A comparison between photon counting histogram and fluorescence intensity distribution analysis.

Photon counting histogram (PCH) and fluorescence intensity distribution analysis (FIDA) are two methods that were developed independently but reported almost simultaneously. Both of them have been successfully applied to fluorescence fluctuation spectroscopy (FFS). Though publications have indicated that they are theoretically equivalent, they are still commonly considered as different methods, especially in their ways to treat the point spread functions (PSFs). In this paper, the two methods are examined in detail for a direct comparison. After a direct proof of the theoretical equivalence, the authors further point out that PCH and FIDA are completely equivalent in the way of modeling PSFs; that is, any modeling approach developed from one of them can always be applied to the other. It is also demonstrated that simplified FIDA and PCH formulas in the form of power series can be applied for fast and precise numerical calculations. The two methods are also compared for their merits in the calculation efficiency.