= 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 function>[Gaussian] image of <standard deviation> $s$ and $N$ independent detected <photons>, the centroid precision scales as
$$
\boxed{\sigma_{\rm loc}\simeq\frac{s}{\sqrt N}.}
$$
Pixelation and background worsen this limit. A useful approximate <variance> for square pixels of width $a$ and background rms noise $b$ <photons> per pixel is
$$
\sigma_{\rm loc}^2\simeq\frac{s^2+a^2/12}{N}+\frac{8\pi s^4b^2}{a^2N^2}.
$$
This estimate requires a correctly specified isolated image and appropriate noise model. Drift, optical aberration, dye motion, linkage offset, <photobleaching>[bleaching] and <motion blur> introduce further errors; localization precision alone does not guarantee absolute positional accuracy.<Precise nanometer localization analysis for individual fluorescent probes by Russell E. Thompson and others>[Photon number, pixel size and background dependence of localization uncertainty]{ref}
In the <Myosin V> measurements, <total internal reflection fluorescence microscopy> reduced background and a two-dimensional <Gaussian function>[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 motion of a two-headed motor>[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 motion of a two-headed motor>[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.<Myosin V Walks Hand-Over-Hand: Single Fluorophore Imaging with 1.5-nm Localization by Ahmet Yildiz and others>[Single-light-chain fluorophore localization, alternating displacements and hand-over-hand interpretation; Science 300, 2061–2065 (2003)]{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.<Sub-diffraction-limit imaging by stochastic optical reconstruction microscopy (STORM) by Michael J. Rust and others>[Sequential sparse activation and localization of fluorophores to reconstruct a super-resolution image]{ref}
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