{ "cells": [ { "cell_type": "markdown", "metadata": { "id": "plVuDI_GfiiW" }, "source": [ " **[MSE672: Introduction to TEM](https://gduscher.github.io/MSE672-Introduction-to-TEM/)** \n", "\n", "
\n", "\n", "\n", "# Electron Optics\n", "\n", "[Download](https://raw.githubusercontent.com/gduscher/MSE672-Introduction-to-TEM//main/Introduction/CH1_07-Electron_Optics.ipynb)\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/Introduction/CH1_07-Electron_Optics.ipynb)\n", " \n", "part of\n", "\n", " **[MSE672: Introduction to Transmission Electron Microscopy](../_MSE672_Intro_TEM.ipynb)**\n", "\n", "**Spring 2026**
\n", "by Gerd Duscher\n", "\n", "Microscopy Facilities
\n", "Institute of Advanced Materials & Manufacturing
\n", "Materials Science & Engineering
\n", "The University of Tennessee, Knoxville\n", "\n", "## Import packages for figures and \n", "### Check Installed Packages" ] }, { "cell_type": "code", "execution_count": 2, "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') < '0.2026.1.2':\n", " print('installing pyTEMlib')\n", " !{sys.executable} -m pip install --upgrade pyTEMlib -q\n", "\n", "print('done')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Load the plotting and figure packages\n", ">Note for Google Colab\n", ">\n", ">The runtime has to be restarted and the code cell below again to enable interactive plotting\n", ">\n", ">in the Menu **Runtime** choose **Restart Runtime** (**Ctrl-M**) " ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "%matplotlib widget\n", "import matplotlib.pylab as plt\n", "import numpy as np\n", "import sys\n", "if 'google.colab' in sys.modules:\n", " from google.colab import output\n", " output.enable_custom_widget_manager()\n", " \n", "import pyTEMlib.animation as animate" ] }, { "cell_type": "markdown", "metadata": { "id": "dfb9CuuUf5qm" }, "source": [ "## Transmission Electron Microscope\n", "\n", "A TEM is a stack of electro-optical elements:\n", "![TEM](images/Zeiss.png)" ] }, { "cell_type": "markdown", "metadata": { "id": "FsGiRUi_gGAG" }, "source": [ "- electron source\n", "- electrostatic lens\n", "- accelerator\n", "- magnetic lens\n", "- magnetic and electrostatic deflectors\n", "- magnetic multipoles\n", "- apertures\n", "- detectors (viewing screen,CCD)\n", "- sample holder\n" ] }, { "cell_type": "markdown", "metadata": { "id": "u-YSfinDgaFA" }, "source": [ "### Start screen on the computer of our TEM: Thermo-Fisher Spectra 300\n", "\n", "![start_screen](images/start_screen_Spectra.png)" ] }, { "cell_type": "markdown", "metadata": { "id": "jqsjOHmEg3p4" }, "source": [ "The big buttons on upper left, we saw already in the last notebook.\n", "\n", "You select the different modes of the TEM with those.\n", "\n", "![TEMmodes.png](images/TEMmodes.png)" ] }, { "cell_type": "markdown", "metadata": { "id": "_PEM-4gqhlWo" }, "source": [ "## Electron Optics - Overview of the Whole System\n", "\n", "We start on the top.\n", "\n", "#### The Electron Gun \n", "The electron gun produces the electrons, focuses them and accelerates\n", "them.\n", "\n", "#### The Condenser \n", "The condenser lens system varies the beam size, the illumination area and the convergence angle.\n", "\n", "#### The Objective Lens\n", "The objective lens does the maximum magnification in imaging mode.\n", "\n", "#### The Intermediate Lens\n", "The Intermediate lens system switches between imaging and\n", "diffraction mode. The objective lens does not magnify anything in diffraction mode, because the back focal plane of the objective lens is object plane of the intermediate plane. The intermediate lens does the maximum magnification.\n", "\n", "#### The Projector Lens \n", "The projector lens system magnifies everything roughly to the\n", "magnification indicated on the display/chosen on the console." ] }, { "cell_type": "markdown", "metadata": { "id": "K82oJmm3iVKj" }, "source": [ "### Electron Optics - Condenser\n", "\n", "The electron optics starts at the cross over which the gun produces in the\n", "differential pumping aperture.\n", "Then we have a condenser lens system with three lenses, three pairs of deflectors, a pair of stigmators and an aperture. \n", "\n", "This allows a very flexible illumination of the specimen." ] }, { "cell_type": "markdown", "metadata": { "id": "WQMzs6txiq4S" }, "source": [ "### Electron Optics - Projective\n", "\n", "The projector lens system in our TEM (Zeiss Libra 200MC) is divided by the electron energy-loss filter into two parts.\n", "\n", "The first part switches from imaging to diffraction and does all the magnification. This part has three\n", "lenses, two pairs of deflectors, a stigmator, and an aperture. \n", "\n", "The second part switches from spectroscopy to imaging or diffraction and does only magnification in spectroscopy mode. This part has three lenses, two pairs\n", "of deflectors, a stigmator, and an aperture." ] }, { "cell_type": "markdown", "metadata": { "id": "HAKbBVLwjDKv" }, "source": [ "## Electron Optics - Ray Diagrams\n", "\n", "To do the optical ray diagram we only have to concern ourselves with the lenses and the apertures.\n", "\n", "Deflectors and stigmators (correcting multipoles) are only used to correct for mechanical misalignment of the optical axis.\n", "The correcting multipoles will be discussed in the phase contrast part of this lecture.\n", "The deflectors will be discussed in the STEM part in detail.\n", "\n", "### Basic Ray Diagram" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "data": { "application/vnd.jupyter.widget-view+json": { "model_id": "0c0bd180f9d44af3b263e2e022ef34b8", "version_major": 2, "version_minor": 0 }, "image/png": 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", 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", 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field is too weak, we call\n", "it underfocus, is it too strong\n", "we speak of overfocus.\n", "\n", "![focus](images/focus.png)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Condenser Ray Diagram\n", "Below is a stack of lenses that is equivalent to the condenser lens system on the Libra 200.\n", "\n", "The objective lens focal length is usually not changed (at least not much), and the sample is in the middle of the objective lens system.\n", "\n", "Change the ``focal lengths`` parameters so that there the illumination changes from parallel to convergent. \n", "\n", "Tip: do not change the gun (first value), and the objective (last two values) values." ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "id": "pEkk_1rHfowo" }, "outputs": [ { "data": { "application/vnd.jupyter.widget-view+json": { "model_id": "980dd12912bc44219b93efc01998338a", "version_major": 2, "version_minor": 0 }, "image/png": 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\n", " " ], "text/plain": [ "Canvas(toolbar=Toolbar(toolitems=[('Home', 'Reset original view', 'home', 'home'), ('Back', 'Back to previous …" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# ------ INPUT ------#\n", "focal_lengths = np.array([50.0, 70.0, 378.0, 127.0 , 50, 50]) # Slightly convergent\n", "\n", "#--------------------#\n", "\n", "# Define lenses here\n", "lens_labels = ['Gun', 'C1', 'C2', 'C3' , 'Objective', '']\n", "lens_positions = np.array([200.0, 400.0, 600.0, 800.0, 1100,1200 ]) # lens positions\n", "\n", "animate.propagate_beam([0,],1, 3, lens_positions, focal_lengths, lens_labels, 'blue')\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "If you select any mode, magnification or brightness, the computer looks up a dataset and provides the stored values of currents to the respective lenses and other optical elements. \n", "\n", "An engineering alignment determines those values and users only have to deal with the fine-tuning of the electron optical system." ] }, { "cell_type": "markdown", "metadata": { "id": "GcfSxvtik6os", "pycharm": { "name": "#%% md\n" } }, "source": [ "## Convergence Angle\n", "\n", "The condensor lens system defines the illumination of the sample and with it the convergence angle (even parallel illumination has ususally a convergence angle of a few $\\mu$rad).\n", "\n", "The convergence angle is set by the condenser lens system and can be measured with a convergent beam electron diffraction (CBED) pattern.\n", "\n", "\n", "Under plane wave illumination the diffraction pattern consists of points. If you imagine a second incident plane wave\n", "with some angle to the first one, there will be two slightly shifted diffraction patterns made out of points.\n", "\n", "\n", "A lot of plane waves with a conical angle distribution will result in small circles instead of a point. The radius of the circle corresponds to the convergence angle. One can easily calculate the convergence angle from a CBED pattern of a known sample." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Summary Ray Optics of TEM\n", "- Lenses provide illumination and magnification\n", "- Lenses switch modes in a TEM\n", "- Lenses allow to select the angles within a TEM\n", "- Apertures help to select the information projected in a TEM\n", "\n", "A detailed understanding of the angles within the TEM allows for a\n", "project oriented experimental setup.\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Navigation\n", "- **Back [Overview](CH1_06-Overview.ipynb)** \n", "- **Next: [Diffraction](../Diffraction/CH2_00-Diffraction.ipynb)** \n", "- **Chapter 1: [Introduction](CH1_00-Introduction.ipynb)** \n", "- **List of Content: [Front](../_MSE672_Intro_TEM.ipynb)** " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Appendix:\n", "### Code for condenser stack ray diagram" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [], "source": [ "# ----------------------------------------------------------------\n", "# Modified from Michael Fairchild :simply draws a thin-lens at the provided location parameters:\n", "# - z: location along the optical axis (in mm)\n", "# - f: focal length (in mm, can be negative if div. lens)\n", "# - diam: lens diameter in mm\n", "# - lens_labels: label to identify the lens on the drawing\n", "# ----------------------------------------------------------------\n", "def add_lens(z, f, diam, lens_labels):\n", " \"\"\"add lens to propagate beam plot\"\"\"\n", " ww, tw, rad = diam / 10.0, diam / 3.0, diam / 2.0\n", " plt.plot([z, z], [-rad, rad], 'k', linewidth=2)\n", " plt.plot([z, z + tw], [-rad, -rad + np.sign(f) * ww], 'k', linewidth=2)\n", " plt.plot([z, z - tw], [-rad, -rad + np.sign(f) * ww], 'k', linewidth=2)\n", " plt.plot([z, z + tw], [rad, rad - np.sign(f) * ww], 'k', linewidth=2)\n", " plt.plot([z, z - tw], [rad, rad - np.sign(f) * ww], 'k', linewidth=2)\n", " plt.plot([z + f, z + f], [-ww, ww], 'k', linewidth=2)\n", " plt.plot([z - f, z - f], [-ww, ww], 'k', linewidth=2)\n", " plt.text(z, rad + 5.0, lens_labels, fontsize=12)\n", " plt.text(z, rad + 2.0, 'f=' + str(int(f)), fontsize=10)\n", "\n", "\n", "def add_aperture(z, diam, radius, lens_labels):\n", " \"\"\"add aperture to propagate beam plot\"\"\"\n", "\n", " ww, tw, rad = diam / 10.0, diam / 3.0, diam / 2.0\n", " radius = radius / 2\n", " plt.plot([z, z], [-rad, -radius], 'k', linewidth=2)\n", " plt.plot([z, z], [rad, radius], 'k', linewidth=2)\n", " plt.text(z, -rad - 2.0, lens_labels, fontsize=12)\n", "\n", "\n", "def propagate_beam(source_position, numerical_aperture, number_of_rays, lens_positions, focal_lengths,\n", " lens_labels='', color='b'):\n", " \"\"\"geometrical propagation of light rays from given source\n", "\n", " Parameters\n", " ----------\n", " source_position: list\n", " location of the source (z0, x0) along and off axis (in mm)\n", " numerical_aperture: float\n", " numerical aperture of the beam (in degrees)\n", " number_of_rays: int\n", " number of rays to trace\n", " lens_positions: numpy array\n", " array with the location of the lenses\n", " focal_lengths: numpy array\n", " array with the focal length of lenses\n", " lens_labels: list of string\n", " label for the nature of lenses\n", " color: str\n", " color of the rays on plot\n", " \"\"\"\n", "\n", " plt.figure()\n", " z_max = 1600.\n", "\n", " # aperture (maximum angle) in radians\n", " apa = numerical_aperture * np.pi / 180.0\n", "\n", " for i in range(np.size(lens_positions)):\n", " add_lens(lens_positions[i], focal_lengths[i], 25, lens_labels[i])\n", "\n", " add_aperture(840, 25, 7, 'CA')\n", "\n", " # position of source is z0,x0\n", " z0 = source_position[0]\n", " if np.size(source_position) == 2:\n", " x0 = source_position[1]\n", " else:\n", " x0 = 0.0\n", "\n", " # list of lens positions\n", " zl1, ff1 = lens_positions[(z0 < lens_positions)], focal_lengths[(z0 < lens_positions)]\n", " nl = np.size(zl1) # number of lenses\n", "\n", " zz, xx, tani = np.zeros(nl + 2), np.zeros(nl + 2), np.zeros(nl + 2)\n", " tan0 = np.tan(apa / 2.0) - np.tan(apa) * np.arange(number_of_rays) / (number_of_rays - 1)\n", "\n", " for i in range(number_of_rays):\n", " tani[0] = tan0[i] # initial incidence angle\n", " zz[0], xx[0] = z0, x0\n", " for j in range(nl):\n", " zz[j + 1] = zl1[j]\n", " xx[j + 1] = xx[j] + (zz[j + 1] - zz[j]) * tani[j]\n", " tani[j + 1] = tani[j] - xx[j + 1] / ff1[j]\n", "\n", " zz[nl + 1] = z_max\n", " xx[nl + 1] = xx[nl] + (zz[nl + 1] - zz[nl]) * tani[nl]\n", " plt.plot(zz, xx, color)\n", " plt.axis([-20, z_max, -20, 20])\n" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] } ], "metadata": { "colab": { "authorship_tag": "ABX9TyPpeUffxRTpGpH529V5WM6r", "collapsed_sections": [], "name": "02_ElectronOptics.ipynb", "provenance": [], "toc_visible": true }, "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" }, "toc": { "base_numbering": "8", "nav_menu": {}, "number_sections": true, "sideBar": true, "skip_h1_title": false, "title_cell": "Table of Contents", "title_sidebar": "Contents", "toc_cell": false, "toc_position": {}, "toc_section_display": true, "toc_window_display": true }, "vscode": { "interpreter": { "hash": "838e0debddb5b6f29d3d8c39ba50ae8c51920a564d3bac000e89375a158a81de" } } }, "nbformat": 4, "nbformat_minor": 4 }