## 3 Results
### Fluorescence Lifetime Mapping to Cross-Sectional Images  
For all cross-sectional fluorescence images (tomograms) taken at each angle and at each delay time, the rate of time-dependent decay was calculated from the fluorescence intensity for each pixel. The fluorescence decay normalized by the initial intensity at a delay time of 0 \(\upmu\)s showed different decay rates between the YPO\({}_{4}\) and NaYF\({}_{4}\) particles (Figure 4a), of which the positions are shown on the tomogram (Figure 4b). The calculated lifetimes of YPO\({}_{4}\): Nd\({}^{3+}\), Yb\({}^{3+}\) and NaYF\({}_{4}\): Nd\({}^{3+}\), Yb\({}^{3+}\) were 296 \(\pm\) 3 \(\upmu\)s and 516 \(\pm\) 39 \(\upmu\)s. Although accuracy of the calculation is still a challenge, the contrast of their fluorescence lifetime was mapped on the cross-sectional images by the NIRF-TGI-CT technique. Stacking these cross-sectional images provides a 3D fluorescence lifetime distribution image that can distinguish phosphors with different fluorescence lifetimes (Video S1). Figure 4: Fluorescence lifetime mapping to cross-sectional and 3D images. (**a**) Cross-sectional images of the fluorescence lifetime difference of NaYF\({}_{4}\): Nd\({}^{3+}\), Yb\({}^{3+}\) and YPO\({}_{4}\): Nd\({}^{3+}\), Yb\({}^{3+}\). Blue dotted lines show the outline of the sample. (**b**) 3D images of the fluorescence lifetimes of NaYF\({}_{4}\): Nd\({}^{3+}\), Yb\({}^{3+}\) and YPO\({}_{4}\): Nd\({}^{3+}\), Yb\({}^{3+}\). 3D images were obtained by stacking the fluorescence lifetime distributions of the cross-sectional images. Figure 3: Two-dimensional projected images and reconstructed cross-sectional images of NIR fluorophores recorded by the NIRF-TGI-CT image acquisition system. (**a**) Two-dimensional projected images acquired from each angle at a delay time of 0 \(\upmu\)s after turning off the laser for excitation. (**b**) Projected images of the fluorescence decay recorded at an indicated delay time from each angle. Integration: 100 \(\upmu\)s. Laser power: 5 W/cm\({}^{2}\). (**c**) Reconstructed cross-sectional images of NIR fluorophores of the sample at each delay time. The dotted blue lines indicate the form of the cylinder-shaped agar gel, which looks rectangular when seen from the side to collect the projected images (**b**), and circular when seen at cross-sections, as shown in (**c**). The red and green in the illustration indicate NaYF\({}_{4}\) and YPO\({}_{4}\) co-doped with Nd\({}^{3+}\) and Yb\({}^{3+}\). Slope Comparison Method (SCM)--Time-Gated Imaging of Fluorescence Lifetime to Obtain Fluorescence Decay with Minimal Number of Delay-Time Points  
Finally, we investigated the NIRF-TGI protocols and methods of fluorescence lifetime calculation to shorten the imaging time of NIRF-TGI-CT. As described in the previous sections, the fluorescence decay was imaged at a total of 21 delay times, 50 \(\upmu\)s each from 0 to 1000 \(\upmu\)s, after blocking the excitation light for each imaging angle. In other words, the cycle of irradiation of pulsed excitation light and image acquisition was repeated 21 times to obtain one NIRF decay image. A method for accurate observation of the fluorescence decay rate (lifetime) with a smaller number of delay time points is needed to map the lifetime to cross-sectional images in a shorter time. In this study, we propose a new method for fluorescence lifetime calculation called the slope comparison method (SCM) with image acquisition at three delay time points (Figure 5). To investigate the performance of the SCM for lifetime calculation, the NIRF decay of NaYF\({}_{4}\): Nd\({}^{3+}\), Yb\({}^{3+}\) (Yb\({}^{3+}\): \({}^{2}\)F\({}_{5/2}\rightarrow{}^{2}\)F\({}_{7/2}\)) particles at 1000 nm with a known lifetime (470 \(\upmu\)s, 25 \({}^{\circ}\)C) was observed with the NIRF-TGI under excitation with a pulsed laser at a wavelength of 808 nm.