3-D Holographic Display Using Strontium Barium Niobate ARL-TR-1520 February
An innovative technique for generating a three-dimensional holographic display using strontium barium niobate (SBN) is discussed. The resultant image is a hologram that can be viewed in real time over a wide perspective or field of view (FOV). The holographic image is free from system-induced aberrations and has a uniform, high quality over the entire FOV. The enhanced image quality results from using a phase-conjugate read beam generated from a second photorefractive crystal acting as a double-pumped phase-conjugate mirror (DPPCM). Multiple three-dimensional images have been stored in the crystal via wavelength multiplexing.
by Christy A. Heid, Brian P. Ketchel, Gary L. Wood,
Richard J. Anderson, and Gregory J. Salamo
3-D Holographic Display Using
Strontium Barium Niobate
ARL-TR-1520 February 1998
Approved for public release; distribution unlimited.
The findings in this report are not to be construed as an official Department of
the Army position unless so designated by other authorized documents.
Citation of manufacturer’s or trade names does not constitute an official
endorsement or approval of the use thereof.
Destroy this report when it is no longer needed. Do not return it to the originator.
Army Research Laboratory
Adelphi, MD 20783-1197
ARL-TR-1520 February 1998
3-D Holographic Display Using
Strontium Barium Niobate
Christy A. Heid, Brian P. Ketchel, Gary L. Wood
Sensors and Electron Devices Directorate, ARL
Richard J. Anderson
National Science Foundation
Gregory J. Salamo
University of Arkansas
Approved for public release; distribution unlimited.
Abstract
An innovative technique for generating a three-dimensional holographic
display using strontium barium niobate (SBN) is discussed. The resultant
image is a hologram that can be viewed in real time over a wide perspective
or field of view (FOV). The holographic image is free from system-induced
aberrations and has a uniform, high quality over the entire FOV. The
enhanced image quality results from using a phase-conjugate read beam
generated from a second photorefractive crystal acting as a double-pumped
phase-conjugate mirror (DPPCM). Multiple three-dimensional images have
been stored in the crystal via wavelength multiplexing.
ii
iii3
Contents
1. Introduction .......................................................................................................................... 1
2. Theory .................................................................................................................................... 2
3. Experimental Setup ............................................................................................................. 5
3.1 Holographic Display ...................................................................................................................... 6
3.2 Image Storage................................................................................................................................. 9
4. Conclusions ......................................................................................................................... 11
Acknowledgements ................................................................................................................. 11
References ................................................................................................................................. 12
Distribution .............................................................................................................................. 13
Report Documentation Page .................................................................................................. 17
Figures
1. Dynamic holography in photorefractive crystals via four-wave mixing.................................... 2
2. Experimental setup used to record and reconstruct a 3-D hologram using SBN ...................... 5
3. 3-D hologram stored in a Ce-doped SBN:60 photorefractive crystal and viewed at various
angles with an FOV of ~14° ............................................................................................................... 7
4. Method of measuring expected FOV for recording a hologram in a crystal of
length Lc .................................................................................................................................................................................... 7
5. Hologram stored in a mosaic of two Ce-doped SBN:60 photorefractive crystals with an FOV
of ~30° ................................................................................................................................................... 8
Tables
1. Relative powers of writing and reading beams used to study wavelength multiplexing in
SBN ........................................................................................................................................................ 9
1
1. Introduction
Present holographic displays, such as those generated by computers or
emulsion films, usually require intermediate preprocessing or postprocessing
and are, therefore, not capable of real-time production and
viewing and have limited information storage capacity. The use of photorefractive
crystals, such as strontium barium niobate (SBN), as a holographic
storage medium eliminates these and other limiting factors. For
example, when a photorefractive storage medium is used, holograms may
be recorded and projected without time-consuming processing and with
greater storage capacity through various forms of multiplexing. Additionally,
the photorefractive recording medium is sensitive to low level intensity
and is reusable. Therefore, previously stored holograms may be
erased, and the crystal can be reused to store other holograms. Until recently,
however, research in photorefractive holography has been limited
to the production of two-dimensional (2-D) holograms and very limited
field-of-view (FOV) 3-D holograms.
The proposed method employs a volume hologram recorded and read in
real time in a photorefractive crystal to produce a 3-D image. This innovative
technique is simple, and it differs from previous attempts at 3-D displays.
We used a photorefractive material, SBN, to record a hologram, and
a phase-conjugate read beam, which is generated from a double-pumped
phase-conjugate mirror (DPPCM), to accurately reproduce the holographic
image in space over a large perspective. The resultant holographic image is
free from system-induced aberrations, may be viewed over a wide range of
angles that can be expanded by the use of a mosaic of crystals, and has uniform
high quality over the entire FOV.
2
2. Theory
The hologram is recorded in SBN by the interference of two writing beams:
a reference beam Eref and an object beam Eo, as shown in figure 1. The intensity
that is created by the interference of the two writing beams, Eref and
Eo, is written as
I E E E E E E E E EE ∝ + ( ) ref o ( ) ref + o = ++ + ref o ref o o ref * * * * , 2 2 (1)
where the grating terms of the intensity are represented by the last two
terms
I E E EE g = + ref o o ref * * . (2)
When two coherent beams interfere in a photorefractive crystal such as
SBN, an index-of-refraction grating is produced via the photorefractive effect
[1]. The gratings are written on the order of the photorefractive time
response, which can be less than 1 s. The time response for these crystals is
intensity dependent, τ = A/I with 0.05 < A < 2 J/cm2, depending on crystal
and dopant type and quality.
The photorefractive effect occurs when two beams of the same frequency
interfere so that a series of light and dark fringes is created by the constructive
and destructive interference of the beams. In the light or high-intensity
regions, free charge carriers are excited by photons into the conduction
band. These charge carriers diffuse into the darker regions of lower intensity.
Once this process occurs, the charge carriers become trapped, which
induces a space-charge distribution. As stated in Poisson’s equation, a
space-charge field results from the space-charge distribution. This spacecharge
field then induces an index grating, via the linear electro-optic,
known as the Pockels effect
∆n nr E = − eff sc
1
2
3 , (3)
Figure 1. Dynamic
holography in
photorefractive
crystals via four-wave
mixing; c -axis is
drawn for a photorefractive
crystal such
as SBN.
a
c
z
x crystal
Eref
Eo
Ed
Eread
3
where n is the index of refraction, reff is the effective electro-optic coefficient,
and Esc is the strength of the space-charge field.
With no applied or photovoltaic electric field, the index-of-refraction grating
is phase shifted by 90° from the intensity grating, which leads to energy
exchange between the two beams. Energy exchange leads to significant
beam fanning if there is sufficient interaction length in the crystal.
Beam fanning is undesirable for the holographic storage crystal because it
will degrade the hologram. Therefore, the crystal used in this study, SBN
doped with cerium, had a length of ~1 mm, which is less than the critical
interaction length.
The hologram is read by the introduction of a third beam Eread, which is
counter-propagating to the reference beam as shown in figure 1. The read
beam is diffracted off the index grating, which has been previously recorded
in the photorefractive material. This process produces the diffracted
wave Ed, and is written as
E E I E E E EE E EE EE E d read ∝= + g read( ) ref o o ref ref = + o read o ref read ** * * , (4)
where I
g is defined in equation (2). The first term on the right-hand side of
the equation,
E EE ref o read * , represents a beam that is diffracted off the index
grating, counter-propagating to the object beam, with wave vector
k k d o 1 = − .
The second term,
EE E o ref read * , represents a beam propagating with wave
vector kd2
= ko – 2kref. Only the first-order wave kd1
will be Bragg-matched
[2], because we are in the thick or volume grating regime. We are in the
thick (volume) grating regime because the following inequality is satisfied:
2πλd » nΛ2 , (5)
where λ is the wavelength in free space, d is the grating thickness, n is the
average index of refraction, and L is the grating period.
There are several advantages to using volume holograms over those recorded
in the thin grating regime. First, the diffraction efficiency of volume
gratings is significantly greater than what is offered by thin gratings because
a volume grating has fewer diffracted orders. Thus, only a single
beam is diffracted from the grating, which eliminates the appearance of
ghost images due to higher order diffraction. Second, there is less angular
spread in the diffracted beam as compared to the beam from a thin grating.
This feature allows numerous holograms to be written and read in the
same crystal, because the Bragg angle is used to selectively store and read
the images. Finally, only light that is incident at the narrow Bragg angle
can be diffracted by these gratings, which minimizes crosstalk during volume
readout.
A simple method of reading the hologram involves using the reflection of
the reference beam from a plane mirror. The generated diffracted beam is
written as follows, where equation (4) is used for a volume grating:
4
E E E E rA e E d o ref read read
ik x o ∝ = x * * , 2 2 (6)
where
E rE read = ref ,
E Aeik x ik z = x z + (such that the beam is propagating in the
x - z plane with wave vector k and amplitude A), and r is the reflection coefficient
of the plane mirror.
The image-bearing beam Ed contains a spatially dependent term because
the read beam is only truly phase-matched on axis. Thus, the maximum
FOV of the hologram is severely restricted as the read beam diverges. This
problem can be remedied by careful collimation of the read beam and reference
beam; however, this is a cumbersome task. It is much easier to use
the laws of nonlinear optics and use a read beam that is naturally selfaligning,
such as a phase-conjugate read beam. Since the phase-conjugate
beam is exactly counter-propagating to the reference beam, it would not
matter if the reference beam is diverging because the read beam will retrace
its path precisely, and read all the written gratings over the entire
beam width. The read beam, which is generated from the phase conjugate
of the reference beam, is written as follows, where equation (4) is used for
a volume grating:
E E E E q E E qI E I I E d ∝ = ∝= o ref read ref o ref o ref read o * * * * , 2 (7)
where
E qE read = ref
* and q is the phase-conjugate reflectivity.
The divergence of the read beam from a plane mirror, evident in equation
(6), is not present when a phase-conjugate read beam is used, as shown in
equation (7). Furthermore, phase conjugation is a process in which the
phase aberrations of an optical system are removed without beam manipulation.
The use of a phase-conjugate read beam also has added benefits
such as higher resolution, a larger FOV, and a simpler, more robust holographic
production [3].
Phase conjugation at low beam powers can be obtained by the use of
photorefractive crystals [4] and generated by four-wave mixing geometries
[5]. One method, which uses the internal reflection of one beam within the
crystal, is called self-pumped phase conjugation. The self-pumped, phaseconjugate
mirror offers reflectivities in the range of 0 ≤ q ≤ 1. However,
reflectivities greater than 1 can be achieved by the use of a DPPCM. We
used the photorefractive crystal SBN doped with cerium as a DPPCM. The
bridge-conjugator geometry was used to generate the phase-conjugate
read beam because a large gain in SBN is easier to achieve [6]. In the bridge
conjugator geometry, the reference and pump beams are incident on opposite
faces of a photorefractive crystal, which are parallel to the
cˆ-axis. Since
the pump beam does not have to be mutually coherent with the reference
beam, the pump beam can be generated from the original laser or a second
laser operating at the same wavelength. Actually, the DPPCM is more efficient
when the beams are not coherent.
5
3. Experimental Setup
The basic principles upon which this three-dimensional display operates
are shown in figure 2. A signal beam, generated from an argon-ion laser
operating at 488 nm, is split into two beams: the object beam (Eo) and reference
beam (Eref). A delay arm was placed in the reference beam path to adjust
the coherence between the two writing beams. The coherence length of
the argon laser was measured to be ~70 mm. To obtain the maximum allowable
FOV of the hologram, it is desirable to completely fill the
photorefractive crystal that is being used as the recording medium. Therefore,
a beam expander is used to increase the reference beam diameter and
to collimate it before it enters the recording medium. The object beam is
incident on the object at an angle, so that the majority of the scattered light
is directed towards the recording medium. Depending on the size of the
object, the object beam may need to be expanded. The scattered object
beams and reference beam cross and interfere in the recording medium. In
this study, the recording material was a photorefractive crystal (strontium
barium niobate Sr0.6Ba0.4Nb2O6 (SBN:60)), which was doped with cerium.
The angle between the reference and object beams was made to correspond
with the largest change in the index of refraction. We performed
two beam coupling experiments on SBN:60 to determine the angle that
achieved the strongest possible photorefractive effect. The optimum angle
for SBN:60 was measured to be within 20° to 40°, and the bisector of this
angle was normal to the incident face of the crystal.
The entrance and exit faces of the crystal were cut parallel to the direction
of the largest electro-optic coefficient (r33 for SBN:60), which was labeled
the
cˆ-axis. The crystal was electrically poled in this same direction to ensure
domain alignment. The
cˆ-axis should lie in the plane of polarization
of the object and reference beams; therefore,
pˆ -polarized light was used in
this study. The entrance and exit faces of the crystal should also be as large
as possible to maximize the FOV, and the crystal thickness should be about
1 mm to minimize the effects of beam fanning (discussed previously). The
dimensions of the photorefractive storage crystal used in this study were
20 × 20 × 1.3 mm.
DPPCM
Photorefractive
storage crystal
c
Ere f
Eread
Eo Mirror
Beam
splitter Ed
Real image plane
Imaging
lens
3-D
object
Epump
To CCD, video camera,
or eye
Beam
condenser
Figure 2.
Experimental setup
used to record and
reconstruct a 3-D
hologram using SBN.
6
The hologram recording process occurs wherever the reference beam and
scattered object beams intersect in the crystal volume. As long as these
beams are mutually coherent and the photorefractive material has sufficient
response, interference will occur, which will result in an intensity
modulation. These interference gratings transform into index-of-refraction
gratings via the photorefractive effect that was discussed previously. The
object is recorded as a conglomeration of index gratings in the crystal volume,
which is referred to as a volume hologram.
After the reference beam transmits through the storage crystal, it is incident
upon a second photorefractive crystal that is used as a DPPCM. The
DPPCM crystal, which is used to obtain the necessary phase-conjugate
read beam, has parameters identical to the storage crystal except for the
dimensions. In our experiment, the DPPCM SBN:60 crystal is 6 mm long,
which provides a sufficient path length for significant beam fanning. Since
the reference beam may be too large in diameter to enter the DPPCM crystal
cleanly, a beam condenser is used. The beam condenser ensures that the
desired beam size is achieved at the entrance face of the crystal. The
DPPCM crystal is oriented so that the reference beam (Eref) and a second
pump beam (Epump) enter opposite faces of the crystal with wave vector
components in the +
cˆ-direction. The pump beam, which was
pˆ -polarized,
originated from a second argon-ion laser, which was operating at 488 nm.
The read beam (Eread) will exactly retrace the original beam’s path from the
DPPCM crystal—through any lenses—to the storage crystal. The read
beam is counter-propagating to the reference beam in the storage crystal.
Consequently, the read beam is perfectly Bragg-matched to the hologram’s
gratings at all points in the crystal. The exact match ensures that all gratings
or holograms are read and allows the maximum perspective (FOV) of
the image for the size of the storage material. Since the read beam is a
phase conjugate, any inhomogeneities or phase-distorting properties of the
optical elements between the DPPCM crystal and the hologram will cancel
out. The Bragg-matched read beam will diffract off these gratings and retrace
the path of the scattered object beam. The diffracted beam from the
storage crystal is separated from the object beam by a beam splitter with an
antireflection coating that is placed between the object and storage crystal.
This process forms the three-dimensional hologram of the object as shown
in figure 2.
3.1 Holographic Display
The three-dimensional hologram is a real image of the object and can be
displayed in free space. The image can be viewed by projection, via lens
relays, directly into the eye or a camera. Figure 3 shows the hologram of
two dice earrings recorded in the SBN:60 photorefractive crystal. The dice
have dimensions of 2 mm on a side. We verified the third dimension of the
image by viewing the hologram at different perspectives, which demonstrated
parallax when we rotated the viewing angle by placing the camera
on a pivot arm. The FOV of the hologram (fig. 3) was measured to be ~14°.
We determined the FOV by the angular range in which the hologram was
7
clearly visible. The expected FOV can be calculated from the diagram
shown in figure 4. The photorefractive recording crystal of length Lc
is
tilted so that the normal to the crystal’s largest face bisects the angle between
the reference and object beams, φ. The object of width s is located a
distance d from the projection of the recording crystal, where the projection
of the crystal is in the plane perpendicular to
v
d . The effective length of the
recording material is
LL s eff = c
cos , − φ
2 (8)
where Lc
cos(φ/2) is the projection of the crystal to the plane normal to
v
d,
and the object size is subtracted so that the entire object is observed
through the FOV. The maximum FOV of the hologram is limited by the angular
range over which the object can be viewed through the crystal. The
FOV is calculated as follows:
FOV
L
d
eff =
2
2 arctan , (9)
where Leff is defined in equation (8) and d is the distance from the object to
the projection of the recording crystal as shown in figure 4.
Lc
s
d
FOV
φ
Reference
beam (Eref)
Object
beam (Eo)
Figure 4. Method of
measuring expected
FOV for recording a
hologram in a crystal
of length Lc.
(c)
Figure 3. 3-D hologram stored in a Ce-doped SBN:60 photorefractive crystal and viewed at various
angles with an FOV of ~14°.
(a) (b)
φ
2
8
Using equations (8) and (9), we calculated the maximum FOV of the hologram
presented in figure 3 to be ~24°, where Lc
= 20 mm, d = 40 mm, φ =
20°, and s = 3 mm. Because of incomplete phase conjugation of the read
beam, the measured FOV of 14° is much less, because the entire region of
the crystal was not used. The alignment of the pump beam and reference
beam in the DPPCM is critical to enhance a large phase-conjugate read
beam.
We used a second, identical photorefractive storage crystal (SBN:60 doped
with cerium with similar dimensions (20 mm × 20 mm × 1.3 mm)) to further
increase the FOV of the hologram. The two storage crystals were tiled
together in a mosaic so that the width of the net storage area was 40 mm
and the height was 20 mm. To produce a collimated reference and read
beam with an elliptical shape that filled the rectangular-shaped storage
crystal, we used a series of spherical and cylindrical lenses. A laser
aplanatic lens and an aplanatic meniscus lens from CVI Laser Corporation
were used to obtain an f number of f/3.3 to reduce distortions when the
reference beam was focused into the DPPCM, and the read beam was expanded
to fill the storage crystal. The hologram recorded in the mosaic of
the two crystals is shown in figure 5. The increased perspective (FOV) is
evident on the die in the background of figure 5, where the side of the die
with the three is visible at one edge of the FOV, as shown in figure 5a;
while at the other edge of the FOV, the side of the die with the six is clearly
visible, as shown in figure 5b. We measured the FOV of the hologram presented
in figure 5 to be ~30° by rotating the camera on a pivot arm that was
centered at the image plane. The hologram is clearly visible through the
entire FOV; however, there was a bright strip of light that appeared due to
scattering when the viewing angle passed through the intersection where
the two crystals were attached by double-sided tape. Using equations (8)
and (9), we calculated the maximum FOV to be ~44°, where Lc
= 40 mm,
d = 45 mm, φ = 20°, and s = 3 mm. As previously stated, the FOV was limited
because the read beam did not fill the entire crystal. The maximum
possible FOV is desired so that the images are more realistic.
We would also like to display the hologram in such a medium that the image
could be viewed at different angles. A scattering liquid was tested, but
proved ineffective since the perspective was lost, and only a 2-D image
was visible.
Figure 5. Hologram
stored in a mosaic of
two Ce-doped SBN:60
photorefractive
crystals with an FOV
of ~30°.
(a) (b)
9
3.2 Image Storage
Presently, much research is focused on studying holographic storage in
photorefractive crystals via angular [7], wavelength [8], and electric-field
[9] multiplexing; however, these images are generally 2-D. We have stored
multiple 3-D holograms in the photorefractive crystal via wavelength multiplexing.
The experimental setup used to study wavelength multiplexing
is shown in figure 2. However, the writing beams originated from an
argon-ion laser that was operating in a multiline configuration. Also, the
DPPCM was not used. The read beam was generated from a second argonion
laser running in a single-line configuration. Several holograms were
written simultaneously at the lasing wavelengths of the argon-ion laser.
The relative powers of the primary lasing wavelengths used to record the
holograms are listed in table 1. We read the individual holograms by tuning
the read beam to a particular wavelength. The relative powers of the
read beam used to reconstruct individual holograms are also listed in
table 1.
The holograms were clearly visible at each wavelength. Band pass filters
were used to shield unwanted scattered light from writing-beam wavelengths
that were not being read. We verified the three-dimensionality of
the hologram by demonstrating parallax, as previously shown in figures 3
and 5.
Permanent storage of holographic images in photorefractive crystals is often
obtained by electrical [10] or thermal [11] fixing of the gratings or by
periodic refreshing [12]. However, we have found that the holograms persist
without any external fixing mechanisms.
To study this effect, we used the experimental setup shown in figure 2 with
the following changes: the beam splitter was removed so that the image
was viewed in the same plane as the object, and the DPPCM was not used.
The read beam was blocked while the hologram was recorded for approximately
5 min at a power of ~5 mW. Next, the recording beams were
blocked, and the object, a dime, was removed so that the holographic image
could be viewed. The hologram was reconstructed with a weaker read
beam of ~0.8 mW. The hologram was quite bright, with a diffraction efficiency
of ~3 percent, and persisted during readout for approximately
30 min without any apparent degradation. The holograms’ long storage
times, achieved without any external fixing mechanisms, could have been
caused by self-enhancement [13].
Wavelength Relative beam power
(nm) Writing Reading
476.5 0.29 1
488 0.76 1
496.5 0.29 0.33
501.7 0.18 0.33
514.5 1 1
Table 1. Relative
powers of writing and
reading beams used to
study wavelength
multiplexing in SBN.
10
A hologram was also recorded in a photorefractive storage crystal for
~5 min; then, it was placed in a sealed, dark box for three days. The hologram
was reconstructed after three days with a read beam of ~1.7 mW, and
the hologram was still quite bright. Since external light will slowly erase
the grating in the crystal, we turned off the room lights during these
measurements.
11
4. Conclusions
A simple method for recording a real-time, 3-D hologram using SBN has
been demonstrated. The 3-D hologram is a realistic image that can be
viewed over a large FOV. A DPPCM was used to produce a phaseconjugate
read beam in order to view the hologram over the maximum
perspective (FOV). We further increased the FOV of the hologram by storing
the hologram in a mosaic of two SBN crystals. Multiple 3-D images
have been stored and read out of the crystal via wavelength multiplexing.
The holograms were also noted to persist without any external fixing
mechanisms. During readout, the holograms persisted for hours. When the
photorefractive storage crystal was kept in a dark environment, the holograms
persisted for days.
Acknowledgements
The principal author is on a fellowship appointment from the American
Society for Engineering Education, Washington, DC, for the U.S. Army Research
Laboratory. The authors wish to thank R. R. Neurgaonkar from
Rockwell International Science Center, Thousand Oaks, CA, for supplying
the photorefractive crystals.
12
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13
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Distribution
14
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(cont'd)
15
Distribution
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Adelphi MD 20783-1197
(cont'd)
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Unclassified
ARL-TR-1520
February 1998 Progress, from Nov. 1996 to Aug. 1997
PE: 611102A
23
3-D Holographic Display Using Strontium Barium Niobate
Christy A. Heid, Brian P. Ketchel, Gary L. Wood (ARL), Richard J.
Anderson (National Science Foundation), and Gregory J. Salamo
(University of Arkansas)
U.S. Army Research Laboratory
Attn: AMSRL-SE-EO (e-mail: cheid@arl.mil)
2800 Powder Mill Road
Adelphi, MD 20783-1197
U.S. Army Research Laboratory
2800 Powder Mill Road
Adelphi, MD 20783-1197
Approved for public release; distribution unlimited.
AMS code: 611102.H44
ARL PR: 8NE3AA
An innovative technique for generating a three-dimensional holographic display using strontium
barium niobate (SBN) is discussed. The resultant image is a hologram that can be viewed in real time
over a wide perspective or field of view (FOV). The holographic image is free from system-induced
aberrations and has a uniform, high quality over the entire FOV. The enhanced image quality results
from using a phase-conjugate read beam generated from a second photorefractive crystal acting as a
double-pumped phase-conjugate mirror (DPPCM). Multiple three-dimensional images have been
stored in the crystal via wavelength multiplexing.
Hologram, 3-D display, photorefraction, phase-conjugate mirror
Unclassified Unclassified UL
17
DEPARTMENT OF THE ARMY An Equal Opportunity Employer
U.S. Army Research Laboratory
2800 Powder Mill Road
Adelphi, MD 20783-1197