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"(ch:electron-microscopybasics)=\n",
"\n",
"# Electron Microscopy basics\n",
"\n",
"(sec:introduction-microscopybasics)=\n",
"\n",
"## Introduction\n",
"\n",
"In this chapter, we will deal with basic knowledge about microscopes in general and electron microscopes specifically. From the basic, general layout and components of a microscope, we will explain the two main modes of image acquisition: wide field recording versus scanning. We will show why the use of electrons lowers the diffraction limit compared to the use of light (or photons) and could theoretically allow for resolution far below a nanometer. In a later chapter, we will see that there are other, practical limitations to the resolution that can be obtained with electron microscopy.\n",
"\n",
"The second part of this chapter, paragraphs 7 and 8, explain the basic components that we encounter in an electron microscope with their relevant properties: electron sources including the concepts of brightness and coherence, and both electrostatic and magnetic electron lenses. The chapter will be concluded with some practical considerations related to the use of electron microscopes.\n",
"\n",
"(sec:basic-microscope-layout)=\n",
"\n",
"## Basic microscope layout\n",
"\n",
"In all microscopes, we can identify some key elements: (i) a source for radiation, e.g. light, (ii) a system with lenses and other components to bring this radiation on (iii) the sample, and (iv) another system with lenses and other components to bring signal from the sample to (v) a detector.\n",
"\n",
"---\n",
"\n",
"\n",
" \n",
"
\n",
"\n",
"---\n",
"\n",
"(sec:wide-field-versus-scanning)=\n",
"\n",
"## Wide field versus scanning\n",
"\n",
"In light microscopy as well as in electron microscopy, we have systems that operate with wide-field illumination (for instance regular, wide-field light microscopes and transmission electron microscopes) and systems that rely on scanning a focused or shaped beam (confocal laser scanning microscopy or light-sheet microscopy, and scanning electron microscopy).\n",
"\n",
"---\n",
"\n",
"\n",
" \n",
"
\n",
"\n",
"---\n",
"\n",
"(sec:the-diffration-limit)=\n",
"\n",
"## The diffraction limit\n",
"\n",
"The main reason for developing microscopy based on electrons, was to find a way to circumvent the diffraction limit of light microscopy. The diffraction limit relates to the wave character of light. Diffraction ({numref}`subsec:diffraction-limit`) occurs when a wave is only partly captured by an aperture (or lens). This leads to a blurring in the image produced by a lens. This blurring is described by the Point Spread Function (PSF). The PSF is the mathematical function for the intensity profile generated by a lens or microscope in case of an infinitely small point source. Due to the blurring, two objects can only be distinguished if they are sufficiently separated. The diffraction limit gives the smallest separation d for two partially overlapping PSFs can still be visibly distinguished ({numref}`fig:AiryDisks`). Thus, it gives a measure for the minimal distance at which the images of two point objects can still be resolved and thereby for the resolution of the lens or microscope. An expression for the diffraction limit was first derived by [Ernst Abbe](https://en.wikipedia.org/wiki/Ernst_Abbe) and is also often referred to as the Abbe limit:\n",
"\n",
"$$\n",
"d = \\frac{\\lambda}{2n \\: sin(\\alpha)}\n",
"$$ (diffraction-limit)\n",
"\n",
"where $\\lambda$ is the wavelength of light used for imaging, $n$ is the refractive index of the medium between lens and object and α is the opening angle of the beam. The product $n \\: sin(α)$ is also know as the numerical aperture (NA) of the lens. We note that for small angles, $sin(α)$ can be approximated as $\\alpha$, if we express the angle in radians. We will later see that we can use this approximation for optics and microscopy with electrons. Note also that for visible light, the diffraction limit is approximately $250-300 \\: nm$."
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