## 2 Materials and Methods
### Phasor Analysis  
Fluorescence intensity decay measured on the samples' surfaces was analyzed using the phasor method; a comprehensive description of this approach can be found elsewhere [34]. In brief, assuming an infinitely short excitation pulse (8-function) and an intrinsic fluoresce decay of \(N\) (\(N\geq 1\)), fluorescent species with distinct fluorescence lifetimes can be modeled by Equation (1):  
\[I(t)=I(0)\sum_{i=0}^{N}\alpha_{i}e^{\frac{-t}{\tau_{i}}} \tag{1}\]  
where \(I(0)\) is the number of the instantly emitted photons at time zero; the coefficient \(\alpha_{i}\), called the pre-exponential factor, is the amplitude; and \(\tau_{i}\) is the fluorescence decay time of the \(i\)-th component of the mixture. The phasor analysis employs the Fourier transformation of the fluorescence intensity decay to produce real and imaginary components \(\mathbf{g}\) and \(\mathbf{s}\), respectively, which are calculated as follows:  
\[g(\omega)=\int_{0}^{T}I(t)\cdot\cos(\omega t)dt/\int_{0}^{T}I(t)dt \tag{2}\]  
\[s(\omega)=\int_{0}^{T}I(t)\cdot\!\!\cdot\!\!\cdot\!\!\cdot\!\!\cdot\!\!\cdot \!\!\cdot\!\!\cdot\!\!\cdot\!\!\cdot\!\!\cdot\!\!\cdot\!\!\cdot\!\!\cdot\!\!\cdot \!\!\cdot\!\!\cdot\!\!\cdot\!\!\cdot\!\!\cdot\!\!\cdot\!\!\cdot\!\!\cdot\!\!\cdot \!\!\cdot\!\!\cdot\!\!\cdot\!\!\cdot\!\!\cdot\!\!\cdot\!\!\cdot\!\!\cdot\!\!\cdot \!\!\cdot\!\!\cdot\!\!\cdot\!\!\cdot\!\!\cdot\!\!\cdot\!\!\cdot\!\!\cdot\!\!\! \cdot\!\!\cdot\!\!\cdot\!\!\cdot\!\!\cdot\!\!\cdot\!\!\cdot\!\!\cdot\!\!\!\cdot \!\!\!\cdot\!\!\cdot\!\!\cdot\!\!\cdot\!\!\cdot\!\!\cdot\!\!\!\cdot\!\!\!\cdot \!\!\!\cdot\!\!\cdot\!\!\cdot\!\!\!\cdot\!\!\!\cdot\!\!\cdot\!\!\!\cdot\!\!\! \cdot\!\!\cdot\!\!\!\cdot\!\!\cdot\!\!\cdot\!\!\cdot\!\!\!\cdot\!\!\!\cdot\!\! \cdot\!\!\!\cdot\!\!\cdot\!\!\!\cdot\!\!\!\cdot\!\!\!\cdot\!\!\!\cdot\!\!\!\cdot \!\!\!\cdot\!\!\!\cdot\!\!\!\cdot\!\!\cdot\!\!\!\cdot\!\!\!\cdot\!\!\!\cdot \!\!\!\cdot\!\!\cdot\!\!\!\cdot\!\!\!\cdot\!\!\cdot\!\!\!\cdot\!\!\!\cdot\!\!\! \cdot\!\!\!\cdot\!\!\!\cdot\!\!\cdot\!\!\cdot\!\!\!\cdot\!\!\cdot\!\!\!\cdot\!\! \cdot\!\!\!\cdot\!\!\!\cdot\!\!\!\cdot\!\!\!\cdot\!\!\cdot\!\!\!\cdot\!\!\!\cdot \!\!\!\cdot\!\!\!\cdot\!\!\!\cdot\!\!\!\cdot\!\!\!\cdot\!\!\!\cdot\!\!\!\cdot\!\!\! \cdot\!\!\!\cdot\!\!\!\cdot\!\!\!\cdot\!\!\!\cdot\!\!\!\cdot\!\!\!\cdot\!\!\!\cdot \!\!\!\cdot\!\!\!\cdot\!\!\!\cdot\!\!\!\cdot\!\!\!\cdot\!\!\!\cdot\!\!\!\cdot\!\!\! \cdot\!\!\!\cdot\!\!\!\cdot\!\!\cdot\!\!\!\cdot\!\!\!\cdot\!\!\!\cdot\!\!\!\!\cdot \!\!\!\cdot\!\!\!\cdot\!\!\!\cdot\!\!\cdot\!\!\!\cdot\!\!\!\cdot\!\!\!\cdot\!\!\!\cdot \!\!\!\cdot\!\!\!\cdot\!\!\!\cdot\!\!\!\cdot\!\!\!\cdot\!\!\!\cdot\!\!\!\cdot \!\!\!\cdot\!\!\!\cdot\!\!\!\cdot\!\!\cdot\!\!\!\cdot\!\!\!\cdot\!\!\!\cdot\!\!\!\! \cdot\!\!\!\cdot\!\!\!\cdot\!\!\cdot\!\!\!\cdot\!\!\!\cdot\!\!\!\cdot\!\!\!\cdot\!\!\!\! \cdot\!\!\!\cdot\!\!\!\cdot\!\!\!\Each fluorescence decay is acquired from a group of pixels to generate FL maps. Fluorescence decay values can be plotted as a single point (phasor) in the phasor plot. For a single-lifetime species (N = 1), the FL can be directly determined by the coordinate values of the phasor. The relationship between the two coordinates of a phasor representing a single-lifetime species can be drawn as a semicircle curve (Equation (5)), centering at (\(g\) = 0.5; \(s\) = 0), with a radius of 0.5 in the phasor plot, called the universal semicircle or the universal trajectory.  
\[\left(g-0.5\right)^{2}+s^{2}=0.25 \tag{5}\]  
For multiple-lifetime species (\(N>1\)), the phasor (\(g\), \(s\)) is a linear combination of multiple phasors, each (\(g_{i}\), \(s_{i}\)) representing an individual species. FL data can be analyzed and interpreted considering the following [34]: First, the universal semicircle is a lifetime ruler for single-lifetime species, and indicates relative changes in lifetime for complex species; the lifetimes increase from right to left--i.e., lifetimes near zero at (\(g\) = 1; \(s\) = 0), and infinite lifetimes at (\(g\) = 0; \(s\) = 0).