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9.2. Parallel Optical Logic and Architectures  48:

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       Fig. 9.10. (a) Dual-rail spatial encoding for 1 and 0, (b) Symbolic substitution rules for binary
       half-addition.


       realized in two stages: recognition and substitution. In the recognition stage,
       all the occurrences of the search pattern in the 2-D input plane are marked in
       parallel. In the substitution stage, the scribe pattern is substituted in all the
       locations where the search pattern is found. In its operation, the recognition
       usually comprises the procedures of replicating, shifting, superimposing of the
       input pattern and thresholding [64]. The substitution phase is functionally
       similar to the recognition phase except for thresholding. Symbolic substitution
       can be performed by coherent correlator architectures, shown in Fig. 9.11. The
       first correlator (P1-P3) performs the recognition phase and the second


                    Ll             L2            L3             L4
                    A      P2 .   A       P3 ,   A      P4  s\  A
                                                                      /-

                                                       /
                                         /                            }
                    \J    /       V              U             V
                         Recognition   Threshold      Substitution    „
             Input       „.,           ™              r- 1            Output
                                                                        r
                         Filter        Device         Filter
                   Correlator 1 (Recognition)  (  l  Correlator 2 (Substitution)  l
             Fig. 9.11. Basic cascaded correlator architecture for symbolic substitution [70].
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