 Solution

Fluorescence localization precision can be much finer than the image width: a fluorescent molecule produces a diffraction-broadened point spread function, but the centre of that distribution can be estimated much more precisely than its width. Fit the measured camera counts to a calibrated point-spread model with position, brightness and background parameters. For an ideal Gaussian image of standard deviation $s$ and $N$ independent detected photons, the centroid precision scales asPixelation and background worsen this limit. A useful approximate variance for square pixels of width $a$ and background rms noise $b$ photons per pixel isThis estimate requires a correctly specified isolated image and appropriate noise model. Drift, optical aberration, dye motion, linkage offset, bleaching and motion blur introduce further errors; localization precision alone does not guarantee absolute positional accuracy.^[ref]

In the Myosin V measurements, total internal reflection fluorescence microscopy reduced background and a two-dimensional Gaussian fit localized a single dye attached to a light chain with roughly $1.5\mathrm{nm}$ precision. The motor's centre advances about $37\mathrm{nm}$ per cycle. A hand-over-hand mechanism instead moves the rear head about $74\mathrm{nm}$ past the stationary front head, exchanging their roles. A label displaced by $x$ from the midpoint therefore gives alternating displacements $37+2x$ and $37-2x$ nm; near a head this tends towards alternating $74$ and $0$ nm. An inchworm model would give approximately uniform $37$ nm label displacements. Resolved unequal alternating steps therefore distinguish the mechanisms, with interpretation depending on the label geometry.^[ref]

For sub-diffraction imaging, arrange that only a sparse, spatially separable subset of fluorophores emits in each frame, localize those emitters, then combine many frames into a map. Photoactivation or reversible stochastic switching provides the sparse subsets. Distinct nearby molecules can then be localized at different times, circumventing overlap of their simultaneously emitted diffraction patterns. The achievable structural resolution depends on photon-limited precision, label density and linkage, repeated blinking, drift correction and specimen motion; arbitrarily many fits to the same dye do not supply missing labels elsewhere. This is the principle behind PALM and STORM, with their different switching strategies.^[ref]