User:Ruetti

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

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 $$i=j$$ for autocorrelation and $$i\neq j$$ for crosscorelation. $$F_D$$ is the fluorescence signal collected at detector $$D$$. $$F_D$$ is of the following form:

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 $$

$$k$$ runs here over all fluorescent species contributing to $$F_D$$. $$\kappa_k$$ is the photon to count conversion efficiency of filter and detector, $$I_{ex}$$ is the spatial distribution of the photon flux density with amplitude $$I_0$$ and $$CEF_k(\vec{r})$$ is the dimensionless optical transfer function of the detector pinhole combination. $$\sigma_k$$ is the molecular absorption cross section, $$q_k$$ the quantumn efficiency and $$C_k$$ the particle concentration.