Localization uncertainty in nta measurements

<p>Tracking error is defined[<a class="litnote tooltip" href="/literature/@catipovic2013">@catipovic2013<span class="tooltiptext">Improving the quantification of Brownian motion</span></a>] as the uncertainty in time and position for each particle. The localization of the particle is limited by the number of photons, shot noise, etc.</p> <p>It must be noted, also that <a class="wikilink" href="/brownian_motion/">brownian motion</a> itself generates localization uncertainties[<a class="litnote tooltip" href="/literature/@ernst2013">@ernst2013<span class="tooltiptext">Measuring a diffusion coefficient by single-particle tracking: statistical analysis of experimental mean squared displacement curves</span></a>]. Although longer exposure times allow the collection of more light, they induce a larger uncertainty if the particles can diffuse a lot during that time window. This is quadratically problematic for small particles, since they scatter less light AND move faster. </p> <p>The <em>reduced localization error</em> can be expressed as:</p> <p>$$x=\frac{\sigma^2}{D\Delta t}$$</p>