{"id":100,"date":"2024-12-04T10:09:00","date_gmt":"2024-12-04T10:09:00","guid":{"rendered":"https:\/\/testwordpress.nano.cnr.it\/?page_id=100"},"modified":"2026-03-14T09:27:32","modified_gmt":"2026-03-14T09:27:32","slug":"electron-beam-shaping","status":"publish","type":"page","link":"https:\/\/tem-s3.nano.cnr.it\/?page_id=100","title":{"rendered":"Electron Beam Shaping"},"content":{"rendered":"\n<h1 class=\"wp-block-heading has-text-align-center\">Electron Beam Shaping<\/h1>\n\n\n\n<div style=\"height:10px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<p class=\"has-text-align-left\">Electron microscopy has, for many years, been related to two concepts: creating approximate plane waves to obtain a sample snapshot or producing very tiny probes to scan the sample for imaging and advanced spectroscopy.<\/p>\n\n\n\n<p class=\"has-text-align-left\">Yet, there is much more to this than simple electron optics, and hints of this have been derived from experiments in light optics, starting from the idea of vortex beams as introduced by M. Berry. Beam shaping is the art of controlling the electron wavefunction before and\/or after the sample. We have been among the pioneers of this idea, with early works on phase holograms and MEMS-based electron optics. Holograms are structured pieces of electron-transparent material that modulate the phase of electrons through their thickness. They are typically created using FIB or EBL structuring techniques.<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"857\" height=\"527\" src=\"https:\/\/tem-s3.nano.cnr.it\/wp-content\/uploads\/2024\/12\/EBS-phaseplates01.png\" alt=\"\" class=\"wp-image-1258\"\/><\/figure>\n<\/div>\n\n\n<p>By using holograms, we are able to control both the amplitude and phase of the electron beam.<\/p>\n\n\n\n<p>In the figure, we show:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>a) the CNR logo created as the diffraction pattern of the hologram above,<\/li>\n\n\n\n<li>b) a combination of two Laguerre-Gaussian beams,<\/li>\n\n\n\n<li>c) a vortex beam.<\/li>\n<\/ul>\n\n\n\n<p>All these beams are examples of the nearly unlimited possibilities that this technique offers, with applications in spectroscopy, diffraction, and imaging.<\/p>\n\n\n\n<p>Holograms can also be used for the correction of spherical aberrations.<\/p>\n\n\n\n<p>The problem with holograms is that:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>1. They are not programmable or tunable.<\/li>\n\n\n\n<li>2. They become charged under the electron beam, and this charging can distort their effect.<\/li>\n<\/ul>\n\n\n\n<p>A solution we found is to work with MEMS electrostatic technology.<\/p>\n\n\n\n<p>We specialize in harmonic phase plates that introduce nearly no obstruction to the electron beam\u2019s path. Using accurate analytical and numerical models, we are able to predict the smooth phase landscape produced by a few electrodes.<\/p>\n\n\n\n<p>Some examples of the possible applications of these phase plates are shown here.<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"1303\" height=\"556\" src=\"https:\/\/tem-s3.nano.cnr.it\/wp-content\/uploads\/2024\/12\/EBS-phaseplates02.png\" alt=\"\" class=\"wp-image-1266\"\/><\/figure>\n<\/div>\n\n\n<p>The implementation of this technology has been made possible thanks to a close collaboration with <strong><a href=\"https:\/\/www.thermofisher.com\/it\/en\/home.html\"><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-vivid-cyan-blue-color\">Thermo Fisher<\/mark><\/a><\/strong>, with whom we developed our unique, specialized aperture holder featuring pass-through fields to control the beam.<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"1303\" height=\"556\" src=\"https:\/\/tem-s3.nano.cnr.it\/wp-content\/uploads\/2024\/12\/EBS-phaseplates03.png\" alt=\"\" class=\"wp-image-1272\"\/><\/figure>\n<\/div>\n\n\n<p>One of the most important results of MEMS technology has been the creation of the first OAM (Orbital Angular Momentum) sorter.<\/p>\n\n\n\n<p>The OAM sorter is a new electron optical element, inspired by light optics, capable of creating on the screen a spectroscopic representation of the angular momentum components of the electron beam after elastic or inelastic interactions with the sample.<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"1303\" height=\"556\" src=\"https:\/\/tem-s3.nano.cnr.it\/wp-content\/uploads\/2024\/12\/EBS-phaseplates04.png\" alt=\"\" class=\"wp-image-1275\"\/><\/figure>\n<\/div>\n\n\n<p>The importance of this element can only be fully appreciated when considering that energy, momentum, and angular momentum are the most important conserved quantities of an electron\u2019s motion, and only now can angular momentum finally be measured.<\/p>\n\n\n\n<p>The technique for this measurement is based on optical conformal mapping of the wavefunction. It uses MEMS phase elements to produce, in the stationary phase approximation, a transformation into log-polar coordinates, such that an azimuthal phase gradient is converted into a linear gradient.<\/p>\n\n\n\n<p>In the figure, we can see in the middle column the initial beam and its transformation into polar coordinates through the sorter. The result, shown on the right, produces an OAM spectrum. The peaks at \u00b14 indicate the beam\u2019s fourfold symmetry.<\/p>\n\n\n\n<p>The concept of geometrical transformation is so revolutionary that it has the potential to transform the very idea of measurement in microscopy, extending far beyond conventional imaging. These MEMS-based electron-optical devices are also being investigated within the <a href=\"https:\/\/ai-tem.nano.cnr.it\">AI-TEM project<\/a> for applications in ghost imaging.<\/p>\n\n\n\n<div class=\"img-slider-comp\">\n  <div class=\"img-slider-img\">\n    <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/tem-s3.nano.cnr.it\/wp-content\/uploads\/2024\/12\/phaseplate-slider01.png\" width=\"500\" height=\"300\">\n  <\/div>\n  <div class=\"img-slider-img img-slider-overlay\">\n    <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/tem-s3.nano.cnr.it\/wp-content\/uploads\/2024\/12\/phaseplate-slider02.png\" width=\"500\" height=\"300\">\n  <\/div>\n<\/div>\n\n<style>\n  * {\n    box-sizing: border-box;\n  }\n\n  .img-slider-comp {\n    position: relative;\n    height: 300px !important; \/* should be the same height as the images *\/\n    transform: translateX(20%);\n  }\n\n  .img-slider-img {\n    position: absolute;\n    overflow: hidden;\n    width: auto ;\n    height: 100% !important;\n  }\n\n  .img-slider-img img {\n    height: 100% !important;\n    object-fit: cover;\n    display: block;\n    vertical-align: middle;\n    overflow: hidden;\n    transform-origin: top left !important;\n  }\n\n  .img-slider-handler {\n    position: absolute;\n    z-index: 9;\n    cursor: ew-resize;\n    \/* set the appearance of the slider: *\/\n    width: 40px;\n    height: 40px;\n    background-color: #2196F3;\n    opacity: 0.7;\n    border-radius: 50%;\n    top:50%;\n    transform: translateY(-50%);\n  }\n<\/style>\n\n<script>\nfunction initComparisons() {\n    var x = document.getElementsByClassName(\"img-slider-overlay\");\n    for (let i = 0; i < x.length; i++) {\n        let img = x[i];\n        let slider = document.createElement(\"DIV\");\n        slider.setAttribute(\"class\", \"img-slider-handler\");\n        img.parentElement.insertBefore(slider, img);\n\n        \/\/ Initial clipping to the left half of the image\n        img.style.clip = `rect(0px, ${img.offsetWidth \/ 2}px, ${img.offsetHeight}px, 0px)`;\n        slider.style.left = (img.offsetWidth \/ 2) - (slider.offsetWidth \/ 2) + \"px\";\n\n        \/\/ Add event listeners\n        slider.addEventListener(\"mousedown\", slideReady);\n        window.addEventListener(\"mouseup\", slideFinish);\n        slider.addEventListener(\"touchstart\", slideReady);\n        window.addEventListener(\"touchend\", slideFinish);\n\n        let clicked = 0;\n\n        function slideReady(e) {\n            e.preventDefault();\n            clicked = 1;\n            window.addEventListener(\"mousemove\", slideMove);\n            window.addEventListener(\"touchmove\", slideMove);\n        }\n\n        function slideFinish() {\n            clicked = 0;\n        }\n\n        function slideMove(e) {\n            if (!clicked) return;\n            let pos = getCursorPos(e);\n            if (pos < 0) pos = 0;\n            if (pos > img.offsetWidth) pos = img.offsetWidth;\n            img.style.clip = `rect(0px, ${pos}px, ${img.offsetHeight}px, 0px)`;\n            slider.style.left = pos - (slider.offsetWidth \/ 2) + \"px\";\n        }\n\n        function getCursorPos(e) {\n            let a = img.getBoundingClientRect();\n            let x = e.pageX - a.left;\n            x -= window.pageXOffset;\n            return x;\n        }\n    }\n}\n\ndocument.addEventListener(\"DOMContentLoaded\", initComparisons);\n<\/script>\n","protected":false},"excerpt":{"rendered":"<p>Electron Beam Shaping Electron microscopy has, for many years, been related to two concepts: creating approximate plane waves to obtain a sample snapshot or producing very tiny probes to scan the sample for imaging and advanced spectroscopy. Yet, there is much more to this than simple electron optics, and hints of this have been derived [&hellip;]<\/p>\n","protected":false},"author":3,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"inline_featured_image":false,"footnotes":""},"class_list":["post-100","page","type-page","status-publish","hentry"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v26.6 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Electron Beam Shaping - TEM Group<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/tem-s3.nano.cnr.it\/?page_id=100\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Electron Beam Shaping - TEM Group\" \/>\n<meta property=\"og:description\" content=\"Electron Beam Shaping Electron microscopy has, for many years, been related to two concepts: creating approximate plane waves to obtain a sample snapshot or producing very tiny probes to scan the sample for imaging and advanced spectroscopy. 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