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Transcript
Wide viewing angle holographic display with a multi spatial light
modulator array
Grzegorz Finke, Tomasz Kozacki, Małgorzata Kujawińska
Warsaw University of Technology, Institute of Micromechanics and Photonics,
8 Sw. Andrzeja Boboli St., 02-525 Warsaw, Poland
ABSTRACT
In the paper we present the design of a wide viewing angle display system capable of displaying digital holograms
captured in a rotary CCD configuration. We have discussed the two possible configurations of multi LC SLMs system:
with a normal LC SLM illumination and with tilted LC SLMs and parallel illumination. The second system was selected
and the tilted plane algorithm, necessary for recalculation of displayed holograms was tested. Finally we have presented
and discussed different means of visual perception of holographic images: with an asymmetric diffuser and with an
eyepiece.
Key words: digital holography, spatial light modulators, 3D displays, tilted plane algorithm
1. INTRODUCTION
Human's natural world perception is three dimensional. No wonder that people want to transfer the third dimension
into entertainment such as TV, cinema or computer games and please their eyes with 3D images. The main idea of
underpinning the 3D experience is that of stereoscopic vision [1]: an observer when viewing a scene sees two slightly
displaced versions of that scene with the left and right eye. Next brain is processing this information and creates a 3D
image. More detailed information about this approach to 3D display devices can be found in [2]. One of the techniques
which allows us to see 3D images is holography. The recording process allows to capture full object wave front
information – its amplitude and phase. Having this information it is possible to reconstruct the optical wave field in
another place and another time [3], using spatial light modulators (SLM). Recreating the full wave field is the only way
by which an observer would be exposed to the same scene that had been recorded.
However, as traditional version of holography gives very good results in this area, thanks to excellent resolution of
holographic films, its digital equivalent sill has a lot to catch up. Usually captured digital holograms were displayed on a
single SLM [4]. However this realization has not fulfilled satisfactory requirements connected with an expectation of a
wide angle optoelectronic reconstruction. This is caused by some SLM limitations. A limited pixel pitch of SLM causes
problems with resolution of displayed holograms which further on delimits the angular view-ability of reconstructed
images. Furthermore a relatively large pixel size results in small parallax, which has crucial meaning for good viewing
quality of 3D objects. Recently several attempts have been made to enhance these features by employing innovative
optoelectronic modules which are adopted to generate a large number of data points [5] or to increase holographic
display angular view ability [6,7].
In this paper we present a holographic display configuration where multiple SLMs aligned in circular configuration
are put to work together. Such configuration of holographic display allows to increase the viewing angle in horizontal
direction and thus to increase the horizontal parallax. The system is based on liquid crystal on silicon high definition
spatial light modulators (LC SLMs). In the paper we discus the final setup arrangement and present results obtained from
two SLMs. The discussion of linking multi CCD digital holographic capture with LC SLM based display system is
presented, allowing in future to display holograms captured for real world objects.
Optics, Photonics, and Digital Technologies for Multimedia Applications, edited by Peter Schelkens,
Touradj Ebrahimi, Gabriel Cristóbal, Frédéric Truchetet, Pasi Saarikko, Proc. of SPIE Vol. 7723,
77230A · © 2010 SPIE · CCC code: 0277-786X/10/$18 · doi: 10.1117/12.855778
Proc. of SPIE Vol. 7723 77230A-1
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2. CAPTURE SYSTEM
The capture system is based on principals of digital holography [8]. Spherical coherent wave illuminates the
imaged object and creates an object wave. The holographic fringes as a result of interference of an object wave with a
plane reference wave are captured by CCDs at detectors' planes. Although a progress has been made in a CCD
technology, i.e. decrease of pixel size and increase of pixel number, still there are not sufficient to register an object
wave scattered from different object perspectives using one CCD camera only. That is why in order to increase viewing
angle, a multi camera system is applied to registers separate perspectives. The cameras are positioned with their normals
pointing toward an object. Otherwise an object wave which goes at certain angle might not fill the whole detector area
or might not be captured due to its high frequency content. This in result will cause the loss of information. This
discussion shows that a circular configuration for multi camera system fits the best to our requirements (Fig.1) and
allows to use optimally entire CCD area.
Fig.1. The setup of a multi CCD digital capture system.
For real objects capturing, the knowledge of geometry of registering setup (e.g. angular and linear separation of
CCDs, pixel pitch, wave length, etc.) is very important from a reconstruction point of view, because this configuration
has to be copied during the reconstruction process. This means that each SLM used in reconstruction process should
recreate the same wave field as the one captured by a corresponding CCD camera during registration (with proper
magnification)
In our work we applied Fresnel, on axis, phase shifted digital holograms (PSDH). The previous experiments [9] had
clearly shown that such holograms allows to utilize in the best way a field spatial bandwidth product. Other techniques
have additional holographic orders, twin images which on the whole result in limited resolution or size of the
reconstruction or, like in the case of Fourier holograms, do not give 3D perception. The application of a phase shifting
technique allows to remove zero order (which for example in Fourier holograms had strong influence on a quality of
reconstructions) and a twin image [10].
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3. RECONSTRUCTION SYSTEM
The reconstruction system (display) utilizes six Liquid Cristal on Silicon Spatial Light Modulators (LC SLM,
model HEP 1080 P) which are illuminated by plane waves. The LC SLMs used in our setup are phase modulators
working in high definition and with a pixel pitch of 8μm square.
As mentioned before the reconstruction system should comply with a registration one. Thus the first assumption
about the SLMs' configuration was to illuminate them along their normals (Setup 1) (Fig.2). This way the direction of
reflected beams from SLMs will be the same as direction of a wave field recorded by CCDs. As a result the holographic
image with multiple perspective (multiple SLM) will be reconstructed according to the capture system
Fig.2. The scheme of a reconstruction configuration with illumination along LC SLMs' normals (Setup 1).
However this type of solution occurred to be complicated in its experimental realization since it was necessary to direct
each illumination beam at a specific angle. Because of that we decided to tilt our SLMs and illuminate them with parallel
beams (Setup 2) as shown in Fig.3. This gives substantial system flexibility in order to generate holographic images for
different reconstruction distances of for various SLM angular separation.
Fig.3. The scheme of a reconstruction configuration with parallel illumination (setup 2)
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In this configuration, since SLMs are arranged on an arc with radius which is two times bigger than the reconstruction
distance with illumination going along its optical axis, an image will appear in its focal.
Both presented configurations with their geometrical features are compared in Table 1. We have examined two
factors - angular orientation of a marginal SLM and angular separation between two adjacent SLMs. The calculations
have been made for three different reconstruction distances with an assumption of a 0.35 fill factor. By the statement of
"fill factor" we mean the ratio of angular dimension of an active LC SLM area to angular separation of SLMs. This fill
factor was calculated by examining the geometrical dimensions and an alignment of CCD cameras in a capture system.
In final reconstruction setup, of course, the display fill factor should comply with the fill factor of registering setup.
Table 1. Comparison of the LC SLM working conditions required for setup 1 and 2
Fill factor W: 0.35 (16.6/47.43)
Rec. Distance R
400mm 600mm
SETUP 1
Angle of
20.286° 13.560°
Normal illumination marginal SLM γ
system
Angular
6.767°
4.520°
separation SLM α
SETUP 2
One direction of
illumination
800mm
10.176°
3.393°
Angle of
marginal SLM γ
10.176°
6.789°
5.094°
Angular
separation SLM α
6.767°
4.520°
3.393°
As it can be seen from the table, the angle of the marginal SLM in the first configuration is two times greater than in the
second one, which in the final result effects a bigger dimension of the setup. This feature as well as simpler illumination
system of the setup 2 decided about the choice of the second setup for the reconstruction system. However the preferred
setup 2 differs substantially from registration configuration. The SLM planes do not coincide with capturing CCD
matrixes. Therefore using the setup 2 we have to recalculate holograms so that they will fit the new geometry. To do this
we have developed a tilted plain algorithm, which is described in section 4.
Also some other geometrical and optical parameters of both systems (capture and display) are different. There
are usually differences in pixel sizes and their numbers, also different wavelengths may be used for capture and display.
We have to consider this effect while linking both systems. This mismatch between hologram's properties and our system
effects optical reconstruction in two ways [11]:
- it modifies the distance of reconstruction plane to SLM plane according to the equation:
z
z
(1)
where zreg is distance between object and detector, λreg/rec is a wave length used during registration and reconstruction
respectively, Δreg/rec is a pixel size of CCD and SLM respectively.
- it modifies the transverse magnification by the factor of:
∆
∆
(2)
Holograms registered for real objects may also have some errors which can be introduced due to instability during the
capture or the phase step error. To avoid them in this paper we study the reconstruction of computer generated
holograms, designed to match the features of our setup.
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4. TILTED PLANE ALGORITHM
The tilted plane pprocedure shall transfer com
mplex opticall field from normal plane ((capture geom
metry) to tiltedd
plane configu
uration, takingg into accountt tilted plane wave illumination. The system geometrry built into th
he tilted planee
algorithm is shown in Figg.4. The algoorithm process a captured optical field so that both configuration
ns (a) and (b)
f
ons.
presented in fig.4
will prodduce the same reconstructio
The procedure off tilted plains w
was tested on
n two SLMs for
f a tilt anglee in the range 2-10o with a 2o incrementt.
w
spectrum
berg Saxton allgorithm [12] and a plane wave
m
We have gen
dified Gerchb
nerated synthettic hologram using the mod
decompositio
nerated for tw
wo objects loccated in two longitudinally
y
gram was gen
on propagationn method [133]. The holog
separated by 3 cm planes. O
UT".
y two phrasess "REAL 3D" and "BY WU
Objects were represented by
In Fiig.5 the resultts of optoelectronic reconsttruction, with the recordingg camera focuused at the first (left image)
and the secon
0o) illustrates the quality off the reconstru
uction of nonnd (right imagges) plane, aree shown. The first image (0
ologram was pprocessed witth algorithm of
processed hologram, displayed at a non
n
o propagation
n-tilted LCoS. Next the ho
yed at a tilted SLM. The deeveloped alggorithm is bassed on a planee
between tilted
d planes, as sshown in fig.44 and display
wave spectru
h
um decomposiition between tilted planes [14]. Normallly it would reesult in an inccrease off spattial bandwidth
product, sincce we get deccreased pixel size and increased numbeer of pixels, which effectss on getting off
d.
o axis field
m field extension [15], so w
However in our
o case there is no necessitty of spectrum
we process onlly the on-axis field and as a
result we obttain field of the same spaatial bandwidtth product as the input onne. The hologgram calculateed in the way
y
described abo
o
ove was displlayed on the tilted LCoS aand the resultts of its reconnstruction aree presented att the next two
w
images (2o,10
correcctly and the setup 2 can bee
0o) in fig.4. Itt is clearly seeen that the tiilted plane prrocedure is working
implemented without introducing errors into a reconsttructed image.
Fig.4. The systtem geometry cconsidered in thhe tilted plane allgorithm a) illu
umination alongg SLM's normall, b) illuminatio
on of tilted SLM
M
Fig.5. Compaarison of reconsstructions of a ssynthetic hologrram with and without
tilted plaane algorithm, captured with a CCD camera.
w
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5. OBSERVATION SYSTEM
The SLM due to its large pixel size produces on axis field only. It gives very good quality real images which
can be easily captured with a CCD camera, however in our system we want to view the reconstructed images with eyes.
Human eyes give 3D perception due to their horizontal separation, therefore our holographic image can give 3D
perception for horizontal separation of the eyes only. For viewing images we will use an asymmetric diffuser, which
diffuses field in one direction (fig.6) only, giving convenient observation conditions. This solution enables to see 3D
scene, however the apertures in vertical direction are matched only. Due to horizontal non matching of apertures the
vertical slices of the object appear. Also some noise caused by the diffuser is present. Exemplary reconstructions are
shown in Fig.7. The noises can be limited by using an illumination source with limited coherence [16]. However the size
of the source shall not decrease contrast of a holographic image [17].
Fig.6. The scheme of reconstruction system with two LC SLMs and an asymmetric diffuser: λ/2 - half wave plate; L1 - converging
lenses; BS - beam splitters; LCoS - HEO 1080P; AD - asymmetrical diffuser.
Fig.7. Optical reconstructions of the hologram viewed at an asymmetrical diffuser and captured by a digital camera located at
different horizontal positions
The reconstruction setup consists of a laser (wavelength 532nm) and two LC SLMs illumination system. The beam
travels through a half wave plate, which sets a proper polarization needed for the best quality of reconstructed
holograms. The polarization is aligned according to LC SLM molecules. A set of pinhole (diameter 5μm), and a
collimating lens generate plane wave illumination. Next a plane wave is divided by a beam splitter, so that two SLMs are
illuminated. One of the SLMs is tilted at an angle of 2o, while the second one is illuminated along its normal. The
asymmetrical diffuser AS is placed in a holographic image plane.
The images in Fig. 7 illustrate how the image changes with the side-movement of a digital camera which
simulates horizontal movement of a head. Both parts of an object (“REAL3D” and “by WUT”) were separated with a
3cm distance in longitudinal direction.
We had considered also another holographic image observation setup in which the observation was performed
through an eyepiece (Fig. 8). This method provides minimum mismatch of apertures of the object wave and an eye and
gives us the best quality of reconstructions so far. Unfortunately small exit pupil causes non convenient viewing
conditions. We have to position properly our eyes to see reconstructed images - eye diaphragm has to be positioned at
Proc. of SPIE Vol. 7723 77230A-6
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holographic display exit pupil. Figure 9 presents some exemplary reconstructions, registered by a digital camera
simulating visual human perception of holographic image.
Fig.8. The scheme of reconstruction system with two LC SLMs and an eyepiece: λ/2 - half wave plate; L1 - collimating lens;
L2 - converging lens (eyepiece); BS - beam splitters; LCoS - HEO 1080P.
0o
2o
Fig.9. Optical reconstruction of the hologram viewed through an eyepiece and captured by a digital camera located at different
horizontal positions
Through both experiments (Fig.7 and Fig.9) is clearly seen that by adding the second SLM we are able to increase the
viewing angle. What is more, an overlapping of two parts of 3D object is noticeable with the horizontal movement of a
camera (eye).
6. CONCLUSIONS
In the paper we have presented the design of a wide viewing angle display system capable of displaying digital
holograms captured in a rotary CCD configuration. We have discussed the two possible configurations of multi LC
SLMs system. The first one with a normal LC SLM illumination and the second one with tilted LC SLMs and parallel
illumination. The second solution gives a simpler setup, however it requires processing of captured holograms. Therefore
we have developed a tilted plane algorithm, necessary for recalculation of holograms. Finally we have presented
different means of visual perception of holographic images: with an asymmetric diffuser and with an eyepiece.
7. ACKNOWLEDGMENTS
The research leading to these results has received funding from the EU 7th Framework Programme FP7/20072013 under agreement 216105 ('Real 3D' Project).
Proc. of SPIE Vol. 7723 77230A-7
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8. BIBLIOGRAPHY
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