2. Figure 1. Computer-
SLM displaying holographic generated
Input: Laser fringe pattern
holography. A
wavefront Output: Diffracted computer calculates
wavefront a holographic fringe
pattern for display
by the spatial light
3D image
modulator (SLM),
which diffracts laser
Viewer(s) light to yield an
interactive, true
Computer 3D image.
Control and interaction via voice, gesture, haptics
Dynamic range in conventional displays is limited human visual system’s depth cues. Stereoscopic,
as each of the display’s pixels is unambiguously autostereoscopic, and volumetric displays are defi-
mapped to a corresponding pixel in the image. cient in some depth cues, or worse, produce con-
flicting cues. This can result in the viewer ex-
Ease of tiling periencing discomfort, nausea, and other negative
CGH pixels need not be contiguous. For exam- effects, especially after long-term use.
ple, high-pixel-count CGH-based displays can be Conflicting depth cues also inhibit performance
made by assembling multiple microdisplay SLMs of various tasks in non-CGH-based displays. In a
into a 2D array. Gaps between the SLMs, neces- stereoscopic (glasses-based) display system, con-
sitated by interface and power connections, are vergence and accommodation (focusing) depth cues
not visible in the image projected from such com- conflict.1 Viewer-position-independent obscuration
puter-generated holograms. In conventional dis- is impossible in volumetric displays. Even advanced
plays, pixel-level continuity and accuracy are multiview autostereoscopic systems, such as inte-
required to prevent the eye from seeing tiling arti- gral imaging systems, generate optical wavefront
facts. approximations and resolutions significantly below
the eye’s visual acuity capabilities.
Tolerance of pixel defects
CGH delocalizes information associated with High system volume and image resolution
any point in a 2D or 3D image and spreads it over The lower resolutions of most display technolo-
the hologram surface. Consequently, “dead” pixels gies, which use geometric optics for ray-based
or even multiple rows or columns of defective pix- approximation, result from their need to minimize
els do not cause noticeable degradation in the diffraction effects. In contrast, holographic systems
image. In contrast, even small numbers of dead pix- directly exploit diffractive effects and therefore can
els are unacceptable in conventional displays, a be more compact as well as deliver images with
major factor in production costs. higher information content. Appropriate CGH
algorithms can adjust image resolution dynamically,
Wide color gamut allowing users to tailor system computing resources
CGH generally requires replay using lasers, for specific activities.
which, though expensive now, are becoming ubiq-
uitous and decreasing in price. A major advantage Artifact-free binary modulation
of lasers is that their monochromaticity, or spectral Displays, particularly microdisplays, are often
purity, yields a very wide color gamut, approaching binary in nature. Examples include Texas Instru-
90 percent of the color range the human eye can ments’ Digital Micromirror Device, various ferro-
perceive. Most existing display systems deliver only electric liquid crystal microdisplays, and Silicon
about 40 percent of the color gamut or less, as they Light Machines’ Grating Light Valve technology. To
use relatively broadband color filters. generate images perceived as having good gray scale,
these devices run at high frame rates and use tem-
Full depth cues poral multiplexing. In some applications, this can
Able to generate a wide range of optical wave- result in image degradation and artifacts. CGH,
fronts, CGH is the only technology capable of syn- however, can produce gray-scale images from binary
thesizing a true 3D image—that is, one with all the fringe patterns, thus no multiplexing is necessary,
August 2005 47
3. Figure 2.
Relationship Diffraction angle Fourier transforming
between image size θ optics
( I) and field of view
3D image
( FOV) in true 3D
SLM
floating-image
pixel spacing p θ Viewing
FOV
generation. I × FOV nx × ny pixels volume
is proportional to
the number of pixels
x
across the SLM, and
z
is independent of
f f
the focal length ( f)
of any optics. The
same relationship
holds for other
hardware frame rates can be reduced, and tempo- requires approximately 1012 pixels.
replay geometries.
ral dither artifacts are absent. Using techniques such as restricting the hologram
to horizontal parallax only—likely to be accept-
Aberration, distortion, able in many, but not all, applications—can reduce
and conformal correction system pixel-count requirements to about 1010.
It is sometimes possible to precompensate the However, this is still three orders of magnitude
CGH pattern to prevent known optical aberrations higher than the pixel counts of other high-end dis-
or imperfections from degrading CGH-generated play systems. The inability to calculate hologram
images. In the case of projecting a 2D image onto fringe patterns or update an SLM system with this
an arbitrary (but known or determinable) 3D sur- many pixels, at interactive rates, remain major bot-
face, a CGH-based projector system can likewise tlenecks to widespread CGH adoption.
produce a compensated, sharply focused image.
Image resolution
CHALLENGES For both 2D and 3D displays, the number of
Despite the unique capabilities of CGH-based dis- resolvable image points NI in any plane of the
play technology, it remains prohibitively expensive image perpendicular to the optical axis is directly
for most commercial applications, largely because related to the computer-generated hologram’s pixel
of the enormous pixel counts required to achieve count NCGH. In fact, NCGH ≥ NI, with typically NCGH
sufficient image resolution and image size (I). In the = 2NI. For many display applications, meeting this
case of direct-view CGH-based displays, generat- constraint is less onerous than a large I × FOV.
ing images with an adequate field of view (FOV) However, for 2D projection systems, in which FOV
also adversely impacts pixel-count requirements. is not a factor due to the scattering of light over a
wide range of angles by the projection screen sur-
Image width and field of view face, image resolution is the primary influence on
For direct-view CGH-based displays, the product system complexity.
of I and FOV is the primary influence on CGH
pixel counts. Image quality
To understand why, consider Figure 2, which The image from a computer-generated hologram
shows a typical Fourier transform configuration cannot contain more information than the holo-
used to generate usable I × FOV irrespective of gram itself. Ingemar Cox and Colin Sheppard2 have
CGH pixel spacing. The angle θ over which light defined and quantified the channel capacity C of
can be diffracted from a hologram fringe pattern is an optical system. In the case of a CGH-based
governed by the grating equation image generation system,
Λ sinθ = λ, C ∝ nx log[Q] ny log[Q] log(1+S/N),
where λ is the replay light wavelength and Λ is the where Q is the number of quantization levels, nx,y
spatial frequency of the fringe diffracting the light. are the resolvable pixels across the hologram
The largest value of θ is given when Λ = 2p, where and/or image, and S/N is the signal-to-noise ratio.
p is the pixel spacing on the SLM displaying the Thus, binary or other highly quantized hologram
CGH pattern. Regardless of the optical elements’ fringe patterns, while maintaining sufficient I ×
apertures and powers, I × FOV is proportional to FOV, can compromise image quality by decreas-
the number of pixels along the appropriate CGH ing the amount of information passing through the
axis. Even for a relatively undemanding worksta- system. System designers must therefore pay care-
tion application with, say, I = 0.5 m and FOV = ful attention to image-resolution, size, field-of-view,
60º, a full-parallax computer-generated hologram and signal-to-noise tradeoffs.
48 Computer
4. Laser speckle enables the reconstructed 3D images to
Unlike conventional volume holograms, com- exhibit hidden-line-removal effects.
puter-generated holograms must be illuminated The ping-pong algorithm first slices the Special attention
(replayed) with narrowband and spatially coher- object into planes perpendicular to the design must be paid to the
ent light—generally from red, green, and blue plane. It then propagates light through the efficiency of the
lasers—to produce color images. In addition to the image’s first plane (plane 1), toward the algorithms used to
high costs associated with this still-maturing tech- design plane, until it meets the next plane
nology, particularly green lasers, speckle can (plane 2). Next, the algorithm applies an
calculate the
adversely affect image quality. Designers can over- occlusion operator that allows the selective holographic fringe
come this problem through various speckle-reduc- attenuation and modulation of light as it patterns.
tion techniques, such as controlling laser system passes through plane 2. It then adds light
coherence.3 In addition, CGH can generate an from plane 2, and propagation proceeds to
image of a surface that appears diffuse without hav- plane 3. The process repeats through the
ing to rapidly vary the optical wavefront’s phase other planes until the light reaches the design plane.
structure, which will reduce perceived speckle. The ping-pong algorithm is easy to code using
standard numerical subroutines. However, the
ALGORITHMS FOR CGH DESIGN basic approach can only generate images of self-
Due to the daunting pixel counts that CGH- luminous objects, so implementing full rendering
based display systems require, special attention effects and lighting models requires enhancements.
must be paid to the efficiency of the algorithms used It is also computationally inefficient. For these rea-
to calculate the holographic fringe patterns.4 These sons, the ping-pong approach is not viable for a
fringe patterns, represented as a 2D array of pixel practical interactive system.
values, are usually analog in form. Some CGH
modulators, such as QinetiQ’s Active Tiling sys- Interference-based algorithms
tem, require converting the analog pixel array dis- These algorithms closely simulate light propa-
tribution into a binary distribution, with as little gation in a conventional interferometric hologram
degradation in the replayed 3D image as possible. recording. They essentially implement a 3D scalar
Minimizing any additional computational load of diffraction integral capable of generating very high
such a binarization step is particularly important quality images including lighting effects and sur-
for highly interactive systems.5 face-reflection properties. Interference-based algo-
For all algorithms, the information for 3D image rithms can reproduce all human visual depth cues
generation is typically exported from a commercial and currently serve as the benchmark for image
3D computer-aided design tool as a triangulated quality.
mesh with material properties. The material prop- QinetiQ has developed this approach in its
erties can include diffuse, specular, and shininess coherent-ray-trace algorithm. This algorithm uses
components. Fourier transform geometry with an off-axis object
Object surface intensities are based on user- to incorporate advanced rendering effects such as
defined material and light properties. The algo- shadowing and Phong shading of curved surfaces.
rithms populate the mesh with points at a density The core calculation consists of a double summa-
high enough that a human observer cannot see tion of all visible object points for each CGH pixel.
them. The display system then holographically This many-to-many mapping between CGH pix-
reconstructs these points. For simplicity we focus els and object points causes high computational
on full-parallax, true 3D image generation, al- loads.
though all approaches can be modified to produce
horizontal-parallax-only holograms, with signifi- Diffraction-specific algorithms
cant savings in computational resources. Mark Lucente pioneered diffraction-specific
CGH computation while at MIT,7 with more recent
Ping-pong algorithm variants of the algorithm featuring Fourier-based
One of the best-known and simplest Fourier- geometries.5 Importantly, these algorithms allow
based CGH algorithms is the ping-pong technique tradeoffs in image quality with computational
devised by Yoshiki Ichioka, Masaharu Izumi, and speed. Diffraction-specific algorithms consider only
Tatsuro Suzuki.6 Building upon the crude first Born the replay of a computer-generated hologram
approximation, or superposition, approach, this rather than its interferometric formation as in
technique introduces an obscuration operator that coherent ray tracing. By controlling the final holo-
August 2005 49
5. Figure 3. CGH
pattern calculation Discrete viewpoint Core diffraction Binarization
pipeline for an pattern and node
rendering node
MAC computation
Open GL capture, via lookup tables
diffraction-specific
…
algorithm system.
• •
To Active Tiling channels
The display system
OpenGL commands
binarizes the Intercept
hologram in the OpenGL Core diffraction
final computational call stream
• pattern and •
MAC computation
phase using a Intelligently via lookup tables
partitioned distribute
approach and then calls • •
passes the results to
the optical
subsystem over • •
the parallel input
architecture.
gram’s information content, which often exceeds throughput of the world’s 130th fastest computer
what the human visual system can interpret, these (www.top500.org/lists/2005/06). In addition, this
algorithms make it possible to achieve coarser res- figure is for 1 frame per second; most likely a sys-
olutions, particularly during interactive image tem will need to meet at least 15 fps or faster to
manipulation, that satisfy many applications. guarantee a perceptually smooth image update
Diffraction-specific algorithms accomplish this during interactive operation. However, in certain
by spatially and spectrally quantizing the hologram circumstances, optimizations can significantly
as hogels and hogel vectors, respectively, that they reduce the computational load.
can manipulate to vary the computational load.
The algorithms can precompute much of the CGH Hardware architectures
calculation, storing the results as diffraction tables The computational load’s large size and method
accessible via lookup during the interactive fringe- of calculation—simple MACs from a lookup
pattern calculation. The computational bottleneck table—largely dictate the appropriate architecture.
in the latter procedure is hogel vector decoding. The entire computation is naturally parallel, with
This step, in many forms of the algorithm, is a sim- each hogel and all rows within each hogel
ple multiplication and accumulation calculation independent. Candidate architectures include
(MAC), open to optimization on numerous archi- supercomputers (massively parallel, nonuniform
tectures. memory architecture systems and high-perfor-
mance clusters), special-purpose CGH compute
COMPUTATIONAL LOADS engines such as MIT’s Cheops,8 symmetric multi-
To better understand CGH computational load processor computers, clusters of commodity PCs
requirements, consider the following example. A and graphics processing units,9 digital signal proces-
horizontal-parallax-only computer-generated holo- sors (DSPs), field-programmable gate arrays
gram with spatial resolution comparable to high- (FPGAs), and application-specific integrated cir-
definition television and a comfortable viewing cuits (ASICs).
zone requires approximately 400,000 horizontal However, DSPs and FPGAs do not provide the
and 1,024 vertical pixels. A 4,096-pixel hogel can kind of close, fast access to large memories that
achieve spatial resolution exceeding common lookup table calculations offer. In addition, ASICs
HDTV specifications, thus generating the hologram are not commercially attractive given the low initial
requires 100 hogels. Given that, on average, each volume of likely electroholography products. Thus,
hogel must generate half of the possible image the most likely hardware architecture is based on
points, the total estimated computational load is high-performance computing systems.
100 (hogels) × 1,024 (image points) × 4,096 (dif- In recent years, we have compared the perfor-
fraction-table lookup entries) × 1,024 rows = 424 mance and cost benefits of different architectures
giga MACs. including the Cray T3E, the SGI Origin, the SGI
Spatial or temporal multiplexing can generate Onyx Reality Engine, and Intel IA-32 processor
color, and requires three times as many MACs. clusters with various interconnects. Our results
Converting a MAC to floating-point operations, indicate that IA-32 systems with a Myrinet inter-
the total computational load for a single frame is connect offer the most cost-effective and flexible
2.6 teraflops, which equates to the sustained high-performance cluster.
50 Computer
6. Figure 4. QinetiQ’s
Replication optics Active Tiling
and shutters system. (a)
Schematic view of
a single channel,
– Electrically
addressed which can generate
– SLM 25 million pixels.
(b) Photo of 1 × 4
channel Active
Optically
Tiling unit capable
addressed
SLM of delivering
full-color,
(a) (b) temporally
multiplexed
computer-generated
holograms with pixel
Parallel inputs nodes—will decrease to a modest cluster of fewer counts up to 10 8.
Many SLM systems have parallel inputs, which than 100 nodes by 2006.
eases the CGH computational challenge. For exam- Finally, for electroholography to be commer-
ple, Figure 3 shows the flow of information from cially successful, CGH systems must exploit a range
the application or data source, with each box rep- of standard and customized visualization software
resenting one or more processing nodes. In the sim- packages. Ideally, users should be able to run their
plest case, each row of nodes could be associated existing applications to drive the display without
with a single hogel, requiring perhaps 100 rows to modification. A particularly powerful approach is
meet the desired image size and field of view. to capture the graphics calls that applications such
Alternatively, the architecture could deploy vary- as OpenGL and DirectX produce and redirect them
ing numbers of processing nodes at each stage to to the cluster-based CGH pattern calculation
improve the update rate or it could use one row to engine.
compute five hogels to reduce the computational
cost. OPTICAL HARDWARE CONSIDERATIONS
The post-MAC result is a gray-scale CGH fringe Researchers have explored a number of SLM
pattern with 32-bit floating-point precision. The technologies, most notably the holovideo system10
display system binarizes the hologram in the final developed by the late Steve Benton and colleagues
computational phase using a partitioned approach5 at MIT. Loosely based on the Scophony TV system
and then passes the results to the optical subsystem of the 1930s, this 18-channel, parallel acousto-
over the parallel input architecture. optic modulator and mechanical scanner can syn-
thesize a 36-million-pixel computer-generated
Optimizations hologram and produce a horizontal-parallax-only
Various optimizations—including pixel prioriti- image of 150 × 75 × 160 mm3 (W × H × D).
zation, dynamic level of detail, and wireframe mode However, it is not possible to scale the current sys-
for interaction5—can either accelerate CGH com- tem to deliver the 1010 pixel counts that a practical
putation by increasing the frame rate or enable holographic workstation requires.
computation at the same frame rate with fewer
resources, thereby reducing cost. Depending on Active Tiling
scene geometry content, these techniques can A more recent development, and probably the
reduce the computational load from 16 to 200 leading scalable solution, is QinetiQ’s Active Tiling
times. This translates to 162 gigaflops per frame at system.11 This system exploits the existing and pro-
the most conservative level of savings. Given that jected strengths of both electrically addressed SLM
a 3-GHz Intel Pentium 4 has a theoretical peak (EASLM) and optically addressed SLM (OASLM)
computational load of 12 Gflops per single-preci- in an optimal way, trading the former’s high tem-
sion floating point, sustained throughput could be poral bandwidth for the latter’s large spatial band-
around 25 percent or 3 Gflops. Therefore, the com- width.
putational load requires 54 processors per frame, As Figure 4a shows, an Active Tiling channel
or 810 for 15 fps. optically replicates or “tiles” output from a fast
QinetiQ researchers have also focused on achiev- EASLM over an area of the OASLM. One config-
ing high, sustained throughputs on IA-32 proces- uration opens shutters in turn to build up the pat-
sors using SSE2 vector capabilities to increase tern on the write side of the OASLM, synchronizing
efficiency. If compute performance continues to the shutters to the EASLM’s appropriate frames.
adhere to Moore’s law, the current requirement for This enables updating the entire OASLM at video
810 IA-32 processors—or 405 dual-processor rates.
August 2005 51
7. pixels m-3; binary pixels, with a spacing of 6.6 µm;
an updatable 1 × 4 channel arrangement (5,120 ×
20,480 pixels = 104 megapixels) in both mono-
chromatic and frame-sequential-color operation;
and designs for scalable channel tilings in both
height and width to deliver systems with a pixel
(a) count in excess of 109.
Replay optics
CGH configuration requires using various opti-
cal elements in conjunction with the SLM holding
the holographic patterns.5 For example, many SLM
pixel spacings are relatively large compared to the
(b)
wavelength of replay light. In such situations, an
optical Fourier replay geometry can substantially
Figure 5. Computer-generated holograms. (a) Monochromatic and (b) color, full- reduce system volumes. Sophisticated multimirror
parallax, 3D image produced by the 10 8 pixel Active Tiling system. configurations, folded in three dimensions, can fur-
ther minimize overall system size. Using inexpen-
sive carbon fiber or electroformed mirrors can also
reduce system costs.
User interaction
An important element of CGH display systems
in many applications is user interaction with the
image. Researchers have developed intuitive inter-
faces using voice, gesture, and haptics. The syner-
gistic effects of 3D sound can also be exploited to
facilitate image interaction and modification.
EXPERIMENTAL RESULTS
Figures 5 and 6 illustrate state-of-the-art true 3D
images generated at QinetiQ laboratories using
Figure 6. Replay of a spatial-multiplexed, 3 × 8 billion-pixel, full-parallax, what we believe to be the largest pixel-count CGH
full-color, 3D image. systems designed for this purpose. We calculated
these computer-generated holograms using a 102-
Active Tiling channels are modular and can be node PC Linux cluster of dual IA-32 Pentium III
stacked together in parallel to deliver the required 1.26-GHz Tualatin-core 512-Kb cache CPUs, with
pixel counts, as Figure 4b shows. This parallel 1 Gbyte of memory per node and two 36-Gbyte
approach also minimizes the required data feed Ultra160 SCSI disk drives, along with a Myrinet
rates for each channel and closely matches the capa- interconnect and a 7.5-Tbyte storage area net-
bilities of cluster-based rendering architectures. work.
A typical Active Tiling channel configuration Figure 5 shows monochromatic and color, full-
consists of a binary, 1,024 × 1,024-pixel ferroelec- parallax, 3D images produced by a computer-
tric crystal on silicon EASLM operating at a 2.5- generated hologram having 108 pixels, while Figure
kHz frame rate; a binary-phase diffractive optical 6 shows a replay of a spatial-multiplexed, 3 × 8 bil-
element and associated refractive optics perform- lion-pixel, full-parallax, full-color, 3D image. As
ing the 5 × 5 replication; and an OASLM using an these images illustrate, standard computer graph-
amorphous silicon photosensor, light-blocking lay- ics techniques can be incorporated into CGH
ers, a dielectric mirror, and a ferroelectric liquid design, including environment mapping, radiosity
crystal output layer. The output for each channel modeling, and transparency effects. When viewed
is therefore 26 million pixels. by eye, the full images look sharp and do not
Current Active Tiling system attributes include appear fuzzy—the eye naturally accommodates as
a pixel areal density of more than 2.2 × 106 pixels the viewer focuses attention on different parts of
cm-2; a compact system volume exceeding 2.4 × 109 the image, as with a real object.
52 Computer
8. he versatility of computer-generated hologra-
T
7. M. Lucente, “Diffraction-Specific Fringe Computa-
phy, combined with its unique ability to pro- tion for Electro-Holography,” doctoral dissertation,
duce full-depth-cue 3D images at beyond eye Dept. of Electrical Eng. and Computer Science, MIT,
resolution, floating in space, and with an extended 1994.
color gamut has led some to label CGH the ultimate 8. V.M. Bove Jr. and J.A. Watlington, “Cheops: A
display technology. However, many CGH-based dis- Reconfigurable Data-Flow System for Video Pro-
plays have an appetite for pixels that can far exceed cessing,” IEEE Trans. Circuits and Systems for Video
other display types. Unique additional computa- Technology, vol. 5, no. 2, 1995, pp. 140-149.
tional operations add to the cost of such systems, 9. V.M. Bove Jr. et al., “Real-Time Holographic Video
particularly high-frame-rate interactive systems. Images with Commodity PC Hardware,” Proc. SPIE,
Thus, for many applications, lower-cost, simpler dis- vol. 5664, SPIE—Int’l Soc. for Optical Eng., 2005,
play technologies will be more appropriate. pp. 255-262.
Nevertheless, with compute power and display 10. P. St.-Hilaire, “Scalable Optical Architecture for Elec-
hardware continuing to decrease in price and other tronic Holography,” Optical Eng., vol. 34, no. 10,
required technologies rapidly advancing, the ques- 1995, pp. 2900-2911.
tion is not whether CGH systems will become a 11. M. Stanley et al., “3D Electronic Holography Dis-
practical generic display technology but, rather, play System Using a 100-Megapixel Spatial Light
how soon. I Modulator,” Proc. SPIE, vol. 5249, SPIE—Int’l Soc.
for Optical Eng., 2003, pp. 297-308.
Acknowledgments
The authors gratefully appreciate the work of all Chris Slinger is a QinetiQ Fellow and technical
members of the holographic imaging project team director of the Optronics Department at QinetiQ
at QinetiQ as well as our academic and commercial Malvern in Great Malvern, United Kingdom. His
collaborators. Funding for this research comes research interests include holography, computer-
from QinetiQ, the UK Ministry of Defence TG7, generated holography, high-performance displays,
the Ford Motor Company, and Holographic and novel imaging systems. Slinger received a
Imaging LLC. D.Phil. in multiple-grating volume holography
from the University of Oxford. He is an Institute
of Physics (IOP) Fellow. Contact him at slinger@
References qinetiq.com.
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August 2005 53