Two-photon excitation fluorescence correlation spectroscopy of diffusion for Gaussian-Lorentzian volumes

Fluorescence correlation spectroscopy (FCS) is valuable in many scientific domains where diffusion plays a fundamental role. One important experimental realization is based on fluorescence induced by two-photon excitation (TPE). In comparison with one-photon excitation (OPE), TPE-FCS defines better the interrogation volume and the background noise is sensibly reduced. Within this context and for overfilled objective lenses, the three-dimensional Gaussian (3DG) approximation, according to which the spectroscopic interaction is spatially defined by Gaussian profiles only, guarantees a simple analytical data interpretation. By contrast, the volume illuminated by the laser beam focused with partially filled objective lenses follows a Gaussian-Lorentzian (GL) distribution that is taken into account by means of numerical methods only. Here we show that contrary to common belief, the assumption of a GL volume does not hamper analytical treatment of TPE-FCS. Differences and similarities in comparison with the 3DG approximation are discussed.