OPTICAL NEURAL NETWORK

Abstract: The optical neural network stores data in holographic form. Radiation from a first source is arranged to interfere with radiation from a second source to produce a matrix of holographic gratings. The gratings represent binary data which is to be stored in a holographic storage medium. The first source of radiation is obtained from a row of electro-optic modulators and the second source is obtained from a column of electro-optic modulators.

Description: OPTICAL NEURAL NETWORK. The present invention relates to an optical neural network, in which data is stored in holographic form. The invention finds application in data storage and processing which use holographic techniques. Considering the prior art, in an article by J.J. Hopfield, entitled "Neural Networks and Physical Systems with Emergent Collective Computation Abilities" Proc. Natl. Sci. USA 79, 2554, 1982, a model is proposed in which many identical components are completely interconnected and, as a result of the simple characteristics of the components and their interconnections, the complete system shows computational properties. The computational properties of this neural network can be sophisticated and include recognition of stored information from a partial input. The key point is that these properties arise from the hardware, and programming as we know it is absent. An optical implementation of a Hopfield model is described in the joint papers by D. Psaltis and N. Farhat entitled "Optical Computing and the Hopfield Model", Paper WB2-4, Proc. of ICO Con. Supporro, August 1984, and "Optical Implementations of the Hopfield Model", Paper WB3-1, Proc. of ICO Con. Supporro, August 1984. However, neither of these papers details a store or do they describe a phase-encoding holographic system s described below. An aim of the present invention is to provide a SUBSTITUTESHEET combined optical/electronic implementation of a Hopfield model which incorporates holographic storage arrangements. According to the present invention there is provided an optical neural network in which data is stored in holographic form, wherein radiation from a source is arranged to interfere with radiation from a second source to produce at least one matrix of holographic gratings representing binary data to be stored in a holographic storage medium. An exemplary embodiment of the invention will now be described with reference to the following drawings wherein: Figure la shows a replay system. Figure lb shows a system including the replay system and a recording system. Figure 2 shows a matrix of gratings as recorded, and; Figure* 3 shows a mask for removing unwanted characteristics of a light source. The network consists of a number of identical components ("neurons") - N say - which are always in a binary state. Thus the state of the ith neuron is Vi - ±1 (1 ) The neurons are interconnected ("synapses"); the strength (weight) of the interconnection between the ith and jth neuron is T • Information is stored in the ij interconnection according to the rule _ M n _M m m ( 2 ) T -Σ T - _ ■ V V i j m»l i j m»=l i j where m labels the binary code of up to N bits which constitutes a piece of information. M such codes are stored. "Computation" is performed by setting the neurons into the state according to the code m i.e. m V — ** V i i This is not recorded. Instead each neuron is subjected to a new input generated from its interconnections. _m V = T V (3) i j=i ij j Since the state of the neuron is limited to +1 (equation 1), the neuron responds to the new input by setting — m itself to sgn V; . That is if the sign is +ve V. — 1, if -ve it goes to -1. The process is then repeated. One consequence is a steady state is reached which is regarded as the final output. If the memory is not over-loaded (M«N) and the codes stored are sufficiently different then the output goes to a steady state which is one of the recorded codes if the input is all or a significant part of a stored code. Thus the memory can be "stimulated" to acknowledge it has received a code earlier in its history and may provide some degree of error correction if suitable triggered by part of a SUBSTITUTE SHEET stored code . This is essentially the Hopfield algorithmic model. Implementation. In a manner to be described, radiation from a row of identical electro-optic modulators (EOM), each the analogue of a neuron, is made to interfere with radiation from an identical column of modulators to produce a " matrix of holographic gratings in a holographic recording medium (such as a photorefractive material), each element in the matrix being the analogue of a -synapse. The m output from the row of modulators relates to V^ , the column to V m and th « matrix of gratings produced corresponds to the rule given by equation 2, where m labels a particular code. This is the recording mode. In a replay mode Figure la the holographic matrix HM is illuminated by sources via a cylindrical lens CL through a row of modulators initially set to be in a desired state V m and the output of the matrix is summed in columns in accordance with equation- 3. The state of the summed columns is assessed and is electronically fed back to the row of modulators. In the implementation to be described, the holographic gratings formed are reflecting gratings and the binary code is imposed by the EOM as a phase shift of 0 or T A half silvered mirror HSM is positioned between the modulators EOM and the holographic matrix HM. A return beam is diverted through a permanent mask UK to a cylindrical lens CLA and then to a row of detectors DTS, having a non-linear feed to the modulators EOM. Referring to Figure lb, a schematic diagram of a complete system is shown. A coherent light source SC illuminates a cylindrical lens CYL, which transmits the light beam onto a first array of electro optic modulator EOMl by way of a partially silvered mirror PSMR. Some of the beam is reflected by the mirror PSMR to a second, single, electro optic modulator EOM2 which is diverted through a cylindrical lens CYLA via reflector G and partially silvered mirror PSMX, to detectors D which feed the i/P, O/P logic circuit L. Circuit L controls the modulators EOMl and EOM2. The beam from the modulators EOMl passes through the half silvered mirror HSM to the hologram store HMS. Part of the beam is reflected through 90 degree rotation, by the mirror HSMW and via shutter S to reflectors A,B and C and presented to the hologram store HMS. A beam, returned from the hologram store HMS is reflected by the mirror HSMW through a mask MA, to the cylindrical lens CYLA, and then to the detectors D, where it interferes with light from the modulators EOM2. The outputs of detectors D feed the output logic circuit L. The prisms E,F and memory switch SW will be described later. Entering Information (Recording) Consider first two colinear, counter propagating optical beams (coherent, same polarization) of uniform and equal amplitude A. These produce a non-uniform intensity given by 2 I NU- A coβ(2kx + 0 a -0 b ) (4) where 0 and 0 are phase shifts on the two a b beams. Here k is the wave vector of the light and x the direction of propagation. In, for example a photorefractive material this non-uniform contribution is the only -contribution to change in permittivity [() . The intensity will give rise to a grating in which the modulation is essentially the same as ^-NU* The stren 9 tn of the grating (depth of modulation) will vary approximately linearly with exposure (amplitude constant) at low levels. From equation 4, if 0 a = 0 b a grating in, say, the zero position will be created while 0 a 0b' with 0a' ^b = ° or 7\ > a grating shifted by A/4, where t is the wavelength of light from the zero position will be formed. This forms the basis of the memory (the weight between interconnections) . To be more specific, visualize the creation of two counter propagating beams except now the 'a' beam consists of N parallel strips of light (parallel in the z direction, see Figure la) each represented by ύT_= A cos(wt - kx + 0 ) (5) where w is the angular frequency of the light, t is time and 0^ « 0 or ^ » and 'b' beam consists of an identical wave front except it is rotated through 90* (i.e. strips parallel to the y direction, but the plane of polarization of 'a' and 'b' beams are maintained parallel. By placing the holographic medium between the two beams a matrix of gratings are recorded as shown in Figure 2. In Figure 2 the elements in the matrix of gratings have been labelled by the relative phase βhift they produce on reflection. (A grating in a zero position gives 0, a grating displaced by ,X / gives 7 (m) Thus to record the code V i this code is superimposed on the array EOMl which produce the phase shifts 0 __, ± m ( ø i = 0 for V i - +1 , i = 7 for V i « -1) on the 'a' beam and 0 on the 'b' beam. In the holographic medium an ξ - j modulation of ΛA cos(2kx + ø j " - ø j 1 ") (6) ij is produced. Additional codes are recorded by giving equal exposure with the appropriate setting of the modulators. Within the limits of linearity we have for M codes 2 M m m o A Σ cos{2kx + 0 - 0 (7) 13 m*l which, because 0^, ^ « 0, 7\ is 2 m T v h cos ( 2kx) Σcos^ cos^ ( 8) i-l m i j m where coεjj , coeφ « ' 1 or -1. j i This matrix agrees with that required in the Hopfield algorithmic model (see equation 2). This is the holographic store. Extracting information (Replay) The matrix is in effect a 2 dimensional array of reflectors. This is now illuminated by the *a' beam with i the EOMl voltages set to V m giving 0_; m . The 'b' beam is switched off using the shutter S {Figure lb) so there is no recording. The beam reflected from the ijth element of the hologram is , _m < -. _. __ m tr °^^.cos0 cos .cos(wt + kx + 0 ) ij i j j with the aid of a cylindrical lens the output from the j elements can be summed to give The contribution arising when j = i is not required in the Hopfield model and has not been included in equation 9. It can be removed by the mask MA carrying opaque squares corresponding to the diagonal elements. While equation 9 is obviously structurally similar to equation 3 as required in the implementation of the model, it has to be converted to a voltage drive which can be fed back into the array EOMl . The encoding is through phase shift 0 and therefore we are only interested in the sign given by equation 9. Finding the sign of equation 9 is equivalent to finding — m sgn V i • A way of finding the sign is as follows:- take another beam from the same coherent source as described above with reference to Figure lb. Pass it through a single array such as EOM2 which is switched in time with a continuous square wave between the 0 and 7T phase shift states. This occurs at a rate which is fast compared with that of the array EOMl. Incorporate in the recorded matrix an extra row and column. Let it be the first row and column and arranged to replay with 0 = 0. Only the reflection from the element i = 1, j = 1 is selected from the first row and column by the mask MA with the appearance shown in Figure 3. The paths in the system are now adjusted so that when the single EOM is switched to 0, light from it interferes constructively with the reference channel (T..). Thus as the modulator switches in the sequence 0, , 0 etc, the o/p in the reference channel, 1 goes high,low,high etc. All other channels will be doing the same or else low, high, low - etc. If the former εgn(V ) is set to 1, if the latter i to -1. This is then fed back onto the row of modulators in the 'a'beam. It is self running and completes the implementation. A volume holographic store has been described. It can have high angular selectivity. As a result, if the angle of incidence of the recording and replay beam are changed through a small angle another T.. matrix can be read and replayed. This could be achieved by introducing an electro-optic deflector into 'a' and 'b' beams and shown as dotted prisms E,F in Figure lb and controlled by a memory switch SW. By switching through discrete angular deflections, the matrix becomes three dimensional with elements T^-:^, k labelling the angular deflection state. Note all the rest of the EOM and electronics remain the same. In effect what we are doing is replacing the single weighted interconnection between neurons by K weighted interconnections where K is. the number of deflection positions. Codes may be stored by selection of the state K as well as by superposition in a fixed state K. Alternatively the code handling may be regarded as two-dimensional for we are effectively storing a code N bits long and K bits wide.

Claims: 270 - 11 - CLAIMS . 1. An optical neural network in which data is stored i holographic form, wherein radiation from a first source is arranged to interfere with radiation from a second source to produce at least one matrix of holographic gratings representing binary data to be stored in a holographic storage medium. 2. An optical neural network as claimed in claim 1, wherein the first source of radiation is obtained from a row of electro-optic modulators and the second source of radiation is obtained from a column of electro-optic modulators. 3. An optical neural network as claimed in claim 1, wherein the second source of radiation is generated from the first source by subjecting the first source to a ninety degree rotation without changing the plane of polarisation. 4. An optical neural network as claimed in claims 2 or 3 wherein the holographic storage medium is illuminated by a radiation beam generated by a row of electro-optic modulators set in a predetermined state, and the output from the storage medium is summed in columns, the states of which are assessed and represent the output data from the storage medium, said output data being arranged to be fed back to control the electro-optic modulators. 5. An optical neural network as claimed in claim 4 wherein the holographic gratings are reflecting gratings. 6. An optical neural network as claimed in claim 5 wherein the binary data is imposed by the electro optic modulators as a phase shift of 0 or Λ " , 7. An optical neural network as claimed in claim 4 wherein, ouput is summed by use of a cylindrical lens. 8. An optical neural network as claimed in claim 7 wherein a mask is positioned in the beam received from the storage medium to remove unwanted characteristics before the beam is passed through the cylindrical lens. 9. An optical neural network as claimed in any preceding claim wherein the holographic storage medium is addressed by way of a controllable optic deflector placed in the path of each addressing beam, and controlled by a memory switching means to control the angle of incidence of the beams. 10. An optical neural network substantially as hereinbefore described. 11. An optical neural network substantially as hereinbefore described with reference to Figures 1 to 3 of the accompanying drawing.

Inventors: PAIGE EDWARD GEORGE SYDNEY, PAIGE, EDWARD, GEORGE, SYDNEY
Applicants: PLESSEY OVERSEAS, PLESSEY OVERSEAS LIMITED
Application year: 1988
Main classification: G11C15
IPC codes: G03H1, G11C11, G11C13