Three-dimensional image reconstruction using strontium barium niobate

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!.

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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