Holographic three-dimensional display is an important display technique because it can provide all depth information of a real or virtual scene without any special eyewear. In recent years, with the development of computer and optoelectronic technology, computer-generated holograms have attracted extensive attention and developed as the most promising method to realize holographic display. However, some bottlenecks still restrict the development of computer-generated holograms, such as heavy computation burden, low image quality, and the complicated system of color holographic display. To overcome these problems, numerous algorithms have been investigated with the aim of color dynamic holographic three-dimensional display. In this review, we will explain the essence of various computer-generated hologram algorithms and provide some insights for future research.

A technique is proposed theoretically and verified experimentally to eliminate a zero-order beam caused by a pixelated phase-only spatial light modulator (SLM) for holographic projection. The formulas for determination of the optical field in the Fourier plane are deduced, and the influence of the pixelated structure of a SLM on the intensity of the zero-order beam is numerically investigated. Two currently existing techniques are studied and a new one is presented. These three techniques are used separately to eliminate the zero-order interruption, and the optical performances of the reconstructed patterns are compared. The new technique results in higher reconstruction quality and diffraction efficiency. A short animated movie is illuminated for holographic projection display. The experimental results show that the zero-order beam can be efficiently eliminated by the new technique. It is believed that this technique can be used in various optical systems that are based on pixelated phase-only SLMs, such as holographic optical tweezers and optical testing systems.

A compact waveguide display system integrating freeform elements and volume holograms is presented here for the first time. The use of freeform elements can broaden the field of view, which limits the applications of a holographic waveguide. An optimized system can achieve a diagonal field of view of 45° when the thickness of the waveguide planar is 3mm. Freeform-elements in-coupler and the volume holograms out-coupler were designed in detail in our study, and the influence of grating configurations on diffraction efficiency was analyzed thoroughly. The off-axis aberrations were well compensated by the in-coupler and the diffraction efficiency of the optimized waveguide display system could reach 87.57%. With integrated design, stability and reliability of this monochromatic display system were achieved and the alignment of the system was easily controlled by the record of the volume holograms, which makes mass production possible.

The tuning of structural, optical, and electrical properties of Al-doped ZnO films deposited by atomic layer deposition technique is reported in this work. With the increasing Al doping level, the evolution from (002) to (100) diffraction peaks indicates the change in growth mode of ZnO films. Spectroscopic ellipsometry has been applied to study the thickness, optical constants, and band gap of AZO films. Due to the increasing carrier concentration after Al doping, a blue shift of band gap and absorption edge can be observed, which can be interpreted by Burstein-Moss effect. The carrier concentration and resistivity are found to vary significantly among different doping concentration, and the optimum value is also discussed. The modulations and improvements of properties are important for Al-doped ZnO films to apply as transparent conductor in various applications.

A fast algorithm with low memory usage is proposed to generate the hologram for full-color 3D display based on a compressed look-up table (C-LUT). The C-LUT is described and built to reduce the memory usage and speed up the calculation of the computer-generated hologram (CGH). Numerical simulations and optical experiments are performed to confirm this method, and several other algorithms are compared. The results show that the memory usage of the C-LUT is kept low when number of depth layers of the 3D object is increased, and the time for building the C-LUT is independent of the number of depth layers of the 3D object. The algorithm based on C-LUT is an efficient method for saving memory usage and calculation time, and it is expected that it could be used for realizing real-time and full-color 3D holographic display in the future.

In the holographic three-dimensional (3D) display, the numerical synthesis of the computer-generated holograms needs tremendous calculation. To solve the problem, a fast polygon-based method based on two-dimensional Fourier analysis of 3D affine transformation is proposed. From one primitive polygon, the proposed method calculates the diffracted optical field of each arbitrary polygon in the 3D model, where the pseudo-inverse matrix, the interpolation, and the compensation of the power spectral density are employed. The proposed method could save the computation time in the hologram synthesis since it does not need the fast Fourier transform for each polygonal surface and the additional diffusion computation. The numerical simulation and the optical experimental results are presented to demonstrate the effectiveness of the method. The results reveal the proposed method could reconstruct the 3D scene with the solid effect and without the depth limitation. The factors that influence the image quality are discussed, and the thresholds are proposed to ensure the reconstruction quality.