{"title": "Experimental Demonstrations of Optical Neural Computers", "book": "Neural Information Processing Systems", "page_first": 377, "page_last": 386, "abstract": null, "full_text": "377 \n\nEXPERIMENTAL  DEMONSTRATIONS  OF \n\nOPTICAL NEURAL  COMPUTERS \n\nKen  Hsu,  David Brady, and Demetri  Psaltis \n\nDepartment of Electrical  Engineering \n\nCalifornia Institute of Technology \n\nPasadena, CA 91125 \n\nABSTRACT \n\nWe  describe  two  expriments  in  optical  neural  computing.  In  the  first \na  closed  optical  feedback  loop  is  used  to  implement  auto-associative  image \nrecall.  In the second a perceptron-Iike learning algorithm is  implemented with \nphotorefractive holography. \n\nINTRODUCTION \n\nThe hardware needs of many neural computing systems  are well matched \nwith  the  capabilities  of  optical  systems l ,2,3.  The  high  interconnectivity \nrequired  by  neural  computers  can  be  simply  implemented  in  optics  because \nchannels  for  optical  signals  may  be  superimposed  in  three  dimensions  with \nlittle or no cross coupling.  Since these channels may be formed holographically, \noptical neural systems can be designed to create and maintain interconnections \nvery  simply.  Thus  the  optical  system  designer  can  to  a  large  extent \navoid  the  analytical  and  topological  problems  of  determining  individual \ninterconnections  for  a  given  neural  system  and  constructing  physical  paths \nfor  these  interconnections. \n\nAn  archetypical design for  a  single  layer of an optical neural computer is \nshown  in  Fig.  1.  Nonlinear  thresholding  elements,  neurons,  are  arranged  on \ntwo dimensional  planes  which  are  interconnected  via  the  third  dimension  by \nholographic  elements.  The key  concerns  in  implementing this  design  involve \nthe  need  for  suitable  nonlinearities  for  the  neural  planes  and  high  capacity, \neasily  modifiable holographic  elements.  While  it  is  possible  to implement the \nneural function  using  entirely  optical  nonlinearities,  for  example  using  etalon \narrays\\ optoelectronic  two  dimensional spatial  light  modulators  (2D  SLMs) \nsuitable  for  this  purpose  are  more  readily  available.  and  their  properties, \ni.e.  speed  and  resolution,  are  well  matched  with  the  requirements  of neural \ncomputation  and  the  limitations  imposed  on  the  system  by  the  holographic \ninterconnections5 ,6.  Just  as  the  main  advantage  of  optics  in  connectionist \nmachines  is  the  fact  that  an  optical  system  is  generally  linear  and  thus \nallows  the  superposition  of connections,  the  main  disadvantage  of optics  is \nthat  good  optical  nonlinearities  are  hard  to  obtain.  Thus  most  SLMs  are \noptoelectronic with a non-linearity mediated by electronic effects.  The need for \noptical nonlinearities arises again when we consider the formation of modifiable \noptical  interconnections,  which  must  be  an  all  optical  process.  In  selecting \n\n@  American Institute of Physics 1988 \n\n\f378 \n\na  holographic  material  for  a  neural  computing  application  we  would  like  to \nhave  the  capability  of  real-time  recording  and  slow  erasure.  Materials  such \nas photographic film  can provide this only with an impractical fixing  process. \nPhotorefractive crystals  are  nonlinear optical  materials  that  promise  to  have \na  relatively fast  recording  response  and  long term memory4,5,6,7,B. \n\n. \" \n\n..... \n\n'. '. \n\n'. \n\n\". '. \n\n. '. \n\n.. \n- ~ :-w:-=7 --\n~---...... \n\n.' \n\n. . \n\nFourier \nlens \nFigure  1.  Optical neural  computer architecture. \n\nhologro.phlc  I\"IealuI\"I \n\nFourier \nlens \n\nIn  this  paper  we  describe  two  experimental  implementations  of optical \nneural  computers  which  demonstrate  how  currently  available  optical  devices \nmay be used  in  this application.  The first  experiment we describe  involves an \noptical associative loop which uses feedback through a neural plane in the form \nof a  pinhole  array  and  a  separate  thresholding  plane to  implement  associate \nregeneration  of  stored  patterns  from  correlated  inputs.  This  experiment \ndemonstrates the input-output dynamics of an optical neural computer similar \nto  that shown  in  Fig.  1,  implemented using  the  Hughes  Liquid  Crystal  Light \nValve.  The second experiment we describe is a single neuron optical perceptron \nimplemented  with  a  photorefractive  crystal.  This  experiment  demonstrates \nhow  the learning dynamics of long  term  memory  may  be controlled optically. \nBy combining these two experiments we should eventually be able to construct \nhigh capacity adaptive optical neural computers. \n\nOPTICAL  ASSOCIATIVE LOOP \n\nA  schematic diagram of the  optical  associative  memory  loop  is  shown  in \nFig.  2.  It  is  comprised  of two cascaded  Vander  Lugt  correlators9.  The  input \nsection of the system from the threshold  device  P1  through the first  hologram \nP2  to  the  pinhole  array  P3  forms  the  first  correlator.  The  feedback  section \nfrom  P3  through  the  second  hologram  P4  back  to  the  threshold  device  P1 \nforms  the second correlator.  An  array of pinholes sits on  the  back focal  plane \nof  L2,  which  coincides  with  the  front  focal  plane  of L3.  The  purpose  of the \npinholes is to link the first  and the second (reversed)  correlator to form a  closed \noptical feedback  loop 10. \n\nThere  are  two  phases  in  operating  this  optical  loop,  the  learning  phase \nIn  the  learning  phase,  the  images  to  be  stored  are \nand  the  recal  phase. \nspatially multiplexed and entered simultaneously on the threshold device.  The \n\n\f379 \n\n~~~*+++~~~~ \n\nthresholded  images  are  Fourier  transformed  by  the  lens  Ll.  The  Fourier \nspectrum  and  a  plane  wave  reference  beam  interfere  at  the  plane  P2  and \nrecord  a  Fourier  transform  hologram.  This  hologram  is  moved  to  plane  P4 \nas  our stored  memory.  We  then  reconstruct  the  images  from  the  memory  to \nform a  new  input to make a  second Fourier transform hologram that will stay \nat  plane  P2. \nThis  completes  the \nlearning phase.  In the  recalling  phase \nan  input  is  imaged  on  the  threshold  Input \ndevice.  This  image  is  correlated  with \nthe  reference  images  in  the  hologram \nat  P2.  If the  correlation  between  the \ninput and  one  of the stored  images  is \nhigh  a  bright  peak  appears  at  one  of \nthe pinholes.  This peak  is  sampled by \nthe  pinhole  to  reconstruct  the  stored \nimage from  the hologram  at  P4.  The \nreconstructed  beam  is  then  imaged \nback to the threshold device to form a \nclosed  loop.  If the overall optical gain \nin  the  loop  exceeds  the  loss  the  loop \nsignal  will  grow  until  the  threshold \ndevice  is  saturated.  In  this  case,  we \ncan  cutoff  the  external  input  image \nand the optical loop  will  be latched at \nthe stable memory. \n\nFigure.  2. \nAll-optical  associative \nloop.  The threshold device is  a  LCLV, \nand  the  holograms  are  thermoplastic \nplates. \n\nPinhole \nArray  - -.... L z \n\n~ -,.....,.- Second \n\nHologram \n\nI \nI \n\nThe key elements in this optical loop are the holograms, the pinhole array, \nand the threshold device.  If we put a  mirror 10  or a  phase conjugate mirror 7 ,11 \nat  the  pinhole  plane  P3  to  reflect  the  correlation  signal  back  through  the \nsystem then we only need one hologram to form a  closed  loop.  The use of two \nholograms, however, improves system performance.  We make the hologram at \nP2  with  a  high  pass  characteristic  so  that  the  input  section  of the  loop  has \nhigh  spectral  discrimination.  On  the  other  hand  we  want  the  images  to  be \nreconstructed  with  high  fidelity  to the original  images.  Thus the hologram at \nplane  P4  must  have  broadband  characteristics.  We  use  a  diffuser  to  achieve \nthis  when  making  this  hologram.  Fig.  3a shows  the  original  images.  Fig.  3b \nand  Fig.  3c  are  the  images  reconstructed  from  first  and  second  holograms, \nrespectively.  As  desired,  Fig.  3b  is  a  high  pass  version  of  the  stored  image \nwhile  Fig.  3c  is  broadband . \n\nEach  of  the  pinholes  at  the  correlation  plane  P3  has  a  diameter  of  60 \nj.lm.  The separations  between the  pinholes  correspond  to  the  separations  of \nthe input images at  plane P 1.  If one of the stored  images appears  at  P 1 there \nwill  be  a  bright spot  at  the  corresponding  pinhole on  plane  P3.  If the  input \nimage  shifts  to  the  position  of  another  image  the  correlation  peak  will  also \n\n\f380 \n\n'\" \n. . \n~  ,  . ( \n\\~ .~ \n\n.a:..J \n\n,.  ' \n~ \n\u2022 \n~ \u2022  -y::' \n.. \n\na. \n\n~. \n\n. \n\n.. \n\ni \n\n\u00b7Il, .' \n.r  ...  I \nK~\u00b7';t \n\nb. \n\n\u2022  L \n\u2022  \u2022 \n\nc. \n\n.# \n\nFigure 3.  (a)  The original images.  (b)The reconstructed images from the high(cid:173)\npass hologram P2.  (c)  The reconstructed images from the band-pass hologram \nP4. \n\nshift  to  another  pinhole.  But  if  the  shift  is  not  an  exact  image  spacing  the \ncorrelation  peak  can  not  pass  the  pinhole  and  we  lose  the  feedback  signal. \nTherefore this is  a  loop with  \"discrete\"  shift invariance.  Without the pinholes \nthe  cross-correlation  noise  and  the  auto-correlation  peak  will  be  fed  back  to \nthe  loop  together and the reconstructed  images won't be recognizable.  There \nis  a  compromise  between the  pinhole  size  and  the  loop  performance.  Small \npinholes  allow  good  memory  discrimination  and  sharp  reconstructed  images, \nbut can cut the signal to below the level that can  be detected by the threshold \ndevice  and  reduce  the  tolerance  of  the  system  to  shifts  in  the  input.  The \nfunction of the pinhole array  in  this  system  might also  be  met  by a  nonlinear \nspatial  light modulator, in which case  we can  achieve full shift invariance 12 \u2022 \n\nThe threshold device at plane PI  is  a  Hughes Liquid Crystal  Light Valve. \nThe  device  has  a  resolution  of  16  Ip/mm  and  uniform  aperture  of  1  inch \ndiameter.  This gives us about  160,000 neurons  at  PI.  In order  to compensate \nfor  the  optical  loss  in  the  loop,  which  is  on  the  order  of  10- 5 ,  we  need  the \nneurons  to  provide  gain  on  the  order  of  105.  In  our  system  this  is  achieved \nby  placing  a  Hamamatsu  image  intensifier  at  the  write  side  of  the  LCLV. \nSince the microchannel plate of the image intensifier can give gains of 104 ,  the \ncombination of the  LCLV and the  image  intensifier can give gains of 106  with \nsensitivity  down to n W /cm2 .  The optical gain  in  the loop can be adjusted  by \nchanging the gain of the image intensifier. \n\nSince  the  activity  of  neurons  and  the  dynamics  of  the  memory  loop  is \na  continuously  evolving  phenomenon,  we  need  to  have a  real  time  device  to \nmonitor and  record  this  behavior.  We do this  by using a  prism  beam splitter \nto  take  part  of the  read  out  beam  from  the  LCLV  and  image  it  onto  a  CCD \ncamera.  The  output  is  displayed on  a  CRT  monitor  and  also  recorded  on  a \nvideo tape recorder.  Unfortunately, in a  paper we can only show static pictures \ntaken from  the screen.  We put a  window at the  CCD  plane so  that each time \nwe  can  pick  up  one  of the  stored  images.  Fig.  4a  shows  the  read  out  image \n\n\f381 \n\na. \n\nb. \n\nc. \n\nFigure 4.  (a)  The external  input to the optical  loop.  (b)  The feedback  image \nsuperimposed with the input image.  (c)  The latched loop  image. \n\nfrom  the  LCLV  which  comes  from  the  external  input  shifted  away  from  its \nstored position.  This shift moves its correlation peak so that it does not match \nthe  position  of the  pinhole.  Thus  there  is  no  feedback  signal  going  through \nthe loop.  If we cut off the input image the read out image will  die out with a \ncharacteristic time on the order of 50 to 100 ms, corresponding to the response \ntime of the LCLV.  Now  we shift  the  input  image  around  trying  to search  for \nthe correct  position.  Once the input image comes close enough  to  the correct \nposition the correlation  peak passes through the right pinhole, giving a  strong \nfeedback  signal  superimposed  with  the  external  input  on  the  neurons.  The \ntotal signal then goes through the feedback loop  and is  amplified continuously \nuntil the neurons are saturated.  Depending on the optical gain of the neurons \nthe  time  required  for  the  loop  to  reach  a  stable  state  is  between  100  ms  and \nseveral seconds.  Fig.  4b shows the superimposed  images of the external  input \nand  the  loop  images.  While  the  feedback  signal  is  shifted  somewhat  with \nIf the \nrespect  to  the  input,  there  is  sufficient  correlation  to  induce  recall. \nneurons  have enough gain then we can cut off the input and the  loop  stays in \nits  stable state.  Otherwise  we  have to  increase  the  neuron  gain  until the loop \ncan sustain itself.  Fig.  4c  shows the image  in  the loop with the input removed \nand  the  memory  latched.  If we  enter  another  image  into  the  system,  again \nwe  have to  shift  the  input  within  the  window  to  search  the memory  until we \nare close enough to  the correct  position.  Then the loop  will  evolve to another \nstable state and give a  correct  output. \n\nThe input  images do  not  need  to  match exactly  with  the memory.  Since \nthe  neurons  can sense  and  amplify  the feedback  signal  produced  by  a  partial \nmatch  between  the  input  and  a  stored  image,  the  stored  memory  can  grow \nin  the  loop.  Thus the loop  has  the capability to  recall  the complete  memory \nfrom  a  partial  input.  Fig.  5a shows  the  image  of  a  half face  input  into  the \nsystem.  Fig.  5b  shows  the  overlap  of  the  input  with  the  complete  face  from \nthe  memory.  Fig.  5c  shows  the  stable  state  of  the  loop  after  we  cut  off  the \nexternal  input.  In order  to have this associative behavior the input must have \nenough correlation  with  the stored  memory  to yield  a  strong feedback signal. \nFor instance, the loop  does  not respond  to the the  presentation of a  picture of \n\n\f382 \n\na. \n\nc. \n\nFigure  5.  (a)  Partial face  used  as  the external  input.  (b)  The superimposed \nimages  of the  partial  input  with  the  complete face  recalled  by  the  loop.  (c) \nThe complete face  latched in  the  loop. \n\na. \n\nb. \n\nc. \n\nFigure 6.  (a)  Rotated image used as the external input.  (b)  The superimposed \nimages  of  the  input  with  the  recalled  image  from  the  loop. \n(c)  The  image \nlatched in  the optical loop. \n\na  person not stored  in  memory. \n\nAnother way to demonstrate the associative behavior of the loop is  to use \na  rotated  image as the  input.  Experiments show  that for  a  small rotation  the \nloop  can  recognize  the  image  very  quickly.  As  the  input  is  rotated  more,  it \ntakes  longer  for  the  loop  to  reach  a  stable  state.  If  it  is  rotated  too  much, \ndepending on the neuron gain, the input won't be recognizable.  Fig.  6a shows \nthe  rotated  input.  Fig.  6b  shows  the  overlap  of loop  image  with  input  after \nwe  turn  on  the  loop  for  several  seconds.  Fig.  6c  shows  the  correct  memory \nrecalled from the loop after we cut the input.  There is  a  trade-off between the \ndegree  of distortion  at  the  input that  the  system  can  tolerate  and  its  ability \nto  discriminate  against  patterns  it  has  not  seen  before.  In  this  system  the \nfeedback  gain  (which  can  be  adjusted  through  the  image  intensifier)  controls \nthis  trade-off. \n\nPHOTOREFRACTIVE PERCEPTRON \n\nHolograms  are  recorded  in  photorefractive  crystals  via  the  electrooptic \nmodulation  of  the  index  of  refraction  by  space  charge  fields  created  by \nthe  migration  of  photogenerated  charge 13 ,14.  Photorefractive  crystals  are \nattractive  for  optical  neural  applications  because  they  may  be  used  to  store \n\n\f383 \n\nlong  term  interactions  between  a  very  large  number  of  neurons.  While \nphotorefractive  recording  does  not  require  a  development step,  the  fact  that \nthe  response  is  not  instantaneous allows  the crystal  to store  long  term  traces \nof  the  learning  process.  Since  the  photorefractive  effect  arises  from  the \nreversible redistribution of a  fixed  pool of charge among a  fixed set of optically \naddressable  trapping sites,  the  photorefractive response  of a  crystal  does  not \ndeteriorate  with  exposure.  Finally,  the  fact  that  photorefractive  holograms \nmay extend over the entire volume of the crystal has previously been shown to \nimply that as many as  1010  interconnections may be stored  in a  single crystal \nwith  the  independence of each interconnection guaranteed by  an  appropriate \nspatial arrangement of the interconnected neurons6 ,5. \n\nIn this section we consider a  rudimentary optical neural system which uses \nthe dynamics of photorefractive crystals to implement perceptron-like learning. \nThe  architecture  of this  system  is  shown  schematically  in  Fig.  7.  The  input \nto  the  system,  x,  corresponds  to  a  two  dimensional  pattern  recorded  from  a \nvideo  monitor onto a  liquid  crystal  light valve.  The  light valve  transfers  this \npattern  on  a  laser  beam.  This  beam  is  split  into  two paths  which  cross  in  a \nphotorefractive crystal.  The light propagating along each path is focused such \nthat an image of the input pattern is  formed on the crystal.  The images along \nboth  paths  are  of the  same  size  and  are  superposed  on  the  crystal,  which  is \nassumed  to  be  thinner  than  the  depth  of focus  of the  images.  The  intensity \ndiffracted  from  one  of the  two  paths onto  the  other  by  a  hologram stored  in \nthe crystal is  isolated by a  polarizer and spatially integrated by a single output \ndetector.  The  thresholded  output of this  detector  corresponds  to  the  output \nof a  neuron  in  a  perceptron. \n\nlaser \n\n~---,t+ - --f4HJ \n\nPB  LCL V  TV \n\nucl \nBS$- -\n\nCOl\"lputer \n\nXtal \n\nPM \n\nFigure  7.  Photorefractive  perceptron.  PB  is  a  polarizing  beam  splitter.  Ll \nand  L2  are  imaging  lenses.  WP  is  a  quarter waveplate.  PM  is  a  piezoelectric \nmirror.  P  is  a  polarizer.  D  is  a  detector.  Solid  lines  show  electronic  control. \nDashed  lines show the optical path. \n\nThe ith component of the input to this system corresponds to the intensity \nin the ith pixel of the input pattern.  The interconnection strength, Wi,  between \nthe  ith  input  and  the  output  neuron  corresponds  to  the  diffraction  efficiency \nof the  hologram  taking  one  path  into  the  other  at  the  ith  pixel  of the  image \nplane.  While  the  dynamics  of  Wi  can  be  quite  complex  in  some  geometries \n\n\f384 \n\nand  crystals,  it  is  possible  to  show  from  the  band  transport  model  for  the \nphotorefractive effect  that under certain circumstances  the time  development \nof Wi  may be modeled by \n\n(1) \n\nwhere m(s)  and 4>(s)  are the modulation depth and phase, respectively, of the \ninterference pattern formed in the crystal between the light in the two paths15 \u2022 \nT  is  a  characteristic  time  constant for  crystal.  T  is  inversely  proportional  to \nthe intensity incident on the ith pixel of the crystal.  Using  Eqn. 1 it is  possible \nto make  Wi(t)  take  any value between 0  and  W m l1Z  by  properly  exposing  the \nith pixel of the crystal to an appropriate modulation depth and intensity.  The \nmodulation depth between two optical beams can be adjusted by a  variety of \nsimple mechanisms.  In Fig. 7 we choose to control met)  using a mirror mounted \non  a  piezoelectric  crystal.  By  varying  the  frequency  and  the  amplitude  of \noscillations in the piezoelectric crystal we can electronically set both met)  and \n4>(t)  over  a  continuous  range  without  changing  the  intensity  in  the  optical \nbeams or interrupting  readout  of the system.  With this  control over met)  it \nis  possible  via the dynamics described  in  Eqn.  (1)  to implement any  learning \nalgorithm for  which Wi  can be limited to the range  (0, w maz ). \n\nThe  architecture  of  Fig.  7  classifies  input  patterns  into  two  classes \naccording  to  the  thresholded  output  of the  detector.  The  goal  of  a  learning \nalgorithm for this system is  to correctly  classify a set of training patterns.  The \nperceptron learning algorithm involves simply testing each training vector and \nadding  training  vectors  which  yield  too  Iowan  output  to  the  weight  vector \nand  subtracting  training  vectors  which  yield  too  high  an  output  from  the \nweight vector until all training vectors are correctly  classified 16.  This training \nalgorithm  is  described  by  the  equation  L\\wi  =  aXj  where  alpha  is  positive \n(negative)  if  the  output  for  x  is  too  low  (high).  An  optical  analog  of  this \nmethod  is  implemented  by  testing  each  training  pattern  and  exposing  the \ncrystal  with  each  incorrectly  classified  pattern.  Training  vectors  that  yield \na  high  output  when  a  low  output  is  desired  are  exposed  at  zero  modulation \ndepth .  Training vectors  that yield  a  low  output when  high  output  is  desired \nare exposed  at a  modulation depth of one. \n\nThe weight vector for the k + 1 th  iteration when erasure occurs in  the kth \n\niteration  is  given by \n\nwhere  we  assume  that the  exposure  time,  L\\t,  is  much less  than  T.  Note  that \nsince  T  is  inversely proportional to the intensity in  the ith  pixel, the change in \n\n(2) \n\n\fWi  is  proportional to the  ith  input.  The weight vector at the k + 1 th  iteration \nwhen recording occurs  in  the  kth  iteration  is  given by \n\n385 \n\nwi(k+ 1)  =  e-r-Wi(k) +2y Wi(k)Wmcue-r- (l-e-r- )  +wmaz(l-e-r-)  (3) \n\n-2~t \n\n-~t \n\n-~t \n\n_  / \n\n-~t  2 \n\nTo lowest order  in  6.t  and  ~, Eqn.  (3)  yields \n\n.,. \n\nw m .... \n\n~t 2 \nwi(k + 1)  =  wi(k) + 2y wi(k)Wmaz(-) + Wmaz(-) \nT \n\n~t \nT \n\n_ / \n\n(4) \n\nOnce again the change in Wi  is  proportional to the ith input. \n\nWe have implemented the architecture of Fig.  7 using a  SBN60:Ce crystal \nprovided  by the Rockwell  International Science  Center.  We  used the 488  nm \nline  of  an  argon  ion  laser  to  record  holograms  in  this  crystal.  Most  of the \npatterns we considered  were  laid out on 10  x  10 grids of pixels,  thus allowing \n100 input channels.  Ultimately, the number of channels which may be achieved \nusing this architecture is  limited by the number of pixels which may be imaged \nonto the crystal with a  depth of focus sufficient to isolate each pixel along the \nlength of the crystal. \n\n1 \n\n2 Y \n\n-\n\u2022\u2022 +.+  ... \nI \na. \n....... \u2022  \u2022 \u2022 \n! \nt \n.....  \u2022 \u2022 \n\n4 \n\n3 \n\n0 \n\n1'1 \n\nj \n8. \nl \n\nI \n\naCOftClS \n\nW \n\n, \n\n0 \n\n~ \n\nCIII) \n\nFigure 8.  Training patterns. \n\nFigure 9.  Output  in  the second training cycle. \n\nUsing the variation on the perceptron learning algorithm described above \nwith  a  fixed  exposure  times  ~tr and  ~te for  recording  and  erasing,  we  have \nbeen  able  to  correctly  classify  various  sets  of input  patterns.  One  particular \nset  which  we  used  is  shown  in  Fig.  8.  In  one  training  sequence,  we  grouped \npatterns  1 and  2  together  with  a  high  output  and  patterns  3  and 4  together \nwith  a  low  output.  After  all  four  patterns  had  been  presented  four  times, \nthe  system  gave  the  correct  output  for  all  patterns.  The  weights  stored  in \nthe crystal  were  corrected  seven  times,  four  times  by  recording  and three  by \nerasing.  Fig.  9a shows  the  output of the  detector  as  pattern  1  is  recorded  in \nthe second  learning  cycle.  The dashed  line  in  this  figure  corresponds  to  the \nthreshold level.  Fig. 9b shows the output of the detector as  pattern 3 is erased \nin  the second  learning cycle. \n\n\f386 \n\nCONCLUSION \n\nThe experiments described in this paper demonstrate how neural network \narchitectures can be implemented using currently available optical devices.  By \ncombining the recall  dynamics of the first  system with the learning capability \nof the second, we can construct sophisticated  optical neural computers. \n\nACKNOWLEDGEMENTS \n\nThe authors thank Ratnakar Neurgaonkar and Rockwell International for \nsupplying the SBN crystal used  in our experiments and Hamamatsu Photonics \nK.K.  for  assistance  with  image  intesifiers.  We  also  thank  Eung  Gi  Paek  and \nKelvin  Wagner for  their contributions to this  research. \n\nThis  research  is  supported  by  the  Defense  Advanced  Research  Projects \nAgency,  the  Army  Research  Office,  and  the  Air  Force  Office  of  Scientific \nResearch. \n\nREFERENCES \n\n1.  Y.  S.  Abu-Mostafa and D.  Psaltis,  Scientific  American, pp.88-95,  March, \n\n1987. \n\n2.  D.  Psaltis  and  N.  H.  Farhat,  Opt.  Lett., 10,(2),98(1985). \n3.  A.  D.  Fisher,  R.  C.  Fukuda, and J.  N.  Lee,  Proc.  SPIE 625, 196(1986). \n4.  K.  Wagner and D.  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