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.