## 4 Results and Validation
### Effect of Excitation Power on FCS Measurements  
Figure 7 shows the effect of excitation power on FCS measurements when the excitation power was varied between 15-50 mW and 10-30 mW for the two different objective lenses, 40\(\times\) and 63\(\times\) respectively, and the corresponding data and FCS model fitting are plotted. Different ranges of excitation power were applied for the objective lenses since the  
Figure 6: The effect of concentration on FCS data obtained from Rhodamine B solution at different concentrations (10 nM, 20 nM and 40 nM) generated by different objective lenses (**a–c**) 40\(\times\) (NA 0.8) and (**d–f**) 63\(\times\) (NA 1.2). Autocorrelation function data (blue) and fitted data (red) are shown. The data was obtained from red channel (580/150 nm) at 800 nm excitation wavelength, 25 mW excitation intensity. effective peak power inside the detection volume is expected to vary due to the difference in NA. The acquired FCS curves were found to depend on excitation intensity for both objective lenses. It is evident from the figure that excitation power will affect both parameters G(0) and diffusion time \(\tau\). In the case of the 40\(\times\) objective lens, reliable FCS data were not obtained when the excitation intensities reached a lower threshold value of 15 mW and higher threshold value 50 mW. A similar behavior was observed for the 63\(\times\) objective lens. Figure 8 shows how the acquired FCS data and fitting parameters depend on the excitation intensity using the 63\(\times\) objective lens. In the figure, the amplitude of autocorrelation function (G(0)), number of molecules (N) and average photon counts (P) are plotted as function of normalized excitation power (I/I\({}_{0}\)), where I\({}_{0}\) was defined as the lowest excitation power for each objective lens. As discussed by others, ref. [29] increased excitation intensity leads to an increase in the size of the excitation volume. Therefore, the number of molecules (N) in the detection volume is expected to increase with power. Due to the inverse relation between G(0) and N, the value of G(0) decreases as excitation power increases in agreement with the experiments (Figure 8a,b). Given that the concentration in the sample is constant, N becomes proportional to the excitation volume which is expected to have an ellipsoid shape. This relationship was demonstrated by fitting the data to a curve were N-(I/I\({}_{0}\))\({}^{3/2}\) (Figure 8b). Subsequently, following this reasoning we can conclude that G(0) follows the relationship G(0) \(\sim\) 1/(I/I\({}_{0}\))\({}^{3/2}\)) (Figure 8a). In Figure 8c the effect of excitation intensity on an average photon count is investigated, demonstrating a quadratic behavior, i.e., \(\sim\) (I/I\({}_{0}\))\({}^{2}\), as expected for two photon excitation [2]. Interestingly in these data, there are no evidence of photobleaching or excitation saturation in contrast to other reports [16; 29; 38]. Similar behavior was observed for the measurements using 40\(\times\) objective lens (Supplementary data, Figure S3). Figure 7: The effect of excitation power on FCS data obtained for Rhodamine B solution. Autocorrelation function data (blue) and fitted data (red) are shown. The data was obtained from red channel (580/150 nm) when excited at 800 nm wavelength using 40\(\times\) (NA 0.8) and 63\(\times\) (NA 1.2) objective lenses. In addition to the above parameters, the relationship between the diffusion time and excitation intensity in the measurements was further investigated. The data from the measurements using 63\(\times\) objective lens are presented in Figure 9. As shown by the figure, the values of the diffusion time were found to decrease when increasing the excitation power. Similar results were obtained using the 40\(\times\) objective lens (Supplementary data, Figure S4). These results were surprising, as according to the previous theory the detected molecules are expected to diffuse through a longer distance at higher excitation intensity since the size of detection volume increases [16; 39].