Objective Phase-only hologram (POH) is favored by many researchers in holographic display technology due to its high diffraction efficiency and zero twin image. Common POH generation algorithms can be divided into iterative and non-iterative methods. The iterative methods require a lot of iterative optimization to obtain the required POH, which needs a large number of iterations and is time-consuming. The error diffusion algorithm does not require iteration and greatly improves the computational speed of POHs. In the traditional error diffusion method, the amplitude of all pixels on the complex amplitude hologram (CAH) is set to 1, and this hologram and its CAH are adopted to compute the error which will be diffused on the CAH to generate the POH. However, since different target images have various amplitude distributions, directly setting the CAH amplitude to 1 is not suitable for all images. Therefore, the quality of the generated POH is not high and the reconstruction image of the hologram cannot obtain a satisfactory display effect. Therefore, we call for a new error diffusion algorithm to improve the reconstructed image quality. Methods To improve the quality of the hologram reconstructed image generated by the error diffusion algorithm, we build a hologram error compensation model based on the bidirectional error diffusion algorithm by analyzing the relationship between the amplitude distribution of the target image and the generated hologram, and propose a new POH generation method. Firstly, the CAH of the target image is computed and its amplitude is set to 1. Secondly, the error between the POH and the original CAH is calculated by the error compensation model. Thirdly, the new error is adopted to generate a new POH by bidirectional error diffusion. Finally, a new error between this new POH and the original CAH is computed and the second error diffusion is carried out to obtain the final POH. Numerical simulations are conducted to compare the hologram reconstruction effect of the two methods. Additionally, the normalized correlation (NC) coefficient and the structural similarity index measure (SSIM) are employed to quantitatively compare and analyze the hologram reconstruction results. Meanwhile, the experimental schematic diagram is drawn and the optical imaging system is built, with the proposed method verified by optical experiments. Results and Discussions By carrying out numerical simulation and optical experiments, the quality of hologram reconstructed images generated by different error diffusion methods is verified. The simulation results of the two error diffusion methods are shown in Fig. 6. The images of the first column in Fig. 6 are reconstructed ones by the traditional method, and contain obvious speckle noise. The images of the second column and third column in Fig. 6 are the reconstructed images of the holograms generated by the first improved error diffusion and second error diffusion respectively. Compared with the first column, the definition of the reconstructed images in the latter two columns is higher. The detail section of the images in the third column contains more information than the second column. For example, the detail part of Fig. 6(c) shows more information on the pepper stalk than that of Fig. 6(b). Additionally, for the detail part of the pirate, the hair of the man in Fig. 6(l) is more clear than that in Fig. 6(k), and the lines of the hair are more obvious. The NC coefficient and the SSIM are respectively adopted in Tables 2 and 3 to evaluate the quality of numerical simulation results of hologram reconstruction images quantitatively. After the first error diffusion, the NC coefficient and the SSIM increase by 0.05-0.14 and 0.036-0.09 respectively. After the second error diffusion, the NC coefficient and the SSIM increase by 0.01-0.026 and 0.025-0.036 respectively. Simulation results reveal that the reconstructed image quality of the proposed method is better than that of the original method. The similarity of the proposed method with the original image is higher, and reconstructed images of the proposed method are more in line with the visual quality requirements of human eyes. The comparison results of optical experiments on hologram reconstructed images by the traditional error diffusion method and the proposed error diffusion method are shown in Fig. 8. Fig. 8 indicates that for different target images, the hologram reconstructed images of the proposed algorithm can be displayed more clearly, but the hologram reconstructed images of the traditional error diffusion algorithm are obviously noisy and blurred. Comparison of the details of the two methods displays the sailboat in Fig. 8(e) and its reflection on the surface of the lake, while the sailboat in Fig. 8(e) is blurred. The pattern on the long spike behind the mans hat in Fig. 8(g) is clear, while the pattern on the long spike in Fig. 8(h) is not clearly seen. The optical experiment results are consistent with those of simulations. The simulation and experimental results show that the proposed error diffusion algorithm is effective in improving the quality of hologram reconstructed images, with the feasibility and superiority of the proposed method verified. Conclusions A bidirectional error diffusion compensation model is built by calculating the new error between CAH and POH. The hologram reconstructed images generated by the model contain more object light wave information. Additionally, the twice error diffusion algorithm is adopted to further improve the holographic display quality. Simulation results show that the reconstructed images generated by the improved method have higher resolution and more detailed information. The NC coefficient and SSIM serve as quantitative evaluation criteria for the simulation results. In Tables 2 and 3, the mean NC and SSIM values of the proposed method are 0.9743 and 0.8630 respectively, 0.0927 and 0.0848 higher than those of the traditional error diffusion method. The optical experiment results show that the reconstructed images generated by the improved algorithm have higher image quality and resolution in detail. Simulations and experimental results prove the effectiveness and feasibility of the improved algorithm, and this algorithm has application significance for computational holographic display.
