The continuous development of 3D display technology has brought society a new research field. Since 3D display technology based on computer generated hologram (CGH) features flexibility, repeatability, and convenience, most universities and research organizations have conducted in-depth research on it. With the increasing research on CGH theory and improving the performance of spatial light modulator (SLM) device structures, applications based on SLM have gradually become a research hotspot in holographic projection, holographic displays, virtual reality/augmented reality (AR/VR) displays, dynamic holography, and color holography. In 3D display, there is a multi-plane display method whose essence is between 2D and 3D, and the method employs a hologram that can display the same or different results at multiple locations. However, there are two main problems in the multi-plane holographic display. One is that the decreased reconstruction quality will accompany the increased number of planes in a multi-plane holographic display, and the other is the non-uniform distribution of the reconstruction image quality among each plane. The main reason is that the planes will interfere with each other, and the interference is random and relatively difficult to control. To improve multi-plane holographic display quality, we propose an improved weighted iterative multi-plane holographic display method. Meanwhile, to reduce the mutual influence among the planes in designing holograms, we introduce weights to control the constraints, and thus the quality distribution of the reconstructed images among multiple planes is more uniform and of higher quality by the constant correction of the weights during the calculation. The results show that the introduction of this method not only does not reduce the calculation speed but also leads to a more uniform quality distribution of the reconstructed image in the multi-plane holographic display. Additionally, the quality is improved to some extent, which provides a new idea for high-quality multi-plane display.

Our design idea is based on the Gerchberg-Saxton (GS) iterative algorithm and is further improved by introducing weights on the holographic plane. Firstly, the output plane complex amplitude is composed according to the amplitude information of the known multi-plane target with random phases. Then, the inverse diffraction is carried out into the holographic plane at a known distance, and all complex amplitudes in the holographic plane are summed up in the weights. The total complex amplitude distribution of the holographic plane is obtained, and the weights are distributed in a weighting. In assigning the weights, the sum of all the weights should be 1. Initially, the weights of each plane are set to be equal. Then, the weights are corrected iteratively by the iterative optimization algorithm according to the C_C value changes, and the purpose of setting the weights is to reduce the mutual influence among the planes. After summing up the weights, we ensure that the influences of the planes are balanced to make the distribution among the planes more uniform. Then we take the phase, keep it unchanged, and combine it with the plane wave amplitude to get the complex amplitude distribution of the holographic plane. Meanwhile, forward diffraction is conducted again to obtain the complex amplitude distribution of the output plane, then its phase is taken and combined with the target amplitude. This process is repeated until the results are satisfied.

Our core content is the weight correction for each plane, the specific correction idea is shown in Fig. 2, and the specific formulas for the correction are Eqs. (3)-(6). For two-plane holography, the quality of reconstructed images in each plane without introducing weights will be randomly distributed, and the reconstructed images in each plane will be qualitatively different when the introduction of the weights among various planes makes the reconstruction of the image distribution quality uniform (Figs. 4 and 12). It is discussed that for each plane with the same or different target images (Fig. 9), the quality of the reconstructed images of various target image types is different. Specifically, the quality of reconstructed images is relatively high under the same target images, and the quality of reconstructed results is poor when the target images are not the same. The differences between the two will become increasingly larger with the rising number of planes. Under the small number of planes, whether the target image is the same has little effect on the quality of the reconstructed image, and under the large number of planes, the quality of the reconstructed image is affected by whether the target images are the same or not (Figs. 6 and 10). For multi-plane holography, the most significant influence is the target image type, the number of planes, and the distance between neighboring planes (Figs. 13 and 14).

To reduce the mutual influence among the planes in the multi-plane display, we propose an improved weighted iterative multi-plane holographic display method by employing the weights. Finally, the control among the planes is controlled according to the interactions among the planes in the process of designing the holograms, and the distribution of the reconstruction image quality among the planes is more uniform. Additionally, without reducing the quality of the reconstructed image, the calculation speed will not be affected. The method is compared and analyzed by the simulation analysis and experimental verification of two to six different target images and the same target image to achieve a more uniform distribution of the reconstructed image quality among the planes. The quality of the reconstructed image is affected by the target image type, in which the quality is relatively high under the same target image, and it is poorer under different target images. The difference between them will become increasingly larger with the rising number of planes. In conclusion, introducing this method reduces mutual interference among reconstructed images in multi-plane holographic displays and their more uniform quality distribution.