377 
EXPERIMENTAL DEMONSTRATIONS OF 
OPTICAL NEURAL COMPUTERS 
Ken Hsu, David Brady, and Demetri Psaltis 
Department of Electrical Engineering 
California Institute of Technology 
Pasadena, CA 91125 
ABSTRACT 
We describe two expriments in optical neural computing. In the first 
a closed optical feedback loop is used to implement auto-associative image 
recall. In the second a perceptron-like learning algorithm is implemented with 
photorefractive holography. 
INTRODUCTION 
The hardware needs of many neural computing systems are well matched 
with the capabilities of optical systems '2's The high interconnectivity 
required by neural computers can be simply implemented in optics because 
channels for optical signals may be superimposed in three dimensions with 
little or no cross coupling. Since these channels may be formed holographically, 
optical neural systems can be designed to create and maintain interconnections 
very simply. Thus the optical system designer can to a large extent 
avoid the analytical and topological problems of determining individual 
interconnections for a given neural system and constructing physical paths 
for these interconnections. 
An archetypical design for a single layer of an optical neural computer is 
shown in Fig. 1. Nonlinear thresholding elements, neurons, are arranged on 
two dimensional planes which are interconnected via the third dimension by 
holographic elements. The key concerns in implementing this design involve 
the need for suitable nonlinearities for the neural planes and high capacity, 
easily modifiable holographic elements. While it is possible to implement the 
neural function using entirely optical nonlinearities, for example using etaIon 
arrays 4, optoelectronic two dimensional spatial light modulators (2D SLMs) 
suitable for this purpose are more readily available. and their properties, 
i.e. speed and resolution, are well matched with the requirements of neural 
computation and the limitations imposed on the system by the holographic 
interconnections 5,6. Just as the main advantage of optics in connectionist 
machines is the fact that an optical system is generally linear and thus 
allows the superposition of connections, the main disadvantage of optics is 
that good optical nonlinearities are hard to obtain. Thus most SLMs are 
optoelectronic with a non-linearity mediated by electronic effects. The need for 
optical nonlinearities arises again when we consider the formation of modifiable 
optical interconnections, which must be an all optical process. In selecting 
American Institute of Physics 1988 
378 
a holographic material for a neural computing application we would like to 
have the capability of real-time recording and slow erasure. Materials such 
as photographic film can provide this only with an impractical fixing process. 
Photorefractive crystals are nonlinear optical materials that promise to have 
a relatively fast recording response and long term memory 4'5'6'7'8 
neural Fourier 
Fourier neural 
plane lens holographic Medium lens plane 
Figure 1. Optical neural computer architecture. 
In this paper we describe two experimental implementations of optical 
neural computers which demonstrate how currently available optical devices 
may be used in this application. The first experiment we describe involves an 
optical associative loop which uses feedback through a neural plane in the form 
of a pinhole array and a separate thresholding plane to implement associate 
regeneration of stored patterns from correlated inputs. This experiment 
demonstrates the input-output dynamics of an optical neural computer similar 
to that shown in Fig. 1, implemented using the Hughes Liquid Crystal Light 
Valve. The second experiment we describe is a single neuron optical perceptron 
implemented with a photorefractive crystal. This experiment demonstrates 
how the learning dynamics of long term memory may be controlled optically. 
By combining these two experiments we should eventually be able to construct 
high capacity adaptive optical neural computers. 
OPTICAL ASSOCIATIVE LOOP 
A schematic diagram of the optical associative memory loop is shown in 
Fig. 2. It is comprised of two cascaded Vander Lugt corrclators 9. The input 
section of the system from the threshold device P1 through the first hologram 
P2 to the pinhole array P3 forms the first correlator. The feedback section 
from P3 through the second hologram P4 back to the threshold device P1 
forms the second corrclator. An array of pinholes sits on the back focal plane 
of L2, which coincides with the front focal plane of L3. The purpose of the 
pinholes is to link the first and the second (reversed) correlator to form a closed 
optical feedback loop . 
There are two phases in operating this optical loop, the learning phase 
and the recal phase. In the learning phase, the images to be stored are 
spatially multiplexcd and entered simultaneously on the threshold device. The 
379 
thresholded images are Fourier transformed by the lens L1. The Fourier 
spectrum and a plane wave reference beam interfere at the plane P2 and 
record a Fourier transform hologram. This hologram is moved to plane P4 
as our stored memory. We then reconstruct the images from the memory to 
form a new input to make a second Fourier transform hologram that will stay 
at plane P2. This completes the 
learning phase. In the recalling phase 
an input is imaged on the threshold 
device. This image is correlated with 
the reference images in the hologram 
at P2. If the correlation between the 
input and one of the stored images is 
high a bright peak appears at one of 
the pinholes. This peak is sampled by 
the pinhole to reconstruct the stored 
image from the hologram at P4. The 
reconstructed beam is then imaged 
back to the threshold device to form a 
closed loop. If the overall optical gain 
in the loop exceeds the loss the loop 
signal will grow until the threshold 
device is saturated. In this case, we 
can cutoff the external input image 
and the optical loop will be latched at 
the stable memory. 
Threshold  
Device uulput 
npm / . 
Hologram 
Pe Second 
Holonrom PKhole 
L 
Figure. 2. All-optical associative 
loop. The threshold device is a LCLV, 
and the holograms are thermoplastic 
plates. 
The key elements in this optical loop arc the holograms, the pinhole array, 
and the threshold device. If we put a mirror  or a phase conjugate mirror TM  
at the pinhole plane P3 to reflect the correlation signal back through the 
system then we only need one hologram to form a closed loop. The use of two 
holograms, however, improves system performance. We make the hologram at 
P2 with a high pass characteristic so that the input section of the loop has 
high spectral discrimination. On the other hand we want the images to be 
reconstructed with high fidelity to the original images. Thus the hologram at 
plane P4 must have broadband characteristics. We use a diffuser to achieve 
this when making this hologram. Fig. 3a shows the original images. Fig. 3b 
and Fig. 3c are the images reconstructed from first and second holograms, 
respectively. As desired, Fig. 3b is a high pass version of the stored image 
while Fig. 3c is broadband. 
Each of the pinholes at the correlation plane P3 has a diameter of 60 
/ra. The separations between the pinholes correspond to the separations of 
the input images at plane P1. If one of the stored images appears at PI there 
will be a bright spot at the corresponding pinhole on plane P3. If the input 
image shifts to the position of another image the correlation peak will also 
380 
a. b. c. 
Figure 3. (a) The original images. (b)The reconstructed images from the high- 
pass hologram P2. (c) The reconstructed images from the band-pass hologram 
P4. 
shift to another pinhole. But if the shift is not an exact image spacing the 
correlation peak can not pass the pinhole and we lose the feedback signal. 
Therefore this is a loop with "discrete" shift invariance. Without the pinholes 
the cross-correlation noise and the auto-correlation peak will be fed back to 
the loop together and the reconstructed images won't be recognizable. There 
is a compromise between the pinhole size and the loop performance. Small 
pinholes allow good memory discrimination and sharp reconstructed images, 
but can cut the signal to below the level that can be detected by the threshold 
device and reduce the tolerance of the system to shifts in the input. The 
function of the pinhole array in this system might also be met by a nonlinear 
spatial light modulator, in which case we can achieve full shift invariance 2. 
The threshold device at plane P1 is a Hughes Liquid Crystal Light Valve. 
The device has a resolution of 16 lp/mm and uniform aperture of I inch 
diameter. This gives us about 160,000 neurons at P1. In order to compensate 
for the optical loss in the loop, which is on the order of 10 -5 , we need the 
neurons to provide gain on the order of 105 . In our system this is achieved 
by placing a Hamamatsu image intensifier at the write side of the LCLV. 
Since the microchannel plate of the image intensifier can give gains of 104, the 
combination of the LCLV and the image intensifier can give gains of 106 with 
sensitivity down to nW/cm 2. The optical gain in the loop can be adjusted by 
changing the gain of the image intensifier. 
Since the activity of neurons and the dynamics of the memory loop is 
a continuously evolving phenomenon, we need to have a real time device to 
monitor and record this behavior. We do this by using a prism beam splitter 
to take part of the read out beam from the LCLV and image it onto a CCD 
camera. The output is displayed on a CRT monitor and also recorded on a 
video tape recorder. Unfortunately, in a paper we can only show static pictures 
taken from the screen. We put a window at the CCD plane so that each time 
we can pick up one of the stored images. Fig. 4a shows the read out image 
381 
a. b. c. 
Figure 4. (a) The external input to the optical loop. (b) The feedback image 
superimposed with the input image. (c) The latched loop image. 
from the LCLV which comes from the external input shifted away from its 
stored position. This shift moves its correlation peak so that it does not match 
the position of the pinhole. Thus there is no feedback signal going through 
the loop. If we cut off the input image the read out image will die out with a 
characteristic time on the order of 50 to 100 ms, corresponding to the response 
time of the LCLV. Now we shift the input image around trying to search for 
the correct position. Once the input image comes close enough to the correct 
position the correlation peak passes through the right pinhole, giving a strong 
feedback signal superimposed with the external input on the neurons. The 
total signal then goes through the feedback loop and is amplified continuously 
until the neurons are saturated. Depending on the optical gain of the neurons 
the time required for the loop to reach a stable state is between 100 ms and 
several seconds. Fig. 4b shows the superimposed images of the external input 
and the loop images. While the feedback signal is shifted somewhat with 
respect to the input, there is sufficient correlation to induce recall. If the 
neurons have enough gain then we can cut off the input and the loop stays in 
its stable state. Otherwise we have to increase the neuron gain until the loop 
can sustain itself. Fig. 4c shows the image in the loop with the input removed 
and the memory latched. If we enter another image into the system, again 
we have to shift the input within the window to search the memory until we 
are close enough to the correct position. Then the loop will evolve to another 
stable state and give a correct output. 
The input images do not need to match exactly with the memory. Since 
the neurons can sense and amplify the feedback signal produced by a partial 
match between the input and a stored image, the stored memory can grow 
in the loop. Thus the loop has the capability to recall the complete memory 
from a partial input. Fig. 5a shows the image of a half face input into the 
system. Fig. 5b shows the overlap of the input with the complete face from 
the memory. Fig. 5c shows the stable state of the loop after we cut off the 
external input. In order to have this associative behavior the input must have 
enough correlation with the stored memory to yield a strong feedback signal. 
For instance, the loop does not respond to the the presentation of a picture of 
382 
a. b. c. 
Figure 5. (a) Partial face used as the external input. (b) The superimposed 
images of the partial input with the complete face recalled by the loop. (c) 
The complete face latched in the loop. 
a. b. c. 
Figure 6. (a) Rotated image used as the external input. (b) The superimposed 
images of the input with the recalled image from the loop. (c) The image 
latched in the optical loop. 
a person not stored in memory. 
Another way to demonstrate the associative behavior of the loop is to use 
a rotated image as the input. Experiments show that for a small rotation the 
loop can recognize the image very quickly. As the input is rotated more, it 
takes longer for the loop to reach a stable state. If it is rotated too much, 
depending on the neuron gain, the input won't be recognizable. Fig. 6a shows 
the rotated input. Fig. 6b shows the overlap of loop image with input after 
we turn on the loop for several seconds. Fig. 6c shows the correct memory 
recalled from the loop after we cut the input. There is a trade-off between the 
degree of distortion at the input that the system can tolerate and its ability 
to discriminate against patterns it has not seen before. In this system the 
feedback gain (which can be adjusted through the image intensifier) controls 
this trade-off. 
PHOTOREFRACTIVE PERCEPTRON 
Holograms are recorded in photorefractive crystals via the electrooptic 
modulation of the index of refraction by space charge fields created by 
the migration of photogenerated charge 3'4. Photorefractive crystals are 
attractive for optical neural applications because they may be used to store 
383 
long term interactions between a very large number of neurons. While 
photorefractive recording does not require a development step, the fact that 
the response is not instantaneous allows the crystal to store long term traces 
of the learning process. Since the photorefractive effect arises from the 
reversible redistribution of a fixed pool of charge among a fixed set of optically 
addressable trapping sites, the photorefractive response of a crystal does not 
deteriorate with exposure. Finally, the fact that photorefractive holograms 
may extend over the entire volume of the crystal has previously been shown to 
imply that as many as 10 l interconnections may be stored in a single crystal 
with the independence of each interconnection guaranteed by an appropriate 
spatial arrangement of the interconnected neurons 6,s. 
In this section we consider a rudimentary optical neural system which uses 
the dynamics of photorefractive crystals to implement perceptron-like learning. 
The architecture of this system is shown schematically in Fig. 7. The input 
to the system, , corresponds to a two dimensional pattern recorded from a 
video monitor onto a liquid crystal light valve. The light valve transfers this 
pattern on a laser beam. This beam is split into two paths which cross in a 
photorefractive crystal. The light propagating along each path is focused such 
that an image of the input pattern is formed on the crystal. The images along 
both paths are of the same size and are superposed on the crystal, which is 
assumed to be thinner than the depth of focus of the images. The intensity 
diffracted from one of the two paths onto the other by a hologram stored in 
the crystal is isolated by a polarizer and spatially integrated by a single output 
detector. The thresholdcd output of this detector corresponds to the output 
of a neuron in a perceptron. 
PB LCLV TV 
L1 .- 
1 
/P, , / 
pM'V 
computer 
Figure 7. Photorefractive perceptton. PB is a polarizing beam splitter. L1 
and L2 are imaging lenses. WP is a quarter waveplate. PM is a piezoelectric 
mirror. P is a polarizer. D is a detector. Solid lines show electronic control. 
Dashed lines show the optical path. 
The i th component of the input to this system corresponds to the intensity 
in the i th pixel of the input pattern. The interconnection strength, wi, between 
the i t input and the output neuron corresponds to the diffraction efficiency 
of the hologram taking one path into the other at the i  pixel of the image 
plane. While the dynamics of wi can be quite complex in some geometries 
384 
and crystals, it is possible to show from the band transport model for the 
photorefractive effect that under certain circumstances the time development 
of wi may be modeled by 
 m(s)e ( )e;dsl 2 (1) 
wi(t) = w,,, I r 
where re(s) and b(s) are the modulation depth and phase, respectively, of the 
interference pattern formed in the crystal between the light in the two paths ls. 
r is a characteristic time constant for crystal. r is inversely proportional to 
the intensity incident on the i th pixel of the crystal. Using Eqn. 1 it is possible 
to make wi(t) take any value between 0 and wm,x by properly exposing the 
i th pixel of the crystal to an appropriate modulation depth and intensity. The 
modulation depth between two optical beams can be adjusted by a variety of 
simple mechanisms. In Fig. 7 we choose to control rn(t) using a mirror mounted 
on a piezoelectric crystal. By varying the frequency and the amplitude of 
oscillations in the piezoelectric crystal we can electronically set both rn(t) and 
b(t) over a continuous range without changing the intensity in the optical 
beams or interrupting readout of the system. With this control over rn(t) it 
is possible via the dynamics described in Eqn. (1) to implement any learning 
algorithm for which wi can be limited to the range (0, win,z). 
The architecture of Fig. 7 classifies input patterns into two classes 
according to the thresholded output of the detector. The goal of a learning 
algorithm for this system is to correctly classify a set of training patterns. The 
perceptron learning algorithm involves simply testing each training vector and 
adding training vectors which yield too low an output to the weight vector 
and subtracting training vectors which yield too high an output from the 
weight vector until all training vectors are correctly classified 16. This training 
algorithm is described by the equation Awi= exi where alpha is positive 
(negative) if the output for  is too low (high). An optical analog of this 
method is implemented by testing each training pattern and exposing the 
crystal with each incorrectly classified pattern. Training vectors that yield 
a high output when a low output is desired are exposed at zero modulation 
depth. Training vectors that yield a low output when high output is desired 
are exposed at a modulation depth of one. 
The weight vector for the k 4- i th iteration when erasure occurs in the k th 
iteration is given by 
--2At 
wi(k + 1) -- e , wi(k)  (1 2At)wi(k) (2) 
where we assume that the exposure time, At, is much less than r. Note that 
since r is inversely proportional to the intensity in the i th pixel, the change in 
385 
w i is proportional to the i th input. The weight vector at the k + I th iteration 
when recording occurs in the k h iteration is given by 
-2, X/''/( -' -' -' ) 
wi(k+l)=e  wi(k)+2 k)wmaxe  (1-e  )+wmax(1-e  )2 (3 
To lowest order in -- and w Eqn. (3) yields 
wi(k 1) wi(k) 2V/wi(k)w.az At 
= ( 
(4) 
Once again the change in wi is proportional to the i t input. 
We have implemented the architecture of Fig. 7 using a SBN60:Ce crystal 
provided by the Rockwell International Science Center. We used the 488 nm 
line of an argon ion laser to record holograms in this crystal. Most of the 
patterns we considered were laid out on 10 x 10 grids of pixels, thus allowing 
100 input channels. Ultimately, the number of channels which may be achieved 
using this architecture is limited by the number of pixels which may be imaged 
onto the crystal with a depth of focus sufficient to isolate each pixel along the 
length of the crystal. 
Figure 8. Training patterns. 
0 & 
Figure 9. Output in the second training cycle. 
Using the variation on the perceptron learning algorithm described above 
with a fixed exposure times Atr and Ate for recording and erasing, we have 
been able to correctly classify various sets of input patterns. One particular 
set which we used is shown in Fig. $. In one training sequence, we grouped 
patterns i and 2 together with a high output and patterns 3 and 4 together 
with a low output. After all four patterns had been presented four times, 
the system gave the correct output for all patterns. The weights stored in 
the crystal were corrected seven times, four times by recording and three by 
erasing. Fig. 9a shows the output of the detector as pattern i is recorded in 
the second learning cycle. The dashed line in this figure corresponds to the 
threshold level. Fig. 9b shows the output of the detector as pattern 3 is erased 
in the second learning cycle. 
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CONCLUSION 
The experiments described in this paper demonstrate how neural network 
architectures can be implemented using currently available optical devices. By 
combining the recall dynamics of the first system with the learning capability 
of the second, we can construct sophisticated optical neural computers. 
ACKNOWLEDGEMENTS 
The authors thank Ratnakar Neurgaonkar and Rockwell International for 
supplying the SBN crystal used in our experiments and Hamamatsu Photonics 
K.K. for assistance with image intesifiers. We also thank Eung Gi Paek and 
Kelvin Wagner for their contributions to this research. 
This research is supported by the Defense Advanced Research Projects 
Office, and the Air Force Office of Scientific 
Agency, the Army Research 
Research. 
REFERENCES 
1. Y. S. Abu-Mostafa and D. Psaltis, Scientific American, pp.88-95, March, 
1987. 
2. D. Psaltis and N.H. Farhat, Opt. Lett., 10,(2), 98(1985). 
3. A.D. Fisher, R. C. Fukuda, and J. N. Lee, Pro. SPIE 625, 196(1986). 
4. K. Wagner and D. Psaltis, Appl. opt., 26(23), pp.5061-5076(1987). 
5. D. Psaltis, D. Brady, and K. Wagner, Applied optics, March 1988. 
6. D. Psaltis, J. Yu, X. G. Gu, and H. Lee, Second Topical Meeting on 
Optical Computing, Incline Village, Nevada, March 16-18,1987. 
7. A. Yariv, S.-K. Kwong, and K. Kyuma, SPIE proc. 613-01,(1986). 
8. D. Z. Anderson, Proceedings of the International Conference on Neural 
Networks, San Diego, June 1987. 
9. A. B. Vander Lugt, IEEE Trans. Inform. Theory, IT-10(2), pp.139- 
145(1964). 
10. E.G. Paek and D. Psaltis, Opt. Eng., 26(5), pp.428-433(1987). 
11. Y. Owechko, G. J. Dunning, E. Marom, and B. H. Softer, Appl. Opt. 
26,(10),1900(1987). 
12. D. Psaltis and 3. Hong, Opt. Eng. 26,10(1987). 
13. N. V. Kuktarev, V. B. Markov, S. G. Odulov, M. S. Soskin, and V. L. 
Vinetskii, Ferroelectrics, 22,949(1979). 
14. J. Feinberg, D. Heiman, A. R. Tanguay, and R. W. Hellwarth, J. Appl. 
Phys. 51,1297(1980). 
15. T. J. Hall, R. Jaura, L. M. Connors, P. D. Foote, Prog. Quan. Electr. 
10,77(1985). 
16. F. Rosenblatt,'Principles of Neurodynamics: Perceptton and the Theory 
of Brain Mechanisms, Spartan Books, Washington,(1961). 
