A method of multiplexing holograms by rotating the material or, equivalently, the recording beams is described. Peristropic (Greek for rotation) multiplexing can be combined with other multiplexing methods to increase the storage density of holographic storage systems. Peristrophic multiplexing is experimentally demonstrated with Du Pont's HRF-150 photopolymer film. We multiplexed a total of 295 holograms in a 38-μm-thick photopolymer film by combining peristrophic multiplexing with angle multiplexing

Curtis, Kevin

Psaltis, Demetri

Pu, Allen

English

Caltech Authors - Main

July 1, 1994 / Vol. 19, No. 13 / OPTICS LETTERS 993
Method for holographic storage using
peristrophic multiplexing
Kevin Curtis, Allen Pu, and Demetri Psaltis
Department of Electrical Engineering, California Institute of Technology, MS 116-81, Pasadena, California 91125
Received January 10, 1994
A method of multiplexing holograms by rotating the material or, equivalently, the recording beams is described.
Peristropic (Greek for rotation) multiplexing can be combined with other multiplexing methods to increase the
storage density of holographic storage systems. Peristrophic multiplexing is experimentally demonstrated with
Du Pont's HRF-150 photopolymer film. We multiplexed a total of 295 holograms in a 38-Aum-thick photopolymer
film by combining peristrophic multiplexing with angle multiplexing.
The number of holograms that can be multiplexed
in a given holographic system is primarily a func-
tion of two parameters-the system's bandwidth (ei-
ther temporal or spatial frequency) and the mate-
rial's dynamic range. Recently, thin-film materials
have been developed with relatively large dynamic
range. An example of such a material is Du Pont's
HRF-150 photopolymer. 1 Previously we reported 10
angle-multiplexed holograms in a 38-,Am-thick film
2
with a diffraction efficiency of 10-3. Since typically
we can work with holographic diffraction efficiencies
of the order of 10-, we have sufficient dynamic range
to record sufficiently more than 10 holograms. The
angular bandwidth limitation can be alleviated by
making the film thicker,3 but scattering increases
rapidly with thickness in these materials. Another
method that has been used to increase the utilization
of the available bandwidth of the system is fractal
sampling grids.4 5
In this Letter we describe peristrophic (Greek for
rotation) multiplexing as a solution to the bandwidth-
limited capacity problem. With this method the
hologram is physically rotated, with the axis of rota-
tion being perpendicular to the film's surface every
time a new hologram is stored. The rotation does
two things. It shifts the reconstructed image away
from the detector, permitting a new hologram to be
stored and viewed without interference, and it can
also cause the stored hologram to become non-Bragg
matched. In addition, peristrophic multiplexing can
be combined with other multiplexing techniques such
as angle and wavelength multiplexing to increase the
storage density and with spatial multiplexing to in-
crease the storage capacity of the system.
The setup for peristrophic multiplexing Fourier
plane holograms is shown in Fig. 1. The reference
plane wave (R) is incident at an angle Or, and the sig-
nal beam (S) is incident at an angle Os, both angles
measured with respect to the film's normal. Taking
the center pixel of the image as the signal and ne-
glecting any effects due to hologram thickness, we
can write the hologram transmittance as
R*S = exp i2iT A ' x) exp(-i27.Ax ' X) (1)
The hologram is then rotated by do about the center
of the x-y plane, as shown in Fig. 1. If it is assumed
that the rotation is small, this results in the coordi-
nates' being transformed according to x' x - ydO
and y' y + xdO. Substituting these relations into
Eq. (1), we can express the hologram in terms of the
unrotated coordinates (x,y):
R*S= exP(j_) Xi27r sin orx j2v sin ax
X exp[ i 2r(sin as + si Or) dY] (2)
After multiplication by R and Fourier transforming,
the last term in Eq. (2) results in a shift in the image.
The rotation required for translation of the image out
of the detector aperture is approximately given by
do Ž d/F
sin 05, + sin 0 (3)
where d is the size of the image detector plane and F
is the focal length of the lens used. For image-plane
holograms the expression is6
do Ž 2A/8
sinO ±, + sn 0 (4)
where 1/8 is the highest spatial frequency in the
image. For image-plane holograms, the undesired
holograms are filtered out at the Fourier plane of
the system. Notice that this method can be com-
bined with other volumetric multiplexing methods to
increase the storage density further.
y
Detecto Aperture
Refeence plane Wave I
Os Z axis-is m's normal
d onSinlbeam Rotation Stage
SLM
Fig. 1. Setup for peristrophic multiplexing. SLM, spa-
tial light modulator.
0146-9592/94/130993-02$6.00/0 K 1994 Optical Society of America
994 OPTICS LETTERS / Vol. 19, No. 13 / July 1, 1994
1 e-05
8e-06
=i
._
6e-06
4e.06
0.0 100.0 200.0 300.0
Hologram Number
Fig. 2. Diffraction efficiency versus hologram number
for 295 holograms stored in 38-jum-thick film.
The Bragg selectivity, assuming that the reference
is given by
R = exp[-i(2irs rX A2rcos A z)]
and the signal is given by
S = exp[-i(X A Z)]
can be calculated with the Born and the paraxial
approximations and integration over the volume of
the hologram. Assuming that the tranverse (x,y)
dimensions of the film are much larger than the band-
width of the images, we can show the Bragg selectiv-
ity to be
da= {~2A[ cosO; 112
tL sin0,(sin0,a + sinor)
where t is the thickness of the material. Using A =
488 nm, t = 38 gim, and 0. = O, = 300 results
in a selectivity of approximately 120. The Bragg-
matching requirement is the dominant effect if dIF >
[2A cos 08 (sin Os + sin 0,)/t sin O,]12. For most mate-
rial thicknesses, the Bragg-matching criterion deter-
mines the required rotation for peristrophic multi-
plexing. In our experiments, because the thickness
of the film is only 38 Aum, the image could be filtered
out before the gratings become non-Bragg matched.
The experimental setup is the same as in Fig. 1,
except that a rotation stage was added to rotate
the film around a vertical axis as well as around
the film's normal. This makes it possible to com-
bine peristrophic and angle multiplexing. The film
was located a significant distance from the Fourier
plane so that the signal beam was approximately
uniform. For each peristrophic position, multiple
holograms are stored by standard angle multiplexing
by rotation of the medium. A spatial light modu-
lator was used to present images (cartoons) to the
system. Each frame is numbered according to the
sequence in which it was stored. The reference and
signal beams were initially incident at ±30° from
the film's normal. The reference-beam intensity was
1.1 mW/cm2, and the signal-beam power was 300 ,uW
in an approximately 1 cm X 0.5 cm area. The film
was rotated in plane by 30 between each set of angle-
multiplexed holograms to permit the other holograms
to be filtered out. Relation (3) predicts a required ro-
tation of approximately 9° for the Fourier-plane holo-
gram, while relation (4) predicts an approximately
1.7° rotation for the image plane. The 30 was ex-
perimentally observed for the in-between (Fresnel)
case that we used. Each angle-multiplexed holo-
gram was also separated by 3°. The initial exposure
time was 0.11 s, but, starting at hologram number
26, we exposed each hologram for 0.005 longer than
the previous hologram to correct for the lost sensi-
tivity because of run time.2 There was a 1.5-s delay
between holograms to allow the rotation stages to
stop completely. 295 holograms were stored in the
polymer by peristrophic multiplexing 59 times and
storing 5 angle-multiplexed holograms with each
peristrophic position. The diffraction efficiency of
the 295 holograms is plotted in Fig. 2. The aver-
age efficiency was -4 x 10-6, and the variations are
due primarily to variation in the average intensity
of the frames. In a separate experiment, we stored
equal-amplitude plane-wave holograms and observed
a decrease in diffraction efficiency proportional to
1/M2 .7
Previously we stored M = 10 holograms with a
roughly 10-13 diffraction efficiency,2 limited by the an-
gular bandwidth of the optical system. Peristrophic
multiplexing made it possible to store M = 295
holograms at the same location with a diffraction
efficiency of -4 X 10-6. Thus, peristrophic multi-
plexing permitted an almost 2-orders-of-magnitude
increase in the storage capacity of the Du Pont pho-
topolymer and changed the limiting factor from the
angular bandwidth of the optical system to the dy-
namic range of the material.
We thank Geoffrey Burr, Sidney Li, and Fai Mok
for their helpful discussions.
Kevin Curtis is also with Northrop Corporation's
B-2 Division, Pico Rivera, California 90660.
References
1. W. K Smothers, T. J. Trout, A. M. Weber, and D. J.
Mickish, presented at Second International Conference
on Holographic Systems, Bath, UK, 1989.
2. K. Curtis and D. Psaltis, Appl. Opt. 31, 7425 (1992).
3. K Curtis and D. Psaltis, in Annual Meeting, Vol. 23 of
1992 OSA Technical Digest Series (Optical Society of
America, Washington, D.C., 1992), paper ThX3.
4. D. Psaltis, D. Brady, X. G. Gu, and S. Lin, Nature
(London) 343, 325 (1990).
5. F. H. Mok, Opt. Lett. 18, 915 (1993).
6. H. Y. S. Li, "Photorefractive 3-D disks for optical data
storage and artificial neural networks," Ph.D. disser-
tation (California Institute of Technology, Pasadena,
Calif., 1994).
7. D. Brady and D. Psaltis, J. Opt. Soc. Am. A 9, 1167
(1992).


Method for holographic storage using peristrophic multiplexing

July 1, 1994 / Vol. 19, No. 13 / OPTICS LETTERS 993
Method for holographic storage using
peristrophic multiplexing
Kevin Curtis, Allen Pu, and Demetri Psaltis
Department of Electrical Engineering, California Institute of Technology, MS 116-81, Pasadena, California 91125
Received January 10, 1994
A method of multiplexing holograms by rotating the material or, equivalently, the recording beams is described.
Peristropic (Greek for rotation) multiplexing can be combined with other multiplexing methods to increase the
storage density of holographic storage systems. Peristrophic multiplexing is experimentally demonstrated with
Du Pont's HRF-150 photopolymer film. We multiplexed a total of 295 holograms in a 38-Aum-thick photopolymer
film by combining peristrophic multiplexing with angle multiplexing.
The number of holograms that can be multiplexed
in a given holographic system is primarily a func-
tion of two parameters-the system's bandwidth (ei-
ther temporal or spatial frequency) and the mate-
rial's dynamic range. Recently, thin-film materials
have been developed with relatively large dynamic
range. An example of such a material is Du Pont's
HRF-150 photopolymer. 1 Previously we reported 10
angle-multiplexed holograms in a 38-,Am-thick film2
with a diffraction efficiency of 10-3. Since typically
we can work with holographic diffraction efficiencies
of the order of 10-, we have sufficient dynamic range
to record sufficiently more than 10 holograms. The
angular bandwidth limitation can be alleviated by
making the film thicker,3 but scattering increases
rapidly with thickness in these materials. Another
method that has been used to increase the utilization
of the available bandwidth of the system is fractal
sampling grids.4 5
In this Letter we describe peristrophic (Greek for
rotation) multiplexing as a solution to the bandwidth-
limited capacity problem. With this method the
hologram is physically rotated, with the axis of rota-
tion being perpendicular to the film's surface every
time a new hologram is stored. The rotation does
two things. It shifts the reconstructed image away
from the detector, permitting a new hologram to be
stored and viewed without interference, and it can
also cause the stored hologram to become non-Bragg
matched. In addition, peristrophic multiplexing can
be combined with other multiplexing techniques such
as angle and wavelength multiplexing to increase the
storage density and with spatial multiplexing to in-
crease the storage capacity of the system.
The setup for peristrophic multiplexing Fourier
plane holograms is shown in Fig. 1. The reference
plane wave (R) is incident at an angle Or, and the sig-
nal beam (S) is incident at an angle Os, both angles
measured with respect to the film's normal. Taking
the center pixel of the image as the signal and ne-
glecting any effects due to hologram thickness, we
can write the hologram transmittance as
R*S = exp i2iT A ' x) exp(-i27.Ax ' X) (1)
The hologram is then rotated by do about the center
of the x-y plane, as shown in Fig. 1. If it is assumed
that the rotation is small, this results in the coordi-
nates' being transformed according to x' x - ydO
and y' y + xdO. Substituting these relations into
Eq. (1), we can express the hologram in terms of the
unrotated coordinates (x,y):
R*S= exP(j_) Xi27r sin orx j2v sin ax
X exp[ i 2r(sin as + si Or) dY] (2)
After multiplication by R and Fourier transforming,
the last term in Eq. (2) results in a shift in the image.
The rotation required for translation of the image out
of the detector aperture is approximately given by
do Ž d/F
sin 05, + sin 0 (3)
where d is the size of the image detector plane and F
is the focal length of the lens used. For image-plane
holograms the expression is6
do Ž 2A/8
sinO ±, + sn 0 (4)
where 1/8 is the highest spatial frequency in the
image. For image-plane holograms, the undesired
holograms are filtered out at the Fourier plane of
the system. Notice that this method can be com-
bined with other volumetric multiplexing methods to
increase the storage density further.
y
Detecto Aperture
Refeence plane Wave I
Os Z axis-is m's normal
d onSinlbeam Rotation Stage
SLM
Fig. 1. Setup for peristrophic multiplexing. SLM, spa-
tial light modulator.
0146-9592/94/130993-02$6.00/0 K 1994 Optical Society of America
994 OPTICS LETTERS / Vol. 19, No. 13 / July 1, 1994
1 e-05
8e-06
=i
._
6e-06
4e.06
0.0 100.0 200.0 300.0
Hologram Number
Fig. 2. Diffraction efficiency versus hologram number
for 295 holograms stored in 38-jum-thick film.
The Bragg selectivity, assuming that the reference
is given by
R = exp[-i(2irs rX A2rcos A z)]
and the signal is given by
S = exp[-i(X A Z)]
can be calculated with the Born and the paraxial
approximations and integration over the volume of
the hologram. Assuming that the tranverse (x,y)
dimensions of the film are much larger than the band-
width of the images, we can show the Bragg selectiv-
ity to be
da= {~2A[ cosO; 112
tL sin0,(sin0,a + sinor)
where t is the thickness of the material. Using A =
488 nm, t = 38 gim, and 0. = O, = 300 results
in a selectivity of approximately 120. The Bragg-
matching requirement is the dominant effect if dIF >
[2A cos 08 (sin Os + sin 0,)/t sin O,]12. For most mate-
rial thicknesses, the Bragg-matching criterion deter-
mines the required rotation for peristrophic multi-
plexing. In our experiments, because the thickness
of the film is only 38 Aum, the image could be filtered
out before the gratings become non-Bragg matched.
The experimental setup is the same as in Fig. 1,
except that a rotation stage was added to rotate
the film around a vertical axis as well as around
the film's normal. This makes it possible to com-
bine peristrophic and angle multiplexing. The film
was located a significant distance from the Fourier
plane so that the signal beam was approximately
uniform. For each peristrophic position, multiple
holograms are stored by standard angle multiplexing
by rotation of the medium. A spatial light modu-
lator was used to present images (cartoons) to the
system. Each frame is numbered according to the
sequence in which it was stored. The reference and
signal beams were initially incident at ±30° from
the film's normal. The reference-beam intensity was
1.1 mW/cm2, and the signal-beam power was 300 ,uW
in an approximately 1 cm X 0.5 cm area. The film
was rotated in plane by 30 between each set of angle-
multiplexed holograms to permit the other holograms
to be filtered out. Relation (3) predicts a required ro-
tation of approximately 9° for the Fourier-plane holo-
gram, while relation (4) predicts an approximately
1.7° rotation for the image plane. The 30 was ex-
perimentally observed for the in-between (Fresnel)
case that we used. Each angle-multiplexed holo-
gram was also separated by 3°. The initial exposure
time was 0.11 s, but, starting at hologram number
26, we exposed each hologram for 0.005 longer than
the previous hologram to correct for the lost sensi-
tivity because of run time.2 There was a 1.5-s delay
between holograms to allow the rotation stages to
stop completely. 295 holograms were stored in the
polymer by peristrophic multiplexing 59 times and
storing 5 angle-multiplexed holograms with each
peristrophic position. The diffraction efficiency of
the 295 holograms is plotted in Fig. 2. The aver-
age efficiency was -4 x 10-6, and the variations are
due primarily to variation in the average intensity
of the frames. In a separate experiment, we stored
equal-amplitude plane-wave holograms and observed
a decrease in diffraction efficiency proportional to1/M2 .7
Previously we stored M = 10 holograms with a
roughly 10-13 diffraction efficiency,2 limited by the an-
gular bandwidth of the optical system. Peristrophic
multiplexing made it possible to store M = 295
holograms at the same location with a diffraction
efficiency of -4 X 10-6. Thus, peristrophic multi-
plexing permitted an almost 2-orders-of-magnitude
increase in the storage capacity of the Du Pont pho-
topolymer and changed the limiting factor from the
angular bandwidth of the optical system to the dy-
namic range of the material.
We thank Geoffrey Burr, Sidney Li, and Fai Mok
for their helpful discussions.
Kevin Curtis is also with Northrop Corporation's
B-2 Division, Pico Rivera, California 90660.
References
1. W. K Smothers, T. J. Trout, A. M. Weber, and D. J.
Mickish, presented at Second International Conference
on Holographic Systems, Bath, UK, 1989.
2. K. Curtis and D. Psaltis, Appl. Opt. 31, 7425 (1992).
3. K Curtis and D. Psaltis, in Annual Meeting, Vol. 23 of
1992 OSA Technical Digest Series (Optical Society of
America, Washington, D.C., 1992), paper ThX3.
4. D. Psaltis, D. Brady, X. G. Gu, and S. Lin, Nature
(London) 343, 325 (1990).
5. F. H. Mok, Opt. Lett. 18, 915 (1993).
6. H. Y. S. Li, "Photorefractive 3-D disks for optical data
storage and artificial neural networks," Ph.D. disser-
tation (California Institute of Technology, Pasadena,
Calif., 1994).
7. D. Brady and D. Psaltis, J. Opt. Soc. Am. A 9, 1167
(1992).


Photorefractive 3-D disks for optical data storage and artificial neural networks,&quot;

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Method for holographic storage using peristrophic multiplexing

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