Invited Paper

Wavefront printing technique with overlapping approach toward highdefinition holographic image reconstruction
K. Wakunami*a, R. Oia, T. Senoha, H. Sasakia, Y. Ichihashia, K. YamamotoaaNational Institute of Information and Communications Technology, 4-2-1,
Nukui-Kitamachi, Koganei, Tokyo, 184-8795, Japan
ABSTRACT
A hologram recording technique, generally called as “wavefront printer”, has been proposed by several research groups
for static three-dimensional (3D) image printing. Because the pixel number of current spatial light modulators (SLMs) is
not enough to reconstruct the entire wavefront in recording process, typically, hologram data is divided into a set of subhologram data and each wavefront is recorded sequentially as a small sub-hologram cell in tiling manner by using X-Y
motorized stage. However since previous works of wavefront printer do not optimize the cell size, the reconstructed
images were degraded by obtrusive split line due to visible cell size caused by too large cell size for human eyesight, orby diffraction effect due to discontinuity of phase distribution caused by too small cell size. In this paper, we introduce
overlapping recording approach of sub-holograms to achieve both conditions: enough smallness of apparent cell size tomake cells invisible and enough largeness of recording cell size to suppress diffraction effect by keeping the phase
continuity of reconstructed wavefront. By considering observing condition and optimization of the amount ofoverlapping and cell size, in the experiment, the proposed approach showed higher quality 3D image reconstruction
while the conventional approach suffered visible split lines and cells.
Keywords: Holographic optical element, Electronic holography system, Holographic projection

1. INTRODUCTION
For static 3D visualization, 3D models designed by computer graphics (CG) can be printed out as full-color holograms
based on the well-known holographic stereogram (HS) technique [1, 2]. However, HS is based on the recording of denselight-rays and thus, the diffraction effect and spatial/angular sampling of light-rays cause degradation of thereconstructed 3D images, especially target 3D objects/scenes are located far from a hologram plane [3-6]. Therefore,
even holography owns potential to full-control of reconstructed wavefront, HS is not a best technique to record an
arbitrary wavefront of target 3D models. Recently, a new hologram recording technique, called as wavefront printer, hasbeen proposed by several research groups [7-9]. In wavefront printing technique, since digitally designed wavefront of atarget 3D object/scene is optically reproduced by computer generated hologram (CGH) and recorded on the hologram
recording material, ideally an arbitrary wavefront with full-control of both amplitude and phase distribution can berecorded. However, because pixel number of current SLM devices is not enough to display the entire hologram data,
generally an entire hologram data is divided into a set of sub-hologram data and a wavefront of each is sequentially
recorded in tiling manner by using X-Y motorized stage. In this case, phase continuity of recorded/reproduced wavefront
is lost between neighboring sub-holograms due to a lack of positioning accuracy of X-Y motorized stage to wavelengthof recording light and the time incoherence recording. This phase discontinuity causes the image degradation inreconstruction by diffraction effect at each sub-hologram when the size of sub-holograms is too small. On the other hand,
if the size of sub-hologram is too large to the eyesight of observers, the split lines and cells of sub-holograms are visible
and this condition also causes the degradation of reconstructed image quality. For the reconstruction of ideal wavefrontof target 3D object/scene, the optimization of recording conditions such as the size of sub-holograms, the way to
dividing and recording an entire hologram data, should be discussed.

Three-Dimensional Imaging, Visualization, and Display 2016, edited by Bahram Javidi, Jung-Young Son, Proc. of SPIE
Vol. 9867, 98670J · © 2016 SPIE · CCC code: 0277-786X/16/$18 · doi: 10.1117/12.2229517

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2. PROPOSED APPROACH
2.1 Wavefront printing techniquePBS

a 532nm\M

LASER

x -y stagePBS/

HWP: half wave plate
PBS: polarizing beam splitter
SSBF: single -side band filter
SLM: spatial light modulator
SF: spatial filter

SSBF

J (j
--¡ F-f -- I---±---I
l!
SLM

M: mirror

t

SF

M

Hologram
plate

Object beam

Reference beam

Figure 1. The optical setup of our wavefront printerAt first, the wavefront printing technique is briefly introduced. Fig.1 shows the optical system of our wavefront printer.
A collimated light at 532 nm of wavelength is split by polarization beam splitter (PBS) and then, two beams will form an
object beam and a reference beam to record a sub-hologram as a reflection-type volume hologram. An object beam ismodulated to a wavefront of a part of target 3D objects/scene by sub-hologram data displayed on a spatial light
modulator (SLM). Undesirable lights: non-diffraction light and conjugate light, are filtered by single-side band filter andhalf-zone plate method [10] in the same manner of our electronic holography systems [11, 12]. Then the reduction
optical system demagnifies the modulated wavefront on a holographic recording film cobestro Bayfol®HX-102
photopolymer material. A reference beam is formed plane wave and is incident to a holographic recording film from the
opposite side of an object beam. Table 1 shows the main parameters of our wavefront printer. Because the pixel numberof current SLM is not enough to reproduce an entire wavefront for practical use, the entire hologram data is divided into
a set of sub-hologram data and wavefront of each is recorded sequentially in tiling manner by using motorized X-Y stage.
After the recording process of all sub-holograms, holographic recording material is then processed by the bleaching so as
to own high transmission at visible light wavelength [13].
Table 1. The main parameters of our wavefront printer.

Parameter

Design value

Wavelength of laser

532 [nm]

Pixel number of sub-hologram

3,600 × 1,800 [pixel]

Pixel pitch of SLM

3.5 [μm]

Magnification of reduction optical system

0.10

Hologram recording material

Cobestro, Bayfol®HX-102

2.2 Image degradation due to the phase discontinuity and the visible sub-hologram cells
Within a sub-hologram region, the arbitral wavefront reproduced by CGH can be recorded. However the dividing
process of the entire hologram causes the phase discontinuity at the split lines of each sub-hologram due to a lack ofpositioning accuracy of X-Y motorized stage and also the time incoherence recording of them. Because of this phase
discontinuity, the reconstructed image will be degraded by undesired diffraction effect. Here let us consider the required
size of phase continuity defined by the size of a sub-hologram to avoid the image degradation under the supposed
observing condition. The required size of phase continuity SP is denoted as the size on the hologram plane in which thereproduced wavefront will be incident to the pupil of the observer’s eye (See Fig.2). We suppose that the target object

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point is ZT behind and observing point is ZO in front of the hologram plane. When the pupil size of the observer’s eye issupposed to be DP, required size of phase continuity area SP is derived as follow:

SP =DP ⋅ Z T
ZT + Z O.

(1)

If the target point is in front of the hologram, ZT becomes negative value. Even an entire hologram data is divided into a
set of sub-hologram data of the size of SH, under the following condition, the phase continuity of reconstructed
wavefront on the hologram is ensured to the observer, i.e. observers do not recognize the image degradation due to thediscontinuity of recorded/reproduced wavefront by the divided hologram. The required condition is
Condition 1: S P ≤ S H .

(2)On the other hand, if the size of sub-hologram is larger than the spatial resolution of observer’s eyesight, observers willrecognize them and the visible cells and split lines will degrade the image quality. Let us consider how size of subhologram is resolved by the supposed observing condition with taking visual acuity into account. Here θE is denoted as
the angular size of the smallest detail observer’s eyesight can resolve. On the hologram plane, the size SE, observers canrecognize the detail, is derived as follow:

SE ≈ ZO ⋅θ E .

(3)

To set the size of sub-holograms smaller than the resolution of observer’s eyesight, i.e. sub-hologram cells and split linesof them are not visible, the following condition should be satisfied,
Condition 2: S E ≥ S H .

(4)Hologram plane
Dp

Target point

,. Sp

<

<

if
>1'

Zo

Zr
(a)

T
Z0

(b)

Figure 2. The required cell size of sub-holograms from the viewpoint of two main factors. (a) SP denotes the required sizeof phase continuity of wavefront incident to the eye pupil of the observer. (b) SE denotes the spatial resolution that isdefined by using the angular size θE of the smallest detail observer’s eyesight can resolve.

To satisfy both conditions 1 and 2 to the size of sub-hologram, the image degradation due to the factors discussed above
can be suppressed. However, in some practical situations, it is difficult to satisfy both conditions 1 and 2 at the sametime. For example, under the following situation that ZT = 100 mm, ZO = 1,000mm, DP = 5.0 mm and θP = 1/60 degrees(= 60/60 of the visual acuity), SP and SE became almost 0.5 mm and 0.3 mm, respectively. It is clear that the conditions 1
and 2 are conflicting. Therefore any overcoming recording approach to satisfy both conditions is required for highquality 3D image reconstruction.

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How about placing the objects in front of the hologram plane?
2.3 Overlapping approach
In this paper, we propose an overlapping approach of recording cells to make it small enough of apparent cell size toobservers with still keeping the phase continuity of reconstructed wavefront to the supposed observing condition. Fig.3
shows the concept of proposed approach. Now the entire hologram data is divided into M × N of sub-hologram dataconsidering an overlapping mentioned later. The first exposure of sub-hologram cell (0, 0) is executed on the hologram
recording film with the cell size of SH. In the region of one exposure (gray area in Fig.2), since the recorded wavefront ofobject light is reproduced from a single SLM, continuity of phase distribution in this region is ensured. Next exposure
position of sub-hologram cell (1, 0) is shifted by DS from sub-hologram cell (0, 0) to X-axis. After recording M times of
sub-holograms to X-axis with same shift value DS, the exposure position of sub-hologram cell (0, 1) is shifted DS to Yaxis. Then M times of exposure of second line are executed. A repetition of N lines of exposures in the same manner as
the first line, the entire hologram can be recorded on the hologram recording film. In the overlapping approach, thephase continuity of wavefront is ensured within the cell size SH, and the appearance cell size becomes at DS. Therefore,both parameters can be set independently, and to optimize DS smaller than SH, it is possible to keep both conditions 1 and2. For simple example, if SH is set at 0.6 mm and DS is set at 0.3 mm, that is a half of SH, the conditions 1 and 2 can besatisfied in the example situation described in 2.2.

(0, 0)(M-1, U;(1, 0)Y

Figure 3. The concept of the overlapping approach. The size SH within the phase continuity is kept and the apparent cell size
DS can be set at different values independently.

3. EXPERIMENTS
3.1 Verification of overlapping approach
To confirm the effect of overlapping approach, we recorded two holograms by proposed approach and general wavefront
printing technique without overlapping of sub-holograms. At first, the entire hologram data was generated based on theholographic stereogram technique [14]. Two 3D objects: the statue of Venus and the characters “NICT” were set behindthe hologram and 320 × 320 of perspective images at 256 × 256 pixels were rendered by using the software blender(https://www.blender.org/). The front view image of target 3D scene is depicted in Fig.4 (a). A set of perspective images
was then calculated its Fourier spectrum by using fast Fourier transform (FFT) algorithm and the interference patterns ofthem with reference light were tiled to form the entire hologram data. Total pixel number of hologram data was 81,920 ×
81,920 pixels. All of hologram calculation processes from a set of perspective images were executed on the
supercomputer TSUBAME2.5 provided by GSIC center in Tokyo Institute of Technology [15].

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The entire hologram data was then divided into a set of sub-hologram data for the wavefront printing. Both overlapping
approach and non-overlapping approach, sub-hologram data is set at 3,600 × 1,800 pixels. In the proposed approach, half
region of overlapping to X and Y axes was employed in the dividing process and thus the total number of sub-holograms
was 45 × 91. Because of magnification of reduction optical system of SLM in the wavefront printer, the size of subhologram on the hologram recording film became 1.2 × 0.6 mm. Since the overlapping to X and Y axes in the proposed
approach, the appearance cell size to the observer became 0.6 × 0.3 mm. Therefore, to Y axis, both conditions 1 and 2
discussed in 2.2 were satisfied theoretically to the example situation described in 2.2. In the conventional recording case,the total number of sub-holograms was 22 × 45 because of non-overlapping, and both recording cell size and theappearance cell size were at 1.2 × 0.6 mm. This means that the phase continuity of wavefront to the observer, thecondition 1, could be satisfied but the appearance cell size was too large to the same observing situation in 2.2.
Table 2. Main parameters of the experiment.

Parameter

Design value

Wavelength of laser

532 [nm]

Pixel number of the entire hologram data

81,920 × 81,920 [pixel]

Number of sub-hologramswith overlapping / without overlapping

45 × 91 / 22 × 45

Size of the entire hologram

29.4 × 29.4 [mm]14,9(a) original CG data(b) non -overlapping(c) with overlapping

Figure 4. Front view images of original 3DCG data and the optical experimental results.

Fig. 4 (b) and (c) show the results of optical reconstruction of proposed method and the conventional method without
overlapping of sub-holograms. It is clear that the case of proposed method (c) reproduced seamless and non-visible
cells/split lines of sub-holograms while the conventional case (b) suffered from visible cells that degrades the image
quality.
3.2 Large size of wavefront printing at over 77 billion samplings by overlapping approach
For high definition holographic reconstruction, hologram size is also important factor for the practical use. We
calculated the hologram data of the wavefront at 10 × 10 cm, and printed out them by wavefront printing technique withoverlapping approach. The hologram calculation was executed in the same manner described in 3.1. Because the pixel
number of hologram data became as large as 278,528 × 278,528 samples, we divided the entire hologram to 17 × 17
elements and calculated them independently by using multiple CPUs on the supercomputer TSUBAME2.5. Fig. 5 shows
the scheme of wavefront printing of 10 × 10 cm hologram. We calculated the hologram data of the real object: theminiature stature of “Buddha” and the virtual CG data “Venus”. In the case of “Buddha”, 47 of multi-view images weretaken from random positions by the camera and then the pictures were combined to generate 3D CG data on the software
123D catch [16].

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Case 2: Target is a virtual object

Case 1: Target is a real object"Venus"Step O. take multi -view images

Step 1. Design 3D CG dataa4v

4 114vii
1!-%+.1(1oa A part of multi-view images of,.gioo,.,1"Buddha""Venus"Step 2. Render a set of multi-view image

Step 1. Generate 3D CG data

Step 4. Print out the hologramby wavefront printer with overlapping approach

Supercomputer
TSUBAME2.5
in Tokyo Inst. of Tech.

Step 3. Calculate the hologram data
at 278,528 x 278,528 samples

Figure 5. The scheme of wavefront printing at the size of 10 × 10 cm of hologram of a real/virtual object.

Table 3. Main parameters of hologram printing at the size of 10 × 10 cm.

Parameter

Design value

Wavelength of laser

532 [nm]

Pixel number of the entire hologram data

278,528 × 278,528 [pixel]

Number of sub-holograms with overlapping

154 × 309

Size of the entire hologram

100 × 100 [mm]Number of multi-view images

544 × 544

Pixel number of a view image

512 × 512 [pixel]

Fig.6 shows the results of recorded holograms with overlapping approach. Both real and virtual objects weresuccessfully printed out on the holograms at the size of 10 × 10 cm. Fig.4 (a) shows the comparison between the newhologram of “venus” and the hologram recorded in the previous experiment described in 3.1. Because the recorded

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holograms own the wavelength selectivity as a principle of reflection-type volume hologram, the holograms could bereconstructed by using the white illumination light source. The recorded holograms also own high transmission to thevisible light after the bleaching process (see Fig.6 (b)).

(b)

(a)

(c)

Figure 6. The results of optical reconstruction. (a) Comparison between the holograms at the size of 10.0 × 10.0 cm and 2.9
× 2.9 cm. (b) and (c) The optically reconstructed image of “Venus” and “Buddha”.

4. DISCUSSIONS AND FUTURE WORKIn the overlapping approach, sub-holograms were multiply recorded on the hologram recording film. This multiple
exposures caused the decreasing of the diffraction efficiency (D. E.) due to the finite dynamic range of the recording
material. To avoid undesirable decreasing of D.E., we will handle to establish the optimization of overlapping
parameters that takes the number of overlapping into account. Full-color wavefront printing will be also focused on in
our future work.

ACKNOWLEDGMENT
This work was supported by JSPS KAKENHI Grant Number 26790064. This work was supported by JSPS KAKENHI
Grant Number 16H01742. This research is supported by the Center of Innovation Program from Japan Science andTechnology Agency, JST. The numerical calculations were carried out on the TSUBAME2.5 supercomputer in theTokyo Institute of Technology.

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