Two-stage modified signed-digit optical computing by spatial data encoding and polarization multiplexing

We propose and demonstrate an effective two-stage modified signed-digit optical computing technique (in contrast to previous three-stage techniques) based on spatial data encoding, polarization multiplexing, and multiple imaging. Our proposed reduction in operation stages requires a reference operation in addition to the transformation and weight operations common to three-stage systems. In our system's first stage a transformation (or weight) operation and a reference operation are implemented in parallel by use of four distinct polarization-multiplexed kernel operations. In the second stage the final desired result (e.g., addition and subtraction) and its complement are obtained in parallel with a single kernel operation. The operation speed of our two-stage modified signed-digit computing method is 33% faster than previous three-stage modified signed-digit algorithms.