## 3 Results  
### Optical Properties of Samples  
NIR fluorophores with different fluorescence lifetimes were prepared by doping guest ions into two different hosts with different phonon energies; NaYF4 and YPO4, and were used as composites by embedding in agar gel. Lanthanide-doped ceramic nanoparticles are used as NIR phosphors because they have the advantage of long lifetimes (several hundred microseconds). This is because of the shielding of 4f electrons by external electrons in the 5s and 5p orbitals for suppressing thermal relaxation, as well as essentially small rates of the optical transition of the 4f electrons with magnetic and forced-electric dipole moment transitions [29]. The guest ions were Nd\({}^{3+}\) as a sensitizer for 808 nm excitation with the \({}^{4}\)I\({}_{9/2}\rightarrow{}^{4}\)F\({}_{5/2}\) transition and Yb\({}^{3+}\) to emit fluorescence in the 1000-1040 nm wavelength range by the \({}^{2}\)F\({}_{5/2}\rightarrow{}^{2}\)F\({}_{7/2}\) transition. As shown in Figure 2a, the targeted fluorescence spectra are well observed for both samples, measured using a spectrometer in the wavelength range of 1000-1040 nm, while both showed their characteristic decay rate (Figure 2b). As shown in the energy level diagram in Figure 2c, minor fluorescence from the Nd\({}^{3+}\) peaked at 1064 nm by the \({}^{4}\)F\({}_{3/2}\rightarrow{}^{4}\)I\({}_{11/2}\) transition is also observed. The fluorescent particles were prepared in sizes so that their fluorescence properties are not affected by anything other than the host material (NaYF4 and YPO4) [23].  
Fluorescence lifetimes vary according to the rates of energy transfer and thermal relaxation of excited photons. For instance, the fluorescence lifetime of NaYF4 nanoparticles co-doped with Nd\({}^{3+}\) and Yb\({}^{3+}\) can be controlled by the dopant ion concentrations and used for multiplex imaging of in vivo deep tissues (stomach and liver) [30]. The fluorescence lifetimes of 4f electrons in trivalent lanthanide ions are also controlled by thermal relaxation, called multi-phonon relaxation (MPR), and radiative transition rates. The MPR strongly depends on the phonon energy of the host [29]. The phonon energies of YPO4 and NaYF4 are 1080 cm\({}^{-1}\)[31] and 300\(-\)400 cm\({}^{-1}\)[32], respectively. Therefore, the fluorescence lifetime of YPO4: Nd\({}^{3+}\), Yb\({}^{3+}\) (240 us) is shorter than that of NaYF4: Nd\({}^{3+}\), Yb\({}^{3+}\) (470 us) (Figure 2b), as determined by analysis using a synchronized system of a photomultiplier detector and a  
Figure 1: Setup of computed tomography (CT) for near-infrared fluorescence (NIRF) time-gated imaging (TGI). (**a**) Schematic illustration of the system for NIRF-TGI combined with CT. (**b**) Time chart of pulsed irradiation for fluorescence excitation at 808 nm, image acquisition using the NIRF-TGI system and time points when the motorized stage rotates, along with the expected profiles of fluorescence decay. This system can acquire projected images at controlled delay times after turning off the excitation laser to record images of fluorescence decay. The projected images of the fluorescence decay of samples can be collected from multiple angles to control the rotation of the stage. As shown in (**c**) the block diagram of the image acquisition and processing for conducting NIRF-TGI-CT, tomographic images are first reconstructed for each delay time by conventional back-projection. Next, the fluorescence lifetimes can be determined at each pixel of the tomograms obtained at multiple delay times.  
pulsed 808 nm laser extracted from an Nd-doped yttrium aluminum garnet laser. Samples of phosphors embedded in agar gel (Figure 2d), a model of tissues containing water, were used for analysis.