User:Ruetti

The general form of the normalized fluctuation correlation function reads as follows:

${\displaystyle G_{ij}={\frac {\langle \delta F_{i}(t)\,\delta F_{j}(t+\tau )\rangle }{\langle F_{i}(t)\rangle \langle F_{j}(t)\rangle }}}$

with ${\displaystyle i=j}$ for autocorrelation and ${\displaystyle i\neq j}$ for crosscorelation. ${\displaystyle F_{D}}$ is the fluorescence signal collected at detector ${\displaystyle D}$. ${\displaystyle F_{D}}$ is of the following form:

${\displaystyle F_{D}=\sum _{k}\kappa _{k}^{D}\int _{V}I_{ex}({\underline {r}})\,CEF_{k}({\underline {r}})\,\sigma _{k}\,q_{k}\,C_{k}({\underline {r}},t)\,dV}$

${\displaystyle k}$ runs here over all fluorescent species contributing to ${\displaystyle F_{D}}$. ${\displaystyle \kappa _{k}}$ is the photon to count conversion efficiency of filter and detector, ${\displaystyle I_{ex}}$ is the spatial distribution of the photon flux density with amplitude ${\displaystyle I_{0}}$ and ${\displaystyle CEF_{k}({\vec {r}})}$ is the dimensionless optical transfer function of the detector pinhole combination. ${\displaystyle \sigma _{k}}$ is the molecular absorption cross section, ${\displaystyle q_{k}}$ the quantumn efficiency and ${\displaystyle C_{k}}$ the particle concentration.