Microscopy, magnification and resolution

Magnification and resolution

Magnification is the number of times larger the image is than the object. It is a ratio, so it has no units. An image can be enlarged without limit, whether or not it contains any further detail.

Resolution is the shortest distance between two points that can still be seen as two points rather than one. It is a length, so it does have units, and the smaller the number the better the instrument. A resolution of 0.1 nm is therefore better than a resolution of 200 nm, because 0.1 is the smaller number.

Magnification beyond what the resolution supports is called empty magnification: the image is larger but contains no additional detail. Resolution sets the limit on the detail available; magnification only sets the size at which it is displayed.

Resolution is limited by wavelength. Two points closer together than roughly half a wavelength of the illuminating radiation cannot be distinguished, because the waves spread and overlap. The half is more precisely a half divided by the lens's numerical aperture, a measure of how wide a cone of light it gathers, which for the best oil-immersion objectives is a little over one.

Visible light runs from about 400 to 700 nm, which places the best light microscope at around 0.2 µm, or 200 nm. A beam of electrons behaves as a wave too, and at the accelerating voltages a transmission electron microscope uses, that wavelength is about 0.004 nm: roughly a hundred thousand times shorter than visible light. A shorter wavelength gives a finer resolution, which is why a TEM resolves about 0.1 nm where light stops at 200 nm.

The half-wavelength rule alone would predict a far finer limit than 0.1 nm. A wave 0.004 nm long would separate points a few thousandths of a nanometre apart, and no transmission electron microscope of this kind achieves that. The limit is set by the lenses rather than by the wavelength. Electrons are focused by magnetic fields, which are cruder than a shaped piece of glass, and the aberrations they introduce blur the image long before the wavelength would.

Describe the drawing

A logarithmic size scale running from 0.1 nanometres to 100 micrometres, one decade per step. Five structures are plotted against it by dashed horizontal lines: a DNA helix at 2 nanometres, a ribosome at 25 nanometres, an HIV particle at 100 nanometres, a bacterium at 2 micrometres and an animal cell at 20 micrometres. Three dashed vertical lines mark the resolving limits of the transmission electron microscope at 0.1 nanometres, the light microscope at 0.2 micrometres and the unaided eye at 0.1 millimetres.

Magnification

How many times larger the image is than the actual object. A ratio, with no units.

Resolution

The minimum distance between two points at which they can still be distinguished as separate. A length, and smaller is better.

Empty magnification

Enlarging an image beyond the detail its resolution contains, so nothing further becomes visible.

Light microscopes, TEM and SEM

The light microscope uses visible light and glass lenses, magnifies usefully to about ×1500 and resolves to about 0.2 µm. It is the only one of the three that can image living material, so a live protoctist can be observed swimming, in colour, in a drop of pond water.

The transmission electron microscope fires a beam of electrons through a very thin section of specimen. Electrons that pass straight through land on a screen or detector below; parts of the specimen stained with heavy metals scatter electrons and come out dark. The result is a flat, two-dimensional section at resolutions down to about 0.1 nm on the best instruments under ideal conditions, and magnifications of half a million times. Most published images of cell ultrastructure are TEM images.

The scanning electron microscope sweeps a beam across the surface of a whole specimen coated in a thin film of metal, and collects the electrons knocked off that surface with detectors placed above it. Because the signal comes from the surface and depends on its shape, the image looks three-dimensional. The cost is resolution: an SEM typically manages a few nanometres, worse than a TEM, though still far beyond anything light can do.

Describe the drawing

Three microscopes drawn side by side as columns. In the light microscope column a lamp sends light down through a whole specimen on a slide to an image below. In the transmission electron microscope column an electron gun sends electrons down through an ultrathin section to an image below. In the scanning electron microscope column the beam strikes the surface of a whole coated specimen and electrons bounce back up to detectors placed either side above it. Under each column are its resolution, its greatest useful magnification, whether the specimen can be alive, and whether the image is two or three dimensional.

Both electron microscopes have to work in a vacuum, because air molecules deflect electrons and the beam would scatter before it reached anything. A vacuum removes the water from a living cell instantly, so in the standard TEM and SEM preparations this course describes the specimen must be dead, fixed and dehydrated before it goes in. Electron micrographs are therefore images of dead material, and any colour on one was added after the image was recorded.

The magnification equation

One relationship links the three quantities, and the units must be converted before the division is carried out.

magnification = image size ÷ actual sizerearranged: actual size = image size ÷ magnification

The image size is measured with a ruler, so it is in millimetres. The actual size of a cell or an organelle is stated in micrometres or nanometres. Convert one to match the other before dividing, so that both lengths are in the same unit. Magnification itself has no units.

1 mm = 1000 µm    1 µm = 1000 nm    1 mm = 1 000 000 nmthe three conversions this topic requires

Many micrographs carry a scale bar instead of a magnification. Measure the bar with a ruler and divide by the length it represents to get the magnification, or compare an object with the bar directly: an organelle three bar-lengths long beside a 1 µm bar is 3 µm long.

Calibrating an eyepiece graticule

A micrograph carries its magnification printed on it. A microscope on the bench does not, so the value of one eyepiece division must be established before any measurement is taken.

There are two scales involved. The eyepiece graticule is a transparent disc with a ruled scale, sitting in the eyepiece. Its divisions are arbitrary, staying the same apparent size whichever objective lens you use, because they are not part of the image of the specimen. The stage micrometer is a slide with a scale of known length: usually 1 mm ruled into 100 parts, so each division is 10 µm. It goes on the stage, where the objective magnifies it along with everything else.

Describe the drawing

Two scales drawn one above the other over the same width. The upper scale is an eyepiece graticule ruled into forty equal divisions numbered zero to forty with no units. The lower scale is a stage micrometer ruled into ten divisions of ten micrometres each, spanning one hundred micrometres in total. Dashed lines join the two ends to show that both scales cover the same field of view, and the arithmetic below divides one hundred micrometres by forty divisions to give 2.5 micrometres per eyepiece division.

The procedure is short. Put the stage micrometer on the stage, focus, and turn the eyepiece until the two scales lie parallel. Count how many eyepiece divisions cover a measured number of stage divisions. Divide the known length by the number of eyepiece divisions to get the value of one division. Then take the micrometer away, put your specimen on, and measure it in eyepiece divisions.

A calibration is valid for one objective lens only. The objective magnifies the stage micrometer but not the graticule, so changing from ×10 to ×40 makes each eyepiece division worth a quarter of its previous value. Calibrate separately for every lens to be used.

Artefacts and interpreting micrographs

Preparing a specimen for an electron microscope alters it. It is fixed in chemicals, dehydrated through a series of solvents, embedded in resin, cut into sections tens of nanometres thick and stained with salts of heavy metals such as lead or osmium. Any of those steps can change what you are looking at.

An artefact is a structure visible in the image that was not present in the living cell. Air bubbles trapped under a coverslip, creases and tears in a section, precipitated stain, and organelles pulled out of shape by dehydration are all artefacts, and early electron microscopists spent years arguing about which structures were real. The mesosome, an infolding of membrane once drawn in every bacterium in every textbook, turned out to be one, produced by the fixing chemicals.

Such disputes are settled by comparing preparation methods. A structure seen after several different preparation methods, and in more than one type of microscope, is probably present in the living cell. A structure that appears only with one particular technique is probably an artefact.

Artefact

A structure seen in a prepared specimen that was not present in the living cell, produced by the preparation or imaging process.

Eyepiece graticule

A ruled scale in the eyepiece whose divisions have no fixed length until it is calibrated.

Stage micrometer

A slide bearing a scale of known length, used to calibrate an eyepiece graticule for one particular objective lens.

A second source of misinterpretation is unrelated to damage. A TEM image is one thin slice through a three-dimensional object. A mitochondrion sliced across its width appears as a small circle; the same mitochondrion sliced along its length appears as a long sausage; and one that happens to be bent can be caught by the knife twice over, so a single organelle turns up in the image as two separate profiles with cytoplasm between them. All three are the same organelle. When a micrograph seems to show organelles of wildly different sizes, or more of them than the cell can plausibly hold, the plane of the section is usually the explanation.

Cell fractionation and ultracentrifugation

A micrograph shows the structure and position of an organelle but not its biochemical activity. Investigating what mitochondria do requires a suspension enriched in mitochondria and little else, which is obtained by cell fractionation.

The first step is homogenisation: the tissue is broken up, usually in a blender, so the cell-surface membranes rupture and the organelles are released into the surrounding solution. That solution is chosen for three properties, and each one prevents a specific accident. It is cold, which slows the enzymes that would otherwise digest the organelles you are trying to collect. It is isotonic with the cells, so no water moves in or out by osmosis and no organelle bursts or shrivels. And it is buffered, so the pH holds steady and the proteins keep the shapes their function depends on. The homogenate is then filtered to take out connective tissue and whole cells that survived the blender.

The separation itself is ultracentrifugation, and the principle is sedimentation rate, which depends on size and density together. The tube is spun, the largest and densest contents travel outwards fastest and collect as a pellet at the bottom, and everything still suspended stays in the supernatant above it. Spin slowly and only the heaviest component pellets. Decant the supernatant into a fresh tube, spin it faster, and the next heaviest pellets in its turn. The organelles come out in order of size and density: nuclei first, then chloroplasts in a plant sample, then mitochondria, then lysosomes, then the endoplasmic reticulum, and the ribosomes last of all at the highest speeds.

A fraction is never pure, only enriched: organelles of similar size and density sediment together, and a mitochondrial pellet carries lysosomes with it.

The sequence above is an order of size and density, not of importance, and it depends on the tissue. An animal tissue contains no chloroplasts, so that step does not occur.