## 4 Results and Validation
### Effect of Time Binning on FCS Measurements  
The impact of time binning on the processed data after autocorrelation and the acquired diffusion times after model fitting was evaluated using TCSPC raw data in form of photon arrival times obtained from measurements of solution with Rhodamine B at different concentrations (10, 20 and 40 nM) using the 63\(\times\) and 40\(\times\) objective lens. The acquired autocorrelated FCS data for a specific measurement (10 nM and 63\(\times\) lens) are plotted for different time binning varied from 10\({}^{3}\)-10\({}^{6}\) ns in Figure 4. It is evident from the figure that at shorter time binning, i.e., 10\({}^{3}\) ns, the autocorrelated data contain too much noise to be relevant, while increasing the time binning excessively (10\({}^{6}\) ns) results in loss of information and the autocorrelation function becomes hardly recognizable. Similar behavior was observed for correlation data acquired from similar solution using 40\(\times\) objective lens (see further Supplementary data, Figure S1). It is clear from this evaluation that the selection of time binning is important in order to generate relevant autocorrelation data that can be subject to further data fitting. This observation agrees with the theoretical concept of FCS as presented by [PERSON] and [PERSON] explained as \"a time interval comparable to the characteristic diffusion time is required to generate autocorrelation function\" [13].  
Figure 3: The effect of numerical aperture on FCS data obtained from Rhodamine B solution at 10 nM concentration acquired by using objective lenses with different numerical aperture (NA), 40\(\times\) (NA 0.8) and 63\(\times\) (NA 1.2). FCS data obtained from SPCM64 software produced by multi-tau algorithm (**a**,**d**), generated by customized algorithm expressed in logarithmic (**b**,**e**) and linear scale (**c**,**f**) The data was obtained from red channel (580/150 nm) at 800 nm excitation wavelength, 25 mW excitation intensity and time binned at 10\({}^{4}\) ns.  
Another way of assessing the effect of time binning is to investigate the photon count per time bin. As discussed previously, the original time correlated photon count data have a binary format where \"0\" means no photon, and \"1\" is a photon counted. As photon counts are sparse, substantial binning can be performed while retaining the binary format of the data vector. This is illustrated in Figure 5 showing the photon count per time bin vector after subject to different amount of binning in the range 10\({}^{3}\)-10\({}^{6}\) ns. As shown by the figure the vector is sparse and binary up to a binning of 10\({}^{3}\) ns. This also explains the lack of autocorrelation information observed for low binning in Figure 4. When increasing the binning (\(>5\times 10^{3}\) ns), the photon counts per time bin start to increase above one, as shown by Figure 5, and the vector is no longer binary. Increasing the binning further both elevate photon counts per time bin and noise level. This agrees with data based on concentration fluctuations should follow Poisson statistics [12]. Similar behavior was observed for correlation data acquired from similar solution using 40\(\times\) objective lens (see further Supplementary data, Figure S2). Therefore, it is important to choose a binning window for which data obey this condition. From these two analyses exploring the effect of time binning, it can be concluded that the optimum time binning is around 10\({}^{4}\)-10\({}^{5}\) ns for this experimental setting. This also verifies the need to validate time-binning before performing any FCS analysis using TCSPC raw data in form of photon arrival times in order to ensure relevance of data.