Page 157 - Introduction to Information Optics

142 2. Signal Processing with Optics

to other neurons. These pathways interconnect with other neurons to form a
network called a neural network. The operation of a neuron is determined by
a transfer function that defines the neuron's output as a function of the input
signals. Every connection entering a neuron has an adaptive coefficient called
a weight assigned to it. The weight determines the interconnection strength
among neurons, and they can be changed through a learning rule that modifies
the weights in response to input signals. The learning rule allows the response
of the neuron to change, depending on the nature of the input signals. This
means that the neural network adapts itself and organizes the information
within itself, which is what we term learning.

2.9.1. OPTICAL NEURAL NETWORKS

Roughly speaking, a one-layer neural network of JV neurons should have N 2
interconnections. The transfer function of a neuron can be described by a
nonlinear relationship such as a step function, making the output of a neuron
either zero or one (binary), or a sigmoid function, which gives rise to analog
values. The state of the ith neuron in the network can be represented by a
retrieval equation, as given by

where u ( is the activation potential of the ith neuron, 7^- is the interconnection
weight matrix (IWM) or associative memory between the jth neuron and the ith
neuron, $ ( is a phase bias, and / is a nonlinear processing operator. In view of
the summation within the retrieval equation, it is essentially a matrix-vector
outer-product operation, which can be optically implemented.
Light beams propagating in space will not interfere with each other, and
optical systems have large space-bandwidth products. These are the traits of
optics that prompted the optical implementation of neural networks (NNs). An
optical NN using a liquid-crystal TV (LCTV) SLM is shown in Fig. 2.51, in
which a lenslet array is used for the interconnection between the IWM and the
input pattern. The transmitted light field after LCTV2 is collected by an
imaging lens, focusing at the lenslet array and imaging onto a CCD array
detector. The array of detected signals is sent to a thresholding circuit and the
final pattern can be viewed at the monitor, and it can be sent back for the next
iteration. The data flow is primarily controlled by the microcomputer, such
that this hybrid optical neural network is indeed an adaptive processor.