Page 565 - Introduction to Information Optics

550 9. Computing with Optics

To reduce the space-bandwidth product, and hence increase the throughput of
a system, it is preferable to reduce the number of columns in the X matrix,
Note that the digits to be added can be interchanged without affecting the final
results. Thus, three columns in the X and Y matrices can be eliminated. We
rewrite the input matrix X by superimposing (OR) all encoded digits in a
column as:

o + z o + ob z + z z + ob ob + ob'], (9.103)

where + denotes a logical OR operation. The corresponding output matrix Y
becomes

Y = [t o z z ob tb}. (9.104)

An exact solution for the M-V equation exists if X is invertible. This implies
that X must be a square matrix. In the previously reported techniques [70],
six pixels are used to encode each TSD digit. To enhance the space-band width
product, here four pixels are used to encode a TSD digit, as shown in Fig. 9.25.
Substituting the encoding patterns into the matrices X and Y, we obtain

0 1 0 0 1 0~|
1 1000 0
X = Y = (9.105)
00111 1
00 1 1 0 Oj

(b)

o+o o+z o+ob z+z z+ob ob+ob

Fig. 9.25. Four-pixel TSD encoding for the digits in (a) the Y matrix and (b) the X matrix [152].