{ "cells": [ { "cell_type": "markdown", "id": "632406a7", "metadata": {}, "source": [ "(ch:tomography)=\n", "# Electron Tomography\n", "\n", "(sec:tomo-introduction)=\n", "## Introduction\n", "\n", "Single-particle analysis (see {numref}`ch:single-particle-analysis`) achieves near-atomic resolution by averaging thousands of identical copies of a purified molecule. But much of biology is irreducibly unique: the arrangement of organelles in a single cell, the architecture of a synaptic vesicle cluster, the organisation of chromatin in a nucleus. These structures cannot be averaged across many copies because each instance is different. **Electron tomography (cryo-ET)** addresses this by reconstructing a three-dimensional volume from a single specimen through a series of images collected at different tilt angles.\n", "\n", "The reconstruction problem in tomography — recovering a 3D volume from a set of 2D projections — is one of the oldest in imaging science, predating cryo-EM entirely. The mathematical basis (the Radon transform and its inverse) was established by Radon in 1917. The same principles underlie medical CT scanning. In electron tomography, however, the dose constraints of radiation-sensitive biological specimens make the problem fundamentally harder: the total electron dose must be spread over all tilt angles, limiting the signal per image to much less than in a single cryo-EM micrograph.\n", "\n", "In the below video, we explain why a unique object requires a different approach than single-particle analysis, how a tilt series is assembled into a sinogram and back projected into a three-dimensional reconstruction, and how tilt range, tilt increment, the missing wedge and weighted back projection determine the quality of that reconstruction.\n", "\n", "---\n", "\n", "