= Solution
\b[Position from many photons.] An isolated <fluorophore> produces a diffraction-broadened <point spread function>, but its unknown center can be inferred much more precisely than the width of that function. Fit a calibrated two-dimensional <Gaussian function> plus background to the detected photon positions or pixel intensities. If the <point spread function> has width $s$ and $N_\gamma$ independent photons are detected, negligible background gives <localization precision> approximately $s/\sqrt{N_\gamma}$. Pixelation and background worsen it; a commonly useful approximate <variance> is
$$
\sigma_x^2\simeq\frac{s^2+a^2/12}{N_\gamma}
+\frac{8\pi s^4\sigma_{\rm bg}^2}{a^2N_\gamma^2},
$$
where $a$ is pixel size in the specimen plane and $\sigma_{\rm bg}$ is background noise per pixel in photon units. Bright, isolated emitters can therefore have nanometre <localization precision> despite a spot hundreds of nanometres wide. Stage drift, finite exposure motion, incorrect fitting, label displacement and <photobleaching> can dominate the photon limit.<Precise nanometer localization analysis for individual fluorescent probes by Russell E. Thompson and others>[Localization-error analysis: photon number, pixel size and background contributions]{ref}
\b[Walking mechanism.] <Myosin V> is a two-headed, processive <molecular motor> that advances along <actin> with center-of-mass steps of about $37\,\mathrm{nm}$. A simple inchworm model retains the identity of the leading head, so a label fixed to one head would move approximately $37\,\mathrm{nm}$ on every cycle. In a hand-over-hand model the heads exchange lead: a label close to one head alternates a displacement near $74\,\mathrm{nm}$ with a near-zero displacement while the other head passes. For a label at offset $x$ from the midpoint, the more general alternating pair is $37-2x$ and $37+2x$ nanometres. The pair sums to $74\,\mathrm{nm}$; individual steps need not always equal $74\,\mathrm{nm}$.
Single-label imaging records a moving spot on a camera while the motor travels along surface-associated <actin>. Fitting the spot in successive frames resolves plateaus and jumps much smaller than the diffraction width. The observed alternating displacements distinguish a passing-head mechanism from uniform inchworm steps. This experiment combines a specific geometric prediction with <single-molecule fluorescence microscopy>; the center-of-mass stride alone would not make that distinction.<Myosin V Walks Hand-Over-Hand: Single Fluorophore Imaging with 1.5-nm Localization by Ahmet Yildiz and others>[Science 300, pp. 2061–2065: single-label tracking, 1.5-nm localization and alternating displacement predictions]{ref}
\b[Resolving a labelled structure.] Accurate localization of one emitter does not automatically resolve two simultaneously overlapping emitters. <Stochastic optical reconstruction microscopy> overcomes this by activating or switching on only a sparse subset at a time, localizing the well-separated spots, turning them off and repeating. The accumulated coordinates reconstruct a densely labelled structure at scales below the diffraction limit. The original demonstration used repeated photoswitching and localization of individual dyes to reconstruct subdiffraction features.<Sub-diffraction-limit imaging by stochastic optical reconstruction microscopy (STORM) by Michael J. Rust and others>[Nature Methods 3, pp. 793–796: sequential localization of photoswitchable fluorophores]{ref}
The useful structural resolution depends on both <localization precision> and label sampling density, as well as drift, fluorophore blinking, optical aberrations and linkage error. Sparse activation separates emitters in time; it does not shrink the diffraction-limited <point spread function>. A reconstructed image must have enough independent labels to represent its finest claimed feature.
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