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Claims  |
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What is claimed is:
1. A method of recording multiplexed holograms in a recording medium,
comprising:
directing a signal light beam and a reference light beam onto a selected
recording spot in said recording medium, said signal and reference light
beams defining a plane of interaction of said recording medium;
successively modulating said signal light beam in accordance with a
succession of holograms to be recorded in said recording medium; and
first rotating at least one of (a) said recording medium and/or (b) said
signal and reference light beams with respect to the other through a
succession of peristrophic multiplexing angles about an axis
non-perpendicular to said plane of interaction contemporaneously with the
successively modulating step, said axis also being one which retains said
signal light beam and said reference light beam on said recording spot.
2. The method of claim 1 wherein said axis non-perpendicular to said plane
of interaction is parallel to said plane of interaction.
3. The method of claim 1 wherein said axis non-perpendicular to said plane
of interaction in non-parallel to said plane of interaction.
4. The method of claim 1 wherein said signal and reference light beams are
stationary and said first rotating step comprises rotating said recording
medium about said axis non-perpendicular to said plane of interaction.
5. The method of claim 1 wherein said recording medium is stationary and
said first rotating step comprises rotating said reference and signal
beams at an incident surface of said recording medium about said axis
non-perpendicular to said plane of interaction.
6. The method of claim 1 wherein successive ones of said succession of
peristrophic multiplexing angles are separated by a predetermined
difference angle.
7. The method of claim 6 wherein said predetermined difference angle is
amount to spatially shift holographic projections of holograms recorded at
successive ones of said angles by a predetermined amount.
8. The method of claim 6 wherein:
a selected hologram recorded in said recording medium is reproducible from
said recording medium by projecting said reference beam onto said selected
spot and providing a detector plane of a particular field of view at a
location in a holographic projection beam path of said selected hologram;
and
said difference angle is an amount to shift out of said field of view an
unselected one of said holograms recorded at a next one of said
peristrophic multiplexing angles relative to the peristrophic multiplexing
angle of said selected hologram.
9. The method of claim 6 wherein:
said selected hologram recorded in a recording medium is reproducible from
said recording medium by projecting said reference beam onto said selected
spot at the peristrophic multiplexing angle of said selected hologram; and
said difference angle is sufficient to create a Bragg mis-match with said
reference beam and an unselected one of said holograms recorded at a next
one of said peristrophic multiplexing angles relative to the peristrophic
multiplexing angle of said selected hologram.
10. The method of claim 1 wherein each of said holograms in said succession
of holograms is recorded in said selected spot at a different peristrophic
multiplexing angle whereby said holograms are peristrophically multiplexed
only.
11. The method of claim 1 further comprising second rotating said recording
medium through a second succession of angular multiplexing angles about an
axis perpendicular to said plane of interaction, wherein at least one of
said first rotating or said second rotating is performed simultaneously
with said successively modulating.
12. The method of claim 11 wherein said successively modulating step
successively modulates said signal beam with a sub-set of said succession
of holograms corresponding to said succession of angular multiplexing
angles while said second rotating step is performed and thereafter said
first rotating step rotates said recording medium to a next one of said
succession of peristrophic multiplexing angles.
13. The method of claim 12 wherein said sub-set of holograms corresponds to
a maximum number of holograms that can be angularly multiplexed in a
single recording spot in said medium.
14. A method of recording multiplexed holograms in a recording medium using
a reference light beam and a signal light beam modulatable with successive
holograms to be recorded, said signal and reference beams defining a plane
of interaction of said recording medium, said method comprising:
recording a first set of plural multiplexed holograms in a selected
recording spot in said recording medium;
rotating at least on of said recording medium and/or said signal and
reference light beams relative to the other through a peristrophic
multiplexing difference angle about an axis non-perpendicular to said
plane of interaction contemporaneously with the successively modulating
step; and
recording a second set of plural multiplexed holograms in said selected
recording spot.
15. The method of claim 14 wherein said axis non-perpendicular to said
plane of interaction is parallel to said plane of interaction.
16. The method of claim 14 wherein said axis non-perpendicular to said
plane of interaction is non-parallel to said plane of interaction.
17. The method of claim 14 wherein said signal and reference light beams
are stationary and said first rotating step comprises rotating said
recording medium about said axis non-perpendicular to said plane of
interaction.
18. The method of claim 14 wherein said recording medium is stationary and
said first rotating step comprises rotating said reference and signal
beams at an incident surface of said recording medium about said axis
non-perpendicular to said plane of interaction.
19. The method of claim 14 wherein said difference angle is sufficient to
spatially shift holographic projections of holograms recorded at
successive ones of said angles by a predetermined amount.
20. The method of claim 14 wherein:
said selected holograms recorded in said recording medium is reproducible
from said recording medium by projecting said reference beam onto said
selected spot and providing a detector plane of a particular field of view
at a location in a holographic projection beam path of said selected
hologram; and
said difference angle is sufficient to shift out of said field of view an
unselected one of said holograms recorded at a next one of said
peristrophic multiplexing angles relative to the peristrophic multiplexing
angle of said selected hologram.
21. The method of claim 14 wherein:
said selected hologram recorded in said recording medium is reproducible
from said recording medium by projecting said reference beam onto said
selected spot at the peristrophic multiplexing angle of said selected
hologram; and
said difference angle is sufficient to create a Bragg mis-match with said
reference beam and an unselected one of said holograms recorded at a next
one of said peristrophic multiplexing angles relative to the peristrophic
multiplexing angle of said selected hologram.
22. The method of claim 14 wherein said step of recording a set of
multiplexed holograms comprises second rotating said recording medium
through a succession of angular multiplexing angles about an axis
perpendicular to said plane of interaction while successively modulating
said signal beam with a corresponding set of successive holograms.
23. The method of claim 22 wherein each of said first and second sets of
multiplexed holograms corresponds to a maximum number of holograms that
can be angularly multiplexed in a single recording spot in said medium.
24. The method of claim 14 wherein the step of recording a first set of
multiplexed holograms employs a holographic multiplexing process.
25. The method of claim 24 wherein said multiplexing processing comprises
one of the following multiplexing processes: (a) angular multiplexing, (b)
wavelength multiplexing; (c) phase code multiplexing;
26. Apparatus for recording multiplexed holograms in a recording medium;
comprising:
an optical element for directing a signal light beam and a reference light
beam onto a selected recording spot in said recording medium, said signal
and reference light beams defining a plane of interaction of said
recording medium;
an element for successively modulating said signal light beam in accordance
with a succession of holograms to be recorded in said recording medium;
and
a rotation device for rotating at least of said recording medium and/or
said signal and reference light beams with respect to the other through a
succession of peristrophic multiplexing angles about an axis
non-perpendicular to said plane of interaction, said axis being one which
retains said light beam and said reference light beam on said recording
spot, said rotation device being operated contemporaneously with said
means for successively modulating.
27. The apparatus of claim 26 wherein said axis non-perpendicular to said
plane of interaction is parallel to said plane of interaction.
28. The apparatus of claim 26 wherein said axis non-perpendicular to said
plane of interaction is non-parallel to said plane of interaction.
29. The apparatus of claim 26 wherein said signal and reference light beams
are stationary and said rotation device comprises means for rotating said
recording medium about said axis non-perpendicular to said plane of
interaction.
30. The apparatus of claim 26 wherein said recording medium is stationary
and said rotation device comprises means for rotating said reference and
signal beams at an incident surface of said recording medium about said
axis non-perpendicular to said plane of interaction.
31. The apparatus of claim 26 wherein successive ones of said succession of
peristrophic multiplexing angles are separated by a predetermined
difference angle.
32. The apparatus of claim 31 wherein said predetermined difference angle
is sufficient to spatially shift holographic projections of holograms
recorded at successive ones of said angles by a predetermined amount.
33. The apparatus of claim 31 wherein:
said selected hologram recorded in said recording medium is reproducible
from said recording medium by projecting said reference beam onto said
selected spot, said apparatus further comprising a detector plane of a
particular field of view at a location in a holographic projection beam
path of said selected hologram; and
said difference angle is sufficient to shift out of said field of view an
unselected one of said holograms recorded at a next one of said
peristrophic multiplexing angles relative to the peristrophic multiplexing
angle of said selected hologram.
34. The apparatus of claim 31 wherein:
said selected hologram recorded in said recording medium is reproducible
from said recording medium by projecting said reference beam onto said
selected spot at the peristrophic multiplexing angle of said selected
hologram; and
said difference angle is sufficient to create a Bragg mis-match with said
reference beam and an unselected one of said holograms recorded at a next
one of said peristrophic multiplexing angles relative to the peristrophic
multiplexing angle of said selected hologram.
35. The apparatus of claim 26 wherein each of said holograms in said
succession of holograms is recorded in said selected spot at a different
peristrophic multiplexing angle whereby said holograms are
peristrophically multiplexed only.
36. The apparatus of claim 26 further comprising section means for rotating
said recording medium through a succession of angular multiplexing angles
about an axis perpendicular to said plane of interaction, wherein said
means for successively modulating operates simultaneously with one of (a)
said first means for rotating, (b) said second means for rotating.
37. The apparatus of claim 36 wherein said succession of holograms
corresponds to said succession of angular multiplexing angles and does not
exceed a maximum number of holograms that can be angularly multiplexed in
a single recording spot in said medium.
38. The apparatus of claim 36 wherein said succession of holograms
corresponds to said succession of peristrophic multiplexing angles and
does not exceed a maximum number of holograms that can be peristrophically
multiplexed in a single recording spot in said medium.
39. A method of processing plural holograms in a recording medium with an
input pattern, comprising:
directing a signal light beam and a reference light beam onto a selected
recording spot in said recording medium, said signal and reference light
beams defining a plane of interaction of said recording medium;
successively modulating said signal light beam in accordance with a
succession of holograms to be recorded in said recording medium; and
first rotating at least one of said recording medium and/or said signal and
reference light beams with respect to the other through a succession of
peristrophic multiplexing angles about an axis non-perpendicular to said
plane of interaction contemporaneously with the successively modulating so
as to record said succession of holograms at different peristrophic
multiplexing angles at said selected recording spot in said medium, said
axis being one which retains said signal light beam and said reference
light beam on said recording spot;
blocking said reference beam from said recording medium while constantly
modulating said signal light beam with said input pattern;
second rotating at least one of said recording medium and said signal and
reference light beams with respect to the other through said succession of
peristrophic multiplexing angles about an axis non-perpendicular to said
plane of interaction; and
detecting a succession of similarity patterns at a correlation detection
plane in line with a path of now-blocked reference beam simultaneously
with said second rotating step.
40. The method of claim 39 wherein said axis non-perpendicular to said
plane of interaction parallel to said plane of interaction.
41. The method of claim 39 wherein said axis non-perpendicular to said
plane of interaction is non-parallel to said plane of interaction.
42. The method of claim 39 wherein said signal and reference light beams
are stationary and said first rotating step comprises rotating said
recording medium about said axis non-perpendicular to said plane of
interaction.
43. The method of claim 39 wherein said recording medium is stationary and
said first rotating step comprises rotating said reference and signal
beams at an incident surface of said recording medium about said axis
non-perpendicular to said plane of interaction.
44. An optical holographic processor including a recording medium for
producing a correlation between an input pattern and one of a succession
of peristrophically multiplexed holograms previously recorded in said
medium by directing a signal light beam and a reference light beam onto a
selected recording spot in said recording medium, said signal and
reference light beams defining a plane of interaction of said recording
medium, successively modulating said signal light beam in accordance with
said succession of holograms while simultaneously rotating one of (a) said
recording medium and (b) said signal and reference light beams relative to
the other through a succession of peristrophic multiplexing angles about
an axis non-perpendicular to said plane of interaction, said processor
comprising:
a means for defining a correlation detection plane in line with a path of
said reference beam;
means for modulating said signal light beam in accordance with said input
pattern while blocking said reference beam from said medium;
means for rotating one of (a) said recording medium and (b) said signal
light beam relative to the other through said succession of peristrophic
multiplexing angles about an axis non-perpendicular to said plane of
interaction, said means for rotating being operable contemporaneously with
said means for modulating so as to produce a succession of similarity
patterns as said correlation detection plane. |
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Claims |
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Description |
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BACKGROUND OF THE INVENTION
1. Technical Field
The present invention relates to holographic memories, holographic storage
systems and holographic processors.
2. Background Art
The number of holograms that can be multiplexed in a given holographic
system is primarily a function of two parameters--the system's bandwidth
(either temporal or spatial frequency) and the material's dynamic range.
Recently, thin film materials have been developed with relatively large
dynamic range. An example of such a material is DuPont's HRF-150
photopolymer. Previously, 10 angle-multiplexed holograms in a 38 .mu.m
thick film with diffraction efficiency of 10.sup.-3 have been reported.
Because it is typical to work with holographic diffraction efficiencies on
the order of 10.sup.-6, there is sufficient dynamic range to record
significantly more than 10 holograms. The angular bandwidth limitation can
be alleviated by making the film thicker but scattering increases rapidly
with thickness in these materials. Another method that has been previously
used to increase the utilization of the available bandwidth of the system
is fractal sampling grids.
SUMMARY OF THE DISCLOSURE
The invention is embodied in a method of recording multiplexed holograms in
a holographic recording medium, constituting the steps of directing a
signal light beam and a reference light beam onto a selected recording
spot in the recording medium, the signal and reference light beams
defining a plane of interaction of the recording medium, successively
modulating the signal light beam in accordance with a succession of
holograms to be recorded in the recording medium and first rotating one of
(a) the recording medium, (b) the signal and reference light beams,
relative to the other through a succession of peristrophic multiplexing
angles about an axis non-perpendicular to the plane of interaction
simultaneously with the successively modulating step.
Successive ones of the succession of peristrophic multiplexing angles are
separated by a predetermined difference angle. The predetermined
difference angle is sufficient to either Bragg mis-match or spatially
shift reconstructed holograms recorded at successive ones of the angles by
a predetermined amount. Specifically, the selected hologram recorded in
the recording medium is reproducible from the recording medium by
projecting the reference beam onto the selected spot and providing a
detector plane of a particular field of view at a location in a
holographic projection beam path of the selected hologram. In one
embodiment, the difference angle is sufficient to spatially filter out
unselected holograms recorded at other peristrophic multiplexing position
(angles) relative to the peristrophic multiplexing angle of the selected
hologram. Alternatively, the difference angle is sufficient to create a
Bragg mis-match with the reference beam and the unselected holograms
recorded at other peristrophic multiplexing angles relative to the
peristrophic multiplexing angle of the selected hologram.
The invention may be combined with other holographic multiplexing
techniques such as, for example, angular multiplexing, wavelength
multiplexing and so forth.
In one embodiment of such a combination, the recording of a set of
successive holograms is simultaneous with the angular multiplexing
rotation through a succession of angles, and is repeated after each
peristrophic rotation of the next peristrophic multiplexing angle for the
recording of the next set of hologram. In this embodiment, the modulating
step successively modulates the signal beam with a set of successive
holograms corresponding to the succession of angular multiplexing angles
while the second rotating step is performed and thereafter the first
rotating step rotates the recording medium to a next one of the succession
of peristrophic multiplexing angles. Preferably, each set of holograms
corresponds to a maximum number of holograms that can be angularly
multiplexed in a single recording spot in the medium.
In another embodiment, the recording of successive holograms is
simultaneous with the peristrophic rotation through a succession of
peristrophic multiplexing angles, and is repeated after each angular
multiplexing rotation to the next angular multiplexing angle for the
recording of the next set of holograms. In this embodiment, each set of
holograms corresponds to the maximum number of holograms that can be
peristrophically multiplexed in a single recording spot in the medium.
In yet another embodiment of the invention, an optical holographic
correlator is realized by reconstructing ("reading out") holograms
recorded in the medium by projecting onto the medium a signal beam from
the spatial light modulator representing, for example, an unknown image,
while blocking the reference beam from the recording medium. This produces
a correlation function at a detector plane at the origin of the
now-blocked reference beam with which the holograms were previously
recorded.
BRIEF DESCRIPTION OF THE DRAWING
FIG. 1 is a schematic diagram of an exemplary holographic storage system
embodying the invention.
FIG. 2 is a schematic diagram of an exemplary holographic correlator
embodying another aspect of the invention.
FIG. 3 is a graph illustrating the diffraction efficiency of each one of a
succession of holograms recorded in the course of a demonstration of the
embodiment of FIG. 1.
DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS
This specification describes peristrophic multiplexing as a solution to the
bandwidth limited density and capacity problem. (The word peristrophic is
Greek for rotation). With this method the hologram is physically rotated
with the axis of rotation being perpendicular to the film's surface every
time a new hologram is stored. The rotation does two things. It shifts the
reconstructed hologram away from the detector allowing 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 or wavelength multiplexing to increase the storage density and with
spatial multiplexing to increase the storage capacity of the system.
Referring to FIG. 1, a beam splitter 10 splits a coherent monochromatic
light beam from a laser 20 into a reference beam (R) and a signal beam (S)
which are directed and collimated by optics 30 to a selected recording
spot 40a in a holographic recording medium 40 such as a thin lithium
niobate film and/or a photopolymer film. A spatial light modulator (SLM)
50 modulates the signal beam S in accordance with an input image I. A lens
55 of focal length F between the SLM 50 and the recording medium 40 is
displaced from both the SLM 50 and the film 40 by its focal length F, as
indicated in the drawing. The signal and reference beams S and R produce
an interference pattern in the holographic recording medium 40 which is at
least semi-permanently recorded therein. In order to read out the recorded
hologram, the reference beam R is projected at the same angle to the same
recording spot 40a, to produce an output beam O incident on a detector
plane or focal plane array 60 through a spatial filter 70 with aperture A.
A lens 80 of focal length F between the detector plane 60 and the film 40
is displaced from both the detector plane 60 and the film 40 by its focal
length F.
Angular multiplexing is conventionally performed by applying a succession
of input images to the spatial light modulator 50 while rotating the
recording medium 40 about the Y axis through a corresponding succession of
angles while the signal and reference beams S and R continue to illuminate
the same recording spot 40a. The Y axis is perpendicular to the plane of
interaction defined by the reference beam R and the signal beam S. The
plane of interaction is defined such that both the reference beam R and
the signal beam S lie in the plane of interaction.
In accordance with the present invention, peristrophic multiplexing is
performed by applying a succession of input images to the spatial light
modulator 50 while rotating the recording medium 40 about any axis that is
not perpendicular to the plane of interaction through a corresponding
succession of angles. In one preferred embodiment, this rotation is
performed about the Z axis (shown in FIG. 1) lying in the plane of
selectivity.
The peristrophic multiplexing process of the invention can be combined with
any holographic multiplexing technique, such as angular multiplexing,
wavelength multiplexing, phase code multiplexing and the like. When
combined with angular multiplexing, the invention is carried out by
angularly multiplexing a maximum number of holograms in the selected
recording spot 40a, rotating the medium by a predetermined angle about the
Z axis (or any axis not perpendicular to the plane of interaction) and
then angularly multiplexing another set of holograms in the same spot.
This sequence is repeated until a maximum range of peristrophic
multiplexing angles (rotation about the Z axis) has been reached. Then,
the entire process is carried out at a next recording spot in the medium.
In an alternative embodiment, the order of the angular multiplexing and
peristrophic multiplexing steps may be reversed, in which case the
rotation about the angular multiplexing Y axis to the next angular
multiplexing angle is followed by a peristrophic rotation (about the Z
axis, for example) through successive peristrophic rotation angles while
recording the next succession of holograms.
In one implementation, synchronization and control electronics 90
synchronizes the spatial light modulator 50 with the motion of a Y-axis
servo 92 governing rotation of the recording medium 40 about the Y axis
during angular multiplexing and a Z-axis servo 94 governing rotation of
the Y-axis servo 92 and the recording medium 40 about the Z axis. In this
implementation, the Z axis servo 94 is stationary while both the Y axis
servo 92 and the recording medium 40 rotate about the Z axis under control
of the Z axis servo 94, although this relationship may be reversed in
other implementations, as in the alternative embodiment described above.
While FIG. 1 has been described in terms of rotating the recording medium,
the invention may be carried out just as well by rotating the signal and
reference beams at their intersection with the recording medium about the
desired axis (e.g., the Z axis) relative to the recording medium 40.
Although the exemplary embodiment of FIG. 1 has been described with
reference to mechanical rotation stages or servos 92, 94 to achieve the
desired angular multiplexing and peristrophic multiplexing rotations, such
rotations are preferably implemented with conventional optical techniques
employing, for example, acousto-optical devices or deflectors, dove
prisms, and so forth.
A selected one of the peristrophically multiplexed holograms thus recorded
in the film 40 is reconstructed or projected onto the detector plane 60
("read out") using the same procedure described above, except that only
the reference beam is projected onto the film 40 as shown, the signal beam
being blocked or turned off by the spatial light modulator 50.
The invention may be used as an optical correlator or holographic processor
illustrated in FIG. 2. This is accomplished after the peristrophically
multiplexed holograms have been recorded in the film 40 as described in
detail above. Than, rather than employing the reference beam to "read out"
previously recorded holograms, a signal beam from the spatial light
modulator 50 representing, for example, an unknown pattern, illuminates a
selected spot on the film 40 while the reference beam is blocked from the
film 40. As shown in FIG. 2, a correlation detector plane 61 lies on the
opposite side of the film 40 aligned with the path of the now-blocked
reference beam of FIG. 1. A lens 81 of focal length F between the film 40
and the correlation plane 61 is displaced from both the film 40 and the
correlation plane 61 by its focal length F.
What is detected at the correlation detector plane 61 is a similarity
pattern, such as a correlation or an inner product, between the pattern
imposed by the spatial light modulator 50 and a particular one of the
peristrophically multiplexed holograms recorded at the selected spot in
the film 40. The particular one multiplexed hologram is determined by the
peristrophic angle or position between the film 40 and the signal beam, as
described in detail above. In other words, different ones of the
peristrophically multiplexed holograms in the selected film spot are
matched (e.g., correlated) with the unknown pattern by rotating the signal
beam from the spatial light modulator 50 through various peristrophic
multiplexing angles, as described above. In one embodiment, the similarity
patterns (e.g., correlations) of all of the peristrophically multiplexed
holograms recorded at the selected spot are rapidly read out one at a time
(sequentially) at the correlation detector plane 61 by rotating either
film 40 (or the signal beam from the SLM 50) through the entire range of
peristrophic multiplexing angles while the SLM 50 continues to project the
"unknown" pattern.
Alternatively, similarity patterns (e.g., correlations) of many or all of
the peristrophically multiplexed holograms in the selected film spot are
read out simultaneously. Such a parallel read-out is accomplished using an
enlarged correlation detector plane 61' (dashed line in FIG. 2). Adjacent
ones of the peristrophically multiplexed holograms appear simultaneously
along the dashed-line arc in the enlarged correlation detector plan 61' of
FIG. 2.
Each similarity pattern thus detected at the detector plane 61 (or 61') is
either a two-dimensional correlation function, a two-dimensional inner
product or a correlation in one dimension and an inner product in the
other dimension, depending upon film thickness and storage format. If the
stored holograms are image plane holograms, then the similarity pattern is
an inner product. If the stored holograms are Fourier plane holgrams, then
the similarity pattern may be a two-dimensional correlation function,
provided the film 40 is sufficiently thin (e.g., 40 microns). Otherwise,
the similarity pattern at the correlation plane 61 is a correlation in one
dimension and an inner product in the other dimension.
In the peristrophic holographic storage system of FIG. 1, the reference
plane wave (R) is incident at an angle .theta..sub.r and the signal beam
(S) is incident at an angle .theta..sub.s, both angles measured with
respect to the film's normal. Taking the center pixel of the hologram as
the signal and neglecting any effects due to hologram thickness, the
hologram transmittance can be written as
##EQU1##
The hologram is then rotated by d.theta. about the center of the x-y plane
as shown in FIG. 1. Assuming the rotation is small, this results in the
coordinates being transformed according to: x'.apprxeq.x-yd.theta., and
y'.apprxeq.y+xd.theta.. Substituting these relations into Eq. 1, the
hologram be expressed in terms of the unrotated coordinates (x, y):
##EQU2##
After multiplying by R and Fourier transforming, the last term in Eq. 2
results a shift in the image. The rotation required to translate the image
out of the detector aperture is approximately given by,
##EQU3##
where d is the size of the image at the detector plane and F is the focal
length of the lens used. For image plane holograms, the expression is
##EQU4##
where 1/.delta. 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 combined with other
multiplexing methods to further increase the storage density.
Alternatively, holograms may be recorded at any intermediate Fresnel
plane.
The Bragg selectivity, assuming the reference is given by
##EQU5##
and assuming the signal is given by
##EQU6##
can be calculated using the Born and paraxial approximations and
integrating over the volume of the hologram. Assuming that the transverse
(x, y) dimensions of the film are much larger than the bandwidth of the
images, the Bragg selectivity can be shown to be
##EQU7##
where t is the thickness of the material. Using .lambda.=488 nm, t=38
.mu.m, and .theta..sub.x =.theta..sub.r =30.degree. results in a
selectivity of about 12.degree.. The Bragg matching requirement is the
dominant effect if
##EQU8##
For most material thicknesses, the Bragg matching criterion determines the
required rotation for peristrophic multiplexing. In our experiments,
because the thickness of the film is only 38 .mu.m, the image could be
filtered out before the gratings become non-Bragg matched.
Experimental Results
The invention was tested using an experimental setup corresponding to FIG.
1 combining 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 using standard angle multiplexing by rotating the medium. A
spatial light modulator (SLM) was used to present holograms to the system.
The reference and signal beams were initially incident at .+-.30+ from the
film's normal. The reference beam intensity was 1.1 mW/cm.sup.2 and the
signal beam had 300 .mu.W in about a 1 cm by 0.5 cm area. The film was
rotated in-plane by 3.degree. between each set of angle-multiplexed
holograms to enable the other holograms to be filtered out.
Equation 3 predicts a required rotation of about 90.degree. for Fourier
plane hologram while Equation 4 predicts about 1.7.degree. rotation for
image plane. The 3.degree. rotation was experimentally observed for the
in-between (Fresnel) case we used. Each angle-multiplexed hologram was
also separated by a 3.degree. rotation. The initial exposure time was 0.11
seconds, but starting at hologram number 26, each hologram was exposed for
0.005 seconds longer than the previous hologram to correct for the lost
sensitivity due to run time. There was a 1.5 second delay between hologram
to allow the rotation stages to completely stop.
In all, 295 holograms 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. 3. Each frame or hologram is numbered in FIG. 3 according to the
sequence in which it was recorded. The average efficiency was
.about.4.times.10.sup.-6 and the variations are primarily due to variation
in the average intensity of the frames. In separate experiment, we stored
equal amplitude plane wave holograms and observed a decrease in
diffraction efficiency proportional to 1/M.sup.2.
Prior to the present invention, we stored M=10 holograms with roughly
10.sup.-3 diffraction efficiency limited by the angular bandwidth of the
optical system. Peristrophic multiplexing made it possible to store M=295
holograms at the same location with a diffraction efficiency of
.about.4.times.10.sup.-6. Thus, peristrophic multiplexing allowed for
almost two orders of magnitude increase in the storage capacity of the
DuPont photopolymer and changed the limiting factor from the angular
bandwidth of the optical system to the dynamic range of the material.
In summary a method of multiplexing holograms by rotating the material or,
equivalently, the recording beams, has been described. Peristrophic
multiplexing can also be combined with other multiplexing methods to
increase the storage density of holographic storage systems. Peristrophic
multiplexing was experimentally demonstrated using DuPont's HRF-150
photopolymer film. A total of 295 holograms were multiplexed in a 38 .mu.m
thick photopolymer film by combining peristrophic multiplexing with angle
multiplexing.
While the invention has been described with reference to the embodiment of
FIG. 1 in which both the reference beam and signal beam approach the
crystal or film 40 from the same side, other arrangements are possible in
which, for example, the signal and reference beam approach the film 40
from opposite sides, in which case the detector plane of FIG. 1 would be
located on the same side of the film 40 with the signal beam.
While the invention has been described in detail by specific reference to
preferred embodiments, it is understood that variations and modifications
thereof may be made without departing from the true spirit and scope of
the invention.
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