## 3 Results
### Fluorescence Lifetime Mapping to Cross-Sectional Images
From the fluorescence images acquired at three delay times of 100, 400, and 1000 \(\upmu\)s, the lifetime can be calculated using the slope obtained by the intensity ratio between 100 and 400 \(\upmu\)s (slope 1), that obtained using the ratio between 400 and 1000 \(\upmu\)s (slope 2), and that obtained using all three data points (slope 3) (Figure 5a). The fluorescence lifetime was calculated by taking the inverse of the fluorescence intensity ratio (slope) observed at different delay times (\(t_{\text{delay}}\)). The three particular time points for the SCM were determined approximately based on the definition of fluorescence  
Figure 5: Calculation of the fluorescence lifetime by the proposed slope comparison method (SCM). (**a**) Slopes that can be used to calculate the lifetime based on data at three decay times. (**b**) Concept of selecting a delay time range (slope 1 or 2) for lifetime calculation from the two slopes in the SCM. At pixels that receive weak fluorescence, slope 1 becomes steeper than slope 2 because the data for slope 2 contains much noise. In this case, slope 1 is selected for lifetime calculation. At pixels that receive strong fluorescence, slope 2 becomes steeper than slope 1 owing to the partial saturation suggested in previous studies [23]. In this case, slope 2 is selected for lifetime calculation. (**c**) Deviation and (**d**) accuracy (relation to true value) of the fluorescence lifetime calculated from each slope in this NIRF-TGI experiment. An arrow presents the true value (470 \(\upmu\)s) of the fluorescence lifetime of phosphor. lifetime as follows: (1) the time immediately after the complete disappearance of excitation light, (2) a time slightly shorter than the expected fluorescence lifetimes, and (3) a time of 2.5-3 times behind the second time point; while the optimal setting way for the three time points is a subject for future study. To ensure linearity between the light intensity and the signal observed at each pixel (grayscale) with a simple NIR camera, the following two points should be considered: (1) If the fluorescence is too weak, the signal-to-noise ratio will be low. (2) If the fluorescence is too strong, partial saturation will cause the grayscale to be lower than the true light level (and thus, the calculated fluorescence lifetime will be longer than the true value) [23]. Therefore, we devised the SCM to select the slope used to calculate the lifetime for each pixel according to the ratio of slope 1 to slope 2. In the SCM, the one with the larger absolute value of the slope between slopes 1 and 2 was used to calculate the fluorescence lifetime (Figure 5b). The fluorescence lifetime calculated by the SCM for NIRF-TGI showed a similar deviation (systematic error) to that obtained by using data from all imaging delay time points (3 points) (Figure 5c). However, the SCM exhibited the lowest inaccuracy (difference from the true value) (Figure 5d). Thus, the SCM can provide the most accurate results for fluorescence lifetime calculation, even when the number of delay time points to be imaged is reduced to shorten the total time of image acquisition.