Therefore, Equations (2-2) and (2-5) represent the time-dependent correlation
function for 3D- and 2D-diffusion, respectively.
Geometry of Focus Volume Obtained by Free Dye Calibration
In order to obtain the molecule diffusion information (zD and N) for unknown
molecules (or molecules with unknown diffusion coefficient D) using Equation (2-2), the
geometry of the focus volume needs to be determined. The dimension of the
observation volume element is defined by the half-axis in length (wz) and radius (wxy),
as shown in the magnified diagram in Figure 2-2. These dimensions can be obtained by
a calibration study using a dye molecule with known diffusion coefficient D.
For a dye molecule with known diffusion coefficient D and known concentration C,
the half-axis width of the focus volume can be obtained:
2
SD xy = 4::: (2-6)
S4D
Due to the relationship between the effective volume of the focus volume (Veff)
and the molecular concentration C:
Vff = (2-7)
NA -C
Therefore, the half-axis length of the focus volume, wz, can be obtained:
V = Z z = 3/2 2 (2-8)
S- zxy
A femtoliter-sized ellipsoid shaped confocal volume with half axis radius wxy and
half axis length wz in the pm range is generally obtained for the geometry of the focus
volume in FCS. This femtoliter-sized, optically defined observation volume is the