Intensity Distribution of a Dilute Solution of Point Emitters under Gaussian Detection

In single-molecule techniques, one often employs a Gaussian illumination profile to measure fluorescence intensities from a dilute solution of molecules. Typically such measurements are performed by single-photon detection and result in a sequence of single-photon arrival times. Here we develop a general framework for calculating the intensity distribution of a dilute solution of Point emitters under Gaussian Detection. We will show that the resulting Intensity distributions dramatically change character at low emitter concentrations when considering different dimensionalities of Gaussian Detection. In particular the one- and two- dimensional solutions are strongly structured, exhibiting discontinuities in their derivative at integer multiples of the brightness. This makes these distributions strong candidates for applications that distinguish and measure concentrations of mixtures of emitters of different brightnesses. Finally, we will discuss a maximum likelihood method to determine concentration and brightness from a sequence of single-photon arrival times.