Photon Counting Histogram Analysis for Two‐Dimensional Systems

Photon counting statistics in 3D photon counting histogram analysis for one‐photon excitation is a function of the number of molecules of particular brightness in the excitation‐detection volume of a confocal microscope. In mathematical form that volume is approximated by a three‐dimensional Gaussian function which is embedded in the PCH theoretical equations. PCH theory assumes that a molecule can be found anywhere inside the excitation‐detection volume with equal probability. However, one can easily imagine systems in which this assumption is violated because molecules are constrained by the geometry of the sample. For example, molecules on a surface or in a membrane would be constrained to two dimensions. To enable the analysis of such systems by PCH, the theoretical framework requires modification. Herein, we present an extension of the PCH analysis to systems where molecules exist in thin structures that are effectively two‐dimensional. The method, aptly called two‐dimensional photon counting histogram (2D PCH), recovers the number of fluorescent particles per unit area and their molecular brightness. Both theoretical background and experimental results are presented. The theory was tested using computer‐simulated and experimental 2D PCHs obtained from confocal experiments. We demonstrate that this modification of the theoretical framework provides a tool to extract data that reveal states of aggregation, surface photophysics, and reactivity.