Week 1.2: Electron Microscopy

Why can't a light microscope resolve atoms, however good the lenses?

Diffraction: waves spread out when they pass through an opening, so a single point becomes a blurry disc with rings (Airy disk). This is a physical limit of light itself, not a lens flaw. Limit ≈ 200–225 nm.

Point spread function (PSF) / Airy disk

The blur pattern one single point turns into after passing through a lens (bright centre + faint rings). Narrow PSF = two close points can still be told apart. Wide PSF = they merge into one blob.

Abbé resolution equation

r = 0.61λ / NA. r = smallest resolvable distance, λ = wavelength, NA = numerical aperture. Shorter λ or larger NA → smaller r → better resolution.

Numerical aperture (NA)

NA = n·sinθ. n = refractive index of the medium (e.g. oil), θ = half-angle of the cone of radiation the lens collects. Wider angle = more information collected.

Effect of aperture size on the PSF

Small aperture → wide PSF → blurry, poor resolution. Large aperture (large angle) → narrow PSF → better resolution.

Light microscope resolution: the numbers

resolution ≈ 225 nm, typical cell is 10–20 µm, so you see the cell but not fine detail.

Why do electrons give better resolution than light?

Electrons can have much shorter de Broglie wavelength than visible light. Since resolution is limited by wavelength, shorter wavelengths allow electron microscopes to distinguish much smaller structures than light microscopes.

Electron microscope NA and resulting resolution

NA is only ~0.01 (magnetic lenses collect narrow angles), but λ is so tiny that resolution is still ~0.15 nm (atomic scale).

Magnification vs resolution

Magnification = size of image / size of object (how BIG). Resolution = how much detail you can distinguish. Magnifying a blur just gives a bigger blur.

Why does an electron microscope need a high vacuum?

Air molecules would scatter the electrons before they reach the sample and the beam would fall apart.

4 things that can happen when radiation hits a sample

1) Absorption 2) Emission (light, electrons, X-rays) 3) Scattering 4) Chemical reactions (→ radiation damage in biological samples).

Elastic scattering

Beam electron bounces off the NUCLEUS (Coulomb/Rutherford scattering). Direction changes (large angle = backscattering), but essentially NO energy is lost. Ping-pong ball off a bowling ball. Small-angle coherent elastic scattering gives diffraction.

Inelastic scattering

Beam electron collides with the ELECTRON CLOUD (similar mass, so energy transfers). Beam electron keeps roughly its direction but loses energy: energy in > energy out. Billiard ball hitting billiard ball.

Elastic vs inelastic: what does each hit?

Elastic → nucleus (no energy loss, big direction change). Inelastic → the sample's own electrons (energy lost, secondary signals produced).

Backscattered electrons (BSE)

Elastic. Higher-energy electrons bounced back out by nuclei. Heavier nuclei (high Z) scatter more → brighter → composition (Z) contrast in SEM.

Secondary electrons (SE)

Inelastic. Loosely bound outer electrons kicked out. Only escape from the top few nm → SEM surface topography.

Characteristic X-ray (EDS/EDX)

Beam kicks out a CORE electron → hole in inner shell → outer electron falls in → releases an X-ray. Its energy is a fingerprint of the element → elemental composition.

Auger electron

Alternative to X-ray emission: the atom passes its relaxation energy to another electron and ejects it. Very surface-sensitive → topmost atomic composition.

EELS (electron energy loss spectroscopy)

Measures how much energy the BEAM electron itself lost during inelastic scattering. That energy loss identifies the element and bonding.

Why is inelastic scattering a problem in TEM?

Electrons that lose energy have a spread of wavelengths → chromatic aberration (blur). It also deposits energy in the sample → radiation damage.

Diffraction spots in TEM

Elastically scattered electrons from a crystal leave at specific angles. Pointing the beam at a diffraction spot tells you about the crystal structure.

Resolution vs 'deconvolution resolution'

Deconvolution resolution = peak width at half height / resolvable difference between peaks.

Why are low-Z elements (C, H, O, N) hard to see in TEM?

Few protons and electrons → they scatter electrons very weakly → low contrast against background.

SEM

Focused beam is SCANNED over the sample surface; detectors catch electrons coming back out (SE and BSE). Images the surface, scan position (x,y) + detected signal → image pixel, looks 3D (good depth info).

TEM

Beam passes THROUGH an ultra-thin sample; detector sits below it. Gives a 2D projection of internal structure at much higher resolution than SEM.

Why is a sample gold-sputtered for SEM?

The surface must be electrically conductive; otherwise electrons build up (charging) and distort the image.

SEM vs TEM resolution

SEM ≈ 3 nm. TEM: practical ≈ 0.2 nm, theoretical < 0.1 nm.

SEM real-world uses

Chip quality control; shampoo/hairspray products; hair morphology (diagnostics, forensics); paint composition to date artwork; identifying asbestos fibres.

FIB-SEM ('what's inside?')

A focused ION beam mills away a thin layer, the SEM images the new surface, repeat → stack of 2D images → aligned into a 3D volume.

Serial block-face SEM

Diamond knife inside the microscope shaves a layer off the block, SEM images the face, repeat. Sample is embedded in resin so it's hard enough to cut. Then align, segment, visualise in 3D (e.g. fly brain connectome).

Negative staining

Heavy-metal stain (e.g. uranyl acetate) pools around the sample and scatters electrons strongly. You image the STAIN's shape, not the molecule itself.

Problems with traditional TEM staining

Resolution limited by stain's grain; only exposed surface visible; sample distorted by fixation, dehydration and stain; low signal-to-noise

Vitreous ice

Sample flash-frozen so water forms glass-like (non-crystalline) ice. Water stays in place → native structure preserved, no dehydration, no stain.

Modern cryo-EM: what changed? (~2 nm → ~0.2 nm)

Vitreous ice, no metal stain, cooling to reduce radiation damage, better microscopes (300 keV, energy filters, direct electron detectors) and better data processing.

Energy filter

Discards inelastically scattered electrons (which cause chromatic blur) before the detector, keeping the sharp elastically scattered ones.

Tungsten filament vs LaB6

Both thermionic (heat frees electrons). Tungsten: cheap, many electrons, lower quality. LaB6: better quality, more expensive.

Cold field emission gun (FEG)

Very sharp tip → huge local field → electrons tunnel out, temperature-independent, highest quality, needs ultra-high vacuum, very clean tip

Thermionic vs field emission mechanism

Thermionic: heat gives electrons enough energy to escape metal. Field emission: quantum tunnelling through the barrier under a strong electric field, no heat.

Spatial Coherence

degree to which electron waves at different spatial positions maintain consistent phase relationship; improved by using smaller electron source + reducing angular spread of the beam; higher spatial coherence helps preserve interference effects + phase contrast

Magnetic (electromagnetic) lenses

Coils carrying current make a magnetic field; magnetic fields bend paths of charged electrons, focusing them onto the sample/detector depending on their position.

TEM column: order of components

Electron source → accelerator → condenser lenses + aperture → sample → objective lens + objective aperture → projector lenses → detector/viewing screen.

Phase contrast

Converts phase differences between scattered + unscattered electron waves into intensity differences, improving visibility of weakly scattering structures such as biological/low-Z materials/weakly scattering. Objective lens recombines scattered + unscattered beams → interference + intensity → contrast.

Contrast transfer function (CTF)

Describes how effectively the EM transfers contrast from structures of different spatial frequencies into final image; decreases as spatial frequency increases. It oscillates: some details correct, some inverted, some lost. Corrected computationally.

Scintillator+CCD vs direct electron detector

Scintillator: electrons → light → fibre optics → CCD (lossy, indirect). Direct: electrons hit the sensor itself → much higher DQE. TimePix = hybrid pixel detector counting single electrons.

DQE (detective quantum efficiency)

How well a detector preserves the signal-to-noise ratio of the incoming electrons. Direct detectors >> scintillator cameras.

Sample stage + tomography (TEM)

TEM grid (holey carbon) sits on a cryo-cooled stage that moves in X, Y, Z and tilts (α). Imaging at many tilt angles → 3D reconstruction (tomography).

Practical TEM room requirements

X-ray shielding box, Faraday cage (blocks external EM interference), concrete floor + active vibration table, temperature stable to ~1°C (metals drift), low-humidity room for sample prep (liquid nitrogen).

GPU vs CPU (cryo-EM processing)

GPU = array of units working in PARALLEL (ideal for bulk image processing). CPU = mostly SERIAL, bit by bit.

Why can't better lenses beat the light microscope's ~200 nm limit?

Because limit is imposed by diffraction due to the wavelength of light, which better lenses cannot eliminate. (r = 0.61λ/NA). With λ ≈ 500 nm and NA ≈ 1, r can't get much smaller; only a shorter λ helps.

Why does raising the accelerating voltage improve resolution?

Higher voltage → electrons gain momentum → shorter de Broglie wavelength (λ = h/p) → smaller r in r = 0.61λ/NA.

A beam electron passes near a nucleus vs near an electron cloud. Which loses energy, and why?

Near the electron cloud (inelastic): similar masses, so energy transfers. Near the nucleus (elastic): nucleus is far heavier, so the electron just changes direction (ping-pong vs bowling ball).

Trace the chain from an inelastic collision to detecting an X-ray.

Beam electron ejects a core electron → hole in the inner shell → outer-shell electron falls into the hole → excess energy released as a characteristic X-ray → detector reads its energy → identifies the element.

Why do heavy elements look brighter in backscattered electron images?

BSE come from elastic scattering off nuclei. More protons (higher Z) = stronger scattering = more electrons bounced back = brighter.

Why does negative staining show the stain rather than the sample?

The heavy-metal stain scatters electrons strongly and pools around the sample, while the low-Z molecule scatters weakly. The contrast is the stain's outline.

Why does an energy filter make TEM images sharper?

It removes inelastically scattered electrons, which have lost energy and so have different wavelengths. Removing them removes chromatic-aberration blur.

Why doesn't a cold FEG need heating?

The very sharp tip creates such a strong local field that electrons tunnel through the barrier (quantum tunnelling), so thermal energy isn't required.

Why must a TEM sample be thin but an SEM sample can be any thickness?

TEM needs electrons to pass through and reach the detector below. SEM only detects electrons emitted from the surface, so depth doesn't matter.

Why is high magnification alone not enough?

Magnification only enlarges the image. Without enough resolution (fine detail), a magnified image is just a bigger blur.

Why did direct electron detectors help cryo-EM?

They skip the electron→light conversion, so less signal is lost (higher DQE). Better signal-to-noise for weakly scattering, unstained, low-dose samples.