Cross-talk in phase encoded volume holographic memories employing unitary matrices

Abstract

The cross-talk noise in phase encoded holographic memories employing unitary matrices is theoretically investigated. After reviewing some earlier work in this area, we derive a relationship for the noise-to-signal ratio for phase-code multiplexing with unitary matrices. The noise-to-signal ratio rises in a zigzag way on increasing the storage capacity. Cross-talk is mainly caused by high-frequency phase codes. Unitary matrices of even orders have only one bad code, while unitary matrices of odd orders have four bad codes. The signal-to-noise ratios of all other codes can in each case be drastically improved by omission of these bad codes. We summarize the optimal orders of Hadamard and unitary matrices for recording a given number of holograms. The unitary matrices can enable us to adjust the available spatial light modulators to achieve the maximum possible storage capacity in both circumstances with and without bad codes.