Nevertheless it is important first to examine line 
network where each element has only two intercon- 
nections, Layer should be desintegrated into several 
pieces or sets of neurons which can operate 
independently. 
Functions of connections between neurons in 
linear parallel networks are significantly more rich 
than in vertical ones.The main goal of this paper is 
to show real possibility of application such neuron 
networks for 2D optical signal treatment. 
2.1 Functioning in general 
Examination of human eye promises not only 
clarification in idea of its layer structure but as 
well enables to mark out several cells between 
layers which bind certain other neurons into a 
network whole. These specific cells are called 
horizontal.They fulfil actions similar to ones of 
springs between metal spheres.Each element of retina 
recieves optical signals and if horizontal 
interconnections are linear, then all information 
will quickly be lost.Consequently, cells between 
neurons should be considered as non linear elements. 
The impetus for the investigations was a theory 
of nonlinear lattices in accordance with which 
whole network can be represented as a set of 
oscillating elements.Specifical feature of this 
structure is definition of external optical field, 
influencing on network as potential, correspondig to 
Toda or Korteveg-de-Vries equations at initial 
moment. The profound theory of those systems one can 
find in /2/, /3/.It is necessary to recall that in 
the finite dimensional case the problem consists in 
finding nxn matrices R and A, known as a Lax pair, 
such, that equations of motion are equivalent to 
the matrix equation 
Sz [R,A] 
where [..] - Lie brackets. 
That this equation implies the eigenvalues of the 
matrix R are conserved in time.It defines descrete 
spectrum for corresponding well known Schrodinger 
equation. Hence each new optical image has own 
collection of spectral components.Single component 
in its turn defines non linear stable wave- soliton. 
Solitons move along network with different 
velocities. Their complete characteristics are 
amplitudes, location at network.Most interesting 
parameter is phase shift between two solitons which 
appears after their collisions. 
2.2 Information processes in networks 
From this starting point we will try to show 
possibilities of networks with non linear 
interconnections to analize information, containing 
in the optical images.Imagine a linear lattice of 
photodetectors with exponential  links.The simplest 
example of this links one can find in /4/.Determine 
a moment of time when all detectors recieve 
simultaneously signals.Then influence of them ceases 
and picture of moving solitons begin to form.If 
network is infinite, then there are descrete and 
continuous spectrums.Continuous component is analog 
of spectrum for linear network. Thus for every 
neuronlike element its outpute is a solution of 
Toda's equation 
d'y ,4^-, onu. d 
52 =e”""se 2e 
where y is a normalized value of charge at the n-th 
output (/5/).Define set Cyl.y2,. + 5 YTis » «VMS at 
moment t=0 as an initial conditions.Let's find all 
spectral components when quantity of neurons is 
great enough to reproduce optical signal with 
expecting acciracy. Values and locations of solitons 
determine two Jost solutions (x), (x) which can 
be found in accordance with oe 
* ¢ 
039 6G) z ep (o -i J ote) (x) sin (e) 
(1) = : 
4) V 60 7 expCilon + Te) pe) emissa 
These equations describe process of Wave 
propagation trough potential 
Kixzx’?) 2 y(x" )sinLk(-x?)] 
In the theory of light scattering this function is 
sometimes called transition function. Thus, solving 
scattering problem for a wave, which propagates to 
(exp(-ikx)) it is necessary to investigate influence 
Of K(x,x") on t£ G0.K(x,x?) is defined by optical 
image forming at the detector plane.We can achieve a 
result, using Monte-Karlo method. Assume, that wave 
propagates through plane parallel nonhomogeneous 
media. The scattering properties are defined by 
Kix,x"). Then express Y (x) as 
(2)  (xyk) = 2 b (Kk) | 
where ho(x,k) = 1 and 
K -ik(æ-x) ; / 
' a / N 
(S) e = "kie safe ach (e) d'e 
This sum consists of components which can be 
called components of i - order of scattering. This 
property enables to classify all optical images from 
the viewpoint of their discrete spectrum. Amplitudes 
of each component of sum are different, but decrease 
when i has tend to increase.If we substitute sum (2) 
with finite series with imax-n then it is necessary 
to choose n, specific for each signal.To achieve the 
purpose of classification and analize extent of 
correspondence between spectrum of signals and 
collection of their discrete components numerical 
experiment was made.As in the scattering theory we 
can express K(x,x") in the form 
? 
- Ss (058) exp[-t(x,2)] (x) 
O(x)2t lv-'* 
where 6, , 6 - scattering and full cross sections, t - 
optical length and g(cos 6) denotes the first 
component (F11) of general transformation matrix by 
Van de Hulst (/6/). © scattering angle. We discuss 
only situation when k = in and 
(4) Klx,x?) 
Kix,x?) = te? Mh, i (^e - c.) 
For linear network we consider only 6 = O.It should 
be noted that solution of eq.1 can be found by two 
ways.First supposes change @ (x) in accordance with 
y{x), and the second change of g(cos © ).Sometimes 
it is more convenient to define g(cos €) in every 
point of network than G .Function M? (x) can be 
found using well known weight method (/7/),averaging 
> & LS Ms [ni 22] 
where xn is determined by Monte-Karlo chain. 
For this numerical experiment g(cos O ) was cal- 
culated. It has been done for characterization of 
real optical field with collection of parameters 
which enables to obtain suitable illustrative 
material and supplementary information for building 
2 D network. To achieve this goal, the diffraction 
task for spherical particles was solved. Gí(cos ) 
18