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Description  |
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TECHNICAL FIELD
The present invention relates to multiplexed volume holographic recording,
readout, and interconnections, and, more particularly, to photonic
interconnections, photonic implementations of neural networks, optical
signal processing, optical information processing and computing, optical
memory, copying of multiplexed volume holograms, and multiplexed volume
holographic optical elements.
BACKGROUND ART
A wide variety of information systems applications exist that require a
high density of interconnections among device or system nodes, or a high
density of rapidly accessible memory, or both. These applications include,
for example, neural networks, telecommunications switching systems,
digital computing, and information (including signal) processing. In many
such applications, key requirements on the chosen interconnection
technology include low insertion losses, high interchannel isolation
(freedom from interchannel crosstalk), a high degree of potential fan-in
and fan-out at each node, weighted interconnection channels, and high
capacity. Comparable requirements exist for the chosen memory technology,
including low latency (rapid information access), parallel information
retrieval, low effective bit error rates (high signal-to-noise ratio),
high density information storage, and input/output compatibility with the
remainder of the system.
In order to satisfy these many and varied requirements, multiplexed volume
holographic optical elements provide an attractive alternative to
electronic implementations of high capacity interconnection and memory
elements. In fact, the very nature of a volume holographic optical element
tends to blur the distinction between a pure interconnection network on
the one hand, and a pure memory subsystem on the other, as it is in many
ways simultaneously well-suited to both roles. Even so, previous methods
for recording information or interconnection patterns in highly
multiplexed volume holographic optical elements, and for reading them out,
have not proven satisfactory in terms of throughput, crosstalk, and
capacity. Furthermore, they have not proven to be manufacturable, due to
the fact that information from a master volume holographic optical element
could not previously be efficiently transferred to or duplicated in
another such element.
In forming multiplexed volume holograms, one of three approaches is
typically taken: (1) sequential, which involves several
temporally-sequenced (and hence incoherent) exposures of the individual
components of the hologram, done by rotating or translating the hologram
(or the source beam, reference beam, or object beam); (2) simultaneous and
fully coherent, which involves the use of two or more mutually coherent
beams, each encoded with information and serving as a reference beam for
the other(s); and (3) some combination of sequential and simultaneous
fully coherent.
The first approach has the major disadvantage that temporal sequencing is
time-consumptive, which can be of considerable importance in applications
envisioned herein, for which the number of independent interconnections
that must be recorded is extremely large. Also, in many holographic
recording materials, sequential exposures tend to erase previously
recorded information, leading to the necessity of incorporating unwieldy
programmed recording sequences in order to result in the storage of a
predetermined set of interconnections.
The second approach is designed to circumvent the above sequencing
difficulties, but suffers instead from the coherent recording of unwanted
interference patterns (holograms) that give rise to deleterious crosstalk
among the various (supposedly independent) reconstructions, as described
in more detail below.
The third approach is subject both to sequential recording time delays and
the necessity for programmed recording schedules, as well as to the
generation of undesirable crosstalk. As such, none of the previously
employed multiplexed recording techniques allows for the generation of
three-dimensional, truly independent interconnections between two or more
two-dimensional planar arrays within the context of a temporally efficient
recording scheme.
In all of the prior art approaches to the holographic recording of a
multiplexed interconnection, two primary forms of interchannel crosstalk
are encountered to a greater or lesser extent. Coherent recording
crosstalk arises from the simultaneous use of multiple object and
reference beams, all mutually coherent with each other. The mutual
coherence causes additional interconnections to be formed other than those
desired. Reconstruction with independently valued inputs results in the
generation of output beams that cross-couple through the undesired
interconnection pathways, which compromises the independence of the
desired interconnection channels.
A second, unrelated form of crosstalk arises due to beam degeneracy, which
occurs whenever a single object beam is used with a set of reference beams
to record a fan-in interconnection to a single output node (e.g., neuron
unit in the case of the photonic implementation of neural networks).
(Fan-in is the connection of multiple interconnection lines to a common
output node.) This latter form of crosstalk is present even when the set
of object beams is recorded sequentially.
Of at least equally serious consequence is the optical throughput loss that
results from interconnection fan-in so constructed as to exhibit beam
degeneracy. In many well-documented cases, this loss is severe, resulting
in at least an (N-1)/N loss (or, equivalently, a 1/N throughput
efficiency) for the case of an N-input, N-output interconnection system,
as reported by J. W. Goodman, Optica Acta, Vol. 32, pages 1489-1496
(1985). This is a truly daunting loss factor for interconnection systems
such as those envisioned for neural networks, which may both require and
be capable of 10.sup.5 to 10.sup.6 inputs and outputs.
In certain types of photorefractive materials, an additional throughput
loss can arise from the incoherent superposition of several gratings
within the same volume of the holographic optical element, due to the
reduction in the effective modulation depth of the recorded holographic
fringes. This effect occurs primarily in photorefractive crystals that
generate an index of refraction or absorption change in response to local
gradients in the intensity distribution, but would not be expected to
occur in linear photorefractive materials that generate an index of
refraction or absorption change in direct proportion to the magnitude of
the local intensity distribution. In a number of cases, this effect can
also result in at least an (N-1)/N loss for the case of an N-input,
N-output interconnection system, as reported by P. Asthana, "Volume
Holographic Techniques for Highly Multiplexed Interconnection
Applications", Ph.D. Dissertation, University of Southern California
(1991), available from University Microfilms, Ann Arbor, Mich.
In the prior art, few attempts have been made to address the extremely
important technological problem of duplicating the contents of a fully
recorded, heavily multiplexed volume holographic optical element or
interconnection device, particularly in the case of neural network
interconnections. For example, to the inventors' knowledge, there is no
known prior technique for rapid copying of a volume hologram that is
angularly multiplexed in two dimensions, other than that described in the
parent application of the present application.
In the case of neural network interconnections, the training and/or
learning sequences may be quite involved; in some cases, the training
and/or learning sequences may result in a unique interconnection, and the
exact learning sequence may not be reproducible in and of itself at all.
In such cases, it is desirable to replicate the contents of the
interconnection medium in such a manner that a fully functional copy is
produced, as characterized by a complete operational set of
interconnections indistinguishable from those implemented by the master.
The method of replication must not demand an extremely lengthy recording
sequence, must not be inefficient in its utilization of the programmed
recording schedule and/or the total optical energy available for
reproduction purposes, and must not induce additional optical throughput
loss or interchannel crosstalk beyond that already incorporated in the
master.
In the parent application of the present application, apparatus for the
incoherent/coherent multiplexed holographic recording of photonic
interconnections and holographic optical elements is described.
Specifically, apparatus for providing multiplexed volume holographic
recording and readout comprises:
(a) means for providing an array of coherent light sources that are
mutually incoherent;
(b) means for simultaneously forming an object beam and a reference beam
from each coherent light source, thereby forming a set of multiplexed
object beams and a separate set of multiplexed reference beams;
(c) means for either independently modulating each object beam, or
spatially modulating a set of object beams so that all object beams are
identically modulated;
(d) means for either independently modulating each reference beam, or
spatially modulating a set of reference beams so that all reference beams
are identically modulated;
(e) a holographic medium capable of simultaneously recording therein a
holographic interference pattern produced by at least a portion of the set
of all modulated multiplexed object beams and of the set of all modulated
multiplexed reference beams pairwise, with all such pairs being mutually
incoherent with respect to one another; and
(f) means for directing at least a portion of the set of modulated object
beams and of the set of modulated reference beams onto the holographic
medium and for interfering the portion of the modulated object beams and
of the set of modulated reference beams, pairwise, inside the holographic
medium.
Although the primary mode of multiplexing is angular, spatial and/or
wavelength multiplexing may also be incorporated.
The architecture and apparatus described in the parent application
significantly reduce coherent recording cross-talk and beam degeneracy
crosstalk, and permit simultaneous network initiation, simultaneous weight
updates, and incoherent summing at each output node without significant
fan-in loss.
Further in accordance with the parent application of the present
application, the above apparatus is provided with means for controllably
blocking the set of object beams such that at least a portion of the set
of reference beams (either modulated or unmodulated) reconstruct a stored
holographic interference pattern. In one embodiment, the reconstructed
pattern is angularly multiplexed and detected in such a manner as to
produce an incoherent summation on a pixel-by-pixel basis of the
reconstructed set of object beams. In this manner, multiplexed volume
holographic recording and readout are provided.
Specific implementations to neural networks, telecommunication
interconnections (e.g., local area networks and long distance switching),
interconnections for digital computing, and multiplexed holographic
optical elements are provided in the parent application.
In addition, apparatus for copying a multiplexed volume hologram is
provided in the parent application. The apparatus comprises:
(a) means for providing an array of coherent light sources that are
mutually incoherent;
(b) means for forming two reference beams from each coherent light source,
thereby forming two sets of multiplexed reference beams, each set at a
different location;
(c) means for directing the first set of reference beams onto the original
multiplexed volume hologram to thereby form a set of output beams;
(d) means for directing the second set of reference beams onto a secondary
holographic recording medium;
(e) means for directing the set of output beams from the original
multiplexed volume hologram onto the secondary holographic recording
medium, with path lengths sufficiently identical to the reference beam
path lengths to permit coherent interference, pairwise, between the output
beams and the second set of reference beams, inside the secondary
holographic recording medium; and
(f) means for simultaneously recording in the secondary holographic medium
a holographic interference pattern produced by the set of output beams and
the second set of reference beams, thereby forming the substantially
identical multiplexed volume hologram.
Portions of the above-described apparatus also possess unique properties
and give rise to useful functions. It is to these unique portions, or
elements, that the present application is directed.
In addition, specific implementations are given that utilize subhologram
formation to avoid throughput losses due to incoherent superposition
effects, that provide for various modes of information transfer from a
master hologram to a copy, that address application areas in optical
memory and optical signal processing, and that exploit the double angular
multiplexing features of the apparatus described in the parent
application.
DISCLOSURE OF INVENTION
In accordance with the invention, a multiplexed volume holographic element
comprises a volume holographic medium capable of storing a holographic
modulation pattern, the holographic modulation pattern comprising a
multiplexed set of modulation pattern components, each of which, when
illuminated by an associated reference beam, leads to a reconstructed beam
such that:
(a) the reconstructed beams that emanate from the holographic medium are at
least partially angularly multiplexed;
(b) a spatial array of pixels is encoded onto each reconstructed beam, as
an image at some plane in space; and
(c) the images of said spatial arrays of pixels from the reconstructed
beams can be made to be substantially coincident in space.
Such multiplexed holographic elements in accordance with the teachings of
the invention can be generated by optically recording a holographic
interference pattern in a photosensitive medium, or by calculating the
holographic modulation pattern on a computer and manufacturing the
holographic element to include the computed modulation pattern. It is
compatible with the apparatus described in the parent application of the
present application. The spatial array images may comprise virtual or real
holographic images. Extensions to holographic records of 3-D images are
provided.
An apparatus for reading out the multiplexed holographic element of the
invention is further provided, and utilizes an array of coherent light
sources that are mutually incoherent, means for modulating the reference
beam generated by each such source, and means for directing at least some
of these reference beams onto the holographic medium, thereby generating a
set of output beams. A recording and readout apparatus that uses a
combination of spatial and angular multiplexing is also provided in
accordance with the invention. Further, two specific means for providing
the requisite 2-D source array are described: a 2-D array of surface
emitting laser diodes; and a set of diffraction gratings, each of a
different frequency, propagating in an acousto-optic cell.
In addition, apparatus for transferring information from a primary volume
holographic optical element to a secondary holographic medium is provided,
comprising:
(a) means for directing at least a portion of each beam of a set of
mutually incoherent reference beams onto the primary volume holographic
optical element, thereby producing a set of output beams;
(b) means for directing at least a portion of each beam of the set of
mutually incoherent reference beams onto the secondary holographic medium;
(c) means for directing the set of output beams from the primary volume
holographic optical element onto the secondary holographic medium, with
beam path geometries appropriate to permit coherent interference between
each output beam and each corresponding reference beam, inside the
secondary holographic medium; and
(d) means for recording in the secondary holographic medium a holographic
interference pattern produced by the set of output beams and the portion
of each beam of the set of mutually incoherent reference beams.
Also provided are means for transferring information from the secondary
holographic medium to the primary holographic medium, thereby enabling
iterative feedback between the two holographic media.
Further in accordance with the invention, apparatus for double angular
multiplexing is provided, comprising means for directing a set of
self-coherent but mutually incoherent beams to a spatial modulation means
for spatially modulating the set of beams, the spatial modulation means
comprising a plurality of pixels, at least one of which pixels is common
to more than one beam, with each beam that shares the common pixel being
angularly multiplexed at the common pixel.
Provision is further given for the spatial modulation means to comprise at
least one of a spatial light modulator, a planar hologram, and a volume
hologram.
Specific implementations are provided to: optical interconnections in
neural networks, digital computing, and telecommunications; holographic
optical elements; optical information processing; and optical memory.
BRIEF DESCRIPTION OF THE DRAWINGS
FIG. 1 is a generalized interconnection, with both fan-out and fan-in;
FIG. 2 is a schematic diagram of fan-out, showing interconnection pathways
and the implementation of analog weights;
FIG. 3 is a schematic diagram of fan-in, showing interconnection pathways
and the implementation of analog weights;
FIG. 4 is a schematic diagram of optical apparatus for simultaneous
incoherent/coherent recording of multiplexed holograms, showing angular
multiplexing of the reference beam set;
FIG. 5 is a schematic diagram of optical apparatus for either simultaneous
or independent readout of multiplexed holograms showing mutual incoherence
of readout (reconstructed) beams;
FIG. 6A is a schematic diagram of optical apparatus for recording of doubly
angularly multiplexed holograms, each a hologram of a 2-D array of pixel
values, while FIG. 6B is a schematic diagram of that portion of the
apparatus of FIG. 6A used in the reconstruction of the recorded images,
showing the incoherent summation on the output plane of the set of
reconstructed images in pixel-by-pixel registry, and FIG. 6C is a
schematic diagram of an acousto-optic deflector based system that
generates an array of coherent but mutually incoherent source beams, as
needed in the apparatus of FIGS. 6A and 6B;
FIGS. 7A-F show schematic diagrams of optical apparatus for one-step
copying or information transfer from a primary multiplexed volume
holographic optical element to a volume holographic medium to yield a
secondary multiplexed volume holographic optical element, with FIG. 7A
depicting apparatus for the case of two transmission holographic elements,
FIG. 7B depicting apparatus for the case of two reflection holographic
elements, FIG. 7C depicting apparatus for the case of a reflection primary
holographic element and a transmission secondary holographic element, FIG.
7D depicting apparatus for the case of a transmission primary hologram and
a reflection secondary hologram, FIG. 7E depicting apparatus for the case
in which both holographic elements comprise hybrids of transmission and
reflection holograms, and FIG. 7F depicting apparatus for two-way
information transfer between the two volume holographic media, yielding a
resonator arrangement;
FIG. 8 is a schematic diagram of the optical interconnection paths due to a
holographic interconnection architecture for the 3:3 fan-out/fan-in case,
constructed such that each input and output node is only singly angularly
encoded, showing the origin of crosstalk and throughput loss due to beam
degeneracy;
FIG. 9, on coordinates of diffraction efficiency and normalized grating
strength (v/.pi.), is a simulation result for the holographic
interconnection architecture of FIG. 8 utilizing the optical beam
propagation method, for the case of sequential recording of the
interconnection gratings, showing the fan-out loss;
FIG. 10, on coordinates of diffraction efficiency and normalized grating
strength (v/.pi.), is a simulation result for the holographic
interconnection architecture of FIG. 8 utilizing the optical beam
propagation method, for the case of simultaneous fully coherent recording
of the interconnection gratings, showing the fan-out throughput loss and
the occurrence of recording-induced crosstalk;
FIG. 11 is a schematic diagram of optical interconnection paths of the
apparatus described in FIG. 6 for the 3:3 fan-out/fan-in case, showing the
angular multiplexing of both object (source) and reference beam sets,
configured to produce angular multiplexing of the reconstruction beam
fan-in to a given output node;
FIG. 12 is a schematic diagram of a multi-function spatial light modulator,
as utilized in the interconnection architecture shown in FIG. 14, showing
the incorporation of multiple photosensitive elements, control
electronics, and multiple modulation elements within each pixel;
FIG. 13, on coordinates of voltage (ordinate) and voltage (abscissa), is a
plot of the output transfer characteristic curves for both outputs of a
dual rail CMOS differential amplifier, with 15 transistors in an area of
2500 .mu.m.sup.2 ;
FIG. 14 is a schematic diagram of a preferred embodiment of apparatus for
the implementation of neural network modules, for the case of Hebbian
learning;
FIG. 15 is a schematic diagram of a preferred embodiment of apparatus for
the implementation of neural network modules, for learning algorithms of
the form .DELTA.w.sub.ij =.alpha.x.sub.i .delta..sub.j ;
FIGS. 16A-C are schematic diagrams of preferred embodiments of means for
generating learning terms .delta..sub.i, for the cases of (A) Widrow-Hoff,
(B) Perceptron, and (C) back propagation learning;
FIG. 17 is a schematic diagram of an alternative embodiment of apparatus
for the implementation of neural network modules;
FIG. 18 is a schematic diagram of apparatus for switching from a set of
wavelength division multiplexed optical input lines to a set of wavelength
division multiplexed optical output lines, wherein the source array and
two spatial light modulators are used to control the routing of the
switch;
FIG. 19A is a schematic diagram of means for providing the source array of
FIG. 18 in the case of a 1-D wavelength division multiplexed (WDM) input
line array and a 1-D wavelength division multiplexed output line array,
showing the center optical frequency v increasing along one direction and
the incorporation of mutual incoherence within a frequency band
.DELTA..nu. about each central optical frequency .nu. along a different,
substantially orthogonal direction, while FIG. 19B is a schematic diagram
of an alternative embodiment utilizing a one-dimensional source array,
with center frequency of each element being different, and a
one-dimensional phase modulator array providing mutual incoherence;
FIG. 20 is a schematic diagram of means for providing the source array of
FIG. 18 in the case of a 2-D WDM input line array and a 2-D WDM output
line array, showing a 2-D laser diode array each element of which has a
different center frequency, and a modulator array;
FIG. 21 is a schematic diagram of method and apparatus for recording of
multiplexed volume holographic optical elements, with one set of beams
modulated independently and the other set of beams modulated spatially but
identically; and
FIG. 22 is a schematic diagram of method and apparatus for recording of
multiplexed volume holographic optical elements, with both sets of beams
(reference and object) modulated independently.
BEST MODES FOR CARRYING OUT THE INVENTION
A. GENERAL
1. Introduction.
The description that follows is primarily directed to neural networks.
However, it will be appreciated by those skilled in the art that a major
component of the architecture and apparatus is generic to a number of
technologies, including telecommunications, digital computing, optical
information processing and computing, optical memory, copying of
multiplexed volume holograms, and holographic optical elements. Specific
applications to these are discussed below.
In considering the teachings of the invention, it is essential to
differentiate between two basic types of optical interactions (as
determined by the nature of the optical signals involved): incoherent and
coherent. Incoherent interactions occur whenever the input signals
temporally dephase over the relevant time of observation (detector
temporal integration window), in that they are either broadband (not
monochromatic) or are narrow band (nearly monochromatic) but separated in
optical frequency by more than the inverse of the observation time.
Interactions in which the input optical signals spatially dephase over the
spatial aperture of the relevant detector wherever the output is utilized
(detector spatial integration window) are also incoherent for all
practical purposes, and will obey certain summation rules. Coherent
interactions occur, on the other hand, whenever the input signals
simultaneously maintain a constant phase relationship over the detector
spatial and temporal integration windows.
From these remarks, it can be seen that it is quite important to understand
the distinction between coherent (or incoherent) light and coherent (or
incoherent) interactions as defined by the eventual detector configuration
and operational parameters. For example, it is perfectly acceptable to
consider a situation in which two mutually coherent (temporally) optical
beams interact to produce an interference pattern with a spatial scale
small compared with the relevant detector aperture. For two such mutually
coherent optical beams propagating at an angle with respect to each other,
the spatial scale of the resultant interference pattern decreases as the
angle between the two beams increases. In such cases, the interaction will
in fact follow incoherent summation rules, as the detector effectively
integrates the spatially varying interference pattern to produce exactly
the same result as the interaction of two mutually incoherent (temporally)
optical beams.
Referring now to the drawings, wherein like numerals of reference designate
like elements throughout, FIG. 1 depicts a generalized interconnection
scheme, showing both fan-in of input beams 10, 10' to nodes 12, 12',
respectively, and fan-out of output beams 10', 10" from the nodes.
The section of the interconnection shown depicts the fan-in to the m.sup.th
node from the (m-1).sup.th node plane (not shown), a fully connected layer
in which the interconnections fan out from each node 12 labeled 1 through
N to the nodes labeled correspondingly 1 through N in the (m+1).sup.th
node plane wherein full fan-in is effected, and fan-out from the
(m+1).sup.th node plane to the (m+2).sup.th node plane (not shown). In
some interconnection schemes, the m.sup.th node plane and the (m+1).sup.th
node plane are one and the same, consisting therefore of a set of nodal
outputs fully interconnected to the corresponding set of nodal inputs in a
feedback arrangement.
The weights w.sub.ij are shown to indicate that each (analog)
interconnection path modifies the output from a given node by means of the
multiplication weight w.sub.ij before fan-in is performed with an
appropriate summing operation at each node input. The weight labeling
scheme employed is as shown, such that the weight w.sub.ij interconnects
the j.sup.th nodal output in a given plane to the i.sup.th nodal input in
the succeeding plane.
FIG. 2 depicts fan-out of a plurality of output beams 10' from a node 12
(i.e., the i.sup.th node) on which at least one input beam 10 is incident.
Each beam 10' is propagated to the next node with a separate and
independent analog weight w.sub.ij as noted above, which is assigned to
each interconnection path.
As depicted in FIG. 2, for the purposes of this invention, the output value
from each given node is common, such that the interconnections represent
true fan-out rather than the individual interconnection of multiple output
ports from a single node.
FIG. 3 depicts fan-in of a plurality of input beams 10 to node 12,
generating at least one output beam 10'. Each beam 10 is modified by a
separate and independent analog weight w.sub.ij, assigned to each
independent interconnection path. True fan-in is achieved by means of an
appropriate summation rule at a single node input, as shown in the Figure.
Pertinent to the invention described in this application, such fan-in can
be provided by a set of optical beams that are incident on a common
detector plane, each incident at a separate angle.
In FIGS. 1, 2, and 3, the triangular symbol utilized to depict each
interconnection node represents not only the indicated direction of data
flow through the node, but also the potential for incorporation of an
input-to-output control transfer function (e.g., a hard or soft threshold
in the case of a neural network) that operates on the fanned-in, summed
inputs to produce a single (usually analog) output value that is fanned
out in turn to the succeeding network stage.
FIGS. 4 and 5 depict schematically how recording (FIG. 4) and
reconstruction (FIG. 5) of a set of holograms is accomplished in
accordance with the invention described in the parent application. In FIG.
4, an array of coherent but mutually incoherent sources 14 generates a set
of beams 10 (two such beams 10a, 10b are shown). A beamsplitter 16 forms a
set of object beams 11 and a set of reference beams 13. The object beams
11 pass through a set of objects (A.sub.1, A.sub.2) 18 to form a set of
object-encoded beams 15, which impinge on element 20 incorporating a
holographic recording medium. As used herein, "20" represents a volume
holographic optical element, comprising a volume holographic medium and
one or more holograms each consisting of a modulation pattern. It will be
appreciated that in some cases, the element 20 will not yet have recorded
therein the holographic modulation pattern and thus will consist only of
the holographic medium. Since the intent is to record such patterns into
the medium, the element 20 is hereinafter referred to as a holographic
element, even though it may not have the holographic patterns recorded
therein.
The reference beams 13 are reflected from a set of mirrors 22 and also
impinge on the holographic element 20, where they interfere with the
object-encoded beams 15 pairwise to form holographic interference patterns
in the recording medium, as is well-known.
It will be noted that the foregoing apparatus permits simultaneous
recording of the objects. Further, a first light source 14a in the source
array 14 is used to generate a first set of two beams 11a and 13a which
are mutually coherent; these beams derive from beam 10a. A second light
source 14b in the source array is used to generate a second set of two
beams 11b and 13b, which are also mutually coherent; these beams derive
from beam 10b. However, since the two light sources 14a and 14b are
mutually incoherent, then beams 10a and 10b are mutually incoherent, and
the two sets of beams derived therefrom are also mutually incoherent and
hence do not mutually interfere to form an interference pattern in the
medium of holographic element 20. While only two light sources 14a, 14b
are described, there is, of course, a plurality of such light sources in
the source array 14, each generating a coherent pair of object and
reference beams, each pair incoherent with all other pairs.
It will be noted that the superposition of a set of optical interference
patterns can be referred to as a set of mutually incoherent optical
interference patterns if all of the pairs of beams that generate each
individual optical interference pattern within the set are individually
coherent but mutually incoherent. Likewise, the set of holographic records
of a set of optical interference patterns can be referred to as a set of
mutually incoherent holographic records if all of the corresponding
optical interference patterns within the set are mutually incoherent.
Finally, each of the set of object beams and each of the set of reference
beams is independently multiplexed in at least one of angle, space, and
wavelength.
In FIG. 5, readout, or reconstruction, is achieved by blocking the object
beams 11. In the case of a holographic optical element, the holographic
element 20 may be read out in a physically distinct optical system, in
which the reference beam phase fronts illuminating the holographic medium
approximate those of the recording system. Readout may be simultaneous and
independent, or individual.
Simultaneous and independent readout is characteristic, for example, of
neural networks, associative memories, and shared memories. Individual
readout, by contrast, is characteristic of conventional optical memory
systems.
In simultaneous and independent readout, output beams 10a' and 10b' are
mutually incoherent, and complete control of what is read out is provided;
that is, one-half of beam 13a and all of beam 13b, or all of beams 13a,
13b, and 13c (not shown), or other combinations may be controllably used
as readout beams, with the modified set of reconstructed output beams
incoherently superimposed in space. For clarity, beam 13c is omitted from
the drawing. If shown, it would be at yet a different angle from beams 13a
and 13b.
In individual readout, any individual readout beam 13j can be modulated and
utilized to reconstruct an individual output beam 10a' or 10b' (or 10c',
etc.) without significant crosstalk.
Virtual images A.sub.1 ' and A.sub.2 ' are generated from the
reconstruction process in the position designated 18' where the objects 18
were located during the recording process, in such a manner that the
reconstructions 10' appear to emanate from the virtual images. As shown in
FIGS. 4 and 5, if the original objects 18 are located at separate
positions in space, then the virtual images 18' are also located at
distinct positions. It will thus be appreciated by one skilled in the art
that in any subsequent image plane of virtual images 18', images of the
objects A.sub.1, A.sub.2, and the like will again be located at separate
positions. Another key point is that the set of reconstructed beams 10'
are all mutually incoherent, and hence obey incoherent summation rules in
any chosen output plane.
FIG. 6A depicts apparatus suitable for the simultaneous recording of doubly
angularly multiplexed holograms, with each hologram comprising a 2-D array
of pixel values. A shutter 24 in the path of the set of object beams 11 is
used to control passage of the set of object beams to the holographic
element 20. During recording, the shutter 24 is open. The set of object
beams 11 passes through a lens 26, which approximately collimates the set
of beams and directs them toward a first spatial light modulator (SLM) 28.
Thus, each pixel of modulator 28 has many mutually incoherent optical
beams (angularly multiplexed) passing through it. (This feature is called
simultaneous spatial modulation of angularly multiplexed incoherent
beams.) The resulting set of modulated beams {A.sub.j } is incident on the
holographic element 20.
The set of reference beams 13 passes through lens 30 and lens 34,
reflecting from mirror 22 in the process; their function, together, is to
focus each beam onto the corresponding pixel of modulator 32. From spatial
light modulator 32, the set of reference beams 13 is directed into the
holographic element 20 by lens 36, where the reference beams interfere
with the object beams to produce a multiplexed hologram with a set of
stored interconnection weights. The interconnection weights can be
dependent on corresponding products of the form A.sub.j x.sub.j, as
described in more detail below.
Finally, it will be noted that the object beams 11 are all at different
angles with respect to each other and that the reference beams 13 are also
all at different angles with respect to each other. As a consequence of
this angular difference, it will be appreciated that these beams are
double (meaning both object and reference beams) angularly multiplexed in
the volume holographic element 20.
It will be further appreciated by those skilled in the art that the
placement of lens 36 determines whether the beams transmitted through the
spatial light modulator 32 are collimated at the entrance plane of the
hologram, focused at the entrance plane of the hologram to form an image
of the spatial light modulator, or form instead expanding or contracting
wavefronts at the entrance plane of the hologram. A second lens (not
shown) placed following spatial light modulator 28 can be adjusted to
focus the two-dimensional Fourier transform of each of the beams
transmitted through spatial light modulator 32 onto spatially separated
regions at the entrance plane of the hologram. This same function can also
be accomplished by appropriate choice and positioning of | | |
