# Three-Dimensional Imaging via Time-Correlated Single-Photon Counting
## 3 Experimental Setup and Results
### High-Resolution Imaging Experiments for Complex Objects  
In this part, two sets of experiments are set to verify the high resolution including the lateral resolution and the axial resolution of the scheme. Firstly, the lateral resolution of our scheme can be calculated by  
\[R=1.22\frac{\lambda z}{D_{0}}\approx 0.5\ \text{mm}, \tag{7}\]  
where \(\lambda\) is the wavelength of the laser, \(D_{0}\) is beam waist diameter of laser, \(z\) is the distance from the target to laser. To further prove the lateral resolution, we choose a dinosaur model with a size of \(8\ \text{cm}\times 6\ \text{cm}\times 2\ \text{cm}\) as the imaging object in this experiment. The experimental process is roughly the same as that of the experiment in Section 3.1. Figure 5 shows the original object and the experimental  
Figure 4: Analysis of noise reduction experiment based on range-gated technology.  
Figure 3: Results of noise reduction experiment based on the range-gated technology. SP represents the number of signal photons. The left side represents the imaging result without gating, and the right side indicates the result with gating. The signal photons decrease from 3000 cps to 500 cps and the noise photons are keep at 10,000 cps.  
imaging result, in which the image resolution of the object is \(512\times 512\), the image depth is 8 bit and the time for one frame is about 6.7 s.  
Then to ensure the axial resolution, a whiteboard (\(5\text{ cm}\times 5\text{ cm}\)) is placed on the stepper motor (TSA150-B, repeat positioning accuracy less than 7 \(\upmu\)m). The stepper motor moves ten times and moves 10 mm each time. The distance that the whiteboard moves is evaluated by the TOF algorithm, defines as:  
\[D=\frac{1}{2}c\times\Delta t, \tag{8}\]  
where \(D\) is the distance, \(c\) is the speed of light and \(\Delta t\) is the time interval. In this experiment, the theoretical total time jitter mainly consists of the pulse width of the laser (\(t_{\text{pulse}}\sim 30\text{ ps}\)), the time jitter of TCSPC module (\(t_{\text{ TCSPC}}\sim 12\text{ ps}\)) and the time jitter of SPD (\(t_{\text{SPD}}\sim 50\text{ ps}\)), as the function of  
\[T_{\sigma}=\sqrt{t_{\text{pulse}}^{2}+t_{\text{ TCSPC}}^{2}+t_{\text{SPD}}^{2}}\approx 60\text{ ps}. \tag{9}\]  
As shown in Figure 6a, the total time jitter measured by the experiment is 90 ps. Therefore the distance error \(D_{\sigma}\) of our scheme is \(D_{\sigma}=1/2\times c\times T_{\sigma}\approx 13.5\text{ mm}\). Because we take the average value of 10 points near the peak position as the measurement value each time, the actual measurement error \(\bar{D}_{\sigma}\) can be decreased to 4.2 mm, as the function:  
\[\bar{D}_{\sigma}=D_{\sigma}/\sqrt{N}. \tag{10}\]  
Figure 6b shows the measurement results and Figure 6c shows the measurement errors which are less than \(\pm 1.5\text{ mm}\).  
Figure 5: (**a**) The original object. (**b**) Experimental imaging result.  
Figure 6: (**a**) Measurement results of laser waveform. The full width half maximum (FWHM) is 90 ps. (**b**) Measurement results: the blue curve is the reference value measured by high precision stepper motor, and the red dots are the measured value of ten experiments. (**c**) The errors between the measured value and the reference value.