Microscopy and Quantitative Images

Two vesicles 150 nm apart, each filled with GFP, look like a single blob in the best ordinary light microscope, and enlarging the picture will never split them. The reason is a property of light, and it sets what you can and cannot conclude from almost every image in cell biology. This lesson works out where the limit comes from, how big it is for a real objective, how other microscopes get past it, and how to read a fluorescence image without being fooled.

The idea: light spreads, so points blur

Think of printing dots with a rubber stamp that has a soft, round face. However small the true point you aim at, the mark is the size of the stamp. Two marks closer than about one stamp-width run together.

A lens does the same thing to light. Light passing through the circular opening of an objective is diffracted, so the image of a single point is a bright disc with faint rings around it, called an Airy pattern. Two independent glowing points give two such patterns, and their intensities add. Resolution is the smallest separation at which two point objects can still be told apart. A common convention, the Rayleigh criterion, calls two points resolved when the centre of one pattern falls on the first dark ring of the other.

Ernst Abbe set out the theory in 1873. Fine detail sends light off at wide angles, and only light the objective collects can rebuild that detail. So the limit depends on the wavelength and on the numerical aperture (NA), which measures how wide a cone of light the objective gathers:

NA = n × sin θ, where n is the refractive index of the medium between lens and sample and θ is the half-angle of the collected cone

Air has n = 1.00, so a dry objective cannot reach NA 1. Immersion oil has n ≈ 1.515, which is why the best objectives are oil lenses with NA near 1.4.

In fluorescence microscopy, the label absorbs light of one colour and emits a longer wavelength, and it is the emission wavelength that sets the blur. You will often read that “the light limit is 200 nm”. That number means nothing until you say which wavelength, which NA, which direction (side to side or along the optical axis) and which criterion.

Computing resolution and sampling

For an ideal widefield fluorescence microscope, the lateral and axial estimates are:

d = 0.61 × λ / NA (lateral, Rayleigh criterion)

dz ≈ 2 × λ × n / NA² (axial, an approximate estimate)

Here is a worked problem. Take an ideal widefield microscope imaging GFP-like fluorescence at λ = 520 nm through an oil objective with NA 1.40 and immersion index n = 1.515. The camera records 100 nm of specimen per pixel. These are ideal-model numbers chosen for the exercise, not a measured point-spread function; a real instrument with aberrations or a thick sample will do worse.

Step 1, lateral resolution. d = 0.61 × 520 / 1.40 = 317.2 / 1.40 = 226.6 nm, about 0.23 µm.

Step 2, sampling. A camera has to record the blur finely enough to show the dip between two points. A common introductory rule is at least two pixels per resolved distance. Here 226.6 / 100 = 2.27 pixels, which just meets the rule. With 150 nm pixels you would have 1.5 pixels per d, and the camera, not the optics, would limit what you see.

Step 3, a weaker objective. Keep λ = 520 nm but use NA 1.00: d = 317.2 / 1.00 = 317.2 nm. Losing 0.4 in NA costs about 90 nm of resolution.

Step 4, axial resolution. dz ≈ 2 × 520 × 1.515 / 1.40² = 1575.6 / 1.96 = 804 nm. That is about 3.5 times worse than the lateral figure. The blurred image of a point is an elongated football, long along the optical axis.

Step 5, the vesicles. Two GFP-labelled vesicles 150 nm apart are closer than 226.6 nm, so this microscope records one merged spot. Enlarging the image afterwards spreads that spot over more screen pixels but adds no information. Magnification without resolution is empty magnification.

Seeing more: confocal, electrons and super-resolution

A widefield microscope illuminates the whole depth of the sample, so light from above and below focus adds haze, which is worst in thick, densely labelled specimens. A confocal microscope scans a focused spot and places a pinhole in front of the detector that blocks most out-of-focus light. Each scan is an optical section, and a stack of sections can be rebuilt into a three-dimensional cell, which is how many organelle volumes in the previous lesson were measured. A confocal is still diffraction limited. Closing the pinhole below one Airy unit buys a little resolution at a real cost in signal.

Electron microscopes use a beam of electrons focused by magnetic lenses. At 100 kV an electron’s wavelength is around 0.004 nm, yet the practical resolution in biological specimens is far coarser, limited by preparation, contrast and beam damage. Transmission EM (TEM) sends electrons through sections about 50 to 100 nm thick of fixed, dehydrated, plastic-embedded cells stained with heavy metals; it shows membranes and organelles, but each image is a two-dimensional projection of dead tissue. Scanning EM (SEM) rasters the beam over a coated surface and shows shape. Fixation can make structures that were never there. In cryo-EM, samples are frozen so fast that water becomes glass-like vitreous ice instead of crystals. Near-atomic cryo-EM structures come from averaging many images of purified particles, not from imaging a whole cell, although cryo-electron tomography of thinned frozen cells now shows molecules in place at lower resolution.

Super-resolution light microscopes get around diffraction by controlling which molecules glow, not by repealing it.

• STED. Hell and Wichmann proposed in 1994 to add a ring-shaped beam that forces excited dye molecules back to the dark state by stimulated emission, leaving only a small centre fluorescent. In 2000 Klar, Jakobs, Dyba, Egner and Hell reported a fluorescent spot about 90 to 110 nm across, with smaller gains in live yeast and E. coli.
• SIM. Structured illumination records the sample under a series of striped patterns and computes an image; Gustafsson reported in 2000 a doubling of lateral resolution.
• PALM and STORM. Published in 2006 by Betzig and colleagues (PALM), by Rust, Bates and Zhuang (STORM), and by Hess, Girirajan and Mason (FPALM), these switch on a sparse few fluorophores at a time, find the centre of each blur, and plot thousands of positions.

Locating one isolated molecule is not the same as resolving two. The centre of a single blur can be found to a few nanometres, and in the shot-noise limit the uncertainty falls as 1/√N for N detected photons. That is localization precision. Resolution also needs enough labelled molecules, a small enough label, and care with blinking, since one fluorescent protein that switches off and on can be counted several times. MINFLUX reported about 1 nm precision in 2017, but on DNA origami, not in a cell.

The 2014 Nobel Prize in Chemistry went to Eric Betzig, Stefan Hell and William E. Moerner. No one person invented super-resolution.

Reading an image like a skeptic

A beautiful image is a measurement, and it needs the same scrutiny as a number in a table. Ask these questions in order.

What is labelled, and how do we know? An antibody (see the purification lesson) can bind the wrong protein. The strongest test of specificity is genetic: the signal should disappear in cells lacking the target. A secondary-only sample checks the secondary antibody. A genetic tag such as GFP, covered in the signalling course along with biosensors in detecting a signal, avoids antibodies but can itself change where a protein goes. Fixation can move proteins too: in primary human lymphatic endothelial cells made to overexpress the receptor, secondary antibodies clustered the receptor LYVE-1 after formaldehyde fixation until glutaraldehyde was added. The long argument over what Golgi’s silver stain showed in nerve tissue, told in the neuron doctrine, was an argument about what a stain reveals.

Are the channels clean? Image single-label samples in every channel to measure bleed-through, where one dye’s light leaks into another’s filter.

Can intensities be compared? Only if every condition was acquired with identical settings, and no pixel of interest sits at the detector’s maximum. A saturated pixel no longer reports how much label is there. Subtract background before measuring, but remember that subtraction removes the average background, not its photon noise.

What does overlap mean? Two colours in the same pixel are within one resolution volume of each other, about 230 nm laterally and 800 nm axially in the worked example. A volume that size can hold thousands of proteins in a typical cell (an order-of-magnitude estimate). Colocalization shows proximity; binding needs a biochemical test or a far finer one.

Design problem

A paper shows that an antibody to protein P stains mitochondria, and a yellow overlap with a mitochondrial marker is offered as proof that P binds the marker. What would you require before accepting either claim?