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3-D Holographic Display Using Strontium Barium Niobate

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ARMY
RESEARCH
LABORATORY
KSKffi£S^äsSs£M%;
3-D
Holographic
Display
Using
Strontium
Barium
Niobate
by
Christy
A.
Heid,
Brian
P.
Ketchel,
Gary
L.
Wood,
Richard
J.
Anderson,
and
Gregory
J.
Salamo
ARL-TR-1520
February
1998
§8©
fttTALITy
INSPECTED
3
19980305
054
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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.
Contents
1.
Introduction
1
2.
Theory
2
3.
Experimental
Setup
5
3.1
Holographic
Display
6
3.2
Image
Storage
9
4.
Conclusions
1
1
Acknowledgements
1
1
References
1
2
Distribution
1
3
Report
Documentation
Page
1
7
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
L
c
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
in
1.
Introduction
Present
holographic
displays,
such
as
those
generated
by
computers
or
emulsion
films,
usually
require
intermediate
preprocessing
or
post-
processing
and
are,
therefore,
not
capable
of
real-time
production
and
viewing
and
have
limited
information
storage
capacity.
The
use
of
photo-
refractive
crystals,
such
as
strontium
barium
niobate
(SBN),
as
a
holo-
graphic
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.
Addition-
ally,
the
photorefractive
recording
medium
is
sensitive
to
low
level
inten-
sity
and
is
reusable.
Therefore,
previously
stored
holograms
may
be
erased,
and
the
crystal
can
be
reused
to
store
other
holograms.
Until
re-
cently,
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
innova-
tive
technique
is
simple,
and
it
differs
from
previous
attempts
at
3-D
dis-
plays.
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
uni-
form
high
quality
over
the
entire
FOV.
2.
Theory
The
hologram
is
recorded
in
SBN
by
the
interference
of
two
writing
beams:
a
reference
beam
E
re
f
and
an
object
beam
E
0
,
as
shown
in
figure
1.
The
in-
tensity
that
is
created
by
the
interference
of
the
two
writing
beams,
E
ref
a
nd
E
0
,
is
written
as
/cc(E
re/
+
E
o
)
(£^
+
£
^|
E
^|
2
+
|
Eo
|
2
+
Er
^
+
EoE;
^
t
(1)
where
the
grating
terms
of
the
intensity
are
represented
by
the
last
two
terms
Ig
=
ErefEo
+
EoKef
(2)
When
two
coherent
beams
interfere
in
a
photorefractive
crystal
such
as
SBN,
an
index-of-refraction
grating
is
produced
via
the
photorefractive
ef-
fect
[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,
T
=
A/1
with
0.05
<
A
<
2
J/cm
2
,
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
construc-
tive
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
inten-
sity.
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
space-
charge
field
then
induces
an
index
grating,
via
the
linear
electro-optic,
known
as
the
Pockels
effect
1
2
An
=
--
n\
g
L
sc
(3)
Figure
1.
Dynamic
holography
in
photorefractive
crystals
via
four-wave
mixing;
c
-axis
is
drawn
for
a
photo-
refractive
crystal
such
as
SBN.
X
crystal
->z
read
o
a
i
where
n
is
the
index
of
refraction,
r
e
^
is
the
effective
electro-optic
coeffi-
cient,
and
E
sc
is
the
strength
of
the
space-charge
field.
With
no
applied
or
photovoltaic
electric
field,
the
index-of-refraction
grat-
ing
is
phase
shifted
by
90°
from
the
intensity
grating,
which
leads
to
en-
ergy
exchange
between
the
two
beams.
Energy
exchange
leads
to
signifi-
cant
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
E
read
,
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
re-
corded
in
the
photorefractive
material.
This
process
produces
the
dif-
fracted
wave
E
d
,
and
is
written
as
E
d
x
E
recd
I
g
=
E
read[
E
ref
E
o
+
E
o
E
ref)
=
E
ref
E
o
E
read
+
E
o
E
ref
E
read
/
(
4
)
where
I
is
defined
in
equation
(2).
The
first
term
on
the
right-hand
side
of
the
equation,
E
re
fE*
0
E
read
,
represents
a
beam
that
is
diffracted
off
the
index
grating,
counter-propagating
to
the
object
beam,
with
wave
vector
^d
x
=~K-
The
second
term,
E
0
E*^E
rettd
,
represents
a
beam
propagating
with
wave
vector
k
d2
=
k
0
-
2k
re
r.
Only
the
first-order
wave
k
dl
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:
2nM
»
nA
2
,
(5)
where
A
is
the
wavelength
in
free
space,
d
is
the
grating
thickness,
n
is
the
average
index
of
refraction,
and
A
is
the
grating
period.
There
are
several
advantages
to
using
volume
holograms
over
those
re-
corded
in
the
thin
grating
regime.
First,
the
diffraction
efficiency
of
volume
gratings
is
significantly
greater
than
what
is
offered
by
thin
gratings
be-
cause
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
vol-
ume
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:
E
d
o
cE;E
ref
E
read
=
rA^
d
e^%
,
(6)
where
E
read
=
rE
re
f,
E
=
Ae
ik
*
x+ik
z
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
E
d
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
ref-
erence
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
self-
aligning,
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
re-
trace
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
d
x
E
o
E
ref
E
read
=
<7|
£
re/|
K
x
tfrefK
=
^refheadK
>
(
7
)
where
E
read
=
qE*
re
f
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
manipu-
lation.
The
use
of
a
phase-conjugate
read
beam
also
has
added
benefits
such
as
higher
resolution,
a
larger
FOV,
and
a
simpler,
more
robust
holo-
graphic
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,
phase-
conjugate
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
oppo-
site
faces
of
a
photorefractive
crystal,
which
are
parallel
to
the
c-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
effi-
cient
when
the
beams
are
not
coherent.
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
(E
0
)
and
refer-
ence
beam
(E
re
X
A
delay
arm
was
placed
in
the
reference
beam
path
to
ad-
just
the
coherence
between
the
two
writing
beams.
The
coherence
length
of
the
argon
laser
was
measured
to
be
~70
mm.
To
obtain
the
maximum
al-
lowable
FOV
of
the
hologram,
it
is
desirable
to
completely
fill
the
photorefractive
crystal
that
is
being
used
as
the
recording
medium.
There-
fore,
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
Sr
0
6
Ba
0
4
Nb
2
0
6
(SBN:60)),
which
was
doped
with
cerium.
The
angle
between
the
reference
and
object
beams
was
made
to
corre-
spond
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
(r
33
for
SBN:60),
which
was
labeled
the
c-axis.
The
crystal
was
electrically
poled
in
this
same
direction
to
en-
sure
domain
alignment.
The
c-axis
should
lie
in
the
plane
of
polarization
of
the
object
and
reference
beams;
therefore,
p
-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
x
20
x
1.3
mm.
Figure
2.
Experimental
setup
used
to
record
and
reconstruct
a
3-D
hologram
using
SBN.
Photorefractive
Mirror
storage
crystal
3-D
—.
object
I
Beam
imaging
s
P
|itter
lens
m
DPPCM
'pump
To
CCD,
video
camera,
or
eye
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
suffi-
cient
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
vol-
ume,
which
is
referred
to
as
a
volume
hologram.
After
the
reference
beam
transmits
through
the
storage
crystal,
it
is
inci-
dent
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
crys-
tal
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
(E
r
J
and
a
second
pump
beam
(E
pump
)
enter
opposite
faces
of
the
crystal
with
wave
vector
components
in
the
+
c
-direction.
The
pump
beam,
which
was
p
-polarized,
originated
from
a
second
argon-ion
laser,
which
was
operating
at
488
run.
The
read
beam
(E
read
)
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
grat-
ings
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
re-
trace
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
demon-
strated
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
clearly
visible.
The
expected
FOV
can
be
calculated
from
the
diagram
shown
in
figure
4.
The
photorefractive
recording
crystal
of
length
L
c
is
tilted
so
that
the
normal
to
the
crystal's
largest
face
bisects
the
angle
be-
tween
the
reference
and
object
beams,
(/>.
The
object
of
width
s
is
located
a
distance
d
from
the
projection
of
the
recording^rystal,
where
the
projection
of
the
crystal
is
in
the
plane
perpendicular
to
d
.
The
effective
length
of
the
recording
material
is
L
<r
:
L
c
cos|
(8)
where
L
c
cos(0/2)
is
the
projection
of
the
crystal
to
the
plane
normal
to
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
an-
gular
range
over
which
the
object
can
be
viewed
through
the
crystal.
The
FOV
is
calculated
as
follows:
FOV
=
2arctan
2d
(9)
where
L^
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.
(a)
(b)
(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°.
Figure
4.
Method
of
measuring
expected
FOV
for
recording
a
hologram
in
a
crystal
of
length
L
c
.
Reference
beam(E
re
/)
,\
Object
J
S
beam
(E
0
)
Using
equatio