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Autoradiography localizes a radioactive label through its effect on a recording medium. In electron microscopy, developed photographic grains are compared with specimen structures; their positions have finite localization precision.

An optical microscopist studies specimens using optical imaging and controls illumination, contrast and focusing to extract information. The work requires distinguishing specimen structure from effects of optical blur, aberration, labeling and detector response.

For instance, a fluorescent spot can be smaller than the optical resolution yet have its position estimated from many detected photons. Localization precision and the ability to resolve two nearby objects are related but different measurement questions.

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 iswhere $a$ is pixel size in the specimen plane and ${\sigma }_{\mathrm{bg}}$ 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.^[ref]

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.^[ref]

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.^[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.

The Stokes–Einstein relation connects thermal diffusion with dissipative mobility. For a dilute suspension of isolated rigid spheres of hydrodynamic radius $a$ in an unbounded Newtonian fluid of viscosity $\eta$,where $\zeta$ is translational drag coefficient, $D$ diffusion coefficient and $T$ absolute temperature. Stokes drag supplies $\zeta =6\pi \eta a$ under no-slip, continuum, low-Reynolds-number conditions. The Einstein diffusion relation $D=k_{B}T/\zeta$ is more general than that particular spherical drag law.

A short equilibrium argument explains the connection. Let a weak external potential $U$ exert force $\mathbf{F}=-\nabla U$, so drift velocity is $\mathbf{F}/\zeta$. The number flux is $\mathbf{j}=n\mathbf{F}/\zeta -D\nabla n$. A Boltzmann distribution $n\propto e^{-U/(k_{B}T)}$ has $\nabla n=n\mathbf{F}/(k_{B}T)$; requiring zero equilibrium flux fixes $D=k_{B}T/\zeta$. thermal fluctuations and viscous dissipation are therefore linked, rather than independent adjustable effects. The original theory also relates diffusion to measured random displacements.^[ref]

On times long compared with momentum relaxation, an isotropic diffusing sphere hassingle-particle tracking can measure the slope. Alternatively, dilute single-scattering dynamic light scattering measures a field correlation $g_1(q,t)=e^{-D{q}^{2}t}$; the corresponding intensity-correlation excess is proportional to $e^{-2D{q}^{2}t}$. The scattering wavenumber and the distinction between field and intensity decay must be retained.

A Stokes-Einstein experimental consistency test independently measures temperature and solvent viscosity, uses a narrow distribution of inert spheres, checks decay rate proportional to $q^2$ or displacement variance proportional to time, and extrapolates toward infinite dilution. Subtract drift, account for wall-enhanced drag, and verify that aggregation is absent. Tracking additionally needs spatial calibration and correction for finite exposure and localization precision. At finite concentration, collective diffusion is not automatically the single-particle self-diffusion in the equation. A hydrodynamic radius is not generally identical to a polymer radius of gyration; nonspherical particles, slip or viscoelastic solvents require a different mobility model.

Stochastic optical reconstruction microscopy separates emitters in time rather than shrinking every illuminating spot. Switch only a sparse subset of labeled molecules into a fluorescent state, localize their individual point spread functions, switch or bleach them off, and repeat. Combining many fitted positions reconstructs structure finer than the individual diffraction-blurred spots.^[ref]

An interesting application is the neuronal axon. STORM revealed approximately $180$–$190\mathrm{nm}$ periodic organization of actin, spectrin and associated proteins, supporting a membrane-associated cytoskeletal architecture that ordinary fluorescence images did not resolve clearly.^[ref]

Localization precision improves with detected photons, but reconstructed resolution also depends on label density, label size, drift and reliable separation of emitters. Many frames are needed, so motion and slow acquisition can limit live imaging. Multiple localizations of one blinking label must not automatically be counted as multiple molecules. A precise molecular fit and a faithful reconstructed biological structure are related but distinct achievements.

Stochastic optical reconstruction microscopy reconstructs an image from the estimated positions of individual fluorescent labels that are observed in sparse subsets over many frames. The experiment repeatedly switches labels between detectable and dark states, fits isolated point spread functions, and combines the localizations.

This separates emitters in time instead of requiring all neighboring labels to be spatially resolved in one exposure. Localization precision depends on detected photons and background; drift, incomplete labeling and simultaneous overlapping emitters constrain final optical resolution. In the original demonstration, reversibly switched dye labels enabled repeated sparse localization.^[ref]