OSA Topical Meeting on Digital Holography and Three-Dimensional Imaging 2009, Vancouver, PDWB38(2009.4)

A High-Definition Full-Parallax CGH Createdby the Polygon-Based Method
1Kyoji Matsushima1 and Sumio Nakahara2

Department of Electrical and Electronic Engineering, 2Department of Mechanical Engineering
Kansai University, Yamate-cho 3-3-35, Suita, Osaka 564-8680, Japan.
matsu@kansai-u.ac.jp

Abstract: A large-scaled full-parallax CGH with 4 billion pixels is produced by a polygon-based
method. The CGH reconstructs a fine 3-D image and gives a large sensation of depth owing to thesilhouette-masking technique.
©2007 Optical Society of America
OCIS codes: (090.1760) Computer holography; (090.2870) Holographic display

1. Introduction
The technology of computer-generated holograms (CGH) has a long history. The technology is the counterpart ofcomputer graphics in 2D images and sometimes expressed as an ideal 3D technology. However, CGHs were just thesubject of academic research and could not produce yet fine 3D images with a large sensation of depth.
Such fine CGHs commonly require a large viewing-zone and image size. Both of them lead to a large pixel size.
However, conventional “ray-oriented” point-based methods are much time-consuming especially in full-parallax
and hidden-surface-removed CGHs. Therefore, it is not easy to produce such fine CGHs by the point-based
methods.
One of the authors has proposed “wave-field oriented” polygon-based method [1] to get over the limits of thepoint-based methods. In this new technique, the object is composed of some polygonal facets; polygons. Eachpolygon is regarded as a surface light source and the object field is computed by totaling the light from polygons.
Several researchers have also proposed improving our method to compute faster at the sacrifice of texture mappingand uniform diffusiveness [2,3].
Occlusion is one of the most important mechanisms in the perception of 3D scenes. To add an effect of mutual
occlusion to the reconstructed 3D scene in CGHs, light shielding by obstacles must be realized in calculating object
fields. This is also one of weak subjects of point-based methods. Since numerical propagation of wave fields is usedin polygon-based methods, such light shielding is simply achieved by the silhouette masking technique [4].
This investigation is intended to produce CGHs reconstructing truly fine 3D images by combination of these
new techniques and fabrication using laser lithography system.
2. Setup of 3D scene of “The Venus” CGH
The CGH created is named “The Venus” because the object given by a set of mesh data is similar to the famous
statue of the Venus of Milo. In addition, wallpaper that is a binary check pattern is placed behind the Venus statue toenhance observer’s sensation of depth. Geometry and dimensions of the objects are shown in Fig. 1. Some detailed
parameters of the hologram and objects are summarized in Table 1.

Venus statue

6.5cm(3D object)
6.5cm

Wallpaper

6.5cm(2D image)
5.8 cm

15cm
Intermediate plane

6.5cm

Hologram
15cm

Fig. 1. Schematic geometry of “The Venus” CGH.

OSA Topical Meeting on Digital Holography and Three-Dimensional Imaging 2009, Vancouver, PDWB38(2009.4)

Table 1. Parameters used for creation of the CGH
Hologram
Pixel sizes
65,536 × 65,536 pixels
Pixel pitches
1 μm × 1 μm
Hologram type
Binary amplitude
Reconstruction wavelength632.8 nmVenus stature
Number of visible polygons (front-face only)
718
Dimensions (W × H × D)
26.7 × 57.8 × 21.8 mm3
Wallpaper
Pixel sizes of texture image
256 × 256 pixels
Dimensions (W × H)
65.5 × 65.5 mm2
3. The polygon method for calculating the field of the 3D object
The polygon method used for calculating the wave field of the Venus object is summarized in Fig. 2, where a cubic
object shown in (a) is used as an example. The surface function for the polygon #2, defined in the local coordinates
peculiar to the polygon #2, is shown in (b). The amplitude and phase distribution give the shape and diffusiveness ofthe polygon, respectively. The surface function is transformed into the wave field in the global coordinates ( xˆ , yˆ , zˆ ) ,in which the hologram is placed in ( xˆ , yˆ , 0) plane, by using the rotational transformation [5] and spectrum
remapping [1]. Here, the transformation matrices between the local and global coordinates are obtained by theRodrigues’ rotation formula.
L o c a lC u b ic o b je c t
c o o r d in a t e sy 23y^2
1G lo b a l
c o o r d in a t e sx^z^x 2Oz2y^N

A m p lit u d e(a )P h a s e

A m p lit u d ex^

(b )

(c )

Fig.2. A summary of the polygon method: (a) an object model, (b) the surface function of the polygon #2 in thelocal coordinates, (c) the amplitude image of the resultant wave field in global coordinates.

The wave field of the 3D object is obtained in an intermediate plane by totaling fields of all polygons of the 3Dobject. The intermediated plane is parallel to the hologram and slices the object at the center as shown in Fig. 1.
There are two reasons why the object field is temporally calculated in the intermediate plane. First, calculating theobject field in the intermediate plane is faster than doing in the hologram plane, because the polygons are closer tothe intermediate plane than the hologram one. Since polygon fields are not diffracted so much in the intermediate
plane, the area for calculating the polygon field is much smaller than that in hologram plane. Secondly, lightshielding of the wallpaper field is necessary for avoiding phantom image of the 3D object, as explained in thefollowing section.
4. Generating the wallpaper field and its shielding by thesilhouette masking techniqueSince wallpaper is parallel to the hologram, the wave field issimply generated by multiplying oversampled and pixel-increased
texture image by a diffuser phase. The generated field should benumerically propagated to the hologram plane. However, if thewallpaper field is simply propagated and added to the field of the3D object, the 3D object would be reconstructed as a phantom
image, because simple superposition involves light transmissionof the 3D object. To shield wallpaper behind the 3D object, the(a)(b)

Fig. 3. The masked wave field of wallpaper (a) and thecombined wave field (b) in the intermediate plane.

OSA Topical Meeting on Digital Holography and Three-Dimensional Imaging 2009, Vancouver, PDWB38(2009.4)

propagation process should be divided into two steps. The wallpaper field is first propagated to the intermediatedplane in which the field of the 3D object is obtained and then masked with the silhouette of the 3D object, as shownin Fig. 3 (a). After the 3D object field is superimposed on the masked wallpaper field as in (b), the combined field isfinally propagated to the hologram plane.
5. Computation and fabrication
The CGH was calculated by using a PC with 4 CPU of AMD Opteron 852 (2.6GHz) and 32 G Bytes RAM. Total
computation time was approximately 45 hours. Longest time was consumed in a double numerical propagation. The
amount of computation time for propagation was 37 hours and accounted for 82% of total computation time, whiletime for producing the 3D object field was 7.6 hours. The CGH was fabricated by DWL 66 laser lithography system
made by Heidelberg Instruments, GmbH.
6. Optical reconstruction and conclusion
We created a high-definition full-parallax CGH of 3D object by using the polygon-based method and the silhouettemasking technique. Photographs of its optical reconstruction, taken from various camera angles, are shown in Fig. 4.
The 3D surface object with shade is clearly reconstructed and occludes light from wallpaper. As a result, theproduced CGH gives a strong sensation of depth and reconstructs the fine 3D image.
7. Acknowledgement
The mesh data of the Venus object is provided courtesy of INRIA by the AIM@SHAPE Shape Repository.
8. References[1] K. Matsushima, “Computer-generated holograms for three-dimensional surface objects with shade and texture,” Appl. Opt. 44,4607–4614(2005).
[2] L. Ahrenberg, P. Benzie, M. Magnor, and J. Watson, “Computer generated holograms from three dimensional meshes using an analytic lighttransport model,” Appl. Opt. 47, 1567–1574(2008).
[3] H. Kim, J. Hahn, and B. Lee, “Mathematical modeling of triangle-mesh-modeled three-dimensional surface objects for digital holography,”Appl. Opt. 47, D117–D127(2008).
[4] A. Kondoh and K. Matsushima, “Hidden surface removal in full-parallax CGHs by silhouette approximation,” Systems and Computers inJapan 38, 53–61(2004).
[5] K. Matsushima, “Formulation of the rotational transformation of wave fields and their application to digital holography,” Appl. Opt. 47,
D110-D116(2008).

(c) High(a) Left(b) Right(d) Low
Fig. 4. Photographs of optical reconstruction of “The Venus” CGH.