Analysis of confocal laser-microscope optics for 3-D fluorescence correlation spectroscopy

Quantitative fluorescence correlation spectroscopy (FCS) and fluorescence photobleaching recovery (FPR) measurements in bulk solution require a well characterized confocal laser microscope optical system. The introduction of a characteristic function, the collection efficiency function (CEF), provides a quantitative theoretical analysis of this system, which yields an interpretation of the FCS and FPR measurements in three dimensions. We demonstrate that when the proper field diaphragm is introduced, the 3-D FCS measurements can be mimicked by a 2-D theory with only minor error. The FPR characteristic recovery time for diffusion is expected to be slightly longer than the corresponding time measured by FCS in the same conditions. This is because the profile of the laser beam used for photobleaching is not affected by the field diaphragm. The CEF is also important for quantitative analysis of standard scanning confocal microscopy when it is carried out using a finite detection pinhole.