Three-dimensional image reconstruction using strontium barium niobate
Brian P. Ketchel
a) and Gary L. Wood
U.S. Army Research Laboratory, ATTN: AMSRL-SE-EO, Adelphi, Maryland 20783-1197
Richard J. Anderson
National Science Foundation, Arlington, Virginia 22230
Gregory J. Salamo
Department of Physics, University of Arkansas, Fayetteville, Arkansas 72701
~
Received 27 December 1996; accepted for publication 29 April 1997!
A definitive demonstration of the use of a photorefractive crystal to project a three-dimensional
image in space is reported on. The image is bright and different perspective views of the object
appear as the viewing direction is changed. ©
1997 American Institute of Physics.
@
S0003-6951~97!00427-0#
Although four-wave mixing in photorefractive crystals
has been used extensively to store and project twodimensional
holographic images, we report a definitive demonstration
of true three dimensional
~3D! image reconstruction
using a photorefractive crystal. The use of an inorganic
photorefractive crystal as a storage medium allows:
~
1! simultaneous recording and read out of three dimensional
~
3D! holograms possessing easily observable parallax;
~
2! the entire holographic process to occur at low light levels
~
e.g., milliwatt levels for the object beam!;
~
3! the entire process to occur without processing/fixing the
material; and
~
4! thousands of holograms to be stored in a relatively small
crystal volume via wavelength and/or angle multiplexing.
Our 3D imaging technique employs a Ce-doped, strontium
barium niobate crystal
@~SBN!:60 2032031.3 mm# as
the storage medium. Figure 1 is a schematic diagram of the
experimental setup used to record and project 3D images.
The summation of light beams scattered off of the object,
E
1 , and the reference beam, E2 , write a hologram in the
form of transmission gratings in the photorefractive crystal.
The read beam,
E3 , counterpropagating to E2 , is produced
by phase conjugation of
E2 by a 13.5312.236 mm, Cedoped,
SBN:60 photorefractive crystal acting as a double
phase conjugate mirror
~DPCM!. The counterpropagating
beam diffracts to form beam
Ed that recreates the recorded
3D image at a distance from the crystal equal to that between
the object and crystal
~e.g., ;40– 80 mm!. A plate beam
splitter, placed between the object and crystal, is used to
view the real 3D image, produced by
Ed . Viewing is accomplished
by:
~
1! using the eye, just as one views a conventional hologram;
~
2! projecting the image onto a screen or into a scattering
cell; or
~
3! using an imaging lens in conjunction with a chargecoupled
device
~CCD! or video camera to magnify and
record the 3D image. In the latter case, different perspectives
are observed by placing the camera and imaging
lens on a goniometer that is rotated about a fixed point
~
e.g., the location of the 3D image!.
Since the recording medium is a photorefractive crystal,
unlike conventional holography where photographic film is
employed, the hologram can occur in real time with continuous
recording and display. The geometry employed in the
current experiment is readily recognized as being typical of
degenerate four-wave mixing, a technique which has been
compared in the literature to conventional holography by
Pepper and Yariv.
1 One major difference, however, is the use
of a DPCM to provide the read beam,
E3 . The use of the
DPCM has three well-documented advantages over other
methods:
~
1! distortion introduced by inhomogeneities in the photorefractive
crystal are eliminated;
2,3
~
2! high resolution holograms are possible;4 and
~
3! as reported here, the 3D image can be observed over a
large perspective range.
One can readily examine the impact of the DPCM on the
perspective range viewed by replacing it with a plane mirror
~
PM! or a separate counterpropagating beam. Analysis
shows that, when this substitution is made, the ability of the
nonphase conjugate counterpropagating beam to fulfill the
Bragg match conditions over the crystal area is extremely
a
!Electronic mail: bketchel@arl.mil FIG. 1. Schematic diagram of experimental apparatus.
Appl. Phys. Lett.
71 (1), 7 July 1997 0003-6951/97/71(1)/7/3/$10.00 © 1997 American Institute of Physics 7
limited. For example, the interference of the two beams,
E1
and
E2 , in the photorefractive crystal yields a corresponding
index grating proportional to
E2E1*1E1E2* . Light scattered
off of the object,
E1 , can be thought of as a summation of
plane waves. In order to reconstruct the object, a third beam,
E
3 , counterpropagating to the reference beam, E2 , essentially
reads the transmission gratings. Considering a single
plane wave, the resulting diffracted field,
Ed , is then given
by
E
d
}E3~E2E1*1E1E2*!5E2E1*E31E1E2*E3 . ~1!
Since we have a thick hologram that requires Bragg matching,
only the first term on the right hand side produces a
diffracted beam.
Ed , therefore, travels in a direction opposite,
k
d
52k1 , to the light scattered off of the object, E1 .
If the read beam is produced by reflection of the reference
beam from a mirror,
M, ~i.e., E35rE2 , where r is the
reflection coefficient of
M), then the radiated term appears
as
E
d
}E1*E2E35rA2 2 exp~2ikxx!E1* , ~2!
where
E25A2exp(ikxx1ikzz) and E35A3exp(ikxx2ikzz). It
has been assumed here that
E2 is traveling as a cone of light
propagated and reflected along the
z direction. As a result, if
a plane mirror is used to provide a read beam, the reflected
plane waves traveling off of the
z axis will not be phase
matched or Bragg matched and some parts of the photorefractive
crystal cannot be read. The consequence of this mismatch
is that the perspective of the image is severely restricted.
As an example, assume that the divergence of the reference
and read beams, which are counterpropagating, are 1
mrad and that the beams are allowed to fill the available area
of the storage crystal. Deviations from the Bragg angle
u B
cause the diffraction efficiency to fall to one-half of its peak
value for (
Du B)1/252G/kg , where G is the coupling coefficient
of the medium and
kg is the wave vector of the grating.
Assuming
G to be of the order of 25 cm21 and lg the grating
wavelength of the order of 1
mm, then (Du B)1/2 becomes 8
3
1024 rad. Therefore, with a 1 mrad beam divergence, i.e.,
k
x
/kz is about 1 mrad, full read out over the entire storage
crystal is expected. In fact, experimentally the observed perspective
for both the DPCM and the PM was nearly the same
at 5°. This compares well with the 5° angle subtended by the
object at the storage crystal. However, when the dimensions
of the storage crystal are large, as in the present experiment,
the reference and read beam must take on greater divergence
for practical reasons. When the divergence was increased by
about a factor of 4, the perspective view using the PM was
decreased by a factor of 4
~as expected! and limited to about
1°, while that obtained using the DPCM held at 5°.
Now consider the case where the read beam,
E3 , is produced
by the DPCM. Since
E3 is proportional to the phase
conjugate of
E2 ~i.e., E35qE2* , where q, the amplitude
phase conjugate reflectivity of the DPCM, which can be less
than, equal to, or greater than unity
!, then all of the plane
waves will be phase-matched, and therefore Bragg matched,
even off of the
z axis. The diffracted beam then becomes the
phase conjugate of beam
E1 , multiplied by a constant term
proportional to the intensity of beams
E2 and E3
E
d
}qE2E2*E1*5quE2u2E1*}qI2E1*5AI2I3E1* . ~3!
Because the diffracted beam is a phase conjugate, it will
retrace itself exactly to the object and reconstruct it. By placing
a beam splitter in the path of this return beam the reconstructed
image
~hologram! of the 3D object can be formed as
a real image. These results, therefore, demonstrate storage
and reconstruction of images with freedom from distortion,
2,3
high resolution,
4 large depth-of-field,5–7 and wide
field-of-view,
8 as reported in previous work, but with a significant
range of perspective only possible due to the use of
the DPCM
9 to provide a Bragg matched read beam over the
entire storage medium.
Figure 2
~a! displays high definition 3D images of a tencent
coin at different perspectives. In order to demonstrate
and measure such perspective, a planar obstacle is placed
;
15 mm in front of the object so that it covers part of the
object at a certain perspective. The difference in parallax
between the obstacle and the object may be recorded as a
function of the angular separation of the observed images. It
is clear from comparison of the parallax seen in the two
images taken at an angular separation of 5° that each image
represents a different perspective of the 3D object. This is
akin to viewing a conventional hologram. If the coin is replaced
by much smaller objects such as a pair of dice measuring
2 mm on each side, one experiences a significant
range of perspective by moving one’s head from side to side
or up or down. Although the series of 3D images shown in
Fig. 2
~b! readily indicate a change of perspective, the phenomena
is best captured by video tape in real-time.
FIG. 2. Different perspectives of 3D images observed by changing the angle
of observation of the imaging lens and CCD camera:
~a! a ten-cent coin,
unobstructed
~top! and with a planar obstacle placed ;15 mm in front of the
object and viewed from two different perspectives
~middle and bottom!; ~b!
a pair of 2 mm dice in space in which the overlap of the front die with
respect to the stem of the rear die disappears and a gap develops between
them as seen when viewed from three different perspectives
~top, middle,
and bottom
!.
8 Appl. Phys. Lett., Vol. 71, No. 1, 7 July 1997 Ketchel et al.
We have demonstrated the use of an SBN photorefractive
crystal to record and project real, high quality, 3D images.
Since SBN photorefractive crystals are generally a few
millimeters thick, the possibility of using Bragg angle or
wavelength selectivity to address, for projection, one of
many recorded 3D images, by either rotating the storage medium
or tuning to a particular wavelength, becomes a realistic
possibility. One might also speculate on the possibility of
‘‘fixing’’ the gratings by either thermal or electrical means to
overcome the fact that the images naturally persist within the
photorefractive crystal only for times on the order of minutes
while being read. If this becomes possible, inorganic crystals
could become 3D projection libraries. Since the maximum
number of distinguishable stored diffraction gratings would
be limited only by the volume of the thick crystal used as the
storage medium their number could be enormous. Our work
indicates that the reported 3D projection technique could
have significant scientific and commercial possibilities, especially
in the area of real-time projection of dynamic 3D images
in space.
The authors thank Dr. R. R. Neuorgankar for the photorefractive
crystals used in these experiments and Dr. Christy
A. Heid for obtaining the pictures used in Fig. 2
~b!.
1
D. M. Pepper, J. Au Yeung, D. Fekete, and A. Yariv, Opt. Lett. 3, 7
~
1978!.
2
N. A. Vainos and M. C. Gower, Opt. Lett. 16, 363 ~1991!.
3
M. C. Bashaw, A. Aharoni, and L. Hesselink, Opt. Lett. 17, 1149 ~1992!;
A. Aharoni, M. C. Bashaw, and L. Hesselink, Appl. Opt.
32, 1973 ~1993!.
4
D. L. Naylor, P. W. Tam, and R. W. Hellwarth, J. Appl. Phys. 72, 5840
~
1992!.
5
S. C. W. Hyde, N. P. Barry, R. Jones, J. C. Dainty, P. M. W. French, M.
B. Klein, and B. A. Wechsler, Opt. Lett.
20, 1331 ~1995!.
6
N. A. Vainos and M. C. Gower, J. Opt. Soc. Am. B 8, 2355 ~1991!.
7
F. Zhao and K. Sayano, Opt. Lett. 21, 1295 ~1996!.
8
L. E. Adams and R. S. Bondurant, Opt. Lett. 16, 832 ~1991!.
9
A self-pumped phase conjugate mirror would also work in this application,
although the DPCM has the advantage of controlled reflectivity and
reflectivity greater than 100%.
Appl. Phys. Lett., Vol. 71, No. 1, 7 July 1997 Ketchel et al. 9
