Page 574 - Introduction to Information Optics

9.6. Optical Implementation 5

Table 9.40
Procedure for Performing the Binary Logic Operations Involved in the Two-Step NSD
Addition/Subtraction [162] where x Represents Input x with Blue Illumination, x
Represents input x with Infrared Illumination, xy Implies the Overlap of x and v, and the
Numbers can be Input with or without Negation
Operation Procedure

Functions Input without negation Input with negation

overlap involves a maximum of three variables. The optical system shown in
Fig. 9.8 can be effectively employed for this implementation. Shutters 1 and 2
are used to control the exposure of blue and infrared light beams. SLMs 1, 2,
and 3 are utilized to input the data arrays. When a complete arithmetic-logic
function is performed, the final result is read with infrared and detected by a
CCD. Since both addition and subtraction are realized by the same logic, the
operands to be added or subtracted are arranged in two sectors for parallel
processing of the two types of operations. The corresponding digits are
matched to each other in the SLMs. For instance, to perform the logic
(a t © £>,)/• on two-dimensional data arrays, first data arrays A and F enter the
system through SLM^ and SLM 3, respectively, with the blue illumination.
Then, data arrays B and F are input through SLM 2 and SLM 3, respectively,
also with blue illumination. Finally, the data arrays A, B, and F are overlapped
with the infrared illumination. Other logic operations are performed in a
similar fashion. Operations («;©&,-)./) on two-dimensional data arrays are
performed by (a) input A with blue illumination, (b) input B with infrared
illumination, (c) input F with infrared illumination, (d) input B with blue
illumination, (e) input AB with infrared illumination, and (f) input BF with
infrared illumination. Operations h f + (a t © b i)g if i on two-dimensional arrays
are performed by (a) input BF with blue illumination, (b) input AF with blue
illumination, (c) input AB with infrared illumination, (d) input AG with
infrared illumination, (e) input BG with infrared illumination, and (f) input H
j
with blue illumination. Operations (a ib i r(a i®b i}j i]g i on two-dimensional
data arrays are performed by (a) input BG with blue illumination, (b) input