For a circular bleach spot of radius  and diffusion-dominated recovery, the fluorescence is described by an equation derived by Soumpasis (which involves modified Bessel functions  and )
with  the characteristic timescale for diffusion, and  is the time.  is the normalized fluorescence (goes to 1 as  goes to infinity). The diffusion timescale for a bleached spot of radius  is , with D the diffusion coefficient.
Note that this is for an instantaneous bleach with a step function profile, i.e., the fraction  of protein assumed to be bleached instantaneously at time  is , and , for  is the distance from the centre of the bleached area. It is also assumed that the recovery can be modelled by diffusion in two dimensions, that is also both uniform and isotropic. In other words, that diffusion is occurring in a uniform medium so the effective diffusion constant D is the same everywhere, and that the diffusion is isotropic, i.e., occurs at the same rate along all axes in the plane.
In practice, in a cell none of these assumptions will be strictly true.
#Bleaching will not be instantaneous. Particularly if strong bleaching of a large area is required, bleaching may take a significant fraction of the diffusion timescale . Then a significant fraction of the bleached protein will diffuse out of the bleached region actually during bleaching. Failing to take account of this will introduce a significant error into D.
#The bleached profile will not be a radial step function. If the bleached spot is effectively a single pixel then the bleaching as a function of position will typically be diffraction limited and determined by the optics of the confocal laser scanning microscope used. This is not a radial step function and also varies along the axis perpendicular to the plane.
#Cells are of course three-dimensional not two-dimensional, as is the bleached volume. Neglecting diffusion out of the plane (we take this to be the xy plane) will be a reasonable approximation only if the fluorescence recovers predominantly via diffusion in this plane. This will be true, for example, if a cylindrical volume is bleached with the axis of the cylinder along the z axis and with this cylindrical volume going through the entire height of the cell. Then diffusion along the z axis does not cause fluorescence recovery as all protein is bleached uniformly along the z axis, and so neglecting it, as Soumpasis equation does, is harmless. However, if diffusion along the z' axis does contribute to fluorescence recovery then it must be accounted for.
#There is no reason to expect the cell cytoplasm or nucleoplasm to be completely spatially uniform or isotropic.
Thus, the equation of Soumpasis is just a useful approximation, that can be used when the assumptions listed above are good approximations to the true situation, and when the recovery of fluorescence is indeed limited by the timescale of diffusion . Note that just because the Soumpasis can be fitted adequately to data does not necessarily imply that the assumptions are true and that diffusion dominates recovery.