We report a novel and fast method for converting a digital, complex Fresnel hologram into a phase-only hologram. Briefly, the pixels in the complex hologram are scanned sequentially in a row by row manner. The odd and even rows are scanned from opposite directions, constituting to a bidirectional error diffusion process. The magnitude of each visited pixel is forced to be a constant value, while preserving the exact phase value. The resulting error is diffused to the neighboring pixels that have not been visited before. The resulting novel phase-only hologram is called the bidirectional error diffusion (BERD) hologram. The reconstructed image from the BERD hologram exhibits high fidelity as compared with those obtained with the original complex hologram.

Computer-generated holography (CGH) is a technique for converting a three-dimensional (3D) object scene into a two-dimensional (2D), complex-valued hologram. One of the major bottlenecks of CGH is the intensive computation that is involved in the hologram generation process. To overcome this problem, numerous research works have been conducted with the aim of reducing arithmetic operations involved in CGH. In this paper, we shall review a number of fast CGH methods that have been developed in the past decade. These methods, which are commonly referred to as point-based CGH, are applied to compute digital Fresnel holograms for an object space that is represented in a point cloud model. While each method has its own strength and weakness, trading off conflicting issues, such as computation efficiency and memory requirement, they also exhibit potential grounds of synergy. We hope that this paper will bring out the essence of each method and provide some insight on how different methods may crossover into better ones.

Optical holography for recording three-dimensional (3-D) scenes can be traced back to the early sixties. Since then, the art of holography has been applied in many areas, primarily as a tool for 3-D imaging, processing, and display. Extension of optical holography to other disciplines, such as optical computing and encryption, has been explored, but the scope of development is relatively limited. However, with the rapid advancements in electronics, computing, and material science technologies, most of the optical processes can be substituted with numerical or digital hardware means, thus leading to the emergence of digital holography. A typical digital holography framework can be encapsulated into three major stages, namely the input, processing, and output stages. The input and output stages are gatekeepers connecting the optical and digital worlds, without which the study on digital holography could only be restricted to theoretical and numerical analysis. In the past few decades, numerous research works have been conducted on these two important areas. In this paper, we shall provide a review on the recent development in these two important areas of digital holography. Selected pieces of important and popular works on the acquisition and display of digital holograms will be reported.

We propose a novel optical method to display a complex Fresnel hologram using a single spatial light modulator (SLM). The method consists of a standard coherent image processing system with a sinusoidal grating at the Fourier plane. Two or three position-shifted amplitude holograms displayed at the input plane of the processing system can be coupled via the grating and will be precisely overlapped at the system’s output plane. As a result, we can synthesize a complex hologram that is free of the twin image and the zero-order light using a single SLM. Because the twin image is not removed via filtering, the full bandwidth of the SLM can be utilized for displaying on-axis holograms. In addition, the degree of freedom of the synthesized complex hologram display can be extended by involving more than three amplitude holograms.

We propose a fast method for generating digital Fresnel holograms based on an interpolated wavefront-recording plane (IWRP) approach. Our method can be divided into two stages. First, a small, virtual IWRP is derived in a computational-free manner. Second, the IWRP is expanded into a Fresnel hologram with a pair of fast Fourier transform processes, which are realized with the graphic processing unit (GPU). We demonstrate state-of-the-art experimental results, capable of generating a 2048x2048 Fresnel hologram of around $4\times {10}^6$object points at a rate of over 40 frames per second.

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