Publication : SPIE Proc. Practical Holography XXV: Materials and Applications, SPIE#7957, San Francisco, 79571A(2011).

1

New techniques for wave-field renderingof polygon-based high-definition CGHs
Hirohito Nishia , Kentaro Higashia , Yasuaki Arimaa , Kyoji Matsushimaa and Sumio Nakaharaba Department of Electrical and Electronic Engineeringb Department of Mechanical Engineering

Kansai University, Yamate-cho 3-3-35, Suita, Osaka 564-8680, Japan
ABSTRACT
Four novel techniques are introduced into polygon-based high-deﬁnition CGHs (PBHD-CGH) that feature thetrue-ﬁne spatial 3D image accompanied with a strong sensation of depth. The ﬁrst is algorithm for creating
specular surfaces based on Phong reﬂection model. This is very useful for providing a feel of material to polygonalsurfaces. The second technique is called digitized holography that replaces the entire processes of classicalholography by their digital counterparts. The wave-ﬁeld of real-existent objects can be optically reconstructedby the digitized holography. This technique makes it possible to edit the 3D scene of holograms or create mixed
3D scene of the real and virtual objects. Another technique for creating PBHD-CGH of real-existent objects is
also proposed by a CG-like method using a 3D laser scanner that measures the 3D shape of the object. Finally,a prototype PBHD-CGH is demonstrated for creating landscape scenery. This CGH is intended to reconstructa scene as if the viewers see mountain scenery through the window given by the CGH.
Keywords: Computer-generated hologram, Polygon-based method, Specular surface, Texture-mapping, Digitized holography, 3D scan, Synthetic aperture digital holography

1. INTRODUCTION
Spatial 3D images optically reconstructed by full-parallax high-deﬁnition computer-generated holograms (HDCGH) are very diﬀerent from that by conventional 3D systems. The full-parallax HD-CGHs give viewers a strong
sensation of depth that never has been caused by the conventional systems providing only binocular disparity.
Recently, we reported a set of techniques to create full-parallax HD-CGHs with more than billions pixels, which
be able to reconstruct occluded 3D scenes constructed of surface-modeled object.1–4 These CGHs are createdby techniques based on the polygon method5 for generating object ﬁelds and the silhouette method3, 14, 15 forlight-shielding. Therefore, the HD-CGHs are called polygon-based high-deﬁnition CGHs (PBHD-CGH).6
In the last meeting, we also introduced a new technique for ﬁeld propagation, named shifted angular spectrum
method,7 into creation of PBHD-CGHs.6, 8 Since this numerical technique removes any constraints on ﬁeld
propagation, PBHD-CGHs gain the freedom of arrangement of the objects in the 3D scenes.
One of advantages of the polygon-based method is similarity to conventional computer graphics based onpolygon models. Techniques of texture-mapping and smooth shading used in CG such as Gouraud and Phongshading are successfully introduced into PBHD-CGHs and put more expression into the reconstructed 3D images.6, 9, 10 We call these techniques wave-ﬁeld rendering.
In this paper, we propose some other rendering techniques for PBHD-CGHs. First, we present a new algorithm
to give metal-like specular surfaces to CG-modeled virtual objects. This is a very important technique to produce
a feel of material of the reconstructed objects. Second, we present techniques to create 3D images of real-existentobjects. Two techniques are proposed for this purpose: One is the use of a 3D scanner and another is digitized
holography. The former is a conventional CG-like technique; the photograph of the real object is texture-mapped
onto the 3D-meshed object whose mesh data is measured by using a 3D laser scanner. The latter is a little
evolutionary; the ﬁelds of real-existent objects are widely captured by using the technique of synthetic aperture
Further author information: (Send correspondence to K. Matsushima)
E-mail: matsu@kansai-u.ac.jp

2

Publication : SPIE Proc. Practical Holography XXV: Materials and Applications, SPIE#7957, San Francisco, 79571A(2011).

Incident light

Reflection light
R

R1
P

1

V
View direction

R2
R3

P

2

P

3

Surface
Figure 1. Phong reﬂection model.

Figure 2. Reﬂection in polygonal surfaces.

digital holography.11 We call this technique digitized holography, because this is the technique completely
replacing classical holography by a modern digital way. Finally, we introduce an attempt to create CGHs thatreconstruct mountain scenery as if viewers see a landscape through the window of the CGH.

2. RENDERING FACETED SPECULAR SURFACES
2.1 Spectral envelope of specular surface function based on Phong reflection model
In the polygon-based method, 3-D objects is composed of many polygons. Each polygon is regarded as a planar
surface source of light whose shape is polygonal. The surface sources are expressed by complex functions referred
to as a surface function. The common form of the surface function is given by:h(x, y) = a(x, y) exp[iϕ(x, y)],(1)where the amplitude distribution a(x, y) gives the shape, texture, and brightness of the polygon, while the phase
distribution ϕ(x, y) provides diﬀusiveness of light. A specular surface obviously has a limited diﬀusiveness incontrast with the diﬀused surfaces. Therefore, the spectrum of the surface functions must be band-limited in
specular surfaces. We make use of Phong model to determine the spectral envelope of phase distribution ϕ(x, y).
Phong reﬂection model is the most popular model for rendering a specular surface in CG. According to Phongmodel, the brightness observed in a view point is given as:
I(V, R) = ks (R · V)α ,(2)

where ks and α are a specular reﬂection and shininess constant, respectively. The vector R = (Rx , Ry , Rz ) gives
the reﬂection direction, whereas the vector V gives the viewer direction, as illustrated in Fig. 1. Supposing thatthe view direction can be interpreted as the unit wave vector of a plane wave, V is given as:
V = λ(u, v, (λ−2 − u2 − v 2 )1/2 ),(3)

where u and v are Fourier frequencies with respect to x and y direction. Substituting Eq. (3) into (2), theenvelope of spectrum of the phase distribution is obtained as following:As (u, v, R)= I(V, R)1/2= ks1/2 [λ(Rx u + Ry v + Rz (λ−2 − u2 − v 2 )1/2 )]α/2 .

(4)

To give a Phong-modeled specular surface to the object, the phase distribution ϕ(x, y) should be modiﬁed so thatits spectral envelope is ﬁtted to the As (u, v, R). In this study, iterative Fourier-transform algorithm (IFTA)12 isused for the modiﬁcation of the spectral envelope of the diﬀusive phase.
In the IFTA, The surface function is ﬁrst Fourier-transformed into spectrum and then only the amplitude
distribution of the spectrum is deformed so that the spectral envelope corresponds with the As (u, v, R). The
deformed spectrum is then transformed back to the complex amplitude in the real space in that only the amplitude
distribution is deformed again so that the amplitude distribution corresponds with the polygonal surface. The
iteration of this procedure generates the surface function of the specular surface whose spectral envelope agrees
with As (u, v, R).

Publication : SPIE Proc. Practical Holography XXV: Materials and Applications, SPIE#7957, San Francisco, 79571A(2011).

Amplitude

Phase

3

Amplitude(d) Spectrum of integrated surface function

Amplitude(a) Diffusive surface function
h(x, y)Amplitude

PhaseH’(u, v; R)H(u, v)

Amplitude(c) Shifted spectrum of specularsurface function

Amplitude(b) Specular surface function

Figure 3. An example of the procedure for generating specular surfaces.

2.2 Rendering object composed of specular surfaces
A specular polygon is created by the method based on the IFTA and Phong reﬂection model in the previous
section. However, the method is too time-consuming to calculate the wave-ﬁeld of an object composed of manypolygons. Each polygon composing the object has its own reﬂection vector of R as shown in Fig. 2. Therefore,
the procedure for the IFTA that involves many iterations of Fourier transform must be performed for eachpolygon. This is the reason why the method is expected to be much time-consuming.
We adopt shifting carrier frequency of the spectrum in order to avoid unnecessary repeat of the IFTA. At
the beginning, a complex function g(x, y) is generated by the method in section 2 using the reﬂection vectorof R = (0, 0, 1). Here, the amplitude of the function is a constant of unity, i.e. |g(x, y)| ≡ 1. Therefore, thiscomplex function is not a surface function but a phase-modulated function given as the following form:
g(x, y) = exp[iϕ′ (x, y)].

(5)

The surface function of a speciﬁc polygonal surface is provided by using the phase-modulated function as follows:h(x, y) = a(x, y)g(x, y),(6)where a(x, y) gives the shape of polygon again. The surface function h(x, y) gives a limited diﬀusiveness basedon Phong model, in which the reﬂection light mainly travels in the normal direction of the surface. To force
the light to travel in arbitrary direction given by R, the function h(x, y) is multiplied by the wave-ﬁeld of aplane-wave traveling in the direction of R as follows:h′ (x, y; R) = h(x, y) exp[ikR · r],(7)

where k is the wavenumber and thus exp[ikR · r] = exp[ik(Rx x + Ry y)] is the plane wave traveling into the R
direction. Equation (7), however, usually causes an aliasing error for the sampling interval of the given (x, y)grid. In the Fourier space, Eq. (7) means that the spectrum H(u, v) = F {h(x, y)} is shifted as follows:
H ′ (u, v; R) =F {h′ (x, y; R)}
Ry
Rx
,v −
).
= H(u −λλ(8)

Publication : SPIE Proc. Practical Holography XXV: Materials and Applications, SPIE#7957, San Francisco, 79571A(2011).

Wallpaper

Venus statue

Virtual light source
Hologramy65

4

1st propagation: 2nd propagation:
2.5 h
2.5 h

x

56

Computingz

65

the Venus field: 3.0 h

65
1 50

Units: mm

1 50

65

Figure 4. The 3-D scene of ”The Metal Venus I”.

Figure 5. Itemized computation time of The Metal Venus
I.

Therefore, we use the spectrum H ′ (u, v; R) instead of using Eq. (7). As a result, the phase-modulated function
g(x, y) generated only once in R = (0, 0, 1) can be used for any direction of R.
Figure 3 shows an example of the procedure of the proposed rendering method for generating specularsurfaces. The diﬀusive light, whose surface function is shown in (a), should be mixed with the light produced
from the specular surface function in (b) for realistic rendering, because the specular-only surfaces lead toa narrow viewing-zone. The diﬀusive surface function (a) is only Fourier transformed, whereas the specularsurface function is Fourier-transformed and then shifted by using Eq. (8) as in (c). These two surface functions
are superposed in the Fourier space, as shown in (d).

2.3 Creation of PBHD-CGH for specular object
We created a PBHD-CGH named “The Metal Venus I” after the ﬁrst PBHD-CGH “The Venus” with a diﬀusive
surface.3 The 3D scene of the CGH illustrated in Fig. 4 is almost the same as that of The Venus. The statueof the Venus is 5.6 cm in height and composed of 1396 polygons. Parameters used for computing the CGH aresummarized in Table 1.

(a) Left(b) Center(c) Right

Figure 6. Photographs of optical reconstructs of The Metal Venus I. The photographs (a)–(c) are taken from diﬀerent
view-points.

Publication : SPIE Proc. Practical Holography XXV: Materials and Applications, SPIE#7957, San Francisco, 79571A(2011).

5

Computation of the CGH was executed by using a PC with four CPUs of the Xeon E7330 (2.4 G Hz) andmemory of 96 G bytes. The total computation time was approximately 8.0 h. The itemized computation time isshown in Fig. 5. The longest time was consumed by computation of the object (Venus statue) ﬁeld. This is 1.5
times longer than the original Venus rendered only with diﬀusive surfaces∗ , because specular ﬁelds are separately
computed and then added to the diﬀusive ﬁeld.
Figure 6 shows the optical reconstruction of The Metal Venus I. It is veriﬁed that the surface brightness ischanged dependently on the view point.

3. RENDERING REAL-EXISTENT OBJECTS BY DIGITIZED HOLOGRAPHY
In classical holography, the object wave of a real-existent object is recorded on light-sensitive ﬁlms by interference with reference waves. Then, the object wave is reconstructed by diﬀraction by the fringe pattern. It istheoretically possible to replace these entire processes by their digital counterparts. In fact, the PBHD-CGHs
allow us to reconstruct completely virtual 3D scenes by diﬀraction by the synthetic fringe pattern. This meansthat the latter half, i.e. reconstruction of object waves, is already realized. However, it is not easy to realize theformer half, recording object wave, by using a digital manner. Although it is theoretically possible to capture
any object ﬁeld by using digital holography (DH), currently available image sensors, in practice, do not meet therequirement of PBHD-CGHs such as pixel sizes and pitches, which make it possible to reconstruct true ﬁne 3D
images.
To resolve the problem, we use the technique of lensless-Fourier synthetic-aperture digital holography (LFSADH).11 This is a type of DH using a spherical reference wave and makes it possible to replace the whole processof the classical holography with digital signal processing (DSP) of optical wave ﬁelds. We refer to this technique
as digitized holography. The digitized holography allows us to digitally edit, archive, transmit, and opticallyreconstruct the wave-ﬁeld of real-existent 3D objects.
In this section, we report a PBHD-CGH created as digitized holography. The CGHs, named “Bear II”
optically reconstruct mixed 3D scenes including CG-modeled 3D objects, 2D digital images, and multiple realexistent objects whose ﬁeld is captured by using the LFSA-DH.

3.1 Principle for reducing sampling intervals and increasing sampling cross section
In the LFSA-DH, the wave-ﬁeld of an object is obtained by Fourier transform of the captured ﬁeld. The samplingintervals of the Fourier-transformed wave-ﬁeld are given by the following equation in the image plane:11
λdR
,
Nx δx
λdR
∆y =
,
Ny δy

∆x =

(9)

where λ and dR are the wavelength and the distance between the center of the spherical reference wave and theimage sensor. Number of the sensor pixels and the sensor pitches are Nx × Ny and δx × δy , respectively.
Since the sampling intervals are reduced with increasing the sensor pixels, the technique of the synthetic
aperture is used for increasing the eﬀective number of the pixels.13 In the synthetic aperture DH, the image
sensor is mechanically translated and captures the wave ﬁeld at diﬀerent positions. Here, an amount of the sensor
shift is set to be smaller than the sensor area in order to overlap the captured ﬁeld at each position. This overlap
area is used for avoiding translation errors and obtaining exact sensor position by use of a correlation function
between the captured ﬁelds.13 As a result, it is possible to integrate all captured ﬁelds into a large-scaled wave
ﬁeld.

∗

According to the early paper, computation time for the object (Venus statue) was 7.6 h.3 However, the time has been
reduced by the improvement of the implement and use of more powerful PCs.

Publication : SPIE Proc. Practical Holography XXV: Materials and Applications, SPIE#7957, San Francisco, 79571A(2011).

BS1

λ = 532 nm 1/2RP1

6

M1

1/2RP2
SF1
ys

Object

xs

BS3

SF3

Image sensor
with motorstage

BS2

M3 with Piezo
shifter

SF2
M2

Figure 7. Experimental setup for capturing a large wave-ﬁeld by synthetic aperture digital holography. M: mirror, BS:beam splitter, RP: retarder plate.

3.2 Experiment for capturing large-scaled wave-fields by LFSA-DHThe experimental setup for capturing large-scaled wave-ﬁelds by the LFSA-DH is shown in Fig. 7. The image
sensor with 3000 × 2200 pixels (Lumenera Lw625) is mechanically translated by a PC-controlled motor-stage.
The fringe pattern is captured 3 times for each position to obtain a complex wave-ﬁeld using the phase-shift
caused by the mirror M3 installed in a Piezo phase-shifter.
Amplitude image of the captured and Fourier-transformed ﬁeld are shown in Fig. 8 (a) and (b), respectively.
The total ﬁeld is obtained by stitching individual ﬁelds captured at 8 × 12 positions. The total cross section of
the captured ﬁeld is 77 × 80mm2 . Here, the distance dR between the reference point source provided by SF3
and the sensor plane is 21.5 cm. This distance is a free parameter and thus determined so that the samplingintervals of the Fourier-transformed ﬁeld is 1.0µm × 1.0µm.

3.3 CGH for mixed 3D scene including virtual and real objects
3.3.1 Mixed 3D scene
The real-existent object, the ornament of a small bear whose wave-ﬁeld is capture by the LFSA-DH, is mixed
with the virtual 3D scene. The design of the scene is shown in Fig. 9. Here, the bear appears twice on the scene,
i.e. the same captured wave-ﬁeld is used twice in the scene. This is impossible in classical holography. Only
digitized holography allows us to edit the 3D scene. Some virtual objects such as 2D wallpaper or 3D bees arearranged behind or in front of a double bear.

(a)

2cm

1cm
1cm
(b)

Figure 8. Amplitude images of the captured (a) and Fourier-transformed ﬁeld (b).

Publication : SPIE Proc. Practical Holography XXV: Materials and Applications, SPIE#7957, San Francisco, 79571A(2011).

7

2D digital image
Captured fieldsof real-existent object
CG-modeled
3D objects
50

65

50
50

Units: mm

65
100

Hologram
Figure 9. The mixed 3D scene of “Bear II” including the ﬁeld of the real-existent object and the CG-modeled virtual
object.

3.3.2 Light-shielding by silhouette method
The light behind the real-existent object must be shielded to prevent the object from being a phantom image andcorrectly reconstruct the occluded scene. The silhouette method3, 14, 15 proposed for light-shielding in synthetic
holography is applied to the real-existent object. The principle of light-shielding in captured ﬁelds is shownin Fig. 10. Since the incident ﬁeld behind the captured object should be shielded over the cross section of theobject, the incident ﬁeld is multiplied by a binary mask that corresponds with the silhouette of the object. Then,the captured ﬁeld is added to the masked ﬁeld. The silhouette-mask image used is shown in Fig. 11 (b). This
image is produced from the amplitude image of (a) that is obtained from a small part of the captured ﬁeld to
avoid blur.
3.3.3 Fabrication and reconstruction of “Bear II”
The number of pixels of the Bear II is approximately 4 G pixels (∼= 65, 536 × 65, 536). Since the pixel pitches are
1.0 µm× 1.0 µm, the viewing angle is 37◦ both in horizontal and vertical. The parameters used are summarizedin Table 1. After calculation of the total wave-ﬁeld of the scene including captured ﬁelds, the fringe pattern isgenerated by numerical interference with the reference wave, and then quantized to produce the binary pattern.
Finally, the binary amplitude hologram is fabricated by using laser lithography system.
Photographs of the optical reconstruction of the Bear II are shown in Fig. 12. It is veriﬁed that occlusion of
the 3D scene is accurately reconstructed, because the appearance of the 3D scene varies when the point of view
changes.
Silhouettemask
ObjectCapturedfield
Incident
field

Figure 10. The principle of the silhouette method in captured ﬁelds.

(a) Amplitude image(b) Silhouette mask

Figure 11. (a) The amplitude image obtained from a smallpart of the captured ﬁeld. (b) The silhouette mask produced from the amplitude image.

Publication : SPIE Proc. Practical Holography XXV: Materials and Applications, SPIE#7957, San Francisco, 79571A(2011).

(a) Left(b) Center

8(c) Right

Figure 12. Photographs of optical reconstruction of the “Bear II” created for the mixed 3D scene including real-existentand virtual objects. Photographs (a) – (c) are taken from diﬀerent view points.

4. RENDERING REAL-EXISTENT OBJECTS BY 3D LASER SCANNER
In holography, the object wave emitted from a real-existent object that is illuminated by coherent light is recordedby optical interference with reference waves. However, recording real-existent objects without illumination bycoherent light sometimes has an advantage. For example, a real building can not be recorded by holography,
because the object is too large to be illuminated by coherent light. In this section, CG-like approach is presented
for recording and reconstructing real-existent 3D objects by using PBHD-CGHs.

4.1 Measurement of 3D objects by using 3D scanner
The shape of 3D objects are measured by a 3D laser scanner, Konica Minolta Vivid 910. This equipment isable to scan a 3D object in 2.5 s and output its 3D shape as polygon mesh data. The measurement error is lessthan ±0.05m in all directions. The Vivid 910 also has a function of capturing the in-line digital image of theobject. Since the polygon method is similar to CG as mentioned above, the digital 2D image can be used for
texture-mapping6, 16 in order to produce more realistic 3D images.
Here, live faces are chosen as the object recorded by the 3D scanner and reconstructed by PBHD-CGHs,
because it is not easy to record live faces by conventional holography. Figure 13 shows snapshots of the scene of
3D measurement of live faces. The CG image rendered by texture-mapping onto the polygon mesh is also shownin Fig. 14

4.2 Fabrication and reconstruction of the PBHD-CGHs
The polygon-meshed object with 2822 polygons is placed at 10 cm behind the hologram plane. The wallpaper
made by 2D digital image is also arranged at 12 cm behind the polygon-meshed object to enhance the depth
3D laser scanner

Figure 13. Snapshots of measurement of the 3D shape oflive faces by using the 3D laser scanner.

Figure 14. Computer graphics of the measured polygon
mesh data.

Publication : SPIE Proc. Practical Holography XXV: Materials and Applications, SPIE#7957, San Francisco, 79571A(2011).

(a) Left(b) Center

9(c) Right

Figure 15. Photographs of optical reconstruction of the fabricated PBHD-CGH. Photographs are taken from diﬀerent
view-points.

sensation. Number of pixels of the calculated and fabricated PBHD-CGH is 131, 072 × 65, 536 pixels. Since thepixel pitched are 0.8 µm both in horizontal and vertical direction, the viewing-angles are approximately 45◦ inboth directions.
Figure 15 shows the optical reconstruction. The reconstructed 3D image is certainly a 3D portrait.

5. RENDERING MOUNTAIN SCENERY
The PBHD-CGH described in this section is intended to reconstruct a scene as if viewers see mountain scenerythrough a window. Since the CGH plays a role of the window, the perspective through the window should varywith change of the viewpoint. Furthermore, the terrain beyond the window should extend as far as viewers cansee.
There are mainly two problems to create the intended CGH. One is how to calculate the wave-ﬁeld of a very
big and uninterrupted object. This is most likely very time-consuming. Another problem is how to preventthe reconstructed 3D scene from be a phantom image. The object model for mountain scenery commonly has
self-occlusion. The silhouette method is used for creating PBHD-CGHs of occluded scenes. In this technique, thewave-ﬁeld behind the object is shielded by the mask obtained from the silhouette of the object. This techniquemakes it possible to create mutual occluded 3D scenes. However, if an object has self occlusion, the object
may be reconstructed as a partial phantom image, because the light-shielding is made for object by object at
this stage. If light is shielded polygon by polygon, self-occlusion can be correctly reconstructed. However, thistechnique is too time-consuming to create HD-CGHs whose number of pixels reach to billion pixels.
Figure 16 is the 3D scene of the prototype CGH “Moutain” reconstructing mountain scenery. The parameters
are shown in Table 1. To resolve the problem mentioned above, we split the object model into several sub-objects
and insert several masks between the sub-objects as shown in Fig. 17. Here, the inserted masks correspond to
Object model of terrain

32

32

5
16

Units: mm

150

50

Figure 16. The 3D scene of the prototype CGH reconstructing mountain scenery.

Figure 17. Schematic illustration of splitting and masking
the object.

10

Publication : SPIE Proc. Practical Holography XXV: Materials and Applications, SPIE#7957, San Francisco, 79571A(2011).

(a) Left(b) Center(c) Right

Figure 18. Photographs of optical reconstruction of the prototype CGH. Photographs (a) – (c) are taken from diﬀerent
view-points.

the shape of cross section of the terrain model. Unfortunately, the positions where masks should be inserted andnecessary number of masks are determined a priori at this stage.
The optical reconstruction is shown in Fig. 18. It is veriﬁed that the mountain scenery is reconstructed asintended.

6. CONCLUSION
Several techniques are newly and successfully introduced into full-parallax polygon-based high-deﬁnition CGHs.
The parameters of the created CGHs are summarized in Table 1. These new techniques are expected to enhance
power of expression of spatial 3D images reconstructed by full-parallax PBHD-CGHs.

ACKNOWLEDGMENTS
The authors thank Prof. Kanaya for his assistance in 3D scan of live faces. The mesh data for the Venus
object is provided courtesy of INRIA by the AIM@SHAPE Shape Repository. This work was supported by the
JSPS.KAKENHI (21500114).

REFERENCES[1] Matsushima, K. and Nakahara, S., “Region segmentation and parallel processing for creating large-scale
CGHs in polygon source method,” Proc. SPIE 7233, 72330E (2009).
Table 1. Summary of parameters of created PBHD-CGHs.
Name

The Metal Venus I

Bear II

Shion

MountainFeatureSpecular surface

Digitized holography

3D scan

Mountain scenery
32K × 32K

64K × 64K

64K × 64K

128K × 64K

Pixel pitchesµm × µm

1.0 × 1.0

1.0 × 1.0

0.8 × 0.8

1.0 × 1.0

Hologram size

mm2

65.5 × 65.5

65.5 × 65.5

105 × 52.4

32.8 × 32.8

Wavelength

nm

633

532

633

633

718

N.A.

2822

919

8.0 c

N.A.

8.6 d

23.0 cNumber of pixels a

Number of polygons b
Computation time

hour

a

1K = 1024bfront-surface onlyc

CPU : XEON E7330 (2.4 G Hz) × 4 (Total 16 processor cores) / Memory : 96 G BytesdCPU : XEON E7540 (2.0 G Hz) × 4 (Total 24 processor cores) / Memory : 256 G Bytes

Publication : SPIE Proc. Practical Holography XXV: Materials and Applications, SPIE#7957, San Francisco, 79571A(2011).

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