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A story from the invisible · TEM

What the Electron Saw

How a TEM image is really made: two electrons, one thin foil, and a pattern assembled from a billion tiny votes. Scroll at your own pace; every panel below is computed, not drawn.

Manisha Tripathy · A scrolling story · Last updated August 18, 2026

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A one-minute story · Chapter one · The Gun

Every image begins at a point. At the top of the column, a tungsten needle so sharp its end is a few hundred atoms wide lets two electrons go in the same femtosecond. By the bottom of the accelerator they are moving at seven tenths the speed of light, and they have not yet noticed each other.

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Speed buys smallness. As the voltage climbs, each electron's wavelength shrinks far below anything light can manage, until the spacing between atomic planes starts to look roomy.

the ruler shrinks until atoms look far apart
What that tiny wavelength buys → a nearly flat Ewald sphere
Chapter two · The Lenses

No glass bends an electron, so the column focuses them with magnetic fields, and inside a magnetic lens an electron does not travel in a line; it spirals. The two of them corkscrewed down together, turn for turn, through lenses that are honest about almost everything.

Still together.

Honest about almost everything: rays that pass far from the axis focus short of the rays that hug it. A perfect point becomes a small apology, and the whole craft of high resolution is the management of that apology.

a point, focused into a small apology
Where the apology becomes rings and ringing → the CTF explorer
Chapter three · The Foil

The foil was sixty nanometers thick, thinner than a soap bubble's wall. Electron A grazed a plane of atoms at exactly the angle the lattice likes, and was turned, losing nothing. Electron B hit the crowd, left some of its energy behind as heat and a bruise, and wandered on with a blurred memory of where it had been.

Signal and noise are not different substances. They are the same electrons, sorted by what they paid at the foil: the elastic ones keep the crystal's geometry in phase, the inelastic ones keep only a receipt for the energy they left behind.

both columns are electrons; only one remembers the lattice
Every fate of the beam, mapped → Elastic vs Inelastic Scattering in TEM
Chapter four · The Pattern

A detector does not take a picture. It keeps score. One dot at a time, the electrons voted, and most votes landed nowhere in particular. The spots are simply the places where the elastic ones could not disagree.

The same pattern, at three honesties of exposure. Statistics is not a nuisance on top of the physics; at this scale, it is the physics.

300, then 30 000, then 3 000 000 electrons
This pattern is real. Index it yourself → the SAED Zone-Axis Indexer

You have never seen an atom. Neither have I. What we have is sharper than seeing: a way to ask a billion electrons the same question, and to keep only the answers they agree on.

A micrograph is not a photograph.
It is a census.

I spend my days asking.

Start with the indexer The whole collection, below ↓
TEM Concepts & Techniques

The whole TEM collection

Hands-on explainers and utilities for transmission electron microscopy, built for students and practitioners. Each opens as its own page.

1 · Diffraction & Indexing

Reading the pattern itself: indexing spots by hand, tilting to a zone axis, and the reciprocal-space geometry underneath both.

Tool

SAED Zone-Axis Indexer

Upload a diffraction pattern, click the transmitted beam and two spots, and get the zone axis: calibration-free ratio + angle matching for FCC, BCC, SC, diamond, HCP, and custom lattices, with a predicted-net overlay to verify.

 Tool

SAED Pattern Simulator

Any zone axis of any of 604 structures (or your CIF), indexed on screen: kinematical or many-beam dynamical intensities with a thickness slider, precession, CBED discs and HOLZ lines, Kikuchi lines, the Ewald-sphere section, your own pattern overlaid with a residual fit, a CTF and HRTEM tableau, Bloch-wave STEM images, and a WebGPU multislice engine for supercells with defects.

 Tool

Ring Pattern Calibration

Load a gold, aluminium or silicon ring pattern: the page refines the centre, finds and assigns the rings to the standard, fits the camera constant, reads the camera length, measures the elliptical distortion and calibrates the image-diffraction rotation, then saves the calibration for the indexer.

 Tool

CBED Symmetry Tables

Buxton’s diffraction-group tables, derived rather than typed: pick a point group and a zone axis to read the whole-pattern, bright-field and dark-field symmetries a CBED pattern must show, or enter the symmetries you observed and list every point group and zone-axis class consistent with them.

 Tool

Kikuchi Map Navigator

A live Kikuchi map for any crystal: hover a band to see every zone axis strung along it, pick where you are and where you want to be, and get the band to follow, the tilt angle, and the double-tilt holder settings that reach it.

 Concept

SAED Indexing, g-Vectors & Real vs. Fake Spots

The by-hand logic behind the indexer: measure two g-vectors from spot ratio and angle, then see whether those two numbers name one zone axis or several at the precision you actually clicked. Score a twin, double diffraction and a second phase against the same extra spots, and tell real Bragg spots from Kikuchi crossings, streaking and detector artifacts.

 Concept

Back Focal Plane & Diffraction Focus

An interactive ray diagram of the TEM back focal plane, showing what the diffraction-focus knob (intermediate lens) actually does and how to get sharp SAED patterns.

 Concept

Grain Orientations & Reciprocal Space

Orientation as a rotation of the reciprocal lattice: zone-axis tilts with Laue circle and Kikuchi lines, misorientation (LAGB, HAGB, twins), polycrystal rings and texture arcs, plus an orientation-terminology reference.

 Concept

CBED & Lamella Thickness

CBED vs SAED, and how two-beam Kossel–Möllenstedt fringes give specimen thickness via the Kelly–Allen extrapolation, an interactive schematic.

 Concept

Reciprocal Space & the Ewald Sphere

The crystal and its inside-out mirror world, side by side; then a live diffraction simulator where voltage flattens the sphere, tilt swings it, and thickness grows the relrods that decide which spots light up.

2 · Imaging & Contrast

What actually makes the image: mass-thickness, diffraction, and phase contrast, the detectors that catch them, and how to read the result honestly.

Concept

The Three Contrasts of TEM

Mass–thickness, diffraction, and phase contrast, one demo each, including a bright-field/dark-field polycrystal tilt simulator and a CTF defocus lattice-fringe demo.

 Concept

STEM Detectors: BF, ABF, ADF & HAADF

Camera length and atomic number sliders map scattering angles onto the detector rings, and a four-detector perovskite simulator shows what each ring actually sees.

 Concept

Scattering in the TEM: One Beam, Many Fates

Elastic or inelastic, signal or artifact: a scattering-channel explorer, a real-space/reciprocal-space dual simulator on one specimen, an artifact clinic, and a signal-vs-artifact verdict table for any 80–300 kV (S)TEM.

 Concept

Weak-Beam Dark Field

Why strong-beam dislocation images are fat, the g–3g tilt walkthrough on the Ewald sphere, a Howie–Whelan dislocation-image simulator, the g·b invisibility criterion, and stacking-fault energy from partial separation.

 Tool

Weak-Beam Tilt Simulator

Do the weak-beam tilts yourself: alpha and beta over a live Kikuchi map, any zone axis, two-beam, then the beam tilt that puts 3g at Bragg, with a dislocation image that narrows as you go.

 Tool

Bend Contours

Why the dark lines move when you tilt: a many-beam simulation of a bent foil of any crystal paints the rocking surface as bright-field and dark-field contours, slides them with the holder tilt, reads the radius of curvature from their spacing, and answers the eleven most asked questions about bend contours.

 Tool

Two-Beam Defect Simulator

Bright-field, dark-field and weak-beam images of dislocations, dipoles, loops and stacking faults by the Howie–Whelan column approximation with anomalous absorption, for any of 604 crystals: inside–outside contrast, alpha fringes, depth oscillations and g·b invisibility, computed column by column in the browser (on the graphics card when there is one).

 Tool

g·b Invisibility Planner

Pick the crystal, the zone axes you can reach and the candidate Burgers vectors: the table gives g·b for every reflection, marks the invisibility conditions and the residual contrast of edge components, finds the smallest set of reflections that tells the candidates apart, and keeps score as you record which images showed the dislocation.

 Tool

Quantitative HAADF

Put a HAADF-STEM image on an absolute scale: normalise to the detector dark level and probe current, find and refine the atomic columns, integrate each over a disc or its Voronoi cell, and compare with the fraction-versus-thickness curves exported by the SAED simulator to estimate thickness and the Z-contrast exponent.

 Concept

HRTEM & FFTs

Are the dots atoms? A defocus/CTF lattice-image simulator with a true atom-column overlay, the Scherzer-defocus CTF, d-spacings measured from a draggable FFT region, and how Fourier filtering can conjure fake lattices from noise.

 Tool

HRTEM Lattice Tool

d-spacings from a high-resolution image: calibrate the scale, take the FFT of a region, pick the spots for spacings and angles with sub-pixel refinement, Bragg-filter with the chosen reflections (with the unfiltered FFT kept in view), and compute moiré spacings for overlapping lattices.

3 · Spectroscopy: EELS & EDS

What the beam paid on the way through, and what the atoms gave back: reading energy-loss spectra, turning one logarithm into a thickness measurement, and putting numbers on core-loss edges and X-ray peaks.

Concept

Reading the EELS Spectrum

Zero-loss, plasmons, and core-loss edges, each explained on a live spectrum; an element edge-energy lookup with overlap warnings; and why EELS resolves chemistry EDS cannot (plus when EDS still wins).

 Tool

EELS Thickness Calculator

Load a low-loss spectrum (CSV, EMSA/MSA, or a built-in demo), set the zero-loss window, and get t/λ plus absolute thickness from the Malis and Iakoubovskii mean-free-path models, honestly error-barred.

 Tool

EELS Core-Loss Quantification

Load a core-loss spectrum (and the low loss): power-law background fitting, window integration, hydrogenic K-shell cross-sections for your collection angle, plural-scattering removal by Fourier-ratio deconvolution or by convolving the cross-section with the low loss, and the areal density and elemental ratios that follow.

 Tool

EDS Quantification

Theoretical Cliff–Lorimer k-factors from cross-sections, fluorescence yields and detector efficiency, the absorption correction as the foil thickens, zeta-factor quantification with thickness, peak-overlap synthesis and least-squares fitting with its variance inflation, and beam broadening against foil thickness for map resolution.

4 · FAQ

Real lab questions, each answered and linked back to the interactive guide that shows the physics.

FAQ

TEM Troubleshooting FAQ

Why does my SAED pattern blur, why does my HRTEM FFT show rings, why is my weak-beam image so dark: real lab questions, each answered and linked to the interactive guide that shows the physics.
Simplifications made in this story
Cite this page: Tripathy, Manisha. “What the Electron Saw.” untethered atom, 2026, https://untetheredatom.com/stories/what-the-electron-saw.
BibTeX 
@misc{tripathy2026electronstory,
  author = {Tripathy, Manisha},
  title  = {What the Electron Saw: How a TEM Image Is Really Made},
  year   = {2026},
  howpublished = {\url{https://untetheredatom.com/stories/what-the-electron-saw}},
  note   = {Illustrated scrolling story}
}
Last updated: August 18, 2026.