Super-resolution microscopy broke a limit by changing what is measured

Abbe's diffraction limit sets the smallest separation two point sources can have and still be resolved in a conventional microscope — roughly half the wavelength. Super-resolution techniques do not violate it. They sidestep it by measuring something other than a direct image.

Structured illumination

Illuminating the sample with a fine periodic pattern produces moiré fringes between the pattern and the sample's structure. Those fringes encode high spatial frequencies that would otherwise fall outside the optical system's passband, shifted down into the range it can transmit.

Recording several images with the pattern at different phases and orientations, then computationally reconstructing, roughly doubles resolution. Fast, gentle and modest in gain.

Depletion approaches

Stimulated emission depletion illuminates with an excitation spot overlaid by a doughnut-shaped depletion beam that switches off fluorescence everywhere except the very centre.

The remaining emitting region is much smaller than the diffraction limit, and scanning it builds an image. Resolution improves with depletion intensity, which is also what limits it: high intensity photobleaches the sample and damages living cells.