Holographic three-dimensional (3D) display technology can effectively reconstruct the wavefront of 3D objects and provide whole depth cues for human eyes, so it has become a research hotspot in the 3D display field. Compared with optical holography, computer-generated holography simulates the recording process of the hologram by computers and adopts the refreshable spatial light modulator instead of holographic recording material as the hologram-carrying media. Due to the above characteristics, computer-generated holography becomes an ideal technology to realize real-time holographic 3D displays and has a broad application prospect in military navigation, industrial manufacturing, medical treatment, education, and entertainment fields. At present, the development of real-time holographic 3D displays is hindered by the huge data of 3D objects, the insufficient modulation capacity of spatial light modulators, and the low display degree of holographic 3D display systems. In order to overcome these problems, researchers have made many innovations from both algorithm and hardware aspects.

We review the progress of real-time holographic 3D displays. Firstly, the basic principle and development history of holography are outlined. Next, the fast calculation methods of computer generated holograms (CGHs) and wavefront coding methods for current spatial light modulators are introduced in detail. Then, the contribution of deep learning to real-time holographic 3D displays is discussed, and some typical holographic display systems are introduced. Finally, the future development of real-time holographic 3D displays is prospected. The fast calculation methods can be classified into algorithm optimization and hardware acceleration. The algorithm optimization mainly simplifies the calculation complexity and reduces the redundant computation of traditional calculation methods, including point-based method, polygon-based method, and layer-based method. Hardware acceleration mainly speeds up the CGH calculation by designing fast calculation algorithms adapted to the hardware platform and optimizing hardware system architectures. The wavefront coding methods for current spatial light modulators can be mainly classified into iterative methods and non-iterative methods. Iterative methods solve the desired phase-only hologram by iterative calculation between the image plane and the hologram plane or pixels in the hologram plane, which are time-consuming. Non-iterative methods convert the diffracted complex wavefront to an intensity-constant distribution analytically. Compared with iterative methods, non-iterative methods are more efficient and suitable for real-time holographic 3D displays. In recent years, deep learning is also introduced into the computer-generated holography field. Deep learning completes the CGH calculation and wavefront coding through the trained neural network, which shows great potential for realizing real-time holographic 3D displays. Furthermore, with the development of algorithms, devices, and systems, the holographic display system is gradually developing towards large size, large field of view, and real-time color display.

Real-time holographic 3D display is the ultimate goal of the holographic 3D display. Although there is still a long way to go, it is believed that there is great potential for the further development of real-time holographic 3D displays in both software (algorithms) and hardware (devices and systems). It is expected that holographic 3D displays will eventually achieve real-time display and come gradually into the market and daily life, thus bringing revolutionary changes to our future life.