Phase-only Fresnel holograms have two major advantages over complex-valued or amplitude-only hologram. First, they can be displayed with a single phase-only SLM, leading to simplification on the holographic display system. Second, due to the high optical efficiency of phase-only holograms, the reconstructed image is brighter than that of an amplitude-only hologram. On the downside, the fidelity of the reconstructed image is degraded as a result of discarding the magnitude component of the hologram. In this chapter, a number of methods, each with pros and cons, for generating phase-only holograms are described. These methods can be divided into two types, iterative and the non-iterative. Iterative methods include the iterative Fresnel transform algorithm (IFTA) and its variants, which find their origin in the classical Gerchberg–Saxton algorithm (GSA). Reconstructed images of a phase-only hologram obtained with IFTA are generally good in quality, but the computation time is rather lengthy. Another iterative method, based on direct binary search (DBS), can be applied in generating binary phase-only holograms. Non-iterative methods are based on modifying the source image in certain ways prior to the generation of the hologram. These include noise addition, patterned phase addition, and downsampling. The modification is similar to overlaying a diffuser onto the image, so that the magnitude of the diffracted waves on the hologram is close to homogeneous. The phase component alone, therefore, can be taken to represent the hologram.

In Chapter 3 a number of methods were described for generating a phase-only hologram of an object. However, these methods are not applicable if the source image of the object is not present, and only its hologram is available. Such a situation happens if a hologram is directly captured from a physical object (for example applying phase-shifting holography), instead of generated from a numerical graphic model. This chapter describes six methods for converting a complex-valued hologram into a phase-only hologram. The first two methods, complex amplitude modulation (CAM) and double-phase methods, convert a complex-valued hologram into a pure phase representation. When the latter is displayed on an SLM with suitable optical filtering, a visual 3-D image is reconstructed. The third to fifth methods apply different variants of the Floyd–Steinberg error diffusion algorithm to convert a complex-valued hologram into a continuous tone phase-only hologram. Among these three error diffusion methods, bi-directional error diffusion results in the best reconstructed image, while the local error diffusion method can be implemented with parallel computing devices such as GPUs. The last method, known as direct binary search (DBS), converts a complex-valued hologram into a binary phase-only hologram through an iterative process. The quality of the reconstructed image is generally poor unless more iterations are performed at the expense of longer computation time. A phase-only hologram generated by error diffusion or DBS can be displayed directly with a phase-only SLM without additional optical processing.

In this chapter, a number of quick methods for generating digital Fresnel holograms are introduced. For an object comprising a small number of depth planes, the layer-based method implemented in the Fourier space is preferred for fast hologram generation. The point-based method is more suitable for generating objects with a large number of object points that are scattered over a wide range of distances from the hologram plane. To enhance the speed of hologram generation with the point-based method, different variants and sizes of the look-up-table (LUT) algorithms to trade-off computation time are described. A number of methods based on the concept of a wavefront recording plane (WPR) are presented. Being different from the LUT approach, the WRP methods speed up the hologram-generation process. Instead of generating the full hologram for each object point, only a small area of fringe patterns is computed on a WRP that is at close proximity to the object space. The computation time is substantially reduced. Further enhancement of the computation speed is attained with the warped wavefront recording plane (WWRP) method. A 3-D object image is decomposed into a 2-D intensity image and a depth map. The intensity image is used to generate an interim hologram on a WRP. Different regions of the hologram fringes on the WRP are resized according to their distances (obtained from the depth map) from the hologram plane to generate a hologram from the WRP.

Digital holography has indeed led to numerous advancement of the classical, analog holographic technology that only permits a hologram to be permanently recorded onto a photographic film. In digital holography, a hologram can be captured from a real object. It can also be numerically generated as an array of numbers that can be stored as digital data, processed through computation, and distributed via digital communication links. In general, the primary purpose of holograms is to display 3-D images. Hence, a digital hologram in digital data form will not be of much practical use if it cannot be visually seen as a 3-D image. This is one of the major disadvantages of a digital hologram compared with the optical hologram, which can be readily captured with our eyes. However, a digital hologram can have different applications apart from generating 3-D images. In fact, recent research has shown that a digital hologram can be utilized in protecting sensitive data (a task referred to as cryptography), or in steganography for embedding large amount of additional data. This chapter describes some of the important applications of digital phase-only holograms in 3-D display, holographic cryptography, and steganography.

The fundamental principles of optical holography for capturing the optical waves of physical objects, and its difference from photography, are described. A photograph can only record a single view of an object scene; a hologram is capable of capturing the entire optical wavefront that impinges on it. There should be little difference between observing a hologram and the physical object scene. Numerical generation of digital holograms, commonly known as computer-generated holography (CGH), is presented. Two important approaches in CGH, the point-based and the layer-based methods, are described. The point-based method is suitable for generating holograms of simple objects with a small number of object points; the layer-based method is preferred for an object scene with a large number of object points concentrated in a few depth planes. The method for recovering a 3-D scene image from a digital hologram is provided. Three different methods for capturing digital holograms of physical object scene are described. The first method is similar to the art of optical holography, but instead of a photographic film, a digital camera is used to record the holographic waves emitted from the scene. As a digital camera can only record intensity information, the method can only be employed to capture an off-axis, amplitude-only hologram. The other two methods, known as phase-shifting holography (PSH) and optical scanning holography (OSH), are capable of capturing both the magnitude and phase components of the holographic signals. PSH is faster in operation, while OSH can be used to capture holograms of large objects. A simplified version of OSH, known as non-diffractive optical scanning holography (ND-OSH), is presented. ND-OSH is similar in principle to OSH, but the complexity of the optical and electronic setups is reduced.