**1. Introduction**

276 Advanced Holography – Metrology and Imaging

[26] J.J. Lunazzi, "*The use of diffractive screens for electronic imaging"*, Proc. of the Holographic

MG, 9-13 de maio de 2006.

*2011 "Which first look review*"",

pe=pdf

Holography%20and%20Applied%20Optics/1427.pdf

PhD Thesis, Campinas State University, 2007

Display Artists and Engineers Club-HODIC meeting, Japan Association of Display Holography, Tokyo, Japan, 1996.08.30 http://arxiv.org/pdf/physics/0609243 [27] *"3D shadowgram projection using a simple diffractive screen"*, José J. Lunazzi, N I. R.

Rodríguez, Proc. of the XXIX Enc. Nac. de Fis. da Mat. Cond., SBF, São Lourenço-

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[28] *"Imagens Por Difração com Luz Branca Sem Elementos Intermediários"*, N. I. R. Rodriguez,

[30] CEOS 2011 video demonstration: "S*ony Autostereoscopic 3D TV without glasses at CES* 

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http://webbif.ifi.unicamp.br/teses/apresentacao.php?filename=IF284 [29] "*Edgelit holography: Extending Size and Color",* Nessbit, R.S., MIT Thesis September 1999

> 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 & Kowarz (1998; 1999); Madrazo & Nieto-Vesperinas (1997); 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.

complexity of the hologram generation algorithms required, and by the poor quality of images

Computer-Generated Phase-Only Holograms for Real-Time Image Display 279

Recently, a great deal of progress has been made in using binary-phase CGHs for projection as detailed in Buckley (2008a;b; 2011a) and a new approach to hologram generation and display, based on a psychometrically-determined perceptual measure of image quality, has been shown to overcome both of these problems and has resulted in the commercialization of a real-time 2D holographic projector. This chapter will bring together, for the first time, the recent theoretical and practical advances in realizing 2D and 3D holographic projection

For video display applications, in which the APL is significantly less than the full-white maximum, a projection display based on phase-only computer generated holography could offer a significant efficiency advantage compared to amplitude-modulating LCOS displays, since light is not blocked from the desired image pixels. Quantifying this benefit has proven difficult, however, since there is widespread disagreement in the published literature from, for example, Bhatia et al. (2009; 2007); Buckley et al. (2008); Lee et al. (2009); Weber (2005) as to an acceptable value to use for the APL. The variation in reported values appears to result

In a generalized display, the light intensity produced *Lout* is related to the video signal voltage *V* by *Lout* ∝ *V<sup>γ</sup>* , where *γ* is the display gamma. To obtain a display intensity response *Lout* which is linear with respect to the video image *P*, the transmit video signal *V* is encoded by an inverse gamma correction function so that *V* ∝ *P*1/*γ*. To ensure a uniform perceptual response, the display gamma is typically set to *γ* = 2.2 to match the approximate lightness

In a projection architecture in which the light sources can be modulated in response to average scene or per-pixel brightness, the resultant efficiency benefit is directly related to the mean value of *Lout*, E [*Lout*], which is clearly not equal to E [*V*] when *γ* � 1. In order to calculate this mean value, and since neither the form of *Lout* nor *V* are known a priori, we must derive

Consider an image pixel *P* that can take a value in the range [0, *p*), quantized into *n* bins of size *<sup>b</sup>* so that *<sup>b</sup>* = *<sup>p</sup>*/*n*. The number of occurrences of a pixel value within the bin [*pi*−1, *<sup>p</sup>*) is

*ki* = *k* (1)

*ki* = *�* (2)

∞ ∑ *i*=1

1 *k*

∞ ∑ *i*=1

We define Pr*n*(*b*) to be the probability that the pixel value will fall into the *bth* bin *n* times. Since each pixel has an equal probability of taking a value in the range [0, *p*), the probability

produced by the binary holograms they generate.

from the point at which the APL measurement is defined.

a statistical model for the pixel distribution pre- and post-gamma.

*ki*, so that the total number of occurrences of that pixel value is

and the total number of occurrences *k* is fixed, so that

systems based on binary phase CGHs.

sensitivity of a human viewer.

where *�* is some positive constant.

**2. Motivation**

(1981); Gu et al. (1986); Roux (1991; 1993); Stuff & Cederquist (1990), self-adjusting CGHs Lofving (1997), aspheric testing Tang & Chang (1992), and wavelength discrimination for wavelength-division multiplexing (WDM) applications Dong et al. (1998; 1996); Layet et al. (1999); Yang et al. (1994).

Despite the obvious benefits of computer-generated holography for a wide range of applications, however, it is only recently that CGHs have been demonstrated for the projection and display of two dimensional video-style images. Indeed, such a method of image projection and display has long been desired, but was never previously realized, due to high computational complexity and poor quality of the resultant images.
