<title>Two Proposed Holographic Numerical Optical Processors</title>

Abstract

Two numerical optical processor configurations are presented. Both systems are based on holographic recording (to form the processing element) and holographic reconstruction (to perform the numerical processing). In these systems, pairs or arrays of pairs of binary words are presented as the input. The output may be the addition, subtraction, multiplication, division, or other operation on the pairs of words. There is one binary word answer for each pair of binary word inputs. Both numerical optical processor configurations use holographic wavefront addition and subtraction to construct Boolean logic operations. However, as contrasted with constructing arithmetic operations through multiple steps of combinational logic, a single-step truth-table look-up processor is devised. Numerical results are obtained with a single optical pass through the system. Both systems require only a limited part of the complete truth table to be recorded. The first system is based on the EXCLUSIVE OR operation performed holographically on binary arrays. The second system, more complex but more powerful, performs an operation that is equivalent to two levels of logic, a NAND and OR followed by another OR operation. For both the EXCLUSIVE OR numerical optical processor and the NAND-OR-OR numerical optical processor, the array sizes during recording and readout and the number of superposed recordings needed are presented and discussed.