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PALM separates emitters in time. A sparse subset of photoactivatable or photoconvertible labels is switched on so that its diffraction-broadened images can be fitted individually; repeated activation, imaging and localization builds a map from many isolated detections. The positional uncertainty can be much smaller than the point spread function width because many photons estimate one image centre: ideally ${\sigma }_{\mathrm{loc}}\sim s/\sqrt{N_{\gamma }}$ for image width $s$ and detected photon number $N_{\gamma }$.

That is fluorescence localization precision, not automatically the structural resolution of the reconstructed cell. Pixelation, background, imperfect optics, drift, label linkage, blinking and labelling density matter. Repeated localizations of one molecule cannot fill unlabelled gaps; a crowded frame with overlapping images cannot simply be treated as many isolated emitters. For a static structural map, the structure must remain sufficiently stable while the many frames are accumulated, or its time dependence must be reconstructed explicitly.

For mobility in living cells, keep activated proteins observable for successive frames and link isolated positions into trajectories before bleaching. Repeating this for successive sparse subsets yields many trajectories without making the entire protein population simultaneously fluorescent. This is the sptPALM strategy.^[ref]

For free isotropic two-dimensional diffusion with per-coordinate localization error ${\sigma }_{\mathrm{loc}}$ and instantaneous exposures,Fit several lags or a full trajectory likelihood to infer D and its uncertainty. Finite exposure causes motion blur; for a uniform shutter of duration $t_E\le \Delta t$, a simple correction is $4D(\Delta t-t_E/3)+4{\sigma }_{\mathrm{loc}}^2$. Confinement, directed motion and switching binding states change the lag dependence. Short tracks, missed detections and false linking in crowded regions can mimic apparent heterogeneity, so mobility classes require explicit measurement-error and tracking controls. A trajectory map recovers dynamics; it is not identical to a static PALM density map.

Sparse photoactivation allows successive positions of individual labelled molecules to be linked into trajectories; activation of fresh subsets yields many tracks in living cells. This extends photoactivated localization microscopy from accumulated positions to mobility. For free two-dimensional diffusion with independent per-coordinate fluorescence localization precision $\sigma$, instantaneous frames give mean squared displacement $4D\Delta t+4{\sigma }^2$. Motion blur, tracking errors, confinement and photobleaching must be accounted for before assigning mobility classes.^[ref]