# Weighted Constraint Iterative Algorithm for Phase Hologram Generation
## 3 Reconstruction Results
Some typical patterns that are often used in beam shaping were also used as the target images to illustrate the effectiveness of WCIA. Figure 7 shows the reconstruction results of these test images with GS and WCIA. The sampling numbers of the images are \(800\times 800\), and the iteration number was set as 100. From the reconstruction results, it can clearly be seen that WCIA can effectively suppress noise while improving the reconstruction quality for these images compared to the GS algorithm. To further validate the feasibility of our proposed algorithm, optical experiments were also performed. The experimental setup is shown in Figure 8. The wavelength of the laser beam was 532 nm. The laser beam was collimated and polarized to achieve a uniform plane wave illumination. In the experiment, we used Holoeye GAEA-2 256 gray-scale level Phase-only SLM. The pixel pitch of the SLM was 3.74 \(\upmu\)m, and the pixel resolution was \(3840\times 2160\). The focal length of the Fourier lens was 200 mm. The reconstructed images were located in the back focal plane of the Fourier lens and were captured directly by a sensor. A linear phase was added on the calculated hologram to separate the reconstructed image from the zero-order noise of SLM [32]. Figure 8: The schematic of the optical setup. Figure 7: Numerical reconstructions: GS algorithm (**top**) and WCIA (**bottom**). The optical reconstruction results of gray test images with GS algorithm and WCIA are shown in Figure 9. To capture the entire image on the sensor, the resolution of the signal region was set as \(960\times 540\). The iteration number was set as 100. Although the reconstructions were affected by the systematic noise, it can be seen that better image quality and more details can be optically reconstructed with our proposed method. A binary ring pattern was also set as the test image to evaluate the optical reconstruction performance of WCIA. In order to avoid the effect of the systematic noise, the time-average method [33] by uploading five sequential holograms obtained with different initial random phase was used here for both these methods. The RMSEs of optical reconstructed images were calculated to compare WCIA with the GS algorithm. Figure 10 shows the optical reconstruction results. To calculate the RMSEs, the same part of the signal region was set as the measured raw data, which is circled by a red rectangle. The measured raw data were transformed into a gray image and then used to calculate the RMSEs. It can be seen that the reconstructed image with WCIA is of lower error. \[\text{SSIM}=\frac{(2\mu_{t}\mu_{r}+c_{1})\cdot(2\sigma_{t,r}+c_{2})}{(\mu_{t}^{2}+ \mu_{r}^{2}+c_{1})\cdot(\sigma_{t}^{2}+\sigma_{r}^{2}+c_{2})} \tag{9}\]0 Optical reconstructions: (**a**) GS algorithm; (**b**) WCIA. \[\text{SSIM}=\frac{(2\mu_{t}\mu_{r}+c_{1})\cdot(2\sigma_{t,r}+c_{2})}{(\mu_{t}^{2}+ \mu_{r}^{2}+c_{1})\cdot(\sigma_{t}^{2}+\sigma_{r}^{2}+c_{2})} \tag{9}\]1 Optical reconstructions: reconstructed “baboon” images with (**a**) GS algorithm and (**b**) WCIA; reconstructed “Goldhill” images with (**c**) GS algorithm and (**d**) WCIA.