## 4 Results and Validation
### Effect of Concentration on FCS Measurements  
Figure 6 shows the effect of concentration on the fluorescence correlation obtained from Rhodamine B solutions using the two different objective lenses 40\(\times\) and 63\(\times\). As seen in the figure, the effect of increasing the concentration results in a reduction of amplitude of the autocorrelation curve. This effect was observed from the experiments performed using both objective lenses. In the case of the 63\(\times\) objective lens, the G(0) value changes  
Figure 4: The effect of time binning in the range 10\({}^{3}\)–10\({}^{6}\) ns when performing autocorrelation on photon count data acquired from Rhodamine B solution at a concentration of 10 nM. The data was obtained from red channel (580/150 nm) at 800 nm excitation wavelength, 25 mW excitation intensity using 63\(\times\) (NA 1.2) objective lens.  
Figure 5: The effect of time binning in the range 10\({}^{3}\)–10\({}^{6}\) ns on photon count rate per time bin from data acquired from Rhodamine B solution at concentration 10 nM. The data was obtained from red channel (580/150 nm) at 800 nm excitation wavelength, 25 mW excitation intensity using 63\(\times\) (NA 1.2) objective lens.  
from 0.6 \(\pm\) 0.03 (10 nM) to 0.15 \(\pm\) 0.03 (40 nM). The value of G(0) change from 0.4 \(\pm\) 0.005 (10 nM) to 5 \(\times\) 10\({}^{-3}\)\(\pm\) 0.006 (40 nM) for the 40\(\times\) objective lens. Since G(0) is inversely proportional to the number of particles in the detection volume and as discussed previously (see Equation (3)), this reduction in G(0) is to be expected and in accordance with the FCS theory as higher concentration corresponds to more particles in the solution.  
Similar to what has been discussed in the previous section (e.g., Figure 4), the acquired diffusion time differs for the two different objective lenses; however, the effect of increasing the concentration is different. As observed from Figure 6 the acquired diffusion time is constant within the concentration range when measured using the 63\(\times\) objective lens; however, when using the 40\(\times\) objective, a substantially longer diffusion time (350 \(\pm\) 60 ms) appears at 40 nM concentration. Furthermore, oscillations are appearing in the autocorrelated data for higher concentrations (>20 nM) and 40\(\times\) objective. The physical interpretations of these oscillations and substantially longer diffusion time are unclear but likely related to the larger and less well-defined extent of the focal volume when using an objective lens with lower NA. It is clear that the 63\(\times\) objective lens yields data being less sensitive to change of concentration and thereby enables a larger operational window for concentration variability when performing FCS measurements. Thus, it is evident that the choice of NA of the objective lens plays a major role in order to generate reliable FCS data. There is an unfortunate trade off and challenge when aiming for using the same objective lens for imaging and FCS acquisition. This is a significant limitation for the applicability of MPM-FCS in biomedical research studies where image acquisition and detection of location within heterogeneous samples are central requirements.