Saturation of fluorescence in flames with a Gaussian laser beam

The method of saturated fluorescence for measuring species concentrations in flames is usually performed with laser beams that do not provide a constant intensity distribution across the focal volume. Because of the intensity distribution across the beam, the fluorescence signal does not depend on laser power or intensity in the same manner as for uniform illumination. This leads to anomolous apparent saturation intensities. In the following, the effect is considered for atomic fluorescence. Relations for the fluorescence signal under two common excitation geometries are derived and uncertainty relations used to consider the benefits of high laser intensity.