## 3 Results  
We have discussed reconstructed complex amplitudes obtained from a non-optimized phase-only hologram, optimized holograms using the conventional algorithm, a scaled diffraction-based algorithm (Proposed method 1), and a combination algorithm (Proposed method 2). Non-optimized phase-only holograms are calculated by simply propagating the object plane using a Fresnel diffraction calculation. The calculation conditions are a wavelength of 532 nm, \(z=0.3\) m and the pixel pitch of the hologram \(p_{h}=8\)\(\upmu\)m. All the calculations were performed using our wave optics library, CWO++ [23]. We used two original objects with complex amplitudes. The first complex-valued object consisted of Mandrill and Pepper images as amplitude and phase, respectively. The second complex-valued object consisted of House and Jelly images as amplitude and phase, respectively. Figure 4 shows the reconstructed amplitude images (upper row) and phase images (bottom row) obtained from a non-optimized hologram and optimized holograms, respectively. The resolution of the holograms is \(1024\times 1024\) pixels. The number of iterations in each iterative algorithm is fixed to \(L=20\). Note that the combination algorithm used the first and second iteration numbers of \(L_{1}=0.8L\) and \(L_{2}=0.2L\). We empirically determined the ratio between \(L_{1}\) and \(L_{2}\). If \(L_{2}\) is large, the effect of improving the image quality cannot be expected to be substantial, and only the calculation time increases. We measured the quality of the reconstructed amplitude and phase images using the peak signal-to-noise ratio (PSNR) between the original and reconstructed images. In the reconstructed amplitude image, the proposed methods can reconstruct better images than the conventional method. In particular, Proposed method 1 had the highest quality. In the reconstructed phase image, Proposed method 1 was slightly inferior to the other methods. In contrast, Proposed method 2 had the highest quality of the reconstructed phase images. The calculation times for the conventional algorithm, Proposed method 1, and Proposed method 2 were 58 s, 15 s, and 23 s, respectively. Proposed methods 1 and 2 can accelerate hologram optimization approximately 4 times and 2.5 times faster, respectively, than the conventional algorithm. The difference  
Figure 5 shows the reconstructed amplitude images (upper row) and phase images (bottom row) obtained from a non-optimized hologram and optimized holograms, respectively. The calculation conditions were the same as those in Figure 4. In this case, the two proposed methods have better quality outcomes than the conventional algorithm. Proposed methods 1 and 2 can also accelerate hologram optimization by approximately 4 times and 2.5 times, respectively, than the conventional algorithm. In particular, the amplitude and phase are the highest in Proposed method 1. Figure 4: Reconstructed amplitude images (**upper row**) and phase images (**bottom row**) obtained from non-optimized hologram and optimized holograms, respectively. Figure 5: Reconstructed amplitude images (**upper row**) and phase images (**bottom row**) obtained from a non-optimized hologram and optimized holograms, respectively  
Figure 6 shows the amplitude images, phase images, and total intensity as a function of the iterations. The left and right columns show the results of the original objects \"Mandrill+Pepper\" and \"House+Jelly,\" respectively. In the graphs, \"Conv,\" \"Pro1,\" and \"Pro2\" denote the conventional algorithm, Proposed method 1, and Proposed method 2, respectively. In the combination algorithm, the iteration numbers of the first and second optimization were \(L_{1}=0.8L\) and \(L_{2}=0.2L\), respectively. Note that we did not perform Proposed method 2 in the \(L=1\) iteration. Regarding the quality of the reconstructed amplitude images of \"Mandrill+Pepper\" and \"House+Jelly,\" Proposed method 1 has a higher quality than the other methods.