## 4 Experiments and Results  
In order to verify the validity of Taylor expansion in the proposed method, we remove Taylor expansion on the basis of TR-PCG and call this method the Rayleigh-Sommerfeld PCG method without Taylor expansion (RS-PCG). Therefore, in our paper, the proposed TR-PCG algorithm is compared with the WRP, the traditional PCG algorithm, the C-PCG, and the RS-PCG. The reconstruction quality of several methods is compared by the Peak Signal to Noise Ratio (PSNR) algorithm. We use the Kinect depth camera to collect depth and color information of the object, conduct simulation experiments in MATLAB 2022 and run them on the PC of Windows 11 64 bit. Figure 2: Schematic diagram of TR-PCG. We verify the effectiveness of the proposed method through simulation experiments. The resolutions of the experimental holograms are set as 1024 \(\times\) 1024 and 2028 \(\times\) 2048, the pixel spacing is set as 7.4\(\upmu\)m and the wavelengths of red, green, and blue light are set at 633 nm, 532 nm, and 473 nm, respectively. We collect several groups of data named as beibei_nini, person with beibei, person with dragon, dragon and person with nini as our experimental object. Table 1 compares the CPU and GPU calculation time of WRP, traditional PCG, C-PCG, RS-PCG, and TR-PCG at 1024 \(\times\) 1024 resolution. Figures 3 and 4 compares the CPU and GPU calculation time of traditional PCG, C-PCG, and TR-PCG at 1024 \(\times\) 1024 resolution. As can be seen in Table 1 and Figures 3 and 4, when the resolution is 1024 \(\times\) 1024, compared with the WRP, the speed of TR-PCG is increased by over 90%. Compared with the traditional PCG, the speed of TR-PCG is increased by about 40%. Compared with the C-PCG, the speed of TR-PCG is improved by about 15-20%. Compared with the RS-PCG, the speed of TR-PCG is improved by about 25%. Table 2 shows the CPU and GPU calculation time of traditional PCG, C-PCG, RS-PCG, and TR-PCG at 2048 \(\times\) 2048 resolution. Figures 5 and 6 compares the CPU and GPU calculation time of traditional PCG, C-PCG and TR-PCG at 2048 \(\times\) 2048 resolution. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multicolumn{2}{c}{**Object**} & \multicolumn{5}{c}{**CPU Running Time**} \\ \hline Name & Number of points & Number of layers & Traditional PCG & C-PCG & RS-PCG & TR-PCG \\ \hline beibei\_nini & 1,255,023 & 473 & 65.854 & 43.171 & 54.377 & 37.633 \\ person with beibei  
As can be seen in Table 2 and Figures 5 and 6, when the resolution is 2048 \(\times\) 2048, compared with the traditional PCG, the speed of TR-PCG is increased by about 40%. Compared with the C-PCG, the speed of TR-PCG is improved by about 20-30%. Compared with the RS-PCG, the speed of TR-PCG is improved by about 30%. 1024 \(\times\) 1024 resolution, the overall speed is somewhat slower. However, TR-PCG has a significant speed increase over the other three methods. Actually, from the Tables 1 and 2 and Figures 3-6, we find that RS-PCG improves the speed by about 1.3 times while TR-PCG improves the speed by about 1.7 times. Therefore, it is obvious that Taylor expansion contributes more than single-precision. Figure 7 shows the reconstructed images of the three methods when the diffraction distance is 24.85 cm and the resolution is 2048 \(\times\) 2048. From left to right are the original image and reconstructed images of traditional PCG, C-PCG, RS-PCG, and TR-PCG. The peak signal-to-noise ratio is the logarithm of the mean square error between the original image and the processed image relative to the square of the maximum value of the signal. In order to measure the image quality after processing, we often refer to the PSNR value to measure whether a processing program is satisfactory. The PSNRs of the reconstructed images are shown in Figure 7b-e. Figure 8 shows holograms generated by R, G, and B channels and reconstructed images of a set of point cloud data when the diffraction distance is 24.95 cm. From top to bottom are holograms of the R, G, and B channels and a full-color reconstructed image.