Page 568 - Introduction to Information Optics

9.6. Optical Implementation 553
9.26(b). For example, the pattern for rf 5l will block the light for input digits 3
and 1, and transmit light for other input digits,
To optically realize the pattern recognition among an input digit combina-
tion and the SCAM patterns, we can overlap the two encoded patterns and
integrate the light intensity of the particular area. In the two addition steps,
each minterm consists of 2 digits (a t and b { in the first step, S^ and C f in the
second step) and therefore consists of 14 transparent-opaque pixels. This
operation is equivalent to performing vector inner product (VIP), where each
vector has 14 binary elements. Each input digit combination (a,.^ or S,C,) is
multiplied by all minterms that are responsible for generating the nonzero
output. If the number of logically minimized minterms in a step is k, there will
be k VIPs for each digit combination, and if one VIP is zero, it indicates a
match. To accomplish this operation, an incoherent correlator-based optoelec-
tronic SCAM processor, shown in Fig. 9.27(a), can be used. Two SLMs,
SLM1, and SLM2, are utilized for encoding the input and storing the
SCAM patterns, respectively. In SLM2, each minterm is stored in a column
and one set of the minterms (the number being k) of a reduced truth table
are displayed side by side. In SLM1, the different input digit combinations
(assume J, J = M + N, where M and N are the numbers of digits for the
fraction and integer parts of a QSD number, respectively) are encoded
separately, and the separation between the two neighboring combinations is /<
times the pixel size p. All correlation outputs, including the desired VIPs, are
produced in the back focal plane of the lens. Postprocessing electronics detects
the intensity values. The operational principle of this unit will be illustrated
next with an example.
As mentioned earlier, the minterms for outputs I and 2 (I, 2, and 3) are
digit-by-digit complement of the corresponding minterms for outputs 1 and 2
(1, 2, and 3), respectively, in step 1 (step 2). With symmetric spatial encoding,
a pattern of 3, 2, 1, or 0 is a 180° rotated version of 3, 2, 1, or 0, respectively.
Therefore, if we display the input pattern in one channel and form a digit-by-
digit complement version of it in another channel by geometric optics, we can
generate all outputs in the two channels using the same SCAM pattern, which
only stores the minterms for the positive or negative outputs. Thus, it is
possible to reduce the number of minterms by 50%; i.e., the number of
minterms to be stored for steps 1 and 2 can be reduced from 20 and 12 to 10
and 6, respectively. The SCAM pattern for the two steps corresponding to the
negative outputs of Table 9.33 are shown in Figs. 9.27(b) and 9.2l(c),
respectively. To obtain the positive outputs in parallel through another
channel, we can either complement the input pattern digit-by-digit and use the
same SCAM pattern, or complement the SCAM pattern digit-by-digit and use
the same input pattern to perform the VIP operations.
For experimental verification, we consider the basic SCAM processor unit
for adding two QSD numbers A and B. In the first step, using the same SCAM