26LaXPw/N9YAOh3TZHCkuQyr5RnrvV8EvEwCAToAAiE4hwuXUn64eqqSYCH25q1T3vfmVjFDM0xebLP3wr5Ic0ucvSGv/EfwyAQAIMwIgOo0eSdH601VD5XRIr6/ZpXkfbw9NwX3Pk877jbn+7l1cDwgAsDwCIDqVc/un6jcXD5Qk/fbdjfpwy77QFDz6bunEXKmhRnr1WvNuIQAAWBQBEJ3OtHNyNGlYT3kN6baX1urb4orgF+p0Sj98WkrqJR3cLi36GfMDAgAsiwCITsfhcOi3PxykYb2SVFpdr+vm/Vd7y2qCX3BMd+nK/5NcHmnzv6Tlvw9+mQAAhAEBEJ1SVIRLz1x3uk5IidXuQ9W6bt5/VVZTH/yCs06TLp1tri9/VFr/evDLBAAgxAiA6LS6x0bq+RvOUGq8R18XleumF1artiEE08MM/Yk08jZz/a1bpV1rgl8mAAAhRABEp5bdPUbzrz9dcR63Ptl2QLe9tFZ1DSG4Nu/Ch6UTLzIHhbxytVS6O/hlAgAQIgRAdHqnZCXqb1OGy+N2Km/jXt3x8lrVNwY5BDpd5v2C006WKvZKL18l1ZYHt0wAAEKEAIguYVTfFP1tyghFup16b0ORZryyTg3BDoFRCdLVr0gxKVLRl9KCa6WGuuCWCQBACBAA0WWM6Z+qp38yXJEup95dX6ifv7Iu+N3B3XpL17wqRcRI2z6Q3rqF6WEAAF0eARBdynkD0vTUT4YpwuXQu+sLNe35z1RV1xDcQnsON6eHcbql9a9Jef9fcMsDACDICIDocs4fmK5nrztd0REufbilRD9+5lMdqgpy1+yJF0iX/8VcXzVH+vh/g1seAABBRABEl3Ru/1S9+NMzlRgdobUFh3Tl06u051B1cAsdcpV04f8z1/Pulz57NrjlAQAQJARAdFnDenXTa9NHKj3Bo817K3T5Xz7Wup2Hglvo2XdIZ88w19+dKX3+f8EtDwCAICAAokvrnx6vhbecrQEZ8dpXXqvJT6/SP7/cE9xCL3hQOusWc/3t26UvFgS3PAAAAowAiC6vR1K0Xv/ZKI0bkKbaBq9ue2mt/vffW+T1GsEp0OGQLvqddPqNkgzpzenSV28EpywAAIKAAAhLiPO49fcpI3TjOTmSpD/+e7NufGF18AaHOBzS+D9Iw66TDK/0xk+5bzAAoMsgAMIyXE6H7rv0ZD026VR53E4t/bpYl/zpI30RrOsCnU7p0iel034sGY3SGzdKa54PTlkAAAQQARCWc+Xp2Vp4yyj1To7R7kPV+tFfV+mFVdtlGEHoEnY6pcvmSCOmSTKkd+6QVv0l8OUAABBABEBY0ilZiXrn9nN00Snpqmv06v63NuiG+Z+puLwm8IU5ndIlT0hn/9x8/v5vpGWPSsEInAAABAABEJaVEBWhv/5kuO6/9GRFup364Jt9uuiPK/TeV4WBL8zhkC54SDrvPvP5st9J7/1a8jYGviwAAPxEAISlORwO3XBOjv55+zk6OTNBB6vqNf0fn+uuV79QaVV9oAuTxvxC+sHvzeef/lV6dYpUH+QJqgEAOE4EQNhC//R4vXnr2frZ2L5yOKQ3Pt+l82cv1ztf7An8tYFn/Uz6n3mSK1L6+p/S85dJlfsDWwYAAH4gAMI2It1O/eoHA/TazSPVNzVWJRW1uv3ltbp+/mfaeaAqsIUNmiRd+6YUlSjt+q/07IXSgW2BLQMAgA4iAMJ2RvTprsU/H60ZF5yoSJdTy77Zp9w/rtDcZd+qpj6A1+z1OVualicl9pIObJX+fr6UvyJwxwcAoIMcRlDmxrCHsrIyJSYmqrS0VAkJCeGuDjrg2+IK/WbRev03/4AkKbt7tO69eKAuOiVDDocjMIWUF0kvXyXtWSs5XNL4R827iATq+ACA48LvNwHQL5xA1uD1Gnpz3W49+t7X2ltWK0k664Tuuv/SU3RyVoD+XOurzfsGr3/NfD7sOunixyV3ZGCODwBoN36/CYB+4QSylsraBv11+Vb9bcU21TZ45XBIE0/roRkXnKjeybH+F2AY0so/SXkPSDKk7LOkK1+Q4tP9PzYAoN34/SYA+oUTyJp2HazSrH99rXe/NOcLdDsduvL0bN0+rp8yE6P9L2BLnvT6NKm2VIpLlyY9I+Wc6/9xAQDtwu83AdAvnEDWtn5XqR5f8o2Wb94nyRxF/JMze+umc09QRmKUfwcv+VZ69VqpeKPkcEpj75FG323eVQQAEFT8fhMA/cIJZA//zT+gx9//Rv/dbg4UiXA5dMXQnrp5zAk6ITWu4weuq5IW/0Ja9w/z+QnnSVf8XYpLDUCtAQBHw+83AdAvnED2YRiGPtxSojkffNs8YtjhkMYPytAtY/tpUI/Ejh983UvSP2dKDdVSfKb0w79KJ4wNTMUBAK3w+00A9AsnkD2t2XFAcz/Yqv98Xdy87Yyc7rp+VB9deHK63K4OdOPu3Si9dp1Ustl8ftYt0vn3SxEBuOYQANACv98EQL9wAtnb10VlemrZVv3zy0I1es2/RlmJUfrJyN666vRe6h57nFO81FVKS+6TVs8zn6cOMLuEM08NcM0BwN74/SYA+oUTCJJUWFqtFz8p0Mv/LdD+yjpJ5oCRCadmafLp2Tq9T7fjm1R68/vSW7dJlcWSM0Iad6806g7J6QrSJwAAe+H3mwDoF04gHKmmvlH//LJQz6/crvW7S5u3n5ASqx+NyNak4T2UFt/O0cOVJdLbd0jfvGs+7zFCuuzPUvrJQag5ANgLv98EQL9wAqEthmFo7c5DWvDfnXrnyz2qqjPvL+xyOnTeSWn6n+E9NfakVEVFfE+LnmFIa/8hvf8bqbbMbA0cPVMafZfk9oTgkwCANfH7TQD0CycQvk9lbYPe/bJQC1bv1JodB5u3x3vcumhQhi4bkqVRfZOPPXCkbI/07l3SN4vN5yknSZfPkbLPCHLtAcCa+P0mAPqFEwjH49viCr22ZqfeWbdHe0prmrenxEXq4sGZumxIlob16ians43rBQ1D2vimOW9g5T5JDun0adK4+6TobiH7DABgBfx+EwD9wgmEjvB6Da3ecVBvf7Fbi9cX6UDTwBFJSonz6MKT03XRKeka2TdZHvd3uomrDpgjhde9aD6PSZYueFA67SfcRQQA2onfbwKgXziB4K/6Rq8+/rZEb6/bo7yNe1Ve29D8WpzHrbEnpSr3lAydd1Kq4qMiDr8xf4XZGrjva/N5j+HSxY9LPYaF+BMAQNfD7zcB0C+cQAikugavPtm2X0s2FmnJhr0qLq9tfs3tdGh4724ac1KqxvRP1cmZCXJ4G6RPn5aW/V6qK5fkkIZfJ513rxSXFr4PAgCdHL/fFguAc+fO1R/+8AcVFhbqlFNO0ZNPPqnRo0cfdf/ly5dr5syZ2rBhg7KysvTLX/5S06dPb3d5nEAIFq/X0Be7Dun9DXu1ZEORtpVUtng9Nd6jMf3NMHhuZoMSP3pE+nKB+WJknHT2DGnkrVJkTOgrDwCdHL/fFgqACxYs0LXXXqu5c+fq7LPP1tNPP61nnnlGGzduVK9evVrtn5+fr0GDBumnP/2pbr75Zn388ce65ZZb9PLLL2vSpEntKpMTCKGyY3+llm/ep+Xf7NPKrftVXd/Y/JrTIZ2Slagr03bq8r1/UcKB9eYL8ZnmIJEhVzOJNAAcgd9vCwXAM888U8OGDdNTTz3VvG3gwIGaOHGiZs2a1Wr/X/3qV3r77be1adOm5m3Tp0/XF198oVWrVrWrTE4ghENtQ6NWbz/YHAi/2Vve/JpDXk1wfaJ7Pa8p3btXktSYerJcuQ9L/S6QjueOJABgUfx+S+5wVyAQ6urqtGbNGv36179usT03N1crV65s8z2rVq1Sbm5ui20XXXSRnn32WdXX1ysiIqLN9wHh5nG7dHa/FJ3dL0W/uXig9pbV6JNt+7Vq636t2rZfb+8fpfeqTtcU1xLd7l6kxH0bpRf/RztjB2nnaXeq94iLlZUUfXy3pwMAWIolAmBJSYkaGxuVnp7eYnt6erqKiorafE9RUVGb+zc0NKikpESZmZmt3lNbW6va2sMX5peVlQWg9oB/0hOidPlpPXT5aT0kSXsOVTcFwhxdtfUi/bBigaa4lii78itlfzxNn344QI9E/ljOnHM0tFeShvfuplOyEhXpZhoZALALSwRAn++2aBiGccxWjrb2b2u7z6xZs/TQQw+12v7aa68pJoaL7dG5DJM0rLdUU3+x/lYxRu7SfCXWFsrpNHRuw2od2PyNNn2TqVWKk9PhUJzHrYQotxKiIxQfFaE4j4tWQgCWVFVVFe4qhJ0lAmBKSopcLler1r7i4uJWrXw+GRkZbe7vdruVnJzc5nvuuecezZw5s/l5WVmZsrOz9aMf/ci21xCgiyndrfrlj8u17v/k9NZLDmmNBurPdRO0qHaIVHY48EW6nTo5M0GDeyRqcM9EDe6RqH5pcYo41m3rAKALKCsr04033hjuaoSVJQJgZGSkhg8frry8PP3whz9s3p6Xl6fLL7+8zfeMHDlS77zzTottS5Ys0YgRI456/Z/H45HH4wlcxYFQS+yhiMv+KJ17p7TicWndSxru3aT5kZtUlniSPkj5sV6rHqEv9lSovKZB63Ye0rqdh5rfHuFyqF9avAZkND0yEzQwI16p8R5aCwGgC7HMKGDfNDB//etfNXLkSP3tb3/T3//+d23YsEG9e/fWPffco927d+uFF16QdHgamJtvvlk//elPtWrVKk2fPp1pYGAvZXukVX+RVj8n1TfNNditj7wj71BBr8v15d46rd91SOt3l+qr3WWqOOJOJUfqFhOhARkJGpAZr4EZCToxPU590+KUEMVgKgCdD7/fFgqAkjkR9GOPPabCwkINGjRIf/zjH3XuuedKkqZOnart27dr2bJlzfsvX75cd955Z/NE0L/61a+YCBr2VHVA+uwZ6ZOnpOoD5rbobtLwqdLpN0qJPWUYhnYdrNbXReX6pqhMm4rK9XVhmfJLKuU9yr8iafEe9UuLU9/UOPVLi2teT0+gxRBA+PD7bbEAGGqcQLCcukpp7T+kVXOkQwXmNodLOvky6czpUvaZreYSrKlv1Ja9Ffq6qExfF5Xr66Iybdlb0eJWdt8V53Grb2qs+jYFwt7JMeqTHKveyTEt73kMAEHA7zcB0C+cQLAsb6P0zb+kT/8qbf/w8PbM08wgeMoPpYioYx6irKZeW4srtHVfpb4trtDWfRXaWlyhHQeq1Hi0JkNJybGR6p0co95NgbDPEcukmAhaDgH4jd9vAqBfOIFgC0XrzSD45WtSY1OrXlSSdNo10rDrpLQBx3W4ugavduyv1NZ9Ffq2uELbSipVsL9K2/dXqaTi6K2GkhQf5Vbv5Bhld4tRj6Ro9ewWrR7dYpqW0VxzCKBd+P0mAPqFEwi2UlkirXlOWj1fKtt1eHuvkea1gidfLkVE+1VERW2Dduyv1I79VU2PSm1vel5YWvO970+IcqvHEeHQ9+iRFKOspCh1j42kBREAv98iAPqFEwi25G2Uvv2PtGa+tPk9yWg0t0clSkOuNlsGM04N+H2Ha+obtfOA2VK4+2CVdh+q1q6D5mP3oWodqKz73mNEupxKT/QoMyFa6YlRykyMUnqCucxIjFJGQpTS4j1yM9chYGn8fhMA/cIJBNsrKzQHjXz+glRacHh72snSkKukwT+SErJCUpWqugbtbgqEuw5Va9fBqsPPD1Z/b/eyj9MhpcR5WobChCilxnvMR5xHafEedY+NJCgCXRS/3wRAv3ACAU28jdLWD6R1/5C+Xnz4WkE5pBPGmi2DAy+VImPDVsW6Bq+Ky2tUVFqjojJzWXjEelFpjfaW1ajhGANUjuRwmANWUuI8h8NhU0D0rafFe5QaF6WEaDddz0Anwu83AdAvnEBAG6oPSRvflL54RSpYdXh7RKwZAk/5odR3nOTufHfV8XoN7a+sOyIkVquwtEb7ymu1r6LWXJbXqqSi9qhzH7Yl0uVUt9gIdY/1KDk2Ut2bHsmxkerWtOweG6nkuEh1j/UoKTpCTieBEQgWfr8JgH7hBAK+x4Ft0pevSl+8LB3cfni7J1EacIk06AopZ4zkjgxbFTui0WvoQGVdq2B4+HlN8/OymrbvnnIsTofULcYMh92PDIixkUqKiVRSTISSYiKUGN20Hh2hxOgIuqSBduL3mwDoF04goJ0MQ9r5qbRhkbThTami6PBrUUlNLYNXSDnnSi5rTeVSU9+okopaHais0/7KOh2oqNPBqsPr+yvrdKCyVger6rW/omOB0Sfe41ZiUzhMio4016Pben44OCZERygqwhXATwx0fvx+EwD9wgkEdIDXK+38RPpqobTxLamy+PBrUYnSiRdJAy6W+l0geeLDV88wqW/06qAvLB7x8AXFQ1X1Kq2u16Gqeh2qrtOhqnqV+xEaJSnS7VRClFsJURGKj3IrIbppGdVyGR8V0fq16AjFe9x0WaNL4febAOgXTiDAT95GacdKs2Vw41tSVcnh11yRZvfwgIulky6W4jPCV89OrqHRq7KaBh2qqtOh6nqVHhEODwdG87Ujn5dW1x/XtYzHEu9xtwqPcVFuxXrcimt6mOsuxTatx3sOv25uc8njpjUSwcfvNwHQL5xAQAB5G6Wd/5W+edccSXxga8vXeww3g+CJuVLG4IDPM2hHXq+h8toGldeYrYhl1U3LpuflNfUq8y2rze1HPi+vqVdtgzegdYp0ORXbFBLjPN8NkK42AqVbMZEuxUS6FR3pUqzHpZgIcz0m0qXoCBetk2iF328CoF84gYAgMQypZLP09bvmY/fqlq/HpZtdxP3Ol044T4rpHp56QrUNjW2GR9/zitoGVdY2qLKuQRW1jaqsNbdV1JjbfM9r6gMbJI8UHdEUBn2hMNKt2CPWYyJcivG4DgfJpv1jPE2vNb031uNucawoN+Gyq+L3mwDoF04gIETKi6Rv/iVtfl/KXyHVVx5+zeGUeoyQTrzQDISZQyUno2G7moZGryprG1VxRCisbAqKh0NkY+vtdQ2qrG1UdV2jquobVF3XaD6vbwxJvSPdTkVHuBQV4Vu65IlwKTrCqagIV/O2qO/s41v3HLGP7zht7++Si7AZMPx+EwD9wgkEhEFDrTm/4JY885Z0+za1fD0m2RxNnHOueQ1h9xPoLrYhr9dQTUOjquoaVVVrhsOquqagWNeoqrqGpmWjqo9Y921vc79683kwWyuPJdLlbA6I0ZEuedxOedxNy4gj1n3bI5yKdLXxWsTh90Y273/k9pbrkW7zOFaazJzfbwKgXziBgE7g0E5p63/MQLhtuVRX3vL1hJ5HBMJzpcQe4aknLKPRa6imvlE19WYorKn3Nj+vqfc2bTNfq/3OPt/dv/qI9333mNX1jaoL8DWW/mgzKLYImq7mwOhxNQVHt1MRrsMhMvI7oTLyiPWI77zPtz051qPEmMBOD8XvNwHQL5xAQCfTWC/t+kzK/1DKX24OKvHWt9yne1/phDFSn3OkXqOkhMzw1BVoB19LZssAaT5q672qbfCqtqHRXNYfsd5wxGvf2a/O91p941H38+3TGdwxrp9m5p4U0GPy+y25w10BAAgYV4TUe5T5GPsrqa7KnHMwf4XZOli4zhxdfGCrtHqe+Z5ufaReIw8/Uk6kyxidhtPpUEykWzFhuFmOYRiqa/S2Dpf1XnP7UQJkXUOj6hrNoFnX4FXtEev1vvXGw0H0yOe+9fqmZW2DVzEeokow0ALoB/4HAXQx1YfMeQfzl5vLvV9JxndaOWKSWwbCzFMtd3cSwO74/SYA+oUTCOjiakrNLuMdq6SCT8zpZhpqWu4TESNlnib1HG6ONu45QkroQSsh0IXx+00A9AsnEGAxDbVS4RfmKOMdq8xlzaHW+8VlmEGwx3BzmTXUlretA7oqfr8JgH7hBAIszuuV9m+Rdq02Wwd3rZb2bpCM78wx53BKqQPMQJg11GwxTD9ZiogOS7UBHBu/3wRAv3ACATZUV2W2EvoC4e41UunO1vs5XGYozBxy+JExiJZCoBPg95sA6BdOIACSzDuV7F5jPgq/kPask6pK2tjRISX3OyIUniqlD5JiU0JdY8DW+P0mAPqFEwhAmwxDKi80w+CRj7Ldbe8fmyaln2I+0k42l6kn0YUMBAm/3wRAv3ACATguFfukoiND4ZfSwe2S2vhn2OE0J63+bjBM6s29jgE/8ftNAPRLaWmpkpKStHPnTtueQAD8VFshlWyWir+WSr6WijeZ6zUH297fHS0l95WST5RS+jUtTzQntGa+QqBdysrKlJ2drUOHDikxMTHc1QkLptf2Q3m5ec/R7OzsMNcEgH2USyqWtCrcFQG6vPLyctsGQFoA/eD1erVnzx7Fx8fLEaBJYX3/K6FV8fvxXR0fvq/247s6Pnxf7cd31X7B/K4Mw1B5ebmysrLktOklFbQA+sHpdKpnz55BOXZCQgL/OLQT39Xx4ftqP76r48P31X58V+0XrO/Kri1/PvaMvQAAADZGAAQAALAZAmAn4/F49MADD8jj8YS7Kp0e39Xx4ftqP76r48P31X58V+3HdxVcDAIBAACwGVoAAQAAbIYACAAAYDMEQAAAAJshAAIAANgMAbATmTt3rnJychQVFaXhw4frww8/DHeVOqUHH3xQDoejxSMjIyPc1eo0VqxYoQkTJigrK0sOh0Nvvvlmi9cNw9CDDz6orKwsRUdHa+zYsdqwYUN4Khtm3/ddTZ06tdW5dtZZZ4WnsmE2a9YsnX766YqPj1daWpomTpyob775psU+nFum9nxXnFuHPfXUUzr11FObJ3weOXKk/vWvfzW/znkVHATATmLBggWaMWOG7r33Xq1du1ajR4/W+PHjVVBQEO6qdUqnnHKKCgsLmx/r168Pd5U6jcrKSg0ZMkRz5sxp8/XHHntMs2fP1pw5c/TZZ58pIyNDF154YfO9re3k+74rSfrBD37Q4lxbvHhxCGvYeSxfvly33nqrPvnkE+Xl5amhoUG5ubmqrKxs3odzy9Se70ri3PLp2bOnfv/732v16tVavXq1xo0bp8svv7w55HFeBYmBTuGMM84wpk+f3mLbgAEDjF//+tdhqlHn9cADDxhDhgwJdzW6BEnGokWLmp97vV4jIyPD+P3vf9+8raamxkhMTDT++te/hqGGncd3vyvDMIzrrrvOuPzyy8NSn86uuLjYkGQsX77cMAzOrWP57ndlGJxb36dbt27GM888w3kVRLQAdgJ1dXVas2aNcnNzW2zPzc3VypUrw1Srzm3Lli3KyspSTk6OrrrqKm3bti3cVeoS8vPzVVRU1OJc83g8GjNmDOfaUSxbtkxpaWnq37+/fvrTn6q4uDjcVeoUSktLJUndu3eXxLl1LN/9rnw4t1prbGzUK6+8osrKSo0cOZLzKogIgJ1ASUmJGhsblZ6e3mJ7enq6ioqKwlSrzuvMM8/UCy+8oPfff19///vfVVRUpFGjRmn//v3hrlqn5zufONfaZ/z48XrxxRe1dOlSPfHEE/rss880btw41dbWhrtqYWUYhmbOnKlzzjlHgwYNksS5dTRtfVcS59Z3rV+/XnFxcfJ4PJo+fboWLVqkk08+mfMqiNzhrgAOczgcLZ4bhtFqG8x/OH0GDx6skSNHqm/fvnr++ec1c+bMMNas6+Bca5/Jkyc3rw8aNEgjRoxQ79699e677+qKK64IY83C67bbbtOXX36pjz76qNVrnFstHe274txq6aSTTtK6det06NAhvfHGG7ruuuu0fPny5tc5rwKPFsBOICUlRS6Xq9X/ZoqLi1v9rwetxcbGavDgwdqyZUu4q9Lp+UZLc651TGZmpnr37m3rc+3222/X22+/rQ8++EA9e/Zs3s651drRvqu22P3cioyMVL9+/TRixAjNmjVLQ4YM0f/+7/9yXgURAbATiIyM1PDhw5WXl9die15enkaNGhWmWnUdtbW12rRpkzIzM8NdlU4vJydHGRkZLc61uro6LV++nHOtHfbv36+dO3fa8lwzDEO33XabFi5cqKVLlyonJ6fF65xbh33fd9UWO59bbTEMQ7W1tZxXwRS24Sdo4ZVXXjEiIiKMZ5991ti4caMxY8YMIzY21ti+fXu4q9bp3HXXXcayZcuMbdu2GZ988olx6aWXGvHx8XxXTcrLy421a9caa9euNSQZs2fPNtauXWvs2LHDMAzD+P3vf28kJiYaCxcuNNavX29cffXVRmZmplFWVhbmmofesb6r8vJy46677jJWrlxp5OfnGx988IExcuRIo0ePHrb8rn72s58ZiYmJxrJly4zCwsLmR1VVVfM+nFum7/uuOLdauueee4wVK1YY+fn5xpdffmn85je/MZxOp7FkyRLDMDivgoUA2In85S9/MXr37m1ERkYaw4YNazFlAA6bPHmykZmZaURERBhZWVnGFVdcYWzYsCHc1eo0PvjgA0NSq8d1111nGIY5XccDDzxgZGRkGB6Pxzj33HON9evXh7fSYXKs76qqqsrIzc01UlNTjYiICKNXr17GddddZxQUFIS72mHR1vckyXjuueea9+HcMn3fd8W51dINN9zQ/NuXmppqnH/++c3hzzA4r4LFYRiGEbr2RgAAAIQb1wACAADYDAEQAADAZgiAAAAANkMABAAAsBkCIAAAgM0QAAEAAGyGAAgAAGAzBEAAAACbIQACAADYDAEQAADAZgiAAAAANkMABAAAsBkCIAAAgM0QAAEAAGyGAAgAAGAzBEAAAACbIQACAADYDAEQAADAZgiAAAAANkMABAAAsBkCIAAAgM0QAAEAAGyGAAgAAGAzBEAAAACbIQACAADYDAEQAADAZgiAAAAANkMABAAAsBkCIAAAgM0QAAEAAGyGAAgAAGAz/z+AJFqxnzCSSgAAAABJRU5ErkJggg==' width=640.0/>\n",
       "            </div>\n",
       "        "
      ],
      "text/plain": [
       "Canvas(toolbar=Toolbar(toolitems=[('Home', 'Reset original view', 'home', 'home'), ('Back', 'Back to previous …"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "Z = 26\n",
    "E_0 = 10 # keV\n",
    "\n",
    "K = -4000\n",
    "I = 1\n",
    "\n",
    "E = energy_scale = np.linspace(.1,30,2048) #in keV\n",
    "N_E = I*K*Z*(E-E_0)/E\n",
    "\n",
    "Z2 = 58\n",
    "E_02 = 10 # keV\n",
    "N_E2 = I*K*Z2*(E-E_02)/E\n",
    "\n",
    "plt.figure()\n",
    "plt.plot(energy_scale, N_E, label= f'{E_0} keV');\n",
    "plt.plot(energy_scale, N_E2, label= f'{E_02} keV');\n",
    "plt.axhline(y=0., color='gray', linestyle='-', linewidth = 0.5)\n",
    "plt.ylim( -1e5, 1e6)\n",
    "plt.legend();"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Please change the atomic number *Z* and the acceleration voltage *E_0* in the code cell \n",
    "above to see the influence of these values on the Bremsstrahlung."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Bremsstrahlung and EDS Background\n",
    "\n",
    "At low energies,  this background above does not look anything like the background we obtain in the EDS spectrum.\n",
    "\n",
    "This is due to the  response of the EDS detector system\n",
    "\n",
    "![X-Ray_Auger](./images/DetectorEfficiency.png).\n",
    "\n",
    "The effect of the detector system will be discussed in the [Detector Efficiency notebook](CH4_15-Detector.ipynb). "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "## Navigation\n",
    "- <font size = \"3\">  **Back: [Introduction to X-Ray](CH4_12-Introduction_X_Rays.ipynb)** </font>\n",
    "- <font size = \"3\">  **Next: [Characteristic X-Rays](CH4_14-Characteristic_X_Rays.ipynb)** </font>\n",
    "- <font size = \"3\">  **Chapter 4: [Spectroscopy](CH4_00-Spectroscopy.ipynb)** </font>\n",
    "- <font size = \"3\">  **List of Content: [Front](../_MSE672_Intro_TEM.ipynb)** </font>\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "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": "3.13.5"
  },
  "vscode": {
   "interpreter": {
    "hash": "838e0debddb5b6f29d3d8c39ba50ae8c51920a564d3bac000e89375a158a81de"
   }
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}