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Despite their esoteric sounding title, computer-generated holograms (CGHs) are now commonplace in a wide variety of applications and are a vital component in some surprisingly familiar consumer products. Such devices can be realized as fixed, etched structures and are commonly called diffractive optical elements (DOEs) or displayed on dynamically addressable liquid-crystal on silicon (LCOS) microdisplays. In either case, the principal attraction is the ability of these devices to generate arbitrary complex-valued optical fields from a small, thin device. As discussed in Bernhardt et al. (1991), one CGH is able to perform the entire functionality associated with a multiple element glass lens design, leading to low-cost, lightweight optical assemblies. Furthermore, the process by which CGHs are made is simple, and lends itself to volume manufacturing through embossing and injection molding techniques; as demonstrated by Buckley & Wilkinson (2006), it is even possible to obtain adequate performance from CGHs patterned onto overhead transparencies from a standard office laser printer. Furthermore it is possible to fabricate phase-modulating DOEs which do not absorb incident optical illumination, leading to very high efficiencies. Naturally, the flexibility and potential of CGH technology and its ability to implement multiple optical functions and exert control over optical fields including very near-field evanescent waves as demonstrated by Brauer & Bryngdahl (1997); Elschner & Schmidt (1998); Gupta & Peng (1991); Kowarz (1995); Liu K 1999); Madrazo N Schmitz et al. (1996); Thompson et al. (1999) has resulted in huge commercial utilization. For example, CD and DVD drives contain a diffractive optical element to appropriately condition and direct the laser beam onto the disc surface and, with the advent of the DVD disc, simultaneous optical pick-up from multiple disc layers can be achieved by employing an injection molded hybrid refractive-diffractive lens. In addition to fixed holograms, there exist numerous methods for representing dynamic CGHs on reconfigurable microdisplay devices. There are a wealth of papers describing dynamic CGHs in applications as diverse as laser beam shapers in Dresel et al. (1996), fanouts and splitters for dynamic routing and multiplexing of laser beams into fibers in telecommunications applications Bengtsson et al. (1996); Gillet & Sheng (2003); Jean-Numa Gillet (1999); Keller & Gmitro (1993), optical traps for biophotonics Jesacher et al. (2004); Sinclair et al. (2004), performing transformations upon optical fields Case et al. 13

Computer-Generated Phase-Only Holograms for Real-Time Image Display